early inclusion of cvc5 proof reconstruction; slightly reorganize smt/z3_reals;

--- a/CONTRIBUTORS	Sat Jun 17 17:41:02 2023 +0200
+++ b/CONTRIBUTORS	Mon Jun 19 22:28:09 2023 +0200
@@ -6,6 +6,10 @@
 Contributions to Isabelle2023
 -----------------------------
 
+* August 2022 - July 2023: Hannah Lachnitt, Stanford and Mathias Fleury, UFR
+  Start work toward reconstructing cvc5 proof in the SMT method. This
+  is currently very experimental and is also changing on the cvc5 side.
+
 * October 2022: Jeremy Sylvestre
   Lemmas for Fun and List.
 

--- a/src/HOL/SMT.thy	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT.thy	Mon Jun 19 22:28:09 2023 +0200
@@ -660,9 +660,11 @@
 ML_file \<open>Tools/SMT/z3_replay_methods.ML\<close>
 ML_file \<open>Tools/SMT/z3_replay.ML\<close>
 ML_file \<open>Tools/SMT/lethe_replay_methods.ML\<close>
+ML_file \<open>Tools/SMT/cvc5_replay_methods.ML\<close>
 ML_file \<open>Tools/SMT/verit_replay_methods.ML\<close>
 ML_file \<open>Tools/SMT/verit_strategies.ML\<close>
 ML_file \<open>Tools/SMT/verit_replay.ML\<close>
+ML_file \<open>Tools/SMT/cvc5_replay.ML\<close>
 ML_file \<open>Tools/SMT/smt_systems.ML\<close>
 
 
@@ -715,7 +717,7 @@
 \<close>
 
 declare [[cvc4_options = ""]]
-declare [[cvc5_options = ""]]
+declare [[cvc5_options = "--proof-format-mode=alethe --proof-granularity=dsl-rewrite"]]
 declare [[verit_options = ""]]
 declare [[z3_options = ""]]
 

--- a/src/HOL/SMT_Examples/Boogie_Dijkstra.certs	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT_Examples/Boogie_Dijkstra.certs	Mon Jun 19 22:28:09 2023 +0200
@@ -2982,2987 +2982,3 @@
 (let ((@x10164 (unit-resolution (def-axiom (or (not $x10073) $x5237 (not $x10274))) (unit-resolution (def-axiom (or $x10274 (not $x5238))) @x10279 $x10274) (or (not $x10073) $x5237))))
 (unit-resolution (unit-resolution @x10164 (unit-resolution @x10020 @x3468 $x10073) $x5237) @x10120 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
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-unsat
-((set-logic AUFLIA)
-(declare-fun ?v0!20 () B_Vertex$)
-(declare-fun ?v0!19 () B_Vertex$)
-(declare-fun ?v1!18 () B_Vertex$)
-(declare-fun ?v0!17 () B_Vertex$)
-(declare-fun ?v1!16 () B_Vertex$)
-(declare-fun ?v0!15 () B_Vertex$)
-(declare-fun ?v0!14 () B_Vertex$)
-(declare-fun ?v0!13 () B_Vertex$)
-(declare-fun ?v0!12 () B_Vertex$)
-(declare-fun ?v0!11 () B_Vertex$)
-(declare-fun ?v1!10 () B_Vertex$)
-(declare-fun ?v1!9 (B_Vertex$) B_Vertex$)
-(declare-fun ?v0!8 () B_Vertex$)
-(declare-fun ?v1!7 (B_Vertex$) B_Vertex$)
-(declare-fun ?v1!6 (B_Vertex$) B_Vertex$)
-(declare-fun ?v0!5 () B_Vertex$)
-(declare-fun ?v0!4 () B_Vertex$)
-(declare-fun ?v1!3 () B_Vertex$)
-(declare-fun ?v0!2 () B_Vertex$)
-(declare-fun ?v1!1 () B_Vertex$)
-(declare-fun ?v0!0 () B_Vertex$)
-(proof
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-(let (($x5237 (fun_app$ ?x260 ?v0!20)))
-(let (($x9037 (not $x5237)))
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-(let (($x2237 (= (+ ?x268 ?x1907 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
-(let (($x286 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x295 (not $x286)))
-(or (>= (+ ?x268 ?x1907) 0) $x295 (not $x2237)))))))) :pattern ( (v_b_SP_G_2$ ?v1) ) :pattern ( (fun_app$ v_b_Visited_G_2$ ?v1) ) :pattern ( (pair$ ?v1 ?v0!20) ) :qid k!38))
-))
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-(let ((?x1907 (* (- 1) ?x1906)))
-(let ((?x1908 (+ b_Infinity$ ?x1907)))
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-(let (($x1904 (= ?v0!20 b_Source$)))
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-(or $x295 $x917 $x1277))))))))) :pattern ( (pair$ ?v1 ?v0) ) :qid k!38))
-))
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-))
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-(let (($x1823 (= ?x1821 ?x1822)))
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-(let ((?x254 (fun_app$a v_b_SP_G_1$ v_b_v_G_1$)))
-(let ((?x1168 (* (- 1) ?x254)))
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-(let (($x1164 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
-(let (($x2712 (or $x1164 $x1170)))
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-(let (($x684 (= ?x298 ?x666)))
-(let (($x687 (and $x286 $x684)))
-(let (($x309 (< ?x268 ?x298)))
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-(let ((@x1317 (trans @x1312 (rewrite (= (and $x1304 (and $x286 $x1301)) $x1313)) (= $x690 $x1313))))
-(let (($x1293 (= (< ?x268 b_Infinity$) (not (<= (+ b_Infinity$ (* (- 1) ?x268)) 0)))))
-(let ((@x1297 (monotonicity (rewrite $x1293) (= (and $x128 (< ?x268 b_Infinity$)) $x1295))))
-(let ((@x1300 (monotonicity @x1297 (= (not (and $x128 (< ?x268 b_Infinity$))) (not $x1295)))))
-(let ((@x1323 (monotonicity @x1300 (quant-intro @x1317 (= $x693 $x1318)) (= $x700 (or (not $x1295) $x1318)))))
-(let (($x1277 (>= (+ ?x152 ?x268 ?x1258) 0)))
-(let (($x917 (<= (+ b_Infinity$ (* (- 1) ?x152)) 0)))
-(let (($x918 (not $x917)))
-(let (($x1271 (and $x286 $x918)))
-(let (($x1274 (not $x1271)))
-(let (($x1281 (or $x1274 $x1277)))
-(let (($x669 (<= ?x298 ?x666)))
-(let (($x676 (or (not (and $x286 (< ?x152 b_Infinity$))) $x669)))
-(let ((@x920 (rewrite (= (< ?x152 b_Infinity$) $x918))))
-(let ((@x1276 (monotonicity (monotonicity @x920 (= (and $x286 (< ?x152 b_Infinity$)) $x1271)) (= (not (and $x286 (< ?x152 b_Infinity$))) $x1274))))
-(let ((@x1286 (quant-intro (monotonicity @x1276 (rewrite (= $x669 $x1277)) (= $x676 $x1281)) (= $x681 $x1284))))
-(let ((@x1329 (monotonicity (monotonicity @x1286 (= (not $x681) $x1287)) (quant-intro @x1323 (= $x705 $x1324)) (= $x733 $x1327))))
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-(let (($x297 (and $x295 $x296)))
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-(let (($x1262 (or $x659 $x1257)))
-(let (($x299 (<= ?x298 ?x268)))
-(let (($x660 (or $x659 $x299)))
-(let ((@x1267 (quant-intro (monotonicity (rewrite (= $x299 $x1257)) (= $x660 $x1262)) (= $x663 $x1265))))
-(let ((@x1335 (monotonicity (monotonicity @x1267 (= (not $x663) $x1268)) (monotonicity @x1286 @x1329 (= $x738 $x1330)) (= $x745 $x1333))))
-(let ((@x1253 (quant-intro (rewrite (= (<= 0 ?x268) (>= ?x268 0))) (= $x294 $x1251))))
-(let ((@x1341 (monotonicity (monotonicity @x1253 (= (not $x294) $x1254)) (monotonicity @x1267 @x1335 (= $x750 $x1336)) (= $x757 $x1339))))
-(let ((@x1347 (monotonicity (monotonicity @x1253 @x1341 (= $x762 $x1342)) (= $x769 $x1345))))
-(let ((@x1356 (monotonicity (monotonicity (monotonicity @x1347 (= $x774 $x1348)) (= $x781 $x1351)) (= $x786 $x1354))))
-(let (($x1238 (>= (+ (fun_app$a v_b_SP_G_1$ ?0) (* (- 1) ?x268)) 0)))
-(let ((@x1244 (quant-intro (rewrite (= (<= ?x268 (fun_app$a v_b_SP_G_1$ ?0)) $x1238)) (= $x285 $x1242))))
-(let ((@x1359 (monotonicity (monotonicity @x1244 (= (not $x285) $x1245)) @x1356 (= $x793 $x1357))))
-(let (($x1227 (and $x1075 (and $x253 (and $x1209 (and $x1204 (and $x261 (and $x1188 $x1194))))))))
-(let (($x1225 (= $x627 (and $x253 (and $x1209 (and $x1204 (and $x261 (and $x1188 $x1194))))))))
-(let ((?x171 (fun_app$a v_b_SP_G_1$ ?0)))
-(let (($x273 (= ?x268 ?x171)))
-(let (($x1170 (<= (+ ?x171 ?x1168 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?0)))) 0)))
-(let (($x1164 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?0)))) 0)))
-(let (($x1174 (and (not $x1164) (not $x1170))))
-(let (($x1191 (or $x1174 $x273)))
-(let (($x267 (and (< (b_G$ (pair$ v_b_v_G_1$ ?0)) b_Infinity$) (< (+ ?x254 (b_G$ (pair$ v_b_v_G_1$ ?0))) ?x171))))
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-(let ((@x1173 (rewrite (= (< (+ ?x254 (b_G$ (pair$ v_b_v_G_1$ ?0))) ?x171) (not $x1170)))))
-(let ((@x1167 (rewrite (= (< (b_G$ (pair$ v_b_v_G_1$ ?0)) b_Infinity$) (not $x1164)))))
-(let ((@x1193 (monotonicity (monotonicity @x1167 @x1173 (= $x267 $x1174)) (= $x609 $x1191))))
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-(let (($x1185 (or $x1177 $x1180)))
-(let ((?x263 (b_G$ (pair$ v_b_v_G_1$ ?0))))
-(let ((?x265 (+ ?x254 ?x263)))
-(let (($x269 (= ?x268 ?x265)))
-(let (($x272 (not $x267)))
-(let (($x603 (or $x272 $x269)))
-(let ((@x1179 (monotonicity (monotonicity @x1167 @x1173 (= $x267 $x1174)) (= $x272 $x1177))))
-(let ((@x1190 (quant-intro (monotonicity @x1179 (rewrite (= $x269 $x1180)) (= $x603 $x1185)) (= $x606 $x1188))))
-(let ((@x1214 (monotonicity @x1190 (quant-intro @x1193 (= $x612 $x1194)) (= $x615 (and $x1188 $x1194)))))
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-(let (($x256 (<= ?x254 ?x171)))
-(let (($x597 (or $x175 $x256)))
-(let ((@x1203 (monotonicity (rewrite (= $x256 (>= (+ ?x171 ?x1168) 0))) (= $x597 $x1201))))
-(let ((@x1220 (monotonicity (quant-intro @x1203 (= $x600 $x1204)) (monotonicity @x1214 (= $x618 (and $x261 (and $x1188 $x1194)))) (= $x621 (and $x1204 (and $x261 (and $x1188 $x1194)))))))
-(let ((@x1223 (monotonicity (rewrite (= $x255 $x1209)) @x1220 (= $x624 (and $x1209 (and $x1204 (and $x261 (and $x1188 $x1194))))))))
-(let (($x997 (<= (+ b_Infinity$ (* (- 1) ?x171)) 0)))
-(let (($x998 (not $x997)))
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-(let ((@x1074 (monotonicity (rewrite (= (< ?x171 b_Infinity$) $x998)) (= (and $x176 (< ?x171 b_Infinity$)) $x1072))))
-(let ((@x1229 (monotonicity (quant-intro @x1074 (= $x206 $x1075)) (monotonicity @x1223 $x1225) (= $x630 $x1227))))
-(let ((@x1237 (monotonicity (trans @x1229 (rewrite (= $x1227 $x1230)) (= $x630 $x1230)) (= (not $x630) $x1235))))
-(let ((@x1365 (monotonicity @x1237 (monotonicity @x1244 @x1359 (= $x798 $x1360)) (= $x805 $x1363))))
-(let ((?x227 (fun_app$a v_b_SP_G_3$ ?0)))
-(let (($x1135 (>= (+ ?x152 ?x227 (* (- 1) (fun_app$a v_b_SP_G_3$ ?1))) 0)))
-(let (($x1094 (<= (+ b_Infinity$ (* (- 1) ?x227)) 0)))
-(let (($x1095 (not $x1094)))
-(let (($x1129 (and $x1095 $x918)))
-(let (($x1132 (not $x1129)))
-(let (($x1138 (or $x1132 $x1135)))
-(let ((?x516 (+ ?x152 ?x227)))
-(let ((?x230 (fun_app$a v_b_SP_G_3$ ?1)))
-(let (($x540 (<= ?x230 ?x516)))
-(let (($x547 (or (not (and (< ?x227 b_Infinity$) (< ?x152 b_Infinity$))) $x540)))
-(let ((@x1131 (monotonicity (rewrite (= (< ?x227 b_Infinity$) $x1095)) @x920 (= (and (< ?x227 b_Infinity$) (< ?x152 b_Infinity$)) $x1129))))
-(let ((@x1134 (monotonicity @x1131 (= (not (and (< ?x227 b_Infinity$) (< ?x152 b_Infinity$))) $x1132))))
-(let ((@x1143 (quant-intro (monotonicity @x1134 (rewrite (= $x540 $x1135)) (= $x547 $x1138)) (= $x552 $x1141))))
-(let ((@x1149 (monotonicity (monotonicity @x1143 (= (not $x552) $x1144)) (= $x568 $x1147))))
-(let (($x1117 (exists ((?v1 B_Vertex$) )(! (let ((?x227 (fun_app$a v_b_SP_G_3$ ?v1)))
-(let ((?x152 (b_G$ (pair$ ?v1 ?0))))
-(and (not (>= (+ ?x227 (* (- 1) (fun_app$a v_b_SP_G_3$ ?0))) 0)) (= (+ ?x152 ?x227 (* (- 1) (fun_app$a v_b_SP_G_3$ ?0))) 0)))) :qid k!38))
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-(let (($x1098 (and $x128 $x1095)))
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-(let ((?x152 (b_G$ (pair$ ?v1 ?0))))
-(let ((?x516 (+ ?x152 ?x227)))
-(let ((?x230 (fun_app$a v_b_SP_G_3$ ?0)))
-(let (($x519 (= ?x230 ?x516)))
-(let (($x231 (< ?x227 ?x230)))
-(and $x231 $x519))))))) :qid k!38))
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-(let (($x532 (or (not (and $x128 (< ?x227 b_Infinity$))) $x525)))
-(let (($x1114 (and (not (>= (+ ?x227 (* (- 1) ?x230)) 0)) (= (+ ?x152 ?x227 (* (- 1) ?x230)) 0))))
-(let (($x519 (= ?x230 ?x516)))
-(let (($x231 (< ?x227 ?x230)))
-(let (($x522 (and $x231 $x519)))
-(let ((@x1116 (monotonicity (rewrite (= $x231 (not (>= (+ ?x227 (* (- 1) ?x230)) 0)))) (rewrite (= $x519 (= (+ ?x152 ?x227 (* (- 1) ?x230)) 0))) (= $x522 $x1114))))
-(let ((@x1100 (monotonicity (rewrite (= (< ?x227 b_Infinity$) $x1095)) (= (and $x128 (< ?x227 b_Infinity$)) $x1098))))
-(let ((@x1122 (monotonicity (monotonicity @x1100 (= (not (and $x128 (< ?x227 b_Infinity$))) $x1101)) (quant-intro @x1116 (= $x525 $x1117)) (= $x532 $x1120))))
-(let ((@x1128 (monotonicity (quant-intro @x1122 (= $x537 $x1123)) (= (not $x537) $x1126))))
-(let ((@x1155 (monotonicity @x1128 (monotonicity @x1143 @x1149 (= $x573 $x1150)) (= $x580 $x1153))))
-(let ((@x1086 (rewrite (= (and $x1078 (and $x209 (and $x212 (and $x214 $x217)))) $x1084))))
-(let (($x488 (and $x209 (and $x212 (and $x214 $x217)))))
-(let (($x502 (and $x207 $x488)))
-(let ((@x1083 (monotonicity (monotonicity (quant-intro @x1074 (= $x206 $x1075)) (= $x207 $x1078)) (= $x502 (and $x1078 $x488)))))
-(let ((@x1091 (monotonicity (trans @x1083 @x1086 (= $x502 $x1084)) (= (not $x502) $x1089))))
-(let ((@x1161 (monotonicity @x1091 (monotonicity (quant-intro @x1122 (= $x537 $x1123)) @x1155 (= $x585 $x1156)) (= $x592 $x1159))))
-(let (($x1065 (= (and $x975 (and $x170 (and $x1046 (and $x1040 (and $x992 $x1032))))) $x1064)))
-(let (($x1062 (= $x477 (and $x975 (and $x170 (and $x1046 (and $x1040 (and $x992 $x1032))))))))
-(let (($x1026 (exists ((?v1 B_Vertex$) )(! (let ((?x171 (fun_app$a v_b_SP_G_1$ ?v1)))
-(let ((?x152 (b_G$ (pair$ ?v1 ?0))))
-(let (($x1007 (= (+ ?x152 ?x171 (* (- 1) (fun_app$a v_b_SP_G_1$ ?0))) 0)))
-(let (($x175 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x1010 (>= (+ ?x171 (* (- 1) (fun_app$a v_b_SP_G_1$ ?0))) 0)))
-(let (($x1012 (not $x1010)))
-(and $x1012 $x175 $x1007))))))) :qid k!38))
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-(let (($x1001 (and $x128 $x998)))
-(let (($x1004 (not $x1001)))
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-(let ((?x152 (b_G$ (pair$ ?v1 ?0))))
-(let ((?x405 (+ ?x152 ?x171)))
-(let ((?x179 (fun_app$a v_b_SP_G_1$ ?0)))
-(let (($x423 (= ?x179 ?x405)))
-(let (($x175 (fun_app$ v_b_Visited_G_1$ ?v1)))
-(let (($x426 (and $x175 $x423)))
-(let (($x190 (< ?x171 ?x179)))
-(and $x190 $x426))))))))) :qid k!38))
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-(let (($x439 (or (not (and $x128 (< ?x171 b_Infinity$))) $x432)))
-(let (($x1007 (= (+ ?x152 ?x171 (* (- 1) (fun_app$a v_b_SP_G_1$ ?1))) 0)))
-(let (($x1010 (>= (+ ?x171 (* (- 1) (fun_app$a v_b_SP_G_1$ ?1))) 0)))
-(let (($x1012 (not $x1010)))
-(let (($x1021 (and $x1012 $x175 $x1007)))
-(let ((?x405 (+ ?x152 ?x171)))
-(let ((?x179 (fun_app$a v_b_SP_G_1$ ?1)))
-(let (($x423 (= ?x179 ?x405)))
-(let (($x426 (and $x175 $x423)))
-(let (($x190 (< ?x171 ?x179)))
-(let (($x429 (and $x190 $x426)))
-(let ((@x1020 (monotonicity (rewrite (= $x190 $x1012)) (monotonicity (rewrite (= $x423 $x1007)) (= $x426 (and $x175 $x1007))) (= $x429 (and $x1012 (and $x175 $x1007))))))
-(let ((@x1025 (trans @x1020 (rewrite (= (and $x1012 (and $x175 $x1007)) $x1021)) (= $x429 $x1021))))
-(let ((@x1003 (monotonicity (rewrite (= (< ?x171 b_Infinity$) $x998)) (= (and $x128 (< ?x171 b_Infinity$)) $x1001))))
-(let ((@x1031 (monotonicity (monotonicity @x1003 (= (not (and $x128 (< ?x171 b_Infinity$))) $x1004)) (quant-intro @x1025 (= $x432 $x1026)) (= $x439 $x1029))))
-(let (($x985 (>= (+ ?x152 ?x171 (* (- 1) ?x179)) 0)))
-(let (($x978 (and $x175 $x918)))
-(let (($x981 (not $x978)))
-(let (($x989 (or $x981 $x985)))
-(let (($x408 (<= ?x179 ?x405)))
-(let (($x415 (or (not (and $x175 (< ?x152 b_Infinity$))) $x408)))
-(let ((@x983 (monotonicity (monotonicity @x920 (= (and $x175 (< ?x152 b_Infinity$)) $x978)) (= (not (and $x175 (< ?x152 b_Infinity$))) $x981))))
-(let ((@x994 (quant-intro (monotonicity @x983 (rewrite (= $x408 $x985)) (= $x415 $x989)) (= $x420 $x992))))
-(let ((@x1051 (monotonicity @x994 (quant-intro @x1031 (= $x444 $x1032)) (= $x454 (and $x992 $x1032)))))
-(let (($x177 (fun_app$ v_b_Visited_G_1$ ?1)))
-(let (($x178 (and $x176 $x177)))
-(let (($x398 (not $x178)))
-(let (($x1037 (or $x398 $x1010)))
-(let (($x180 (<= ?x179 ?x171)))
-(let (($x399 (or $x398 $x180)))
-(let ((@x1042 (quant-intro (monotonicity (rewrite (= $x180 $x1010)) (= $x399 $x1037)) (= $x402 $x1040))))
-(let ((@x1048 (quant-intro (rewrite (= (<= 0 ?x171) (>= ?x171 0))) (= $x173 $x1046))))
-(let ((@x1057 (monotonicity @x1048 (monotonicity @x1042 @x1051 (= $x457 (and $x1040 (and $x992 $x1032)))) (= $x460 (and $x1046 (and $x1040 (and $x992 $x1032)))))))
-(let ((@x1060 (monotonicity @x1057 (= $x463 (and $x170 (and $x1046 (and $x1040 (and $x992 $x1032))))))))
-(let (($x969 (exists ((?v1 B_Vertex$) )(! (let ((?x152 (b_G$ (pair$ ?v1 ?0))))
-(let ((?x124 (v_b_SP_G_0$ ?v1)))
-(let (($x952 (= (+ ?x124 (* (- 1) (v_b_SP_G_0$ ?0)) ?x152) 0)))
-(let (($x133 (fun_app$ v_b_Visited_G_0$ ?v1)))
-(let (($x902 (>= (+ ?x124 (* (- 1) (v_b_SP_G_0$ ?0))) 0)))
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-(let (($x949 (not $x946)))
-(let (($x972 (or $x949 $x969)))
-(let (($x165 (exists ((?v1 B_Vertex$) )(! (let (($x133 (fun_app$ v_b_Visited_G_0$ ?v1)))
-(let (($x163 (and $x133 (= (v_b_SP_G_0$ ?0) (+ (v_b_SP_G_0$ ?v1) (b_G$ (pair$ ?v1 ?0)))))))
-(and (< (v_b_SP_G_0$ ?v1) (v_b_SP_G_0$ ?0)) $x163))) :qid k!38))
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-(let (($x952 (= (+ (v_b_SP_G_0$ ?0) (* (- 1) (v_b_SP_G_0$ ?1)) ?x152) 0)))
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-(let (($x164 (and (< (v_b_SP_G_0$ ?0) (v_b_SP_G_0$ ?1)) (and $x133 (= (v_b_SP_G_0$ ?1) (+ (v_b_SP_G_0$ ?0) ?x152))))))
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-(let ((@x954 (rewrite (= (= (v_b_SP_G_0$ ?1) (+ (v_b_SP_G_0$ ?0) ?x152)) $x952))))
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-(let ((@x1377 (monotonicity (monotonicity @x936 (= (not $x388) $x937)) (monotonicity @x977 @x1371 (= $x822 $x1372)) (= $x829 $x1375))))
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-(let (($x378 (or $x377 $x148)))
-(let ((@x911 (quant-intro (monotonicity (rewrite (= $x148 $x902)) (= $x378 $x906)) (= $x381 $x909))))
-(let ((@x1383 (monotonicity (monotonicity @x911 (= (not $x381) $x912)) (monotonicity @x936 @x1377 (= $x834 $x1378)) (= $x841 $x1381))))
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-(let ((@x1389 (monotonicity (monotonicity @x896 (= (not $x144) $x897)) (monotonicity @x911 @x1383 (= $x846 $x1384)) (= $x853 $x1387))))
-(let ((@x1395 (monotonicity (monotonicity @x896 @x1389 (= $x858 $x1390)) (= $x865 $x1393))))
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-(let (($x311 (and $x286 (= (v_b_SP_G_2$ ?0) (+ (v_b_SP_G_2$ ?v1) (b_G$ (pair$ ?v1 ?0)))))))
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-(let ((@x707 (quant-intro (trans @x698 (rewrite (= (=> $x308 $x693) $x700)) (= $x314 $x700)) (= $x315 $x705))))
-(let ((@x714 (trans (monotonicity @x707 (= $x316 (and $x705 false))) (rewrite (= (and $x705 false) false)) (= $x316 false))))
-(let ((@x721 (trans (monotonicity @x714 (= $x317 (=> false true))) (rewrite (= (=> false true) true)) (= $x317 true))))
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-(let (($x153 (< ?x152 b_Infinity$)))
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-(let ((@x776 (monotonicity (trans @x767 (rewrite (= (=> $x292 $x762) $x769)) (= $x325 $x769)) (= (and $x292 $x325) $x774))))
-(let ((@x649 (quant-intro (rewrite (= (=> $x286 $x273) (or $x295 $x273))) (= $x288 $x647))))
-(let ((@x654 (monotonicity @x649 (rewrite (= (and true true) true)) (= $x290 (and $x647 true)))))
-(let ((@x779 (monotonicity (trans @x654 (rewrite (= (and $x647 true) $x647)) (= $x290 $x647)) @x776 (= $x327 (=> $x647 $x774)))))
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-(let ((@x797 (trans (monotonicity @x788 (= $x329 (=> $x285 $x786))) (rewrite (= (=> $x285 $x786) $x793)) (= $x329 $x793))))
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-(let ((@x617 (monotonicity (quant-intro (rewrite (= (=> $x267 $x269) $x603)) (= $x271 $x606)) (quant-intro (rewrite (= (=> $x272 $x273) $x609)) (= $x275 $x612)) (= (and $x271 $x275) $x615))))
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-(let ((@x635 (monotonicity (monotonicity (monotonicity @x626 $x628) (= $x281 $x630)) (= $x282 (and true $x630)))))
-(let ((@x641 (monotonicity (trans @x635 (rewrite (= (and true $x630) $x630)) (= $x282 $x630)) (= $x283 (and true $x630)))))
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-(let (($x228 (< ?x227 b_Infinity$)))
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-(let (($x240 (=> $x238 (<= ?x230 (+ ?x227 ?x152)))))
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-(let ((?x232 (+ ?x227 ?x152)))
-(let ((?x230 (fun_app$a v_b_SP_G_3$ ?0)))
-(let (($x231 (< ?x227 ?x230)))
-(and $x231 (= ?x230 ?x232))))))) :qid k!38))
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-(and $x190 (and $x175 (= ?x179 ?x184))))))))) :qid k!38))
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-(let (($x366 (and true $x363)))
-(let ((@x357 (quant-intro (rewrite (= (=> $x128 (= ?x124 b_Infinity$)) $x352)) (= $x131 $x355))))
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-(let ((@x351 (quant-intro (rewrite (= (=> $x123 (= ?x124 0)) (or $x128 (= ?x124 0)))) (= $x127 $x349))))
-(let ((@x365 (monotonicity @x351 @x362 (= (and $x127 (and $x131 (and $x135 true))) $x363))))
-(let ((@x372 (trans (monotonicity @x365 (= $x139 $x366)) (rewrite (= $x366 $x363)) (= $x139 $x363))))
-(let ((@x376 (trans (monotonicity @x372 (= $x140 $x366)) (rewrite (= $x366 $x363)) (= $x140 $x363))))
-(let ((@x881 (trans (monotonicity @x376 @x872 (= $x343 (=> $x363 $x870))) (rewrite (= (=> $x363 $x870) $x877)) (= $x343 $x877))))
-(let ((@x1406 (trans (monotonicity @x881 (= $x344 (not $x877))) (monotonicity @x1401 (= (not $x877) $x1402)) (= $x344 $x1402))))
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-(let ((@x5498 (mp ((_ quant-inst ?v0!5) (or (not $x3488) (or $x1533 $x5648))) @x5494 (or (not $x3488) $x1533 $x5648))))
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-(let (($x5117 (= b_Infinity$ ?x1470)))
-(let ((@x5579 (symm (commutativity (= $x5117 (= ?x1470 b_Infinity$))) (= (= ?x1470 b_Infinity$) $x5117))))
-(let (($x3131 (= ?x1470 b_Infinity$)))
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-(let ((@x1452 (nnf-pos (refl (~ (or $x128 (= ?x124 0)) (or $x128 (= ?x124 0)))) (~ $x349 $x349))))
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-(let ((@x5606 (trans @x5457 (rewrite (= (or false $x142) $x142)) (= (or (not (= b_Source$ b_Source$)) $x142) $x142))))
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-(let ((@x5799 (trans @x4948 (rewrite (= $x3145 $x3145)) (= (or $x5885 (or (not (= b_Source$ b_Source$)) $x142)) $x3145))))
-(let ((@x5800 (mp ((_ quant-inst b_Source$) (or $x5885 (or (not (= b_Source$ b_Source$)) $x142))) @x5799 $x3145)))
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-(let (($x2237 (= (+ ?x268 ?x1907 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
-(let (($x286 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x295 (not $x286)))
-(or (>= (+ ?x268 ?x1907) 0) $x295 (not $x2237)))))))) :qid k!38))
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-(let ((?x152 (b_G$ (pair$ ?v1 ?v0))))
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-(let (($x286 (fun_app$ v_b_Visited_G_2$ ?v1)))
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-(or $x286 $x2763 $x1257))))) :qid k!38))
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-(let ((?x254 (fun_app$a v_b_SP_G_1$ v_b_v_G_1$)))
-(let ((?x1168 (* (- 1) ?x254)))
-(let (($x1170 (<= (+ ?x171 ?x1168 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
-(let (($x1164 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0)))) 0)))
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-(let ((?x254 (fun_app$a v_b_SP_G_1$ v_b_v_G_1$)))
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-(let (($x1164 (<= (+ b_Infinity$ (* (- 1) ?x263)) 0)))
-(or $x1164 $x1170 $x1180)))))))) :qid k!38))
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-(let (($x917 (<= (+ b_Infinity$ (* (- 1) ?x152)) 0)))
-(let (($x1094 (<= (+ b_Infinity$ (* (- 1) ?x227)) 0)))
-(or $x1094 $x917 $x1135)))))) :qid k!38))
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-(let (($x2171 (<= (+ ?x227 (* (- 1) (fun_app$a v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
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-(let (($x123 (= ?v0 b_Source$)))
-(or $x123 $x1094 $x2612)))))))) :qid k!38))
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-(let (($x997 (<= (+ b_Infinity$ (* (- 1) ?x171)) 0)))
-(let (($x123 (= ?v0 b_Source$)))
-(or $x123 $x997 $x2546)))))))) :qid k!38))
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-(or $x176 $x917 $x985))))))) :qid k!38))
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-(or $x175 (not (fun_app$ v_b_Visited_G_1$ ?v0)) $x1010)))) :qid k!38))
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-(let ((@x3541 (monotonicity (monotonicity @x3535 (= (or $x1533 $x1538 (not $x2446)) $x3536)) (= $x2454 $x3539))))
-(let ((@x3824 (monotonicity @x3541 (monotonicity @x3818 (= $x2954 $x3819)) (= $x2959 $x3822))))
-(let ((@x3523 (quant-intro (refl (= (or $x134 $x917 $x928) (or $x134 $x917 $x928))) (= $x2431 $x3519))))
-(let ((@x3830 (monotonicity (monotonicity @x3523 (= (not $x2431) $x3524)) (monotonicity @x3824 (= (not $x2959) $x3825)) (= (or (not $x2431) (not $x2959)) $x3828))))
-(let ((@x3839 (monotonicity (monotonicity (monotonicity @x3830 (= $x2968 $x3831)) (= $x2973 $x3834)) (= (not $x2973) $x3837))))
-(let (($x2381 (or $x133 (not (fun_app$ v_b_Visited_G_0$ ?1)) $x902)))
-(let ((@x3517 (monotonicity (quant-intro (refl (= $x2381 $x2381)) (= $x2386 $x3510)) (= (not $x2386) $x3515))))
-(let ((@x3845 (monotonicity (monotonicity @x3517 @x3839 (= (or (not $x2386) (not $x2973)) $x3840)) (= $x2982 $x3843))))
-(let ((@x3851 (monotonicity (monotonicity @x3845 (= $x2987 $x3846)) (= (not $x2987) $x3849))))
-(let ((@x3505 (quant-intro (refl (= (>= ?x124 0) (>= ?x124 0))) (= $x894 $x3501))))
-(let ((@x3854 (monotonicity (monotonicity @x3505 (= $x897 $x3506)) @x3851 (= (or $x897 (not $x2987)) $x3852))))
-(let ((@x3863 (monotonicity (monotonicity (monotonicity @x3854 (= $x2995 $x3855)) (= $x3000 $x3858)) (= (not $x3000) $x3861))))
-(let ((@x3869 (monotonicity (monotonicity @x3863 (= (or $x864 (not $x3000)) $x3864)) (= $x3008 $x3867))))
-(let (($x2246 (forall ((?v1 B_Vertex$) )(! (let ((?x1906 (v_b_SP_G_2$ ?v0!20)))
-(let ((?x1907 (* (- 1) ?x1906)))
-(let ((?x268 (v_b_SP_G_2$ ?v1)))
-(let (($x2237 (= (+ ?x268 ?x1907 (b_G$ (pair$ ?v1 ?v0!20))) 0)))
-(let (($x286 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x2240 (and (not (>= (+ ?x268 ?x1907) 0)) $x286 $x2237)))
-(not $x2240))))))) :qid k!38))
-))
-(let (($x1910 (not $x1909)))
-(let (($x1905 (not $x1904)))
-(let (($x2255 (and $x1284 $x1905 $x1910 $x2246)))
-(let (($x1886 (not (and $x1878 (not $x1883)))))
-(let (($x1892 (or $x1886 $x1891)))
-(let (($x1893 (not $x1892)))
-(let (($x2260 (or $x1893 $x2255)))
-(let (($x2263 (and $x1265 $x2260)))
-(let (($x1859 (not (and (not $x1855) $x1857))))
-(let (($x1865 (or $x1859 $x1864)))
-(let (($x1866 (not $x1865)))
-(let (($x2266 (or $x1866 $x2263)))
-(let (($x2269 (and $x1251 $x2266)))
-(let (($x2272 (or $x1843 $x2269)))
-(let (($x2275 (and $x292 $x2272)))
-(let (($x2278 (or $x768 $x2275)))
-(let (($x2281 (and $x647 $x2278)))
-(let (($x2284 (or $x1825 $x2281)))
-(let (($x2287 (and $x1242 $x2284)))
-(let (($x2290 (or $x1808 $x2287)))
-(let (($x1774 (not $x1773)))
-(let (($x1769 (not $x1768)))
-(let (($x2296 (and $x1769 $x1774 $x253 $x1209 $x1204 $x261 $x1188 $x1194 $x2290)))
-(let (($x1744 (not $x243)))
-(let (($x1747 (and $x1141 $x1744)))
-(let (($x1728 (not (and (not $x1719) (not $x1725)))))
-(let (($x2207 (or $x1728 $x2204)))
-(let (($x2210 (not $x2207)))
-(let (($x2213 (or $x2210 $x1747)))
-(let (($x2198 (forall ((?v0 B_Vertex$) )(! (let ((?x227 (fun_app$a v_b_SP_G_3$ ?v0)))
-(let ((?x2186 (+ ?x227 (* (- 1) (fun_app$a v_b_SP_G_3$ (?v1!9 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!9 ?v0) ?v0))))))
-(let (($x2187 (= ?x2186 0)))
-(let (($x2171 (<= (+ ?x227 (* (- 1) (fun_app$a v_b_SP_G_3$ (?v1!9 ?v0)))) 0)))
-(let (($x2192 (and (not $x2171) $x2187)))
-(let (($x1094 (<= (+ b_Infinity$ (* (- 1) ?x227)) 0)))
-(let (($x1095 (not $x1094)))
-(let (($x123 (= ?v0 b_Source$)))
-(let (($x128 (not $x123)))
-(let (($x1098 (and $x128 $x1095)))
-(let (($x1101 (not $x1098)))
-(or $x1101 $x2192)))))))))))) :qid k!38))
-))
-(let (($x2216 (and $x2198 $x2213)))
-(let (($x2152 (forall ((?v1 B_Vertex$) )(! (let ((?x1656 (fun_app$a v_b_SP_G_3$ ?v0!8)))
-(let ((?x1657 (* (- 1) ?x1656)))
-(let ((?x227 (fun_app$a v_b_SP_G_3$ ?v1)))
-(let (($x2143 (= (+ ?x227 ?x1657 (b_G$ (pair$ ?v1 ?v0!8))) 0)))
-(let (($x2146 (and (not (>= (+ ?x227 ?x1657) 0)) $x2143)))
-(not $x2146)))))) :qid k!38))
-))
-(let (($x1660 (not $x1659)))
-(let (($x1655 (not $x1654)))
-(let (($x2158 (and $x1655 $x1660 $x2152)))
-(let (($x2219 (or $x2158 $x2216)))
-(let (($x1636 (forall ((?v0 B_Vertex$) )(! (let (($x997 (<= (+ b_Infinity$ (* (- 1) (fun_app$a v_b_SP_G_1$ ?v0))) 0)))
-(let (($x998 (not $x997)))
-(let (($x175 (fun_app$ v_b_Visited_G_1$ ?v0)))
-(let (($x176 (not $x175)))
-(let (($x1072 (and $x176 $x998)))
-(not $x1072)))))) :qid k!38))
-))
-(let (($x2225 (and $x1636 $x209 $x212 $x214 $x217 $x2219)))
-(let (($x2301 (or $x2225 $x2296)))
-(let (($x2135 (forall ((?v0 B_Vertex$) )(! (let ((?x171 (fun_app$a v_b_SP_G_1$ ?v0)))
-(let ((?x2123 (+ ?x171 (* (- 1) (fun_app$a v_b_SP_G_1$ (?v1!7 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!7 ?v0) ?v0))))))
-(let (($x2124 (= ?x2123 0)))
-(let ((?x1608 (?v1!7 ?v0)))
-(let (($x1613 (fun_app$ v_b_Visited_G_1$ ?x1608)))
-(let (($x2129 (and (not (<= (+ ?x171 (* (- 1) (fun_app$a v_b_SP_G_1$ ?x1608))) 0)) $x1613 $x2124)))
-(let (($x997 (<= (+ b_Infinity$ (* (- 1) ?x171)) 0)))
-(let (($x998 (not $x997)))
-(let (($x123 (= ?v0 b_Source$)))
-(let (($x128 (not $x123)))
-(let (($x1001 (and $x128 $x998)))
-(let (($x1004 (not $x1001)))
-(or $x1004 $x2129))))))))))))) :qid k!38))
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-(let (($x2097 (forall ((?v0 B_Vertex$) )(! (let ((?x124 (v_b_SP_G_0$ ?v0)))
-(let ((?x2085 (+ ?x124 (* (- 1) (v_b_SP_G_0$ (?v1!6 ?v0))) (* (- 1) (b_G$ (pair$ (?v1!6 ?v0) ?v0))))))
-(let (($x2086 (= ?x2085 0)))
-(let ((?x1573 (?v1!6 ?v0)))
-(let (($x1578 (fun_app$ v_b_Visited_G_0$ ?x1573)))
-(let (($x2091 (and (not (<= (+ ?x124 (* (- 1) (v_b_SP_G_0$ ?x1573))) 0)) $x1578 $x2086)))
-(let (($x123 (= ?v0 b_Source$)))
-(let (($x128 (not $x123)))
-(let (($x946 (and $x128 (not (<= (+ b_Infinity$ (* (- 1) ?x124)) 0)))))
-(let (($x949 (not $x946)))
-(or $x949 $x2091))))))))))) :qid k!38))
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-(let (($x2310 (and $x2097 $x170 $x1046 $x1040 $x992 $x2135 $x2301)))
-(let (($x1562 (forall ((?v1 B_Vertex$) )(! (let ((?x1535 (v_b_SP_G_0$ ?v0!5)))
-(let ((?x1536 (* (- 1) ?x1535)))
-(let ((?x124 (v_b_SP_G_0$ ?v1)))
-(let (($x133 (fun_app$ v_b_Visited_G_0$ ?v1)))
-(let (($x1549 (and (not (>= (+ ?x124 ?x1536) 0)) $x133 (= (+ ?x124 ?x1536 (b_G$ (pair$ ?v1 ?v0!5))) 0))))
-(not $x1549)))))) :qid k!38))
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-(let (($x2057 (and $x1534 $x1539 $x1562)))
-(let (($x2315 (or $x2057 $x2310)))
-(let (($x2318 (and $x934 $x2315)))
-(let (($x1515 (not (and $x1507 (not $x1512)))))
-(let (($x2046 (or $x1515 $x2043)))
-(let (($x2049 (not $x2046)))
-(let (($x2321 (or $x2049 $x2318)))
-(let (($x2324 (and $x909 $x2321)))
-(let (($x1488 (not (and (not $x1484) $x1486))))
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-(let (($x2327 (or $x1495 $x2324)))
-(let (($x2330 (and $x894 $x2327)))
-(let (($x2333 (or $x1472 $x2330)))
-(let (($x2336 (and $x142 $x2333)))
-(let (($x2339 (or $x864 $x2336)))
-(let ((@x2937 (rewrite (= (and $x1769 $x1774 $x253 $x1209 $x1204 $x261 $x2731 $x2737 $x2923) $x2935))))
-(let (($x2237 (= (+ ?x268 ?x1907 (b_G$ (pair$ ?0 ?v0!20))) 0)))
-(let (($x2240 (and (not (>= (+ ?x268 ?x1907) 0)) $x286 $x2237)))
-(let (($x2243 (not $x2240)))
-(let ((@x2838 (monotonicity (rewrite (= $x2240 (not $x2832))) (= $x2243 (not (not $x2832))))))
-(let ((@x2845 (quant-intro (trans @x2838 (rewrite (= (not (not $x2832)) $x2832)) (= $x2243 $x2832)) (= $x2246 $x2843))))
-(let ((@x2815 (monotonicity (rewrite (= $x1271 (not (or $x295 $x917)))) (= $x1274 (not (not (or $x295 $x917)))))))
-(let ((@x2819 (trans @x2815 (rewrite (= (not (not (or $x295 $x917))) (or $x295 $x917))) (= $x1274 (or $x295 $x917)))))
-(let ((@x2827 (trans (monotonicity @x2819 (= $x1281 (or (or $x295 $x917) $x1277))) (rewrite (= (or (or $x295 $x917) $x1277) (or $x295 $x917 $x1277))) (= $x1281 (or $x295 $x917 $x1277)))))
-(let ((@x2848 (monotonicity (quant-intro @x2827 (= $x1284 $x2828)) @x2845 (= $x2255 (and $x2828 $x1905 $x1910 $x2843)))))
-(let ((@x2856 (trans @x2848 (rewrite (= (and $x2828 $x1905 $x1910 $x2843) $x2852)) (= $x2255 $x2852))))
-(let ((@x2793 (monotonicity (rewrite (= (and $x1878 (not $x1883)) (not (or $x2786 $x1883)))) (= $x1886 (not (not (or $x2786 $x1883)))))))
-(let ((@x2797 (trans @x2793 (rewrite (= (not (not (or $x2786 $x1883))) (or $x2786 $x1883))) (= $x1886 (or $x2786 $x1883)))))
-(let ((@x2805 (trans (monotonicity @x2797 (= $x1892 (or (or $x2786 $x1883) $x1891))) (rewrite (= (or (or $x2786 $x1883) $x1891) $x2801)) (= $x1892 $x2801))))
-(let ((@x2859 (monotonicity (monotonicity @x2805 (= $x1893 $x2806)) @x2856 (= $x2260 $x2857))))
-(let ((@x2780 (rewrite (= (or (or $x286 (not $x296)) $x1257) (or $x286 (not $x296) $x1257)))))
-(let ((@x2772 (rewrite (= (not (not (or $x286 (not $x296)))) (or $x286 (not $x296))))))
-(let ((@x2770 (monotonicity (rewrite (= $x297 (not (or $x286 (not $x296))))) (= $x659 (not (not (or $x286 (not $x296))))))))
-(let ((@x2777 (monotonicity (trans @x2770 @x2772 (= $x659 (or $x286 (not $x296)))) (= $x1262 (or (or $x286 (not $x296)) $x1257)))))
-(let ((@x2785 (quant-intro (trans @x2777 @x2780 (= $x1262 (or $x286 (not $x296) $x1257))) (= $x1265 $x2783))))
-(let ((@x2870 (trans (monotonicity @x2785 @x2859 (= $x2263 (and $x2783 $x2857))) (rewrite (= (and $x2783 $x2857) $x2866)) (= $x2263 $x2866))))
-(let ((@x2747 (monotonicity (rewrite (= (and (not $x1855) $x1857) (not (or $x1855 $x2740)))) (= $x1859 (not (not (or $x1855 $x2740)))))))
-(let ((@x2751 (trans @x2747 (rewrite (= (not (not (or $x1855 $x2740))) (or $x1855 $x2740))) (= $x1859 (or $x1855 $x2740)))))
-(let ((@x2759 (trans (monotonicity @x2751 (= $x1865 (or (or $x1855 $x2740) $x1864))) (rewrite (= (or (or $x1855 $x2740) $x1864) $x2755)) (= $x1865 $x2755))))
-(let ((@x2873 (monotonicity (monotonicity @x2759 (= $x1866 $x2760)) @x2870 (= $x2266 $x2871))))
-(let ((@x2883 (trans (monotonicity @x2873 (= $x2269 (and $x1251 $x2871))) (rewrite (= (and $x1251 $x2871) $x2879)) (= $x2269 $x2879))))
-(let ((@x2889 (monotonicity (monotonicity @x2883 (= $x2272 $x2884)) (= $x2275 (and $x292 $x2884)))))
-(let ((@x2899 (monotonicity (trans @x2889 (rewrite (= (and $x292 $x2884) $x2892)) (= $x2275 $x2892)) (= $x2278 $x2897))))
-(let ((@x2909 (trans (monotonicity @x2899 (= $x2281 (and $x647 $x2897))) (rewrite (= (and $x647 $x2897) $x2905)) (= $x2281 $x2905))))
-(let ((@x2915 (monotonicity (monotonicity @x2909 (= $x2284 $x2910)) (= $x2287 (and $x1242 $x2910)))))
-(let ((@x2925 (monotonicity (trans @x2915 (rewrite (= (and $x1242 $x2910) $x2918)) (= $x2287 $x2918)) (= $x2290 $x2923))))
-(let ((@x2736 (monotonicity (rewrite (= $x1174 (not (or $x1164 $x1170)))) (= $x1191 (or (not (or $x1164 $x1170)) $x273)))))
-(let ((@x2718 (monotonicity (rewrite (= $x1174 (not (or $x1164 $x1170)))) (= $x1177 (not (not (or $x1164 $x1170)))))))
-(let ((@x2722 (trans @x2718 (rewrite (= (not (not (or $x1164 $x1170))) (or $x1164 $x1170))) (= $x1177 (or $x1164 $x1170)))))
-(let ((@x2730 (trans (monotonicity @x2722 (= $x1185 (or (or $x1164 $x1170) $x1180))) (rewrite (= (or (or $x1164 $x1170) $x1180) (or $x1164 $x1170 $x1180))) (= $x1185 (or $x1164 $x1170 $x1180)))))
-(let ((@x2928 (monotonicity (quant-intro @x2730 (= $x1188 $x2731)) (quant-intro @x2736 (= $x1194 $x2737)) @x2925 (= $x2296 (and $x1769 $x1774 $x253 $x1209 $x1204 $x261 $x2731 $x2737 $x2923)))))
-(let ((@x2654 (monotonicity (rewrite (= $x1129 (not (or $x1094 $x917)))) (= $x1132 (not (not (or $x1094 $x917)))))))
-(let ((@x2658 (trans @x2654 (rewrite (= (not (not (or $x1094 $x917))) (or $x1094 $x917))) (= $x1132 (or $x1094 $x917)))))
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-(let ((@x2632 (monotonicity (rewrite (= (and (not $x1719) (not $x1725)) (not (or $x1719 $x1725)))) (= $x1728 (not (not (or $x1719 $x1725)))))))
-(let ((@x2636 (trans @x2632 (rewrite (= (not (not (or $x1719 $x1725))) (or $x1719 $x1725))) (= $x1728 (or $x1719 $x1725)))))
-(let ((@x2644 (trans (monotonicity @x2636 (= $x2207 (or (or $x1719 $x1725) $x2204))) (rewrite (= (or (or $x1719 $x1725) $x2204) $x2640)) (= $x2207 $x2640))))
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-(let ((@x2605 (monotonicity (rewrite (= $x1098 (not (or $x123 $x1094)))) (= $x1101 (not (not (or $x123 $x1094)))))))
-(let ((@x2609 (trans @x2605 (rewrite (= (not (not (or $x123 $x1094))) (or $x123 $x1094))) (= $x1101 (or $x123 $x1094)))))
-(let ((@x2617 (monotonicity @x2609 (rewrite (= (and (not $x2171) $x2187) $x2612)) (= (or $x1101 (and (not $x2171) $x2187)) (or (or $x123 $x1094) $x2612)))))
-(let ((@x2622 (trans @x2617 (rewrite (= (or (or $x123 $x1094) $x2612) $x2618)) (= (or $x1101 (and (not $x2171) $x2187)) $x2618))))
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-(let (($x2146 (and (not (>= (+ ?x227 ?x1657) 0)) $x2143)))
-(let (($x2149 (not $x2146)))
-(let ((@x2581 (monotonicity (rewrite (= $x2146 (not $x2575))) (= $x2149 (not (not $x2575))))))
-(let ((@x2588 (quant-intro (trans @x2581 (rewrite (= (not (not $x2575)) $x2575)) (= $x2149 $x2575)) (= $x2152 $x2586))))
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-(let ((@x2566 (monotonicity (rewrite (= $x1072 (not (or $x175 $x997)))) (= (not $x1072) (not (not (or $x175 $x997)))))))
-(let ((@x2570 (trans @x2566 (rewrite (= (not (not (or $x175 $x997))) (or $x175 $x997))) (= (not $x1072) (or $x175 $x997)))))
-(let ((@x2699 (monotonicity (quant-intro @x2570 (= $x1636 $x2571)) @x2696 (= $x2225 (and $x2571 $x209 $x212 $x214 $x217 $x2694)))))
-(let ((@x2711 (trans @x2699 (rewrite (= (and $x2571 $x209 $x212 $x214 $x217 $x2694) $x2707)) (= $x2225 $x2707))))
-(let ((?x1608 (?v1!7 ?0)))
-(let (($x1613 (fun_app$ v_b_Visited_G_1$ ?x1608)))
-(let (($x2129 (and (not $x2108) $x1613 $x2124)))
-(let (($x2132 (or $x1004 $x2129)))
-(let ((@x2538 (monotonicity (rewrite (= $x1001 (not (or $x123 $x997)))) (= $x1004 (not (not (or $x123 $x997)))))))
-(let ((@x2542 (trans @x2538 (rewrite (= (not (not (or $x123 $x997))) (or $x123 $x997))) (= $x1004 (or $x123 $x997)))))
-(let ((@x2551 (monotonicity @x2542 (rewrite (= $x2129 $x2546)) (= $x2132 (or (or $x123 $x997) $x2546)))))
-(let ((@x2556 (trans @x2551 (rewrite (= (or (or $x123 $x997) $x2546) $x2552)) (= $x2132 $x2552))))
-(let ((@x2516 (monotonicity (rewrite (= $x978 (not (or $x176 $x917)))) (= $x981 (not (not (or $x176 $x917)))))))
-(let ((@x2520 (trans @x2516 (rewrite (= (not (not (or $x176 $x917))) (or $x176 $x917))) (= $x981 (or $x176 $x917)))))
-(let ((@x2528 (trans (monotonicity @x2520 (= $x989 (or (or $x176 $x917) $x985))) (rewrite (= (or (or $x176 $x917) $x985) (or $x176 $x917 $x985))) (= $x989 (or $x176 $x917 $x985)))))
-(let ((@x2504 (rewrite (= (or (or $x175 (not $x177)) $x1010) (or $x175 (not $x177) $x1010)))))
-(let ((@x2496 (rewrite (= (not (not (or $x175 (not $x177)))) (or $x175 (not $x177))))))
-(let ((@x2494 (monotonicity (rewrite (= $x178 (not (or $x175 (not $x177))))) (= $x398 (not (not (or $x175 (not $x177))))))))
-(let ((@x2501 (monotonicity (trans @x2494 @x2496 (= $x398 (or $x175 (not $x177)))) (= $x1037 (or (or $x175 (not $x177)) $x1010)))))
-(let ((@x2509 (quant-intro (trans @x2501 @x2504 (= $x1037 (or $x175 (not $x177) $x1010))) (= $x1040 $x2507))))
-(let ((?x1573 (?v1!6 ?0)))
-(let (($x1578 (fun_app$ v_b_Visited_G_0$ ?x1573)))
-(let (($x2091 (and (not $x2070) $x1578 $x2086)))
-(let (($x2094 (or $x949 $x2091)))
-(let ((@x2465 (monotonicity (rewrite (= $x946 (not (or $x123 $x942)))) (= $x949 (not (not (or $x123 $x942)))))))
-(let ((@x2469 (trans @x2465 (rewrite (= (not (not (or $x123 $x942))) (or $x123 $x942))) (= $x949 (or $x123 $x942)))))
-(let ((@x2478 (monotonicity @x2469 (rewrite (= $x2091 $x2473)) (= $x2094 (or (or $x123 $x942) $x2473)))))
-(let ((@x2483 (trans @x2478 (rewrite (= (or (or $x123 $x942) $x2473) $x2479)) (= $x2094 $x2479))))
-(let ((@x2945 (monotonicity (quant-intro @x2483 (= $x2097 $x2484)) @x2509 (quant-intro @x2528 (= $x992 $x2529)) (quant-intro @x2556 (= $x2135 $x2557)) (monotonicity @x2711 (trans @x2928 @x2937 (= $x2296 $x2935)) (= $x2301 $x2940)) (= $x2310 (and $x2484 $x170 $x1046 $x2507 $x2529 $x2557 $x2940)))))
-(let ((@x2958 (trans @x2945 (rewrite (= (and $x2484 $x170 $x1046 $x2507 $x2529 $x2557 $x2940) $x2954)) (= $x2310 $x2954))))
-(let (($x1549 (and (not (>= (+ ?x124 ?x1536) 0)) $x133 (= (+ ?x124 ?x1536 (b_G$ (pair$ ?0 ?v0!5))) 0))))
-(let (($x1559 (not $x1549)))
-(let ((@x2441 (monotonicity (rewrite (= $x1549 (not $x2435))) (= $x1559 (not (not $x2435))))))
-(let ((@x2448 (quant-intro (trans @x2441 (rewrite (= (not (not $x2435)) $x2435)) (= $x1559 $x2435)) (= $x1562 $x2446))))
-(let ((@x2458 (trans (monotonicity @x2448 (= $x2057 (and $x1534 $x1539 $x2446))) (rewrite (= (and $x1534 $x1539 $x2446) $x2454)) (= $x2057 $x2454))))
-(let ((@x2418 (monotonicity (rewrite (= $x921 (not (or $x134 $x917)))) (= $x924 (not (not (or $x134 $x917)))))))
-(let ((@x2422 (trans @x2418 (rewrite (= (not (not (or $x134 $x917))) (or $x134 $x917))) (= $x924 (or $x134 $x917)))))
-(let ((@x2430 (trans (monotonicity @x2422 (= $x931 (or (or $x134 $x917) $x928))) (rewrite (= (or (or $x134 $x917) $x928) (or $x134 $x917 $x928))) (= $x931 (or $x134 $x917 $x928)))))
-(let ((@x2964 (monotonicity (quant-intro @x2430 (= $x934 $x2431)) (monotonicity @x2458 @x2958 (= $x2315 $x2959)) (= $x2318 (and $x2431 $x2959)))))
-(let ((@x2396 (monotonicity (rewrite (= (and $x1507 (not $x1512)) (not (or $x2389 $x1512)))) (= $x1515 (not (not (or $x2389 $x1512)))))))
-(let ((@x2400 (trans @x2396 (rewrite (= (not (not (or $x2389 $x1512))) (or $x2389 $x1512))) (= $x1515 (or $x2389 $x1512)))))
-(let ((@x2408 (trans (monotonicity @x2400 (= $x2046 (or (or $x2389 $x1512) $x2043))) (rewrite (= (or (or $x2389 $x1512) $x2043) $x2404)) (= $x2046 $x2404))))
-(let ((@x2975 (monotonicity (monotonicity @x2408 (= $x2049 $x2409)) (trans @x2964 (rewrite (= (and $x2431 $x2959) $x2968)) (= $x2318 $x2968)) (= $x2321 $x2973))))
-(let (($x2382 (= (or (or $x133 (not (fun_app$ v_b_Visited_G_0$ ?1))) $x902) $x2381)))
-(let (($x2379 (= $x906 (or (or $x133 (not (fun_app$ v_b_Visited_G_0$ ?1))) $x902))))
-(let (($x2367 (or $x133 (not (fun_app$ v_b_Visited_G_0$ ?1)))))
-(let ((@x2373 (monotonicity (rewrite (= $x146 (not $x2367))) (= $x377 (not (not $x2367))))))
-(let ((@x2380 (monotonicity (trans @x2373 (rewrite (= (not (not $x2367)) $x2367)) (= $x377 $x2367)) $x2379)))
-(let ((@x2388 (quant-intro (trans @x2380 (rewrite $x2382) (= $x906 $x2381)) (= $x909 $x2386))))
-(let ((@x2986 (trans (monotonicity @x2388 @x2975 (= $x2324 (and $x2386 $x2973))) (rewrite (= (and $x2386 $x2973) $x2982)) (= $x2324 $x2982))))
-(let ((@x2350 (monotonicity (rewrite (= (and (not $x1484) $x1486) (not (or $x1484 $x2343)))) (= $x1488 (not (not (or $x1484 $x2343)))))))
-(let ((@x2354 (trans @x2350 (rewrite (= (not (not (or $x1484 $x2343))) (or $x1484 $x2343))) (= $x1488 (or $x1484 $x2343)))))
-(let ((@x2362 (trans (monotonicity @x2354 (= $x1494 (or (or $x1484 $x2343) $x1493))) (rewrite (= (or (or $x1484 $x2343) $x1493) $x2358)) (= $x1494 $x2358))))
-(let ((@x2989 (monotonicity (monotonicity @x2362 (= $x1495 $x2363)) @x2986 (= $x2327 $x2987))))
-(let ((@x2999 (trans (monotonicity @x2989 (= $x2330 (and $x894 $x2987))) (rewrite (= (and $x894 $x2987) $x2995)) (= $x2330 $x2995))))
-(let ((@x3005 (monotonicity (monotonicity @x2999 (= $x2333 $x3000)) (= $x2336 (and $x142 $x3000)))))
-(let ((@x3015 (monotonicity (trans @x3005 (rewrite (= (and $x142 $x3000) $x3008)) (= $x2336 $x3008)) (= $x2339 $x3013))))
-(let (($x1933 (forall ((?v1 B_Vertex$) )(! (let ((?x1906 (v_b_SP_G_2$ ?v0!20)))
-(let ((?x1907 (* (- 1) ?x1906)))
-(let ((?x268 (v_b_SP_G_2$ ?v1)))
-(let (($x286 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(let (($x1920 (and (not (>= (+ ?x268 ?x1907) 0)) $x286 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x268 ?x1907) 0))))
-(not $x1920)))))) :qid k!38))
-))
-(let (($x1927 (not (not (and $x1905 $x1910)))))
-(let (($x1937 (and $x1927 $x1933)))
-(let (($x1942 (and $x1284 $x1937)))
-(let (($x1946 (or $x1893 $x1942)))
-(let (($x1950 (and $x1265 $x1946)))
-(let (($x1954 (or $x1866 $x1950)))
-(let (($x1958 (and $x1251 $x1954)))
-(let (($x1962 (or $x1843 $x1958)))
-(let (($x1837 (not $x768)))
-(let (($x1966 (and $x1837 $x1962)))
-(let (($x1970 (or $x768 $x1966)))
-(let (($x1974 (and $x647 $x1970)))
-(let (($x1978 (or $x1825 $x1974)))
-(let (($x1982 (and $x1242 $x1978)))
-(let (($x1986 (or $x1808 $x1982)))
-(let (($x1796 (and (and $x1769 $x1774) $x253 $x1209 $x1204 $x261 $x1188 $x1194)))
-(let (($x1990 (and $x1796 $x1986)))
-(let (($x1734 (not (or $x1728 (>= (+ ?x1722 ?x1716 ?x1730) 0)))))
-(let (($x1751 (or $x1734 $x1747)))
-(let (($x1708 (forall ((?v0 B_Vertex$) )(! (let ((?x227 (fun_app$a v_b_SP_G_3$ ?v0)))
-(let ((?x1092 (* (- 1) ?x227)))
-(let ((?x1694 (fun_app$a v_b_SP_G_3$ (?v1!9 ?v0))))
-(let ((?x1699 (b_G$ (pair$ (?v1!9 ?v0) ?v0))))
-(let (($x1701 (= (+ ?x1699 ?x1694 ?x1092) 0)))
-(let (($x1702 (and (not (>= (+ ?x1694 ?x1092) 0)) $x1701)))
-(let (($x1094 (<= (+ b_Infinity$ ?x1092) 0)))
-(let (($x1095 (not $x1094)))
-(let (($x123 (= ?v0 b_Source$)))
-(let (($x128 (not $x123)))
-(let (($x1098 (and $x128 $x1095)))
-(let (($x1101 (not $x1098)))
-(or $x1101 $x1702))))))))))))) :qid k!38))
-))
-(let (($x1755 (and $x1708 $x1751)))
-(let (($x1682 (forall ((?v1 B_Vertex$) )(! (let ((?x1656 (fun_app$a v_b_SP_G_3$ ?v0!8)))
-(let ((?x1657 (* (- 1) ?x1656)))
-(let ((?x227 (fun_app$a v_b_SP_G_3$ ?v1)))
-(let (($x1670 (and (not (>= (+ ?x227 ?x1657) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x227 ?x1657) 0))))
-(not $x1670))))) :qid k!38))
-))
-(let (($x1676 (not (not (and $x1655 $x1660)))))
-(let (($x1686 (and $x1676 $x1682)))
-(let (($x1759 (or $x1686 $x1755)))
-(let (($x1647 (and $x1636 $x209 $x212 $x214 $x217)))
-(let (($x1763 (and $x1647 $x1759)))
-(let (($x1994 (or $x1763 $x1990)))
-(let (($x1624 (forall ((?v0 B_Vertex$) )(! (let ((?x171 (fun_app$a v_b_SP_G_1$ ?v0)))
-(let ((?x995 (* (- 1) ?x171)))
-(let ((?x1608 (?v1!7 ?v0)))
-(let ((?x1609 (fun_app$a v_b_SP_G_1$ ?x1608)))
-(let ((?x1615 (b_G$ (pair$ ?x1608 ?v0))))
-(let (($x1617 (= (+ ?x1615 ?x1609 ?x995) 0)))
-(let (($x1613 (fun_app$ v_b_Visited_G_1$ ?x1608)))
-(let (($x1618 (and (not (>= (+ ?x1609 ?x995) 0)) $x1613 $x1617)))
-(let (($x997 (<= (+ b_Infinity$ ?x995) 0)))
-(let (($x998 (not $x997)))
-(let (($x123 (= ?v0 b_Source$)))
-(let (($x128 (not $x123)))
-(let (($x1001 (and $x128 $x998)))
-(let (($x1004 (not $x1001)))
-(or $x1004 $x1618))))))))))))))) :qid k!38))
-))
-(let (($x1589 (forall ((?v0 B_Vertex$) )(! (let ((?x1580 (b_G$ (pair$ (?v1!6 ?v0) ?v0))))
-(let ((?x124 (v_b_SP_G_0$ ?v0)))
-(let ((?x940 (* (- 1) ?x124)))
-(let ((?x1573 (?v1!6 ?v0)))
-(let ((?x1574 (v_b_SP_G_0$ ?x1573)))
-(let (($x1582 (= (+ ?x1574 ?x940 ?x1580) 0)))
-(let (($x1578 (fun_app$ v_b_Visited_G_0$ ?x1573)))
-(let (($x1583 (and (not (>= (+ ?x1574 ?x940) 0)) $x1578 $x1582)))
-(let (($x123 (= ?v0 b_Source$)))
-(let (($x128 (not $x123)))
-(let (($x946 (and $x128 (not (<= (+ b_Infinity$ ?x940) 0)))))
-(let (($x949 (not $x946)))
-(or $x949 $x1583))))))))))))) :qid k!38))
-))
-(let (($x1627 (and $x1589 $x170 $x1046 $x1040 $x992 $x1624)))
-(let (($x1998 (and $x1627 $x1994)))
-(let (($x1556 (not (not (and $x1534 $x1539)))))
-(let (($x1566 (and $x1556 $x1562)))
-(let (($x2002 (or $x1566 $x1998)))
-(let (($x2006 (and $x934 $x2002)))
-(let (($x1522 (not (or $x1515 (>= (+ ?x1516 ?x1518 ?x1509) 0)))))
-(let (($x2010 (or $x1522 $x2006)))
-(let (($x2014 (and $x909 $x2010)))
-(let (($x2018 (or $x1495 $x2014)))
-(let (($x2022 (and $x894 $x2018)))
-(let (($x2026 (or $x1472 $x2022)))
-(let (($x1466 (not $x864)))
-(let (($x2030 (and $x1466 $x2026)))
-(let (($x2034 (or $x864 $x2030)))
-(let (($x1920 (and (not (>= (+ ?x268 ?x1907) 0)) $x286 (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x268 ?x1907) 0))))
-(let (($x1930 (not $x1920)))
-(let (($x2235 (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x268 ?x1907) (+ ?x268 ?x1907 (b_G$ (pair$ ?0 ?v0!20))))))
-(let ((@x2239 (monotonicity (rewrite $x2235) (= (= (+ (b_G$ (pair$ ?0 ?v0!20)) ?x268 ?x1907) 0) $x2237))))
-(let ((@x2248 (quant-intro (monotonicity (monotonicity @x2239 (= $x1920 $x2240)) (= $x1930 $x2243)) (= $x1933 $x2246))))
-(let ((@x2251 (monotonicity (rewrite (= $x1927 (and $x1905 $x1910))) @x2248 (= $x1937 (and (and $x1905 $x1910) $x2246)))))
-(let ((@x2259 (trans (monotonicity @x2251 (= $x1942 (and $x1284 (and (and $x1905 $x1910) $x2246)))) (rewrite (= (and $x1284 (and (and $x1905 $x1910) $x2246)) $x2255)) (= $x1942 $x2255))))
-(let ((@x2268 (monotonicity (monotonicity (monotonicity @x2259 (= $x1946 $x2260)) (= $x1950 $x2263)) (= $x1954 $x2266))))
-(let ((@x2277 (monotonicity (rewrite (= $x1837 $x292)) (monotonicity (monotonicity @x2268 (= $x1958 $x2269)) (= $x1962 $x2272)) (= $x1966 $x2275))))
-(let ((@x2286 (monotonicity (monotonicity (monotonicity @x2277 (= $x1970 $x2278)) (= $x1974 $x2281)) (= $x1978 $x2284))))
-(let ((@x2295 (monotonicity (monotonicity (monotonicity @x2286 (= $x1982 $x2287)) (= $x1986 $x2290)) (= $x1990 (and $x1796 $x2290)))))
-(let ((@x2206 (monotonicity (rewrite (= (+ ?x1722 ?x1716 ?x1730) ?x2201)) (= (>= (+ ?x1722 ?x1716 ?x1730) 0) $x2204))))
-(let ((@x2209 (monotonicity @x2206 (= (or $x1728 (>= (+ ?x1722 ?x1716 ?x1730) 0)) $x2207))))
-(let (($x2192 (and (not $x2171) $x2187)))
-(let (($x2195 (or $x1101 $x2192)))
-(let ((?x1092 (* (- 1) ?x227)))
-(let ((?x1694 (fun_app$a v_b_SP_G_3$ (?v1!9 ?0))))
-(let ((?x1699 (b_G$ (pair$ (?v1!9 ?0) ?0))))
-(let (($x1701 (= (+ ?x1699 ?x1694 ?x1092) 0)))
-(let (($x1702 (and (not (>= (+ ?x1694 ?x1092) 0)) $x1701)))
-(let (($x1705 (or $x1101 $x1702)))
-(let ((@x2184 (monotonicity (rewrite (= (+ ?x1699 ?x1694 ?x1092) (+ ?x1092 ?x1694 ?x1699))) (= $x1701 (= (+ ?x1092 ?x1694 ?x1699) 0)))))
-(let ((@x2191 (trans @x2184 (rewrite (= (= (+ ?x1092 ?x1694 ?x1699) 0) $x2187)) (= $x1701 $x2187))))
-(let ((@x2168 (monotonicity (rewrite (= (+ ?x1694 ?x1092) (+ ?x1092 ?x1694))) (= (>= (+ ?x1694 ?x1092) 0) (>= (+ ?x1092 ?x1694) 0)))))
-(let ((@x2175 (trans @x2168 (rewrite (= (>= (+ ?x1092 ?x1694) 0) $x2171)) (= (>= (+ ?x1694 ?x1092) 0) $x2171))))
-(let ((@x2194 (monotonicity (monotonicity @x2175 (= (not (>= (+ ?x1694 ?x1092) 0)) (not $x2171))) @x2191 (= $x1702 $x2192))))
-(let ((@x2218 (monotonicity (quant-intro (monotonicity @x2194 (= $x1705 $x2195)) (= $x1708 $x2198)) (monotonicity (monotonicity @x2209 (= $x1734 $x2210)) (= $x1751 $x2213)) (= $x1755 $x2216))))
-(let (($x1670 (and (not (>= (+ ?x227 ?x1657) 0)) (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x227 ?x1657) 0))))
-(let (($x1679 (not $x1670)))
-(let (($x2141 (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x227 ?x1657) (+ ?x227 ?x1657 (b_G$ (pair$ ?0 ?v0!8))))))
-(let ((@x2145 (monotonicity (rewrite $x2141) (= (= (+ (b_G$ (pair$ ?0 ?v0!8)) ?x227 ?x1657) 0) $x2143))))
-(let ((@x2154 (quant-intro (monotonicity (monotonicity @x2145 (= $x1670 $x2146)) (= $x1679 $x2149)) (= $x1682 $x2152))))
-(let ((@x2157 (monotonicity (rewrite (= $x1676 (and $x1655 $x1660))) @x2154 (= $x1686 (and (and $x1655 $x1660) $x2152)))))
-(let ((@x2162 (trans @x2157 (rewrite (= (and (and $x1655 $x1660) $x2152) $x2158)) (= $x1686 $x2158))))
-(let ((@x2224 (monotonicity (monotonicity @x2162 @x2218 (= $x1759 $x2219)) (= $x1763 (and $x1647 $x2219)))))
-(let ((@x2303 (monotonicity (trans @x2224 (rewrite (= (and $x1647 $x2219) $x2225)) (= $x1763 $x2225)) (trans @x2295 (rewrite (= (and $x1796 $x2290) $x2296)) (= $x1990 $x2296)) (= $x1994 $x2301))))
-(let ((?x995 (* (- 1) ?x171)))
-(let ((?x1609 (fun_app$a v_b_SP_G_1$ ?x1608)))
-(let ((?x1615 (b_G$ (pair$ ?x1608 ?0))))
-(let (($x1617 (= (+ ?x1615 ?x1609 ?x995) 0)))
-(let (($x1618 (and (not (>= (+ ?x1609 ?x995) 0)) $x1613 $x1617)))
-(let (($x1621 (or $x1004 $x1618)))
-(let ((@x2121 (monotonicity (rewrite (= (+ ?x1615 ?x1609 ?x995) (+ ?x995 ?x1609 ?x1615))) (= $x1617 (= (+ ?x995 ?x1609 ?x1615) 0)))))
-(let ((@x2128 (trans @x2121 (rewrite (= (= (+ ?x995 ?x1609 ?x1615) 0) $x2124)) (= $x1617 $x2124))))
-(let ((@x2105 (monotonicity (rewrite (= (+ ?x1609 ?x995) (+ ?x995 ?x1609))) (= (>= (+ ?x1609 ?x995) 0) (>= (+ ?x995 ?x1609) 0)))))
-(let ((@x2112 (trans @x2105 (rewrite (= (>= (+ ?x995 ?x1609) 0) $x2108)) (= (>= (+ ?x1609 ?x995) 0) $x2108))))
-(let ((@x2131 (monotonicity (monotonicity @x2112 (= (not (>= (+ ?x1609 ?x995) 0)) (not $x2108))) @x2128 (= $x1618 $x2129))))
-(let (($x1582 (= (+ (v_b_SP_G_0$ ?x1573) (* (- 1) ?x124) (b_G$ (pair$ ?x1573 ?0))) 0)))
-(let (($x1583 (and (not (>= (+ (v_b_SP_G_0$ ?x1573) (* (- 1) ?x124)) 0)) $x1578 $x1582)))
-(let (($x1586 (or $x949 $x1583)))
-(let (($x2081 (= (+ (* (- 1) ?x124) (v_b_SP_G_0$ ?x1573) (b_G$ (pair$ ?x1573 ?0))) 0)))
-(let (($x2079 (= (+ (v_b_SP_G_0$ ?x1573) (* (- 1) ?x124) (b_G$ (pair$ ?x1573 ?0))) (+ (* (- 1) ?x124) (v_b_SP_G_0$ ?x1573) (b_G$ (pair$ ?x1573 ?0))))))
-(let ((@x2090 (trans (monotonicity (rewrite $x2079) (= $x1582 $x2081)) (rewrite (= $x2081 $x2086)) (= $x1582 $x2086))))
-(let (($x2076 (= (not (>= (+ (v_b_SP_G_0$ ?x1573) (* (- 1) ?x124)) 0)) (not $x2070))))
-(let (($x1576 (>= (+ (v_b_SP_G_0$ ?x1573) (* (- 1) ?x124)) 0)))
-(let (($x2063 (= (+ (v_b_SP_G_0$ ?x1573) (* (- 1) ?x124)) (+ (* (- 1) ?x124) (v_b_SP_G_0$ ?x1573)))))
-(let ((@x2067 (monotonicity (rewrite $x2063) (= $x1576 (>= (+ (* (- 1) ?x124) (v_b_SP_G_0$ ?x1573)) 0)))))
-(let ((@x2074 (trans @x2067 (rewrite (= (>= (+ (* (- 1) ?x124) (v_b_SP_G_0$ ?x1573)) 0) $x2070)) (= $x1576 $x2070))))
-(let ((@x2096 (monotonicity (monotonicity (monotonicity @x2074 $x2076) @x2090 (= $x1583 $x2091)) (= $x1586 $x2094))))
-(let ((@x2306 (monotonicity (quant-intro @x2096 (= $x1589 $x2097)) (quant-intro (monotonicity @x2131 (= $x1621 $x2132)) (= $x1624 $x2135)) (= $x1627 (and $x2097 $x170 $x1046 $x1040 $x992 $x2135)))))
-(let ((@x2309 (monotonicity @x2306 @x2303 (= $x1998 (and (and $x2097 $x170 $x1046 $x1040 $x992 $x2135) $x2301)))))
-(let ((@x2314 (trans @x2309 (rewrite (= (and (and $x2097 $x170 $x1046 $x1040 $x992 $x2135) $x2301) $x2310)) (= $x1998 $x2310))))
-(let ((@x2056 (monotonicity (rewrite (= $x1556 (and $x1534 $x1539))) (= $x1566 (and (and $x1534 $x1539) $x1562)))))
-(let ((@x2061 (trans @x2056 (rewrite (= (and (and $x1534 $x1539) $x1562) $x2057)) (= $x1566 $x2057))))
-(let ((@x2320 (monotonicity (monotonicity @x2061 @x2314 (= $x2002 $x2315)) (= $x2006 $x2318))))
-(let ((@x2045 (monotonicity (rewrite (= (+ ?x1516 ?x1518 ?x1509) ?x2040)) (= (>= (+ ?x1516 ?x1518 ?x1509) 0) $x2043))))
-(let ((@x2048 (monotonicity @x2045 (= (or $x1515 (>= (+ ?x1516 ?x1518 ?x1509) 0)) $x2046))))
-(let ((@x2323 (monotonicity (monotonicity @x2048 (= $x1522 $x2049)) @x2320 (= $x2010 $x2321))))
-(let ((@x2332 (monotonicity (monotonicity (monotonicity @x2323 (= $x2014 $x2324)) (= $x2018 $x2327)) (= $x2022 $x2330))))
-(let ((@x2338 (monotonicity (rewrite (= $x1466 $x142)) (monotonicity @x2332 (= $x2026 $x2333)) (= $x2030 $x2336))))
-(let (($x1921 (exists ((?v1 B_Vertex$) )(! (let ((?x1906 (v_b_SP_G_2$ ?v0!20)))
-(let ((?x1907 (* (- 1) ?x1906)))
-(let ((?x268 (v_b_SP_G_2$ ?v1)))
-(let (($x286 (fun_app$ v_b_Visited_G_2$ ?v1)))
-(and (not (>= (+ ?x268 ?x1907) 0)) $x286 (= (+ (b_G$ (pair$ ?v1 ?v0!20)) ?x268 ?x1907) 0)))))) :qid k!38))
-))
-(let ((@x1939 (nnf-neg (refl (~ $x1927 $x1927)) (nnf-neg (refl (~ $x1930 $x1930)) (~ (not $x1921) $x1933)) (~ (not (or (not (and $x1905 $x1910)) $x1921)) $x1937))))
-(let ((@x1941 (trans (sk (~ (not $x1324) (not (or (not (and $x1905 $x1910)) $x1921)))) @x1939 (~ (not $x1324) $x1937))))
-(let ((@x1902 (nnf-neg (nnf-pos (refl (~ $x1281 $x1281)) (~ $x1284 $x1284)) (~ (not $x1287) $x1284))))
-(let ((@x1949 (nnf-neg (sk (~ $x1287 $x1893)) (nnf-neg @x1902 @x1941 (~ (not $x1327) $x1942)) (~ (not $x1330) $x1946))))
-(let ((@x1875 (nnf-neg (nnf-pos (refl (~ $x1262 $x1262)) (~ $x1265 $x1265)) (~ (not $x1268) $x1265))))
-(let ((@x1957 (nnf-neg (sk (~ $x1268 $x1866)) (nnf-neg @x1875 @x1949 (~ (not $x1333) $x1950)) (~ (not $x1336) $x1954))))
-(let ((@x1852 (nnf-neg (nnf-pos (refl (~ (>= ?x268 0) (>= ?x268 0))) (~ $x1251 $x1251)) (~ (not $x1254) $x1251))))
-(let ((@x1965 (nnf-neg (sk (~ $x1254 $x1843)) (nnf-neg @x1852 @x1957 (~ (not $x1339) $x1958)) (~ (not $x1342) $x1962))))
-(let ((@x1973 (nnf-neg (refl (~ $x768 $x768)) (nnf-neg (refl (~ $x1837 $x1837)) @x1965 (~ (not $x1345) $x1966)) (~ (not $x1348) $x1970))))
-(let ((@x1834 (nnf-neg (nnf-pos (refl (~ (or $x295 $x273) (or $x295 $x273))) (~ $x647 $x647)) (~ (not $x780) $x647))))
-(let ((@x1981 (nnf-neg (sk (~ $x780 $x1825)) (nnf-neg @x1834 @x1973 (~ (not $x1351) $x1974)) (~ (not $x1354) $x1978))))
-(let ((@x1817 (nnf-neg (nnf-pos (refl (~ $x1238 $x1238)) (~ $x1242 $x1242)) (~ (not $x1245) $x1242))))
-(let ((@x1989 (nnf-neg (sk (~ $x1245 $x1808)) (nnf-neg @x1817 @x1981 (~ (not $x1357) $x1982)) (~ (not $x1360) $x1986))))
-(let ((@x1798 (monotonicity (sk (~ $x1075 (and $x1769 $x1774))) (refl (~ $x253 $x253)) (refl (~ $x1209 $x1209)) (nnf-pos (refl (~ $x1201 $x1201)) (~ $x1204 $x1204)) (refl (~ $x261 $x261)) (nnf-pos (refl (~ $x1185 $x1185)) (~ $x1188 $x1188)) (nnf-pos (refl (~ $x1191 $x1191)) (~ $x1194 $x1194)) (~ $x1230 $x1796))))
-(let ((@x1993 (nnf-neg (nnf-neg @x1798 (~ (not $x1235) $x1796)) @x1989 (~ (not $x1363) $x1990))))
-(let ((@x1743 (nnf-neg (nnf-pos (refl (~ $x1138 $x1138)) (~ $x1141 $x1141)) (~ (not $x1144) $x1141))))
-(let ((@x1754 (nnf-neg (sk (~ $x1144 $x1734)) (nnf-neg @x1743 (refl (~ $x1744 $x1744)) (~ (not $x1147) $x1747)) (~ (not $x1150) $x1751))))
-(let ((@x1710 (nnf-pos (monotonicity (refl (~ $x1101 $x1101)) (sk (~ $x1117 $x1702)) (~ $x1120 $x1705)) (~ $x1123 $x1708))))
-(let ((@x1758 (nnf-neg (nnf-neg @x1710 (~ (not $x1126) $x1708)) @x1754 (~ (not $x1153) $x1755))))
-(let (($x1671 (exists ((?v1 B_Vertex$) )(! (let ((?x1656 (fun_app$a v_b_SP_G_3$ ?v0!8)))
-(let ((?x1657 (* (- 1) ?x1656)))
-(let ((?x227 (fun_app$a v_b_SP_G_3$ ?v1)))
-(and (not (>= (+ ?x227 ?x1657) 0)) (= (+ (b_G$ (pair$ ?v1 ?v0!8)) ?x227 ?x1657) 0))))) :qid k!38))
-))
-(let ((@x1688 (nnf-neg (refl (~ $x1676 $x1676)) (nnf-neg (refl (~ $x1679 $x1679)) (~ (not $x1671) $x1682)) (~ (not (or (not (and $x1655 $x1660)) $x1671)) $x1686))))
-(let ((@x1690 (trans (sk (~ $x1126 (not (or (not (and $x1655 $x1660)) $x1671)))) @x1688 (~ $x1126 $x1686))))
-(let ((@x1649 (monotonicity (nnf-neg (refl (~ (not $x1072) (not $x1072))) (~ $x1078 $x1636)) (refl (~ $x209 $x209)) (refl (~ $x212 $x212)) (refl (~ $x214 $x214)) (refl (~ $x217 $x217)) (~ $x1084 $x1647))))
-(let ((@x1766 (nnf-neg (nnf-neg @x1649 (~ (not $x1089) $x1647)) (nnf-neg @x1690 @x1758 (~ (not $x1156) $x1759)) (~ (not $x1159) $x1763))))
-(let ((@x1626 (nnf-pos (monotonicity (refl (~ $x1004 $x1004)) (sk (~ $x1026 $x1618)) (~ $x1029 $x1621)) (~ $x1032 $x1624))))
-(let ((@x1591 (nnf-pos (monotonicity (refl (~ $x949 $x949)) (sk (~ $x969 $x1583)) (~ $x972 $x1586)) (~ $x975 $x1589))))
-(let ((@x1629 (monotonicity @x1591 (refl (~ $x170 $x170)) (nnf-pos (refl (~ (>= ?x171 0) (>= ?x171 0))) (~ $x1046 $x1046)) (nnf-pos (refl (~ $x1037 $x1037)) (~ $x1040 $x1040)) (nnf-pos (refl (~ $x989 $x989)) (~ $x992 $x992)) @x1626 (~ $x1064 $x1627))))
-(let ((@x2001 (nnf-neg (nnf-neg @x1629 (~ (not $x1069) $x1627)) (nnf-neg @x1766 @x1993 (~ (not $x1366) $x1994)) (~ (not $x1369) $x1998))))
-(let (($x1550 (exists ((?v1 B_Vertex$) )(! (let ((?x1535 (v_b_SP_G_0$ ?v0!5)))
-(let ((?x1536 (* (- 1) ?x1535)))
-(let ((?x124 (v_b_SP_G_0$ ?v1)))
-(let (($x133 (fun_app$ v_b_Visited_G_0$ ?v1)))
-(and (not (>= (+ ?x124 ?x1536) 0)) $x133 (= (+ ?x124 ?x1536 (b_G$ (pair$ ?v1 ?v0!5))) 0)))))) :qid k!38))
-))
-(let ((@x1568 (nnf-neg (refl (~ $x1556 $x1556)) (nnf-neg (refl (~ $x1559 $x1559)) (~ (not $x1550) $x1562)) (~ (not (or (not (and $x1534 $x1539)) $x1550)) $x1566))))
-(let ((@x1570 (trans (sk (~ (not $x975) (not (or (not (and $x1534 $x1539)) $x1550)))) @x1568 (~ (not $x975) $x1566))))
-(let ((@x1531 (nnf-neg (nnf-pos (refl (~ $x931 $x931)) (~ $x934 $x934)) (~ (not $x937) $x934))))
-(let ((@x2009 (nnf-neg @x1531 (nnf-neg @x1570 @x2001 (~ (not $x1372) $x2002)) (~ (not $x1375) $x2006))))
-(let ((@x1504 (nnf-neg (nnf-pos (refl (~ $x906 $x906)) (~ $x909 $x909)) (~ (not $x912) $x909))))
-(let ((@x2017 (nnf-neg @x1504 (nnf-neg (sk (~ $x937 $x1522)) @x2009 (~ (not $x1378) $x2010)) (~ (not $x1381) $x2014))))
-(let ((@x1481 (nnf-neg (nnf-pos (refl (~ (>= ?x124 0) (>= ?x124 0))) (~ $x894 $x894)) (~ (not $x897) $x894))))
-(let ((@x2025 (nnf-neg @x1481 (nnf-neg (sk (~ $x912 $x1495)) @x2017 (~ (not $x1384) $x2018)) (~ (not $x1387) $x2022))))
-(let ((@x2033 (nnf-neg (refl (~ $x1466 $x1466)) (nnf-neg (sk (~ $x897 $x1472)) @x2025 (~ (not $x1390) $x2026)) (~ (not $x1393) $x2030))))
-(let ((@x2037 (mp~ (not-or-elim (mp (asserted $x344) @x1406 $x1402) (not $x1396)) (nnf-neg (refl (~ $x864 $x864)) @x2033 (~ (not $x1396) $x2034)) $x2034)))
-(let ((@x3873 (mp (mp (mp @x2037 (monotonicity @x2338 (= $x2034 $x2339)) $x2339) @x3015 $x3013) (monotonicity @x3869 (= $x3013 $x3870)) $x3870)))
-(let ((@x4276 (unit-resolution @x3873 (lemma (unit-resolution @x5800 @x3487 (hypothesis $x864) false) $x142) $x3867)))
-(let ((@x4278 (unit-resolution (def-axiom (or $x3861 $x1472 $x3855)) (unit-resolution (def-axiom (or $x3864 $x3858)) @x4276 $x3858) (lemma @x5085 $x1471) $x3855)))
-(let ((@x3051 (unit-resolution ((_ quant-inst ?v0!2) (or (not $x3495) $x2343)) @x3500 (hypothesis $x1486) false)))
-(let ((@x4352 (unit-resolution (def-axiom (or $x3849 $x2363 $x3843)) (unit-resolution (def-axiom (or $x2358 $x1486)) (lemma @x3051 $x2343) $x2358) (unit-resolution (def-axiom (or $x3852 $x3846)) @x4278 $x3846) $x3843)))
-(let ((@x4355 (unit-resolution (def-axiom (or $x3837 $x2409 $x3831)) (unit-resolution (def-axiom (or $x3840 $x3834)) @x4352 $x3834) (unit-resolution (def-axiom (or $x2404 $x1507)) (lemma @x4007 $x2389) $x2404) $x3831)))
-(let ((@x4357 (unit-resolution (def-axiom (or $x3825 $x3539 $x3819)) (unit-resolution (def-axiom (or $x3828 $x3822)) @x4355 $x3822) (lemma @x3189 $x3536) $x3819)))
-(let ((@x4135 (unit-resolution (def-axiom (or $x3816 $x170)) @x4357 $x170)))
-(let ((@x4159 (hypothesis $x3652)))
-(let ((@x4139 (unit-resolution (def-axiom (or $x3649 $x214)) @x4159 $x214)))
-(let ((@x4149 (unit-resolution (def-axiom (or $x3625 $x1744)) (trans (monotonicity @x4139 (= ?x242 ?x169)) @x4135 $x243) $x3625)))
-(let (($x1720 (not $x1719)))
-(let ((@x3125 (hypothesis $x2645)))
-(let (($x4264 (>= (+ ?x1716 (* (- 1) (fun_app$a v_b_SP_G_1$ ?v1!10))) 0)))
-(let ((@x4002 (symm (hypothesis $x214) (= v_b_SP_G_1$ v_b_SP_G_3$))))
-(let ((@x5768 (symm (monotonicity @x4002 (= (fun_app$a v_b_SP_G_1$ ?v1!10) ?x1716)) (= ?x1716 (fun_app$a v_b_SP_G_1$ ?v1!10)))))
-(let ((@x5656 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1716 (fun_app$a v_b_SP_G_1$ ?v1!10))) $x4264)) @x5768 $x4264)))
-(let (($x5398 (<= (+ b_Infinity$ (* (- 1) (fun_app$a v_b_SP_G_1$ ?v1!10))) 0)))
-(let (($x5689 (fun_app$ v_b_Visited_G_1$ ?v1!10)))
-(let (($x6142 (not $x5689)))
-(let ((?x5569 (fun_app$a v_b_SP_G_1$ ?v1!10)))
-(let ((?x5512 (fun_app$a v_b_SP_G_1$ ?v0!11)))
-(let ((?x5709 (* (- 1) ?x5512)))
-(let ((?x4184 (+ ?x1722 ?x5709 ?x5569)))
-(let (($x4211 (>= ?x4184 0)))
-(let ((?x4266 (+ ?x1729 ?x5709)))
-(let (($x4267 (<= ?x4266 0)))
-(let ((@x4273 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1729 ?x5512)) $x4267)) (symm (monotonicity @x4002 (= ?x5512 ?x1729)) (= ?x1729 ?x5512)) $x4267)))
-(let ((@x4363 ((_ th-lemma arith farkas 1 -1 -1 1) (hypothesis $x4267) (hypothesis $x4264) (hypothesis $x4211) (hypothesis (not $x2204)) false)))
-(let ((@x4274 (unit-resolution (lemma @x4363 (or (not $x4211) (not $x4267) (not $x4264) $x2204)) @x4273 @x5656 (unit-resolution (def-axiom (or $x2640 (not $x2204))) @x3125 (not $x2204)) (not $x4211))))
-(let (($x4220 (or $x3573 $x6142 $x1725 $x4211)))
-(let (($x5674 (or $x6142 $x1725 (>= (+ ?x1722 ?x5569 ?x5709) 0))))
-(let (($x4221 (or $x3573 $x5674)))
-(let ((@x4210 (monotonicity (rewrite (= (+ ?x1722 ?x5569 ?x5709) ?x4184)) (= (>= (+ ?x1722 ?x5569 ?x5709) 0) $x4211))))
-(let ((@x4224 (monotonicity (monotonicity @x4210 (= $x5674 (or $x6142 $x1725 $x4211))) (= $x4221 (or $x3573 (or $x6142 $x1725 $x4211))))))
-(let ((@x4227 (trans @x4224 (rewrite (= (or $x3573 (or $x6142 $x1725 $x4211)) $x4220)) (= $x4221 $x4220))))
-(let ((@x4360 (unit-resolution (mp ((_ quant-inst ?v0!11 ?v1!10) $x4221) @x4227 $x4220) (unit-resolution (def-axiom (or $x3816 $x3568)) @x4357 $x3568) (unit-resolution (def-axiom (or $x2640 (not $x1725))) @x3125 (not $x1725)) (or $x6142 $x4211))))
-(let (($x5857 (or $x5689 $x5398)))
-(let ((@x5652 (mp ((_ quant-inst ?v1!10) (or $x3590 $x5857)) (rewrite (= (or $x3590 $x5857) (or $x3590 $x5689 $x5398))) (or $x3590 $x5689 $x5398))))
-(let ((@x4367 (unit-resolution (unit-resolution @x5652 (hypothesis $x3585) $x5857) (unit-resolution @x4360 @x4274 $x6142) $x5398)))
-(let ((@x4362 ((_ th-lemma arith farkas -1 1 1) @x4367 @x5656 (unit-resolution (def-axiom (or $x2640 $x1720)) @x3125 $x1720) false)))
-(let ((@x4151 (unit-resolution (lemma @x4362 (or $x2640 $x3590 $x2703)) (unit-resolution (def-axiom (or $x3649 $x3585)) @x4159 $x3585) @x4139 $x2640)))
-(let ((@x4161 (unit-resolution (def-axiom (or $x3637 $x3631)) (unit-resolution (def-axiom (or $x3634 $x2645 $x3628)) @x4151 @x4149 $x3634) $x3637)))
-(let ((@x4158 (unit-resolution (def-axiom (or $x3646 $x3606 $x3640)) @x4161 (unit-resolution (def-axiom (or $x3649 $x3643)) @x4159 $x3643) $x3606)))
-(let (($x3139 (<= (+ b_Infinity$ (* (- 1) (fun_app$a v_b_SP_G_1$ ?v0!8))) 0)))
-(let ((?x5112 (fun_app$a v_b_SP_G_1$ ?v0!8)))
-(let ((?x5119 (* (- 1) ?x5112)))
-(let ((?x3935 (?v1!7 ?v0!8)))
-(let ((?x3976 (pair$ ?x3935 ?v0!8)))
-(let ((?x3971 (b_G$ ?x3976)))
-(let ((?x3928 (fun_app$a v_b_SP_G_1$ ?x3935)))
-(let ((?x3958 (+ ?x3928 ?x3971 ?x5119)))
-(let (($x3970 (= ?x3958 0)))
-(let (($x3980 (not $x3970)))
-(let (($x3930 (fun_app$ v_b_Visited_G_1$ ?x3935)))
-(let (($x3959 (not $x3930)))
-(let (($x3890 (>= (+ ?x3928 ?x5119) 0)))
-(let (($x4009 (or $x3890 $x3959 $x3980)))
-(let ((?x4378 (fun_app$a v_b_SP_G_3$ ?x3935)))
-(let ((?x4397 (* (- 1) ?x4378)))
-(let ((?x4601 (+ ?x3928 ?x4397)))
-(let (($x4605 (>= ?x4601 0)))
-(let ((@x4642 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x3928 ?x4378)) $x4605)) (symm (monotonicity (hypothesis $x214) (= ?x4378 ?x3928)) (= ?x3928 ?x4378)) $x4605)))
-(let ((?x4137 (+ ?x1656 ?x5119)))
-(let (($x4122 (>= ?x4137 0)))
-(let ((@x4625 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1656 ?x5112)) $x4122)) (symm (monotonicity @x4002 (= ?x5112 ?x1656)) (= ?x1656 ?x5112)) $x4122)))
-(let (($x4065 (<= ?x3958 0)))
-(let ((@x5126 (unit-resolution (def-axiom (or $x4009 $x3970)) (hypothesis (not $x4009)) $x3970)))
-(let (($x4604 (<= ?x4601 0)))
-(let ((@x5858 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x3928 ?x4378)) $x4604)) (symm (monotonicity (hypothesis $x214) (= ?x4378 ?x3928)) (= ?x3928 ?x4378)) $x4604)))
-(let (($x4121 (<= ?x4137 0)))
-(let ((@x5140 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1656 ?x5112)) $x4121)) (symm (monotonicity @x4002 (= ?x5112 ?x1656)) (= ?x1656 ?x5112)) $x4121)))
-(let (($x4058 (>= ?x3958 0)))
-(let (($x4399 (<= (+ ?x1656 ?x4397) 0)))
-(let (($x4338 (not $x4399)))
-(let ((@x4989 (unit-resolution (def-axiom (or $x4009 (not $x3890))) (hypothesis (not $x4009)) (not $x3890))))
-(let ((@x5003 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 -1) (or $x4338 (not $x4122) $x3890 (not $x4605))) @x4989 @x4625 @x4642 $x4338)))
-(let (($x4758 (not $x4605)))
-(let (($x4757 (not $x4122)))
-(let (($x4898 (or $x4399 $x3600 (not $x4058) (not $x4121) (not $x4604) (not $x4065) $x4757 $x4758)))
-(let ((?x5665 (* (- 1) ?x3971)))
-(let ((?x4417 (+ ?x1656 ?x5665 ?x4397)))
-(let (($x4445 (>= ?x4417 0)))
-(let ((@x5038 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1 -1) (or $x4445 (not $x4065) $x4757 $x4758)) (hypothesis $x4065) (hypothesis $x4122) (hypothesis $x4605) $x4445)))
-(let (($x4444 (<= ?x4417 0)))
-(let ((@x4331 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1 -1) (or $x4444 (not $x4058) (not $x4121) (not $x4604))) (hypothesis $x4058) (hypothesis $x4121) (hypothesis $x4604) $x4444)))
-(let (($x4418 (= ?x4417 0)))
-(let (($x4428 (not $x4418)))
-(let (($x4430 (or $x4399 $x4428)))
-(let (($x4447 (or $x3600 $x4399 $x4428)))
-(let (($x4384 (>= (+ ?x4378 ?x1657) 0)))
-(let (($x4388 (or $x4384 (not (= (+ ?x4378 ?x1657 ?x3971) 0)))))
-(let (($x4432 (or $x3600 $x4388)))
-(let ((@x4414 (monotonicity (rewrite (= (+ ?x4378 ?x1657 ?x3971) (+ ?x1657 ?x3971 ?x4378))) (= (= (+ ?x4378 ?x1657 ?x3971) 0) (= (+ ?x1657 ?x3971 ?x4378) 0)))))
-(let ((@x4427 (trans @x4414 (rewrite (= (= (+ ?x1657 ?x3971 ?x4378) 0) $x4418)) (= (= (+ ?x4378 ?x1657 ?x3971) 0) $x4418))))
-(let ((@x4396 (monotonicity (rewrite (= (+ ?x4378 ?x1657) (+ ?x1657 ?x4378))) (= $x4384 (>= (+ ?x1657 ?x4378) 0)))))
-(let ((@x4406 (trans @x4396 (rewrite (= (>= (+ ?x1657 ?x4378) 0) $x4399)) (= $x4384 $x4399))))
-(let ((@x4446 (monotonicity @x4406 (monotonicity @x4427 (= (not (= (+ ?x4378 ?x1657 ?x3971) 0)) $x4428)) (= $x4388 $x4430))))
-(let ((@x4442 (trans (monotonicity @x4446 (= $x4432 (or $x3600 $x4430))) (rewrite (= (or $x3600 $x4430) $x4447)) (= $x4432 $x4447))))
-(let ((@x5041 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!8)) $x4432) @x4442 $x4447) (hypothesis $x3595) $x4430)))
-(let ((@x4897 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4418 (not $x4444) (not $x4445))) (unit-resolution @x5041 (hypothesis $x4338) $x4428) @x4331 @x5038 false)))
-(let ((@x3135 (unit-resolution (lemma @x4897 $x4898) @x5003 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3980 $x4058)) @x5126 $x4058) (hypothesis $x3595) @x5140 @x5858 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x3980 $x4065)) @x5126 $x4065) @x4625 @x4642 false)))
-(let ((@x4168 (unit-resolution (lemma @x3135 (or $x4009 $x3600 $x2703)) (unit-resolution (def-axiom (or $x3603 $x3595)) @x4158 $x3595) @x4139 $x4009)))
-(let ((@x4189 (unit-resolution (def-axiom (or $x3816 $x3576)) @x4357 $x3576)))
-(let (($x4014 (not $x4009)))
-(let (($x4042 (or $x3581 $x1654 $x3139 $x4014)))
-(let (($x3956 (<= (+ ?x5112 (* (- 1) ?x3928)) 0)))
-(let (($x3033 (or $x1654 $x3139 (not (or $x3956 $x3959 (not (= (+ ?x5112 (* (- 1) ?x3928) ?x5665) 0)))))))
-(let (($x4043 (or $x3581 $x3033)))
-(let (($x3964 (= (not (or $x3956 $x3959 (not (= (+ ?x5112 (* (- 1) ?x3928) ?x5665) 0)))) $x4014)))
-(let (($x4010 (= (or $x3956 $x3959 (not (= (+ ?x5112 (* (- 1) ?x3928) ?x5665) 0))) $x4009)))
-(let (($x5977 (= (+ ?x5112 (* (- 1) ?x3928) ?x5665) 0)))
-(let ((@x3929 (rewrite (= (+ ?x5112 (* (- 1) ?x3928) ?x5665) (+ (* (- 1) ?x3928) ?x5665 ?x5112)))))
-(let ((@x3957 (monotonicity @x3929 (= $x5977 (= (+ (* (- 1) ?x3928) ?x5665 ?x5112) 0)))))
-(let ((@x3988 (trans @x3957 (rewrite (= (= (+ (* (- 1) ?x3928) ?x5665 ?x5112) 0) $x3970)) (= $x5977 $x3970))))
-(let ((@x3898 (monotonicity (rewrite (= (+ ?x5112 (* (- 1) ?x3928)) (+ (* (- 1) ?x3928) ?x5112))) (= $x3956 (<= (+ (* (- 1) ?x3928) ?x5112) 0)))))
-(let ((@x3927 (trans @x3898 (rewrite (= (<= (+ (* (- 1) ?x3928) ?x5112) 0) $x3890)) (= $x3956 $x3890))))
-(let ((@x4011 (monotonicity (monotonicity @x3927 (monotonicity @x3988 (= (not $x5977) $x3980)) $x4010) $x3964)))
-(let ((@x4050 (monotonicity (monotonicity @x4011 (= $x3033 (or $x1654 $x3139 $x4014))) (= $x4043 (or $x3581 (or $x1654 $x3139 $x4014))))))
-(let ((@x4053 (trans @x4050 (rewrite (= (or $x3581 (or $x1654 $x3139 $x4014)) $x4042)) (= $x4043 $x4042))))
-(let ((@x4248 (unit-resolution (mp ((_ quant-inst ?v0!8) $x4043) @x4053 $x4042) @x4189 (unit-resolution (def-axiom (or $x3603 $x1655)) @x4158 $x1655) (or $x3139 $x4014))))
-(let (($x4136 (= ?x1656 ?x5112)))
-(let ((@x4235 (monotonicity (symm @x4139 (= v_b_SP_G_1$ v_b_SP_G_3$)) (= ?x5112 ?x1656))))
-(let ((@x4237 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4136) $x4122)) (symm @x4235 $x4136) $x4122)))
-(let ((@x4238 ((_ th-lemma arith farkas 1 -1 1) @x4237 (unit-resolution @x4248 @x4168 $x3139) (unit-resolution (def-axiom (or $x3603 $x1660)) @x4158 $x1660) false)))
-(let ((@x4802 (unit-resolution (def-axiom (or $x3813 $x3652 $x3807)) (lemma @x4238 $x3649) (unit-resolution (def-axiom (or $x3816 $x3810)) @x4357 $x3810) $x3807)))
-(let ((@x6739 (symm (unit-resolution (def-axiom (or $x3804 $x261)) @x4802 $x261) (= ?x260 v_b_Visited_G_2$))))
-(let ((@x10168 (symm (monotonicity @x6739 (= $x5237 (fun_app$ v_b_Visited_G_2$ ?v0!20))) (= (fun_app$ v_b_Visited_G_2$ ?v0!20) $x5237))))
-(let ((@x10119 (monotonicity @x10168 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!20)) $x9037))))
-(let (($x4298 (fun_app$ v_b_Visited_G_2$ ?v0!20)))
-(let (($x4299 (not $x4298)))
-(let ((?x4413 (fun_app$a v_b_SP_G_1$ ?v0!20)))
-(let ((?x4438 (* (- 1) ?x4413)))
-(let ((?x4439 (+ ?x1906 ?x4438)))
-(let (($x6002 (>= ?x4439 0)))
-(let (($x9479 (not $x6002)))
-(let ((@x9476 (hypothesis $x6002)))
-(let (($x9588 (or (not (<= (+ ?x1906 (* (- 1) (v_b_SP_G_2$ (?v1!7 ?v0!20)))) 0)) $x9479)))
-(let ((?x4661 (?v1!7 ?v0!20)))
-(let ((?x4662 (fun_app$a v_b_SP_G_1$ ?x4661)))
-(let ((?x4663 (* (- 1) ?x4662)))
-(let ((?x4664 (+ ?x4413 ?x4663)))
-(let (($x4665 (<= ?x4664 0)))
-(let ((?x4668 (pair$ ?x4661 ?v0!20)))
-(let ((?x4669 (b_G$ ?x4668)))
-(let ((?x4670 (* (- 1) ?x4669)))
-(let ((?x4671 (+ ?x4413 ?x4663 ?x4670)))
-(let (($x4672 (= ?x4671 0)))
-(let (($x4673 (not $x4672)))
-(let (($x4666 (fun_app$ v_b_Visited_G_1$ ?x4661)))
-(let (($x4667 (not $x4666)))
-(let (($x4674 (or $x4665 $x4667 $x4673)))
-(let (($x4675 (not $x4674)))
-(let (($x1884 (not $x1883)))
-(let ((@x8699 (hypothesis $x2806)))
-(let (($x7517 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!19)))) 0)))
-(let ((?x7554 (pair$ v_b_v_G_1$ ?v0!19)))
-(let ((?x7555 (b_G$ ?x7554)))
-(let ((?x7388 (fun_app$a v_b_SP_G_1$ ?v0!19)))
-(let ((?x7461 (* (- 1) ?x7388)))
-(let (($x4944 (>= (+ ?x254 ?x7461 ?x7555) 0)))
-(let (($x8378 (or $x7517 $x4944)))
-(let ((?x7471 (+ ?x254 ?x1889 ?x7555)))
-(let (($x6876 (= ?x7471 0)))
-(let (($x8868 (not $x6876)))
-(let (($x6123 (>= ?x7471 0)))
-(let (($x8149 (not $x6123)))
-(let ((?x7512 (* (- 1) ?x7555)))
-(let ((?x9069 (+ ?x1880 ?x7512)))
-(let (($x8504 (>= ?x9069 0)))
-(let (($x6383 (= ?v1!18 v_b_v_G_1$)))
-(let (($x5168 (fun_app$ v_b_Visited_G_1$ ?v1!18)))
-(let (($x6179 (not $x5168)))
-(let (($x7401 (<= (+ ?x1888 ?x7461) 0)))
-(let ((?x5283 (b_G$ (pair$ v_b_v_G_1$ ?v0!13))))
-(let ((?x5139 (+ ?x254 ?x1805 ?x5283)))
-(let (($x4859 (= ?x5139 0)))
-(let (($x4202 (>= (+ ?x254 (* (- 1) ?x1803) ?x5283) 0)))
-(let (($x3165 (<= (+ b_Infinity$ (* (- 1) ?x5283)) 0)))
-(let (($x4930 (or $x3165 $x4202)))
-(let (($x4933 (not $x4930)))
-(let ((@x4771 (monotonicity (commutativity (= (= ?x1803 ?x1804) (= ?x1804 ?x1803))) (= (not (= ?x1803 ?x1804)) (not (= ?x1804 ?x1803))))))
-(let (($x4765 (not (= ?x1803 ?x1804))))
-(let ((@x4772 (mp (unit-resolution ((_ th-lemma arith triangle-eq) (or $x4765 $x1807)) (hypothesis $x1808) $x4765) @x4771 (not (= ?x1804 ?x1803)))))
-(let (($x4288 (= ?x1804 ?x1803)))
-(let (($x4284 (or $x4933 $x4288)))
-(let ((@x4803 (unit-resolution (def-axiom (or $x3804 $x3673)) @x4802 $x3673)))
-(let (($x4290 (or $x3678 $x4933 $x4288)))
-(let (($x4289 (or (not (or $x3165 (<= (+ ?x1803 ?x1168 (* (- 1) ?x5283)) 0))) $x4288)))
-(let (($x4291 (or $x3678 $x4289)))
-(let (($x3167 (<= (+ ?x1803 ?x1168 (* (- 1) ?x5283)) 0)))
-(let ((@x4198 (rewrite (= (+ ?x1803 ?x1168 (* (- 1) ?x5283)) (+ ?x1168 ?x1803 (* (- 1) ?x5283))))))
-(let ((@x4195 (monotonicity @x4198 (= $x3167 (<= (+ ?x1168 ?x1803 (* (- 1) ?x5283)) 0)))))
-(let ((@x5138 (trans @x4195 (rewrite (= (<= (+ ?x1168 ?x1803 (* (- 1) ?x5283)) 0) $x4202)) (= $x3167 $x4202))))
-(let ((@x4283 (monotonicity (monotonicity @x5138 (= (or $x3165 $x3167) $x4930)) (= (not (or $x3165 $x3167)) $x4933))))
-(let ((@x4294 (monotonicity (monotonicity @x4283 (= $x4289 $x4284)) (= $x4291 (or $x3678 $x4284)))))
-(let ((@x5050 (mp ((_ quant-inst ?v0!13) $x4291) (trans @x4294 (rewrite (= (or $x3678 $x4284) $x4290)) (= $x4291 $x4290)) $x4290)))
-(let ((@x4805 (unit-resolution (def-axiom (or $x4930 (not $x3165))) (unit-resolution (unit-resolution @x5050 @x4803 $x4284) @x4772 $x4933) (not $x3165))))
-(let ((@x4788 (unit-resolution (def-axiom (or $x4930 (not $x4202))) (unit-resolution (unit-resolution @x5050 @x4803 $x4284) @x4772 $x4933) (not $x4202))))
-(let (($x5127 (or $x3165 $x4202 $x4859)))
-(let ((@x4789 (unit-resolution (def-axiom (or $x3804 $x3665)) @x4802 $x3665)))
-(let (($x5129 (or $x3670 $x3165 $x4202 $x4859)))
-(let (($x4192 (or $x3165 $x3167 (= (+ ?x254 ?x5283 ?x1805) 0))))
-(let (($x5130 (or $x3670 $x4192)))
-(let ((@x4861 (monotonicity (rewrite (= (+ ?x254 ?x5283 ?x1805) ?x5139)) (= (= (+ ?x254 ?x5283 ?x1805) 0) $x4859))))
-(let ((@x5135 (monotonicity (monotonicity @x5138 @x4861 (= $x4192 $x5127)) (= $x5130 (or $x3670 $x5127)))))
-(let ((@x5160 (mp ((_ quant-inst ?v0!13) $x5130) (trans @x5135 (rewrite (= (or $x3670 $x5127) $x5129)) (= $x5130 $x5129)) $x5129)))
-(let ((@x4787 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4859) (>= ?x5139 0))) (unit-resolution (unit-resolution @x5160 @x4789 $x5127) @x4788 @x4805 $x4859) (>= ?x5139 0))))
-(let ((@x4795 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (<= ?x1806 0) $x1807)) (hypothesis $x1808) (<= ?x1806 0))))
-(let ((@x5162 (unit-resolution (def-axiom (or $x3801 $x1808 $x3795)) (unit-resolution (def-axiom (or $x3804 $x3798)) @x4802 $x3798) $x3798)))
-(let ((@x4711 (unit-resolution @x5162 (lemma ((_ th-lemma arith farkas 1 -1 1) @x4795 @x4788 @x4787 false) $x1807) $x3795)))
-(let ((@x4714 (unit-resolution (def-axiom (or $x3792 $x3681)) @x4711 $x3681)))
-(let (($x6395 (or $x3686 $x7401)))
-(let ((@x8489 (monotonicity (rewrite (= (+ ?x7388 ?x1889) (+ ?x1889 ?x7388))) (= (>= (+ ?x7388 ?x1889) 0) (>= (+ ?x1889 ?x7388) 0)))))
-(let ((@x7634 (trans @x8489 (rewrite (= (>= (+ ?x1889 ?x7388) 0) $x7401)) (= (>= (+ ?x7388 ?x1889) 0) $x7401))))
-(let ((@x8284 (trans (monotonicity @x7634 (= (or $x3686 (>= (+ ?x7388 ?x1889) 0)) $x6395)) (rewrite (= $x6395 $x6395)) (= (or $x3686 (>= (+ ?x7388 ?x1889) 0)) $x6395))))
-(let ((@x8710 (unit-resolution (mp ((_ quant-inst ?v0!19) (or $x3686 (>= (+ ?x7388 ?x1889) 0))) @x8284 $x6395) @x4714 $x7401)))
-(let (($x8129 (>= (+ ?x1887 (* (- 1) (fun_app$a v_b_SP_G_1$ ?v1!18))) 0)))
-(let ((?x6950 (fun_app$a v_b_SP_G_1$ ?v1!18)))
-(let (($x6951 (= ?x1887 ?x6950)))
-(let (($x1819 (fun_app$ v_b_Visited_G_2$ ?v0!14)))
-(let (($x3393 (not $x1823)))
-(let (($x5543 (fun_app$ v_b_Visited_G_1$ ?v0!14)))
-(let (($x5064 (= ?v0!14 v_b_v_G_1$)))
-(let (($x6244 (or $x5064 $x5543)))
-(let (($x5974 (fun_app$ ?x260 ?v0!14)))
-(let (($x6373 (= $x5974 $x6244)))
-(let (($x3463 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(! (let (($x63 (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3)))
-(= $x63 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :pattern ( (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) ) :qid k!34))
-))
-(let (($x73 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(! (let (($x63 (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3)))
-(= $x63 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!34))
-))
-(let (($x63 (fun_app$ (fun_upd$ ?3 ?2 ?1) ?0)))
-(let (($x70 (= $x63 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0)))))
-(let (($x68 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) (?v3 B_Vertex$) )(! (let (($x63 (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3)))
-(= $x63 (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) :qid k!34))
-))
-(let ((@x72 (rewrite (= (= $x63 (ite (= ?0 ?2) ?1 (fun_app$ ?3 ?0))) $x70))))
-(let ((@x1438 (mp~ (mp (asserted $x68) (quant-intro @x72 (= $x68 $x73)) $x73) (nnf-pos (refl (~ $x70 $x70)) (~ $x73 $x73)) $x73)))
-(let ((@x3468 (mp @x1438 (quant-intro (refl (= $x70 $x70)) (= $x73 $x3463)) $x3463)))
-(let (($x4134 (not $x3463)))
-(let (($x5805 (or $x4134 $x6373)))
-(let ((@x5853 (monotonicity (rewrite (= (ite $x5064 true $x5543) $x6244)) (= (= $x5974 (ite $x5064 true $x5543)) $x6373))))
-(let ((@x3152 (monotonicity @x5853 (= (or $x4134 (= $x5974 (ite $x5064 true $x5543))) $x5805))))
-(let ((@x4912 (trans @x3152 (rewrite (= $x5805 $x5805)) (= (or $x4134 (= $x5974 (ite $x5064 true $x5543))) $x5805))))
-(let ((@x4913 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!14) (or $x4134 (= $x5974 (ite $x5064 true $x5543)))) @x4912 $x5805)))
-(let ((@x5240 (mp (hypothesis $x1819) (symm (monotonicity @x6739 (= $x5974 $x1819)) (= $x1819 $x5974)) $x5974)))
-(let ((@x5728 (unit-resolution (def-axiom (or (not $x6373) (not $x5974) $x6244)) @x5240 (unit-resolution @x4913 @x3468 $x6373) $x6244)))
-(let ((@x7078 (hypothesis $x3393)))
-(let ((?x3063 (v_b_SP_G_2$ v_b_v_G_1$)))
-(let (($x3024 (= ?x3063 ?x254)))
-(let ((?x3076 (pair$ v_b_v_G_1$ v_b_v_G_1$)))
-(let ((?x3077 (b_G$ ?x3076)))
-(let (($x3038 (>= ?x3077 0)))
-(let (($x3080 (<= (+ b_Infinity$ (* (- 1) ?x3077)) 0)))
-(let (($x4540 (or $x3080 $x3038)))
-(let (($x6342 (= ?x3077 0)))
-(let (($x3469 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)) :pattern ( (pair$ ?v0 ?v1) ) :qid k!36))
-))
-(let (($x95 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (or (not (= ?v0 ?v1)) (= (b_G$ (pair$ ?v0 ?v1)) 0)) :qid k!36))
-))
-(let (($x92 (or (not (= ?1 ?0)) (= (b_G$ (pair$ ?1 ?0)) 0))))
-(let (($x89 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x80 (= ?v0 ?v1)))
-(=> $x80 (= (b_G$ (pair$ ?v0 ?v1)) 0))) :qid k!36))
-))
-(let ((@x94 (rewrite (= (=> (= ?1 ?0) (= (b_G$ (pair$ ?1 ?0)) 0)) $x92))))
-(let ((@x1443 (mp~ (mp (asserted $x89) (quant-intro @x94 (= $x89 $x95)) $x95) (nnf-pos (refl (~ $x92 $x92)) (~ $x95 $x95)) $x95)))
-(let ((@x3474 (mp @x1443 (quant-intro (refl (= $x92 $x92)) (= $x95 $x3469)) $x3469)))
-(let (($x3045 (not $x3469)))
-(let (($x6595 (or $x3045 $x6342)))
-(let ((@x6585 (monotonicity (rewrite (= (= v_b_v_G_1$ v_b_v_G_1$) true)) (= (not (= v_b_v_G_1$ v_b_v_G_1$)) (not true)))))
-(let ((@x6587 (trans @x6585 (rewrite (= (not true) false)) (= (not (= v_b_v_G_1$ v_b_v_G_1$)) false))))
-(let ((@x6590 (monotonicity @x6587 (= (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x6342) (or false $x6342)))))
-(let ((@x6594 (trans @x6590 (rewrite (= (or false $x6342) $x6342)) (= (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x6342) $x6342))))
-(let ((@x6599 (monotonicity @x6594 (= (or $x3045 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x6342)) $x6595))))
-(let ((@x6602 (trans @x6599 (rewrite (= $x6595 $x6595)) (= (or $x3045 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x6342)) $x6595))))
-(let ((@x6603 (mp ((_ quant-inst v_b_v_G_1$ v_b_v_G_1$) (or $x3045 (or (not (= v_b_v_G_1$ v_b_v_G_1$)) $x6342))) @x6602 $x6595)))
-(let ((@x6616 (lemma (unit-resolution @x6603 @x3474 (hypothesis (not $x6342)) false) $x6342)))
-(let ((@x7085 (unit-resolution (def-axiom (or $x4540 (not $x3038))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6342) $x3038)) @x6616 $x3038) $x4540)))
-(let (($x4579 (not $x4540)))
-(let (($x4550 (or $x4579 $x3024)))
-(let (($x4556 (or $x3678 $x4579 $x3024)))
-(let (($x3874 (or (not (or $x3080 (<= (+ ?x254 ?x1168 (* (- 1) ?x3077)) 0))) $x3024)))
-(let (($x4557 (or $x3678 $x3874)))
-(let (($x3062 (<= (+ ?x254 ?x1168 (* (- 1) ?x3077)) 0)))
-(let ((@x4468 (monotonicity (rewrite (= (+ ?x254 ?x1168 (* (- 1) ?x3077)) (* (- 1) ?x3077))) (= $x3062 (<= (* (- 1) ?x3077) 0)))))
-(let ((@x4485 (trans @x4468 (rewrite (= (<= (* (- 1) ?x3077) 0) $x3038)) (= $x3062 $x3038))))
-(let ((@x4549 (monotonicity (monotonicity @x4485 (= (or $x3080 $x3062) $x4540)) (= (not (or $x3080 $x3062)) $x4579))))
-(let ((@x4561 (monotonicity (monotonicity @x4549 (= $x3874 $x4550)) (= $x4557 (or $x3678 $x4550)))))
-(let ((@x4574 (mp ((_ quant-inst v_b_v_G_1$) $x4557) (trans @x4561 (rewrite (= (or $x3678 $x4550) $x4556)) (= $x4557 $x4556)) $x4556)))
-(let ((@x7095 (trans (monotonicity (hypothesis $x5064) (= ?x1821 ?x3063)) (unit-resolution (unit-resolution @x4574 @x4803 $x4550) @x7085 $x3024) (= ?x1821 ?x254))))
-(let ((@x7096 (trans @x7095 (symm (monotonicity (hypothesis $x5064) (= ?x1822 ?x254)) (= ?x254 ?x1822)) $x1823)))
-(let ((@x6504 (unit-resolution (lemma (unit-resolution @x7078 @x7096 false) (or (not $x5064) $x1823)) @x7078 (not $x5064))))
-(let ((@x6501 (unit-resolution (def-axiom (or (not $x6244) $x5064 $x5543)) @x6504 (or (not $x6244) $x5543))))
-(let (($x6879 (>= (+ ?x254 (* (- 1) ?x1822)) 0)))
-(let (($x7105 (not $x6879)))
-(let (($x6372 (>= (+ ?x254 (* (- 1) ?x1822) (b_G$ (pair$ v_b_v_G_1$ ?v0!14))) 0)))
-(let (($x6043 (not $x6372)))
-(let (($x5623 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
-(let (($x6328 (or $x5623 $x6372)))
-(let (($x5555 (not $x6328)))
-(let (($x5565 (or $x3678 $x5555 $x1823)))
-(let (($x5711 (<= (+ ?x1822 ?x1168 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
-(let (($x5760 (or (not (or $x5623 $x5711)) $x1823)))
-(let (($x5490 (or $x3678 $x5760)))
-(let (($x5031 (<= (+ ?x1168 ?x1822 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) 0)))
-(let (($x5019 (= (+ ?x1822 ?x1168 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))) (+ ?x1168 ?x1822 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v0!14)))))))
-(let ((@x6180 (trans (monotonicity (rewrite $x5019) (= $x5711 $x5031)) (rewrite (= $x5031 $x6372)) (= $x5711 $x6372))))
-(let ((@x5556 (monotonicity (monotonicity @x6180 (= (or $x5623 $x5711) $x6328)) (= (not (or $x5623 $x5711)) $x5555))))
-(let ((@x4918 (monotonicity (monotonicity @x5556 (= $x5760 (or $x5555 $x1823))) (= $x5490 (or $x3678 (or $x5555 $x1823))))))
-(let ((@x6362 (trans @x4918 (rewrite (= (or $x3678 (or $x5555 $x1823)) $x5565)) (= $x5490 $x5565))))
-(let ((@x6339 (unit-resolution (def-axiom (or $x6328 $x6043)) (unit-resolution (mp ((_ quant-inst ?v0!14) $x5490) @x6362 $x5565) @x4803 @x7078 $x5555) $x6043)))
-(let ((?x5617 (pair$ v_b_v_G_1$ ?v0!14)))
-(let ((?x5621 (b_G$ ?x5617)))
-(let (($x6266 (>= ?x5621 0)))
-(let ((@x6636 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x5621 0)) $x6266)) (hypothesis (not $x6266)) (not (= ?x5621 0)))))
-(let (($x6078 (= v_b_v_G_1$ ?v0!14)))
-(let (($x6076 (<= ?x5621 0)))
-(let ((@x6410 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x6266 $x6076)) (hypothesis (not $x6266)) $x6076)))
-(let (($x6080 (or $x6078 (not $x6076))))
-(let (($x3475 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x80 (= ?v0 ?v1)))
-(or $x80 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))) :pattern ( (pair$ ?v0 ?v1) ) :qid k!37))
-))
-(let (($x116 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let (($x80 (= ?v0 ?v1)))
-(or $x80 (not (<= (b_G$ (pair$ ?v0 ?v1)) 0)))) :qid k!37))
-))
-(let (($x80 (= ?1 ?0)))
-(let (($x113 (or $x80 (not (<= (b_G$ (pair$ ?1 ?0)) 0)))))
-(let (($x101 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x29 (pair$ ?v0 ?v1)))
-(let ((?x81 (b_G$ ?x29)))
-(let (($x98 (< 0 ?x81)))
-(=> (not (= ?v0 ?v1)) $x98)))) :qid k!37))
-))
-(let (($x106 (forall ((?v0 B_Vertex$) (?v1 B_Vertex$) )(! (let ((?x29 (pair$ ?v0 ?v1)))
-(let ((?x81 (b_G$ ?x29)))
-(let (($x98 (< 0 ?x81)))
-(let (($x80 (= ?v0 ?v1)))
-(or $x80 $x98))))) :qid k!37))
-))
-(let ((?x29 (pair$ ?1 ?0)))
-(let ((?x81 (b_G$ ?x29)))
-(let (($x98 (< 0 ?x81)))
-(let ((@x115 (monotonicity (rewrite (= $x98 (not (<= ?x81 0)))) (= (or $x80 $x98) $x113))))
-(let ((@x108 (quant-intro (rewrite (= (=> (not $x80) $x98) (or $x80 $x98))) (= $x101 $x106))))
-(let ((@x121 (mp (asserted $x101) (trans @x108 (quant-intro @x115 (= $x106 $x116)) (= $x101 $x116)) $x116)))
-(let ((@x3480 (mp (mp~ @x121 (nnf-pos (refl (~ $x113 $x113)) (~ $x116 $x116)) $x116) (quant-intro (refl (= $x113 $x113)) (= $x116 $x3475)) $x3475)))
-(let ((@x6389 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or (not $x3475) $x6080)) (rewrite (= (or (not $x3475) $x6080) (or (not $x3475) $x6078 (not $x6076)))) (or (not $x3475) $x6078 (not $x6076)))))
-(let (($x6086 (= ?x5621 0)))
-(let (($x6096 (or (not $x6078) $x6086)))
-(let ((@x6264 (mp ((_ quant-inst v_b_v_G_1$ ?v0!14) (or $x3045 $x6096)) (rewrite (= (or $x3045 $x6096) (or $x3045 (not $x6078) $x6086))) (or $x3045 (not $x6078) $x6086))))
-(let ((@x6993 (unit-resolution (unit-resolution @x6264 @x3474 $x6096) (unit-resolution (unit-resolution @x6389 @x3480 $x6080) @x6410 $x6078) @x6636 false)))
-(let ((@x7107 (lemma ((_ th-lemma arith farkas 1 -1 1) (hypothesis $x6266) (hypothesis $x6043) (hypothesis $x6879) false) (or (not $x6266) $x6372 $x7105))))
-(let ((@x6134 (unit-resolution (unit-resolution @x7107 (lemma @x6993 $x6266) (or $x6372 $x7105)) @x6339 $x7105)))
-(let ((@x6066 (unit-resolution (def-axiom (or $x3804 $x253)) @x4802 $x253)))
-(let ((@x6683 (unit-resolution (def-axiom (or $x3816 $x3560)) @x4357 $x3560)))
-(let (($x6034 (= (or $x3565 (or $x252 (not $x5543) $x6879)) (or $x3565 $x252 (not $x5543) $x6879))))
-(let ((@x6556 (mp ((_ quant-inst ?v0!14 v_b_v_G_1$) (or $x3565 (or $x252 (not $x5543) $x6879))) (rewrite $x6034) (or $x3565 $x252 (not $x5543) $x6879))))
-(let ((@x6850 (unit-resolution @x6556 @x6683 @x6066 @x6134 (unit-resolution @x6501 @x5728 $x5543) false)))
-(let ((@x5791 (unit-resolution (lemma @x6850 $x1824) (unit-resolution (def-axiom (or $x1824 $x3393)) (hypothesis $x1825) $x3393) (unit-resolution (def-axiom (or $x1824 $x1819)) (hypothesis $x1825) $x1819) false)))
-(let ((@x9261 (unit-resolution (def-axiom (or $x3789 $x1825 $x3783)) (unit-resolution (def-axiom (or $x3792 $x3786)) @x4711 $x3786) $x3786)))
-(let ((@x9263 (unit-resolution (def-axiom (or $x3780 $x3690)) (unit-resolution @x9261 (lemma @x5791 $x1824) $x3783) $x3690)))
-(let ((@x6271 (mp ((_ quant-inst ?v1!18) (or $x3695 (or $x2786 $x6951))) (rewrite (= (or $x3695 (or $x2786 $x6951)) (or $x3695 $x2786 $x6951))) (or $x3695 $x2786 $x6951))))
-(let ((@x5205 (unit-resolution @x6271 @x9263 (unit-resolution (def-axiom (or $x2801 $x1878)) @x8699 $x1878) $x6951)))
-(let ((@x8621 ((_ th-lemma arith assign-bounds -1 -1 1) (or (not (>= (+ ?x1880 ?x6950 ?x7461) 0)) (not $x7401) $x1891 (not $x8129)))))
-(let ((@x8189 (unit-resolution @x8621 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6951) $x8129)) @x5205 $x8129) (unit-resolution (def-axiom (or $x2801 (not $x1891))) @x8699 (not $x1891)) @x8710 (not (>= (+ ?x1880 ?x6950 ?x7461) 0)))))
-(let (($x5620 (= (or $x3573 (or $x6179 $x1883 (>= (+ ?x1880 ?x6950 ?x7461) 0))) (or $x3573 $x6179 $x1883 (>= (+ ?x1880 ?x6950 ?x7461) 0)))))
-(let ((@x7205 (mp ((_ quant-inst ?v0!19 ?v1!18) (or $x3573 (or $x6179 $x1883 (>= (+ ?x1880 ?x6950 ?x7461) 0)))) (rewrite $x5620) (or $x3573 $x6179 $x1883 (>= (+ ?x1880 ?x6950 ?x7461) 0)))))
-(let ((@x8192 (unit-resolution @x7205 (unit-resolution (def-axiom (or $x3816 $x3568)) @x4357 $x3568) (unit-resolution (def-axiom (or $x2801 $x1884)) @x8699 $x1884) (or $x6179 (>= (+ ?x1880 ?x6950 ?x7461) 0)))))
-(let (($x8059 (or $x6383 $x5168)))
-(let (($x4914 (fun_app$ ?x260 ?v1!18)))
-(let (($x8555 (= $x4914 $x8059)))
-(let (($x7052 (or $x4134 $x8555)))
-(let ((@x8554 (monotonicity (rewrite (= (ite $x6383 true $x5168) $x8059)) (= (= $x4914 (ite $x6383 true $x5168)) $x8555))))
-(let ((@x8280 (monotonicity @x8554 (= (or $x4134 (= $x4914 (ite $x6383 true $x5168))) $x7052))))
-(let ((@x7080 (trans @x8280 (rewrite (= $x7052 $x7052)) (= (or $x4134 (= $x4914 (ite $x6383 true $x5168))) $x7052))))
-(let ((@x7791 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!18) (or $x4134 (= $x4914 (ite $x6383 true $x5168)))) @x7080 $x7052)))
-(let ((@x8161 (mp (unit-resolution (def-axiom (or $x2801 $x1878)) @x8699 $x1878) (symm (monotonicity @x6739 (= $x4914 $x1878)) (= $x1878 $x4914)) $x4914)))
-(let ((@x8162 (unit-resolution (def-axiom (or (not $x8555) (not $x4914) $x8059)) @x8161 (unit-resolution @x7791 @x3468 $x8555) $x8059)))
-(let ((@x8163 (unit-resolution (def-axiom (or (not $x8059) $x6383 $x5168)) @x8162 (unit-resolution @x8192 @x8189 $x6179) $x6383)))
-(let ((@x5864 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1880 ?x7555)) $x8504)) (monotonicity (monotonicity @x8163 (= ?x1879 ?x7554)) (= ?x1880 ?x7555)) $x8504)))
-(let (($x7609 (>= (+ ?x1887 (* (- 1) ?x3063)) 0)))
-(let ((@x5835 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1887 ?x3063)) $x7609)) (monotonicity @x8163 (= ?x1887 ?x3063)) $x7609)))
-(let ((?x3064 (* (- 1) ?x3063)))
-(let ((?x3904 (+ ?x254 ?x3064)))
-(let (($x3905 (<= ?x3904 0)))
-(let (($x4587 (= ?x254 ?x3063)))
-(let ((@x8351 (mp (unit-resolution (unit-resolution @x4574 @x4803 $x4550) @x7085 $x3024) (symm (commutativity (= $x4587 $x3024)) (= $x3024 $x4587)) $x4587)))
-(let ((@x8148 ((_ th-lemma arith farkas 1 -1 1 -1 1) (hypothesis $x6123) (hypothesis (not $x1891)) (hypothesis $x7609) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x4587) $x3905)) @x8351 $x3905) (hypothesis $x8504) false)))
-(let ((@x6098 (unit-resolution (lemma @x8148 (or $x8149 $x1891 (not $x7609) (not $x8504))) (unit-resolution (def-axiom (or $x2801 (not $x1891))) @x8699 (not $x1891)) @x5835 @x5864 $x8149)))
-(let ((@x8175 (unit-resolution (def-axiom (or $x8378 (not $x7517))) (hypothesis (not $x8378)) (not $x7517))))
-(let (($x7000 (not $x4944)))
-(let ((@x8640 (unit-resolution (def-axiom (or $x8378 $x7000)) (hypothesis (not $x8378)) $x7000)))
-(let (($x6310 (or $x7517 $x4944 $x6876)))
-(let (($x7071 (or $x3670 $x7517 $x4944 $x6876)))
-(let (($x7524 (<= (+ ?x7388 ?x1168 ?x7512) 0)))
-(let (($x7589 (or $x7517 $x7524 (= (+ ?x254 ?x7555 ?x1889) 0))))
-(let (($x6768 (or $x3670 $x7589)))
-(let ((@x6946 (monotonicity (rewrite (= (+ ?x254 ?x7555 ?x1889) ?x7471)) (= (= (+ ?x254 ?x7555 ?x1889) 0) $x6876))))
-(let ((@x7308 (monotonicity (rewrite (= (+ ?x7388 ?x1168 ?x7512) (+ ?x1168 ?x7388 ?x7512))) (= $x7524 (<= (+ ?x1168 ?x7388 ?x7512) 0)))))
-(let ((@x8377 (trans @x7308 (rewrite (= (<= (+ ?x1168 ?x7388 ?x7512) 0) $x4944)) (= $x7524 $x4944))))
-(let ((@x6639 (monotonicity (monotonicity @x8377 @x6946 (= $x7589 $x6310)) (= $x6768 (or $x3670 $x6310)))))
-(let ((@x6030 (mp ((_ quant-inst ?v0!19) $x6768) (trans @x6639 (rewrite (= (or $x3670 $x6310) $x7071)) (= $x6768 $x7071)) $x7071)))
-(let ((@x8762 (unit-resolution (unit-resolution @x6030 @x4789 $x6310) @x8640 @x8175 (hypothesis $x8868) false)))
-(let ((@x8475 (unit-resolution (lemma @x8762 (or $x8378 $x6876)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x8868 $x6123)) @x6098 $x8868) $x8378)))
-(let ((@x8713 (lemma ((_ th-lemma arith farkas -1 -1 1) @x8710 (hypothesis $x8149) (hypothesis $x4944) false) (or $x7000 $x6123))))
-(let ((@x7808 (unit-resolution (def-axiom (or (not $x8378) $x7517 $x4944)) (unit-resolution @x8713 @x6098 $x7000) @x8475 $x7517)))
-(let ((@x7807 ((_ th-lemma arith farkas 1 -1 1) @x5864 @x7808 (unit-resolution (def-axiom (or $x2801 $x1884)) @x8699 $x1884) false)))
-(let (($x3381 (not $x1864)))
-(let ((@x6859 (hypothesis $x2760)))
-(let ((@x6910 (unit-resolution (def-axiom (or $x2755 $x3381)) @x6859 $x3381)))
-(let (($x6437 (<= (+ ?x254 (* (- 1) (fun_app$a v_b_SP_G_1$ ?v1!16))) 0)))
-(let (($x4947 (fun_app$ v_b_Visited_G_1$ ?v1!16)))
-(let (($x6336 (= ?v1!16 v_b_v_G_1$)))
-(let (($x8534 (or $x6336 $x4947)))
-(let (($x6263 (fun_app$ ?x260 ?v1!16)))
-(let (($x6346 (= $x6263 $x8534)))
-(let (($x8582 (or $x4134 $x6346)))
-(let ((@x8309 (monotonicity (rewrite (= (ite $x6336 true $x4947) $x8534)) (= (= $x6263 (ite $x6336 true $x4947)) $x6346))))
-(let ((@x8586 (monotonicity @x8309 (= (or $x4134 (= $x6263 (ite $x6336 true $x4947))) $x8582))))
-(let ((@x8591 (trans @x8586 (rewrite (= $x8582 $x8582)) (= (or $x4134 (= $x6263 (ite $x6336 true $x4947))) $x8582))))
-(let ((@x8592 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v1!16) (or $x4134 (= $x6263 (ite $x6336 true $x4947)))) @x8591 $x8582)))
-(let ((@x7062 (monotonicity (symm (monotonicity @x6739 (= $x6263 $x1855)) (= $x1855 $x6263)) (= (not $x1855) (not $x6263)))))
-(let ((@x7109 (mp (unit-resolution (def-axiom (or $x2755 (not $x1855))) @x6859 (not $x1855)) @x7062 (not $x6263))))
-(let ((@x7053 (unit-resolution (def-axiom (or (not $x6346) $x6263 (not $x8534))) @x7109 (unit-resolution @x8592 @x3468 $x6346) (not $x8534))))
-(let (($x7664 (or $x4947 $x6437)))
-(let ((@x7108 (unit-resolution (def-axiom (or $x3804 $x3655)) @x4802 $x3655)))
-(let (($x6930 (or $x3660 $x4947 $x6437)))
-(let (($x7189 (>= (+ (fun_app$a v_b_SP_G_1$ ?v1!16) ?x1168) 0)))
-(let (($x7192 (or $x4947 $x7189)))
-(let (($x7392 (or $x3660 $x7192)))
-(let ((@x6696 (rewrite (= (>= (+ ?x1168 (fun_app$a v_b_SP_G_1$ ?v1!16)) 0) $x6437))))
-(let (($x7657 (= (+ (fun_app$a v_b_SP_G_1$ ?v1!16) ?x1168) (+ ?x1168 (fun_app$a v_b_SP_G_1$ ?v1!16)))))
-(let ((@x6394 (monotonicity (rewrite $x7657) (= $x7189 (>= (+ ?x1168 (fun_app$a v_b_SP_G_1$ ?v1!16)) 0)))))
-(let ((@x7789 (monotonicity (monotonicity (trans @x6394 @x6696 (= $x7189 $x6437)) (= $x7192 $x7664)) (= $x7392 (or $x3660 $x7664)))))
-(let ((@x7788 (mp ((_ quant-inst ?v1!16) $x7392) (trans @x7789 (rewrite (= (or $x3660 $x7664) $x6930)) (= $x7392 $x6930)) $x6930)))
-(let ((@x7110 (unit-resolution (unit-resolution @x7788 @x7108 $x7664) (unit-resolution (def-axiom (or $x8534 (not $x4947))) @x7053 (not $x4947)) $x6437)))
-(let (($x6906 (<= (+ (v_b_SP_G_2$ ?v0!17) (* (- 1) (fun_app$a v_b_SP_G_1$ ?v0!17))) 0)))
-(let (($x7394 (or $x3686 $x6906)))
-(let (($x6869 (>= (+ (fun_app$a v_b_SP_G_1$ ?v0!17) (* (- 1) (v_b_SP_G_2$ ?v0!17))) 0)))
-(let (($x7794 (>= (+ (* (- 1) (v_b_SP_G_2$ ?v0!17)) (fun_app$a v_b_SP_G_1$ ?v0!17)) 0)))
-(let (($x7505 (= (+ (fun_app$a v_b_SP_G_1$ ?v0!17) (* (- 1) (v_b_SP_G_2$ ?v0!17))) (+ (* (- 1) (v_b_SP_G_2$ ?v0!17)) (fun_app$a v_b_SP_G_1$ ?v0!17)))))
-(let ((@x6937 (trans (monotonicity (rewrite $x7505) (= $x6869 $x7794)) (rewrite (= $x7794 $x6906)) (= $x6869 $x6906))))
-(let ((@x7419 (trans (monotonicity @x6937 (= (or $x3686 $x6869) $x7394)) (rewrite (= $x7394 $x7394)) (= (or $x3686 $x6869) $x7394))))
-(let (($x6920 (>= (+ (v_b_SP_G_2$ ?v1!16) (* (- 1) (fun_app$a v_b_SP_G_1$ ?v1!16))) 0)))
-(let ((?x6958 (fun_app$a v_b_SP_G_1$ ?v1!16)))
-(let ((?x1860 (v_b_SP_G_2$ ?v1!16)))
-(let (($x6841 (= ?x1860 ?x6958)))
-(let (($x7027 (>= (+ ?x254 (b_G$ (pair$ v_b_v_G_1$ ?v1!16)) (* (- 1) ?x6958)) 0)))
-(let (($x6231 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ ?v1!16)))) 0)))
-(let (($x7455 (or $x6231 $x7027)))
-(let ((?x6824 (pair$ v_b_v_G_1$ ?v1!16)))
-(let ((?x6825 (b_G$ ?x6824)))
-(let ((?x6938 (* (- 1) ?x1860)))
-(let ((?x6929 (+ ?x254 ?x6938 ?x6825)))
-(let (($x7553 (= ?x6929 0)))
-(let (($x7206 (not $x7553)))
-(let (($x6067 (<= ?x6929 0)))
-(let (($x6919 (not $x6067)))
-(let (($x6631 (fun_app$ v_b_Visited_G_1$ ?v0!17)))
-(let (($x6844 (= ?v0!17 v_b_v_G_1$)))
-(let (($x6265 (or $x6844 $x6631)))
-(let (($x6895 (fun_app$ ?x260 ?v0!17)))
-(let (($x6665 (= $x6895 $x6265)))
-(let (($x5717 (or $x4134 $x6665)))
-(let ((@x6990 (monotonicity (rewrite (= (ite $x6844 true $x6631) $x6265)) (= (= $x6895 (ite $x6844 true $x6631)) $x6665))))
-(let ((@x7528 (monotonicity @x6990 (= (or $x4134 (= $x6895 (ite $x6844 true $x6631))) $x5717))))
-(let ((@x7133 (trans @x7528 (rewrite (= $x5717 $x5717)) (= (or $x4134 (= $x6895 (ite $x6844 true $x6631))) $x5717))))
-(let ((@x7043 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!17) (or $x4134 (= $x6895 (ite $x6844 true $x6631)))) @x7133 $x5717)))
-(let ((@x7214 (mp (unit-resolution (def-axiom (or $x2755 $x1857)) @x6859 $x1857) (symm (monotonicity @x6739 (= $x6895 $x1857)) (= $x1857 $x6895)) $x6895)))
-(let ((@x7215 (unit-resolution (def-axiom (or (not $x6665) (not $x6895) $x6265)) @x7214 (unit-resolution @x7043 @x3468 $x6665) $x6265)))
-(let (($x7558 (<= ?x6825 0)))
-(let (($x7559 (not $x7558)))
-(let ((@x6953 (symm (commutativity (= (= v_b_v_G_1$ ?v1!16) $x6336)) (= $x6336 (= v_b_v_G_1$ ?v1!16)))))
-(let ((@x6769 (mp (hypothesis (not $x6336)) (monotonicity @x6953 (= (not $x6336) (not (= v_b_v_G_1$ ?v1!16)))) (not (= v_b_v_G_1$ ?v1!16)))))
-(let (($x7557 (= v_b_v_G_1$ ?v1!16)))
-(let (($x7560 (or $x7557 $x7559)))
-(let ((@x5992 (mp ((_ quant-inst v_b_v_G_1$ ?v1!16) (or (not $x3475) $x7560)) (rewrite (= (or (not $x3475) $x7560) (or (not $x3475) $x7557 $x7559))) (or (not $x3475) $x7557 $x7559))))
-(let ((@x6161 (hypothesis $x3381)))
-(let ((?x6285 (fun_app$a v_b_SP_G_1$ ?v0!17)))
-(let ((?x6904 (* (- 1) ?x6285)))
-(let ((?x7131 (+ ?x254 ?x6904)))
-(let (($x6000 (>= ?x7131 0)))
-(let (($x6858 (not $x6844)))
-(let ((?x1861 (v_b_SP_G_2$ ?v0!17)))
-(let (($x6188 (= ?x1861 ?x3063)))
-(let (($x5847 (not $x6188)))
-(let ((?x5089 (+ ?x1861 ?x3064)))
-(let (($x5848 (<= ?x5089 0)))
-(let (($x6925 (not $x5848)))
-(let ((@x6267 (hypothesis $x6067)))
-(let (($x3906 (>= ?x3904 0)))
-(let (($x4341 (or $x3686 $x3906)))
-(let ((@x4906 ((_ quant-inst v_b_v_G_1$) $x4341)))
-(let ((@x6160 (unit-resolution @x4906 @x4714 $x3906)))
-(let ((@x6971 (lemma ((_ th-lemma arith farkas 1 1 1 1 1) @x6267 (hypothesis $x5848) @x6161 @x6160 (hypothesis $x7559) false) (or $x6925 $x6919 $x1864 $x7558))))
-(let ((@x6928 (unit-resolution @x6971 @x6267 @x6161 (unit-resolution (unit-resolution @x5992 @x3480 $x7560) @x6769 $x7559) $x6925)))
-(let ((@x6532 ((_ th-lemma arith triangle-eq) (or $x5847 $x5848))))
-(let ((@x5114 (unit-resolution (hypothesis $x5847) (monotonicity (hypothesis $x6844) $x6188) false)))
-(let ((@x5115 (lemma @x5114 (or $x6858 $x6188))))
-(let ((@x8623 (def-axiom (or (not $x6265) $x6844 $x6631))))
-(let ((@x4834 (unit-resolution @x8623 (unit-resolution @x5115 (unit-resolution @x6532 @x6928 $x5847) $x6858) (hypothesis $x6265) $x6631)))
-(let (($x5475 (= (or $x3565 (or $x252 (not $x6631) $x6000)) (or $x3565 $x252 (not $x6631) $x6000))))
-(let ((@x5735 (mp ((_ quant-inst ?v0!17 v_b_v_G_1$) (or $x3565 (or $x252 (not $x6631) $x6000))) (rewrite $x5475) (or $x3565 $x252 (not $x6631) $x6000))))
-(let ((@x6914 ((_ th-lemma arith farkas 1 1 1 1 1) @x6267 (unit-resolution @x5735 @x6683 @x6066 @x4834 $x6000) (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3686 $x6869)) @x7419 $x7394) @x4714 $x6906) @x6161 (unit-resolution (unit-resolution @x5992 @x3480 $x7560) @x6769 $x7559) false)))
-(let ((@x7217 (unit-resolution (lemma @x6914 (or $x6919 $x1864 (not $x6265) $x6336)) @x6910 @x7215 (unit-resolution (def-axiom (or $x8534 (not $x6336))) @x7053 (not $x6336)) $x6919)))
-(let ((@x6357 (unit-resolution (def-axiom (or $x7455 (not $x6231))) (hypothesis (not $x7455)) (not $x6231))))
-(let ((@x6426 (unit-resolution (def-axiom (or $x7455 (not $x7027))) (hypothesis (not $x7455)) (not $x7027))))
-(let (($x7603 (or $x6231 $x7027 $x7553)))
-(let (($x5113 (or $x3670 $x6231 $x7027 $x7553)))
-(let (($x6826 (<= (+ ?x6958 ?x1168 (* (- 1) ?x6825)) 0)))
-(let (($x6927 (or $x6231 $x6826 (= (+ ?x254 ?x6825 ?x6938) 0))))
-(let (($x7688 (or $x3670 $x6927)))
-(let ((@x7602 (monotonicity (rewrite (= (+ ?x254 ?x6825 ?x6938) ?x6929)) (= (= (+ ?x254 ?x6825 ?x6938) 0) $x7553))))
-(let ((@x7947 (rewrite (= (+ ?x6958 ?x1168 (* (- 1) ?x6825)) (+ ?x1168 (* (- 1) ?x6825) ?x6958)))))
-(let ((@x7737 (monotonicity @x7947 (= $x6826 (<= (+ ?x1168 (* (- 1) ?x6825) ?x6958) 0)))))
-(let ((@x8385 (trans @x7737 (rewrite (= (<= (+ ?x1168 (* (- 1) ?x6825) ?x6958) 0) $x7027)) (= $x6826 $x7027))))
-(let ((@x6604 (monotonicity (monotonicity @x8385 @x7602 (= $x6927 $x7603)) (= $x7688 (or $x3670 $x7603)))))
-(let ((@x7391 (mp ((_ quant-inst ?v1!16) $x7688) (trans @x6604 (rewrite (= (or $x3670 $x7603) $x5113)) (= $x7688 $x5113)) $x5113)))
-(let ((@x4197 (unit-resolution (unit-resolution @x7391 @x4789 $x7603) @x6426 @x6357 (hypothesis $x7206) false)))
-(let ((@x7250 (unit-resolution (lemma @x4197 (or $x7455 $x7553)) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7206 $x6067)) @x7217 $x7206) $x7455)))
-(let (($x7639 (not $x7455)))
-(let (($x7673 (or $x7639 $x6841)))
-(let (($x7669 (or $x3678 $x7639 $x6841)))
-(let ((@x7671 (monotonicity (monotonicity @x8385 (= (or $x6231 $x6826) $x7455)) (= (not (or $x6231 $x6826)) $x7639))))
-(let ((@x7677 (monotonicity (monotonicity @x7671 (= (or (not (or $x6231 $x6826)) $x6841) $x7673)) (= (or $x3678 (or (not (or $x6231 $x6826)) $x6841)) (or $x3678 $x7673)))))
-(let ((@x7387 (trans @x7677 (rewrite (= (or $x3678 $x7673) $x7669)) (= (or $x3678 (or (not (or $x6231 $x6826)) $x6841)) $x7669))))
-(let ((@x7252 (unit-resolution (mp ((_ quant-inst ?v1!16) (or $x3678 (or (not (or $x6231 $x6826)) $x6841))) @x7387 $x7669) @x4803 $x7673)))
-(let ((@x7315 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6841) $x6920)) (unit-resolution @x7252 @x7250 $x6841) $x6920)))
-(let ((@x7323 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 -1 -1) (or (not $x6000) (not $x6437) (not $x6920) (not $x6906) $x1864)) @x7315 (unit-resolution (mp ((_ quant-inst ?v0!17) (or $x3686 $x6869)) @x7419 $x7394) @x4714 $x6906) @x7110 @x6910 (not $x6000))))
-(let ((@x7351 (unit-resolution ((_ th-lemma arith assign-bounds -1 1 -1 1) (or $x6925 (not $x3906) (not $x6437) (not $x6920) $x1864)) @x7315 @x6160 @x7110 @x6910 $x6925)))
-(let ((@x7364 (unit-resolution @x8623 (unit-resolution @x5115 (unit-resolution @x6532 @x7351 $x5847) $x6858) @x7215 $x6631)))
-(let (($x6106 (not (<= (b_G$ (pair$ v_b_v_G_1$ ?v0!15)) 0))))
-(let (($x5808 (= v_b_v_G_1$ ?v0!15)))
-(let (($x5324 (not $x5808)))
-(let ((@x6624 (symm (commutativity (= $x5808 (= ?v0!15 v_b_v_G_1$))) (= (= ?v0!15 v_b_v_G_1$) $x5808))))
-(let (($x6044 (= ?v0!15 v_b_v_G_1$)))
-(let (($x6867 (not $x6044)))
-(let (($x5521 (fun_app$ v_b_Visited_G_1$ ?v0!15)))
-(let (($x6849 (or $x6044 $x5521)))
-(let (($x6408 (fun_app$ ?x260 ?v0!15)))
-(let (($x6494 (= $x6408 $x6849)))
-(let (($x5683 (or $x4134 $x6494)))
-(let ((@x6072 (monotonicity (rewrite (= (ite $x6044 true $x5521) $x6849)) (= (= $x6408 (ite $x6044 true $x5521)) $x6494))))
-(let ((@x6772 (monotonicity @x6072 (= (or $x4134 (= $x6408 (ite $x6044 true $x5521))) $x5683))))
-(let ((@x5812 (trans @x6772 (rewrite (= $x5683 $x5683)) (= (or $x4134 (= $x6408 (ite $x6044 true $x5521))) $x5683))))
-(let ((@x5804 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!15) (or $x4134 (= $x6408 (ite $x6044 true $x5521)))) @x5812 $x5683)))
-(let ((@x6715 (symm (monotonicity @x6739 (= $x6408 (fun_app$ v_b_Visited_G_2$ ?v0!15))) (= (fun_app$ v_b_Visited_G_2$ ?v0!15) $x6408))))
-(let ((@x6719 (monotonicity @x6715 (= (not (fun_app$ v_b_Visited_G_2$ ?v0!15)) (not $x6408)))))
-(let (($x6151 (fun_app$ v_b_Visited_G_2$ ?v0!15)))
-(let (($x6527 (not $x6151)))
-(let ((@x6833 (hypothesis $x1843)))
-(let (($x6836 (or (not (>= (+ ?x1841 (* (- 1) (fun_app$a v_b_SP_G_1$ ?v0!15))) 0)) $x1842)))
-(let (($x6830 (>= (+ ?x1841 (* (- 1) (fun_app$a v_b_SP_G_1$ ?v0!15))) 0)))
-(let ((?x6459 (fun_app$a v_b_SP_G_1$ ?v0!15)))
-(let (($x6119 (>= ?x6459 0)))
-(let ((@x4713 (unit-resolution (def-axiom (or $x3816 $x3551)) @x4357 $x3551)))
-(let ((@x6834 ((_ th-lemma arith farkas -1 1 1) @x6833 (unit-resolution ((_ quant-inst ?v0!15) (or $x3556 $x6119)) @x4713 $x6119) (hypothesis $x6830) false)))
-(let ((@x6656 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1841 ?x6459)) $x6830)) (unit-resolution (lemma @x6834 $x6836) @x6833 (not $x6830)) (not (= ?x1841 ?x6459)))))
-(let (($x6618 (= (or $x3695 (or $x6527 (= ?x1841 ?x6459))) (or $x3695 $x6527 (= ?x1841 ?x6459)))))
-(let ((@x6610 (mp ((_ quant-inst ?v0!15) (or $x3695 (or $x6527 (= ?x1841 ?x6459)))) (rewrite $x6618) (or $x3695 $x6527 (= ?x1841 ?x6459)))))
-(let ((@x6720 (mp (unit-resolution @x6610 (hypothesis $x3690) @x6656 $x6527) @x6719 (not $x6408))))
-(let ((@x6725 (unit-resolution (def-axiom (or (not $x6494) $x6408 (not $x6849))) @x6720 (unit-resolution @x5804 @x3468 $x6494) (not $x6849))))
-(let ((@x6488 (mp (unit-resolution (def-axiom (or $x6849 $x6867)) @x6725 $x6867) (monotonicity @x6624 (= $x6867 $x5324)) $x5324)))
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-(let ((@x5318 (mp ((_ quant-inst v_b_v_G_1$ ?v0!15) (or (not $x3475) $x6164)) (rewrite (= (or (not $x3475) $x6164) (or (not $x3475) $x5808 $x6106))) (or (not $x3475) $x5808 $x6106))))
-(let (($x3157 (>= ?x169 0)))
-(let ((?x4056 (+ ?x169 ?x1168)))
-(let (($x6181 (<= ?x4056 0)))
-(let (($x3907 (= v_b_v_G_1$ b_Source$)))
-(let ((?x3908 (?v1!7 v_b_v_G_1$)))
-(let ((?x3915 (pair$ ?x3908 v_b_v_G_1$)))
-(let ((?x3916 (b_G$ ?x3915)))
-(let ((?x3917 (* (- 1) ?x3916)))
-(let ((?x3909 (fun_app$a v_b_SP_G_1$ ?x3908)))
-(let ((?x3910 (* (- 1) ?x3909)))
-(let ((?x3918 (+ ?x254 ?x3910 ?x3917)))
-(let (($x3919 (= ?x3918 0)))
-(let (($x3913 (fun_app$ v_b_Visited_G_1$ ?x3908)))
-(let (($x3914 (not $x3913)))
-(let ((?x3911 (+ ?x254 ?x3910)))
-(let (($x3912 (<= ?x3911 0)))
-(let (($x3921 (or $x3912 $x3914 (not $x3919))))
-(let (($x4342 (>= ?x3911 0)))
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-(let (($x6866 (<= ?x5981 0)))
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-(let (($x6303 (<= (+ b_Infinity$ (* (- 1) ?x6529)) 0)))
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-(let (($x6685 (or $x3678 $x6288 $x6486)))
-(let (($x6462 (or (not (or $x6303 (<= (+ ?x6459 ?x1168 (* (- 1) ?x6529)) 0))) $x6486)))
-(let (($x6686 (or $x3678 $x6462)))
-(let (($x5681 (<= (+ ?x6459 ?x1168 (* (- 1) ?x6529)) 0)))
-(let ((@x3990 (rewrite (= (+ ?x6459 ?x1168 (* (- 1) ?x6529)) (+ ?x1168 ?x6459 (* (- 1) ?x6529))))))
-(let ((@x4138 (monotonicity @x3990 (= $x5681 (<= (+ ?x1168 ?x6459 (* (- 1) ?x6529)) 0)))))
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-(let ((@x6693 (monotonicity (monotonicity @x3932 (= (or $x6303 $x5681) $x3933)) (= (not (or $x6303 $x5681)) $x6288))))
-(let ((@x6509 (monotonicity (monotonicity @x6693 (= $x6462 (or $x6288 $x6486))) (= $x6686 (or $x3678 (or $x6288 $x6486))))))
-(let ((@x5868 (trans @x6509 (rewrite (= (or $x3678 (or $x6288 $x6486)) $x6685)) (= $x6686 $x6685))))
-(let ((@x6885 (unit-resolution (def-axiom (or $x3933 (not $x6303))) (hypothesis $x6288) (not $x6303))))
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-(let (($x4983 (or $x6303 $x5936 $x6554)))
-(let (($x3903 (or $x3670 $x6303 $x5936 $x6554)))
-(let (($x5258 (or $x6303 $x5681 (= (+ ?x254 ?x6529 ?x6364) 0))))
-(let (($x4854 (or $x3670 $x5258)))
-(let ((@x4987 (monotonicity (rewrite (= (+ ?x254 ?x6529 ?x6364) ?x5981)) (= (= (+ ?x254 ?x6529 ?x6364) 0) $x6554))))
-(let ((@x5496 (monotonicity (monotonicity @x3932 @x4987 (= $x5258 $x4983)) (= $x4854 (or $x3670 $x4983)))))
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-(let ((@x6871 ((_ th-lemma arith farkas 1 1 1 1 1) @x6833 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6554) $x6866)) @x6099 $x6866) (unit-resolution ((_ quant-inst (?v1!7 v_b_v_G_1$)) (or $x3556 $x5838)) @x4713 $x5838) @x6790 (unit-resolution (unit-resolution @x5318 @x3480 $x6164) @x6488 $x6106) false)))
-(let ((@x6225 (unit-resolution (lemma @x6871 (or $x3695 $x1842 $x6807)) (hypothesis $x3690) @x6833 $x6807)))
-(let ((@x3174 (def-axiom (or $x3921 (not $x3912)))))
-(let ((@x6645 (unit-resolution @x3174 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x4342 $x3912)) @x6225 $x3912) $x3921)))
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-(let ((@x4617 (mp ((_ quant-inst v_b_v_G_1$) (or $x3581 (or $x3907 $x1208 $x3922))) (rewrite (= (or $x3581 (or $x3907 $x1208 $x3922)) $x4599)) $x4599)))
-(let ((@x6649 (unit-resolution @x4617 @x4189 (unit-resolution (def-axiom (or $x3804 $x1209)) @x4802 $x1209) (or $x3907 $x3922))))
-(let ((@x5588 (symm (monotonicity (unit-resolution @x6649 @x6645 $x3907) (= ?x254 ?x169)) (= ?x169 ?x254))))
-(let ((@x5241 ((_ th-lemma arith farkas 1 1 1 1 1) @x6833 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x6554) $x6866)) @x6099 $x6866) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x169 ?x254)) $x6181)) @x5588 $x6181) (unit-resolution ((_ th-lemma arith triangle-eq) (or $x2947 $x3157)) @x4135 $x3157) (unit-resolution (unit-resolution @x5318 @x3480 $x6164) @x6488 $x6106) false)))
-(let ((@x8742 (unit-resolution (def-axiom (or $x3780 $x3774)) (unit-resolution @x9261 (lemma @x5791 $x1824) $x3783) $x3774)))
-(let (($x4076 (= ?x291 ?x169)))
-(let (($x4073 (<= (+ ?x169 ?x1168 (* (- 1) (b_G$ (pair$ v_b_v_G_1$ b_Source$)))) 0)))
-(let (($x4071 (<= (+ b_Infinity$ (* (- 1) (b_G$ (pair$ v_b_v_G_1$ b_Source$)))) 0)))
-(let (($x4074 (or $x4071 $x4073)))
-(let (($x3924 (>= ?x254 0)))
-(let (($x4636 (or $x3556 $x3924)))
-(let ((@x4637 ((_ quant-inst v_b_v_G_1$) $x4636)))
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-(let ((?x4062 (b_G$ ?x4061)))
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-(let (($x5333 (= ?x4062 0)))
-(let (($x5329 (<= ?x4062 0)))
-(let (($x4173 (<= ?x291 0)))
-(let ((?x4078 (* (- 1) ?x291)))
-(let ((?x4144 (+ ?x169 ?x4078)))
-(let (($x4145 (>= ?x4144 0)))
-(let (($x4905 (or $x3686 $x4145)))
-(let ((@x5229 ((_ quant-inst b_Source$) $x4905)))
-(let (($x3158 (<= ?x169 0)))
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-(let ((@x4827 (unit-resolution ((_ th-lemma arith assign-bounds -1 1) (or $x4173 (not $x3158) (not $x4145))) @x4838 (unit-resolution @x5229 @x4714 $x4145) $x4173)))
-(let ((?x4096 (+ ?x254 ?x4078 ?x4062)))
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-(let (($x4102 (or $x4071 $x4073 $x4099)))
-(let (($x4105 (or $x3670 $x4071 $x4073 $x4099)))
-(let (($x4095 (or $x4071 $x4073 (= (+ ?x254 ?x4062 ?x4078) 0))))
-(let (($x4106 (or $x3670 $x4095)))
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-(let ((@x4110 (monotonicity (monotonicity @x4101 (= $x4095 $x4102)) (= $x4106 (or $x3670 $x4102)))))
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-(let ((@x5939 ((_ th-lemma arith farkas -1 1 -1 1) (hypothesis $x3924) (hypothesis $x4173) (hypothesis (not $x5329)) (hypothesis $x4116) false)))
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-(let (($x5274 (= (or (not $x3475) (or $x3907 (not $x5329))) (or (not $x3475) $x3907 (not $x5329)))))
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-(let ((@x5099 (rewrite (= (or $x3045 (or (not $x3907) $x5333)) (or $x3045 (not $x3907) $x5333)))))
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-(let ((@x4868 (unit-resolution @x5081 @x3474 (unit-resolution @x5275 @x3480 (unit-resolution @x4867 @x4846 @x4827 $x5329) $x3907) $x5333)))
-(let ((@x4872 ((_ th-lemma arith farkas -1 1 1 1) @x4838 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x5333) $x5863)) @x4868 $x5863) (unit-resolution (def-axiom (or $x4074 (not $x4073))) @x5775 (not $x4073)) (unit-resolution @x4637 @x4713 $x3924) false)))
-(let (($x4077 (or $x4075 $x4076)))
-(let (($x5055 (or $x3678 $x4075 $x4076)))
-(let ((@x5303 (mp ((_ quant-inst b_Source$) (or $x3678 $x4077)) (rewrite (= (or $x3678 $x4077) $x5055)) $x5055)))
-(let ((@x8878 (unit-resolution (unit-resolution @x5303 @x4803 $x4077) (lemma @x4872 $x4074) $x4076)))
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-(let ((@x8755 (unit-resolution (def-axiom (or $x3768 $x3762)) (unit-resolution @x9287 @x8742 $x3771) $x3762)))
-(let ((@x8979 (unit-resolution (def-axiom (or $x3765 $x1843 $x3759)) @x8755 (unit-resolution (lemma @x5241 (or $x3695 $x1842)) @x9263 $x1842) $x3759)))
-(let ((@x9416 (unit-resolution (def-axiom (or $x3753 $x2760 $x3747)) (unit-resolution (def-axiom (or $x3756 $x3750)) @x8979 $x3750) $x3750)))
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-(let ((@x9454 (unit-resolution (def-axiom (or $x3741 $x2806 $x3735)) (unit-resolution (def-axiom (or $x3744 $x3738)) @x9452 $x3738) $x3738)))
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-(let ((@x9475 (unit-resolution (def-axiom (or $x3732 $x1910)) @x9455 $x1910)))
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-(let ((@x9241 (unit-resolution (lemma @x9478 (or $x9479 (not (<= (+ b_Infinity$ ?x4438) 0)))) @x9476 (not (<= (+ b_Infinity$ ?x4438) 0)))))
-(let (($x4660 (<= (+ b_Infinity$ ?x4438) 0)))
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-(let ((@x9599 (unit-resolution @x7305 @x4189 (unit-resolution (def-axiom (or $x3732 $x1905)) @x9455 $x1905) (or $x4660 $x4675))))
-(let ((@x9582 (unit-resolution @x9599 @x9241 $x4675)))
-(let ((?x4717 (v_b_SP_G_2$ ?x4661)))
-(let ((?x4720 (* (- 1) ?x4717)))
-(let ((?x4721 (+ ?x4662 ?x4720)))
-(let (($x4728 (>= ?x4721 0)))
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-(let ((@x8898 (unit-resolution (lemma @x9586 $x9588) @x9476 (not (<= (+ ?x1906 ?x4720) 0)))))
-(let ((?x7341 (+ ?x1906 ?x4670 ?x4720)))
-(let (($x7121 (= ?x7341 0)))
-(let (($x5719 (<= ?x7341 0)))
-(let (($x4844 (<= (+ b_Infinity$ ?x4670) 0)))
-(let (($x8387 (not $x4844)))
-(let (($x7025 (>= ?x4671 0)))
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-(let (($x4825 (>= ?x4662 0)))
-(let ((@x8897 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1 -1) (or $x8387 (not $x4825) (not $x7025) $x1909 $x9479)) @x9475 (or $x8387 (not $x4825) (not $x7025) $x9479))))
-(let ((@x8874 (unit-resolution @x8897 (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3556 $x4825)) @x4713 $x4825) @x9476 @x8158 $x8387)))
-(let (($x4709 (fun_app$ v_b_Visited_G_2$ ?x4661)))
-(let ((@x6057 (monotonicity (symm (hypothesis $x261) (= ?x260 v_b_Visited_G_2$)) (= (fun_app$ ?x260 ?x4661) $x4709))))
-(let ((@x6061 (monotonicity (symm @x6057 (= $x4709 (fun_app$ ?x260 ?x4661))) (= (not $x4709) (not (fun_app$ ?x260 ?x4661))))))
-(let (($x6003 (fun_app$ ?x260 ?x4661)))
-(let (($x6010 (= ?x4661 v_b_v_G_1$)))
-(let (($x6013 (or $x6010 $x4666)))
-(let (($x6016 (= $x6003 $x6013)))
-(let (($x6019 (or $x4134 $x6016)))
-(let ((@x6018 (monotonicity (rewrite (= (ite $x6010 true $x4666) $x6013)) (= (= $x6003 (ite $x6010 true $x4666)) $x6016))))
-(let ((@x6023 (monotonicity @x6018 (= (or $x4134 (= $x6003 (ite $x6010 true $x4666))) $x6019))))
-(let ((@x6026 (trans @x6023 (rewrite (= $x6019 $x6019)) (= (or $x4134 (= $x6003 (ite $x6010 true $x4666))) $x6019))))
-(let ((@x6027 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true (?v1!7 ?v0!20)) (or $x4134 (= $x6003 (ite $x6010 true $x4666)))) @x6026 $x6019)))
-(let ((@x6050 (unit-resolution (def-axiom (or (not $x6016) $x6003 (not $x6013))) (unit-resolution (def-axiom (or $x6013 $x4667)) (hypothesis $x4666) $x6013) (or (not $x6016) $x6003))))
-(let ((@x6063 (unit-resolution (unit-resolution @x6050 (unit-resolution @x6027 @x3468 $x6016) $x6003) (mp (hypothesis (not $x4709)) @x6061 (not $x6003)) false)))
-(let ((@x8957 (unit-resolution (lemma @x6063 (or $x4709 $x2930 $x4667)) (unit-resolution (def-axiom (or $x3804 $x261)) @x4802 $x261) (or $x4709 $x4667))))
-(let ((@x8892 (unit-resolution @x8957 (unit-resolution (def-axiom (or $x4674 $x4666)) @x9582 $x4666) $x4709)))
-(let (($x4710 (not $x4709)))
-(let (($x6183 (or $x3720 $x4710 $x4844 $x5719)))
-(let (($x4848 (>= (+ ?x4669 ?x4717 ?x1907) 0)))
-(let (($x4849 (or $x4710 $x4844 $x4848)))
-(let (($x7891 (or $x3720 $x4849)))
-(let ((@x7340 (monotonicity (rewrite (= (+ ?x4669 ?x4717 ?x1907) (+ ?x1907 ?x4669 ?x4717))) (= $x4848 (>= (+ ?x1907 ?x4669 ?x4717) 0)))))
-(let ((@x7415 (trans @x7340 (rewrite (= (>= (+ ?x1907 ?x4669 ?x4717) 0) $x5719)) (= $x4848 $x5719))))
-(let ((@x7922 (monotonicity (monotonicity @x7415 (= $x4849 (or $x4710 $x4844 $x5719))) (= $x7891 (or $x3720 (or $x4710 $x4844 $x5719))))))
-(let ((@x7119 (trans @x7922 (rewrite (= (or $x3720 (or $x4710 $x4844 $x5719)) $x6183)) (= $x7891 $x6183))))
-(let ((@x8954 (unit-resolution (mp ((_ quant-inst ?v0!20 (?v1!7 ?v0!20)) $x7891) @x7119 $x6183) (unit-resolution (def-axiom (or $x3732 $x3715)) @x9455 $x3715) @x8892 (or $x4844 $x5719))))
-(let (($x8133 (>= ?x7341 0)))
-(let ((@x9055 (unit-resolution ((_ th-lemma arith assign-bounds -1 -1 -1) (or $x8133 (not $x7025) $x9479 (not $x4728))) (unit-resolution ((_ quant-inst (?v1!7 ?v0!20)) (or $x3686 $x4728)) @x4714 $x4728) @x8158 @x9476 $x8133)))
-(let ((@x9049 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x7121 (not $x5719) (not $x8133))) @x9055 (unit-resolution @x8954 @x8874 $x5719) $x7121)))
-(let (($x7918 (not $x7121)))
-(let ((?x4888 (+ ?x1906 ?x4720)))
-(let (($x7874 (<= ?x4888 0)))
-(let (($x8072 (or $x3729 $x7874 $x4710 $x7918)))
-(let (($x4877 (>= (+ ?x4717 ?x1907) 0)))
-(let (($x4881 (or $x4877 $x4710 (not (= (+ ?x4717 ?x1907 ?x4669) 0)))))
-(let (($x8040 (or $x3729 $x4881)))
-(let ((@x6258 (monotonicity (rewrite (= (+ ?x4717 ?x1907 ?x4669) (+ ?x1907 ?x4669 ?x4717))) (= (= (+ ?x4717 ?x1907 ?x4669) 0) (= (+ ?x1907 ?x4669 ?x4717) 0)))))
-(let ((@x7178 (trans @x6258 (rewrite (= (= (+ ?x1907 ?x4669 ?x4717) 0) $x7121)) (= (= (+ ?x4717 ?x1907 ?x4669) 0) $x7121))))
-(let ((@x7871 (monotonicity (rewrite (= (+ ?x4717 ?x1907) (+ ?x1907 ?x4717))) (= $x4877 (>= (+ ?x1907 ?x4717) 0)))))
-(let ((@x7892 (trans @x7871 (rewrite (= (>= (+ ?x1907 ?x4717) 0) $x7874)) (= $x4877 $x7874))))
-(let ((@x8041 (monotonicity @x7892 (monotonicity @x7178 (= (not (= (+ ?x4717 ?x1907 ?x4669) 0)) $x7918)) (= $x4881 (or $x7874 $x4710 $x7918)))))
-(let ((@x8107 (trans (monotonicity @x8041 (= $x8040 (or $x3729 (or $x7874 $x4710 $x7918)))) (rewrite (= (or $x3729 (or $x7874 $x4710 $x7918)) $x8072)) (= $x8040 $x8072))))
-(let ((@x9051 (unit-resolution (mp ((_ quant-inst (?v1!7 ?v0!20)) $x8040) @x8107 $x8072) (unit-resolution (def-axiom (or $x3732 $x3724)) @x9455 $x3724) @x8892 (or $x7874 $x7918))))
-(let ((@x10024 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not (= ?x1906 ?x4413)) $x6002)) (lemma (unit-resolution @x9051 @x9049 @x8898 false) $x9479) (not (= ?x1906 ?x4413)))))
-(let (($x4420 (= ?x1906 ?x4413)))
-(let (($x4423 (or $x4299 $x4420)))
-(let (($x8830 (or $x3695 $x4299 $x4420)))
-(let ((@x8691 (mp ((_ quant-inst ?v0!20) (or $x3695 $x4423)) (rewrite (= (or $x3695 $x4423) $x8830)) $x8830)))
-(let ((@x10120 (mp (unit-resolution (unit-resolution @x8691 @x9263 $x4423) @x10024 $x4299) @x10119 $x9037)))
-(let (($x4629 (fun_app$ v_b_Visited_G_1$ ?v0!20)))
-(let (($x5238 (= ?v0!20 v_b_v_G_1$)))
-(let (($x10274 (or $x5238 $x4629)))
-(let (($x10073 (= $x5237 $x10274)))
-(let (($x10506 (or $x4134 $x10073)))
-(let ((@x10500 (monotonicity (rewrite (= (ite $x5238 true $x4629) $x10274)) (= (= $x5237 (ite $x5238 true $x4629)) $x10073))))
-(let ((@x10183 (monotonicity @x10500 (= (or $x4134 (= $x5237 (ite $x5238 true $x4629))) $x10506))))
-(let ((@x10372 (trans @x10183 (rewrite (= $x10506 $x10506)) (= (or $x4134 (= $x5237 (ite $x5238 true $x4629))) $x10506))))
-(let ((@x10020 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true ?v0!20) (or $x4134 (= $x5237 (ite $x5238 true $x4629)))) @x10372 $x10506)))
-(let ((?x4454 (pair$ v_b_v_G_1$ ?v0!20)))
-(let ((?x4455 (b_G$ ?x4454)))
-(let ((?x4507 (+ ?x254 ?x1907 ?x4455)))
-(let (($x4527 (<= ?x4507 0)))
-(let (($x8001 (= ?x4507 0)))
-(let ((?x9161 (+ ?x254 ?x4438 ?x4455)))
-(let (($x9165 (>= ?x9161 0)))
-(let ((?x4456 (* (- 1) ?x4455)))
-(let ((?x4457 (+ b_Infinity$ ?x4456)))
-(let (($x4458 (<= ?x4457 0)))
-(let (($x8810 (or $x4458 $x9165)))
-(let (($x8814 (not $x8810)))
-(let (($x8919 (or $x8814 $x4420)))
-(let (($x8679 (or $x3678 $x8814 $x4420)))
-(let (($x4463 (or (not (or $x4458 (<= (+ ?x4413 ?x1168 ?x4456) 0))) $x4420)))
-(let (($x9386 (or $x3678 $x4463)))
-(let ((@x9164 (monotonicity (rewrite (= (+ ?x4413 ?x1168 ?x4456) (+ ?x1168 ?x4413 ?x4456))) (= (<= (+ ?x4413 ?x1168 ?x4456) 0) (<= (+ ?x1168 ?x4413 ?x4456) 0)))))
-(let ((@x8891 (trans @x9164 (rewrite (= (<= (+ ?x1168 ?x4413 ?x4456) 0) $x9165)) (= (<= (+ ?x4413 ?x1168 ?x4456) 0) $x9165))))
-(let ((@x8813 (monotonicity @x8891 (= (or $x4458 (<= (+ ?x4413 ?x1168 ?x4456) 0)) $x8810))))
-(let ((@x8815 (monotonicity @x8813 (= (not (or $x4458 (<= (+ ?x4413 ?x1168 ?x4456) 0))) $x8814))))
-(let ((@x9295 (monotonicity (monotonicity @x8815 (= $x4463 $x8919)) (= $x9386 (or $x3678 $x8919)))))
-(let ((@x9441 (mp ((_ quant-inst ?v0!20) $x9386) (trans @x9295 (rewrite (= (or $x3678 $x8919) $x8679)) (= $x9386 $x8679)) $x8679)))
-(let ((@x9984 (unit-resolution (def-axiom (or $x8810 (not $x4458))) (hypothesis $x8814) (not $x4458))))
-(let ((@x9985 (unit-resolution (def-axiom (or $x8810 (not $x9165))) (hypothesis $x8814) (not $x9165))))
-(let (($x8926 (or $x4458 $x9165 $x8001)))
-(let (($x8928 (or $x3670 $x4458 $x9165 $x8001)))
-(let (($x4460 (<= (+ ?x4413 ?x1168 ?x4456) 0)))
-(let (($x4506 (or $x4458 $x4460 (= (+ ?x254 ?x4455 ?x1907) 0))))
-(let (($x8929 (or $x3670 $x4506)))
-(let ((@x8925 (monotonicity (rewrite (= (+ ?x254 ?x4455 ?x1907) ?x4507)) (= (= (+ ?x254 ?x4455 ?x1907) 0) $x8001))))
-(let ((@x8953 (monotonicity (monotonicity @x8891 @x8925 (= $x4506 $x8926)) (= $x8929 (or $x3670 $x8926)))))
-(let ((@x8682 (mp ((_ quant-inst ?v0!20) $x8929) (trans @x8953 (rewrite (= (or $x3670 $x8926) $x8928)) (= $x8929 $x8928)) $x8928)))
-(let ((@x9987 (unit-resolution (unit-resolution @x8682 @x4789 $x8926) @x9985 @x9984 (hypothesis (not $x8001)) false)))
-(let ((@x10276 (unit-resolution (lemma @x9987 (or $x8810 $x8001)) (unit-resolution (unit-resolution @x9441 @x4803 $x8919) @x10024 $x8814) $x8001)))
-(let ((?x4401 (+ ?x1906 ?x3064)))
-(let (($x6992 (<= ?x4401 0)))
-(let ((?x4566 (+ ?x1906 ?x3064 ?x4456)))
-(let (($x6987 (= ?x4566 0)))
-(let (($x4590 (>= ?x4566 0)))
-(let ((@x9966 (unit-resolution ((_ th-lemma arith assign-bounds 1 -1) (or (not $x4527) $x4590 (not $x3906))) @x6160 (or (not $x4527) $x4590))))
-(let (($x4589 (<= ?x4566 0)))
-(let (($x4181 (>= ?x3063 0)))
-(let (($x6279 (or $x3703 $x4181)))
-(let ((@x6374 ((_ quant-inst v_b_v_G_1$) $x6279)))
-(let ((@x9257 (unit-resolution @x6374 (unit-resolution (def-axiom (or $x3756 $x3698)) @x8979 $x3698) $x4181)))
-(let (($x4146 (fun_app$ v_b_Visited_G_2$ v_b_v_G_1$)))
-(let (($x3097 (fun_app$ ?x260 v_b_v_G_1$)))
-(let (($x3456 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(! (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v1) ?v2) :pattern ( (fun_upd$ ?v0 ?v1 ?v2) ) :qid k!33))
-))
-(let (($x55 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(! (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v1) ?v2) :qid k!33))
-))
-(let (($x52 (= (fun_app$ (fun_upd$ ?2 ?1 ?0) ?1) ?0)))
-(let (($x50 (forall ((?v0 B_Vertex_bool_fun$) (?v1 B_Vertex$) (?v2 Bool) )(! (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v1) ?v2) :qid k!33))
-))
-(let ((@x54 (rewrite (= (= (fun_app$ (fun_upd$ ?2 ?1 ?0) ?1) ?0) $x52))))
-(let ((@x1427 (mp~ (mp (asserted $x50) (quant-intro @x54 (= $x50 $x55)) $x55) (nnf-pos (refl (~ $x52 $x52)) (~ $x55 $x55)) $x55)))
-(let ((@x3461 (mp @x1427 (quant-intro (refl (= $x52 $x52)) (= $x55 $x3456)) $x3456)))
-(let (($x4383 (or (not $x3456) $x3097)))
-(let ((@x4480 (monotonicity (rewrite (= (= $x3097 true) $x3097)) (= (or (not $x3456) (= $x3097 true)) $x4383))))
-(let ((@x4483 (trans @x4480 (rewrite (= $x4383 $x4383)) (= (or (not $x3456) (= $x3097 true)) $x4383))))
-(let ((@x4484 (mp ((_ quant-inst v_b_Visited_G_1$ v_b_v_G_1$ true) (or (not $x3456) (= $x3097 true))) @x4483 $x4383)))
-(let ((@x9972 (mp (unit-resolution @x4484 @x3461 $x3097) (monotonicity @x6739 (= $x3097 $x4146)) $x4146)))
-(let ((@x5439 (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x4590 $x4589)) (hypothesis (not $x4589)) $x4590)))
-(let (($x4147 (not $x4146)))
-(let (($x5371 (or $x3720 $x4147 $x4458 $x4589)))
-(let ((?x5354 (+ ?x4455 ?x3063 ?x1907)))
-(let (($x5355 (>= ?x5354 0)))
-(let (($x5358 (or $x4147 $x4458 $x5355)))
-(let (($x5372 (or $x3720 $x5358)))
-(let ((@x5363 (monotonicity (rewrite (= ?x5354 (+ ?x1907 ?x3063 ?x4455))) (= $x5355 (>= (+ ?x1907 ?x3063 ?x4455) 0)))))
-(let ((@x5367 (trans @x5363 (rewrite (= (>= (+ ?x1907 ?x3063 ?x4455) 0) $x4589)) (= $x5355 $x4589))))
-(let ((@x5376 (monotonicity (monotonicity @x5367 (= $x5358 (or $x4147 $x4458 $x4589))) (= $x5372 (or $x3720 (or $x4147 $x4458 $x4589))))))
-(let ((@x5380 (trans @x5376 (rewrite (= (or $x3720 (or $x4147 $x4458 $x4589)) $x5371)) (= $x5372 $x5371))))
-(let ((@x5381 (mp ((_ quant-inst ?v0!20 v_b_v_G_1$) $x5372) @x5380 $x5371)))
-(let ((@x5443 (unit-resolution @x5381 (hypothesis $x3715) (hypothesis $x4146) (hypothesis (not $x4589)) $x4458)))
-(let ((@x5447 (lemma ((_ th-lemma arith farkas 1 1 1 1) @x5443 (hypothesis $x4181) @x5439 (hypothesis $x1910) false) (or $x4589 (not $x4181) $x1909 $x3720 $x4147))))
-(let ((@x9976 (unit-resolution (unit-resolution @x5447 @x9972 (or $x4589 (not $x4181) $x1909 $x3720)) @x9257 (or $x4589 $x1909 $x3720))))
-(let ((@x9977 (unit-resolution @x9976 (unit-resolution (def-axiom (or $x3732 $x3715)) @x9455 $x3715) @x9475 $x4589)))
-(let ((@x9991 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x6987 (not $x4589) (not $x4590))) @x9977 (or $x6987 (not $x4590)))))
-(let ((@x9992 (unit-resolution @x9991 (unit-resolution @x9966 (hypothesis $x4527) $x4590) $x6987)))
-(let (($x7023 (not $x6987)))
-(let (($x6921 (or $x3729 $x6992 $x4147 $x7023)))
-(let (($x4536 (>= (+ ?x3063 ?x1907) 0)))
-(let (($x4548 (or $x4536 $x4147 (not (= (+ ?x3063 ?x1907 ?x4455) 0)))))
-(let (($x8524 (or $x3729 $x4548)))
-(let ((@x7245 (monotonicity (rewrite (= (+ ?x3063 ?x1907 ?x4455) (+ ?x1907 ?x3063 ?x4455))) (= (= (+ ?x3063 ?x1907 ?x4455) 0) (= (+ ?x1907 ?x3063 ?x4455) 0)))))
-(let ((@x7022 (trans @x7245 (rewrite (= (= (+ ?x1907 ?x3063 ?x4455) 0) $x6987)) (= (= (+ ?x3063 ?x1907 ?x4455) 0) $x6987))))
-(let ((@x7049 (monotonicity (rewrite (= (+ ?x3063 ?x1907) (+ ?x1907 ?x3063))) (= $x4536 (>= (+ ?x1907 ?x3063) 0)))))
-(let ((@x8373 (trans @x7049 (rewrite (= (>= (+ ?x1907 ?x3063) 0) $x6992)) (= $x4536 $x6992))))
-(let ((@x7936 (monotonicity @x8373 (monotonicity @x7022 (= (not (= (+ ?x3063 ?x1907 ?x4455) 0)) $x7023)) (= $x4548 (or $x6992 $x4147 $x7023)))))
-(let ((@x8581 (trans (monotonicity @x7936 (= $x8524 (or $x3729 (or $x6992 $x4147 $x7023)))) (rewrite (= (or $x3729 (or $x6992 $x4147 $x7023)) $x6921)) (= $x8524 $x6921))))
-(let ((@x8053 (mp ((_ quant-inst v_b_v_G_1$) $x8524) @x8581 $x6921)))
-(let ((@x9995 (unit-resolution @x8053 (unit-resolution (def-axiom (or $x3732 $x3724)) @x9455 $x3724) @x9972 (or $x6992 $x7023))))
-(let (($x5406 (<= ?x4455 0)))
-(let (($x5407 (not $x5406)))
-(let (($x5405 (= v_b_v_G_1$ ?v0!20)))
-(let (($x5409 (not $x5405)))
-(let ((@x10003 (monotonicity (symm (commutativity (= $x5405 $x5238)) (= $x5238 $x5405)) (= (not $x5238) $x5409))))
-(let (($x5408 (or $x5405 $x5407)))
-(let (($x3099 (not $x3475)))
-(let (($x9955 (or $x3099 $x5405 $x5407)))
-(let ((@x9962 (mp ((_ quant-inst v_b_v_G_1$ ?v0!20) (or $x3099 $x5408)) (rewrite (= (or $x3099 $x5408) $x9955)) $x9955)))
-(let ((@x10006 (unit-resolution (unit-resolution @x9962 @x3480 $x5408) (mp (hypothesis (not $x5238)) @x10003 $x5409) $x5407)))
-(let ((@x10007 ((_ th-lemma arith farkas -1 -1 1 1) @x6160 @x10006 (hypothesis $x4527) (unit-resolution @x9995 @x9992 $x6992) false)))
-(let ((@x10279 (unit-resolution (lemma @x10007 (or (not $x4527) $x5238)) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x8001) $x4527)) @x10276 $x4527) $x5238)))
-(let ((@x10164 (unit-resolution (def-axiom (or (not $x10073) $x5237 (not $x10274))) (unit-resolution (def-axiom (or $x10274 (not $x5238))) @x10279 $x10274) (or (not $x10073) $x5237))))
-(unit-resolution (unit-resolution @x10164 (unit-resolution @x10020 @x3468 $x10073) $x5237) @x10120 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
-

--- a/src/HOL/SMT_Examples/Boogie_Max.certs	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT_Examples/Boogie_Max.certs	Mon Jun 19 22:28:09 2023 +0200
@@ -1,4 +1,4 @@
-c35b5996e10ca92422b72151cf73d5012ace7376 778 0
+ae712ba60be9be1bab4bc3570ac5c4aec9bad512 778 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!3 () Int)

--- a/src/HOL/SMT_Examples/SMT_Examples.certs	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples.certs	Mon Jun 19 22:28:09 2023 +0200
@@ -1,11 +1,11 @@
-a734af99f317b55130e169b140843e673d0bbf01 6 0
+f4ff5c44833ca360a0e6110670545870e993732e 6 0
 unsat
 ((set-logic AUFLIA)
 (proof
 (let ((@x30 (rewrite (= (not true) false))))
 (mp (asserted (not true)) @x30 false))))
 
-eb38970c345df6ae8f92f5d2a32e1df00c1810c4 7 0
+44c9e70361e406cdaa5515db0484a14de1f3823e 7 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -13,7 +13,7 @@
 (let ((@x40 (trans @x36 (rewrite (= (not true) false)) (= (not (or p$ (not p$))) false))))
 (mp (asserted (not (or p$ (not p$)))) @x40 false)))))
 
-90627d309f442a71678bb840dcccd56e1b045c47 9 0
[phone]d4dfc4babb357dafe234a81ef017f2c 9 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -23,7 +23,7 @@
 (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= (and p$ true) p$)) false))))
 (mp (asserted (not (= (and p$ true) p$))) @x47 false)))))))
 
-2e6261dc2fb735b96a2f84163499f5c9d8e8eedd 13 0
+0a1454d805d51972201b1f0614ae4d2b1ee0c238 13 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -37,7 +37,7 @@
 (let (($x29 (or p$ q$)))
 (mp (and-elim (not-or-elim @x44 (and $x29 (not p$))) $x29) @x58 false)))))))))))
 
-fe66a69b0868f46c9e6ca7e18abaa9fea0c65469 11 0
[phone]b57502835b641cecdefffafb46f85d80 11 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -49,7 +49,7 @@
 (let ((@x45 (trans (monotonicity (rewrite (= $x34 true)) (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false))))
 (mp (asserted $x35) @x45 false)))))))))
 
-b277fe65c25f9907a259feaedc5175c049c9c801 23 0
+20bc477eba70622207284dac695d9d5d493c254c 23 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -73,7 +73,7 @@
 (let ((@x58 (monotonicity (trans @x49 (rewrite (= (=> $x31 $x44) $x51)) (= $x37 $x51)) (= $x38 $x56))))
 (mp (asserted $x38) (trans @x58 @x67 (= $x38 false)) false)))))))))))))))))))))
 
-dff507d4f869feeb53f9c0e7c162387d22d810bc 24 0
+31d9c9d3ff37ebd83ab46c7b87647ef17b2c57d5 24 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -98,7 +98,7 @@
 (let ((@x82 (trans (monotonicity @x75 (= $x37 (not true))) (rewrite (= (not true) false)) (= $x37 false))))
 (mp (asserted $x37) @x82 false))))))))))))))))))))))
 
-fe2fe85fa0d71650d19542c615cfac479267b69e 39 0
+330b2c9cc52cf5f35a134a2209b0d4127652f7c0 39 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -138,7 +138,7 @@
 (let ((@x40 (mp (asserted (or a$ (or b$ (or c$ d$)))) (rewrite (= (or a$ (or b$ (or c$ d$))) $x37)) $x37)))
 (mp @x40 @x202 false)))))))))))))))))))))))))))))))))))))
 
-8dc4f44af8f07f7b856e596119d1bf43f2c6acd5 27 0
+ad87d7e797bdb9354f6592e3ce911c29af823c87 27 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -166,7 +166,7 @@
 (let ((@x61 ((_ quant-inst a$ b$) $x149)))
 (unit-resolution @x61 @x485 @x57 false)))))))))))))))))))
 
-fbb0a55c0a093161da67da5e523c4888aceb6463 637 0
[phone]c818c9d90b517b53e98cbd0b98a4 637 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -804,7 +804,7 @@
 (let ((@x1722 (unit-resolution @x1662 (unit-resolution @x472 @x1718 $x467) (unit-resolution @x565 @x1715 $x482) $x355)))
 (unit-resolution @x1647 @x1722 (unit-resolution @x472 @x1718 $x467) (unit-resolution @x565 @x1715 $x482) (unit-resolution @x480 @x1718 $x397) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-66bb17e2a985817e38bb524b89cc9e978af0b717 38 0
+53d98ae38981e94d40d6d86fc0074ee3a2e0fb7e 38 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!0 () Int)
@@ -843,7 +843,7 @@
 (let ((@x79 (and-elim (mp @x72 @x77 (and $x48 $x63)) $x48)))
 (unit-resolution @x79 @x81 false))))))))))))))))))))
 
-99dcee13708acddf74f37ffb7cd9ae6e8a0075ec 53 0
+e22c0f9d8d283fe65facdddeef75c43b520c8702 53 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!0 () A$)
@@ -897,7 +897,7 @@
 (let ((@x161 ((_ quant-inst c$) $x160)))
 (unit-resolution @x161 @x485 (unit-resolution @x525 @x485 $x517) false)))))))))))))))))))))))))))))))))))))))
 
-00c35e7818bb5885a6737b5ca032b22e4d0651de 53 0
+3b83f9f26b0c0bdbb99d25d8249a78edb7dbd8f3 53 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!3 () A$)
@@ -951,15 +951,7 @@
 (let ((@x211 ((_ quant-inst c$) $x549)))
 (unit-resolution @x211 @x199 (unit-resolution @x592 @x199 $x584) false)))))))))))))))))))))))))))))))))))))))
 
-c19ad9760d0e770b48c0b0ab02c85b7759923c37 7 0
-unsat
-((set-logic AUFLIA)
-(proof
-(let ((@x35 (monotonicity (rewrite (= (= 3 3) true)) (= (not (= 3 3)) (not true)))))
-(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3 3)) false))))
-(mp (asserted (not (= 3 3))) @x39 false)))))
-
-083a9501b1863f5626ecc25e47e5b4723fa35e4c 26 0
+c5dafcf16dd97b4d38e39a04bbc990e4ad5fdbd3 26 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -986,7 +978,15 @@
 (let ((@x70 ((_ quant-inst x$) $x156)))
 (unit-resolution @x70 @x491 @x49 false)))))))))))))))))))
 
-ca11536c17f1a809ef914163583a39e63cac09fe 7 0
+c810fdd7e33dce88857a4a5d351d4d48aeec706d 7 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (= 3 3) true)) (= (not (= 3 3)) (not true)))))
+(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3 3)) false))))
+(mp (asserted (not (= 3 3))) @x39 false)))))
+
+4405deb1e8af2d0b383b4c76fef214640ee54b60 7 0
 unsat
 ((set-logic AUFLIRA)
 (proof
@@ -994,7 +994,7 @@
 (let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= 3.0 3.0)) false))))
 (mp (asserted (not (= 3.0 3.0))) @x39 false)))))
 
-2c3a6e6c7a46e7827f5375992c43691797675fb4 9 0
+9db6968bb918051eba4a8f252eb4d7b31abc0008 9 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1004,7 +1004,7 @@
 (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (+ 3 1) 4)) false))))
 (mp (asserted (not (= (+ 3 1) 4))) @x48 false)))))))
 
-86d19ef9c3bc052a9b275d334060669ee12e3d9f 16 0
+4236229b55c8c35ee3fdabff17499992a72bc2e9 16 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1021,7 +1021,7 @@
 (let ((@x63 (trans (monotonicity @x56 (= $x35 (not true))) (rewrite (= (not true) false)) (= $x35 false))))
 (mp (asserted $x35) @x63 false))))))))))))))
 
-90702d41b7fbf1b5314911474ac4ef6b0a538702 11 0
+edfffa3c123ab0c63cd525084a50aa3c5ed5a484 11 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1033,20 +1033,7 @@
 (let ((@x59 (trans @x55 (rewrite (= (not true) false)) (= (not (< 5 (ite (<= 3 8) 8 3))) false))))
 (mp (asserted (not (< 5 (ite (<= 3 8) 8 3)))) @x59 false)))))))))
 
-64a2205da8c28e8b966affffd8a102cee58f8182 12 0
-unsat
-((set-logic AUFLIA)
-(proof
-(let ((?x31 (p$ true)))
-(let (($x29 (< 2 3)))
-(let ((?x30 (p$ $x29)))
-(let (($x32 (= ?x30 ?x31)))
-(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
-(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
-(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
-(mp (asserted (not $x32)) @x53 false))))))))))
-
-55237afc0063a0033b90584d4ec259d5a3fd7fb2 88 0
+f9514ad0d68d1d07ca6390dfeefcb474eb113622 88 0
 unsat
 ((set-logic AUFLIRA)
 (proof
@@ -1135,7 +1122,37 @@
 (let ((@x234 (unit-resolution @x136 (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) $x133)))
 ((_ th-lemma arith farkas -2 1 -1 -1 1) (unit-resolution @x138 (lemma @x231 (not $x134)) $x83) @x221 @x126 @x226 (unit-resolution @x159 @x234 $x149) false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-75006e522c60f9ebc5a1fb2e97d7836a131ae07a 18 0
+dfe0238fb899e04c38457f444509fee29d6fc513 12 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x31 (p$ true)))
+(let (($x29 (< 2 3)))
+(let ((?x30 (p$ $x29)))
+(let (($x32 (= ?x30 ?x31)))
+(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
+(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
+(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
+(mp (asserted (not $x32)) @x53 false))))))))))
+
+46bed4652ccbc7e1a58c0efb03590e49ee15643a 16 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x33 (< x$ 1)))
+(let ((?x37 (+ 3 x$)))
+(let (($x40 (<= 4 ?x37)))
+(let (($x43 (or $x40 $x33)))
+(let (($x46 (not $x43)))
+(let ((@x57 (monotonicity (rewrite (= $x40 (>= x$ 1))) (rewrite (= $x33 (not (>= x$ 1)))) (= $x43 (or (>= x$ 1) (not (>= x$ 1)))))))
+(let ((@x61 (trans @x57 (rewrite (= (or (>= x$ 1) (not (>= x$ 1))) true)) (= $x43 true))))
+(let ((@x68 (trans (monotonicity @x61 (= $x46 (not true))) (rewrite (= (not true) false)) (= $x46 false))))
+(let ((@x42 (monotonicity (rewrite (= (+ x$ 3) ?x37)) (= (<= 4 (+ x$ 3)) $x40))))
+(let ((@x48 (monotonicity (monotonicity @x42 (= (or (<= 4 (+ x$ 3)) $x33) $x43)) (= (not (or (<= 4 (+ x$ 3)) $x33)) $x46))))
+(let ((@x70 (trans @x48 @x68 (= (not (or (<= 4 (+ x$ 3)) $x33)) false))))
+(mp (asserted (not (or (<= 4 (+ x$ 3)) $x33))) @x70 false))))))))))))))
+
+ef89c4f1b53c97f5cf2e25105c9bb8f92779adb7 18 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1154,24 +1171,7 @@
 (let ((@x83 (mp (asserted $x58) (trans (monotonicity @x66 (= $x58 $x67)) @x80 (= $x58 $x70)) $x70)))
 (mp @x83 @x90 false))))))))))))))))
 
-6e50a07d4733dc226c34529a521dbca5a402a4bc 16 0
-unsat
-((set-logic AUFLIA)
-(proof
-(let (($x33 (< x$ 1)))
-(let ((?x37 (+ 3 x$)))
-(let (($x40 (<= 4 ?x37)))
-(let (($x43 (or $x40 $x33)))
-(let (($x46 (not $x43)))
-(let ((@x57 (monotonicity (rewrite (= $x40 (>= x$ 1))) (rewrite (= $x33 (not (>= x$ 1)))) (= $x43 (or (>= x$ 1) (not (>= x$ 1)))))))
-(let ((@x61 (trans @x57 (rewrite (= (or (>= x$ 1) (not (>= x$ 1))) true)) (= $x43 true))))
-(let ((@x68 (trans (monotonicity @x61 (= $x46 (not true))) (rewrite (= (not true) false)) (= $x46 false))))
-(let ((@x42 (monotonicity (rewrite (= (+ x$ 3) ?x37)) (= (<= 4 (+ x$ 3)) $x40))))
-(let ((@x48 (monotonicity (monotonicity @x42 (= (or (<= 4 (+ x$ 3)) $x33) $x43)) (= (not (or (<= 4 (+ x$ 3)) $x33)) $x46))))
-(let ((@x70 (trans @x48 @x68 (= (not (or (<= 4 (+ x$ 3)) $x33)) false))))
-(mp (asserted (not (or (<= 4 (+ x$ 3)) $x33))) @x70 false))))))))))))))
-
-d6bf5820bec5d7ead5e685100a8340a2aff662a5 11 0
+77b18cda19c5fffd05747f5d9240aebf138e344d 11 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1183,7 +1183,7 @@
 (let ((@x57 (trans @x53 (rewrite (= (not true) false)) (= (not (not (= (+ 2 2) 5))) false))))
 (mp (asserted (not (not (= (+ 2 2) 5)))) @x57 false)))))))))
 
-fed37fb0fa432306b32161f6e523d7ad41178ad7 19 0
+42e94ca5e1eca47637b565820dbeb8f0c3f0cfbe 19 0
 unsat
 ((set-logic AUFLIRA)
 (proof
@@ -1203,7 +1203,7 @@
 (let ((@x67 (mp (asserted (not (< a$ 0.0))) @x66 $x58)))
 ((_ th-lemma arith farkas 7 3/2 1) @x67 @x52 @x40 false)))))))))))))))))
 
-a02473f328cfd27bbc383138b9013877d7082823 22 0
+0be06fbd57421bc1e05bb76b65b7d775f798777d 22 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1226,7 +1226,7 @@
 (let ((@x78 (trans (monotonicity @x71 (= $x40 (not true))) (rewrite (= (not true) false)) (= $x40 false))))
 (mp (asserted $x40) @x78 false))))))))))))))))))))
 
-a84aad2a73200dc9fcbd27c3e18e7303dda77b8a 159 0
+d419775b36e6eb4a3ae9788e677f2c6bd6596508 159 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -1386,28 +1386,7 @@
 (let ((@x433 (mp (not-or-elim @x205 (not $x57)) @x432 $x422)))
 (unit-resolution @x433 @x488 (mp @x478 @x480 $x44) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-f4dbaa29f0930512af8d8cd1b59c69b2a627ac2b 20 0
-unsat
-((set-logic AUFLIRA)
-(proof
-(let ((?x30 (* 2.0 x$)))
-(let ((?x32 (+ ?x30 1.0)))
-(let ((?x28 (+ x$ x$)))
-(let (($x33 (< ?x28 ?x32)))
-(let (($x34 (or false $x33)))
-(let (($x35 (or $x33 $x34)))
-(let (($x36 (not $x35)))
-(let ((@x67 (monotonicity (rewrite (= (< ?x30 (+ 1.0 ?x30)) true)) (= (not (< ?x30 (+ 1.0 ?x30))) (not true)))))
-(let ((@x71 (trans @x67 (rewrite (= (not true) false)) (= (not (< ?x30 (+ 1.0 ?x30))) false))))
-(let ((?x40 (+ 1.0 ?x30)))
-(let (($x43 (< ?x30 ?x40)))
-(let ((@x45 (monotonicity (rewrite (= ?x28 ?x30)) (rewrite (= ?x32 ?x40)) (= $x33 $x43))))
-(let ((@x52 (trans (monotonicity @x45 (= $x34 (or false $x43))) (rewrite (= (or false $x43) $x43)) (= $x34 $x43))))
-(let ((@x59 (trans (monotonicity @x45 @x52 (= $x35 (or $x43 $x43))) (rewrite (= (or $x43 $x43) $x43)) (= $x35 $x43))))
-(let ((@x62 (monotonicity @x59 (= $x36 (not $x43)))))
-(mp (asserted $x36) (trans @x62 @x71 (= $x36 false)) false))))))))))))))))))
-
-55e13b57ccd7045141601604fad3c105a2794c19 878 0
+8eb414a6a3d3ad6d5e5412da8fced2ed014e80e6 878 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2286,7 +2265,28 @@
 (let ((@x1972 (unit-resolution @x623 (unit-resolution @x625 (unit-resolution @x1804 @x1969 $x823) $x363) $x620)))
 (unit-resolution @x926 @x1972 @x1966 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-faad33b2f84ccaf1e2790bec1489d8a4c6b742a9 113 0
+acc0a8679fada55f807fa45c47b89f2dc4f0cc19 20 0
+unsat
+((set-logic AUFLIRA)
+(proof
+(let ((?x30 (* 2.0 x$)))
+(let ((?x32 (+ ?x30 1.0)))
+(let ((?x28 (+ x$ x$)))
+(let (($x33 (< ?x28 ?x32)))
+(let (($x34 (or false $x33)))
+(let (($x35 (or $x33 $x34)))
+(let (($x36 (not $x35)))
+(let ((@x67 (monotonicity (rewrite (= (< ?x30 (+ 1.0 ?x30)) true)) (= (not (< ?x30 (+ 1.0 ?x30))) (not true)))))
+(let ((@x71 (trans @x67 (rewrite (= (not true) false)) (= (not (< ?x30 (+ 1.0 ?x30))) false))))
+(let ((?x40 (+ 1.0 ?x30)))
+(let (($x43 (< ?x30 ?x40)))
+(let ((@x45 (monotonicity (rewrite (= ?x28 ?x30)) (rewrite (= ?x32 ?x40)) (= $x33 $x43))))
+(let ((@x52 (trans (monotonicity @x45 (= $x34 (or false $x43))) (rewrite (= (or false $x43) $x43)) (= $x34 $x43))))
+(let ((@x59 (trans (monotonicity @x45 @x52 (= $x35 (or $x43 $x43))) (rewrite (= (or $x43 $x43) $x43)) (= $x35 $x43))))
+(let ((@x62 (monotonicity @x59 (= $x36 (not $x43)))))
+(mp (asserted $x36) (trans @x62 @x71 (= $x36 false)) false))))))))))))))))))
+
+f2ecc8d02c730cd119d0a8be84bc5bf03ed0f98b 113 0
 unsat
 ((set-logic <null>)
 (proof
@@ -2400,7 +2400,7 @@
 (let ((@x74 (mp (asserted $x36) @x73 $x67)))
 ((_ th-lemma arith farkas -1 1 1) @x74 (unit-resolution ((_ th-lemma arith) (or false $x305)) (true-axiom true) $x305) @x332 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-054d158bf38c0362154ef81cac0cc403f00fe2d7 112 0
+2b90909cb79318775a857f179e3de90ebc09360b 112 0
 unsat
 ((set-logic <null>)
 (proof
@@ -2513,7 +2513,7 @@
 (let ((@x70 (mp (asserted (not (< (+ x$ (+ ?x29 ?x29)) (+ x$ 3)))) @x69 $x63)))
 ((_ th-lemma arith farkas -1 1 1) @x70 @x331 (unit-resolution ((_ th-lemma arith) (or false $x319)) (true-axiom true) $x319) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-62c4b764a3697fd9b8f73fa2aa0e093ddab1835d 32 0
+9e8bd1ccee1598c51f1f67ef729241282bee8975 32 0
 unsat
 ((set-logic <null>)
 (proof
@@ -2546,7 +2546,7 @@
 (let ((@x117 (unit-resolution ((_ th-lemma arith assign-bounds 1) (or $x102 (not $x100))) (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x95) $x100)) @x98 $x100) $x102)))
 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x28 (not $x101) (not $x102))) @x117 @x110 @x30 false))))))))))))))))))))))))))))))
 
-cbe2ad2be523199183bc675f533d4cb9b488ff3c 12 0
+e975f8a0748f1ab04103c4bce1c336d67c9ddc7f 12 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2559,7 +2559,7 @@
 (let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= $x29 false))))
 (mp (asserted $x29) @x46 false)))))))))
 
-9161d7d93581f36f7a468a5d2ec4a4f93f49bded 12 0
+693a453fa295b294a12bfe4fc2548b88f93af81d 12 0
 unsat
 ((set-logic AUFLIRA)
 (proof
@@ -2572,7 +2572,7 @@
 (let ((@x46 (trans @x42 (rewrite (= (not true) false)) (= $x29 false))))
 (mp (asserted $x29) @x46 false)))))))))
 
-a6a1ed7d9ca2dde49ccb419a5c671f6cb54cc6db 22 0
+da9745bea43c7d7581f4f1a982ea54a4f665c150 22 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2595,7 +2595,7 @@
 (let ((@x49 (mp~ (mp (asserted $x30) (monotonicity @x40 (= $x30 $x41)) $x41) @x48 $x46)))
 (mp (mp @x49 @x54 $x52) (rewrite (= $x52 false)) false)))))))))))))
 
-8d4ad6d4dd3d24ade2dee49ac9ccd7dc4eb5a126 22 0
+d1b4498be99afb5671326f37a46458328653a778 22 0
 unsat
 ((set-logic AUFLIRA)
 (proof
@@ -2618,7 +2618,7 @@
 (let ((@x48 (mp~ (mp (asserted $x29) (monotonicity @x39 (= $x29 $x40)) $x40) @x47 $x45)))
 (mp (mp @x48 @x53 $x51) (rewrite (= $x51 false)) false)))))))))))))
 
-129394c26840800397440346d2be8228f88432bf 31 0
+47b866c871f79f79347596e68e9f0a6717e9f9ae 31 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!0 () Int)
@@ -2650,7 +2650,7 @@
 (let ((@x74 (mp (mp~ (mp (asserted $x32) @x51 $x49) @x67 $x63) (quant-intro (rewrite (= $x60 $x54)) (= $x63 $x71)) $x71)))
 (mp @x74 (rewrite (= $x71 false)) false))))))))))))))))))
 
-874267db756bf9fbfe33e5bcc1c8d446bb786208 22 0
+f8895baf351fb020e98a9589d9032cb37daead5c 22 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v1!0 () Int)
@@ -2673,7 +2673,7 @@
 (let ((@x70 (trans (symm (and-elim @x65 (= ?v0!1 0)) (= 0 ?v0!1)) @x68 (= 0 ?v1!0))))
 (mp (trans @x70 @x67 (= 0 1)) (rewrite (= (= 0 1) false)) false))))))))))))))))
 
-a1990b1f2b40273080891d8099cbf8be7a3bff08 55 0
+c6ae686b0a4faf5664648d4de310ae4c5a1de7ec 55 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2729,7 +2729,7 @@
 (let ((@x50 (monotonicity @x47 (= $x36 $x48))))
 (mp (asserted $x36) (trans @x50 @x101 (= $x36 false)) false)))))))))))))))))))))))))))
 
-714d9704b498d8f69a61aec61e9ab9fbb7c490e0 42 0
+326e4de3d7358a1ce81c3b38c63746b57dca63fa 42 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2772,7 +2772,7 @@
 (let ((@x60 (monotonicity (quant-intro @x54 (= $x37 $x55)) (= $x38 $x58))))
 (mp (asserted $x38) (trans @x60 @x97 (= $x38 false)) false))))))))))))))))))))))))))
 
-e41ae3e6173a8a45d2e1293e87000046d27321f4 32 0
+8948c34be010e83eefa29947fdeb482617c77a6d 32 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2805,7 +2805,7 @@
 (let ((@x53 (monotonicity @x50 (= $x37 $x51))))
 (mp (asserted $x37) (trans @x53 @x76 (= $x37 false)) false)))))))))))))))))))
 
-349db302a77644aba10e708ffed825b615312604 43 0
+933b139b2a650c91137f9f7c9b004c8f0d9521d1 43 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!1 () Int)
@@ -2849,7 +2849,7 @@
 (let ((@x103 (not-or-elim @x102 $x81)))
 (unit-resolution (unit-resolution ((_ th-lemma arith triangle-eq) (or $x87 $x84 $x93)) @x103 (or $x87 $x93)) @x106 @x105 false)))))))))))))))))))))))))))))))))
 
-b9376e0ba9a01161166fc671c9275872a16f237f 46 0
+b488c2ec223d613631144f2dcdf7e5867fbbb258 46 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!0 () Int)
@@ -2896,7 +2896,7 @@
 (let ((@x109 (lemma @x108 $x84)))
 (unit-resolution (unit-resolution (def-axiom (or $x88 $x83 $x86)) @x92 (or $x83 $x86)) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x93 $x85)) @x109 $x93) (unit-resolution ((_ th-lemma arith farkas 1 1) (or $x87 $x85)) @x109 $x87) false)))))))))))))))))))))))))))))))))
 
-71f3749978d74887262db57fc45e685f1b58a1fe 31 0
+da417520952f17eeef46bee85072a2ecad83fc46 31 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -2928,7 +2928,7 @@
 (let ((@x66 (mp~ (mp (asserted $x33) @x60 $x56) (nnf-pos (refl (~ $x53 $x53)) (~ $x56 $x56)) $x56)))
 (unit-resolution @x66 @x464 false)))))))))))))))))))))))))
 
-416c05cb2acf4da101c1b31aeeea71fb83ecd69a 62 0
+623edcfe9613936b08dbdc0269a0746af35c83aa 62 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v0!1 () Int)
@@ -2991,7 +2991,7 @@
 (let ((@x515 (unit-resolution (def-axiom (or z3name!0 $x220)) (unit-resolution @x131 @x238 $x88) $x220)))
 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x220) (>= ?x96 3))) @x515 @x245 false))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-742e196ba0cf000357e0842d69c2a9fdddbb46b5 39 0
+42b10c0c66daf8181b08c93c22f4ecaa3220e964 39 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3031,53 +3031,7 @@
 (let ((@x75 (trans @x71 (rewrite (= (not (not $x61)) $x61)) (= $x39 $x61))))
 (mp (asserted $x39) (trans @x75 @x85 (= $x39 false)) false)))))))))))))))))))))))
 
-d772bd969a6ce5898850d584bb29d59c8304fae6 45 0
-unsat
-((set-logic AUFLIRA)
-(declare-fun ?v1!1 () Int)
-(declare-fun ?v2!0 () Real)
-(proof
-(let (($x105 (<= ?v1!1 (- 1))))
-(let (($x107 (or (not (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0.0)))) (not $x105))))
-(let (($x88 (forall ((?v1 Int) (?v2 Real) )(! (or (not (and (not (<= ?v1 0)) (not (<= ?v2 0.0)))) (not (<= ?v1 (- 1)))) :qid k!4))
-))
-(let (($x91 (not $x88)))
-(let (($x37 (exists ((?v0 Int) )(! (forall ((?v1 Int) (?v2 Real) )(! (let (($x31 (and (< 0 ?v1) (< 0.0 ?v2))))
-(=> $x31 (< (- 1) ?v1))) :qid k!4))
- :qid k!4))
-))
-(let (($x27 (not $x37)))
-(let (($x54 (forall ((?v1 Int) (?v2 Real) )(! (let (($x42 (< (- 1) ?v1)))
-(or (not (and (< 0 ?v1) (< 0.0 ?v2))) $x42)) :qid k!4))
-))
-(let (($x85 (or (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))) (not (<= ?1 (- 1))))))
-(let (($x42 (< (- 1) ?1)))
-(let (($x49 (or (not (and (< 0 ?1) (< 0.0 ?0))) $x42)))
-(let (($x79 (= (not (and (< 0 ?1) (< 0.0 ?0))) (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))))))
-(let (($x31 (and (< 0 ?1) (< 0.0 ?0))))
-(let ((@x77 (monotonicity (rewrite (= (< 0 ?1) (not (<= ?1 0)))) (rewrite (= (< 0.0 ?0) (not (<= ?0 0.0)))) (= $x31 (and (not (<= ?1 0)) (not (<= ?0 0.0)))))))
-(let ((@x87 (monotonicity (monotonicity @x77 $x79) (rewrite (= $x42 (not (<= ?1 (- 1))))) (= $x49 $x85))))
-(let ((@x93 (monotonicity (quant-intro @x87 (= $x54 $x88)) (= (not $x54) $x91))))
-(let (($x57 (exists ((?v0 Int) )(! (forall ((?v1 Int) (?v2 Real) )(! (let (($x42 (< (- 1) ?v1)))
-(or (not (and (< 0 ?v1) (< 0.0 ?v2))) $x42)) :qid k!4))
- :qid k!4))
-))
-(let (($x36 (forall ((?v1 Int) (?v2 Real) )(! (let (($x31 (and (< 0 ?v1) (< 0.0 ?v2))))
-(=> $x31 (< (- 1) ?v1))) :qid k!4))
-))
-(let ((@x44 (monotonicity (rewrite (= (- 1) (- 1))) (= (< (- 1) ?1) $x42))))
-(let ((@x47 (monotonicity @x44 (= (=> $x31 (< (- 1) ?1)) (=> $x31 $x42)))))
-(let ((@x53 (trans @x47 (rewrite (= (=> $x31 $x42) $x49)) (= (=> $x31 (< (- 1) ?1)) $x49))))
-(let ((@x63 (trans (quant-intro (quant-intro @x53 (= $x36 $x54)) (= $x37 $x57)) (elim-unused (= $x57 $x54)) (= $x37 $x54))))
-(let ((@x95 (trans (monotonicity @x63 (= $x27 (not $x54))) @x93 (= $x27 $x91))))
-(let ((@x111 (mp~ (mp (asserted $x27) @x95 $x91) (sk (~ $x91 (not $x107))) (not $x107))))
-(let ((@x117 (not-or-elim @x111 $x105)))
-(let (($x99 (<= ?v1!1 0)))
-(let (($x100 (not $x99)))
-(let ((@x115 (and-elim (not-or-elim @x111 (and $x100 (not (<= ?v2!0 0.0)))) $x100)))
-(unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x105) $x99)) @x115 @x117 false))))))))))))))))))))))))))))))
-
-aa1f4d1a333204b725ef94e682d891f7a12a55b7 52 0
+a32c06c0a3798bb49bc988f268a9de26ca0e273b 52 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v1!1 () Int)
@@ -3130,7 +3084,53 @@
 (let ((@x117 (and-elim (not-or-elim @x112 (and $x100 $x102)) $x102)))
 ((_ th-lemma arith farkas 1 1 1) @x117 @x116 @x118 false)))))))))))))))))))))))))))))))))))
 
-658167ac53fd7dc613987fbbc3cae6d25535a8f0 110 0
+dd6dcae1cf0d709ea38f21e7928a94234cce9953 45 0
+unsat
+((set-logic AUFLIRA)
+(declare-fun ?v1!1 () Int)
+(declare-fun ?v2!0 () Real)
+(proof
+(let (($x105 (<= ?v1!1 (- 1))))
+(let (($x107 (or (not (and (not (<= ?v1!1 0)) (not (<= ?v2!0 0.0)))) (not $x105))))
+(let (($x88 (forall ((?v1 Int) (?v2 Real) )(! (or (not (and (not (<= ?v1 0)) (not (<= ?v2 0.0)))) (not (<= ?v1 (- 1)))) :qid k!4))
+))
+(let (($x91 (not $x88)))
+(let (($x37 (exists ((?v0 Int) )(! (forall ((?v1 Int) (?v2 Real) )(! (let (($x31 (and (< 0 ?v1) (< 0.0 ?v2))))
+(=> $x31 (< (- 1) ?v1))) :qid k!4))
+ :qid k!4))
+))
+(let (($x27 (not $x37)))
+(let (($x54 (forall ((?v1 Int) (?v2 Real) )(! (let (($x42 (< (- 1) ?v1)))
+(or (not (and (< 0 ?v1) (< 0.0 ?v2))) $x42)) :qid k!4))
+))
+(let (($x85 (or (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))) (not (<= ?1 (- 1))))))
+(let (($x42 (< (- 1) ?1)))
+(let (($x49 (or (not (and (< 0 ?1) (< 0.0 ?0))) $x42)))
+(let (($x79 (= (not (and (< 0 ?1) (< 0.0 ?0))) (not (and (not (<= ?1 0)) (not (<= ?0 0.0)))))))
+(let (($x31 (and (< 0 ?1) (< 0.0 ?0))))
+(let ((@x77 (monotonicity (rewrite (= (< 0 ?1) (not (<= ?1 0)))) (rewrite (= (< 0.0 ?0) (not (<= ?0 0.0)))) (= $x31 (and (not (<= ?1 0)) (not (<= ?0 0.0)))))))
+(let ((@x87 (monotonicity (monotonicity @x77 $x79) (rewrite (= $x42 (not (<= ?1 (- 1))))) (= $x49 $x85))))
+(let ((@x93 (monotonicity (quant-intro @x87 (= $x54 $x88)) (= (not $x54) $x91))))
+(let (($x57 (exists ((?v0 Int) )(! (forall ((?v1 Int) (?v2 Real) )(! (let (($x42 (< (- 1) ?v1)))
+(or (not (and (< 0 ?v1) (< 0.0 ?v2))) $x42)) :qid k!4))
+ :qid k!4))
+))
+(let (($x36 (forall ((?v1 Int) (?v2 Real) )(! (let (($x31 (and (< 0 ?v1) (< 0.0 ?v2))))
+(=> $x31 (< (- 1) ?v1))) :qid k!4))
+))
+(let ((@x44 (monotonicity (rewrite (= (- 1) (- 1))) (= (< (- 1) ?1) $x42))))
+(let ((@x47 (monotonicity @x44 (= (=> $x31 (< (- 1) ?1)) (=> $x31 $x42)))))
+(let ((@x53 (trans @x47 (rewrite (= (=> $x31 $x42) $x49)) (= (=> $x31 (< (- 1) ?1)) $x49))))
+(let ((@x63 (trans (quant-intro (quant-intro @x53 (= $x36 $x54)) (= $x37 $x57)) (elim-unused (= $x57 $x54)) (= $x37 $x54))))
+(let ((@x95 (trans (monotonicity @x63 (= $x27 (not $x54))) @x93 (= $x27 $x91))))
+(let ((@x111 (mp~ (mp (asserted $x27) @x95 $x91) (sk (~ $x91 (not $x107))) (not $x107))))
+(let ((@x117 (not-or-elim @x111 $x105)))
+(let (($x99 (<= ?v1!1 0)))
+(let (($x100 (not $x99)))
+(let ((@x115 (and-elim (not-or-elim @x111 (and $x100 (not (<= ?v2!0 0.0)))) $x100)))
+(unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x105) $x99)) @x115 @x117 false))))))))))))))))))))))))))))))
+
+3eba422177cb1a37290b37910c836f326aae81a7 110 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3241,7 +3241,7 @@
 (let ((@x125 (mp (mp @x110 (quant-intro @x115 (= $x107 $x116)) $x116) (quant-intro (rewrite (= $x113 $x104)) (= $x116 $x122)) $x122)))
 (mp (mp @x125 @x156 $x152) @x180 false))))))))))))))))))))))))))))))))))))))))))))))
 
-ec42cd87fa1228ca157b6059baa64bb1eb437d48 23 0
+cf55ed5d5e3fbc48182cb17ef320bda064703b0c 23 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v1!0 () Int)
@@ -3265,7 +3265,7 @@
 (let ((@x73 (not-or-elim @x70 $x62)))
 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x62) (not $x64))) @x73 @x74 false)))))))))))))))))
 
-e0b55f4468e9d2470373689927a3a9ab1ac26d87 26 0
+47c99edbec21b5ca2d3944c6aeff150e7def6e0b 26 0
 unsat
 ((set-logic <null>)
 (proof
@@ -3292,7 +3292,7 @@
 (let ((@x73 (and-elim (not-or-elim (mp (asserted $x35) @x69 $x65) $x52) $x49)))
 ((_ th-lemma arith farkas 1 1 1) @x73 @x72 @x74 false))))))))))))))))))))))))
 
-14471384dcc76beb9e9e05cc2b020e277bc6dec7 26 0
+d19214170f32152ce058c34f982fe481da9e80ff 26 0
 unsat
 ((set-logic <null>)
 (proof
@@ -3319,7 +3319,7 @@
 (let ((@x92 (trans @x88 (rewrite (= (not true) false)) (= $x39 false))))
 (mp (asserted $x39) @x92 false))))))))))))))))))))))))
 
-251ff9654bce931059979b6f6ebb89ed7adb1f46 23 0
+6338e51142f708a9900dc576fef69c89a46c7f58 23 0
 unsat
 ((set-logic <null>)
 (proof
@@ -3343,7 +3343,7 @@
 (let ((@x82 (trans (monotonicity @x75 (= $x39 (not true))) (rewrite (= (not true) false)) (= $x39 false))))
 (mp (asserted $x39) @x82 false)))))))))))))))))))))
 
-eaadcda722e0f2320e16a98d649f8db4cfbfc7ee 51 0
+760eefae5bab2da16eec8daa0cc978ac4329de62 51 0
 unsat
 ((set-logic <null>)
 (proof
@@ -3395,7 +3395,7 @@
 (let ((@x152 (trans (monotonicity @x145 (= $x52 (not true))) (rewrite (= (not true) false)) (= $x52 false))))
 (mp (asserted $x52) @x152 false)))))))))))))))))))))))))))))))))))))))))))))))))
 
-97fbe4b306ce04830904de9c18fd2eef3d92ff14 12 0
+12dc1d685081b4234b95f046bcf34da3681d7c1e 12 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3408,7 +3408,7 @@
 (let ((@x37 (rewrite (= $x34 $x32))))
 (mp (asserted $x34) (trans @x37 @x39 (= $x34 false)) false))))))))))
 
-c87ffca7b379061d55a2b7af6a0c81bd41a8c4dc 23 0
+f2f21091bf9deb3a38832129de5449a872415f16 23 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3432,7 +3432,7 @@
 (let ((@x70 (not-or-elim (mp (asserted $x36) (trans @x44 @x66 (= $x36 $x64)) $x64) $x45)))
 (unit-resolution ((_ th-lemma arith farkas 1 1) $x61) @x70 @x71 false)))))))))))))))))))))
 
-61914002c318176ad9a312fe098a2c60b9897e26 22 0
+dbe03d888710bfc170c0322723b6fe3d138c2de7 22 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3455,7 +3455,7 @@
 (let ((@x50 (monotonicity @x47 (= $x36 (not (< 0 (ite $x32 0 1)))))))
 (mp (asserted $x36) (trans @x50 @x73 (= $x36 false)) false))))))))))))))))))))
 
-8b73614ff24556cd5cdf357f7135fa992f035643 37 0
+30cc2762602a7a30eb3ec186f081112e21381d17 37 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3493,7 +3493,7 @@
 (let ((@x119 (not-or-elim (mp (asserted $x42) @x115 $x111) $x86)))
 (unit-resolution ((_ th-lemma arith farkas 1 1) (or (not $x86) (not $x91))) @x119 @x126 false)))))))))))))))))))))))))))))))))))
 
-89694a345fbe7a5ab77e70a58babfff7e73da738 64 0
+093b4bdc35e8040f16c5dca022c87a6f58a6b797 64 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3558,74 +3558,7 @@
 (let ((@x526 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x229) $x237)) (unit-resolution (def-axiom (or $x76 $x229)) @x533 $x229) $x237)))
 ((_ th-lemma arith farkas 1 1 1) (unit-resolution @x545 (unit-resolution @x552 @x565 $x234) $x337) @x533 @x526 false))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-b5fca6c6782410deb719c8da4ee5b4bae9e51cbe 23 0
-unsat
-((set-logic AUFLIA)
-(proof
-(let (($x40 (= x$ a$)))
-(let ((?x36 (pair$ x$ y$)))
-(let ((?x37 (fst$ ?x36)))
-(let (($x39 (= ?x37 a$)))
-(let ((@x50 (monotonicity (rewrite (= (=> $x39 $x40) (or (not $x39) $x40))) (= (not (=> $x39 $x40)) (not (or (not $x39) $x40))))))
-(let ((@x51 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) $x39)))
-(let (($x56 (= ?x37 x$)))
-(let (($x478 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :pattern ( (pair$ ?v0 ?v1) ) :qid k!12))
-))
-(let (($x32 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :qid k!12))
-))
-(let (($x31 (= (fst$ (pair$ ?1 ?0)) ?1)))
-(let ((@x55 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32)))
-(let ((@x483 (mp @x55 (quant-intro (refl (= $x31 $x31)) (= $x32 $x478)) $x478)))
-(let (($x62 (or (not $x478) $x56)))
-(let ((@x149 ((_ quant-inst x$ y$) $x62)))
-(let ((@x150 (trans (symm (unit-resolution @x149 @x483 $x56) (= x$ ?x37)) @x51 $x40)))
-(let ((@x54 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) (not $x40))))
-(unit-resolution @x54 @x150 false)))))))))))))))))))
-
-d8b36ba641e8fd3207b81ac452cde17bed425388 42 0
-unsat
-((set-logic AUFLIA)
-(proof
-(let ((?x59 (snd$a p2$)))
-(let ((?x58 (fst$a p1$)))
-(let (($x60 (= ?x58 ?x59)))
-(let ((?x55 (pair$ y$ x$)))
-(let (($x56 (= p2$ ?x55)))
-(let ((?x52 (pair$a x$ y$)))
-(let (($x53 (= p1$ ?x52)))
-(let (($x57 (and $x53 $x56)))
-(let ((@x70 (monotonicity (rewrite (= (=> $x57 $x60) (or (not $x57) $x60))) (= (not (=> $x57 $x60)) (not (or (not $x57) $x60))))))
-(let ((@x71 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) $x57)))
-(let ((@x74 (and-elim @x71 $x56)))
-(let ((@x504 (symm (monotonicity @x74 (= ?x59 (snd$a ?x55))) (= (snd$a ?x55) ?x59))))
-(let ((?x100 (snd$a ?x55)))
-(let (($x185 (= ?x100 x$)))
-(let (($x534 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :pattern ( (pair$ ?v0 ?v1) ) :qid k!21))
-))
-(let (($x47 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :qid k!21))
-))
-(let (($x46 (= (snd$a (pair$ ?1 ?0)) ?0)))
-(let ((@x96 (mp~ (asserted $x47) (nnf-pos (refl (~ $x46 $x46)) (~ $x47 $x47)) $x47)))
-(let ((@x539 (mp @x96 (quant-intro (refl (= $x46 $x46)) (= $x47 $x534)) $x534)))
-(let (($x190 (or (not $x534) $x185)))
-(let ((@x191 ((_ quant-inst y$ x$) $x190)))
-(let ((?x187 (fst$a ?x52)))
-(let (($x188 (= ?x187 x$)))
-(let (($x522 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :pattern ( (pair$a ?v0 ?v1) ) :qid k!19))
-))
-(let (($x39 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :qid k!19))
-))
-(let (($x38 (= (fst$a (pair$a ?1 ?0)) ?1)))
-(let ((@x90 (mp~ (asserted $x39) (nnf-pos (refl (~ $x38 $x38)) (~ $x39 $x39)) $x39)))
-(let ((@x527 (mp @x90 (quant-intro (refl (= $x38 $x38)) (= $x39 $x522)) $x522)))
-(let (($x162 (or (not $x522) $x188)))
-(let ((@x292 ((_ quant-inst x$ y$) $x162)))
-(let ((@x505 (trans (monotonicity (and-elim @x71 $x53) (= ?x58 ?x187)) (unit-resolution @x292 @x527 $x188) (= ?x58 x$))))
-(let ((@x489 (trans @x505 (symm (unit-resolution @x191 @x539 $x185) (= x$ ?x100)) (= ?x58 ?x100))))
-(let ((@x76 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) (not $x60))))
-(unit-resolution @x76 (trans @x489 @x504 $x60) false))))))))))))))))))))))))))))))))))))
-
-6bc8eb1ffd043b94d9f9af6ecb9089d7d193f8db 264 0
+c03c5a5464afed237861dfdc891e37969d566ebb 264 0
 unsat
 ((set-logic AUFLIA)
 (declare-fun ?v1!0 (Nat$) Nat$)
@@ -3890,7 +3823,74 @@
 (let ((@x133 (not-or-elim (mp (asserted $x96) @x129 $x125) (not (>= ?x89 1)))))
 ((_ th-lemma arith farkas -4 1 1) @x133 (unit-resolution (def-axiom (or $x683 $x668)) @x479 $x668) @x551 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-5e4cb132f817e2256c61e4ec223d6759992674e9 51 0
+60d94e0cd230c2f830228f101b7544d16a19dfd6 23 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let (($x40 (= x$ a$)))
+(let ((?x36 (pair$ x$ y$)))
+(let ((?x37 (fst$ ?x36)))
+(let (($x39 (= ?x37 a$)))
+(let ((@x50 (monotonicity (rewrite (= (=> $x39 $x40) (or (not $x39) $x40))) (= (not (=> $x39 $x40)) (not (or (not $x39) $x40))))))
+(let ((@x51 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) $x39)))
+(let (($x56 (= ?x37 x$)))
+(let (($x478 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :pattern ( (pair$ ?v0 ?v1) ) :qid k!12))
+))
+(let (($x32 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$ (pair$ ?v0 ?v1)) ?v0) :qid k!12))
+))
+(let (($x31 (= (fst$ (pair$ ?1 ?0)) ?1)))
+(let ((@x55 (mp~ (asserted $x32) (nnf-pos (refl (~ $x31 $x31)) (~ $x32 $x32)) $x32)))
+(let ((@x483 (mp @x55 (quant-intro (refl (= $x31 $x31)) (= $x32 $x478)) $x478)))
+(let (($x62 (or (not $x478) $x56)))
+(let ((@x149 ((_ quant-inst x$ y$) $x62)))
+(let ((@x150 (trans (symm (unit-resolution @x149 @x483 $x56) (= x$ ?x37)) @x51 $x40)))
+(let ((@x54 (not-or-elim (mp (asserted (not (=> $x39 $x40))) @x50 (not (or (not $x39) $x40))) (not $x40))))
+(unit-resolution @x54 @x150 false)))))))))))))))))))
+
+abc6aef55894d3d204d52d3df341120d4c77014e 42 0
+unsat
+((set-logic AUFLIA)
+(proof
+(let ((?x59 (snd$a p2$)))
+(let ((?x58 (fst$a p1$)))
+(let (($x60 (= ?x58 ?x59)))
+(let ((?x55 (pair$ y$ x$)))
+(let (($x56 (= p2$ ?x55)))
+(let ((?x52 (pair$a x$ y$)))
+(let (($x53 (= p1$ ?x52)))
+(let (($x57 (and $x53 $x56)))
+(let ((@x70 (monotonicity (rewrite (= (=> $x57 $x60) (or (not $x57) $x60))) (= (not (=> $x57 $x60)) (not (or (not $x57) $x60))))))
+(let ((@x71 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) $x57)))
+(let ((@x74 (and-elim @x71 $x56)))
+(let ((@x504 (symm (monotonicity @x74 (= ?x59 (snd$a ?x55))) (= (snd$a ?x55) ?x59))))
+(let ((?x100 (snd$a ?x55)))
+(let (($x185 (= ?x100 x$)))
+(let (($x534 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :pattern ( (pair$ ?v0 ?v1) ) :qid k!21))
+))
+(let (($x47 (forall ((?v0 B$) (?v1 A$) )(! (= (snd$a (pair$ ?v0 ?v1)) ?v1) :qid k!21))
+))
+(let (($x46 (= (snd$a (pair$ ?1 ?0)) ?0)))
+(let ((@x96 (mp~ (asserted $x47) (nnf-pos (refl (~ $x46 $x46)) (~ $x47 $x47)) $x47)))
+(let ((@x539 (mp @x96 (quant-intro (refl (= $x46 $x46)) (= $x47 $x534)) $x534)))
+(let (($x190 (or (not $x534) $x185)))
+(let ((@x191 ((_ quant-inst y$ x$) $x190)))
+(let ((?x187 (fst$a ?x52)))
+(let (($x188 (= ?x187 x$)))
+(let (($x522 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :pattern ( (pair$a ?v0 ?v1) ) :qid k!19))
+))
+(let (($x39 (forall ((?v0 A$) (?v1 B$) )(! (= (fst$a (pair$a ?v0 ?v1)) ?v0) :qid k!19))
+))
+(let (($x38 (= (fst$a (pair$a ?1 ?0)) ?1)))
+(let ((@x90 (mp~ (asserted $x39) (nnf-pos (refl (~ $x38 $x38)) (~ $x39 $x39)) $x39)))
+(let ((@x527 (mp @x90 (quant-intro (refl (= $x38 $x38)) (= $x39 $x522)) $x522)))
+(let (($x162 (or (not $x522) $x188)))
+(let ((@x292 ((_ quant-inst x$ y$) $x162)))
+(let ((@x505 (trans (monotonicity (and-elim @x71 $x53) (= ?x58 ?x187)) (unit-resolution @x292 @x527 $x188) (= ?x58 x$))))
+(let ((@x489 (trans @x505 (symm (unit-resolution @x191 @x539 $x185) (= x$ ?x100)) (= ?x58 ?x100))))
+(let ((@x76 (not-or-elim (mp (asserted (not (=> $x57 $x60))) @x70 (not (or (not $x57) $x60))) (not $x60))))
+(unit-resolution @x76 (trans @x489 @x504 $x60) false))))))))))))))))))))))))))))))))))))
+
+d251f21fb3589ab6ed61bce83e553bbcd5ee429c 51 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3942,7 +3942,7 @@
 (let ((@x78 (not-or-elim (mp (asserted (not (=> $x54 $x62))) @x72 (not (or (not $x54) $x62))) (not $x62))))
 (unit-resolution @x78 @x462 false)))))))))))))))))))))))))))))))))))))))))))
 
-a7a12d91db289166a47592e85e858193337352b3 24 0
[phone]da2461e9c7ce3d0e407b7bc16 24 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -3967,7 +3967,7 @@
 (let ((@x80 (mp (not-or-elim @x70 (not $x44)) (rewrite (= (not $x44) $x77)) $x77)))
 (mp @x80 @x93 false))))))))))))))))))))))
 
-007c741fde1e8e6491cbd3c04ab271d45f47868f 45 0
+847a42093e0c7ebac5b356b94c79945004bf96e9 45 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4013,7 +4013,7 @@
 (let ((@x496 ((_ quant-inst x$) $x163)))
 (unit-resolution @x496 @x508 (unit-resolution @x84 (lemma @x495 $x47) $x73) false)))))))))))))))))))))))))))))))))
 
-1e460cc19bd04463ff2cfe3d4f84064a301cbc7a 11 0
+7db89748bff125dc0b538776ae3b570548832266 11 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4025,19 +4025,19 @@
 (let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
 (mp (asserted $x32) @x42 false))))))))
 
-45adc4aad0a65892aab62fc883141746ca482192 11 0
+f60c850fda8f88ddfddcac265e198fed2855c01b 11 0
 unsat
 ((set-logic AUFLIA)
 (proof
-(let (($x29 (forall ((?v0 A$) )(! (p$ ?v0) :qid k!6))
+(let (($x29 (forall ((?v0 A$) )(! (g$ ?v0) :qid k!7))
 ))
-(let (($x30 (not $x29)))
-(let (($x31 (or $x29 $x30)))
+(let (($x30 (f$ $x29)))
+(let (($x31 (=> $x30 true)))
 (let (($x32 (not $x31)))
 (let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
 (mp (asserted $x32) @x42 false))))))))
 
-dc9c699374a745fbbd7639b7a8a0668e412a34bb 46 0
+f9e10e513fd0588f5d6c281610f4889bb0668a34 46 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4084,7 +4084,7 @@
 (let ((@x478 (mp ((_ quant-inst 3 42) (or (not $x52) $x171)) (trans (monotonicity @x131 $x137) (rewrite (= $x134 $x134)) $x137) $x134)))
 (unit-resolution (unit-resolution @x478 @x78 $x168) (mp @x77 @x472 (not $x168)) false)))))))))))))))))))))))))))))))))))
 
-85b5834715b5e4e1024c8904c8b28a8b2abf704f 75 0
+88fa92ffd8ea964848bdbb197defe1efa7fdd2e7 75 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4160,19 +4160,19 @@
 (let ((@x82 (asserted $x81)))
 (unit-resolution @x82 @x466 false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-41140cb6c9910268908cf109c82533c28c91e219 11 0
+f06072929c8d142e53379b87462f703ce8c8fca8 11 0
 unsat
 ((set-logic AUFLIA)
 (proof
-(let (($x29 (forall ((?v0 A$) )(! (g$ ?v0) :qid k!7))
+(let (($x29 (forall ((?v0 A$) )(! (p$ ?v0) :qid k!6))
 ))
-(let (($x30 (f$ $x29)))
-(let (($x31 (=> $x30 true)))
+(let (($x30 (not $x29)))
+(let (($x31 (or $x29 $x30)))
 (let (($x32 (not $x31)))
 (let ((@x42 (trans (monotonicity (rewrite (= $x31 true)) (= $x32 (not true))) (rewrite (= (not true) false)) (= $x32 false))))
 (mp (asserted $x32) @x42 false))))))))
 
-4244be0c19336abc9efe7cacc29f63cb8c90bbc9 109 0
+c36d2d391586c8a6d1e6b8e7a73bd245b4c2def7 109 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4282,7 +4282,7 @@
 (let ((@x81 (asserted $x80)))
 (unit-resolution @x81 (trans @x397 ((_ th-lemma arith eq-propagate 1 1 -4 -4) @x410 @x422 @x428 @x438 (= ?x490 6)) $x79) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-341760516a6945174e657494d3881bda7f0b1219 348 0
+703387d92be4ef7e4f1bc652b2328a3b33f53830 348 0
 unsat
 ((set-logic <null>)
 (proof
@@ -4631,7 +4631,7 @@
 (let ((@x895 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x117 $x807 (not $x673))) @x891 (or $x807 (not $x673)))))
 ((_ th-lemma arith farkas -2 -2 1 -1 1 1) (unit-resolution @x895 @x889 $x807) @x485 @x745 @x488 (unit-resolution ((_ th-lemma arith triangle-eq) (or $x134 $x679)) @x584 $x679) (unit-resolution ((_ th-lemma arith) (or false $x564)) @x26 $x564) false)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
 
-e7854e1b6f2371461d17d5751e574a95a9d2644d 64 0
+9c0ac00b9444829edc9751ffc537b6a41af5144b 64 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4696,7 +4696,7 @@
 (let ((@x570 (mp ((_ quant-inst (sup$ ?x108) (sup$ ?x111) (sup$ ?x108)) (or $x251 (or $x160 $x247 $x117))) (rewrite (= (or $x251 (or $x160 $x247 $x117)) $x252)) $x252)))
 (unit-resolution @x570 @x584 @x114 @x116 @x119 false)))))))))))))))))))))))))))))))))))))))
 
-53256a17fda698860255ca06ca403057a7847e4b 25 0
+3d46cc152552934c74a9b7e72f528acd2da80760 25 0
 unsat
 ((set-logic AUFLIA)
 (proof
@@ -4722,7 +4722,7 @@
 (let ((@x258 ((_ quant-inst 1) $x257)))
 (unit-resolution @x258 @x620 @x145 false))))))))))))))))))
 
-9b9a3d55dfc209ebb876a6eb9fcfbca8df90f899 101 0
+83f2e868ac360af426c9844684088eb79f31b9ad 101 0
 unsat
 ((set-logic AUFLIA)
 (proof

--- a/src/HOL/SMT_Examples/SMT_Examples_Verit.certs	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples_Verit.certs	Mon Jun 19 22:28:09 2023 +0200
@@ -1,16 +1,16 @@
-ae54fcb9dfe8ac3652092131f8427bebbd05402c 9 0
+95a654bfff554e647800fe77ff2ba30347402e24 9 0
 unsat
-(assume axiom0 (! (not true) :named @p_1))
+(assume a0 (! (not true) :named @p_1))
 (step t2 (cl (! (= @p_1 false) :named @p_2)) :rule not_simplify)
 (step t3 (cl (! (not @p_2) :named @p_4) (! (not @p_1) :named @p_3) false) :rule equiv_pos2)
 (step t4 (cl (not @p_3) true) :rule not_not)
 (step t5 (cl @p_4 true false) :rule th_resolution :premises (t4 t3))
-(step t6 (cl false) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl false) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl (not false)) :rule false)
 (step t8 (cl) :rule resolution :premises (t6 t7))
-ef08efbe2a4fd690de84a4f2f024c061b9c72554 12 0
+064ce4a7bbfaa11e79501270fc838c420c703181 12 0
 unsat
-(assume axiom0 (! (not (! (or p$ (not p$)) :named @p_1)) :named @p_2))
+(assume a0 (! (not (! (or p$ (not p$)) :named @p_1)) :named @p_2))
 (step t2 (cl (= @p_1 true)) :rule or_simplify)
 (step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
 (step t4 (cl (= @p_3 false)) :rule not_simplify)
@@ -18,12 +18,12 @@
 (step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
 (step t7 (cl (not @p_5) @p_1) :rule not_not)
 (step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
-(step t9 (cl false) :rule th_resolution :premises (axiom0 t5 t8))
+(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
 (step t10 (cl (not false)) :rule false)
 (step t11 (cl) :rule resolution :premises (t9 t10))
-b753d4b1e8a27c132b8339803a4e586242a9eed9 17 0
+d4888d8ad473d347e6ab6d509244a7583a7babd4 17 0
 unsat
-(assume axiom0 (! (not (! (= (! (and p$ true) :named @p_1) p$) :named @p_3)) :named @p_5))
+(assume a0 (! (not (! (= (! (and p$ true) :named @p_1) p$) :named @p_3)) :named @p_5))
 (step t2 (cl (= @p_1 (! (and p$) :named @p_2))) :rule and_simplify)
 (step t3 (cl (= @p_2 p$)) :rule and_simplify)
 (step t4 (cl @p_3) :rule trans :premises (t2 t3))
@@ -36,17 +36,17 @@
 (step t11 (cl (! (not @p_7) :named @p_9) (! (not @p_5) :named @p_8) false) :rule equiv_pos2)
 (step t12 (cl (not @p_8) @p_3) :rule not_not)
 (step t13 (cl @p_9 @p_3 false) :rule th_resolution :premises (t12 t11))
-(step t14 (cl false) :rule th_resolution :premises (axiom0 t10 t13))
+(step t14 (cl false) :rule th_resolution :premises (a0 t10 t13))
 (step t15 (cl (not false)) :rule false)
 (step t16 (cl) :rule resolution :premises (t14 t15))
-3aef0472082a0952dd5c0083a53b60410a65fb15 15 0
+337e2bffaa7ce02e1ab772f593ffdbb243d5e449 15 0
 unsat
-(assume axiom0 (! (not (! (=> (! (and (! (or p$ q$) :named @p_8) (! (not p$) :named @p_9)) :named @p_2) q$) :named @p_6)) :named @p_1))
+(assume a0 (! (not (! (=> (! (and (! (or p$ q$) :named @p_8) (! (not p$) :named @p_9)) :named @p_2) q$) :named @p_6)) :named @p_1))
 (step t2 (cl (! (= @p_1 (! (and @p_2 (! (not q$) :named @p_10)) :named @p_4)) :named @p_3)) :rule bool_simplify)
 (step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_1) :named @p_5) @p_4) :rule equiv_pos2)
 (step t4 (cl (not @p_5) @p_6) :rule not_not)
 (step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_4) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl (! (= @p_4 (! (and @p_8 @p_9 @p_10) :named @p_12)) :named @p_11)) :rule ac_simp)
 (step t8 (cl (not @p_11) (not @p_4) @p_12) :rule equiv_pos2)
 (step t9 (cl @p_12) :rule th_resolution :premises (t6 t7 t8))
@@ -55,35 +55,35 @@
 (step t12 (cl @p_9) :rule and :premises (t9))
 (step t13 (cl @p_10) :rule and :premises (t9))
 (step t14 (cl) :rule resolution :premises (t11 t12 t13))
-a4d4a57bc38d3365a195600a7f29533d2f85c08f 12 0
+10d84ea161ad298d0be18624997ac708a1f26ba1 12 0
 unsat
-(assume axiom0 (! (not (! (=> (! (or (and a$ b$) (and c$ d$)) :named @p_1) @p_1) :named @p_6)) :named @p_2))
+(assume a0 (! (not (! (=> (! (or (and a$ b$) (and c$ d$)) :named @p_1) @p_1) :named @p_6)) :named @p_2))
 (step t2 (cl (! (= @p_2 (! (and @p_1 (not @p_1)) :named @p_4)) :named @p_3)) :rule bool_simplify)
 (step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_2) :named @p_5) @p_4) :rule equiv_pos2)
 (step t4 (cl (not @p_5) @p_6) :rule not_not)
 (step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_4) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl (! (= @p_4 false) :named @p_8)) :rule and_simplify)
 (step t8 (cl (not @p_8) (not @p_4) false) :rule equiv_pos2)
 (step t9 (cl false) :rule th_resolution :premises (t6 t7 t8))
 (step t10 (cl (not false)) :rule false)
 (step t11 (cl) :rule resolution :premises (t9 t10))
-f8a0f590e48624e657155c162af04ac8e33a73bd 12 0
+9edc95cdafbdeeaebc87884ea4bcc53a0e812967 12 0
 unsat
-(assume axiom0 (! (not (! (=> (! (or (and p1$ p2$) p3$) :named @p_2) (! (or (! (=> p1$ (or (and p3$ p2$) (and p1$ p3$))) :named @p_10) p1$) :named @p_3)) :named @p_7)) :named @p_1))
+(assume a0 (! (not (! (=> (! (or (and p1$ p2$) p3$) :named @p_2) (! (or (! (=> p1$ (or (and p3$ p2$) (and p1$ p3$))) :named @p_10) p1$) :named @p_3)) :named @p_7)) :named @p_1))
 (step t2 (cl (! (= @p_1 (! (and @p_2 (! (not @p_3) :named @p_9)) :named @p_5)) :named @p_4)) :rule bool_simplify)
 (step t3 (cl (! (not @p_4) :named @p_8) (! (not @p_1) :named @p_6) @p_5) :rule equiv_pos2)
 (step t4 (cl (not @p_6) @p_7) :rule not_not)
 (step t5 (cl @p_8 @p_7 @p_5) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_5) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl @p_5) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl @p_9) :rule and :premises (t6))
 (step t8 (cl (not @p_10)) :rule not_or :premises (t7))
 (step t9 (cl p1$) :rule not_implies1 :premises (t8))
 (step t10 (cl (not p1$)) :rule not_or :premises (t7))
 (step t11 (cl) :rule resolution :premises (t10 t9))
-2815beadf2b8b0fa1acb410b1f6d788eddf2d2da 29 0
+f8dcc171fd9ab79494da2e1c5e4771e075fd9d51 29 0
 unsat
-(assume axiom0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9) p$) :named @p_10)) :named @p_11))
+(assume a0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9) p$) :named @p_10)) :named @p_11))
 (step t2 (cl (= @p_1 true)) :rule equiv_simplify)
 (step t3 (cl (= @p_2 (! (= true p$) :named @p_3))) :rule cong :premises (t2))
 (step t4 (cl (= @p_3 p$)) :rule equiv_simplify)
@@ -108,19 +108,19 @@
 (step t23 (cl (! (not @p_13) :named @p_15) (! (not @p_11) :named @p_14) false) :rule equiv_pos2)
 (step t24 (cl (not @p_14) @p_10) :rule not_not)
 (step t25 (cl @p_15 @p_10 false) :rule th_resolution :premises (t24 t23))
-(step t26 (cl false) :rule th_resolution :premises (axiom0 t22 t25))
+(step t26 (cl false) :rule th_resolution :premises (a0 t22 t25))
 (step t27 (cl (not false)) :rule false)
 (step t28 (cl) :rule resolution :premises (t26 t27))
-324d7169fc854a8e46b44966c6d6829b24a059d5 59 0
+ef250e7a4e9499952e8416cff69ed029a37c7aa3 59 0
 unsat
-(assume axiom0 (! (or a$ (or b$ (or c$ d$))) :named @p_1))
-(assume axiom2 (! (or (! (not (! (or a$ (! (and c$ (! (not c$) :named @p_40)) :named @p_4)) :named @p_5)) :named @p_8) b$) :named @p_9))
-(assume axiom3 (! (or (! (not (! (and b$ (! (or x$ (not x$)) :named @p_13)) :named @p_14)) :named @p_17) c$) :named @p_18))
-(assume axiom4 (! (or (! (not (! (or d$ false) :named @p_22)) :named @p_24) c$) :named @p_25))
-(assume axiom5 (! (not (! (or c$ (! (and (! (not p$) :named @p_34) (! (or p$ (! (and q$ (not q$)) :named @p_29)) :named @p_30)) :named @p_33)) :named @p_36)) :named @p_39))
+(assume a0 (! (or a$ (or b$ (or c$ d$))) :named @p_1))
+(assume a2 (! (or (! (not (! (or a$ (! (and c$ (! (not c$) :named @p_40)) :named @p_4)) :named @p_5)) :named @p_8) b$) :named @p_9))
+(assume a3 (! (or (! (not (! (and b$ (! (or x$ (not x$)) :named @p_13)) :named @p_14)) :named @p_17) c$) :named @p_18))
+(assume a4 (! (or (! (not (! (or d$ false) :named @p_22)) :named @p_24) c$) :named @p_25))
+(assume a5 (! (not (! (or c$ (! (and (! (not p$) :named @p_34) (! (or p$ (! (and q$ (not q$)) :named @p_29)) :named @p_30)) :named @p_33)) :named @p_36)) :named @p_39))
 (step t6 (cl (! (= @p_1 (! (or a$ b$ c$ d$) :named @p_3)) :named @p_2)) :rule ac_simp)
 (step t7 (cl (not @p_2) (not @p_1) @p_3) :rule equiv_pos2)
-(step t8 (cl @p_3) :rule th_resolution :premises (axiom0 t6 t7))
+(step t8 (cl @p_3) :rule th_resolution :premises (a0 t6 t7))
 (step t9 (cl (= @p_4 false)) :rule and_simplify)
 (step t10 (cl (= @p_5 (! (or a$ false) :named @p_6))) :rule cong :premises (t9))
 (step t11 (cl (= @p_6 (! (or a$) :named @p_7))) :rule or_simplify)
@@ -129,7 +129,7 @@
 (step t14 (cl (= @p_8 (! (not a$) :named @p_10))) :rule cong :premises (t13))
 (step t15 (cl (! (= @p_9 (! (or @p_10 b$) :named @p_12)) :named @p_11)) :rule cong :premises (t14))
 (step t16 (cl (not @p_11) (not @p_9) @p_12) :rule equiv_pos2)
-(step t17 (cl @p_12) :rule th_resolution :premises (axiom2 t15 t16))
+(step t17 (cl @p_12) :rule th_resolution :premises (a2 t15 t16))
 (step t18 (cl (= @p_13 true)) :rule or_simplify)
 (step t19 (cl (= @p_14 (! (and b$ true) :named @p_15))) :rule cong :premises (t18))
 (step t20 (cl (= @p_15 (! (and b$) :named @p_16))) :rule and_simplify)
@@ -138,14 +138,14 @@
 (step t23 (cl (= @p_17 (! (not b$) :named @p_19))) :rule cong :premises (t22))
 (step t24 (cl (! (= @p_18 (! (or @p_19 c$) :named @p_21)) :named @p_20)) :rule cong :premises (t23))
 (step t25 (cl (not @p_20) (not @p_18) @p_21) :rule equiv_pos2)
-(step t26 (cl @p_21) :rule th_resolution :premises (axiom3 t24 t25))
+(step t26 (cl @p_21) :rule th_resolution :premises (a3 t24 t25))
 (step t27 (cl (= @p_22 (! (or d$) :named @p_23))) :rule or_simplify)
 (step t28 (cl (= @p_23 d$)) :rule or_simplify)
 (step t29 (cl (= @p_22 d$)) :rule trans :premises (t27 t28))
 (step t30 (cl (= @p_24 (! (not d$) :named @p_26))) :rule cong :premises (t29))
 (step t31 (cl (! (= @p_25 (! (or @p_26 c$) :named @p_28)) :named @p_27)) :rule cong :premises (t30))
 (step t32 (cl (not @p_27) (not @p_25) @p_28) :rule equiv_pos2)
-(step t33 (cl @p_28) :rule th_resolution :premises (axiom4 t31 t32))
+(step t33 (cl @p_28) :rule th_resolution :premises (a4 t31 t32))
 (step t34 (cl (= @p_29 false)) :rule and_simplify)
 (step t35 (cl (= @p_30 (! (or p$ false) :named @p_31))) :rule cong :premises (t34))
 (step t36 (cl (= @p_31 (! (or p$) :named @p_32))) :rule or_simplify)
@@ -162,7 +162,7 @@
 (step t47 (cl (! (not @p_41) :named @p_43) (! (not @p_39) :named @p_42) @p_40) :rule equiv_pos2)
 (step t48 (cl (not @p_42) @p_36) :rule not_not)
 (step t49 (cl @p_43 @p_36 @p_40) :rule th_resolution :premises (t48 t47))
-(step t50 (cl @p_40) :rule th_resolution :premises (axiom5 t46 t49))
+(step t50 (cl @p_40) :rule th_resolution :premises (a5 t46 t49))
 (step t51 (cl a$ b$ c$ d$) :rule or :premises (t8))
 (step t52 (cl @p_10 b$) :rule or :premises (t17))
 (step t53 (cl @p_19 c$) :rule or :premises (t26))
@@ -171,10 +171,10 @@
 (step t56 (cl @p_26) :rule resolution :premises (t54 t50))
 (step t57 (cl a$) :rule resolution :premises (t51 t55 t50 t56))
 (step t58 (cl) :rule resolution :premises (t52 t55 t57))
-e724b7ec8c17b26e1986911ee66a23de60e69502 38 0
+a331481eed4f18a666baadda4e1010ca7a295ccf 38 0
 unsat
-(assume axiom0 (! (forall ((?v0 A$) (?v1 A$)) (! (= (! (symm_f$ ?v0 ?v1) :named @p_2) (! (symm_f$ ?v1 ?v0) :named @p_6)) :named @p_8)) :named @p_1))
-(assume axiom1 (! (not (! (and (! (= a$ a$) :named @p_19) (! (= (symm_f$ a$ b$) (symm_f$ b$ a$)) :named @p_21)) :named @p_20)) :named @p_24))
+(assume a0 (! (forall ((?v0 A$) (?v1 A$)) (! (= (! (symm_f$ ?v0 ?v1) :named @p_2) (! (symm_f$ ?v1 ?v0) :named @p_6)) :named @p_8)) :named @p_1))
+(assume a1 (! (not (! (and (! (= a$ a$) :named @p_19) (! (= (symm_f$ a$ b$) (symm_f$ b$ a$)) :named @p_21)) :named @p_20)) :named @p_24))
 (anchor :step t3 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 A$) veriT_vr1)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl)
 (step t3.t2 (cl (! (= ?v1 veriT_vr1) :named @p_4)) :rule refl)
@@ -185,7 +185,7 @@
 (step t3.t7 (cl (= @p_8 (! (= @p_3 @p_7) :named @p_9))) :rule cong :premises (t3.t3 t3.t6))
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$) (veriT_vr1 A$)) @p_9) :named @p_11)) :named @p_10)) :rule bind)
 (step t4 (cl (not @p_10) (not @p_1) @p_11) :rule equiv_pos2)
-(step t5 (cl @p_11) :rule th_resolution :premises (axiom0 t3 t4))
+(step t5 (cl @p_11) :rule th_resolution :premises (a0 t3 t4))
 (anchor :step t6 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 A$) veriT_vr3)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_14)) :rule refl)
 (step t6.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_13)) :rule refl)
@@ -206,171 +206,826 @@
 (step t15 (cl (! (not @p_25) :named @p_28) (! (not @p_24) :named @p_27) @p_26) :rule equiv_pos2)
 (step t16 (cl (not @p_27) @p_20) :rule not_not)
 (step t17 (cl @p_28 @p_20 @p_26) :rule th_resolution :premises (t16 t15))
-(step t18 (cl @p_26) :rule th_resolution :premises (axiom1 t14 t17))
+(step t18 (cl @p_26) :rule th_resolution :premises (a1 t14 t17))
 (step t19 (cl (or (! (not @p_18) :named @p_29) @p_21)) :rule forall_inst :args ((:= veriT_vr2 a$) (:= veriT_vr3 b$)))
 (step t20 (cl @p_29 @p_21) :rule or :premises (t19))
 (step t21 (cl) :rule resolution :premises (t20 t8 t18))
-2b0e7825d38340699ae4fceb3006d5eb0b5a0628 333 0
+8616c6debd3ebae49adf8409b8c1ecb6665bc881 654 0
 unsat
-(assume axiom0 (not x0$))
-(assume axiom1 (not x30$))
-(assume axiom2 (not x29$))
-(assume axiom3 (not x59$))
-(assume axiom4 (! (or x1$ (or x31$ x0$)) :named @p_57))
-(assume axiom6 (! (or x3$ (or x33$ x2$)) :named @p_60))
-(assume axiom7 (! (or x4$ (or x34$ x3$)) :named @p_63))
-(assume axiom8 (or x35$ x4$))
-(assume axiom9 (! (or x5$ (or x36$ x30$)) :named @p_66))
-(assume axiom11 (! (or x7$ (or x38$ (or x6$ x32$))) :named @p_69))
-(assume axiom13 (! (or x9$ (or x40$ (or x8$ x34$))) :named @p_72))
-(assume axiom16 (! (or x11$ (or x43$ (or x10$ x37$))) :named @p_75))
-(assume axiom18 (! (or x13$ (or x45$ (or x12$ x39$))) :named @p_78))
-(assume axiom20 (! (or x47$ (or x14$ x41$)) :named @p_81))
-(assume axiom21 (! (or x15$ (or x48$ x42$)) :named @p_84))
-(assume axiom23 (! (or x17$ (or x50$ (or x16$ x44$))) :named @p_87))
-(assume axiom25 (! (or x19$ (or x52$ (or x18$ x46$))) :named @p_90))
-(assume axiom28 (! (or x21$ (or x55$ (or x20$ x49$))) :named @p_93))
-(assume axiom30 (! (or x23$ (or x57$ (or x22$ x51$))) :named @p_96))
-(assume axiom32 (! (or x59$ (or x24$ x53$)) :named @p_99))
-(assume axiom33 (or x25$ x54$))
-(assume axiom35 (! (or x27$ (or x26$ x56$)) :named @p_102))
-(assume axiom37 (! (or x29$ (or x28$ x58$)) :named @p_105))
-(assume axiom41 (or (! (not x2$) :named @p_1) (! (not x32$) :named @p_2)))
-(assume axiom42 (or @p_1 (! (not x1$) :named @p_3)))
-(assume axiom43 (or @p_2 @p_3))
-(assume axiom47 (or (! (not x4$) :named @p_4) (! (not x34$) :named @p_5)))
-(assume axiom48 (or @p_4 (! (not x3$) :named @p_6)))
-(assume axiom49 (or @p_5 @p_6))
-(assume axiom54 (or (! (not x6$) :named @p_7) (! (not x37$) :named @p_8)))
-(assume axiom55 (or @p_7 (! (not x5$) :named @p_9)))
-(assume axiom56 (or @p_7 (! (not x31$) :named @p_10)))
-(assume axiom57 (or @p_8 @p_9))
-(assume axiom58 (or @p_8 @p_10))
-(assume axiom59 (or @p_9 @p_10))
-(assume axiom63 (or (! (not x38$) :named @p_11) @p_7))
-(assume axiom64 (or @p_11 @p_2))
-(assume axiom66 (or (! (not x8$) :named @p_12) (! (not x39$) :named @p_13)))
-(assume axiom67 (or @p_12 (! (not x7$) :named @p_14)))
-(assume axiom68 (or @p_12 (! (not x33$) :named @p_15)))
-(assume axiom69 (or @p_13 @p_14))
-(assume axiom70 (or @p_13 @p_15))
-(assume axiom71 (or @p_14 @p_15))
-(assume axiom78 (or (! (not x41$) :named @p_16) (! (not x9$) :named @p_17)))
-(assume axiom79 (or @p_16 (! (not x35$) :named @p_18)))
-(assume axiom80 (or @p_17 @p_18))
-(assume axiom81 (or (! (not x10$) :named @p_19) (! (not x42$) :named @p_20)))
-(assume axiom82 (or @p_19 (! (not x36$) :named @p_21)))
-(assume axiom83 (or @p_20 @p_21))
-(assume axiom90 (or (! (not x12$) :named @p_22) (! (not x44$) :named @p_23)))
-(assume axiom91 (or @p_22 (! (not x11$) :named @p_24)))
-(assume axiom92 (or @p_22 @p_11))
-(assume axiom93 (or @p_23 @p_24))
-(assume axiom94 (or @p_23 @p_11))
-(assume axiom95 (or @p_24 @p_11))
-(assume axiom99 (or (! (not x45$) :named @p_25) @p_22))
-(assume axiom100 (or @p_25 @p_13))
-(assume axiom102 (or (! (not x14$) :named @p_26) (! (not x46$) :named @p_27)))
-(assume axiom103 (or @p_26 (! (not x13$) :named @p_28)))
-(assume axiom104 (or @p_26 (! (not x40$) :named @p_29)))
-(assume axiom105 (or @p_27 @p_28))
-(assume axiom106 (or @p_27 @p_29))
-(assume axiom107 (or @p_28 @p_29))
-(assume axiom113 (or (! (not x48$) :named @p_41) @p_20))
-(assume axiom114 (or (! (not x16$) :named @p_30) (! (not x49$) :named @p_31)))
-(assume axiom115 (or @p_30 (! (not x15$) :named @p_32)))
-(assume axiom116 (or @p_30 (! (not x43$) :named @p_33)))
-(assume axiom117 (or @p_31 @p_32))
-(assume axiom118 (or @p_31 @p_33))
-(assume axiom119 (or @p_32 @p_33))
-(assume axiom126 (or (! (not x18$) :named @p_34) (! (not x51$) :named @p_35)))
-(assume axiom127 (or @p_34 (! (not x17$) :named @p_36)))
-(assume axiom128 (or @p_34 @p_25))
-(assume axiom129 (or @p_35 @p_36))
-(assume axiom130 (or @p_35 @p_25))
-(assume axiom131 (or @p_36 @p_25))
-(assume axiom134 (or (! (not x19$) :named @p_37) @p_27))
-(assume axiom138 (or (! (not x53$) :named @p_38) @p_37))
-(assume axiom139 (or @p_38 (! (not x47$) :named @p_39)))
-(assume axiom140 (or @p_37 @p_39))
-(assume axiom141 (or (! (not x20$) :named @p_40) (! (not x54$) :named @p_42)))
-(assume axiom142 (or @p_40 @p_41))
-(assume axiom143 (or @p_42 @p_41))
-(assume axiom150 (or (! (not x22$) :named @p_43) (! (not x56$) :named @p_44)))
-(assume axiom151 (or @p_43 (! (not x21$) :named @p_45)))
-(assume axiom152 (or @p_43 (! (not x50$) :named @p_46)))
-(assume axiom153 (or @p_44 @p_45))
-(assume axiom154 (or @p_44 @p_46))
-(assume axiom155 (or @p_45 @p_46))
-(assume axiom162 (or (! (not x24$) :named @p_47) (! (not x58$) :named @p_48)))
-(assume axiom163 (or @p_47 (! (not x23$) :named @p_49)))
-(assume axiom164 (or @p_47 (! (not x52$) :named @p_50)))
-(assume axiom165 (or @p_48 @p_49))
-(assume axiom166 (or @p_48 @p_50))
-(assume axiom167 (or @p_49 @p_50))
-(assume axiom172 (or (! (not x26$) :named @p_51) (! (not x25$) :named @p_52)))
-(assume axiom173 (or @p_51 (! (not x55$) :named @p_53)))
-(assume axiom174 (or @p_52 @p_53))
-(assume axiom178 (or (! (not x28$) :named @p_54) (! (not x27$) :named @p_55)))
-(assume axiom179 (or @p_54 (! (not x57$) :named @p_56)))
-(assume axiom180 (or @p_55 @p_56))
+(assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uua$ ?v0) :named @p_13) (! (line_integral_exists$ f$ (! (insert$ j$ bot$) :named @p_7)) :named @p_12)) :named @p_15)) :named @p_11))
+(assume a1 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_25) (! (line_integral_exists$ f$ (! (insert$ i$ bot$) :named @p_5)) :named @p_24)) :named @p_27)) :named @p_23))
+(assume a2 (! (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (! (= (! (case_prod$ ?v0 ?v1) :named @p_36) (! (fun_app$a (! (fun_app$ ?v0 (! (fst$ ?v1) :named @p_40)) :named @p_42) (! (snd$ ?v1) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
+(assume a3 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (! (=> (! (= (! (insert$ ?v0 bot$) :named @p_3) (! (insert$ ?v1 bot$) :named @p_64)) :named @p_66) (! (= ?v0 ?v1) :named @p_70)) :named @p_72)) :named @p_62))
+(assume a4 (! (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (! (= ?v1 (! (snd$ (! (pair$ ?v0 ?v1) :named @p_87)) :named @p_89)) :named @p_91)) :named @p_85))
+(assume a5 (! (forall ((?v0 Real) (?v1 Real)) (! (= ?v1 (! (snd$a (! (fun_app$b (! (pair$a ?v0) :named @p_102) ?v1) :named @p_105)) :named @p_107)) :named @p_109)) :named @p_101))
+(assume a6 (! (member$ (! (pair$ k$ g$) :named @p_403) one_chain_typeI$) :named @p_402))
+(assume a7 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (= bot$ (! (inf$ ?v0 (! (insert$ ?v1 ?v2) :named @p_1)) :named @p_122)) :named @p_124) (! (and (! (not (! (member$a ?v1 ?v0) :named @p_128)) :named @p_130) (! (= bot$ (! (inf$ ?v0 ?v2) :named @p_133)) :named @p_135)) :named @p_137)) :named @p_139)) :named @p_120))
+(assume a8 (! (finite$ bot$) :named @p_414))
+(assume a9 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (! (=> (! (finite$ ?v0) :named @p_4) (! (finite$ (! (insert$ ?v1 ?v0) :named @p_160)) :named @p_162)) :named @p_164)) :named @p_157))
+(assume a10 (! (= i$ (! (fun_app$b (pair$a 1.0) 0.0) :named @p_417)) :named @p_499))
+(assume a11 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (=> (! (member$a ?v0 ?v1) :named @p_176) (! (= ?v1 (! (insert$ ?v0 ?v1) :named @p_2)) :named @p_181)) :named @p_183)) :named @p_175))
+(assume a12 (! (= j$ (! (fun_app$b (pair$a 0.0) 1.0) :named @p_419)) :named @p_500))
+(assume a13 (! (forall ((?v0 Real_real_prod_set$)) (! (= bot$ (! (inf$ ?v0 bot$) :named @p_196)) :named @p_198)) :named @p_195))
+(assume a14 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (insert$ ?v0 @p_1) :named @p_208) (! (insert$ ?v1 (! (insert$ ?v0 ?v2) :named @p_213)) :named @p_215)) :named @p_217)) :named @p_206))
+(assume a15 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (= @p_2 (! (sup$ @p_3 ?v1) :named @p_236)) :named @p_238)) :named @p_231))
+(assume a16 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (! (=> (! (and @p_4 (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v2) :named @p_252) ?v3) :named @p_254) (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v4) :named @p_257) ?v3) :named @p_260) (! (and (! (= ?v0 (! (sup$ ?v2 ?v4) :named @p_265)) :named @p_267) (! (= bot$ (! (inf$ ?v2 ?v4) :named @p_269)) :named @p_271)) :named @p_273)) :named @p_275)) :named @p_277)) :named @p_279) (! (= (! (line_integral$ ?v1 ?v0 ?v3) :named @p_281) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_283) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_285)) :named @p_287)) :named @p_289)) :named @p_291)) :named @p_250))
+(assume a17 (! (and (! (= (one_chain_line_integral$ f$ @p_5 one_chain_typeI$) (one_chain_line_integral$ f$ @p_5 one_chain_typeII$)) :named @p_337) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeI$) :named @p_9) (! (case_prod$ uu$ ?v0) :named @p_6)) :named @p_326)) :named @p_322) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeII$) :named @p_8) @p_6) :named @p_331)) :named @p_328)) :named @p_333)) :named @p_336))
+(assume a18 (! (and (! (= (one_chain_line_integral$ f$ @p_7 one_chain_typeII$) (one_chain_line_integral$ f$ @p_7 one_chain_typeI$)) :named @p_377) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_8 (! (case_prod$ uua$ ?v0) :named @p_10)) :named @p_366)) :named @p_362) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_9 @p_10) :named @p_371)) :named @p_368)) :named @p_373)) :named @p_376))
+(assume a19 (not (! (= (! (line_integral$ f$ (! (insert$ i$ @p_7) :named @p_407) g$) :named @p_462) (! (+ (! (line_integral$ f$ @p_5 g$) :named @p_404) (! (line_integral$ f$ @p_7 g$) :named @p_405)) :named @p_463)) :named @p_410)))
+(anchor :step t21 :args ((:= (?v0 Int) veriT_vr0)))
+(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
+(step t21.t2 (cl (= @p_13 (! (fun_app$ uua$ veriT_vr0) :named @p_14))) :rule cong :premises (t21.t1))
+(step t21.t3 (cl (= @p_15 (! (= @p_12 @p_14) :named @p_16))) :rule cong :premises (t21.t2))
+(step t21 (cl (! (= @p_11 (! (forall ((veriT_vr0 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
+(step t22 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2)
+(step t23 (cl @p_18) :rule th_resolution :premises (a0 t21 t22))
+(anchor :step t24 :args ((:= (veriT_vr0 Int) veriT_vr1)))
+(step t24.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl)
+(step t24.t2 (cl (= @p_14 (! (fun_app$ uua$ veriT_vr1) :named @p_19))) :rule cong :premises (t24.t1))
+(step t24.t3 (cl (= @p_16 (! (= @p_12 @p_19) :named @p_20))) :rule cong :premises (t24.t2))
+(step t24 (cl (! (= @p_18 (! (forall ((veriT_vr1 Int)) @p_20) :named @p_22)) :named @p_21)) :rule bind)
+(step t25 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2)
+(step t26 (cl @p_22) :rule th_resolution :premises (t23 t24 t25))
+(anchor :step t27 :args ((:= (?v0 Int) veriT_vr2)))
+(step t27.t1 (cl (= ?v0 veriT_vr2)) :rule refl)
+(step t27.t2 (cl (= @p_25 (! (fun_app$ uu$ veriT_vr2) :named @p_26))) :rule cong :premises (t27.t1))
+(step t27.t3 (cl (= @p_27 (! (= @p_24 @p_26) :named @p_28))) :rule cong :premises (t27.t2))
+(step t27 (cl (! (= @p_23 (! (forall ((veriT_vr2 Int)) @p_28) :named @p_30)) :named @p_29)) :rule bind)
+(step t28 (cl (not @p_29) (not @p_23) @p_30) :rule equiv_pos2)
+(step t29 (cl @p_30) :rule th_resolution :premises (a1 t27 t28))
+(anchor :step t30 :args ((:= (veriT_vr2 Int) veriT_vr3)))
+(step t30.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl)
+(step t30.t2 (cl (= @p_26 (! (fun_app$ uu$ veriT_vr3) :named @p_31))) :rule cong :premises (t30.t1))
+(step t30.t3 (cl (= @p_28 (! (= @p_24 @p_31) :named @p_32))) :rule cong :premises (t30.t2))
+(step t30 (cl (! (= @p_30 (! (forall ((veriT_vr3 Int)) @p_32) :named @p_34)) :named @p_33)) :rule bind)
+(step t31 (cl (not @p_33) (not @p_30) @p_34) :rule equiv_pos2)
+(step t32 (cl @p_34) :rule th_resolution :premises (t29 t30 t31))
+(anchor :step t33 :args ((:= (?v0 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr4) (:= (?v1 Int_real_real_real_prod_fun_prod$) veriT_vr5)))
+(step t33.t1 (cl (! (= ?v0 veriT_vr4) :named @p_38)) :rule refl)
+(step t33.t2 (cl (! (= ?v1 veriT_vr5) :named @p_39)) :rule refl)
+(step t33.t3 (cl (= @p_36 (! (case_prod$ veriT_vr4 veriT_vr5) :named @p_37))) :rule cong :premises (t33.t1 t33.t2))
+(step t33.t4 (cl @p_38) :rule refl)
+(step t33.t5 (cl @p_39) :rule refl)
+(step t33.t6 (cl (= @p_40 (! (fst$ veriT_vr5) :named @p_41))) :rule cong :premises (t33.t5))
+(step t33.t7 (cl (= @p_42 (! (fun_app$ veriT_vr4 @p_41) :named @p_43))) :rule cong :premises (t33.t4 t33.t6))
+(step t33.t8 (cl @p_39) :rule refl)
+(step t33.t9 (cl (= @p_44 (! (snd$ veriT_vr5) :named @p_45))) :rule cong :premises (t33.t8))
+(step t33.t10 (cl (= @p_46 (! (fun_app$a @p_43 @p_45) :named @p_47))) :rule cong :premises (t33.t7 t33.t9))
+(step t33.t11 (cl (= @p_48 (! (= @p_37 @p_47) :named @p_49))) :rule cong :premises (t33.t3 t33.t10))
+(step t33 (cl (! (= @p_35 (! (forall ((veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr5 Int_real_real_real_prod_fun_prod$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
+(step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
+(step t35 (cl @p_51) :rule th_resolution :premises (a2 t33 t34))
+(anchor :step t36 :args ((:= (veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr6) (:= (veriT_vr5 Int_real_real_real_prod_fun_prod$) veriT_vr7)))
+(step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl)
+(step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl)
+(step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2))
+(step t36.t4 (cl @p_53) :rule refl)
+(step t36.t5 (cl @p_54) :rule refl)
+(step t36.t6 (cl (= @p_41 (! (fst$ veriT_vr7) :named @p_55))) :rule cong :premises (t36.t5))
+(step t36.t7 (cl (= @p_43 (! (fun_app$ veriT_vr6 @p_55) :named @p_56))) :rule cong :premises (t36.t4 t36.t6))
+(step t36.t8 (cl @p_54) :rule refl)
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+(step t36.t10 (cl (= @p_47 (! (fun_app$a @p_56 @p_57) :named @p_58))) :rule cong :premises (t36.t7 t36.t9))
+(step t36.t11 (cl (= @p_49 (! (= @p_52 @p_58) :named @p_59))) :rule cong :premises (t36.t3 t36.t10))
+(step t36 (cl (! (= @p_51 (! (forall ((veriT_vr6 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr7 Int_real_real_real_prod_fun_prod$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
+(step t37 (cl (not @p_60) (not @p_51) @p_61) :rule equiv_pos2)
+(step t38 (cl @p_61) :rule th_resolution :premises (t35 t36 t37))
+(anchor :step t39 :args ((:= (?v0 Real_real_prod$) veriT_vr8) (:= (?v1 Real_real_prod$) veriT_vr9)))
+(step t39.t1 (cl (! (= ?v0 veriT_vr8) :named @p_68)) :rule refl)
+(step t39.t2 (cl (= @p_3 (! (insert$ veriT_vr8 bot$) :named @p_63))) :rule cong :premises (t39.t1))
+(step t39.t3 (cl (! (= ?v1 veriT_vr9) :named @p_69)) :rule refl)
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+(step t39.t5 (cl (= @p_66 (! (= @p_63 @p_65) :named @p_67))) :rule cong :premises (t39.t2 t39.t4))
+(step t39.t6 (cl @p_68) :rule refl)
+(step t39.t7 (cl @p_69) :rule refl)
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+(step t39.t9 (cl (= @p_72 (! (=> @p_67 @p_71) :named @p_73))) :rule cong :premises (t39.t5 t39.t8))
+(step t39 (cl (! (= @p_62 (! (forall ((veriT_vr8 Real_real_prod$) (veriT_vr9 Real_real_prod$)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
+(step t40 (cl (not @p_74) (not @p_62) @p_75) :rule equiv_pos2)
+(step t41 (cl @p_75) :rule th_resolution :premises (a3 t39 t40))
+(anchor :step t42 :args ((:= (veriT_vr8 Real_real_prod$) veriT_vr10) (:= (veriT_vr9 Real_real_prod$) veriT_vr11)))
+(step t42.t1 (cl (! (= veriT_vr8 veriT_vr10) :named @p_79)) :rule refl)
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+(step t42.t3 (cl (! (= veriT_vr9 veriT_vr11) :named @p_80)) :rule refl)
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+(step t42.t5 (cl (= @p_67 (! (= @p_76 @p_77) :named @p_78))) :rule cong :premises (t42.t2 t42.t4))
+(step t42.t6 (cl @p_79) :rule refl)
+(step t42.t7 (cl @p_80) :rule refl)
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+(step t42.t9 (cl (= @p_73 (! (=> @p_78 @p_81) :named @p_82))) :rule cong :premises (t42.t5 t42.t8))
+(step t42 (cl (! (= @p_75 (! (forall ((veriT_vr10 Real_real_prod$) (veriT_vr11 Real_real_prod$)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
+(step t43 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
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+(anchor :step t45 :args ((:= (?v0 Int) veriT_vr12) (:= (?v1 Real_real_real_prod_fun$) veriT_vr13)))
+(step t45.t1 (cl (! (= ?v1 veriT_vr13) :named @p_86)) :rule refl)
+(step t45.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
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+(step t45.t5 (cl (= @p_89 (! (snd$ @p_88) :named @p_90))) :rule cong :premises (t45.t4))
+(step t45.t6 (cl (= @p_91 (! (= veriT_vr13 @p_90) :named @p_92))) :rule cong :premises (t45.t1 t45.t5))
+(step t45 (cl (! (= @p_85 (! (forall ((veriT_vr12 Int) (veriT_vr13 Real_real_real_prod_fun$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
+(step t46 (cl (not @p_93) (not @p_85) @p_94) :rule equiv_pos2)
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+(anchor :step t48 :args ((:= (veriT_vr12 Int) veriT_vr14) (:= (veriT_vr13 Real_real_real_prod_fun$) veriT_vr15)))
+(step t48.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_95)) :rule refl)
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+(step t48.t5 (cl (= @p_90 (! (snd$ @p_96) :named @p_97))) :rule cong :premises (t48.t4))
+(step t48.t6 (cl (= @p_92 (! (= veriT_vr15 @p_97) :named @p_98))) :rule cong :premises (t48.t1 t48.t5))
+(step t48 (cl (! (= @p_94 (! (forall ((veriT_vr14 Int) (veriT_vr15 Real_real_real_prod_fun$)) @p_98) :named @p_100)) :named @p_99)) :rule bind)
+(step t49 (cl (not @p_99) (not @p_94) @p_100) :rule equiv_pos2)
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+(anchor :step t51 :args ((:= (?v0 Real) veriT_vr16) (:= (?v1 Real) veriT_vr17)))
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+(step t51.t2 (cl (= ?v0 veriT_vr16)) :rule refl)
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+(step t51.t4 (cl @p_104) :rule refl)
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+(step t51.t6 (cl (= @p_107 (! (snd$a @p_106) :named @p_108))) :rule cong :premises (t51.t5))
+(step t51.t7 (cl (= @p_109 (! (= veriT_vr17 @p_108) :named @p_110))) :rule cong :premises (t51.t1 t51.t6))
+(step t51 (cl (! (= @p_101 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_110) :named @p_112)) :named @p_111)) :rule bind)
+(step t52 (cl (not @p_111) (not @p_101) @p_112) :rule equiv_pos2)
+(step t53 (cl @p_112) :rule th_resolution :premises (a5 t51 t52))
+(anchor :step t54 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
+(step t54.t1 (cl (! (= veriT_vr17 veriT_vr19) :named @p_114)) :rule refl)
+(step t54.t2 (cl (= veriT_vr16 veriT_vr18)) :rule refl)
+(step t54.t3 (cl (= @p_103 (! (pair$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2))
+(step t54.t4 (cl @p_114) :rule refl)
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+(step t54.t6 (cl (= @p_108 (! (snd$a @p_115) :named @p_116))) :rule cong :premises (t54.t5))
+(step t54.t7 (cl (= @p_110 (! (= veriT_vr19 @p_116) :named @p_117))) :rule cong :premises (t54.t1 t54.t6))
+(step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind)
+(step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2)
+(step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55))
+(anchor :step t57 :args ((:= (?v0 Real_real_prod_set$) veriT_vr20) (:= (?v1 Real_real_prod$) veriT_vr21) (:= (?v2 Real_real_prod_set$) veriT_vr22)))
+(step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl)
+(step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl)
+(step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl)
+(step t57.t4 (cl (= @p_1 (! (insert$ veriT_vr21 veriT_vr22) :named @p_121))) :rule cong :premises (t57.t2 t57.t3))
+(step t57.t5 (cl (= @p_122 (! (inf$ veriT_vr20 @p_121) :named @p_123))) :rule cong :premises (t57.t1 t57.t4))
+(step t57.t6 (cl (= @p_124 (! (= bot$ @p_123) :named @p_125))) :rule cong :premises (t57.t5))
+(step t57.t7 (cl @p_126) :rule refl)
+(step t57.t8 (cl @p_127) :rule refl)
+(step t57.t9 (cl (= @p_128 (! (member$a veriT_vr21 veriT_vr20) :named @p_129))) :rule cong :premises (t57.t7 t57.t8))
+(step t57.t10 (cl (= @p_130 (! (not @p_129) :named @p_131))) :rule cong :premises (t57.t9))
+(step t57.t11 (cl @p_127) :rule refl)
+(step t57.t12 (cl @p_132) :rule refl)
+(step t57.t13 (cl (= @p_133 (! (inf$ veriT_vr20 veriT_vr22) :named @p_134))) :rule cong :premises (t57.t11 t57.t12))
+(step t57.t14 (cl (= @p_135 (! (= bot$ @p_134) :named @p_136))) :rule cong :premises (t57.t13))
+(step t57.t15 (cl (= @p_137 (! (and @p_131 @p_136) :named @p_138))) :rule cong :premises (t57.t10 t57.t14))
+(step t57.t16 (cl (= @p_139 (! (= @p_125 @p_138) :named @p_140))) :rule cong :premises (t57.t6 t57.t15))
+(step t57 (cl (! (= @p_120 (! (forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind)
+(step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2)
+(step t59 (cl @p_142) :rule th_resolution :premises (a7 t57 t58))
+(anchor :step t60 :args ((:= (veriT_vr20 Real_real_prod_set$) veriT_vr23) (:= (veriT_vr21 Real_real_prod$) veriT_vr24) (:= (veriT_vr22 Real_real_prod_set$) veriT_vr25)))
+(step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl)
+(step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl)
+(step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl)
+(step t60.t4 (cl (= @p_121 (! (insert$ veriT_vr24 veriT_vr25) :named @p_143))) :rule cong :premises (t60.t2 t60.t3))
+(step t60.t5 (cl (= @p_123 (! (inf$ veriT_vr23 @p_143) :named @p_144))) :rule cong :premises (t60.t1 t60.t4))
+(step t60.t6 (cl (= @p_125 (! (= bot$ @p_144) :named @p_145))) :rule cong :premises (t60.t5))
+(step t60.t7 (cl @p_146) :rule refl)
+(step t60.t8 (cl @p_147) :rule refl)
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+(step t60.t10 (cl (= @p_131 (! (not @p_148) :named @p_149))) :rule cong :premises (t60.t9))
+(step t60.t11 (cl @p_147) :rule refl)
+(step t60.t12 (cl @p_150) :rule refl)
+(step t60.t13 (cl (= @p_134 (! (inf$ veriT_vr23 veriT_vr25) :named @p_151))) :rule cong :premises (t60.t11 t60.t12))
+(step t60.t14 (cl (= @p_136 (! (= bot$ @p_151) :named @p_152))) :rule cong :premises (t60.t13))
+(step t60.t15 (cl (= @p_138 (! (and @p_149 @p_152) :named @p_153))) :rule cong :premises (t60.t10 t60.t14))
+(step t60.t16 (cl (= @p_140 (! (= @p_145 @p_153) :named @p_154))) :rule cong :premises (t60.t6 t60.t15))
+(step t60 (cl (! (= @p_142 (! (forall ((veriT_vr23 Real_real_prod_set$) (veriT_vr24 Real_real_prod$) (veriT_vr25 Real_real_prod_set$)) @p_154) :named @p_156)) :named @p_155)) :rule bind)
+(step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2)
+(step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61))
+(anchor :step t63 :args ((:= (?v0 Real_real_prod_set$) veriT_vr26) (:= (?v1 Real_real_prod$) veriT_vr27)))
+(step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl)
+(step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1))
+(step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl)
+(step t63.t4 (cl @p_159) :rule refl)
+(step t63.t5 (cl (= @p_160 (! (insert$ veriT_vr27 veriT_vr26) :named @p_161))) :rule cong :premises (t63.t3 t63.t4))
+(step t63.t6 (cl (= @p_162 (! (finite$ @p_161) :named @p_163))) :rule cong :premises (t63.t5))
+(step t63.t7 (cl (= @p_164 (! (=> @p_158 @p_163) :named @p_165))) :rule cong :premises (t63.t2 t63.t6))
+(step t63 (cl (! (= @p_157 (! (forall ((veriT_vr26 Real_real_prod_set$) (veriT_vr27 Real_real_prod$)) @p_165) :named @p_167)) :named @p_166)) :rule bind)
+(step t64 (cl (not @p_166) (not @p_157) @p_167) :rule equiv_pos2)
+(step t65 (cl @p_167) :rule th_resolution :premises (a9 t63 t64))
+(anchor :step t66 :args ((:= (veriT_vr26 Real_real_prod_set$) veriT_vr28) (:= (veriT_vr27 Real_real_prod$) veriT_vr29)))
+(step t66.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_169)) :rule refl)
+(step t66.t2 (cl (= @p_158 (! (finite$ veriT_vr28) :named @p_168))) :rule cong :premises (t66.t1))
+(step t66.t3 (cl (= veriT_vr27 veriT_vr29)) :rule refl)
+(step t66.t4 (cl @p_169) :rule refl)
+(step t66.t5 (cl (= @p_161 (! (insert$ veriT_vr29 veriT_vr28) :named @p_170))) :rule cong :premises (t66.t3 t66.t4))
+(step t66.t6 (cl (= @p_163 (! (finite$ @p_170) :named @p_171))) :rule cong :premises (t66.t5))
+(step t66.t7 (cl (= @p_165 (! (=> @p_168 @p_171) :named @p_172))) :rule cong :premises (t66.t2 t66.t6))
+(step t66 (cl (! (= @p_167 (! (forall ((veriT_vr28 Real_real_prod_set$) (veriT_vr29 Real_real_prod$)) @p_172) :named @p_174)) :named @p_173)) :rule bind)
+(step t67 (cl (not @p_173) (not @p_167) @p_174) :rule equiv_pos2)
+(step t68 (cl @p_174) :rule th_resolution :premises (t65 t66 t67))
+(anchor :step t69 :args ((:= (?v0 Real_real_prod$) veriT_vr30) (:= (?v1 Real_real_prod_set$) veriT_vr31)))
+(step t69.t1 (cl (! (= ?v0 veriT_vr30) :named @p_179)) :rule refl)
+(step t69.t2 (cl (! (= ?v1 veriT_vr31) :named @p_178)) :rule refl)
+(step t69.t3 (cl (= @p_176 (! (member$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2))
+(step t69.t4 (cl @p_178) :rule refl)
+(step t69.t5 (cl @p_179) :rule refl)
+(step t69.t6 (cl @p_178) :rule refl)
+(step t69.t7 (cl (= @p_2 (! (insert$ veriT_vr30 veriT_vr31) :named @p_180))) :rule cong :premises (t69.t5 t69.t6))
+(step t69.t8 (cl (= @p_181 (! (= veriT_vr31 @p_180) :named @p_182))) :rule cong :premises (t69.t4 t69.t7))
+(step t69.t9 (cl (= @p_183 (! (=> @p_177 @p_182) :named @p_184))) :rule cong :premises (t69.t3 t69.t8))
+(step t69 (cl (! (= @p_175 (! (forall ((veriT_vr30 Real_real_prod$) (veriT_vr31 Real_real_prod_set$)) @p_184) :named @p_186)) :named @p_185)) :rule bind)
+(step t70 (cl (not @p_185) (not @p_175) @p_186) :rule equiv_pos2)
+(step t71 (cl @p_186) :rule th_resolution :premises (a11 t69 t70))
+(anchor :step t72 :args ((:= (veriT_vr30 Real_real_prod$) veriT_vr32) (:= (veriT_vr31 Real_real_prod_set$) veriT_vr33)))
+(step t72.t1 (cl (! (= veriT_vr30 veriT_vr32) :named @p_189)) :rule refl)
+(step t72.t2 (cl (! (= veriT_vr31 veriT_vr33) :named @p_188)) :rule refl)
+(step t72.t3 (cl (= @p_177 (! (member$a veriT_vr32 veriT_vr33) :named @p_187))) :rule cong :premises (t72.t1 t72.t2))
+(step t72.t4 (cl @p_188) :rule refl)
+(step t72.t5 (cl @p_189) :rule refl)
+(step t72.t6 (cl @p_188) :rule refl)
+(step t72.t7 (cl (= @p_180 (! (insert$ veriT_vr32 veriT_vr33) :named @p_190))) :rule cong :premises (t72.t5 t72.t6))
+(step t72.t8 (cl (= @p_182 (! (= veriT_vr33 @p_190) :named @p_191))) :rule cong :premises (t72.t4 t72.t7))
+(step t72.t9 (cl (= @p_184 (! (=> @p_187 @p_191) :named @p_192))) :rule cong :premises (t72.t3 t72.t8))
+(step t72 (cl (! (= @p_186 (! (forall ((veriT_vr32 Real_real_prod$) (veriT_vr33 Real_real_prod_set$)) @p_192) :named @p_194)) :named @p_193)) :rule bind)
+(step t73 (cl (not @p_193) (not @p_186) @p_194) :rule equiv_pos2)
+(step t74 (cl @p_194) :rule th_resolution :premises (t71 t72 t73))
+(anchor :step t75 :args ((:= (?v0 Real_real_prod_set$) veriT_vr34)))
+(step t75.t1 (cl (= ?v0 veriT_vr34)) :rule refl)
+(step t75.t2 (cl (= @p_196 (! (inf$ veriT_vr34 bot$) :named @p_197))) :rule cong :premises (t75.t1))
+(step t75.t3 (cl (= @p_198 (! (= bot$ @p_197) :named @p_199))) :rule cong :premises (t75.t2))
+(step t75 (cl (! (= @p_195 (! (forall ((veriT_vr34 Real_real_prod_set$)) @p_199) :named @p_201)) :named @p_200)) :rule bind)
+(step t76 (cl (not @p_200) (not @p_195) @p_201) :rule equiv_pos2)
+(step t77 (cl @p_201) :rule th_resolution :premises (a13 t75 t76))
+(anchor :step t78 :args ((:= (veriT_vr34 Real_real_prod_set$) veriT_vr35)))
+(step t78.t1 (cl (= veriT_vr34 veriT_vr35)) :rule refl)
+(step t78.t2 (cl (= @p_197 (! (inf$ veriT_vr35 bot$) :named @p_202))) :rule cong :premises (t78.t1))
+(step t78.t3 (cl (= @p_199 (! (= bot$ @p_202) :named @p_203))) :rule cong :premises (t78.t2))
+(step t78 (cl (! (= @p_201 (! (forall ((veriT_vr35 Real_real_prod_set$)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
+(step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2)
+(step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79))
+(anchor :step t81 :args ((:= (?v0 Real_real_prod$) veriT_vr36) (:= (?v1 Real_real_prod$) veriT_vr37) (:= (?v2 Real_real_prod_set$) veriT_vr38)))
+(step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl)
+(step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl)
+(step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl)
+(step t81.t4 (cl (= @p_1 (! (insert$ veriT_vr37 veriT_vr38) :named @p_207))) :rule cong :premises (t81.t2 t81.t3))
+(step t81.t5 (cl (= @p_208 (! (insert$ veriT_vr36 @p_207) :named @p_209))) :rule cong :premises (t81.t1 t81.t4))
+(step t81.t6 (cl @p_210) :rule refl)
+(step t81.t7 (cl @p_211) :rule refl)
+(step t81.t8 (cl @p_212) :rule refl)
+(step t81.t9 (cl (= @p_213 (! (insert$ veriT_vr36 veriT_vr38) :named @p_214))) :rule cong :premises (t81.t7 t81.t8))
+(step t81.t10 (cl (= @p_215 (! (insert$ veriT_vr37 @p_214) :named @p_216))) :rule cong :premises (t81.t6 t81.t9))
+(step t81.t11 (cl (= @p_217 (! (= @p_209 @p_216) :named @p_218))) :rule cong :premises (t81.t5 t81.t10))
+(step t81 (cl (! (= @p_206 (! (forall ((veriT_vr36 Real_real_prod$) (veriT_vr37 Real_real_prod$) (veriT_vr38 Real_real_prod_set$)) @p_218) :named @p_220)) :named @p_219)) :rule bind)
+(step t82 (cl (not @p_219) (not @p_206) @p_220) :rule equiv_pos2)
+(step t83 (cl @p_220) :rule th_resolution :premises (a14 t81 t82))
+(anchor :step t84 :args ((:= (veriT_vr36 Real_real_prod$) veriT_vr39) (:= (veriT_vr37 Real_real_prod$) veriT_vr40) (:= (veriT_vr38 Real_real_prod_set$) veriT_vr41)))
+(step t84.t1 (cl (! (= veriT_vr36 veriT_vr39) :named @p_224)) :rule refl)
+(step t84.t2 (cl (! (= veriT_vr37 veriT_vr40) :named @p_223)) :rule refl)
+(step t84.t3 (cl (! (= veriT_vr38 veriT_vr41) :named @p_225)) :rule refl)
+(step t84.t4 (cl (= @p_207 (! (insert$ veriT_vr40 veriT_vr41) :named @p_221))) :rule cong :premises (t84.t2 t84.t3))
+(step t84.t5 (cl (= @p_209 (! (insert$ veriT_vr39 @p_221) :named @p_222))) :rule cong :premises (t84.t1 t84.t4))
+(step t84.t6 (cl @p_223) :rule refl)
+(step t84.t7 (cl @p_224) :rule refl)
+(step t84.t8 (cl @p_225) :rule refl)
+(step t84.t9 (cl (= @p_214 (! (insert$ veriT_vr39 veriT_vr41) :named @p_226))) :rule cong :premises (t84.t7 t84.t8))
+(step t84.t10 (cl (= @p_216 (! (insert$ veriT_vr40 @p_226) :named @p_227))) :rule cong :premises (t84.t6 t84.t9))
+(step t84.t11 (cl (= @p_218 (! (= @p_222 @p_227) :named @p_228))) :rule cong :premises (t84.t5 t84.t10))
+(step t84 (cl (! (= @p_220 (! (forall ((veriT_vr39 Real_real_prod$) (veriT_vr40 Real_real_prod$) (veriT_vr41 Real_real_prod_set$)) @p_228) :named @p_230)) :named @p_229)) :rule bind)
+(step t85 (cl (not @p_229) (not @p_220) @p_230) :rule equiv_pos2)
+(step t86 (cl @p_230) :rule th_resolution :premises (t83 t84 t85))
+(anchor :step t87 :args ((:= (?v0 Real_real_prod$) veriT_vr42) (:= (?v1 Real_real_prod_set$) veriT_vr43)))
+(step t87.t1 (cl (! (= ?v0 veriT_vr42) :named @p_233)) :rule refl)
+(step t87.t2 (cl (! (= ?v1 veriT_vr43) :named @p_235)) :rule refl)
+(step t87.t3 (cl (= @p_2 (! (insert$ veriT_vr42 veriT_vr43) :named @p_232))) :rule cong :premises (t87.t1 t87.t2))
+(step t87.t4 (cl @p_233) :rule refl)
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+(step t87.t6 (cl @p_235) :rule refl)
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+(step t87.t8 (cl (= @p_238 (! (= @p_232 @p_237) :named @p_239))) :rule cong :premises (t87.t3 t87.t7))
+(step t87 (cl (! (= @p_231 (! (forall ((veriT_vr42 Real_real_prod$) (veriT_vr43 Real_real_prod_set$)) @p_239) :named @p_241)) :named @p_240)) :rule bind)
+(step t88 (cl (not @p_240) (not @p_231) @p_241) :rule equiv_pos2)
+(step t89 (cl @p_241) :rule th_resolution :premises (a15 t87 t88))
+(anchor :step t90 :args ((:= (veriT_vr42 Real_real_prod$) veriT_vr44) (:= (veriT_vr43 Real_real_prod_set$) veriT_vr45)))
+(step t90.t1 (cl (! (= veriT_vr42 veriT_vr44) :named @p_243)) :rule refl)
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+(step t90.t3 (cl (= @p_232 (! (insert$ veriT_vr44 veriT_vr45) :named @p_242))) :rule cong :premises (t90.t1 t90.t2))
+(step t90.t4 (cl @p_243) :rule refl)
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+(step t90.t6 (cl @p_245) :rule refl)
+(step t90.t7 (cl (= @p_237 (! (sup$ @p_244 veriT_vr45) :named @p_246))) :rule cong :premises (t90.t5 t90.t6))
+(step t90.t8 (cl (= @p_239 (! (= @p_242 @p_246) :named @p_247))) :rule cong :premises (t90.t3 t90.t7))
+(step t90 (cl (! (= @p_241 (! (forall ((veriT_vr44 Real_real_prod$) (veriT_vr45 Real_real_prod_set$)) @p_247) :named @p_249)) :named @p_248)) :rule bind)
+(step t91 (cl (not @p_248) (not @p_241) @p_249) :rule equiv_pos2)
+(step t92 (cl @p_249) :rule th_resolution :premises (t89 t90 t91))
+(anchor :step t93 :args ((:= (?v0 Real_real_prod_set$) veriT_vr46) (:= (?v1 Real_real_prod_real_real_prod_fun$) veriT_vr47) (:= (?v2 Real_real_prod_set$) veriT_vr48) (:= (?v3 Real_real_real_prod_fun$) veriT_vr49) (:= (?v4 Real_real_prod_set$) veriT_vr50)))
+(step t93.t1 (cl (! (= ?v0 veriT_vr46) :named @p_262)) :rule refl)
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+(step t93.t3 (cl (! (= ?v1 veriT_vr47) :named @p_256)) :rule refl)
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+(step t93.t6 (cl (! (= ?v3 veriT_vr49) :named @p_259)) :rule refl)
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+(step t93.t9 (cl (! (= ?v4 veriT_vr50) :named @p_264)) :rule refl)
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+(step t93.t17 (cl (= @p_267 (! (= veriT_vr46 @p_266) :named @p_268))) :rule cong :premises (t93.t13 t93.t16))
+(step t93.t18 (cl @p_263) :rule refl)
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+(step t93.t21 (cl (= @p_271 (! (= bot$ @p_270) :named @p_272))) :rule cong :premises (t93.t20))
+(step t93.t22 (cl (= @p_273 (! (and @p_268 @p_272) :named @p_274))) :rule cong :premises (t93.t17 t93.t21))
+(step t93.t23 (cl (= @p_275 (! (and @p_261 @p_274) :named @p_276))) :rule cong :premises (t93.t12 t93.t22))
+(step t93.t24 (cl (= @p_277 (! (and @p_255 @p_276) :named @p_278))) :rule cong :premises (t93.t7 t93.t23))
+(step t93.t25 (cl (= @p_279 (! (and @p_251 @p_278) :named @p_280))) :rule cong :premises (t93.t2 t93.t24))
+(step t93.t26 (cl @p_256) :rule refl)
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+(step t93.t29 (cl (= @p_281 (! (line_integral$ veriT_vr47 veriT_vr46 veriT_vr49) :named @p_282))) :rule cong :premises (t93.t26 t93.t27 t93.t28))
+(step t93.t30 (cl @p_256) :rule refl)
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+(step t93.t34 (cl @p_256) :rule refl)
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+(step t93.t38 (cl (= @p_287 (! (+ @p_284 @p_286) :named @p_288))) :rule cong :premises (t93.t33 t93.t37))
+(step t93.t39 (cl (= @p_289 (! (= @p_282 @p_288) :named @p_290))) :rule cong :premises (t93.t29 t93.t38))
+(step t93.t40 (cl (= @p_291 (! (=> @p_280 @p_290) :named @p_292))) :rule cong :premises (t93.t25 t93.t39))
+(step t93 (cl (! (= @p_250 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_292) :named @p_294)) :named @p_293)) :rule bind)
+(step t94 (cl (not @p_293) (not @p_250) @p_294) :rule equiv_pos2)
+(step t95 (cl @p_294) :rule th_resolution :premises (a16 t93 t94))
+(anchor :step t96 :args ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)))
+(step t96.t1 (cl (= @p_280 (! (and @p_251 @p_255 @p_261 @p_268 @p_272) :named @p_295))) :rule ac_simp)
+(step t96.t2 (cl (= @p_292 (! (=> @p_295 @p_290) :named @p_296))) :rule cong :premises (t96.t1))
+(step t96 (cl (! (= @p_294 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_296) :named @p_298)) :named @p_297)) :rule bind)
+(step t97 (cl (not @p_297) (not @p_294) @p_298) :rule equiv_pos2)
+(step t98 (cl @p_298) :rule th_resolution :premises (t95 t96 t97))
+(anchor :step t99 :args ((:= (veriT_vr46 Real_real_prod_set$) veriT_vr51) (:= (veriT_vr47 Real_real_prod_real_real_prod_fun$) veriT_vr52) (:= (veriT_vr48 Real_real_prod_set$) veriT_vr53) (:= (veriT_vr49 Real_real_real_prod_fun$) veriT_vr54) (:= (veriT_vr50 Real_real_prod_set$) veriT_vr55)))
+(step t99.t1 (cl (! (= veriT_vr46 veriT_vr51) :named @p_306)) :rule refl)
+(step t99.t2 (cl (= @p_251 (! (finite$ veriT_vr51) :named @p_299))) :rule cong :premises (t99.t1))
+(step t99.t3 (cl (! (= veriT_vr47 veriT_vr52) :named @p_302)) :rule refl)
+(step t99.t4 (cl (! (= veriT_vr48 veriT_vr53) :named @p_307)) :rule refl)
+(step t99.t5 (cl (= @p_253 (! (line_integral_exists$ veriT_vr52 veriT_vr53) :named @p_300))) :rule cong :premises (t99.t3 t99.t4))
+(step t99.t6 (cl (! (= veriT_vr49 veriT_vr54) :named @p_304)) :rule refl)
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+(step t99.t8 (cl @p_302) :rule refl)
+(step t99.t9 (cl (! (= veriT_vr50 veriT_vr55) :named @p_308)) :rule refl)
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+(step t99.t11 (cl @p_304) :rule refl)
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+(step t99.t13 (cl @p_306) :rule refl)
+(step t99.t14 (cl @p_307) :rule refl)
+(step t99.t15 (cl @p_308) :rule refl)
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+(step t99.t17 (cl (= @p_268 (! (= veriT_vr51 @p_309) :named @p_310))) :rule cong :premises (t99.t13 t99.t16))
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+(step t99.t19 (cl @p_308) :rule refl)
+(step t99.t20 (cl (= @p_270 (! (inf$ veriT_vr53 veriT_vr55) :named @p_311))) :rule cong :premises (t99.t18 t99.t19))
+(step t99.t21 (cl (= @p_272 (! (= bot$ @p_311) :named @p_312))) :rule cong :premises (t99.t20))
+(step t99.t22 (cl (= @p_295 (! (and @p_299 @p_301 @p_305 @p_310 @p_312) :named @p_313))) :rule cong :premises (t99.t2 t99.t7 t99.t12 t99.t17 t99.t21))
+(step t99.t23 (cl @p_302) :rule refl)
+(step t99.t24 (cl @p_306) :rule refl)
+(step t99.t25 (cl @p_304) :rule refl)
+(step t99.t26 (cl (= @p_282 (! (line_integral$ veriT_vr52 veriT_vr51 veriT_vr54) :named @p_314))) :rule cong :premises (t99.t23 t99.t24 t99.t25))
+(step t99.t27 (cl @p_302) :rule refl)
+(step t99.t28 (cl @p_307) :rule refl)
+(step t99.t29 (cl @p_304) :rule refl)
+(step t99.t30 (cl (= @p_284 (! (line_integral$ veriT_vr52 veriT_vr53 veriT_vr54) :named @p_315))) :rule cong :premises (t99.t27 t99.t28 t99.t29))
+(step t99.t31 (cl @p_302) :rule refl)
+(step t99.t32 (cl @p_308) :rule refl)
+(step t99.t33 (cl @p_304) :rule refl)
+(step t99.t34 (cl (= @p_286 (! (line_integral$ veriT_vr52 veriT_vr55 veriT_vr54) :named @p_316))) :rule cong :premises (t99.t31 t99.t32 t99.t33))
+(step t99.t35 (cl (= @p_288 (! (+ @p_315 @p_316) :named @p_317))) :rule cong :premises (t99.t30 t99.t34))
+(step t99.t36 (cl (= @p_290 (! (= @p_314 @p_317) :named @p_318))) :rule cong :premises (t99.t26 t99.t35))
+(step t99.t37 (cl (= @p_296 (! (=> @p_313 @p_318) :named @p_319))) :rule cong :premises (t99.t22 t99.t36))
+(step t99 (cl (! (= @p_298 (! (forall ((veriT_vr51 Real_real_prod_set$) (veriT_vr52 Real_real_prod_real_real_prod_fun$) (veriT_vr53 Real_real_prod_set$) (veriT_vr54 Real_real_real_prod_fun$) (veriT_vr55 Real_real_prod_set$)) @p_319) :named @p_321)) :named @p_320)) :rule bind)
+(step t100 (cl (not @p_320) (not @p_298) @p_321) :rule equiv_pos2)
+(step t101 (cl @p_321) :rule th_resolution :premises (t98 t99 t100))
+(anchor :step t102 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr56)))
+(step t102.t1 (cl (! (= ?v0 veriT_vr56) :named @p_324)) :rule refl)
+(step t102.t2 (cl (= @p_9 (! (member$ veriT_vr56 one_chain_typeI$) :named @p_323))) :rule cong :premises (t102.t1))
+(step t102.t3 (cl @p_324) :rule refl)
+(step t102.t4 (cl (! (= @p_6 (! (case_prod$ uu$ veriT_vr56) :named @p_325)) :named @p_330)) :rule cong :premises (t102.t3))
+(step t102.t5 (cl (= @p_326 (! (=> @p_323 @p_325) :named @p_327))) :rule cong :premises (t102.t2 t102.t4))
+(step t102 (cl (= @p_322 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_327) :named @p_334))) :rule bind)
+(anchor :step t103 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr56)))
+(step t103.t1 (cl @p_324) :rule refl)
+(step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1))
+(step t103.t3 (cl @p_324) :rule refl)
+(step t103.t4 (cl @p_330) :rule cong :premises (t103.t3))
+(step t103.t5 (cl (= @p_331 (! (=> @p_329 @p_325) :named @p_332))) :rule cong :premises (t103.t2 t103.t4))
+(step t103 (cl (= @p_328 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_332) :named @p_335))) :rule bind)
+(step t104 (cl (= @p_333 (! (and @p_334 @p_335) :named @p_338))) :rule cong :premises (t102 t103))
+(step t105 (cl (! (= @p_336 (! (and @p_337 @p_338) :named @p_340)) :named @p_339)) :rule cong :premises (t104))
+(step t106 (cl (not @p_339) (not @p_336) @p_340) :rule equiv_pos2)
+(step t107 (cl @p_340) :rule th_resolution :premises (a17 t105 t106))
+(step t108 (cl (! (= @p_340 (! (and @p_337 @p_334 @p_335) :named @p_342)) :named @p_341)) :rule ac_simp)
+(step t109 (cl (not @p_341) (not @p_340) @p_342) :rule equiv_pos2)
+(step t110 (cl @p_342) :rule th_resolution :premises (t107 t108 t109))
+(anchor :step t111 :args ((:= (veriT_vr56 Int_real_real_real_prod_fun_prod$) veriT_vr57)))
+(step t111.t1 (cl (! (= veriT_vr56 veriT_vr57) :named @p_344)) :rule refl)
+(step t111.t2 (cl (= @p_329 (! (member$ veriT_vr57 one_chain_typeII$) :named @p_343))) :rule cong :premises (t111.t1))
+(step t111.t3 (cl @p_344) :rule refl)
+(step t111.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr57) :named @p_345))) :rule cong :premises (t111.t3))
+(step t111.t5 (cl (= @p_332 (! (=> @p_343 @p_345) :named @p_346))) :rule cong :premises (t111.t2 t111.t4))
+(step t111 (cl (= @p_335 (! (forall ((veriT_vr57 Int_real_real_real_prod_fun_prod$)) @p_346) :named @p_347))) :rule bind)
+(step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111))
+(step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2)
+(step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113))
+(anchor :step t115 :args ((:= (veriT_vr56 Int_real_real_real_prod_fun_prod$) veriT_vr58)))
+(step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl)
+(step t115.t2 (cl (= @p_323 (! (member$ veriT_vr58 one_chain_typeI$) :named @p_350))) :rule cong :premises (t115.t1))
+(step t115.t3 (cl @p_351) :rule refl)
+(step t115.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr58) :named @p_352))) :rule cong :premises (t115.t3))
+(step t115.t5 (cl (= @p_327 (! (=> @p_350 @p_352) :named @p_353))) :rule cong :premises (t115.t2 t115.t4))
+(step t115 (cl (= @p_334 (! (forall ((veriT_vr58 Int_real_real_real_prod_fun_prod$)) @p_353) :named @p_358))) :rule bind)
+(anchor :step t116 :args ((:= (veriT_vr57 Int_real_real_real_prod_fun_prod$) veriT_vr59)))
+(step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl)
+(step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1))
+(step t116.t3 (cl @p_355) :rule refl)
+(step t116.t4 (cl (= @p_345 (! (case_prod$ uu$ veriT_vr59) :named @p_356))) :rule cong :premises (t116.t3))
+(step t116.t5 (cl (= @p_346 (! (=> @p_354 @p_356) :named @p_357))) :rule cong :premises (t116.t2 t116.t4))
+(step t116 (cl (= @p_347 (! (forall ((veriT_vr59 Int_real_real_real_prod_fun_prod$)) @p_357) :named @p_359))) :rule bind)
+(step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116))
+(step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2)
+(step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118))
+(anchor :step t120 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr60)))
+(step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl)
+(step t120.t2 (cl (= @p_8 (! (member$ veriT_vr60 one_chain_typeII$) :named @p_363))) :rule cong :premises (t120.t1))
+(step t120.t3 (cl @p_364) :rule refl)
+(step t120.t4 (cl (! (= @p_10 (! (case_prod$ uua$ veriT_vr60) :named @p_365)) :named @p_370)) :rule cong :premises (t120.t3))
+(step t120.t5 (cl (= @p_366 (! (=> @p_363 @p_365) :named @p_367))) :rule cong :premises (t120.t2 t120.t4))
+(step t120 (cl (= @p_362 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_367) :named @p_374))) :rule bind)
+(anchor :step t121 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr60)))
+(step t121.t1 (cl @p_364) :rule refl)
+(step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1))
+(step t121.t3 (cl @p_364) :rule refl)
+(step t121.t4 (cl @p_370) :rule cong :premises (t121.t3))
+(step t121.t5 (cl (= @p_371 (! (=> @p_369 @p_365) :named @p_372))) :rule cong :premises (t121.t2 t121.t4))
+(step t121 (cl (= @p_368 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_372) :named @p_375))) :rule bind)
+(step t122 (cl (= @p_373 (! (and @p_374 @p_375) :named @p_378))) :rule cong :premises (t120 t121))
+(step t123 (cl (! (= @p_376 (! (and @p_377 @p_378) :named @p_380)) :named @p_379)) :rule cong :premises (t122))
+(step t124 (cl (not @p_379) (not @p_376) @p_380) :rule equiv_pos2)
+(step t125 (cl @p_380) :rule th_resolution :premises (a18 t123 t124))
+(step t126 (cl (! (= @p_380 (! (and @p_377 @p_374 @p_375) :named @p_382)) :named @p_381)) :rule ac_simp)
+(step t127 (cl (not @p_381) (not @p_380) @p_382) :rule equiv_pos2)
+(step t128 (cl @p_382) :rule th_resolution :premises (t125 t126 t127))
+(anchor :step t129 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr61)))
+(step t129.t1 (cl (! (= veriT_vr60 veriT_vr61) :named @p_384)) :rule refl)
+(step t129.t2 (cl (= @p_369 (! (member$ veriT_vr61 one_chain_typeI$) :named @p_383))) :rule cong :premises (t129.t1))
+(step t129.t3 (cl @p_384) :rule refl)
+(step t129.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr61) :named @p_385))) :rule cong :premises (t129.t3))
+(step t129.t5 (cl (= @p_372 (! (=> @p_383 @p_385) :named @p_386))) :rule cong :premises (t129.t2 t129.t4))
+(step t129 (cl (= @p_375 (! (forall ((veriT_vr61 Int_real_real_real_prod_fun_prod$)) @p_386) :named @p_387))) :rule bind)
+(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129))
+(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2)
+(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131))
+(anchor :step t133 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr62)))
+(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl)
+(step t133.t2 (cl (= @p_363 (! (member$ veriT_vr62 one_chain_typeII$) :named @p_390))) :rule cong :premises (t133.t1))
+(step t133.t3 (cl @p_391) :rule refl)
+(step t133.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr62) :named @p_392))) :rule cong :premises (t133.t3))
+(step t133.t5 (cl (= @p_367 (! (=> @p_390 @p_392) :named @p_393))) :rule cong :premises (t133.t2 t133.t4))
+(step t133 (cl (= @p_374 (! (forall ((veriT_vr62 Int_real_real_real_prod_fun_prod$)) @p_393) :named @p_398))) :rule bind)
+(anchor :step t134 :args ((:= (veriT_vr61 Int_real_real_real_prod_fun_prod$) veriT_vr63)))
+(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl)
+(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1))
+(step t134.t3 (cl @p_395) :rule refl)
+(step t134.t4 (cl (= @p_385 (! (case_prod$ uua$ veriT_vr63) :named @p_396))) :rule cong :premises (t134.t3))
+(step t134.t5 (cl (= @p_386 (! (=> @p_394 @p_396) :named @p_397))) :rule cong :premises (t134.t2 t134.t4))
+(step t134 (cl (= @p_387 (! (forall ((veriT_vr63 Int_real_real_real_prod_fun_prod$)) @p_397) :named @p_399))) :rule bind)
+(step t135 (cl (! (= @p_389 (! (and @p_377 @p_398 @p_399) :named @p_401)) :named @p_400)) :rule cong :premises (t133 t134))
+(step t136 (cl (not @p_400) (not @p_389) @p_401) :rule equiv_pos2)
+(step t137 (cl @p_401) :rule th_resolution :premises (t132 t135 t136))
+(step t138 (cl @p_358) :rule and :premises (t119))
+(step t139 (cl @p_399) :rule and :premises (t137))
+(step t140 (cl (or (! (not @p_399) :named @p_422) (! (=> @p_402 (! (case_prod$ uua$ @p_403) :named @p_421)) :named @p_420))) :rule forall_inst :args ((:= veriT_vr63 @p_403)))
+(step t141 (cl (or (! (not @p_358) :named @p_427) (! (=> @p_402 (! (case_prod$ uu$ @p_403) :named @p_426)) :named @p_424))) :rule forall_inst :args ((:= veriT_vr58 @p_403)))
+(step t142 (cl (or (! (not @p_321) :named @p_406) (! (=> (! (and (! (finite$ @p_5) :named @p_415) (! (fun_app$a @p_12 g$) :named @p_409) (! (fun_app$a @p_24 g$) :named @p_408) (! (= @p_5 (! (sup$ @p_7 @p_5) :named @p_466)) :named @p_430) (! (= bot$ (inf$ @p_7 @p_5)) :named @p_431)) :named @p_429) (! (= @p_404 (! (+ @p_405 @p_404) :named @p_528)) :named @p_433)) :named @p_432))) :rule forall_inst :args ((:= veriT_vr51 @p_5) (:= veriT_vr52 f$) (:= veriT_vr53 @p_7) (:= veriT_vr54 g$) (:= veriT_vr55 @p_5)))
+(step t143 (cl (or @p_406 (! (=> (! (and (! (finite$ @p_407) :named @p_412) @p_408 @p_409 (! (= @p_407 (sup$ @p_5 @p_7)) :named @p_411) (! (= bot$ (inf$ @p_5 @p_7)) :named @p_437)) :named @p_434) @p_410) :named @p_438))) :rule forall_inst :args ((:= veriT_vr51 @p_407) (:= veriT_vr52 f$) (:= veriT_vr53 @p_5) (:= veriT_vr54 g$) (:= veriT_vr55 @p_7)))
+(step t144 (cl (or (! (not @p_249) :named @p_441) @p_411)) :rule forall_inst :args ((:= veriT_vr44 i$) (:= veriT_vr45 @p_7)))
+(step t145 (cl (or (! (not @p_230) :named @p_442) (! (= @p_407 (! (insert$ j$ @p_5) :named @p_467)) :named @p_443))) :rule forall_inst :args ((:= veriT_vr39 j$) (:= veriT_vr40 i$) (:= veriT_vr41 bot$)))
+(step t146 (cl (or (! (not @p_194) :named @p_447) (! (=> (! (member$a i$ @p_7) :named @p_445) (! (= @p_7 @p_407) :named @p_446)) :named @p_444))) :rule forall_inst :args ((:= veriT_vr32 i$) (:= veriT_vr33 @p_7)))
+(step t147 (cl (or (! (not @p_174) :named @p_413) (! (=> (! (finite$ @p_7) :named @p_416) @p_412) :named @p_448))) :rule forall_inst :args ((:= veriT_vr28 @p_7) (:= veriT_vr29 i$)))
+(step t148 (cl (or @p_413 (! (=> @p_414 @p_415) :named @p_449))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 i$)))
+(step t149 (cl (or @p_413 (! (=> @p_414 @p_416) :named @p_451))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 j$)))
+(step t150 (cl (or (! (not @p_119) :named @p_418) (! (= 0.0 (! (snd$a @p_417) :named @p_495)) :named @p_454))) :rule forall_inst :args ((:= veriT_vr18 1.0) (:= veriT_vr19 0.0)))
+(step t151 (cl (or @p_418 (! (= 1.0 (! (snd$a @p_419) :named @p_496)) :named @p_455))) :rule forall_inst :args ((:= veriT_vr18 0.0) (:= veriT_vr19 1.0)))
+(step t152 (cl (or (! (not @p_100) :named @p_456) (! (= g$ (! (snd$ @p_403) :named @p_471)) :named @p_457))) :rule forall_inst :args ((:= veriT_vr14 k$) (:= veriT_vr15 g$)))
+(step t153 (cl (or (! (not @p_84) :named @p_461) (! (=> (! (= @p_7 @p_5) :named @p_459) (! (= j$ i$) :named @p_460)) :named @p_458))) :rule forall_inst :args ((:= veriT_vr10 i$) (:= veriT_vr11 j$)))
+(step t154 (cl (! (not @p_420) :named @p_423) (! (not @p_402) :named @p_425) @p_421) :rule implies_pos)
+(step t155 (cl @p_422 @p_420) :rule or :premises (t140))
+(step t156 (cl @p_423 @p_421) :rule resolution :premises (t154 a6))
+(step t157 (cl @p_420) :rule resolution :premises (t155 t139))
+(step t158 (cl @p_421) :rule resolution :premises (t156 t157))
+(step t159 (cl (! (not @p_424) :named @p_428) @p_425 @p_426) :rule implies_pos)
+(step t160 (cl @p_427 @p_424) :rule or :premises (t141))
+(step t161 (cl @p_428 @p_426) :rule resolution :premises (t159 a6))
+(step t162 (cl @p_424) :rule resolution :premises (t160 t138))
+(step t163 (cl @p_426) :rule resolution :premises (t161 t162))
+(step t164 (cl @p_429 (not @p_415) (! (not @p_409) :named @p_436) (! (not @p_408) :named @p_435) (not @p_430) (not @p_431)) :rule and_neg)
+(step t165 (cl (not @p_432) (not @p_429) @p_433) :rule implies_pos)
+(step t166 (cl @p_406 @p_432) :rule or :premises (t142))
+(step t167 (cl @p_432) :rule resolution :premises (t166 t101))
+(step t168 (cl @p_434 (not @p_412) @p_435 @p_436 (not @p_411) (! (not @p_437) :named @p_515)) :rule and_neg)
+(step t169 (cl (! (not @p_438) :named @p_439) (! (not @p_434) :named @p_440) @p_410) :rule implies_pos)
+(step t170 (cl @p_406 @p_438) :rule or :premises (t143))
+(step t171 (cl @p_439 @p_440) :rule resolution :premises (t169 a19))
+(step t172 (cl @p_438) :rule resolution :premises (t170 t101))
+(step t173 (cl @p_440) :rule resolution :premises (t171 t172))
+(step t174 (cl @p_441 @p_411) :rule or :premises (t144))
+(step t175 (cl @p_411) :rule resolution :premises (t174 t92))
+(step t176 (cl @p_442 @p_443) :rule or :premises (t145))
+(step t177 (cl @p_443) :rule resolution :premises (t176 t86))
+(step t178 (cl (not @p_444) (! (not @p_445) :named @p_470) @p_446) :rule implies_pos)
+(step t179 (cl @p_447 @p_444) :rule or :premises (t146))
+(step t180 (cl @p_444) :rule resolution :premises (t179 t74))
+(step t181 (cl (not @p_448) (not @p_416) @p_412) :rule implies_pos)
+(step t182 (cl @p_413 @p_448) :rule or :premises (t147))
+(step t183 (cl @p_448) :rule resolution :premises (t182 t68))
+(step t184 (cl (! (not @p_449) :named @p_450) (! (not @p_414) :named @p_452) @p_415) :rule implies_pos)
+(step t185 (cl @p_413 @p_449) :rule or :premises (t148))
+(step t186 (cl @p_450 @p_415) :rule resolution :premises (t184 a8))
+(step t187 (cl @p_449) :rule resolution :premises (t185 t68))
+(step t188 (cl @p_415) :rule resolution :premises (t186 t187))
+(step t189 (cl (! (not @p_451) :named @p_453) @p_452 @p_416) :rule implies_pos)
+(step t190 (cl @p_413 @p_451) :rule or :premises (t149))
+(step t191 (cl @p_453 @p_416) :rule resolution :premises (t189 a8))
+(step t192 (cl @p_451) :rule resolution :premises (t190 t68))
+(step t193 (cl @p_416) :rule resolution :premises (t191 t192))
+(step t194 (cl @p_412) :rule resolution :premises (t181 t193 t183))
+(step t195 (cl @p_418 @p_454) :rule or :premises (t150))
+(step t196 (cl @p_454) :rule resolution :premises (t195 t56))
+(step t197 (cl @p_418 @p_455) :rule or :premises (t151))
+(step t198 (cl @p_455) :rule resolution :premises (t197 t56))
+(step t199 (cl @p_456 @p_457) :rule or :premises (t152))
+(step t200 (cl @p_457) :rule resolution :premises (t199 t50))
+(step t201 (cl (not @p_458) (! (not @p_459) :named @p_507) @p_460) :rule implies_pos)
+(step t202 (cl @p_461 @p_458) :rule or :premises (t153))
+(step t203 (cl @p_458) :rule resolution :premises (t202 t44))
+(step t204 (cl (or @p_410 (! (not (! (<= @p_462 @p_463) :named @p_534)) :named @p_464) (! (not (! (<= @p_463 @p_462) :named @p_535)) :named @p_465))) :rule la_disequality)
+(step t205 (cl @p_410 @p_464 @p_465) :rule or :premises (t204))
+(step t206 (cl @p_464 @p_465) :rule resolution :premises (t205 a19))
+(step t207 (cl (or @p_441 (! (= @p_466 @p_467) :named @p_474))) :rule forall_inst :args ((:= veriT_vr44 j$) (:= veriT_vr45 @p_5)))
+(step t208 (cl (or @p_447 (! (=> (! (member$a j$ @p_5) :named @p_468) (! (= @p_5 @p_467) :named @p_477)) :named @p_475))) :rule forall_inst :args ((:= veriT_vr32 j$) (:= veriT_vr33 @p_5)))
+(step t209 (cl (or (! (not @p_156) :named @p_469) (! (= @p_437 (! (and (! (not @p_468) :named @p_476) (! (= bot$ (inf$ @p_5 bot$)) :named @p_479)) :named @p_478)) :named @p_482))) :rule forall_inst :args ((:= veriT_vr23 @p_5) (:= veriT_vr24 j$) (:= veriT_vr25 bot$)))
+(step t210 (cl (or @p_469 (! (= @p_431 (! (and @p_470 (! (= bot$ (inf$ @p_7 bot$)) :named @p_485)) :named @p_483)) :named @p_487))) :rule forall_inst :args ((:= veriT_vr23 @p_7) (:= veriT_vr24 i$) (:= veriT_vr25 bot$)))
+(step t211 (cl (or (! (not @p_61) :named @p_472) (! (= @p_426 (! (fun_app$a (! (fun_app$ uu$ (! (fst$ @p_403) :named @p_473)) :named @p_508) @p_471) :named @p_489)) :named @p_488))) :rule forall_inst :args ((:= veriT_vr6 uu$) (:= veriT_vr7 @p_403)))
+(step t212 (cl (or @p_472 (! (= @p_421 (! (fun_app$a (! (fun_app$ uua$ @p_473) :named @p_509) @p_471) :named @p_492)) :named @p_491))) :rule forall_inst :args ((:= veriT_vr6 uua$) (:= veriT_vr7 @p_403)))
+(step t213 (cl @p_441 @p_474) :rule or :premises (t207))
+(step t214 (cl @p_474) :rule resolution :premises (t213 t92))
+(step t215 (cl (not @p_475) @p_476 @p_477) :rule implies_pos)
+(step t216 (cl @p_447 @p_475) :rule or :premises (t208))
+(step t217 (cl @p_475) :rule resolution :premises (t216 t74))
+(step t218 (cl (not (! (not @p_470) :named @p_484)) @p_445) :rule not_not)
+(step t219 (cl @p_478 (! (not @p_476) :named @p_480) (! (not @p_479) :named @p_481)) :rule and_neg)
+(step t220 (cl (not @p_480) @p_468) :rule not_not)
+(step t221 (cl @p_478 @p_468 @p_481) :rule th_resolution :premises (t220 t219))
+(step t222 (cl (not @p_482) @p_437 (! (not @p_478) :named @p_516)) :rule equiv_pos1)
+(step t223 (cl @p_469 @p_482) :rule or :premises (t209))
+(step t224 (cl @p_482) :rule resolution :premises (t223 t62))
+(step t225 (cl @p_483 @p_484 (! (not @p_485) :named @p_486)) :rule and_neg)
+(step t226 (cl @p_483 @p_445 @p_486) :rule th_resolution :premises (t218 t225))
+(step t227 (cl (not @p_487) @p_431 (not @p_483)) :rule equiv_pos1)
+(step t228 (cl @p_469 @p_487) :rule or :premises (t210))
+(step t229 (cl @p_487) :rule resolution :premises (t228 t62))
+(step t230 (cl (! (not @p_488) :named @p_490) (not @p_426) @p_489) :rule equiv_pos2)
+(step t231 (cl @p_472 @p_488) :rule or :premises (t211))
+(step t232 (cl @p_490 @p_489) :rule resolution :premises (t230 t163))
+(step t233 (cl @p_488) :rule resolution :premises (t231 t38))
+(step t234 (cl @p_489) :rule resolution :premises (t232 t233))
+(step t235 (cl (! (not @p_491) :named @p_493) (not @p_421) @p_492) :rule equiv_pos2)
+(step t236 (cl @p_472 @p_491) :rule or :premises (t212))
+(step t237 (cl @p_493 @p_492) :rule resolution :premises (t235 t158))
+(step t238 (cl @p_491) :rule resolution :premises (t236 t38))
+(step t239 (cl @p_492) :rule resolution :premises (t237 t238))
+(step t240 (cl (or (! (not @p_205) :named @p_494) @p_479)) :rule forall_inst :args ((:= veriT_vr35 @p_5)))
+(step t241 (cl (or @p_494 @p_485)) :rule forall_inst :args ((:= veriT_vr35 @p_7)))
+(step t242 (cl @p_494 @p_479) :rule or :premises (t240))
+(step t243 (cl @p_479) :rule resolution :premises (t242 t80))
+(step t244 (cl @p_494 @p_485) :rule or :premises (t241))
+(step t245 (cl @p_485) :rule resolution :premises (t244 t80))
+(step t246 (cl (! (= @p_7 @p_7) :named @p_520)) :rule eq_reflexive)
+(step t247 (cl (not (! (= 1.0 0.0) :named @p_497))) :rule la_generic :args ((- 1)))
+(step t248 (cl (! (not @p_455) :named @p_505) (not (! (= @p_495 @p_496) :named @p_498)) (! (not @p_454) :named @p_506) @p_497) :rule eq_transitive)
+(step t249 (cl (not (! (= @p_417 @p_419) :named @p_501)) @p_498) :rule eq_congruent)
+(step t250 (cl (! (not @p_499) :named @p_502) (! (not @p_460) :named @p_503) (! (not @p_500) :named @p_504) @p_501) :rule eq_transitive)
+(step t251 (cl @p_498 @p_502 @p_503 @p_504) :rule th_resolution :premises (t249 t250))
+(step t252 (cl @p_505 @p_506 @p_497 @p_502 @p_503 @p_504) :rule th_resolution :premises (t248 t251))
+(step t253 (cl @p_505 @p_506 @p_502 @p_503 @p_504) :rule th_resolution :premises (t247 t252))
+(step t254 (cl @p_503) :rule resolution :premises (t253 a10 a12 t196 t198))
+(step t255 (cl @p_507) :rule resolution :premises (t201 t254 t203))
+(step t256 (cl (! (= f$ f$) :named @p_523)) :rule eq_reflexive)
+(step t257 (cl (! (= g$ g$) :named @p_524)) :rule eq_reflexive)
+(step t258 (cl (! (= @p_405 @p_405) :named @p_527)) :rule eq_reflexive)
+(step t259 (cl (or (! (not @p_34) :named @p_510) (! (= @p_24 @p_508) :named @p_511))) :rule forall_inst :args ((:= veriT_vr3 @p_473)))
+(step t260 (cl (or (! (not @p_22) :named @p_512) (! (= @p_12 @p_509) :named @p_513))) :rule forall_inst :args ((:= veriT_vr1 @p_473)))
+(step t261 (cl @p_510 @p_511) :rule or :premises (t259))
+(step t262 (cl @p_511) :rule resolution :premises (t261 t32))
+(step t263 (cl @p_512 @p_513) :rule or :premises (t260))
+(step t264 (cl @p_513) :rule resolution :premises (t263 t26))
+(step t265 (cl (not @p_511) (! (not @p_457) :named @p_514) @p_408 (not @p_489)) :rule eq_congruent_pred)
+(step t266 (cl @p_408) :rule resolution :premises (t265 t200 t234 t262))
+(step t267 (cl (not @p_513) @p_514 @p_409 (not @p_492)) :rule eq_congruent_pred)
+(step t268 (cl @p_409) :rule resolution :premises (t267 t200 t239 t264))
+(step t269 (cl @p_515) :rule resolution :premises (t168 t268 t194 t173 t175 t266))
+(step t270 (cl @p_516) :rule resolution :premises (t222 t269 t224))
+(step t271 (cl @p_468) :rule resolution :premises (t221 t270 t243))
+(step t272 (cl @p_477) :rule resolution :premises (t215 t271 t217))
+(step t273 (cl (! (not @p_477) :named @p_517) (not @p_474) @p_430) :rule eq_transitive)
+(step t274 (cl @p_430) :rule resolution :premises (t273 t214 t272))
+(step t275 (cl @p_517 (! (not @p_443) :named @p_518) (! (= @p_5 @p_407) :named @p_519)) :rule eq_transitive)
+(step t276 (cl @p_518 @p_517 @p_519) :rule eq_transitive)
+(step t277 (cl (not @p_520) (! (not @p_446) :named @p_521) (! (not @p_519) :named @p_522) @p_459) :rule eq_transitive)
+(step t278 (cl @p_521 @p_522 @p_459) :rule th_resolution :premises (t277 t246))
+(step t279 (cl @p_521 @p_459 @p_518 @p_517) :rule th_resolution :premises (t278 t276))
+(step t280 (cl @p_521) :rule resolution :premises (t279 t177 t255 t272))
+(step t281 (cl (not @p_523) @p_522 (! (not @p_524) :named @p_525) (! (= @p_462 @p_404) :named @p_526)) :rule eq_congruent)
+(step t282 (cl @p_522 @p_525 @p_526) :rule th_resolution :premises (t281 t256))
+(step t283 (cl @p_522 @p_526) :rule th_resolution :premises (t282 t257))
+(step t284 (cl @p_526 @p_517 @p_518) :rule th_resolution :premises (t283 t275))
+(step t285 (cl @p_470) :rule resolution :premises (t178 t280 t180))
+(step t286 (cl @p_483) :rule resolution :premises (t226 t285 t245))
+(step t287 (cl @p_431) :rule resolution :premises (t227 t286 t229))
+(step t288 (cl @p_429) :rule resolution :premises (t164 t287 t188 t266 t268 t274))
+(step t289 (cl @p_433) :rule resolution :premises (t165 t288 t167))
+(step t290 (cl (not @p_527) (! (not @p_526) :named @p_529) (! (= (! (+ @p_405 @p_462) :named @p_531) @p_528) :named @p_530)) :rule eq_congruent)
+(step t291 (cl @p_529 @p_530) :rule th_resolution :premises (t290 t258))
+(step t292 (cl @p_530 @p_517 @p_518) :rule th_resolution :premises (t291 t284))
+(step t293 (cl (! (not @p_433) :named @p_532) (not @p_530) (! (= @p_404 @p_531) :named @p_533)) :rule eq_transitive)
+(step t294 (cl @p_532 @p_533 @p_517 @p_518) :rule th_resolution :premises (t293 t292))
+(step t295 (cl @p_534 @p_529 (! (not @p_533) :named @p_536)) :rule la_generic :args (1.0 (- 2) (- 1)))
+(step t296 (cl @p_534 @p_517 @p_518 @p_532) :rule th_resolution :premises (t295 t284 t294))
+(step t297 (cl @p_534) :rule resolution :premises (t296 t289 t177 t272))
+(step t298 (cl @p_465) :rule resolution :premises (t206 t297))
+(step t299 (cl @p_535 @p_529 @p_536) :rule la_generic :args (1.0 2 1))
+(step t300 (cl @p_535 @p_517 @p_518 @p_532) :rule th_resolution :premises (t299 t284 t294))
+(step t301 (cl) :rule resolution :premises (t300 t289 t177 t298 t272))
+a5b152c08be1e0a4da353f094af8f11f36a16f52 333 0
+unsat
+(assume a0 (not x0$))
+(assume a1 (not x30$))
+(assume a2 (not x29$))
+(assume a3 (not x59$))
+(assume a4 (! (or x1$ (or x31$ x0$)) :named @p_57))
+(assume a6 (! (or x3$ (or x33$ x2$)) :named @p_60))
+(assume a7 (! (or x4$ (or x34$ x3$)) :named @p_63))
+(assume a8 (or x35$ x4$))
+(assume a9 (! (or x5$ (or x36$ x30$)) :named @p_66))
+(assume a11 (! (or x7$ (or x38$ (or x6$ x32$))) :named @p_69))
+(assume a13 (! (or x9$ (or x40$ (or x8$ x34$))) :named @p_72))
+(assume a16 (! (or x11$ (or x43$ (or x10$ x37$))) :named @p_75))
+(assume a18 (! (or x13$ (or x45$ (or x12$ x39$))) :named @p_78))
+(assume a20 (! (or x47$ (or x14$ x41$)) :named @p_81))
+(assume a21 (! (or x15$ (or x48$ x42$)) :named @p_84))
+(assume a23 (! (or x17$ (or x50$ (or x16$ x44$))) :named @p_87))
+(assume a25 (! (or x19$ (or x52$ (or x18$ x46$))) :named @p_90))
+(assume a28 (! (or x21$ (or x55$ (or x20$ x49$))) :named @p_93))
+(assume a30 (! (or x23$ (or x57$ (or x22$ x51$))) :named @p_96))
+(assume a32 (! (or x59$ (or x24$ x53$)) :named @p_99))
+(assume a33 (or x25$ x54$))
+(assume a35 (! (or x27$ (or x26$ x56$)) :named @p_102))
+(assume a37 (! (or x29$ (or x28$ x58$)) :named @p_105))
+(assume a41 (or (! (not x2$) :named @p_1) (! (not x32$) :named @p_2)))
+(assume a42 (or @p_1 (! (not x1$) :named @p_3)))
+(assume a43 (or @p_2 @p_3))
+(assume a47 (or (! (not x4$) :named @p_4) (! (not x34$) :named @p_5)))
+(assume a48 (or @p_4 (! (not x3$) :named @p_6)))
+(assume a49 (or @p_5 @p_6))
+(assume a54 (or (! (not x6$) :named @p_7) (! (not x37$) :named @p_8)))
+(assume a55 (or @p_7 (! (not x5$) :named @p_9)))
+(assume a56 (or @p_7 (! (not x31$) :named @p_10)))
+(assume a57 (or @p_8 @p_9))
+(assume a58 (or @p_8 @p_10))
+(assume a59 (or @p_9 @p_10))
+(assume a63 (or (! (not x38$) :named @p_11) @p_7))
+(assume a64 (or @p_11 @p_2))
+(assume a66 (or (! (not x8$) :named @p_12) (! (not x39$) :named @p_13)))
+(assume a67 (or @p_12 (! (not x7$) :named @p_14)))
+(assume a68 (or @p_12 (! (not x33$) :named @p_15)))
+(assume a69 (or @p_13 @p_14))
+(assume a70 (or @p_13 @p_15))
+(assume a71 (or @p_14 @p_15))
+(assume a78 (or (! (not x41$) :named @p_16) (! (not x9$) :named @p_17)))
+(assume a79 (or @p_16 (! (not x35$) :named @p_18)))
+(assume a80 (or @p_17 @p_18))
+(assume a81 (or (! (not x10$) :named @p_19) (! (not x42$) :named @p_20)))
+(assume a82 (or @p_19 (! (not x36$) :named @p_21)))
+(assume a83 (or @p_20 @p_21))
+(assume a90 (or (! (not x12$) :named @p_22) (! (not x44$) :named @p_23)))
+(assume a91 (or @p_22 (! (not x11$) :named @p_24)))
+(assume a92 (or @p_22 @p_11))
+(assume a93 (or @p_23 @p_24))
+(assume a94 (or @p_23 @p_11))
+(assume a95 (or @p_24 @p_11))
+(assume a99 (or (! (not x45$) :named @p_25) @p_22))
+(assume a100 (or @p_25 @p_13))
+(assume a102 (or (! (not x14$) :named @p_26) (! (not x46$) :named @p_27)))
+(assume a103 (or @p_26 (! (not x13$) :named @p_28)))
+(assume a104 (or @p_26 (! (not x40$) :named @p_29)))
+(assume a105 (or @p_27 @p_28))
+(assume a106 (or @p_27 @p_29))
+(assume a107 (or @p_28 @p_29))
+(assume a113 (or (! (not x48$) :named @p_41) @p_20))
+(assume a114 (or (! (not x16$) :named @p_30) (! (not x49$) :named @p_31)))
+(assume a115 (or @p_30 (! (not x15$) :named @p_32)))
+(assume a116 (or @p_30 (! (not x43$) :named @p_33)))
+(assume a117 (or @p_31 @p_32))
+(assume a118 (or @p_31 @p_33))
+(assume a119 (or @p_32 @p_33))
+(assume a126 (or (! (not x18$) :named @p_34) (! (not x51$) :named @p_35)))
+(assume a127 (or @p_34 (! (not x17$) :named @p_36)))
+(assume a128 (or @p_34 @p_25))
+(assume a129 (or @p_35 @p_36))
+(assume a130 (or @p_35 @p_25))
+(assume a131 (or @p_36 @p_25))
+(assume a134 (or (! (not x19$) :named @p_37) @p_27))
+(assume a138 (or (! (not x53$) :named @p_38) @p_37))
+(assume a139 (or @p_38 (! (not x47$) :named @p_39)))
+(assume a140 (or @p_37 @p_39))
+(assume a141 (or (! (not x20$) :named @p_40) (! (not x54$) :named @p_42)))
+(assume a142 (or @p_40 @p_41))
+(assume a143 (or @p_42 @p_41))
+(assume a150 (or (! (not x22$) :named @p_43) (! (not x56$) :named @p_44)))
+(assume a151 (or @p_43 (! (not x21$) :named @p_45)))
+(assume a152 (or @p_43 (! (not x50$) :named @p_46)))
+(assume a153 (or @p_44 @p_45))
+(assume a154 (or @p_44 @p_46))
+(assume a155 (or @p_45 @p_46))
+(assume a162 (or (! (not x24$) :named @p_47) (! (not x58$) :named @p_48)))
+(assume a163 (or @p_47 (! (not x23$) :named @p_49)))
+(assume a164 (or @p_47 (! (not x52$) :named @p_50)))
+(assume a165 (or @p_48 @p_49))
+(assume a166 (or @p_48 @p_50))
+(assume a167 (or @p_49 @p_50))
+(assume a172 (or (! (not x26$) :named @p_51) (! (not x25$) :named @p_52)))
+(assume a173 (or @p_51 (! (not x55$) :named @p_53)))
+(assume a174 (or @p_52 @p_53))
+(assume a178 (or (! (not x28$) :named @p_54) (! (not x27$) :named @p_55)))
+(assume a179 (or @p_54 (! (not x57$) :named @p_56)))
+(assume a180 (or @p_55 @p_56))
 (step t102 (cl (! (= @p_57 (! (or x1$ x31$ x0$) :named @p_59)) :named @p_58)) :rule ac_simp)
 (step t103 (cl (not @p_58) (not @p_57) @p_59) :rule equiv_pos2)
-(step t104 (cl @p_59) :rule th_resolution :premises (axiom4 t102 t103))
+(step t104 (cl @p_59) :rule th_resolution :premises (a4 t102 t103))
 (step t105 (cl (! (= @p_60 (! (or x3$ x33$ x2$) :named @p_62)) :named @p_61)) :rule ac_simp)
 (step t106 (cl (not @p_61) (not @p_60) @p_62) :rule equiv_pos2)
-(step t107 (cl @p_62) :rule th_resolution :premises (axiom6 t105 t106))
+(step t107 (cl @p_62) :rule th_resolution :premises (a6 t105 t106))
 (step t108 (cl (! (= @p_63 (! (or x4$ x34$ x3$) :named @p_65)) :named @p_64)) :rule ac_simp)
 (step t109 (cl (not @p_64) (not @p_63) @p_65) :rule equiv_pos2)
-(step t110 (cl @p_65) :rule th_resolution :premises (axiom7 t108 t109))
+(step t110 (cl @p_65) :rule th_resolution :premises (a7 t108 t109))
 (step t111 (cl (! (= @p_66 (! (or x5$ x36$ x30$) :named @p_68)) :named @p_67)) :rule ac_simp)
 (step t112 (cl (not @p_67) (not @p_66) @p_68) :rule equiv_pos2)
-(step t113 (cl @p_68) :rule th_resolution :premises (axiom9 t111 t112))
+(step t113 (cl @p_68) :rule th_resolution :premises (a9 t111 t112))
 (step t114 (cl (! (= @p_69 (! (or x7$ x38$ x6$ x32$) :named @p_71)) :named @p_70)) :rule ac_simp)
 (step t115 (cl (not @p_70) (not @p_69) @p_71) :rule equiv_pos2)
-(step t116 (cl @p_71) :rule th_resolution :premises (axiom11 t114 t115))
+(step t116 (cl @p_71) :rule th_resolution :premises (a11 t114 t115))
 (step t117 (cl (! (= @p_72 (! (or x9$ x40$ x8$ x34$) :named @p_74)) :named @p_73)) :rule ac_simp)
 (step t118 (cl (not @p_73) (not @p_72) @p_74) :rule equiv_pos2)
-(step t119 (cl @p_74) :rule th_resolution :premises (axiom13 t117 t118))
+(step t119 (cl @p_74) :rule th_resolution :premises (a13 t117 t118))
 (step t120 (cl (! (= @p_75 (! (or x11$ x43$ x10$ x37$) :named @p_77)) :named @p_76)) :rule ac_simp)
 (step t121 (cl (not @p_76) (not @p_75) @p_77) :rule equiv_pos2)
-(step t122 (cl @p_77) :rule th_resolution :premises (axiom16 t120 t121))
+(step t122 (cl @p_77) :rule th_resolution :premises (a16 t120 t121))
 (step t123 (cl (! (= @p_78 (! (or x13$ x45$ x12$ x39$) :named @p_80)) :named @p_79)) :rule ac_simp)
 (step t124 (cl (not @p_79) (not @p_78) @p_80) :rule equiv_pos2)
-(step t125 (cl @p_80) :rule th_resolution :premises (axiom18 t123 t124))
+(step t125 (cl @p_80) :rule th_resolution :premises (a18 t123 t124))
 (step t126 (cl (! (= @p_81 (! (or x47$ x14$ x41$) :named @p_83)) :named @p_82)) :rule ac_simp)
 (step t127 (cl (not @p_82) (not @p_81) @p_83) :rule equiv_pos2)
-(step t128 (cl @p_83) :rule th_resolution :premises (axiom20 t126 t127))
+(step t128 (cl @p_83) :rule th_resolution :premises (a20 t126 t127))
 (step t129 (cl (! (= @p_84 (! (or x15$ x48$ x42$) :named @p_86)) :named @p_85)) :rule ac_simp)
 (step t130 (cl (not @p_85) (not @p_84) @p_86) :rule equiv_pos2)
-(step t131 (cl @p_86) :rule th_resolution :premises (axiom21 t129 t130))
+(step t131 (cl @p_86) :rule th_resolution :premises (a21 t129 t130))
 (step t132 (cl (! (= @p_87 (! (or x17$ x50$ x16$ x44$) :named @p_89)) :named @p_88)) :rule ac_simp)
 (step t133 (cl (not @p_88) (not @p_87) @p_89) :rule equiv_pos2)
-(step t134 (cl @p_89) :rule th_resolution :premises (axiom23 t132 t133))
+(step t134 (cl @p_89) :rule th_resolution :premises (a23 t132 t133))
 (step t135 (cl (! (= @p_90 (! (or x19$ x52$ x18$ x46$) :named @p_92)) :named @p_91)) :rule ac_simp)
 (step t136 (cl (not @p_91) (not @p_90) @p_92) :rule equiv_pos2)
-(step t137 (cl @p_92) :rule th_resolution :premises (axiom25 t135 t136))
+(step t137 (cl @p_92) :rule th_resolution :premises (a25 t135 t136))
 (step t138 (cl (! (= @p_93 (! (or x21$ x55$ x20$ x49$) :named @p_95)) :named @p_94)) :rule ac_simp)
 (step t139 (cl (not @p_94) (not @p_93) @p_95) :rule equiv_pos2)
-(step t140 (cl @p_95) :rule th_resolution :premises (axiom28 t138 t139))
+(step t140 (cl @p_95) :rule th_resolution :premises (a28 t138 t139))
 (step t141 (cl (! (= @p_96 (! (or x23$ x57$ x22$ x51$) :named @p_98)) :named @p_97)) :rule ac_simp)
 (step t142 (cl (not @p_97) (not @p_96) @p_98) :rule equiv_pos2)
-(step t143 (cl @p_98) :rule th_resolution :premises (axiom30 t141 t142))
+(step t143 (cl @p_98) :rule th_resolution :premises (a30 t141 t142))
 (step t144 (cl (! (= @p_99 (! (or x59$ x24$ x53$) :named @p_101)) :named @p_100)) :rule ac_simp)
 (step t145 (cl (not @p_100) (not @p_99) @p_101) :rule equiv_pos2)
-(step t146 (cl @p_101) :rule th_resolution :premises (axiom32 t144 t145))
+(step t146 (cl @p_101) :rule th_resolution :premises (a32 t144 t145))
 (step t147 (cl (! (= @p_102 (! (or x27$ x26$ x56$) :named @p_104)) :named @p_103)) :rule ac_simp)
 (step t148 (cl (not @p_103) (not @p_102) @p_104) :rule equiv_pos2)
-(step t149 (cl @p_104) :rule th_resolution :premises (axiom35 t147 t148))
+(step t149 (cl @p_104) :rule th_resolution :premises (a35 t147 t148))
 (step t150 (cl (! (= @p_105 (! (or x29$ x28$ x58$) :named @p_107)) :named @p_106)) :rule ac_simp)
 (step t151 (cl (not @p_106) (not @p_105) @p_107) :rule equiv_pos2)
-(step t152 (cl @p_107) :rule th_resolution :premises (axiom37 t150 t151))
+(step t152 (cl @p_107) :rule th_resolution :premises (a37 t150 t151))
 (step t153 (cl x1$ x31$ x0$) :rule or :premises (t104))
-(step t154 (cl x1$ x31$) :rule resolution :premises (t153 axiom0))
+(step t154 (cl x1$ x31$) :rule resolution :premises (t153 a0))
 (step t155 (cl x3$ x33$ x2$) :rule or :premises (t107))
 (step t156 (cl x4$ x34$ x3$) :rule or :premises (t110))
-(step t157 (cl x35$ x4$) :rule or :premises (axiom8))
+(step t157 (cl x35$ x4$) :rule or :premises (a8))
 (step t158 (cl x5$ x36$ x30$) :rule or :premises (t113))
-(step t159 (cl x5$ x36$) :rule resolution :premises (t158 axiom1))
+(step t159 (cl x5$ x36$) :rule resolution :premises (t158 a1))
 (step t160 (cl x7$ x38$ x6$ x32$) :rule or :premises (t116))
 (step t161 (cl x9$ x40$ x8$ x34$) :rule or :premises (t119))
 (step t162 (cl x11$ x43$ x10$ x37$) :rule or :premises (t122))
@@ -382,89 +1037,89 @@
 (step t168 (cl x21$ x55$ x20$ x49$) :rule or :premises (t140))
 (step t169 (cl x23$ x57$ x22$ x51$) :rule or :premises (t143))
 (step t170 (cl x59$ x24$ x53$) :rule or :premises (t146))
-(step t171 (cl x24$ x53$) :rule resolution :premises (t170 axiom3))
-(step t172 (cl x25$ x54$) :rule or :premises (axiom33))
+(step t171 (cl x24$ x53$) :rule resolution :premises (t170 a3))
+(step t172 (cl x25$ x54$) :rule or :premises (a33))
 (step t173 (cl x27$ x26$ x56$) :rule or :premises (t149))
 (step t174 (cl x29$ x28$ x58$) :rule or :premises (t152))
-(step t175 (cl x28$ x58$) :rule resolution :premises (t174 axiom2))
-(step t176 (cl @p_1 @p_2) :rule or :premises (axiom41))
-(step t177 (cl @p_1 @p_3) :rule or :premises (axiom42))
-(step t178 (cl @p_2 @p_3) :rule or :premises (axiom43))
-(step t179 (cl @p_4 @p_5) :rule or :premises (axiom47))
-(step t180 (cl @p_4 @p_6) :rule or :premises (axiom48))
-(step t181 (cl @p_5 @p_6) :rule or :premises (axiom49))
-(step t182 (cl @p_7 @p_8) :rule or :premises (axiom54))
-(step t183 (cl @p_7 @p_9) :rule or :premises (axiom55))
-(step t184 (cl @p_7 @p_10) :rule or :premises (axiom56))
-(step t185 (cl @p_8 @p_9) :rule or :premises (axiom57))
-(step t186 (cl @p_8 @p_10) :rule or :premises (axiom58))
-(step t187 (cl @p_9 @p_10) :rule or :premises (axiom59))
-(step t188 (cl @p_11 @p_7) :rule or :premises (axiom63))
-(step t189 (cl @p_11 @p_2) :rule or :premises (axiom64))
-(step t190 (cl @p_12 @p_13) :rule or :premises (axiom66))
-(step t191 (cl @p_12 @p_14) :rule or :premises (axiom67))
-(step t192 (cl @p_12 @p_15) :rule or :premises (axiom68))
-(step t193 (cl @p_13 @p_14) :rule or :premises (axiom69))
-(step t194 (cl @p_13 @p_15) :rule or :premises (axiom70))
-(step t195 (cl @p_14 @p_15) :rule or :premises (axiom71))
-(step t196 (cl @p_16 @p_17) :rule or :premises (axiom78))
-(step t197 (cl @p_16 @p_18) :rule or :premises (axiom79))
-(step t198 (cl @p_17 @p_18) :rule or :premises (axiom80))
-(step t199 (cl @p_19 @p_20) :rule or :premises (axiom81))
-(step t200 (cl @p_19 @p_21) :rule or :premises (axiom82))
-(step t201 (cl @p_20 @p_21) :rule or :premises (axiom83))
-(step t202 (cl @p_22 @p_23) :rule or :premises (axiom90))
-(step t203 (cl @p_22 @p_24) :rule or :premises (axiom91))
-(step t204 (cl @p_22 @p_11) :rule or :premises (axiom92))
-(step t205 (cl @p_23 @p_24) :rule or :premises (axiom93))
-(step t206 (cl @p_23 @p_11) :rule or :premises (axiom94))
-(step t207 (cl @p_24 @p_11) :rule or :premises (axiom95))
-(step t208 (cl @p_25 @p_22) :rule or :premises (axiom99))
-(step t209 (cl @p_25 @p_13) :rule or :premises (axiom100))
-(step t210 (cl @p_26 @p_27) :rule or :premises (axiom102))
-(step t211 (cl @p_26 @p_28) :rule or :premises (axiom103))
-(step t212 (cl @p_26 @p_29) :rule or :premises (axiom104))
-(step t213 (cl @p_27 @p_28) :rule or :premises (axiom105))
-(step t214 (cl @p_27 @p_29) :rule or :premises (axiom106))
-(step t215 (cl @p_28 @p_29) :rule or :premises (axiom107))
-(step t216 (cl @p_41 @p_20) :rule or :premises (axiom113))
-(step t217 (cl @p_30 @p_31) :rule or :premises (axiom114))
-(step t218 (cl @p_30 @p_32) :rule or :premises (axiom115))
-(step t219 (cl @p_30 @p_33) :rule or :premises (axiom116))
-(step t220 (cl @p_31 @p_32) :rule or :premises (axiom117))
-(step t221 (cl @p_31 @p_33) :rule or :premises (axiom118))
-(step t222 (cl @p_32 @p_33) :rule or :premises (axiom119))
-(step t223 (cl @p_34 @p_35) :rule or :premises (axiom126))
-(step t224 (cl @p_34 @p_36) :rule or :premises (axiom127))
-(step t225 (cl @p_34 @p_25) :rule or :premises (axiom128))
-(step t226 (cl @p_35 @p_36) :rule or :premises (axiom129))
-(step t227 (cl @p_35 @p_25) :rule or :premises (axiom130))
-(step t228 (cl @p_36 @p_25) :rule or :premises (axiom131))
-(step t229 (cl @p_37 @p_27) :rule or :premises (axiom134))
-(step t230 (cl @p_38 @p_37) :rule or :premises (axiom138))
-(step t231 (cl @p_38 @p_39) :rule or :premises (axiom139))
-(step t232 (cl @p_37 @p_39) :rule or :premises (axiom140))
-(step t233 (cl @p_40 @p_42) :rule or :premises (axiom141))
-(step t234 (cl @p_40 @p_41) :rule or :premises (axiom142))
-(step t235 (cl @p_42 @p_41) :rule or :premises (axiom143))
-(step t236 (cl @p_43 @p_44) :rule or :premises (axiom150))
-(step t237 (cl @p_43 @p_45) :rule or :premises (axiom151))
-(step t238 (cl @p_43 @p_46) :rule or :premises (axiom152))
-(step t239 (cl @p_44 @p_45) :rule or :premises (axiom153))
-(step t240 (cl @p_44 @p_46) :rule or :premises (axiom154))
-(step t241 (cl @p_45 @p_46) :rule or :premises (axiom155))
-(step t242 (cl @p_47 @p_48) :rule or :premises (axiom162))
-(step t243 (cl @p_47 @p_49) :rule or :premises (axiom163))
-(step t244 (cl @p_47 @p_50) :rule or :premises (axiom164))
-(step t245 (cl @p_48 @p_49) :rule or :premises (axiom165))
-(step t246 (cl @p_48 @p_50) :rule or :premises (axiom166))
-(step t247 (cl @p_49 @p_50) :rule or :premises (axiom167))
-(step t248 (cl @p_51 @p_52) :rule or :premises (axiom172))
-(step t249 (cl @p_51 @p_53) :rule or :premises (axiom173))
-(step t250 (cl @p_52 @p_53) :rule or :premises (axiom174))
-(step t251 (cl @p_54 @p_55) :rule or :premises (axiom178))
-(step t252 (cl @p_54 @p_56) :rule or :premises (axiom179))
-(step t253 (cl @p_55 @p_56) :rule or :premises (axiom180))
+(step t175 (cl x28$ x58$) :rule resolution :premises (t174 a2))
+(step t176 (cl @p_1 @p_2) :rule or :premises (a41))
+(step t177 (cl @p_1 @p_3) :rule or :premises (a42))
+(step t178 (cl @p_2 @p_3) :rule or :premises (a43))
+(step t179 (cl @p_4 @p_5) :rule or :premises (a47))
+(step t180 (cl @p_4 @p_6) :rule or :premises (a48))
+(step t181 (cl @p_5 @p_6) :rule or :premises (a49))
+(step t182 (cl @p_7 @p_8) :rule or :premises (a54))
+(step t183 (cl @p_7 @p_9) :rule or :premises (a55))
+(step t184 (cl @p_7 @p_10) :rule or :premises (a56))
+(step t185 (cl @p_8 @p_9) :rule or :premises (a57))
+(step t186 (cl @p_8 @p_10) :rule or :premises (a58))
+(step t187 (cl @p_9 @p_10) :rule or :premises (a59))
+(step t188 (cl @p_11 @p_7) :rule or :premises (a63))
+(step t189 (cl @p_11 @p_2) :rule or :premises (a64))
+(step t190 (cl @p_12 @p_13) :rule or :premises (a66))
+(step t191 (cl @p_12 @p_14) :rule or :premises (a67))
+(step t192 (cl @p_12 @p_15) :rule or :premises (a68))
+(step t193 (cl @p_13 @p_14) :rule or :premises (a69))
+(step t194 (cl @p_13 @p_15) :rule or :premises (a70))
+(step t195 (cl @p_14 @p_15) :rule or :premises (a71))
+(step t196 (cl @p_16 @p_17) :rule or :premises (a78))
+(step t197 (cl @p_16 @p_18) :rule or :premises (a79))
+(step t198 (cl @p_17 @p_18) :rule or :premises (a80))
+(step t199 (cl @p_19 @p_20) :rule or :premises (a81))
+(step t200 (cl @p_19 @p_21) :rule or :premises (a82))
+(step t201 (cl @p_20 @p_21) :rule or :premises (a83))
+(step t202 (cl @p_22 @p_23) :rule or :premises (a90))
+(step t203 (cl @p_22 @p_24) :rule or :premises (a91))
+(step t204 (cl @p_22 @p_11) :rule or :premises (a92))
+(step t205 (cl @p_23 @p_24) :rule or :premises (a93))
+(step t206 (cl @p_23 @p_11) :rule or :premises (a94))
+(step t207 (cl @p_24 @p_11) :rule or :premises (a95))
+(step t208 (cl @p_25 @p_22) :rule or :premises (a99))
+(step t209 (cl @p_25 @p_13) :rule or :premises (a100))
+(step t210 (cl @p_26 @p_27) :rule or :premises (a102))
+(step t211 (cl @p_26 @p_28) :rule or :premises (a103))
+(step t212 (cl @p_26 @p_29) :rule or :premises (a104))
+(step t213 (cl @p_27 @p_28) :rule or :premises (a105))
+(step t214 (cl @p_27 @p_29) :rule or :premises (a106))
+(step t215 (cl @p_28 @p_29) :rule or :premises (a107))
+(step t216 (cl @p_41 @p_20) :rule or :premises (a113))
+(step t217 (cl @p_30 @p_31) :rule or :premises (a114))
+(step t218 (cl @p_30 @p_32) :rule or :premises (a115))
+(step t219 (cl @p_30 @p_33) :rule or :premises (a116))
+(step t220 (cl @p_31 @p_32) :rule or :premises (a117))
+(step t221 (cl @p_31 @p_33) :rule or :premises (a118))
+(step t222 (cl @p_32 @p_33) :rule or :premises (a119))
+(step t223 (cl @p_34 @p_35) :rule or :premises (a126))
+(step t224 (cl @p_34 @p_36) :rule or :premises (a127))
+(step t225 (cl @p_34 @p_25) :rule or :premises (a128))
+(step t226 (cl @p_35 @p_36) :rule or :premises (a129))
+(step t227 (cl @p_35 @p_25) :rule or :premises (a130))
+(step t228 (cl @p_36 @p_25) :rule or :premises (a131))
+(step t229 (cl @p_37 @p_27) :rule or :premises (a134))
+(step t230 (cl @p_38 @p_37) :rule or :premises (a138))
+(step t231 (cl @p_38 @p_39) :rule or :premises (a139))
+(step t232 (cl @p_37 @p_39) :rule or :premises (a140))
+(step t233 (cl @p_40 @p_42) :rule or :premises (a141))
+(step t234 (cl @p_40 @p_41) :rule or :premises (a142))
+(step t235 (cl @p_42 @p_41) :rule or :premises (a143))
+(step t236 (cl @p_43 @p_44) :rule or :premises (a150))
+(step t237 (cl @p_43 @p_45) :rule or :premises (a151))
+(step t238 (cl @p_43 @p_46) :rule or :premises (a152))
+(step t239 (cl @p_44 @p_45) :rule or :premises (a153))
+(step t240 (cl @p_44 @p_46) :rule or :premises (a154))
+(step t241 (cl @p_45 @p_46) :rule or :premises (a155))
+(step t242 (cl @p_47 @p_48) :rule or :premises (a162))
+(step t243 (cl @p_47 @p_49) :rule or :premises (a163))
+(step t244 (cl @p_47 @p_50) :rule or :premises (a164))
+(step t245 (cl @p_48 @p_49) :rule or :premises (a165))
+(step t246 (cl @p_48 @p_50) :rule or :premises (a166))
+(step t247 (cl @p_49 @p_50) :rule or :premises (a167))
+(step t248 (cl @p_51 @p_52) :rule or :premises (a172))
+(step t249 (cl @p_51 @p_53) :rule or :premises (a173))
+(step t250 (cl @p_52 @p_53) :rule or :premises (a174))
+(step t251 (cl @p_54 @p_55) :rule or :premises (a178))
+(step t252 (cl @p_54 @p_56) :rule or :premises (a179))
+(step t253 (cl @p_55 @p_56) :rule or :premises (a180))
 (step t254 (cl x48$ x47$ @p_27) :rule resolution :premises (t222 t165 t162 t201 t200 t207 t159 t160 t187 t186 t184 t154 t177 t176 t155 t192 t191 t161 t180 t179 t157 t197 t196 t164 t214 t210))
 (step t255 (cl x47$ x45$ x12$ x38$ @p_9) :rule resolution :premises (t196 t161 t164 t181 t215 t211 t155 t163 t195 t193 t191 t160 t178 t177 t154 t187 t183))
 (step t256 (cl x47$ x45$ x17$ x50$ @p_32) :rule resolution :premises (t196 t161 t164 t181 t215 t211 t155 t163 t195 t193 t191 t160 t178 t177 t154 t186 t182 t162 t200 t159 t255 t206 t205 t202 t166 t222 t218))
@@ -544,11 +1199,11 @@
 (step t330 (cl x36$) :rule resolution :premises (t159 t328))
 (step t331 (cl x42$) :rule resolution :premises (t287 t329))
 (step t332 (cl) :rule resolution :premises (t201 t330 t331))
-5895c6070af96c275f3f46cd6f9c0ddc1803c656 64 0
+a73b15b00e6e103b31fc48e963d878be9038a417 64 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (! (=> (! (p$ veriT_vr2) :named @p_20) (! (forall ((veriT_vr3 Int)) (! (or @p_20 (! (p$ veriT_vr3) :named @p_24)) :named @p_25)) :named @p_21)) :named @p_26))) :named @p_33))
 (define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (or (p$ @p_33) @p_24))) :named @p_37))
-(assume axiom0 (! (not (! (forall ((?v0 Int)) (! (=> (! (p$ ?v0) :named @p_1) (! (forall ((?v1 Int)) (! (or @p_1 (! (p$ ?v1) :named @p_8)) :named @p_10)) :named @p_4)) :named @p_12)) :named @p_2)) :named @p_14))
+(assume a0 (! (not (! (forall ((?v0 Int)) (! (=> (! (p$ ?v0) :named @p_1) (! (forall ((?v1 Int)) (! (or @p_1 (! (p$ ?v1) :named @p_8)) :named @p_10)) :named @p_4)) :named @p_12)) :named @p_2)) :named @p_14))
 (anchor :step t2 :args ((:= (?v0 Int) veriT_vr0)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
 (step t2.t2 (cl (! (= @p_1 (! (p$ veriT_vr0) :named @p_3)) :named @p_7)) :rule cong :premises (t2.t1))
@@ -565,7 +1220,7 @@
 (step t4 (cl (! (not @p_16) :named @p_19) (! (not @p_14) :named @p_18) @p_17) :rule equiv_pos2)
 (step t5 (cl (not @p_18) @p_2) :rule not_not)
 (step t6 (cl @p_19 @p_2 @p_17) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_17) :rule th_resolution :premises (axiom0 t3 t6))
+(step t7 (cl @p_17) :rule th_resolution :premises (a0 t3 t6))
 (anchor :step t8 :args ((:= (veriT_vr0 Int) veriT_vr2)))
 (step t8.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_22)) :rule refl)
 (step t8.t2 (cl (! (= @p_3 @p_20) :named @p_23)) :rule cong :premises (t8.t1))
@@ -609,13 +1264,13 @@
 (step t26 (cl @p_48) :rule and :premises (t24))
 (step t27 (cl (not @p_32)) :rule not_or :premises (t26))
 (step t28 (cl) :rule resolution :premises (t27 t25))
-92a1094a80c0dcb33184d755df79398cf322af19 155 0
+9024ca3fa3536be727200e6a5ffc1df778e7e505 155 0
 unsat
 (define-fun veriT_sk0 () A$ (! (choice ((veriT_vr3 A$)) (! (ite x$ (! (p$ true veriT_vr3) :named @p_48) (! (p$ false veriT_vr3) :named @p_50)) :named @p_51)) :named @p_62))
-(assume axiom0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
-(assume axiom1 (not (= (exists ((?v0 A$)) (p$ x$ ?v0)) (p$ x$ c$))))
-(step t3 (cl (! (forall ((?v1 A$)) (! (and (! (= (! (p$ false ?v1) :named @p_2) false) :named @p_4) (! (= (! (p$ true ?v1) :named @p_7) true) :named @p_9)) :named @p_11)) :named @p_1)) :rule bfun_elim :premises (axiom0))
-(step t4 (cl (! (not (! (= (! (exists ((?v0 A$)) (! (ite x$ (! (p$ true ?v0) :named @p_27) (! (p$ false ?v0) :named @p_30)) :named @p_32)) :named @p_26) (! (ite x$ (! (p$ true c$) :named @p_91) (! (p$ false c$) :named @p_93)) :named @p_36)) :named @p_34)) :named @p_37)) :rule bfun_elim :premises (axiom1))
+(assume a0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
+(assume a1 (not (= (exists ((?v0 A$)) (p$ x$ ?v0)) (p$ x$ c$))))
+(step t3 (cl (! (forall ((?v1 A$)) (! (and (! (= (! (p$ false ?v1) :named @p_2) false) :named @p_4) (! (= (! (p$ true ?v1) :named @p_7) true) :named @p_9)) :named @p_11)) :named @p_1)) :rule bfun_elim :premises (a0))
+(step t4 (cl (! (not (! (= (! (exists ((?v0 A$)) (! (ite x$ (! (p$ true ?v0) :named @p_27) (! (p$ false ?v0) :named @p_30)) :named @p_32)) :named @p_26) (! (ite x$ (! (p$ true c$) :named @p_91) (! (p$ false c$) :named @p_93)) :named @p_36)) :named @p_34)) :named @p_37)) :rule bfun_elim :premises (a1))
 (anchor :step t5 :args ((:= (?v1 A$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v1 veriT_vr0) :named @p_6)) :rule refl)
 (step t5.t2 (cl (= @p_2 (! (p$ false veriT_vr0) :named @p_3))) :rule cong :premises (t5.t1))
@@ -765,13 +1420,13 @@
 (step t108 (cl (or @p_84 @p_92)) :rule forall_inst :args ((:= veriT_vr4 c$)))
 (step t109 (cl @p_84 @p_92) :rule or :premises (t108))
 (step t110 (cl) :rule resolution :premises (t109 t104 t107))
-811ced85456c84c67b4bd2d5cedbf22b20ed06ce 143 0
+6388f32213a8f0cba4b8bfe24dbcf79d47d5c156 143 0
 unsat
 (define-fun veriT_sk2 () A$ (! (choice ((veriT_vr9 A$)) (! (ite x$ (! (p$ true veriT_vr9) :named @p_48) (! (p$ false veriT_vr9) :named @p_50)) :named @p_51)) :named @p_62))
-(assume axiom0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
-(assume axiom2 (not (= (exists ((?v0 A$)) (p$ x$ ?v0)) (p$ x$ c$))))
-(step t3 (cl (! (forall ((?v1 A$)) (! (and (! (= (! (p$ false ?v1) :named @p_2) false) :named @p_4) (! (= (! (p$ true ?v1) :named @p_7) true) :named @p_9)) :named @p_11)) :named @p_1)) :rule bfun_elim :premises (axiom0))
-(step t4 (cl (! (not (! (= (! (exists ((?v0 A$)) (! (ite x$ (! (p$ true ?v0) :named @p_27) (! (p$ false ?v0) :named @p_30)) :named @p_32)) :named @p_26) (! (ite x$ (! (p$ true c$) :named @p_91) (p$ false c$)) :named @p_36)) :named @p_34)) :named @p_37)) :rule bfun_elim :premises (axiom2))
+(assume a0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
+(assume a2 (not (= (exists ((?v0 A$)) (p$ x$ ?v0)) (p$ x$ c$))))
+(step t3 (cl (! (forall ((?v1 A$)) (! (and (! (= (! (p$ false ?v1) :named @p_2) false) :named @p_4) (! (= (! (p$ true ?v1) :named @p_7) true) :named @p_9)) :named @p_11)) :named @p_1)) :rule bfun_elim :premises (a0))
+(step t4 (cl (! (not (! (= (! (exists ((?v0 A$)) (! (ite x$ (! (p$ true ?v0) :named @p_27) (! (p$ false ?v0) :named @p_30)) :named @p_32)) :named @p_26) (! (ite x$ (! (p$ true c$) :named @p_91) (p$ false c$)) :named @p_36)) :named @p_34)) :named @p_37)) :rule bfun_elim :premises (a2))
 (anchor :step t5 :args ((:= (?v1 A$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v1 veriT_vr0) :named @p_6)) :rule refl)
 (step t5.t2 (cl (= @p_2 (! (p$ false veriT_vr0) :named @p_3))) :rule cong :premises (t5.t1))
@@ -909,10 +1564,10 @@
 (step t96 (cl (or @p_84 @p_106)) :rule forall_inst :args ((:= veriT_vr10 c$)))
 (step t97 (cl @p_84 @p_106) :rule or :premises (t96))
 (step t98 (cl) :rule resolution :premises (t97 t94 t95))
-fa33723879319b6b43d6be3aebc3d4bf112ced6c 57 0
+8a6f5819f9bec363751118815580748c0df0e998 57 0
 unsat
-(assume axiom0 (! (ite (! (p$ x$) :named @p_2) (! (not (! (exists ((?v0 A$)) (! (p$ ?v0) :named @p_1)) :named @p_3)) :named @p_5) (! (forall ((?v0 A$)) (! (not @p_1) :named @p_10)) :named @p_7)) :named @p_12))
-(assume axiom1 (! (not (! (=> @p_2 (! (p$ y$) :named @p_35)) :named @p_39)) :named @p_34))
+(assume a0 (! (ite (! (p$ x$) :named @p_2) (! (not (! (exists ((?v0 A$)) (! (p$ ?v0) :named @p_1)) :named @p_3)) :named @p_5) (! (forall ((?v0 A$)) (! (not @p_1) :named @p_10)) :named @p_7)) :named @p_12))
+(assume a1 (! (not (! (=> @p_2 (! (p$ y$) :named @p_35)) :named @p_39)) :named @p_34))
 (anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_8)) :rule refl)
 (step t3.t2 (cl (! (= @p_1 (! (p$ veriT_vr0) :named @p_4)) :named @p_9)) :rule cong :premises (t3.t1))
@@ -925,7 +1580,7 @@
 (step t5 (cl (= @p_7 (! (forall ((veriT_vr0 A$)) @p_11) :named @p_14))) :rule bind)
 (step t6 (cl (! (= @p_12 (! (ite @p_2 @p_13 @p_14) :named @p_16)) :named @p_15)) :rule cong :premises (t4 t5))
 (step t7 (cl (not @p_15) (not @p_12) @p_16) :rule equiv_pos2)
-(step t8 (cl @p_16) :rule th_resolution :premises (axiom0 t6 t7))
+(step t8 (cl @p_16) :rule th_resolution :premises (a0 t6 t7))
 (anchor :step t9 :args ((:= (veriT_vr0 A$) veriT_vr1)))
 (step t9.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl)
 (step t9.t2 (cl (= @p_4 (! (p$ veriT_vr1) :named @p_17))) :rule cong :premises (t9.t1))
@@ -956,7 +1611,7 @@
 (step t25 (cl (! (not @p_36) :named @p_40) (! (not @p_34) :named @p_38) @p_37) :rule equiv_pos2)
 (step t26 (cl (not @p_38) @p_39) :rule not_not)
 (step t27 (cl @p_40 @p_39 @p_37) :rule th_resolution :premises (t26 t25))
-(step t28 (cl @p_37) :rule th_resolution :premises (axiom1 t24 t27))
+(step t28 (cl @p_37) :rule th_resolution :premises (a1 t24 t27))
 (step t29 (cl (= @p_31 @p_41)) :rule not_simplify)
 (step t30 (cl (! (= @p_33 (! (ite @p_2 @p_41 @p_27) :named @p_43)) :named @p_42)) :rule cong :premises (t29))
 (step t31 (cl (not @p_42) (not @p_33) @p_43) :rule equiv_pos2)
@@ -967,9 +1622,9 @@
 (step t36 (cl (or @p_30 @p_44)) :rule forall_inst :args ((:= veriT_vr2 x$)))
 (step t37 (cl @p_30 @p_44) :rule or :premises (t36))
 (step t38 (cl) :rule resolution :premises (t37 t34 t35))
-3a011b0429bfc23b05e60ee65e41832adbfa1a5a 12 0
+ccb9d5509f5273cf85143c83133df9d0fe59cf61 12 0
 unsat
-(assume axiom0 (! (not (! (= 3 3) :named @p_1)) :named @p_2))
+(assume a0 (! (not (! (= 3 3) :named @p_1)) :named @p_2))
 (step t2 (cl (= @p_1 true)) :rule eq_simplify)
 (step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
 (step t4 (cl (= @p_3 false)) :rule not_simplify)
@@ -977,12 +1632,12 @@
 (step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
 (step t7 (cl (not @p_5) @p_1) :rule not_not)
 (step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
-(step t9 (cl false) :rule th_resolution :premises (axiom0 t5 t8))
+(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
 (step t10 (cl (not false)) :rule false)
 (step t11 (cl) :rule resolution :premises (t9 t10))
-ed9c8e3326f1e52cfa128cd451ceb8afc62fa2fc 12 0
+fa126f313953bee2fb2b0380ecf176cbb28700f5 12 0
 unsat
-(assume axiom0 (! (not (! (= 3.0 3.0) :named @p_1)) :named @p_2))
+(assume a0 (! (not (! (= 3.0 3.0) :named @p_1)) :named @p_2))
 (step t2 (cl (= @p_1 true)) :rule eq_simplify)
 (step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
 (step t4 (cl (= @p_3 false)) :rule not_simplify)
@@ -990,22 +1645,12 @@
 (step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
 (step t7 (cl (not @p_5) @p_1) :rule not_not)
 (step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
-(step t9 (cl false) :rule th_resolution :premises (axiom0 t5 t8))
+(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
 (step t10 (cl (not false)) :rule false)
 (step t11 (cl) :rule resolution :premises (t9 t10))
-1702d82a39b3f9713bf57e315ab761c4a81dbe59 9 0
+2b1aff746608c673784b02123c7a44746cecbe40 15 0
 unsat
-(assume axiom0 (not (! (= (! (+ x$ (+ y$ z$)) :named @p_2) (! (+ y$ (+ z$ x$)) :named @p_3)) :named @p_1)))
-(step t2 (cl (or @p_1 (! (not (! (<= @p_2 @p_3) :named @p_6)) :named @p_4) (! (not (! (<= @p_3 @p_2) :named @p_7)) :named @p_5))) :rule la_disequality)
-(step t3 (cl @p_1 @p_4 @p_5) :rule or :premises (t2))
-(step t4 (cl @p_4 @p_5) :rule resolution :premises (t3 axiom0))
-(step t5 (cl @p_6) :rule la_generic :args (1))
-(step t6 (cl @p_5) :rule resolution :premises (t4 t5))
-(step t7 (cl @p_7) :rule la_generic :args (1))
-(step t8 (cl) :rule resolution :premises (t7 t6))
-ffb6c06c5ee6006629798f020d7438a4445f818d 15 0
-unsat
-(assume axiom0 (! (not (! (= (+ 3 1) 4) :named @p_1)) :named @p_3))
+(assume a0 (! (not (! (= (+ 3 1) 4) :named @p_1)) :named @p_3))
 (step t2 (cl @p_1) :rule sum_simplify)
 (step t3 (cl (= @p_1 (! (= 4 4) :named @p_2))) :rule cong :premises (t2))
 (step t4 (cl (= @p_2 true)) :rule eq_simplify)
@@ -1016,12 +1661,22 @@
 (step t9 (cl (! (not @p_5) :named @p_7) (! (not @p_3) :named @p_6) false) :rule equiv_pos2)
 (step t10 (cl (not @p_6) @p_1) :rule not_not)
 (step t11 (cl @p_7 @p_1 false) :rule th_resolution :premises (t10 t9))
-(step t12 (cl false) :rule th_resolution :premises (axiom0 t8 t11))
+(step t12 (cl false) :rule th_resolution :premises (a0 t8 t11))
 (step t13 (cl (not false)) :rule false)
 (step t14 (cl) :rule resolution :premises (t12 t13))
-dc0e836fbcd3ce41657a40fc20a29630682bbe52 18 0
+c6b09353a7be5ebe2570119db169d6f24068d0d9 9 0
 unsat
-(assume axiom0 (! (not (! (< 5 (! (ite (! (<= 3 8) :named @p_1) 8 3) :named @p_2)) :named @p_4)) :named @p_6))
+(assume a0 (not (! (= (! (+ x$ (+ y$ z$)) :named @p_2) (! (+ y$ (+ z$ x$)) :named @p_3)) :named @p_1)))
+(step t2 (cl (or @p_1 (! (not (! (<= @p_2 @p_3) :named @p_6)) :named @p_4) (! (not (! (<= @p_3 @p_2) :named @p_7)) :named @p_5))) :rule la_disequality)
+(step t3 (cl @p_1 @p_4 @p_5) :rule or :premises (t2))
+(step t4 (cl @p_4 @p_5) :rule resolution :premises (t3 a0))
+(step t5 (cl @p_6) :rule la_generic :args (1))
+(step t6 (cl @p_5) :rule resolution :premises (t4 t5))
+(step t7 (cl @p_7) :rule la_generic :args (1))
+(step t8 (cl) :rule resolution :premises (t7 t6))
+91dfb7793d7cbf20aa8e7b00578ee445d34e2640 18 0
+unsat
+(assume a0 (! (not (! (< 5 (! (ite (! (<= 3 8) :named @p_1) 8 3) :named @p_2)) :named @p_4)) :named @p_6))
 (step t2 (cl (= @p_1 true)) :rule comp_simplify)
 (step t3 (cl (= @p_2 (! (ite true 8 3) :named @p_3))) :rule cong :premises (t2))
 (step t4 (cl (= 8 @p_3)) :rule ite_simplify)
@@ -1035,17 +1690,17 @@
 (step t12 (cl (! (not @p_8) :named @p_10) (! (not @p_6) :named @p_9) false) :rule equiv_pos2)
 (step t13 (cl (not @p_9) @p_4) :rule not_not)
 (step t14 (cl @p_10 @p_4 false) :rule th_resolution :premises (t13 t12))
-(step t15 (cl false) :rule th_resolution :premises (axiom0 t11 t14))
+(step t15 (cl false) :rule th_resolution :premises (a0 t11 t14))
 (step t16 (cl (not false)) :rule false)
 (step t17 (cl) :rule resolution :premises (t15 t16))
-00e71b7773518acdf4ff42fd31ed0e8e2cc40c59 52 0
+97cec8dc2da703d81d93c4024dc370fb1ecba1f5 52 0
 unsat
-(assume axiom0 (! (not (! (<= (! (ite (! (< (! (+ x$ y$) :named @p_1) 0.0) :named @p_6) (! (- @p_1) :named @p_7) @p_1) :named @p_3) (+ (! (ite (! (< x$ 0.0) :named @p_8) (! (- x$) :named @p_9) x$) :named @p_4) (! (ite (! (< y$ 0.0) :named @p_10) (! (- y$) :named @p_11) y$) :named @p_5))) :named @p_15)) :named @p_2))
+(assume a0 (! (not (! (<= (! (ite (! (< (! (+ x$ y$) :named @p_1) 0.0) :named @p_6) (! (- @p_1) :named @p_7) @p_1) :named @p_3) (+ (! (ite (! (< x$ 0.0) :named @p_8) (! (- x$) :named @p_9) x$) :named @p_4) (! (ite (! (< y$ 0.0) :named @p_10) (! (- y$) :named @p_11) y$) :named @p_5))) :named @p_15)) :named @p_2))
 (step t2 (cl (! (= @p_2 (! (and (! (not (! (<= @p_3 (+ @p_4 @p_5)) :named @p_28)) :named @p_17) (! (ite @p_6 (! (= @p_7 @p_3) :named @p_20) (! (= @p_1 @p_3) :named @p_19)) :named @p_18) (! (ite @p_8 (! (= @p_9 @p_4) :named @p_23) (! (= x$ @p_4) :named @p_22)) :named @p_21) (! (ite @p_10 (! (= @p_11 @p_5) :named @p_26) (! (= y$ @p_5) :named @p_25)) :named @p_24)) :named @p_13)) :named @p_12)) :rule ite_intro)
 (step t3 (cl (! (not @p_12) :named @p_16) (! (not @p_2) :named @p_14) @p_13) :rule equiv_pos2)
 (step t4 (cl (not @p_14) @p_15) :rule not_not)
 (step t5 (cl @p_16 @p_15 @p_13) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_13) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl @p_13) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl @p_17) :rule and :premises (t6))
 (step t8 (cl @p_18) :rule and :premises (t6))
 (step t9 (cl @p_6 @p_19) :rule ite1 :premises (t8))
@@ -1091,10 +1746,10 @@
 (step t49 (cl @p_19) :rule resolution :premises (t9 t48))
 (step t50 (cl @p_28 @p_36 @p_31 @p_29 @p_34) :rule la_generic :args (1.0 2.0 1 (- 1) (- 1)))
 (step t51 (cl) :rule resolution :premises (t50 t7 t49 t45 t46 t43))
-402dc6e98a3b5a465e12e6bcdd5fca0ae68d74d8 19 0
+7769e70c7b5fc90175ef68eb5528034a2de273a9 19 0
 unsat
-(assume axiom0 (not (= (p$ (! (< 2 3) :named @p_2)) (! (p$ true) :named @p_1))))
-(step t2 (cl (! (not (! (= @p_1 (! (ite @p_2 @p_1 (! (p$ false) :named @p_4)) :named @p_3)) :named @p_6)) :named @p_8)) :rule bfun_elim :premises (axiom0))
+(assume a0 (not (= (p$ (! (< 2 3) :named @p_2)) (! (p$ true) :named @p_1))))
+(step t2 (cl (! (not (! (= @p_1 (! (ite @p_2 @p_1 (! (p$ false) :named @p_4)) :named @p_3)) :named @p_6)) :named @p_8)) :rule bfun_elim :premises (a0))
 (step t3 (cl (= @p_2 true)) :rule comp_simplify)
 (step t4 (cl (= @p_3 (! (ite true @p_1 @p_4) :named @p_5))) :rule cong :premises (t3))
 (step t5 (cl (= @p_1 @p_5)) :rule ite_simplify)
@@ -1111,9 +1766,9 @@
 (step t16 (cl false) :rule th_resolution :premises (t2 t12 t15))
 (step t17 (cl (not false)) :rule false)
 (step t18 (cl) :rule resolution :premises (t16 t17))
-ed3db2a47b567944ed8f84b91963c7783c1f6052 14 0
+8efe160efd738ec7872179ed94f190d410e1ef4b 14 0
 unsat
-(assume axiom0 (! (not (! (or (! (<= 4 (! (+ x$ 3) :named @p_1)) :named @p_2) (! (< x$ 1) :named @p_6)) :named @p_4)) :named @p_7))
+(assume a0 (! (not (! (or (! (<= 4 (! (+ x$ 3) :named @p_1)) :named @p_2) (! (< x$ 1) :named @p_6)) :named @p_4)) :named @p_7))
 (step t2 (cl (= @p_1 (! (+ 3 x$) :named @p_3))) :rule sum_simplify)
 (step t3 (cl (= @p_2 (! (<= 4 @p_3) :named @p_5))) :rule cong :premises (t2))
 (step t4 (cl (= @p_4 (! (or @p_5 @p_6) :named @p_8))) :rule cong :premises (t3))
@@ -1121,26 +1776,26 @@
 (step t6 (cl (! (not @p_9) :named @p_12) (! (not @p_7) :named @p_11) @p_10) :rule equiv_pos2)
 (step t7 (cl (not @p_11) @p_4) :rule not_not)
 (step t8 (cl @p_12 @p_4 @p_10) :rule th_resolution :premises (t7 t6))
-(step t9 (cl @p_10) :rule th_resolution :premises (axiom0 t5 t8))
+(step t9 (cl @p_10) :rule th_resolution :premises (a0 t5 t8))
 (step t10 (cl (not @p_5)) :rule not_or :premises (t9))
 (step t11 (cl (not @p_6)) :rule not_or :premises (t9))
 (step t12 (cl @p_6 @p_5) :rule la_generic :args (1 1))
 (step t13 (cl) :rule resolution :premises (t12 t10 t11))
-d2678f4fb6d818fd1c6e93a61560f2dfba8a9409 9 0
+2644c68299be3dd9fabbbba4920be4f3ffe3485b 9 0
 unsat
-(assume axiom1 (! (= y$ (! (+ x$ 4) :named @p_1)) :named @p_2))
-(assume axiom2 (not (! (< 0 (- y$ x$)) :named @p_6)))
+(assume a1 (! (= y$ (! (+ x$ 4) :named @p_1)) :named @p_2))
+(assume a2 (not (! (< 0 (- y$ x$)) :named @p_6)))
 (step t3 (cl (= @p_1 (! (+ 4 x$) :named @p_3))) :rule sum_simplify)
 (step t4 (cl (! (= @p_2 (! (= y$ @p_3) :named @p_5)) :named @p_4)) :rule cong :premises (t3))
 (step t5 (cl (not @p_4) (not @p_2) @p_5) :rule equiv_pos2)
-(step t6 (cl @p_5) :rule th_resolution :premises (axiom1 t4 t5))
+(step t6 (cl @p_5) :rule th_resolution :premises (a1 t4 t5))
 (step t7 (cl @p_6 (not @p_5)) :rule la_generic :args (1 1))
-(step t8 (cl) :rule resolution :premises (t7 t6 axiom2))
-4e88c3cf4e2da31d65e91a3805e3cea4a5a2813d 20 0
+(step t8 (cl) :rule resolution :premises (t7 t6 a2))
+478778f1172d1db195bd4eb0883b9dd6613297c3 20 0
 unsat
-(assume axiom0 (! (not (! (not (! (= (! (+ 2 2) :named @p_3) 5) :named @p_2)) :named @p_5)) :named @p_1))
+(assume a0 (! (not (! (not (! (= (! (+ 2 2) :named @p_3) 5) :named @p_2)) :named @p_5)) :named @p_1))
 (step t2 (cl (! (not @p_1) :named @p_9) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 axiom0))
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
 (step t4 (cl (= @p_3 4)) :rule sum_simplify)
 (step t5 (cl (= @p_2 (! (= 5 4) :named @p_4))) :rule cong :premises (t4))
 (step t6 (cl (= @p_4 false)) :rule eq_simplify)
@@ -1157,23 +1812,23 @@
 (step t17 (cl false) :rule th_resolution :premises (t3 t13 t16))
 (step t18 (cl @p_6) :rule false)
 (step t19 (cl) :rule resolution :premises (t17 t18))
-3bbfe9f2086fe18bc1f9eeb965fef30f8b2c9daa 6 0
+04820c02101d5d6a8a322ddf869652416ac9ae19 6 0
 unsat
-(assume axiom0 (! (< (+ (* 3 x$) (* 7 a$)) 4) :named @p_3))
-(assume axiom1 (! (< 3 (* 2 x$)) :named @p_1))
-(assume axiom2 (not (! (< a$ 0) :named @p_2)))
+(assume a0 (! (< (+ (* 3 x$) (* 7 a$)) 4) :named @p_3))
+(assume a1 (! (< 3 (* 2 x$)) :named @p_1))
+(assume a2 (not (! (< a$ 0) :named @p_2)))
 (step t4 (cl (not @p_1) @p_2 (not @p_3)) :rule la_generic :args ((div 3 2) 7 1))
-(step t5 (cl) :rule resolution :premises (t4 axiom0 axiom1 axiom2))
-dbde8d1b71dac8b258507f86acdbe195bf64b2b7 29 0
+(step t5 (cl) :rule resolution :premises (t4 a0 a1 a2))
+699e547ad956b6867c5f571d9e08d46038579011 29 0
 unsat
-(assume axiom0 (! (not (! (= (! (or (! (<= 0 (! (+ y$ (! (* (! (- 1) :named @p_14) x$) :named @p_15)) :named @p_16)) :named @p_3) (or (! (not (! (<= 0 x$) :named @p_1)) :named @p_4) @p_1)) :named @p_2) (! (not false) :named @p_7)) :named @p_5)) :named @p_8))
+(assume a0 (! (not (! (= (! (or (! (<= 0 (! (+ y$ (! (* (! (- 1) :named @p_14) x$) :named @p_15)) :named @p_16)) :named @p_3) (or (! (not (! (<= 0 x$) :named @p_1)) :named @p_4) @p_1)) :named @p_2) (! (not false) :named @p_7)) :named @p_5)) :named @p_8))
 (step t2 (cl (= @p_2 (! (or @p_3 @p_4 @p_1) :named @p_6))) :rule ac_simp)
 (step t3 (cl (= @p_5 (! (= @p_6 @p_7) :named @p_9))) :rule cong :premises (t2))
 (step t4 (cl (! (= @p_8 (! (not @p_9) :named @p_11)) :named @p_10)) :rule cong :premises (t3))
 (step t5 (cl (! (not @p_10) :named @p_13) (! (not @p_8) :named @p_12) @p_11) :rule equiv_pos2)
 (step t6 (cl (not @p_12) @p_5) :rule not_not)
 (step t7 (cl @p_13 @p_5 @p_11) :rule th_resolution :premises (t6 t5))
-(step t8 (cl @p_11) :rule th_resolution :premises (axiom0 t4 t7))
+(step t8 (cl @p_11) :rule th_resolution :premises (a0 t4 t7))
 (step t9 (cl (= @p_14 (- 1))) :rule minus_simplify)
 (step t10 (cl (= @p_15 (! (* (- 1) x$) :named @p_17))) :rule cong :premises (t9))
 (step t11 (cl (= @p_16 (! (+ y$ @p_17) :named @p_18))) :rule cong :premises (t10))
@@ -1194,37 +1849,15 @@
 (step t26 (cl false) :rule th_resolution :premises (t8 t22 t25))
 (step t27 (cl @p_7) :rule false)
 (step t28 (cl) :rule resolution :premises (t26 t27))
-d6ba634ec42000181b77274dd94c91d844cf476e 21 0
+bf46578ff4814695a5afd6f19836b2d606a6b97c 62 0
 unsat
-(assume axiom0 (! (not (! (or (! (< (! (+ x$ x$) :named @p_11) (! (+ (! (* 2.0 x$) :named @p_10) 1.0) :named @p_9)) :named @p_1) (or false @p_1)) :named @p_2)) :named @p_3))
-(step t2 (cl (= @p_2 (! (or @p_1 false) :named @p_4))) :rule ac_simp)
-(step t3 (cl (! (= @p_3 (! (not @p_4) :named @p_6)) :named @p_5)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_5) :named @p_8) (! (not @p_3) :named @p_7) @p_6) :rule equiv_pos2)
-(step t5 (cl (not @p_7) @p_2) :rule not_not)
-(step t6 (cl @p_8 @p_2 @p_6) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_6) :rule th_resolution :premises (axiom0 t3 t6))
-(step t8 (cl (= @p_9 (! (+ 1.0 @p_10) :named @p_12))) :rule sum_simplify)
-(step t9 (cl (= @p_1 (! (< @p_11 @p_12) :named @p_13))) :rule cong :premises (t8))
-(step t10 (cl (= @p_4 (! (or @p_13 false) :named @p_14))) :rule cong :premises (t9))
-(step t11 (cl (= @p_14 (! (or @p_13) :named @p_15))) :rule or_simplify)
-(step t12 (cl (= @p_15 @p_13)) :rule or_simplify)
-(step t13 (cl (= @p_4 @p_13)) :rule trans :premises (t10 t11 t12))
-(step t14 (cl (! (= @p_6 (! (not @p_13) :named @p_17)) :named @p_16)) :rule cong :premises (t13))
-(step t15 (cl (! (not @p_16) :named @p_19) (! (not @p_6) :named @p_18) @p_17) :rule equiv_pos2)
-(step t16 (cl (not @p_18) @p_4) :rule not_not)
-(step t17 (cl @p_19 @p_4 @p_17) :rule th_resolution :premises (t16 t15))
-(step t18 (cl @p_17) :rule th_resolution :premises (t7 t14 t17))
-(step t19 (cl @p_13) :rule la_tautology)
-(step t20 (cl) :rule resolution :premises (t19 t18))
-95657842b84a23b6c0020065f8c8597823332a77 62 0
-unsat
-(assume axiom0 (! (not (! (or (! (and (! (< n$ m$) :named @p_1) (! (< m$ n$a) :named @p_3)) :named @p_11) (or (! (and @p_1 (! (= m$ n$a) :named @p_6)) :named @p_12) (or (! (and (! (< n$ n$a) :named @p_8) (! (< n$a m$) :named @p_2)) :named @p_13) (or (! (and (! (= n$ n$a) :named @p_5) @p_2) :named @p_14) (or (! (and (! (= n$ m$) :named @p_4) @p_3) :named @p_15) (or (! (and @p_2 (! (< m$ n$) :named @p_7)) :named @p_16) (or (! (and @p_2 @p_4) :named @p_17) (or (! (and (! (< n$a n$) :named @p_9) @p_1) :named @p_18) (or (! (and @p_5 @p_1) :named @p_19) (or (! (and @p_6 @p_7) :named @p_20) (or (! (and @p_7 @p_8) :named @p_21) (or (! (and @p_7 @p_5) :named @p_22) (or (! (and @p_3 @p_9) :named @p_23) (or (! (and @p_4 @p_8) :named @p_24) (or (! (and @p_6 @p_9) :named @p_25) (! (and @p_6 @p_4) :named @p_26)))))))))))))))) :named @p_10)) :named @p_27))
+(assume a0 (! (not (! (or (! (and (! (< n$ m$) :named @p_1) (! (< m$ n$a) :named @p_3)) :named @p_11) (or (! (and @p_1 (! (= m$ n$a) :named @p_6)) :named @p_12) (or (! (and (! (< n$ n$a) :named @p_8) (! (< n$a m$) :named @p_2)) :named @p_13) (or (! (and (! (= n$ n$a) :named @p_5) @p_2) :named @p_14) (or (! (and (! (= n$ m$) :named @p_4) @p_3) :named @p_15) (or (! (and @p_2 (! (< m$ n$) :named @p_7)) :named @p_16) (or (! (and @p_2 @p_4) :named @p_17) (or (! (and (! (< n$a n$) :named @p_9) @p_1) :named @p_18) (or (! (and @p_5 @p_1) :named @p_19) (or (! (and @p_6 @p_7) :named @p_20) (or (! (and @p_7 @p_8) :named @p_21) (or (! (and @p_7 @p_5) :named @p_22) (or (! (and @p_3 @p_9) :named @p_23) (or (! (and @p_4 @p_8) :named @p_24) (or (! (and @p_6 @p_9) :named @p_25) (! (and @p_6 @p_4) :named @p_26)))))))))))))))) :named @p_10)) :named @p_27))
 (step t2 (cl (= @p_10 (! (or @p_11 @p_12 @p_13 @p_14 @p_15 @p_16 @p_17 @p_18 @p_19 @p_20 @p_21 @p_22 @p_23 @p_24 @p_25 @p_26) :named @p_28))) :rule ac_simp)
 (step t3 (cl (! (= @p_27 (! (not @p_28) :named @p_30)) :named @p_29)) :rule cong :premises (t2))
 (step t4 (cl (! (not @p_29) :named @p_32) (! (not @p_27) :named @p_31) @p_30) :rule equiv_pos2)
 (step t5 (cl (not @p_31) @p_10) :rule not_not)
 (step t6 (cl @p_32 @p_10 @p_30) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_30) :rule th_resolution :premises (axiom0 t3 t6))
+(step t7 (cl @p_30) :rule th_resolution :premises (a0 t3 t6))
 (step t8 (cl (not @p_11)) :rule not_or :premises (t7))
 (step t9 (cl (! (not @p_1) :named @p_33) (! (not @p_3) :named @p_38)) :rule not_and :premises (t8))
 (step t10 (cl (not @p_12)) :rule not_or :premises (t7))
@@ -1279,253 +1912,36 @@
 (step t59 (cl @p_40) :rule resolution :premises (t17 t57))
 (step t60 (cl @p_50) :rule resolution :premises (t42 t58))
 (step t61 (cl) :rule resolution :premises (t35 t59 t54 t60))
-ce9ae392bbb004278cf4005c9cdc4ec6dc2c6c3e 16 0
-unsat
-(assume axiom0 (! (not (! (not (! (exists ((?v0 Real)) false) :named @p_2)) :named @p_3)) :named @p_1))
-(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 axiom0))
-(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
-(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
-(step t8 (cl (not @p_6) @p_3) :rule not_not)
-(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
-(step t10 (cl (not @p_7) false) :rule not_not)
-(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
-(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
-(step t13 (cl false) :rule th_resolution :premises (t10 t12))
-(step t14 (cl @p_4) :rule false)
-(step t15 (cl) :rule resolution :premises (t13 t14))
-be1ac1d3f1b32c69d4c86a7bb2fc544d58daa87d 16 0
-unsat
-(assume axiom0 (! (not (! (not (! (exists ((?v0 Int)) false) :named @p_2)) :named @p_3)) :named @p_1))
-(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 axiom0))
-(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
-(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
-(step t8 (cl (not @p_6) @p_3) :rule not_not)
-(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
-(step t10 (cl (not @p_7) false) :rule not_not)
-(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
-(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
-(step t13 (cl false) :rule th_resolution :premises (t10 t12))
-(step t14 (cl @p_4) :rule false)
-(step t15 (cl) :rule resolution :premises (t13 t14))
-7c2862b95580cb7e81a355724e88267dce92987c 44 0
-unsat
-(assume axiom0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (=> (! (and (! (= 0 ?v0) :named @p_2) (! (= 1 ?v1) :named @p_4)) :named @p_6) (! (not (! (= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_1)) :named @p_14))
-(anchor :step t2 :args ((:= (?v0 Int) 0) (:= (?v1 Int) 1)))
-(step t2.t1 (cl @p_2) :rule refl)
-(step t2.t2 (cl (= @p_2 (! (= 0 0) :named @p_3))) :rule cong :premises (t2.t1))
-(step t2.t3 (cl @p_4) :rule refl)
-(step t2.t4 (cl (= @p_4 (! (= 1 1) :named @p_5))) :rule cong :premises (t2.t3))
-(step t2.t5 (cl (= @p_6 (! (and @p_3 @p_5) :named @p_7))) :rule cong :premises (t2.t2 t2.t4))
-(step t2.t6 (cl @p_2) :rule refl)
-(step t2.t7 (cl @p_4) :rule refl)
-(step t2.t8 (cl (= @p_8 (! (= 0 1) :named @p_9))) :rule cong :premises (t2.t6 t2.t7))
-(step t2.t9 (cl (= @p_10 (! (not @p_9) :named @p_11))) :rule cong :premises (t2.t8))
-(step t2.t10 (cl (= @p_12 (! (=> @p_7 @p_11) :named @p_13))) :rule cong :premises (t2.t5 t2.t9))
-(step t2 (cl (= @p_1 @p_13)) :rule onepoint)
-(step t3 (cl (! (= @p_14 (! (not @p_13) :named @p_16)) :named @p_15)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_14) :named @p_17) @p_16) :rule equiv_pos2)
-(step t5 (cl (not @p_17) @p_1) :rule not_not)
-(step t6 (cl @p_18 @p_1 @p_16) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_16) :rule th_resolution :premises (axiom0 t3 t6))
-(step t8 (cl (! (= @p_16 (! (and @p_7 (! (not @p_11) :named @p_23)) :named @p_20)) :named @p_19)) :rule bool_simplify)
-(step t9 (cl (! (not @p_19) :named @p_22) (! (not @p_16) :named @p_21) @p_20) :rule equiv_pos2)
-(step t10 (cl (not @p_21) @p_13) :rule not_not)
-(step t11 (cl @p_22 @p_13 @p_20) :rule th_resolution :premises (t10 t9))
-(step t12 (cl @p_20) :rule th_resolution :premises (t7 t8 t11))
-(step t13 (cl (! (= @p_20 (! (and @p_3 @p_5 @p_23) :named @p_25)) :named @p_24)) :rule ac_simp)
-(step t14 (cl (not @p_24) (not @p_20) @p_25) :rule equiv_pos2)
-(step t15 (cl @p_25) :rule th_resolution :premises (t12 t13 t14))
-(step t16 (cl (= @p_3 true)) :rule eq_simplify)
-(step t17 (cl (= @p_5 true)) :rule eq_simplify)
-(step t18 (cl (= @p_9 false)) :rule eq_simplify)
-(step t19 (cl (= @p_11 (! (not false) :named @p_26))) :rule cong :premises (t18))
-(step t20 (cl (= @p_26 true)) :rule not_simplify)
-(step t21 (cl (= @p_11 true)) :rule trans :premises (t19 t20))
-(step t22 (cl (= @p_23 (! (not true) :named @p_27))) :rule cong :premises (t21))
-(step t23 (cl (= @p_27 false)) :rule not_simplify)
-(step t24 (cl (= @p_23 false)) :rule trans :premises (t22 t23))
-(step t25 (cl (= @p_25 (! (and true true false) :named @p_28))) :rule cong :premises (t16 t17 t24))
-(step t26 (cl (= @p_28 (! (and false) :named @p_29))) :rule and_simplify)
-(step t27 (cl (= @p_29 false)) :rule and_simplify)
-(step t28 (cl (! (= @p_25 false) :named @p_30)) :rule trans :premises (t25 t26 t27))
-(step t29 (cl (not @p_30) (not @p_25) false) :rule equiv_pos2)
-(step t30 (cl false) :rule th_resolution :premises (t15 t28 t29))
-(step t31 (cl @p_26) :rule false)
-(step t32 (cl) :rule resolution :premises (t30 t31))
-632d72943748607b3a6a192dc119caef23e9e71d 74 0
+8bfcf7a37e6d407d5cd3eb931a35cdc0c65c7e57 21 0
 unsat
-(define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (=> (! (< veriT_vr2 veriT_vr3) :named @p_30) (! (< (! (+ 1 (! (* 2 veriT_vr2) :named @p_32)) :named @p_33) (! (* 2 veriT_vr3) :named @p_35)) :named @p_36)) :named @p_37)))) :named @p_43))
-(define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (=> (< @p_43 veriT_vr3) (< (+ 1 (* 2 @p_43)) @p_35)))) :named @p_44))
-(assume axiom0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (=> (! (< ?v0 ?v1) :named @p_2) (! (< (! (+ (! (* 2 ?v0) :named @p_5) 1) :named @p_7) (! (* 2 ?v1) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_1)) :named @p_16))
-(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
-(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
-(step t2.t2 (cl (! (= ?v1 veriT_vr1) :named @p_9)) :rule refl)
-(step t2.t3 (cl (= @p_2 (! (< veriT_vr0 veriT_vr1) :named @p_3))) :rule cong :premises (t2.t1 t2.t2))
-(step t2.t4 (cl @p_4) :rule refl)
-(step t2.t5 (cl (= @p_5 (! (* 2 veriT_vr0) :named @p_6))) :rule cong :premises (t2.t4))
-(step t2.t6 (cl (= @p_7 (! (+ @p_6 1) :named @p_8))) :rule cong :premises (t2.t5))
-(step t2.t7 (cl @p_9) :rule refl)
-(step t2.t8 (cl (= @p_10 (! (* 2 veriT_vr1) :named @p_11))) :rule cong :premises (t2.t7))
-(step t2.t9 (cl (= @p_12 (! (< @p_8 @p_11) :named @p_13))) :rule cong :premises (t2.t6 t2.t8))
-(step t2.t10 (cl (= @p_14 (! (=> @p_3 @p_13) :named @p_15))) :rule cong :premises (t2.t3 t2.t9))
-(step t2 (cl (= @p_1 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_15) :named @p_17))) :rule bind)
-(step t3 (cl (! (= @p_16 (! (not @p_17) :named @p_19)) :named @p_18)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_18) :named @p_21) (! (not @p_16) :named @p_20) @p_19) :rule equiv_pos2)
-(step t5 (cl (not @p_20) @p_1) :rule not_not)
-(step t6 (cl @p_21 @p_1 @p_19) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_19) :rule th_resolution :premises (axiom0 t3 t6))
-(anchor :step t8 :args ((veriT_vr0 Int) (veriT_vr1 Int)))
-(step t8.t1 (cl (= @p_8 (! (+ 1 @p_6) :named @p_22))) :rule sum_simplify)
-(step t8.t2 (cl (= @p_13 (! (< @p_22 @p_11) :named @p_23))) :rule cong :premises (t8.t1))
-(step t8.t3 (cl (= @p_15 (! (=> @p_3 @p_23) :named @p_24))) :rule cong :premises (t8.t2))
-(step t8 (cl (= @p_17 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_24) :named @p_25))) :rule bind)
-(step t9 (cl (! (= @p_19 (! (not @p_25) :named @p_27)) :named @p_26)) :rule cong :premises (t8))
-(step t10 (cl (! (not @p_26) :named @p_29) (! (not @p_19) :named @p_28) @p_27) :rule equiv_pos2)
-(step t11 (cl (not @p_28) @p_17) :rule not_not)
-(step t12 (cl @p_29 @p_17 @p_27) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_27) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
-(step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_31)) :rule refl)
-(step t14.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_34)) :rule refl)
-(step t14.t3 (cl (= @p_3 @p_30)) :rule cong :premises (t14.t1 t14.t2))
-(step t14.t4 (cl @p_31) :rule refl)
-(step t14.t5 (cl (= @p_6 @p_32)) :rule cong :premises (t14.t4))
-(step t14.t6 (cl (= @p_22 @p_33)) :rule cong :premises (t14.t5))
-(step t14.t7 (cl @p_34) :rule refl)
-(step t14.t8 (cl (= @p_11 @p_35)) :rule cong :premises (t14.t7))
-(step t14.t9 (cl (= @p_23 @p_36)) :rule cong :premises (t14.t6 t14.t8))
-(step t14.t10 (cl (= @p_24 @p_37)) :rule cong :premises (t14.t3 t14.t9))
-(step t14 (cl (= @p_25 (! (forall ((veriT_vr2 Int) (veriT_vr3 Int)) @p_37) :named @p_38))) :rule bind)
-(step t15 (cl (! (= @p_27 (! (not @p_38) :named @p_40)) :named @p_39)) :rule cong :premises (t14))
-(step t16 (cl (! (not @p_39) :named @p_42) (! (not @p_27) :named @p_41) @p_40) :rule equiv_pos2)
-(step t17 (cl (not @p_41) @p_25) :rule not_not)
-(step t18 (cl @p_42 @p_25 @p_40) :rule th_resolution :premises (t17 t16))
-(step t19 (cl @p_40) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
-(step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_46)) :rule refl)
-(step t20.t2 (cl (! (= veriT_vr3 veriT_sk1) :named @p_49)) :rule refl)
-(step t20.t3 (cl (= @p_30 (! (< veriT_sk0 veriT_sk1) :named @p_45))) :rule cong :premises (t20.t1 t20.t2))
-(step t20.t4 (cl @p_46) :rule refl)
-(step t20.t5 (cl (= @p_32 (! (* 2 veriT_sk0) :named @p_47))) :rule cong :premises (t20.t4))
-(step t20.t6 (cl (= @p_33 (! (+ 1 @p_47) :named @p_48))) :rule cong :premises (t20.t5))
-(step t20.t7 (cl @p_49) :rule refl)
-(step t20.t8 (cl (= @p_35 (! (* 2 veriT_sk1) :named @p_50))) :rule cong :premises (t20.t7))
-(step t20.t9 (cl (= @p_36 (! (< @p_48 @p_50) :named @p_51))) :rule cong :premises (t20.t6 t20.t8))
-(step t20.t10 (cl (= @p_37 (! (=> @p_45 @p_51) :named @p_52))) :rule cong :premises (t20.t3 t20.t9))
-(step t20 (cl (= @p_38 @p_52)) :rule sko_forall)
-(step t21 (cl (! (= @p_40 (! (not @p_52) :named @p_54)) :named @p_53)) :rule cong :premises (t20))
-(step t22 (cl (! (not @p_53) :named @p_56) (! (not @p_40) :named @p_55) @p_54) :rule equiv_pos2)
-(step t23 (cl (not @p_55) @p_38) :rule not_not)
-(step t24 (cl @p_56 @p_38 @p_54) :rule th_resolution :premises (t23 t22))
-(step t25 (cl @p_54) :rule th_resolution :premises (t19 t21 t24))
-(step t26 (cl (! (= @p_54 (! (and @p_45 (! (not @p_51) :named @p_61)) :named @p_58)) :named @p_57)) :rule bool_simplify)
-(step t27 (cl (! (not @p_57) :named @p_60) (! (not @p_54) :named @p_59) @p_58) :rule equiv_pos2)
-(step t28 (cl (not @p_59) @p_52) :rule not_not)
-(step t29 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t28 t27))
-(step t30 (cl @p_58) :rule th_resolution :premises (t25 t26 t29))
-(step t31 (cl @p_45) :rule and :premises (t30))
-(step t32 (cl @p_61) :rule and :premises (t30))
-(step t33 (cl @p_51 (not @p_45)) :rule la_generic :args ((div 1 2) 1))
-(step t34 (cl) :rule resolution :premises (t33 t31 t32))
-b3000c2a2d0d57028ec3d5228440616f9e6398d4 84 0
+(assume a0 (! (not (! (or (! (< (! (+ x$ x$) :named @p_11) (! (+ (! (* 2.0 x$) :named @p_10) 1.0) :named @p_9)) :named @p_1) (or false @p_1)) :named @p_2)) :named @p_3))
+(step t2 (cl (= @p_2 (! (or @p_1 false) :named @p_4))) :rule ac_simp)
+(step t3 (cl (! (= @p_3 (! (not @p_4) :named @p_6)) :named @p_5)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_5) :named @p_8) (! (not @p_3) :named @p_7) @p_6) :rule equiv_pos2)
+(step t5 (cl (not @p_7) @p_2) :rule not_not)
+(step t6 (cl @p_8 @p_2 @p_6) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_6) :rule th_resolution :premises (a0 t3 t6))
+(step t8 (cl (= @p_9 (! (+ 1.0 @p_10) :named @p_12))) :rule sum_simplify)
+(step t9 (cl (= @p_1 (! (< @p_11 @p_12) :named @p_13))) :rule cong :premises (t8))
+(step t10 (cl (= @p_4 (! (or @p_13 false) :named @p_14))) :rule cong :premises (t9))
+(step t11 (cl (= @p_14 (! (or @p_13) :named @p_15))) :rule or_simplify)
+(step t12 (cl (= @p_15 @p_13)) :rule or_simplify)
+(step t13 (cl (= @p_4 @p_13)) :rule trans :premises (t10 t11 t12))
+(step t14 (cl (! (= @p_6 (! (not @p_13) :named @p_17)) :named @p_16)) :rule cong :premises (t13))
+(step t15 (cl (! (not @p_16) :named @p_19) (! (not @p_6) :named @p_18) @p_17) :rule equiv_pos2)
+(step t16 (cl (not @p_18) @p_4) :rule not_not)
+(step t17 (cl @p_19 @p_4 @p_17) :rule th_resolution :premises (t16 t15))
+(step t18 (cl @p_17) :rule th_resolution :premises (t7 t14 t17))
+(step t19 (cl @p_13) :rule la_tautology)
+(step t20 (cl) :rule resolution :premises (t19 t18))
+4aba1ea4675669f505d0a9484fd751da13811782 371 0
 unsat
-(define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (or (! (< 2 (! (+ veriT_vr2 veriT_vr3) :named @p_29)) :named @p_30) (! (= 2 @p_29) :named @p_34) (! (< @p_29 2) :named @p_35)) :named @p_36)))) :named @p_42))
-(define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (or (< 2 (! (+ @p_42 veriT_vr3) :named @p_43)) (= 2 @p_43) (< @p_43 2)))) :named @p_45))
-(assume axiom0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (or (! (< 2 (! (+ ?v0 ?v1) :named @p_1)) :named @p_4) (! (or (! (= 2 @p_1) :named @p_9) (! (< @p_1 2) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2)) :named @p_17))
-(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
-(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
-(step t2.t2 (cl (! (= ?v1 veriT_vr1) :named @p_7)) :rule refl)
-(step t2.t3 (cl (! (= @p_1 (! (+ veriT_vr0 veriT_vr1) :named @p_3)) :named @p_8)) :rule cong :premises (t2.t1 t2.t2))
-(step t2.t4 (cl (= @p_4 (! (< 2 @p_3) :named @p_5))) :rule cong :premises (t2.t3))
-(step t2.t5 (cl @p_6) :rule refl)
-(step t2.t6 (cl @p_7) :rule refl)
-(step t2.t7 (cl @p_8) :rule cong :premises (t2.t5 t2.t6))
-(step t2.t8 (cl (= @p_9 (! (= 2 @p_3) :named @p_10))) :rule cong :premises (t2.t7))
-(step t2.t9 (cl @p_6) :rule refl)
-(step t2.t10 (cl @p_7) :rule refl)
-(step t2.t11 (cl @p_8) :rule cong :premises (t2.t9 t2.t10))
-(step t2.t12 (cl (= @p_11 (! (< @p_3 2) :named @p_12))) :rule cong :premises (t2.t11))
-(step t2.t13 (cl (= @p_13 (! (or @p_10 @p_12) :named @p_14))) :rule cong :premises (t2.t8 t2.t12))
-(step t2.t14 (cl (= @p_15 (! (or @p_5 @p_14) :named @p_16))) :rule cong :premises (t2.t4 t2.t13))
-(step t2 (cl (= @p_2 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_16) :named @p_18))) :rule bind)
-(step t3 (cl (! (= @p_17 (! (not @p_18) :named @p_20)) :named @p_19)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_19) :named @p_22) (! (not @p_17) :named @p_21) @p_20) :rule equiv_pos2)
-(step t5 (cl (not @p_21) @p_2) :rule not_not)
-(step t6 (cl @p_22 @p_2 @p_20) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_20) :rule th_resolution :premises (axiom0 t3 t6))
-(anchor :step t8 :args ((veriT_vr0 Int) (veriT_vr1 Int)))
-(step t8.t1 (cl (= @p_16 (! (or @p_5 @p_10 @p_12) :named @p_23))) :rule ac_simp)
-(step t8 (cl (= @p_18 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_23) :named @p_24))) :rule bind)
-(step t9 (cl (! (= @p_20 (! (not @p_24) :named @p_26)) :named @p_25)) :rule cong :premises (t8))
-(step t10 (cl (! (not @p_25) :named @p_28) (! (not @p_20) :named @p_27) @p_26) :rule equiv_pos2)
-(step t11 (cl (not @p_27) @p_18) :rule not_not)
-(step t12 (cl @p_28 @p_18 @p_26) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_26) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
-(step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_31)) :rule refl)
-(step t14.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_32)) :rule refl)
-(step t14.t3 (cl (! (= @p_3 @p_29) :named @p_33)) :rule cong :premises (t14.t1 t14.t2))
-(step t14.t4 (cl (= @p_5 @p_30)) :rule cong :premises (t14.t3))
-(step t14.t5 (cl @p_31) :rule refl)
-(step t14.t6 (cl @p_32) :rule refl)
-(step t14.t7 (cl @p_33) :rule cong :premises (t14.t5 t14.t6))
-(step t14.t8 (cl (= @p_10 @p_34)) :rule cong :premises (t14.t7))
-(step t14.t9 (cl @p_31) :rule refl)
-(step t14.t10 (cl @p_32) :rule refl)
-(step t14.t11 (cl @p_33) :rule cong :premises (t14.t9 t14.t10))
-(step t14.t12 (cl (= @p_12 @p_35)) :rule cong :premises (t14.t11))
-(step t14.t13 (cl (= @p_23 @p_36)) :rule cong :premises (t14.t4 t14.t8 t14.t12))
-(step t14 (cl (= @p_24 (! (forall ((veriT_vr2 Int) (veriT_vr3 Int)) @p_36) :named @p_37))) :rule bind)
-(step t15 (cl (! (= @p_26 (! (not @p_37) :named @p_39)) :named @p_38)) :rule cong :premises (t14))
-(step t16 (cl (! (not @p_38) :named @p_41) (! (not @p_26) :named @p_40) @p_39) :rule equiv_pos2)
-(step t17 (cl (not @p_40) @p_24) :rule not_not)
-(step t18 (cl @p_41 @p_24 @p_39) :rule th_resolution :premises (t17 t16))
-(step t19 (cl @p_39) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
-(step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_47)) :rule refl)
-(step t20.t2 (cl (! (= veriT_vr3 veriT_sk1) :named @p_48)) :rule refl)
-(step t20.t3 (cl (! (= @p_29 (! (+ veriT_sk0 veriT_sk1) :named @p_44)) :named @p_49)) :rule cong :premises (t20.t1 t20.t2))
-(step t20.t4 (cl (= @p_30 (! (< 2 @p_44) :named @p_46))) :rule cong :premises (t20.t3))
-(step t20.t5 (cl @p_47) :rule refl)
-(step t20.t6 (cl @p_48) :rule refl)
-(step t20.t7 (cl @p_49) :rule cong :premises (t20.t5 t20.t6))
-(step t20.t8 (cl (= @p_34 (! (= 2 @p_44) :named @p_50))) :rule cong :premises (t20.t7))
-(step t20.t9 (cl @p_47) :rule refl)
-(step t20.t10 (cl @p_48) :rule refl)
-(step t20.t11 (cl @p_49) :rule cong :premises (t20.t9 t20.t10))
-(step t20.t12 (cl (= @p_35 (! (< @p_44 2) :named @p_51))) :rule cong :premises (t20.t11))
-(step t20.t13 (cl (= @p_36 (! (or @p_46 @p_50 @p_51) :named @p_52))) :rule cong :premises (t20.t4 t20.t8 t20.t12))
-(step t20 (cl (= @p_37 @p_52)) :rule sko_forall)
-(step t21 (cl (! (= @p_39 (! (not @p_52) :named @p_54)) :named @p_53)) :rule cong :premises (t20))
-(step t22 (cl (! (not @p_53) :named @p_56) (! (not @p_39) :named @p_55) @p_54) :rule equiv_pos2)
-(step t23 (cl (not @p_55) @p_37) :rule not_not)
-(step t24 (cl @p_56 @p_37 @p_54) :rule th_resolution :premises (t23 t22))
-(step t25 (cl @p_54) :rule th_resolution :premises (t19 t21 t24))
-(step t26 (cl (not @p_46)) :rule not_or :premises (t25))
-(step t27 (cl (not @p_50)) :rule not_or :premises (t25))
-(step t28 (cl (not @p_51)) :rule not_or :premises (t25))
-(step t29 (cl (or @p_50 (! (not (! (<= 2 @p_44) :named @p_59)) :named @p_57) (! (not (! (<= @p_44 2) :named @p_60)) :named @p_58))) :rule la_disequality)
-(step t30 (cl @p_50 @p_57 @p_58) :rule or :premises (t29))
-(step t31 (cl @p_57 @p_58) :rule resolution :premises (t30 t27))
-(step t32 (cl @p_59 @p_51) :rule la_generic :args (1 1))
-(step t33 (cl @p_59) :rule resolution :premises (t32 t28))
-(step t34 (cl @p_58) :rule resolution :premises (t31 t33))
-(step t35 (cl @p_60 @p_46) :rule la_generic :args (1 1))
-(step t36 (cl) :rule resolution :premises (t35 t26 t34))
-ea93df392983d8a481a89ee529b9a9f976280447 371 0
-unsat
-(assume axiom0 (! (not (! (=> (! (and (! (= x3$ (- (! (ite (! (< x2$ 0) :named @p_30) (! (- x2$) :named @p_31) x2$) :named @p_21) x1$)) :named @p_9) (and (! (= x4$ (- (! (ite (! (< x3$ 0) :named @p_32) (! (- x3$) :named @p_33) x3$) :named @p_22) x2$)) :named @p_10) (and (! (= x5$ (- (! (ite (! (< x4$ 0) :named @p_34) (! (- x4$) :named @p_35) x4$) :named @p_23) x3$)) :named @p_11) (and (! (= x6$ (- (! (ite (! (< x5$ 0) :named @p_36) (! (- x5$) :named @p_37) x5$) :named @p_24) x4$)) :named @p_12) (and (! (= x7$ (- (! (ite (! (< x6$ 0) :named @p_38) (! (- x6$) :named @p_39) x6$) :named @p_25) x5$)) :named @p_13) (and (! (= x8$ (- (! (ite (! (< x7$ 0) :named @p_40) (! (- x7$) :named @p_41) x7$) :named @p_26) x6$)) :named @p_14) (and (! (= x9$ (- (! (ite (! (< x8$ 0) :named @p_42) (! (- x8$) :named @p_43) x8$) :named @p_27) x7$)) :named @p_15) (and (! (= x10$ (- (! (ite (! (< x9$ 0) :named @p_44) (! (- x9$) :named @p_45) x9$) :named @p_28) x8$)) :named @p_16) (! (= x11$ (- (! (ite (! (< x10$ 0) :named @p_46) (! (- x10$) :named @p_47) x10$) :named @p_29) x9$)) :named @p_17))))))))) :named @p_2) (! (and (! (= x1$ x10$) :named @p_70) (! (= x2$ x11$) :named @p_71)) :named @p_3)) :named @p_7)) :named @p_1))
+(assume a0 (! (not (! (=> (! (and (! (= x3$ (- (! (ite (! (< x2$ 0) :named @p_30) (! (- x2$) :named @p_31) x2$) :named @p_21) x1$)) :named @p_9) (and (! (= x4$ (- (! (ite (! (< x3$ 0) :named @p_32) (! (- x3$) :named @p_33) x3$) :named @p_22) x2$)) :named @p_10) (and (! (= x5$ (- (! (ite (! (< x4$ 0) :named @p_34) (! (- x4$) :named @p_35) x4$) :named @p_23) x3$)) :named @p_11) (and (! (= x6$ (- (! (ite (! (< x5$ 0) :named @p_36) (! (- x5$) :named @p_37) x5$) :named @p_24) x4$)) :named @p_12) (and (! (= x7$ (- (! (ite (! (< x6$ 0) :named @p_38) (! (- x6$) :named @p_39) x6$) :named @p_25) x5$)) :named @p_13) (and (! (= x8$ (- (! (ite (! (< x7$ 0) :named @p_40) (! (- x7$) :named @p_41) x7$) :named @p_26) x6$)) :named @p_14) (and (! (= x9$ (- (! (ite (! (< x8$ 0) :named @p_42) (! (- x8$) :named @p_43) x8$) :named @p_27) x7$)) :named @p_15) (and (! (= x10$ (- (! (ite (! (< x9$ 0) :named @p_44) (! (- x9$) :named @p_45) x9$) :named @p_28) x8$)) :named @p_16) (! (= x11$ (- (! (ite (! (< x10$ 0) :named @p_46) (! (- x10$) :named @p_47) x10$) :named @p_29) x9$)) :named @p_17))))))))) :named @p_2) (! (and (! (= x1$ x10$) :named @p_70) (! (= x2$ x11$) :named @p_71)) :named @p_3)) :named @p_7)) :named @p_1))
 (step t2 (cl (! (= @p_1 (! (and @p_2 (! (not @p_3) :named @p_18)) :named @p_5)) :named @p_4)) :rule bool_simplify)
 (step t3 (cl (! (not @p_4) :named @p_8) (! (not @p_1) :named @p_6) @p_5) :rule equiv_pos2)
 (step t4 (cl (not @p_6) @p_7) :rule not_not)
 (step t5 (cl @p_8 @p_7 @p_5) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_5) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl @p_5) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl (! (= @p_5 (! (and @p_9 @p_10 @p_11 @p_12 @p_13 @p_14 @p_15 @p_16 @p_17 @p_18) :named @p_20)) :named @p_19)) :rule ac_simp)
 (step t8 (cl (not @p_19) (not @p_5) @p_20) :rule equiv_pos2)
 (step t9 (cl @p_20) :rule th_resolution :premises (t6 t7 t8))
@@ -1890,10 +2306,249 @@
 (step t368 (cl @p_74) :rule resolution :premises (t31 t367))
 (step t369 (cl @p_140) :rule resolution :premises (t107 t367 t368 t365))
 (step t370 (cl) :rule resolution :premises (t243 t368 t327 t326 t366 t308 t369))
-eddc1b21e40e4136745e32bdb4d4d38dda531d49 67 0
+3982a32a09aa6c7a103906438cf1f4eedfd441ab 16 0
+unsat
+(assume a0 (! (not (! (not (! (exists ((?v0 Int)) false) :named @p_2)) :named @p_3)) :named @p_1))
+(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
+(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
+(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
+(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
+(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
+(step t8 (cl (not @p_6) @p_3) :rule not_not)
+(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
+(step t10 (cl (not @p_7) false) :rule not_not)
+(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
+(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
+(step t13 (cl false) :rule th_resolution :premises (t10 t12))
+(step t14 (cl @p_4) :rule false)
+(step t15 (cl) :rule resolution :premises (t13 t14))
+74d9e4df0e27627f80a8b0c06331b33d5f261c17 16 0
+unsat
+(assume a0 (! (not (! (not (! (exists ((?v0 Real)) false) :named @p_2)) :named @p_3)) :named @p_1))
+(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
+(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
+(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
+(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
+(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
+(step t8 (cl (not @p_6) @p_3) :rule not_not)
+(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
+(step t10 (cl (not @p_7) false) :rule not_not)
+(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
+(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
+(step t13 (cl false) :rule th_resolution :premises (t10 t12))
+(step t14 (cl @p_4) :rule false)
+(step t15 (cl) :rule resolution :premises (t13 t14))
+17b588accea82f232f85c0c80edac2592c83c741 44 0
+unsat
+(assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (=> (! (and (! (= 0 ?v0) :named @p_2) (! (= 1 ?v1) :named @p_4)) :named @p_6) (! (not (! (= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_1)) :named @p_14))
+(anchor :step t2 :args ((:= (?v0 Int) 0) (:= (?v1 Int) 1)))
+(step t2.t1 (cl @p_2) :rule refl)
+(step t2.t2 (cl (= @p_2 (! (= 0 0) :named @p_3))) :rule cong :premises (t2.t1))
+(step t2.t3 (cl @p_4) :rule refl)
+(step t2.t4 (cl (= @p_4 (! (= 1 1) :named @p_5))) :rule cong :premises (t2.t3))
+(step t2.t5 (cl (= @p_6 (! (and @p_3 @p_5) :named @p_7))) :rule cong :premises (t2.t2 t2.t4))
+(step t2.t6 (cl @p_2) :rule refl)
+(step t2.t7 (cl @p_4) :rule refl)
+(step t2.t8 (cl (= @p_8 (! (= 0 1) :named @p_9))) :rule cong :premises (t2.t6 t2.t7))
+(step t2.t9 (cl (= @p_10 (! (not @p_9) :named @p_11))) :rule cong :premises (t2.t8))
+(step t2.t10 (cl (= @p_12 (! (=> @p_7 @p_11) :named @p_13))) :rule cong :premises (t2.t5 t2.t9))
+(step t2 (cl (= @p_1 @p_13)) :rule onepoint)
+(step t3 (cl (! (= @p_14 (! (not @p_13) :named @p_16)) :named @p_15)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_14) :named @p_17) @p_16) :rule equiv_pos2)
+(step t5 (cl (not @p_17) @p_1) :rule not_not)
+(step t6 (cl @p_18 @p_1 @p_16) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_16) :rule th_resolution :premises (a0 t3 t6))
+(step t8 (cl (! (= @p_16 (! (and @p_7 (! (not @p_11) :named @p_23)) :named @p_20)) :named @p_19)) :rule bool_simplify)
+(step t9 (cl (! (not @p_19) :named @p_22) (! (not @p_16) :named @p_21) @p_20) :rule equiv_pos2)
+(step t10 (cl (not @p_21) @p_13) :rule not_not)
+(step t11 (cl @p_22 @p_13 @p_20) :rule th_resolution :premises (t10 t9))
+(step t12 (cl @p_20) :rule th_resolution :premises (t7 t8 t11))
+(step t13 (cl (! (= @p_20 (! (and @p_3 @p_5 @p_23) :named @p_25)) :named @p_24)) :rule ac_simp)
+(step t14 (cl (not @p_24) (not @p_20) @p_25) :rule equiv_pos2)
+(step t15 (cl @p_25) :rule th_resolution :premises (t12 t13 t14))
+(step t16 (cl (= @p_3 true)) :rule eq_simplify)
+(step t17 (cl (= @p_5 true)) :rule eq_simplify)
+(step t18 (cl (= @p_9 false)) :rule eq_simplify)
+(step t19 (cl (= @p_11 (! (not false) :named @p_26))) :rule cong :premises (t18))
+(step t20 (cl (= @p_26 true)) :rule not_simplify)
+(step t21 (cl (= @p_11 true)) :rule trans :premises (t19 t20))
+(step t22 (cl (= @p_23 (! (not true) :named @p_27))) :rule cong :premises (t21))
+(step t23 (cl (= @p_27 false)) :rule not_simplify)
+(step t24 (cl (= @p_23 false)) :rule trans :premises (t22 t23))
+(step t25 (cl (= @p_25 (! (and true true false) :named @p_28))) :rule cong :premises (t16 t17 t24))
+(step t26 (cl (= @p_28 (! (and false) :named @p_29))) :rule and_simplify)
+(step t27 (cl (= @p_29 false)) :rule and_simplify)
+(step t28 (cl (! (= @p_25 false) :named @p_30)) :rule trans :premises (t25 t26 t27))
+(step t29 (cl (not @p_30) (not @p_25) false) :rule equiv_pos2)
+(step t30 (cl false) :rule th_resolution :premises (t15 t28 t29))
+(step t31 (cl @p_26) :rule false)
+(step t32 (cl) :rule resolution :premises (t30 t31))
+126e26a1f138f1b616eeae4aad01c11068cd71e0 74 0
+unsat
+(define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (=> (! (< veriT_vr2 veriT_vr3) :named @p_30) (! (< (! (+ 1 (! (* 2 veriT_vr2) :named @p_32)) :named @p_33) (! (* 2 veriT_vr3) :named @p_35)) :named @p_36)) :named @p_37)))) :named @p_43))
+(define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (=> (< @p_43 veriT_vr3) (< (+ 1 (* 2 @p_43)) @p_35)))) :named @p_44))
+(assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (=> (! (< ?v0 ?v1) :named @p_2) (! (< (! (+ (! (* 2 ?v0) :named @p_5) 1) :named @p_7) (! (* 2 ?v1) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_1)) :named @p_16))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
+(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
+(step t2.t2 (cl (! (= ?v1 veriT_vr1) :named @p_9)) :rule refl)
+(step t2.t3 (cl (= @p_2 (! (< veriT_vr0 veriT_vr1) :named @p_3))) :rule cong :premises (t2.t1 t2.t2))
+(step t2.t4 (cl @p_4) :rule refl)
+(step t2.t5 (cl (= @p_5 (! (* 2 veriT_vr0) :named @p_6))) :rule cong :premises (t2.t4))
+(step t2.t6 (cl (= @p_7 (! (+ @p_6 1) :named @p_8))) :rule cong :premises (t2.t5))
+(step t2.t7 (cl @p_9) :rule refl)
+(step t2.t8 (cl (= @p_10 (! (* 2 veriT_vr1) :named @p_11))) :rule cong :premises (t2.t7))
+(step t2.t9 (cl (= @p_12 (! (< @p_8 @p_11) :named @p_13))) :rule cong :premises (t2.t6 t2.t8))
+(step t2.t10 (cl (= @p_14 (! (=> @p_3 @p_13) :named @p_15))) :rule cong :premises (t2.t3 t2.t9))
+(step t2 (cl (= @p_1 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_15) :named @p_17))) :rule bind)
+(step t3 (cl (! (= @p_16 (! (not @p_17) :named @p_19)) :named @p_18)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_18) :named @p_21) (! (not @p_16) :named @p_20) @p_19) :rule equiv_pos2)
+(step t5 (cl (not @p_20) @p_1) :rule not_not)
+(step t6 (cl @p_21 @p_1 @p_19) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_19) :rule th_resolution :premises (a0 t3 t6))
+(anchor :step t8 :args ((veriT_vr0 Int) (veriT_vr1 Int)))
+(step t8.t1 (cl (= @p_8 (! (+ 1 @p_6) :named @p_22))) :rule sum_simplify)
+(step t8.t2 (cl (= @p_13 (! (< @p_22 @p_11) :named @p_23))) :rule cong :premises (t8.t1))
+(step t8.t3 (cl (= @p_15 (! (=> @p_3 @p_23) :named @p_24))) :rule cong :premises (t8.t2))
+(step t8 (cl (= @p_17 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_24) :named @p_25))) :rule bind)
+(step t9 (cl (! (= @p_19 (! (not @p_25) :named @p_27)) :named @p_26)) :rule cong :premises (t8))
+(step t10 (cl (! (not @p_26) :named @p_29) (! (not @p_19) :named @p_28) @p_27) :rule equiv_pos2)
+(step t11 (cl (not @p_28) @p_17) :rule not_not)
+(step t12 (cl @p_29 @p_17 @p_27) :rule th_resolution :premises (t11 t10))
+(step t13 (cl @p_27) :rule th_resolution :premises (t7 t9 t12))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
+(step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_31)) :rule refl)
+(step t14.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_34)) :rule refl)
+(step t14.t3 (cl (= @p_3 @p_30)) :rule cong :premises (t14.t1 t14.t2))
+(step t14.t4 (cl @p_31) :rule refl)
+(step t14.t5 (cl (= @p_6 @p_32)) :rule cong :premises (t14.t4))
+(step t14.t6 (cl (= @p_22 @p_33)) :rule cong :premises (t14.t5))
+(step t14.t7 (cl @p_34) :rule refl)
+(step t14.t8 (cl (= @p_11 @p_35)) :rule cong :premises (t14.t7))
+(step t14.t9 (cl (= @p_23 @p_36)) :rule cong :premises (t14.t6 t14.t8))
+(step t14.t10 (cl (= @p_24 @p_37)) :rule cong :premises (t14.t3 t14.t9))
+(step t14 (cl (= @p_25 (! (forall ((veriT_vr2 Int) (veriT_vr3 Int)) @p_37) :named @p_38))) :rule bind)
+(step t15 (cl (! (= @p_27 (! (not @p_38) :named @p_40)) :named @p_39)) :rule cong :premises (t14))
+(step t16 (cl (! (not @p_39) :named @p_42) (! (not @p_27) :named @p_41) @p_40) :rule equiv_pos2)
+(step t17 (cl (not @p_41) @p_25) :rule not_not)
+(step t18 (cl @p_42 @p_25 @p_40) :rule th_resolution :premises (t17 t16))
+(step t19 (cl @p_40) :rule th_resolution :premises (t13 t15 t18))
+(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
+(step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_46)) :rule refl)
+(step t20.t2 (cl (! (= veriT_vr3 veriT_sk1) :named @p_49)) :rule refl)
+(step t20.t3 (cl (= @p_30 (! (< veriT_sk0 veriT_sk1) :named @p_45))) :rule cong :premises (t20.t1 t20.t2))
+(step t20.t4 (cl @p_46) :rule refl)
+(step t20.t5 (cl (= @p_32 (! (* 2 veriT_sk0) :named @p_47))) :rule cong :premises (t20.t4))
+(step t20.t6 (cl (= @p_33 (! (+ 1 @p_47) :named @p_48))) :rule cong :premises (t20.t5))
+(step t20.t7 (cl @p_49) :rule refl)
+(step t20.t8 (cl (= @p_35 (! (* 2 veriT_sk1) :named @p_50))) :rule cong :premises (t20.t7))
+(step t20.t9 (cl (= @p_36 (! (< @p_48 @p_50) :named @p_51))) :rule cong :premises (t20.t6 t20.t8))
+(step t20.t10 (cl (= @p_37 (! (=> @p_45 @p_51) :named @p_52))) :rule cong :premises (t20.t3 t20.t9))
+(step t20 (cl (= @p_38 @p_52)) :rule sko_forall)
+(step t21 (cl (! (= @p_40 (! (not @p_52) :named @p_54)) :named @p_53)) :rule cong :premises (t20))
+(step t22 (cl (! (not @p_53) :named @p_56) (! (not @p_40) :named @p_55) @p_54) :rule equiv_pos2)
+(step t23 (cl (not @p_55) @p_38) :rule not_not)
+(step t24 (cl @p_56 @p_38 @p_54) :rule th_resolution :premises (t23 t22))
+(step t25 (cl @p_54) :rule th_resolution :premises (t19 t21 t24))
+(step t26 (cl (! (= @p_54 (! (and @p_45 (! (not @p_51) :named @p_61)) :named @p_58)) :named @p_57)) :rule bool_simplify)
+(step t27 (cl (! (not @p_57) :named @p_60) (! (not @p_54) :named @p_59) @p_58) :rule equiv_pos2)
+(step t28 (cl (not @p_59) @p_52) :rule not_not)
+(step t29 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t28 t27))
+(step t30 (cl @p_58) :rule th_resolution :premises (t25 t26 t29))
+(step t31 (cl @p_45) :rule and :premises (t30))
+(step t32 (cl @p_61) :rule and :premises (t30))
+(step t33 (cl @p_51 (not @p_45)) :rule la_generic :args ((div 1 2) 1))
+(step t34 (cl) :rule resolution :premises (t33 t31 t32))
+8ef63c3af9accda70a9adb945698c9dc83c299cb 84 0
+unsat
+(define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (or (! (< 2 (! (+ veriT_vr2 veriT_vr3) :named @p_29)) :named @p_30) (! (= 2 @p_29) :named @p_34) (! (< @p_29 2) :named @p_35)) :named @p_36)))) :named @p_42))
+(define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (or (< 2 (! (+ @p_42 veriT_vr3) :named @p_43)) (= 2 @p_43) (< @p_43 2)))) :named @p_45))
+(assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (or (! (< 2 (! (+ ?v0 ?v1) :named @p_1)) :named @p_4) (! (or (! (= 2 @p_1) :named @p_9) (! (< @p_1 2) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2)) :named @p_17))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
+(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
+(step t2.t2 (cl (! (= ?v1 veriT_vr1) :named @p_7)) :rule refl)
+(step t2.t3 (cl (! (= @p_1 (! (+ veriT_vr0 veriT_vr1) :named @p_3)) :named @p_8)) :rule cong :premises (t2.t1 t2.t2))
+(step t2.t4 (cl (= @p_4 (! (< 2 @p_3) :named @p_5))) :rule cong :premises (t2.t3))
+(step t2.t5 (cl @p_6) :rule refl)
+(step t2.t6 (cl @p_7) :rule refl)
+(step t2.t7 (cl @p_8) :rule cong :premises (t2.t5 t2.t6))
+(step t2.t8 (cl (= @p_9 (! (= 2 @p_3) :named @p_10))) :rule cong :premises (t2.t7))
+(step t2.t9 (cl @p_6) :rule refl)
+(step t2.t10 (cl @p_7) :rule refl)
+(step t2.t11 (cl @p_8) :rule cong :premises (t2.t9 t2.t10))
+(step t2.t12 (cl (= @p_11 (! (< @p_3 2) :named @p_12))) :rule cong :premises (t2.t11))
+(step t2.t13 (cl (= @p_13 (! (or @p_10 @p_12) :named @p_14))) :rule cong :premises (t2.t8 t2.t12))
+(step t2.t14 (cl (= @p_15 (! (or @p_5 @p_14) :named @p_16))) :rule cong :premises (t2.t4 t2.t13))
+(step t2 (cl (= @p_2 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_16) :named @p_18))) :rule bind)
+(step t3 (cl (! (= @p_17 (! (not @p_18) :named @p_20)) :named @p_19)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_19) :named @p_22) (! (not @p_17) :named @p_21) @p_20) :rule equiv_pos2)
+(step t5 (cl (not @p_21) @p_2) :rule not_not)
+(step t6 (cl @p_22 @p_2 @p_20) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_20) :rule th_resolution :premises (a0 t3 t6))
+(anchor :step t8 :args ((veriT_vr0 Int) (veriT_vr1 Int)))
+(step t8.t1 (cl (= @p_16 (! (or @p_5 @p_10 @p_12) :named @p_23))) :rule ac_simp)
+(step t8 (cl (= @p_18 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_23) :named @p_24))) :rule bind)
+(step t9 (cl (! (= @p_20 (! (not @p_24) :named @p_26)) :named @p_25)) :rule cong :premises (t8))
+(step t10 (cl (! (not @p_25) :named @p_28) (! (not @p_20) :named @p_27) @p_26) :rule equiv_pos2)
+(step t11 (cl (not @p_27) @p_18) :rule not_not)
+(step t12 (cl @p_28 @p_18 @p_26) :rule th_resolution :premises (t11 t10))
+(step t13 (cl @p_26) :rule th_resolution :premises (t7 t9 t12))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
+(step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_31)) :rule refl)
+(step t14.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_32)) :rule refl)
+(step t14.t3 (cl (! (= @p_3 @p_29) :named @p_33)) :rule cong :premises (t14.t1 t14.t2))
+(step t14.t4 (cl (= @p_5 @p_30)) :rule cong :premises (t14.t3))
+(step t14.t5 (cl @p_31) :rule refl)
+(step t14.t6 (cl @p_32) :rule refl)
+(step t14.t7 (cl @p_33) :rule cong :premises (t14.t5 t14.t6))
+(step t14.t8 (cl (= @p_10 @p_34)) :rule cong :premises (t14.t7))
+(step t14.t9 (cl @p_31) :rule refl)
+(step t14.t10 (cl @p_32) :rule refl)
+(step t14.t11 (cl @p_33) :rule cong :premises (t14.t9 t14.t10))
+(step t14.t12 (cl (= @p_12 @p_35)) :rule cong :premises (t14.t11))
+(step t14.t13 (cl (= @p_23 @p_36)) :rule cong :premises (t14.t4 t14.t8 t14.t12))
+(step t14 (cl (= @p_24 (! (forall ((veriT_vr2 Int) (veriT_vr3 Int)) @p_36) :named @p_37))) :rule bind)
+(step t15 (cl (! (= @p_26 (! (not @p_37) :named @p_39)) :named @p_38)) :rule cong :premises (t14))
+(step t16 (cl (! (not @p_38) :named @p_41) (! (not @p_26) :named @p_40) @p_39) :rule equiv_pos2)
+(step t17 (cl (not @p_40) @p_24) :rule not_not)
+(step t18 (cl @p_41 @p_24 @p_39) :rule th_resolution :premises (t17 t16))
+(step t19 (cl @p_39) :rule th_resolution :premises (t13 t15 t18))
+(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
+(step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_47)) :rule refl)
+(step t20.t2 (cl (! (= veriT_vr3 veriT_sk1) :named @p_48)) :rule refl)
+(step t20.t3 (cl (! (= @p_29 (! (+ veriT_sk0 veriT_sk1) :named @p_44)) :named @p_49)) :rule cong :premises (t20.t1 t20.t2))
+(step t20.t4 (cl (= @p_30 (! (< 2 @p_44) :named @p_46))) :rule cong :premises (t20.t3))
+(step t20.t5 (cl @p_47) :rule refl)
+(step t20.t6 (cl @p_48) :rule refl)
+(step t20.t7 (cl @p_49) :rule cong :premises (t20.t5 t20.t6))
+(step t20.t8 (cl (= @p_34 (! (= 2 @p_44) :named @p_50))) :rule cong :premises (t20.t7))
+(step t20.t9 (cl @p_47) :rule refl)
+(step t20.t10 (cl @p_48) :rule refl)
+(step t20.t11 (cl @p_49) :rule cong :premises (t20.t9 t20.t10))
+(step t20.t12 (cl (= @p_35 (! (< @p_44 2) :named @p_51))) :rule cong :premises (t20.t11))
+(step t20.t13 (cl (= @p_36 (! (or @p_46 @p_50 @p_51) :named @p_52))) :rule cong :premises (t20.t4 t20.t8 t20.t12))
+(step t20 (cl (= @p_37 @p_52)) :rule sko_forall)
+(step t21 (cl (! (= @p_39 (! (not @p_52) :named @p_54)) :named @p_53)) :rule cong :premises (t20))
+(step t22 (cl (! (not @p_53) :named @p_56) (! (not @p_39) :named @p_55) @p_54) :rule equiv_pos2)
+(step t23 (cl (not @p_55) @p_37) :rule not_not)
+(step t24 (cl @p_56 @p_37 @p_54) :rule th_resolution :premises (t23 t22))
+(step t25 (cl @p_54) :rule th_resolution :premises (t19 t21 t24))
+(step t26 (cl (not @p_46)) :rule not_or :premises (t25))
+(step t27 (cl (not @p_50)) :rule not_or :premises (t25))
+(step t28 (cl (not @p_51)) :rule not_or :premises (t25))
+(step t29 (cl (or @p_50 (! (not (! (<= 2 @p_44) :named @p_59)) :named @p_57) (! (not (! (<= @p_44 2) :named @p_60)) :named @p_58))) :rule la_disequality)
+(step t30 (cl @p_50 @p_57 @p_58) :rule or :premises (t29))
+(step t31 (cl @p_57 @p_58) :rule resolution :premises (t30 t27))
+(step t32 (cl @p_59 @p_51) :rule la_generic :args (1 1))
+(step t33 (cl @p_59) :rule resolution :premises (t32 t28))
+(step t34 (cl @p_58) :rule resolution :premises (t31 t33))
+(step t35 (cl @p_60 @p_46) :rule la_generic :args (1 1))
+(step t36 (cl) :rule resolution :premises (t35 t26 t34))
+009068a6f752b63c0ec5b63adbd0474d11cb4745 67 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr1 Int)) (not (! (ite (! (< 0 veriT_vr1) :named @p_27) (! (< 0 (! (+ 1 veriT_vr1) :named @p_29)) :named @p_30) (! (< veriT_vr1 1) :named @p_31)) :named @p_32))) :named @p_38))
-(assume axiom0 (! (not (! (forall ((?v0 Int)) (! (ite (! (< 0 ?v0) :named @p_2) (! (< 0 (! (+ ?v0 1) :named @p_5)) :named @p_7) (! (< ?v0 1) :named @p_9)) :named @p_11)) :named @p_1)) :named @p_13))
+(assume a0 (! (not (! (forall ((?v0 Int)) (! (ite (! (< 0 ?v0) :named @p_2) (! (< 0 (! (+ ?v0 1) :named @p_5)) :named @p_7) (! (< ?v0 1) :named @p_9)) :named @p_11)) :named @p_1)) :named @p_13))
 (anchor :step t2 :args ((:= (?v0 Int) veriT_vr0)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (< 0 veriT_vr0) :named @p_3))) :rule cong :premises (t2.t1))
@@ -1908,7 +2563,7 @@
 (step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_13) :named @p_17) @p_16) :rule equiv_pos2)
 (step t5 (cl (not @p_17) @p_1) :rule not_not)
 (step t6 (cl @p_18 @p_1 @p_16) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_16) :rule th_resolution :premises (axiom0 t3 t6))
+(step t7 (cl @p_16) :rule th_resolution :premises (a0 t3 t6))
 (anchor :step t8 :args ((veriT_vr0 Int)))
 (step t8.t1 (cl (= @p_6 (! (+ 1 veriT_vr0) :named @p_19))) :rule sum_simplify)
 (step t8.t2 (cl (= @p_8 (! (< 0 @p_19) :named @p_20))) :rule cong :premises (t8.t1))
@@ -1958,10 +2613,10 @@
 (step t32 (cl @p_50) :rule resolution :premises (t26 t31))
 (step t33 (cl @p_43 @p_39) :rule la_generic :args (1 1))
 (step t34 (cl) :rule resolution :premises (t33 t31 t32))
-3b346287f457d2c0655eb09f3d5280a06ca3434a 107 0
+72ef753af86f7012e75f73f9bc2d3adda07e800b 107 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr1 Int)) (not (! (or (! (< veriT_vr1 0) :named @p_37) (! (< 0 veriT_vr1) :named @p_39)) :named @p_40))) :named @p_51))
-(assume axiom0 (! (not (! (< 0 (! (ite (! (forall ((?v0 Int)) (! (or (! (< ?v0 0) :named @p_2) (! (< 0 ?v0) :named @p_5)) :named @p_7)) :named @p_1) (! (- 1) :named @p_11) 3) :named @p_9)) :named @p_12)) :named @p_14))
+(assume a0 (! (not (! (< 0 (! (ite (! (forall ((?v0 Int)) (! (or (! (< ?v0 0) :named @p_2) (! (< 0 ?v0) :named @p_5)) :named @p_7)) :named @p_1) (! (- 1) :named @p_11) 3) :named @p_9)) :named @p_12)) :named @p_14))
 (anchor :step t2 :args ((:= (?v0 Int) veriT_vr0)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (< veriT_vr0 0) :named @p_3))) :rule cong :premises (t2.t1))
@@ -1975,7 +2630,7 @@
 (step t6 (cl (! (not @p_16) :named @p_19) (! (not @p_14) :named @p_18) @p_17) :rule equiv_pos2)
 (step t7 (cl (not @p_18) @p_12) :rule not_not)
 (step t8 (cl @p_19 @p_12 @p_17) :rule th_resolution :premises (t7 t6))
-(step t9 (cl @p_17) :rule th_resolution :premises (axiom0 t5 t8))
+(step t9 (cl @p_17) :rule th_resolution :premises (a0 t5 t8))
 (step t10 (cl (= @p_11 (- 1))) :rule minus_simplify)
 (step t11 (cl (= @p_13 (! (ite @p_10 (- 1) 3) :named @p_20))) :rule cong :premises (t10))
 (step t12 (cl (= @p_15 (! (< 0 @p_20) :named @p_21))) :rule cong :premises (t11))
@@ -2066,17 +2721,17 @@
 (step t71 (cl @p_85) :rule false)
 (step t72 (cl @p_65 false) :rule or :premises (t70))
 (step t73 (cl) :rule resolution :premises (t72 t63 t71))
-f2b4e98e9e25f5e157253b295acc06d5501334ba 74 0
+79c36cccfa675d72431ed7e3c2f6afc45f85907a 74 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (=> (! (and (! (< 0 veriT_vr2) :named @p_27) (! (< 0 veriT_vr3) :named @p_28)) :named @p_29) (! (< 0 (! (+ veriT_vr2 veriT_vr3) :named @p_32)) :named @p_33)) :named @p_34)))) :named @p_40))
 (define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (=> (and (< 0 @p_40) @p_28) (< 0 (+ @p_40 veriT_vr3))))) :named @p_41))
-(assume axiom0 (! (not (! (exists ((?v0 Int)) (! (forall ((?v1 Int) (?v2 Int)) (! (=> (! (and (! (< 0 ?v1) :named @p_8) (! (< 0 ?v2) :named @p_10)) :named @p_12) (! (< 0 (! (+ ?v1 ?v2) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_2)) :named @p_1)) :named @p_3))
+(assume a0 (! (not (! (exists ((?v0 Int)) (! (forall ((?v1 Int) (?v2 Int)) (! (=> (! (and (! (< 0 ?v1) :named @p_8) (! (< 0 ?v2) :named @p_10)) :named @p_12) (! (< 0 (! (+ ?v1 ?v2) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_2)) :named @p_1)) :named @p_3))
 (step t2 (cl (= @p_1 @p_2)) :rule qnt_rm_unused)
 (step t3 (cl (! (= @p_3 (! (not @p_2) :named @p_5)) :named @p_4)) :rule cong :premises (t2))
 (step t4 (cl (! (not @p_4) :named @p_7) (! (not @p_3) :named @p_6) @p_5) :rule equiv_pos2)
 (step t5 (cl (not @p_6) @p_1) :rule not_not)
 (step t6 (cl @p_7 @p_1 @p_5) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_5) :rule th_resolution :premises (axiom0 t3 t6))
+(step t7 (cl @p_5) :rule th_resolution :premises (a0 t3 t6))
 (anchor :step t8 :args ((:= (?v1 Int) veriT_vr0) (:= (?v2 Int) veriT_vr1)))
 (step t8.t1 (cl (! (= ?v1 veriT_vr0) :named @p_14)) :rule refl)
 (step t8.t2 (cl (= @p_8 (! (< 0 veriT_vr0) :named @p_9))) :rule cong :premises (t8.t1))
@@ -2141,17 +2796,17 @@
 (step t36 (cl @p_58) :rule and :premises (t33))
 (step t37 (cl (not @p_43) @p_48 (not @p_42)) :rule la_generic :args (1 1 1))
 (step t38 (cl) :rule resolution :premises (t37 t34 t35 t36))
-373457faab0c37c0d0d8b85464bbfee7e80cb98a 77 0
+967b369bde4b5569be04c05ebef7c7c11a7dd949 77 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Real)) (! (=> (! (and (! (< 0 veriT_vr2) :named @p_32) (! (< 0.0 veriT_vr3) :named @p_33)) :named @p_34) (! (< (- 1) veriT_vr2) :named @p_36)) :named @p_37)))) :named @p_43))
 (define-fun veriT_sk1 () Real (! (choice ((veriT_vr3 Real)) (not (=> (and (< 0 @p_43) @p_33) (< (- 1) @p_43)))) :named @p_45))
-(assume axiom0 (! (not (! (exists ((?v0 Int)) (! (forall ((?v1 Int) (?v2 Real)) (! (=> (! (and (! (< 0 ?v1) :named @p_9) (! (< 0.0 ?v2) :named @p_11)) :named @p_13) (! (< (! (- 1) :named @p_8) ?v1) :named @p_16)) :named @p_18)) :named @p_2)) :named @p_1)) :named @p_3))
+(assume a0 (! (not (! (exists ((?v0 Int)) (! (forall ((?v1 Int) (?v2 Real)) (! (=> (! (and (! (< 0 ?v1) :named @p_9) (! (< 0.0 ?v2) :named @p_11)) :named @p_13) (! (< (! (- 1) :named @p_8) ?v1) :named @p_16)) :named @p_18)) :named @p_2)) :named @p_1)) :named @p_3))
 (step t2 (cl (= @p_1 @p_2)) :rule qnt_rm_unused)
 (step t3 (cl (! (= @p_3 (! (not @p_2) :named @p_5)) :named @p_4)) :rule cong :premises (t2))
 (step t4 (cl (! (not @p_4) :named @p_7) (! (not @p_3) :named @p_6) @p_5) :rule equiv_pos2)
 (step t5 (cl (not @p_6) @p_1) :rule not_not)
 (step t6 (cl @p_7 @p_1 @p_5) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_5) :rule th_resolution :premises (axiom0 t3 t6))
+(step t7 (cl @p_5) :rule th_resolution :premises (a0 t3 t6))
 (anchor :step t8 :args ((:= (?v1 Int) veriT_vr0) (:= (?v2 Real) veriT_vr1)))
 (step t8.t1 (cl (! (= ?v1 veriT_vr0) :named @p_15)) :rule refl)
 (step t8.t2 (cl (= @p_9 (! (< 0 veriT_vr0) :named @p_10))) :rule cong :premises (t8.t1))
@@ -2219,16 +2874,16 @@
 (step t41 (cl @p_59) :rule and :premises (t39))
 (step t42 (cl @p_49 (not @p_44)) :rule la_generic :args (1.0 1.0))
 (step t43 (cl) :rule resolution :premises (t42 t40 t41))
-3b8147fceb728295aa24bd5bef9bf1721184b75c 49 0
+ad30a685f8670d5c182050b2758f164c00fa02de 49 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr1 Int)) (not (! (or (! (< 0 veriT_vr1) :named @p_20) (! (< veriT_vr1 1) :named @p_22)) :named @p_23))) :named @p_29))
-(assume axiom0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (or (! (< 0 ?v1) :named @p_9) (! (< ?v1 1) :named @p_12)) :named @p_2)) :named @p_1)) :named @p_3))
+(assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (or (! (< 0 ?v1) :named @p_9) (! (< ?v1 1) :named @p_12)) :named @p_2)) :named @p_1)) :named @p_3))
 (step t2 (cl (= @p_1 (! (forall ((?v1 Int)) @p_2) :named @p_4))) :rule qnt_rm_unused)
 (step t3 (cl (! (= @p_3 (! (not @p_4) :named @p_6)) :named @p_5)) :rule cong :premises (t2))
 (step t4 (cl (! (not @p_5) :named @p_8) (! (not @p_3) :named @p_7) @p_6) :rule equiv_pos2)
 (step t5 (cl (not @p_7) @p_1) :rule not_not)
 (step t6 (cl @p_8 @p_1 @p_6) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_6) :rule th_resolution :premises (axiom0 t3 t6))
+(step t7 (cl @p_6) :rule th_resolution :premises (a0 t3 t6))
 (anchor :step t8 :args ((:= (?v1 Int) veriT_vr0)))
 (step t8.t1 (cl (! (= ?v1 veriT_vr0) :named @p_11)) :rule refl)
 (step t8.t2 (cl (= @p_9 (! (< 0 veriT_vr0) :named @p_10))) :rule cong :premises (t8.t1))
@@ -2269,36 +2924,36 @@
 (step t27 (cl (not @p_32)) :rule not_or :premises (t25))
 (step t28 (cl @p_32 @p_30) :rule la_generic :args (1 1))
 (step t29 (cl) :rule resolution :premises (t28 t26 t27))
-467ecef4941df0c9404f2c8e1d81f077fb40e73a 7 0
+c9141d00ebba589372c1920648d35b166a7ea6d0 7 0
 unsat
-(assume axiom0 (! (not (! (not (! (= 1 (* 2 (of_nat$ x$))) :named @p_2)) :named @p_3)) :named @p_1))
+(assume a0 (! (not (! (not (! (= 1 (* 2 (of_nat$ x$))) :named @p_2)) :named @p_3)) :named @p_1))
 (step t2 (cl (not @p_1) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 axiom0))
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
 (step t4 (cl @p_3 @p_3) :rule lia_generic)
 (step t5 (cl @p_3) :rule contraction :premises (t4))
 (step t6 (cl) :rule resolution :premises (t5 t3))
-3549c5e5446637c428a1dc6a809dddaffe6daeca 11 0
+5c421c4131db57d719eecccd76e666bae936fa11 11 0
 unsat
-(assume axiom0 (! (not (! (=> (! (< (! (of_nat$ a$) :named @p_1) 3) :named @p_3) (! (< (* 2 @p_1) 7) :named @p_4)) :named @p_8)) :named @p_2))
+(assume a0 (! (not (! (=> (! (< (! (of_nat$ a$) :named @p_1) 3) :named @p_3) (! (< (* 2 @p_1) 7) :named @p_4)) :named @p_8)) :named @p_2))
 (step t2 (cl (! (= @p_2 (! (and @p_3 (! (not @p_4) :named @p_10)) :named @p_6)) :named @p_5)) :rule bool_simplify)
 (step t3 (cl (! (not @p_5) :named @p_9) (! (not @p_2) :named @p_7) @p_6) :rule equiv_pos2)
 (step t4 (cl (not @p_7) @p_8) :rule not_not)
 (step t5 (cl @p_9 @p_8 @p_6) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_6) :rule th_resolution :premises (axiom0 t2 t5))
+(step t6 (cl @p_6) :rule th_resolution :premises (a0 t2 t5))
 (step t7 (cl @p_3) :rule and :premises (t6))
 (step t8 (cl @p_10) :rule and :premises (t6))
 (step t9 (cl @p_4 (not @p_3)) :rule la_generic :args ((div 1 2) 1))
 (step t10 (cl) :rule resolution :premises (t9 t7 t8))
-af4e96cd41efee9e27fd5c2ad7650835fd28bdc9 21 0
+92da6e97ba29a34a876c0fa16d5e6d53b05316de 21 0
 unsat
-(assume axiom0 (! (not (! (< (! (* 0 (! (+ 1 (! (of_nat$ y$) :named @p_2)) :named @p_1)) :named @p_3) (! (ite (! (< @p_1 @p_2) :named @p_12) 0 (! (- @p_1 @p_2) :named @p_13)) :named @p_5)) :named @p_4)) :named @p_6))
+(assume a0 (! (not (! (< (! (* 0 (! (+ 1 (! (of_nat$ y$) :named @p_2)) :named @p_1)) :named @p_3) (! (ite (! (< @p_1 @p_2) :named @p_12) 0 (! (- @p_1 @p_2) :named @p_13)) :named @p_5)) :named @p_4)) :named @p_6))
 (step t2 (cl (= 0 @p_3)) :rule prod_simplify)
 (step t3 (cl (= @p_4 (! (< 0 @p_5) :named @p_7))) :rule cong :premises (t2))
 (step t4 (cl (! (= @p_6 (! (not @p_7) :named @p_9)) :named @p_8)) :rule cong :premises (t3))
 (step t5 (cl (! (not @p_8) :named @p_11) (! (not @p_6) :named @p_10) @p_9) :rule equiv_pos2)
 (step t6 (cl (not @p_10) @p_4) :rule not_not)
 (step t7 (cl @p_11 @p_4 @p_9) :rule th_resolution :premises (t6 t5))
-(step t8 (cl @p_9) :rule th_resolution :premises (axiom0 t4 t7))
+(step t8 (cl @p_9) :rule th_resolution :premises (a0 t4 t7))
 (step t9 (cl (! (= @p_9 (! (and (! (not (! (< 0 @p_5) :named @p_21)) :named @p_18) (! (ite @p_12 (= 0 @p_5) (! (= @p_13 @p_5) :named @p_20)) :named @p_19)) :named @p_15)) :named @p_14)) :rule ite_intro)
 (step t10 (cl (! (not @p_14) :named @p_17) (! (not @p_9) :named @p_16) @p_15) :rule equiv_pos2)
 (step t11 (cl (not @p_16) @p_7) :rule not_not)
@@ -2311,16 +2966,16 @@
 (step t18 (cl @p_20) :rule resolution :premises (t16 t17))
 (step t19 (cl @p_21 (not @p_20)) :rule la_generic :args (1 (- 1)))
 (step t20 (cl) :rule resolution :premises (t19 t14 t18))
-efbe007514b68c6b40ac16694834314f7692069b 33 0
+d2911e8674cbcffa4830ead7c6ef3c57cef2d6fa 33 0
 unsat
-(assume axiom0 (! (not (! (or false (or (! (= (! (ite (! (< 0 (! (+ 1 (! (of_nat$ y$) :named @p_1)) :named @p_2)) :named @p_13) true false) :named @p_3) (! (= @p_1 (! (ite (! (< @p_2 1) :named @p_27) 0 (! (- @p_2 1) :named @p_28)) :named @p_26)) :named @p_14)) :named @p_5) (! (=> (! (not @p_3) :named @p_15) false) :named @p_6))) :named @p_4)) :named @p_7))
-(assume axiom1 (! (<= 0 @p_1) :named @p_34))
+(assume a0 (! (not (! (or false (or (! (= (! (ite (! (< 0 (! (+ 1 (! (of_nat$ y$) :named @p_1)) :named @p_2)) :named @p_13) true false) :named @p_3) (! (= @p_1 (! (ite (! (< @p_2 1) :named @p_27) 0 (! (- @p_2 1) :named @p_28)) :named @p_26)) :named @p_14)) :named @p_5) (! (=> (! (not @p_3) :named @p_15) false) :named @p_6))) :named @p_4)) :named @p_7))
+(assume a1 (! (<= 0 @p_1) :named @p_34))
 (step t3 (cl (= @p_4 (! (or false @p_5 @p_6) :named @p_8))) :rule ac_simp)
 (step t4 (cl (! (= @p_7 (! (not @p_8) :named @p_10)) :named @p_9)) :rule cong :premises (t3))
 (step t5 (cl (! (not @p_9) :named @p_12) (! (not @p_7) :named @p_11) @p_10) :rule equiv_pos2)
 (step t6 (cl (not @p_11) @p_4) :rule not_not)
 (step t7 (cl @p_12 @p_4 @p_10) :rule th_resolution :premises (t6 t5))
-(step t8 (cl @p_10) :rule th_resolution :premises (axiom0 t4 t7))
+(step t8 (cl @p_10) :rule th_resolution :premises (a0 t4 t7))
 (step t9 (cl (= @p_3 @p_13)) :rule ite_simplify)
 (step t10 (cl (= @p_5 (! (= @p_13 @p_14) :named @p_19))) :rule cong :premises (t9))
 (step t11 (cl (= @p_15 (! (not @p_13) :named @p_16))) :rule cong :premises (t9))
@@ -2344,11 +2999,11 @@
 (step t29 (cl @p_33) :rule and :premises (t28))
 (step t30 (cl @p_16) :rule not_or :premises (t29))
 (step t31 (cl @p_13 (not @p_34)) :rule la_generic :args (1 1))
-(step t32 (cl) :rule resolution :premises (t31 t30 axiom1))
-d3c98c27318a98e589a892ffe99adffc556ea833 76 0
+(step t32 (cl) :rule resolution :premises (t31 t30 a1))
+1b01a203f415236790472915120aeba1d69e507b 76 0
 unsat
-(assume axiom4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (nat$ ?v0) :named @p_3)) :named @p_5) (! (ite (! (<= 0 ?v0) :named @p_8) ?v0 0) :named @p_10)) :named @p_12)) :named @p_2))
-(assume axiom1 (! (not (! (= (! (ite (! (< x$ 0) :named @p_25) (! (- x$) :named @p_26) x$) :named @p_1) (of_nat$ (nat$ @p_1))) :named @p_30)) :named @p_24))
+(assume a4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (nat$ ?v0) :named @p_3)) :named @p_5) (! (ite (! (<= 0 ?v0) :named @p_8) ?v0 0) :named @p_10)) :named @p_12)) :named @p_2))
+(assume a1 (! (not (! (= (! (ite (! (< x$ 0) :named @p_25) (! (- x$) :named @p_26) x$) :named @p_1) (of_nat$ (nat$ @p_1))) :named @p_30)) :named @p_24))
 (anchor :step t3 :args ((:= (?v0 Int) veriT_vr0)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_7)) :rule refl)
 (step t3.t2 (cl (= @p_3 (! (nat$ veriT_vr0) :named @p_4))) :rule cong :premises (t3.t1))
@@ -2360,7 +3015,7 @@
 (step t3.t8 (cl (= @p_12 (! (= @p_6 @p_11) :named @p_13))) :rule cong :premises (t3.t3 t3.t7))
 (step t3 (cl (! (= @p_2 (! (forall ((veriT_vr0 Int)) @p_13) :named @p_15)) :named @p_14)) :rule bind)
 (step t4 (cl (not @p_14) (not @p_2) @p_15) :rule equiv_pos2)
-(step t5 (cl @p_15) :rule th_resolution :premises (axiom4 t3 t4))
+(step t5 (cl @p_15) :rule th_resolution :premises (a4 t3 t4))
 (anchor :step t6 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_18)) :rule refl)
 (step t6.t2 (cl (= @p_4 (! (nat$ veriT_vr1) :named @p_16))) :rule cong :premises (t6.t1))
@@ -2377,7 +3032,7 @@
 (step t10 (cl (! (not @p_27) :named @p_31) (! (not @p_24) :named @p_29) @p_28) :rule equiv_pos2)
 (step t11 (cl (not @p_29) @p_30) :rule not_not)
 (step t12 (cl @p_31 @p_30 @p_28) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_28) :rule th_resolution :premises (axiom1 t9 t12))
+(step t13 (cl @p_28) :rule th_resolution :premises (a1 t9 t12))
 (step t14 (cl @p_32) :rule and :premises (t13))
 (step t15 (cl @p_33) :rule and :premises (t13))
 (step t16 (cl @p_25 @p_34) :rule ite1 :premises (t15))
@@ -2422,13 +3077,13 @@
 (step t50 (cl @p_62 @p_64 @p_58 (! (not @p_35) :named @p_65)) :rule la_generic :args (1 1 1 (- 1)))
 (step t51 (cl @p_62 @p_64 @p_65 @p_61 @p_55) :rule th_resolution :premises (t50 t42))
 (step t52 (cl) :rule resolution :premises (t51 t48 t49 t32 t39 t44))
-d4fe162ae425370cea445760001be7c859bc0288 337 0
+59999ffb5d66c5ffe3c4bd998e52a95d515ab9b4 337 0
 unsat
 (define-fun veriT_sk1 () Nat$ (! (choice ((veriT_vr18 Nat$)) (not (! (=> (! (dvd$ veriT_vr18 (! (nat$ (! (+ 1 (! (* 4 (! (of_nat$ m$) :named @p_3)) :named @p_117)) :named @p_119)) :named @p_120)) :named @p_206) (! (or (! (= 1 (! (of_nat$ veriT_vr18) :named @p_171)) :named @p_208) (! (= (! (of_nat$ @p_120) :named @p_158) @p_171) :named @p_210)) :named @p_211)) :named @p_205))) :named @p_172))
-(assume axiom0 (! (forall ((?v0 Nat$)) (! (= (! (prime_nat$ ?v0) :named @p_7) (! (and (! (< 1 (! (of_nat$ ?v0) :named @p_1)) :named @p_10) (! (forall ((?v1 Nat$)) (! (=> (! (dvd$ ?v1 ?v0) :named @p_14) (! (or (! (= 1 (! (of_nat$ ?v1) :named @p_2)) :named @p_17) (! (= @p_1 @p_2) :named @p_21)) :named @p_23)) :named @p_25)) :named @p_12)) :named @p_27)) :named @p_29)) :named @p_4))
-(assume axiom1 (! (not (! (=> (! (prime_nat$ (! (nat$ (! (+ @p_117 1) :named @p_116)) :named @p_118)) :named @p_109) (! (<= 1 @p_3) :named @p_110)) :named @p_114)) :named @p_108))
-(assume axiom2 (! (forall ((?v0 Nat$)) (! (<= 0 @p_1) :named @p_127)) :named @p_125))
-(assume axiom4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (nat$ ?v0) :named @p_136)) :named @p_138) (! (ite (! (<= 0 ?v0) :named @p_141) ?v0 0) :named @p_143)) :named @p_145)) :named @p_135))
+(assume a0 (! (forall ((?v0 Nat$)) (! (= (! (prime_nat$ ?v0) :named @p_7) (! (and (! (< 1 (! (of_nat$ ?v0) :named @p_1)) :named @p_10) (! (forall ((?v1 Nat$)) (! (=> (! (dvd$ ?v1 ?v0) :named @p_14) (! (or (! (= 1 (! (of_nat$ ?v1) :named @p_2)) :named @p_17) (! (= @p_1 @p_2) :named @p_21)) :named @p_23)) :named @p_25)) :named @p_12)) :named @p_27)) :named @p_29)) :named @p_4))
+(assume a1 (! (not (! (=> (! (prime_nat$ (! (nat$ (! (+ @p_117 1) :named @p_116)) :named @p_118)) :named @p_109) (! (<= 1 @p_3) :named @p_110)) :named @p_114)) :named @p_108))
+(assume a2 (! (forall ((?v0 Nat$)) (! (<= 0 @p_1) :named @p_127)) :named @p_125))
+(assume a4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (nat$ ?v0) :named @p_136)) :named @p_138) (! (ite (! (<= 0 ?v0) :named @p_141) ?v0 0) :named @p_143)) :named @p_145)) :named @p_135))
 (anchor :step t5 :args ((:= (?v0 Nat$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
 (step t5.t2 (cl (= @p_7 (! (prime_nat$ veriT_vr0) :named @p_8))) :rule cong :premises (t5.t1))
@@ -2454,7 +3109,7 @@
 (step t5.t8 (cl (= @p_29 (! (= @p_8 @p_28) :named @p_30))) :rule cong :premises (t5.t2 t5.t7))
 (step t5 (cl (! (= @p_4 (! (forall ((veriT_vr0 Nat$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
 (step t6 (cl (not @p_31) (not @p_4) @p_32) :rule equiv_pos2)
-(step t7 (cl @p_32) :rule th_resolution :premises (axiom0 t5 t6))
+(step t7 (cl @p_32) :rule th_resolution :premises (a0 t5 t6))
 (anchor :step t8 :args ((veriT_vr0 Nat$)))
 (step t8.t1 (cl (= @p_30 (! (and (! (=> @p_8 @p_28) :named @p_52) (! (=> @p_28 @p_8) :named @p_65)) :named @p_33))) :rule connective_def)
 (step t8 (cl (! (= @p_32 (! (forall ((veriT_vr0 Nat$)) @p_33) :named @p_35)) :named @p_34)) :rule bind)
@@ -2581,7 +3236,7 @@
 (step t21 (cl (! (not @p_111) :named @p_115) (! (not @p_108) :named @p_113) @p_112) :rule equiv_pos2)
 (step t22 (cl (not @p_113) @p_114) :rule not_not)
 (step t23 (cl @p_115 @p_114 @p_112) :rule th_resolution :premises (t22 t21))
-(step t24 (cl @p_112) :rule th_resolution :premises (axiom1 t20 t23))
+(step t24 (cl @p_112) :rule th_resolution :premises (a1 t20 t23))
 (step t25 (cl (= @p_116 @p_119)) :rule sum_simplify)
 (step t26 (cl (= @p_118 @p_120)) :rule cong :premises (t25))
 (step t27 (cl (= @p_109 (! (prime_nat$ @p_120) :named @p_121))) :rule cong :premises (t26))
@@ -2594,7 +3249,7 @@
 (step t31.t3 (cl (= @p_127 (! (<= 0 @p_126) :named @p_128))) :rule cong :premises (t31.t2))
 (step t31 (cl (! (= @p_125 (! (forall ((veriT_vr8 Nat$)) @p_128) :named @p_130)) :named @p_129)) :rule bind)
 (step t32 (cl (not @p_129) (not @p_125) @p_130) :rule equiv_pos2)
-(step t33 (cl @p_130) :rule th_resolution :premises (axiom2 t31 t32))
+(step t33 (cl @p_130) :rule th_resolution :premises (a2 t31 t32))
 (anchor :step t34 :args ((:= (veriT_vr8 Nat$) veriT_vr9)))
 (step t34.t1 (cl (= veriT_vr8 veriT_vr9)) :rule refl)
 (step t34.t2 (cl (= @p_126 (! (of_nat$ veriT_vr9) :named @p_131))) :rule cong :premises (t34.t1))
@@ -2613,7 +3268,7 @@
 (step t37.t8 (cl (= @p_145 (! (= @p_139 @p_144) :named @p_146))) :rule cong :premises (t37.t3 t37.t7))
 (step t37 (cl (! (= @p_135 (! (forall ((veriT_vr12 Int)) @p_146) :named @p_148)) :named @p_147)) :rule bind)
 (step t38 (cl (not @p_147) (not @p_135) @p_148) :rule equiv_pos2)
-(step t39 (cl @p_148) :rule th_resolution :premises (axiom4 t37 t38))
+(step t39 (cl @p_148) :rule th_resolution :premises (a4 t37 t38))
 (anchor :step t40 :args ((:= (veriT_vr12 Int) veriT_vr13)))
 (step t40.t1 (cl (! (= veriT_vr12 veriT_vr13) :named @p_151)) :rule refl)
 (step t40.t2 (cl (= @p_137 (! (nat$ veriT_vr13) :named @p_149))) :rule cong :premises (t40.t1))
@@ -2760,18 +3415,18 @@
 (step t84 (cl (! (not @p_246) :named @p_253) (! (not @p_244) :named @p_254) @p_251) :rule eq_transitive)
 (step t85 (cl @p_252 @p_110 @p_253 @p_254) :rule th_resolution :premises (t83 t84))
 (step t86 (cl) :rule resolution :premises (t85 t44 t67 t82 t79))
-8d6d329bb2354ffa218e4b6256b283b3915c3682 7 0
+195c5f4e7eb20baa5a32cf916824c8152dd91637 7 0
 unsat
-(assume axiom0 (! (not (! (not (! (= 1 (* 2 x$)) :named @p_2)) :named @p_3)) :named @p_1))
+(assume a0 (! (not (! (not (! (= 1 (* 2 x$)) :named @p_2)) :named @p_3)) :named @p_1))
 (step t2 (cl (not @p_1) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 axiom0))
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
 (step t4 (cl @p_3 @p_3) :rule lia_generic)
 (step t5 (cl @p_3) :rule contraction :premises (t4))
 (step t6 (cl) :rule resolution :premises (t5 t3))
-1cf2d299f7ccd81bab0d38f30ec8595b5f133da6 35 0
+f45af256a4bceda428e7fbee4e1e3dbdf14a491e 35 0
 unsat
-(assume axiom0 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$ (! (pair$ ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
-(assume axiom1 (! (not (! (=> (! (= (! (fst$ (pair$ x$ y$)) :named @p_26) a$) :named @p_18) (! (= x$ a$) :named @p_19)) :named @p_23)) :named @p_17))
+(assume a0 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$ (! (pair$ ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
+(assume a1 (! (not (! (=> (! (= (! (fst$ (pair$ x$ y$)) :named @p_26) a$) :named @p_18) (! (= x$ a$) :named @p_19)) :named @p_23)) :named @p_17))
 (anchor :step t3 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 B$) veriT_vr1)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_2)) :rule refl)
 (step t3.t2 (cl @p_2) :rule refl)
@@ -2781,7 +3436,7 @@
 (step t3.t6 (cl (= @p_7 (! (= veriT_vr0 @p_6) :named @p_8))) :rule cong :premises (t3.t1 t3.t5))
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$) (veriT_vr1 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
 (step t4 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
-(step t5 (cl @p_10) :rule th_resolution :premises (axiom0 t3 t4))
+(step t5 (cl @p_10) :rule th_resolution :premises (a0 t3 t4))
 (anchor :step t6 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 B$) veriT_vr3)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_11)) :rule refl)
 (step t6.t2 (cl @p_11) :rule refl)
@@ -2796,7 +3451,7 @@
 (step t10 (cl (! (not @p_20) :named @p_24) (! (not @p_17) :named @p_22) @p_21) :rule equiv_pos2)
 (step t11 (cl (not @p_22) @p_23) :rule not_not)
 (step t12 (cl @p_24 @p_23 @p_21) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_21) :rule th_resolution :premises (axiom1 t9 t12))
+(step t13 (cl @p_21) :rule th_resolution :premises (a1 t9 t12))
 (step t14 (cl @p_18) :rule and :premises (t13))
 (step t15 (cl @p_25) :rule and :premises (t13))
 (step t16 (cl (or (! (not @p_16) :named @p_27) (! (= x$ @p_26) :named @p_28))) :rule forall_inst :args ((:= veriT_vr2 x$) (:= veriT_vr3 y$)))
@@ -2804,11 +3459,11 @@
 (step t18 (cl @p_28) :rule resolution :premises (t17 t8))
 (step t19 (cl (not @p_28) (not @p_18) @p_19) :rule eq_transitive)
 (step t20 (cl) :rule resolution :premises (t19 t14 t15 t18))
-48c92486160c88d9d50f41cf6a3fd33cb769b2b7 67 0
+22e3ad7a3ba163eb9b2786d30a493e2c63cf8f81 67 0
 unsat
-(assume axiom1 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$a (! (pair$a ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
-(assume axiom3 (! (forall ((?v0 B$) (?v1 A$)) (! (= ?v1 (! (snd$a (! (pair$ ?v0 ?v1) :named @p_19)) :named @p_21)) :named @p_23)) :named @p_17))
-(assume axiom4 (! (not (! (=> (! (and (! (= p1$ (! (pair$a x$ y$) :named @p_47)) :named @p_41) (! (= p2$ (! (pair$ y$ x$) :named @p_46)) :named @p_42)) :named @p_34) (! (= (! (fst$a p1$) :named @p_52) (! (snd$a p2$) :named @p_54)) :named @p_35)) :named @p_39)) :named @p_33))
+(assume a1 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$a (! (pair$a ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
+(assume a3 (! (forall ((?v0 B$) (?v1 A$)) (! (= ?v1 (! (snd$a (! (pair$ ?v0 ?v1) :named @p_19)) :named @p_21)) :named @p_23)) :named @p_17))
+(assume a4 (! (not (! (=> (! (and (! (= p1$ (! (pair$a x$ y$) :named @p_47)) :named @p_41) (! (= p2$ (! (pair$ y$ x$) :named @p_46)) :named @p_42)) :named @p_34) (! (= (! (fst$a p1$) :named @p_52) (! (snd$a p2$) :named @p_54)) :named @p_35)) :named @p_39)) :named @p_33))
 (anchor :step t4 :args ((:= (?v0 A$) veriT_vr4) (:= (?v1 B$) veriT_vr5)))
 (step t4.t1 (cl (! (= ?v0 veriT_vr4) :named @p_2)) :rule refl)
 (step t4.t2 (cl @p_2) :rule refl)
@@ -2818,7 +3473,7 @@
 (step t4.t6 (cl (= @p_7 (! (= veriT_vr4 @p_6) :named @p_8))) :rule cong :premises (t4.t1 t4.t5))
 (step t4 (cl (! (= @p_1 (! (forall ((veriT_vr4 A$) (veriT_vr5 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
 (step t5 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
-(step t6 (cl @p_10) :rule th_resolution :premises (axiom1 t4 t5))
+(step t6 (cl @p_10) :rule th_resolution :premises (a1 t4 t5))
 (anchor :step t7 :args ((:= (veriT_vr4 A$) veriT_vr6) (:= (veriT_vr5 B$) veriT_vr7)))
 (step t7.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_11)) :rule refl)
 (step t7.t2 (cl @p_11) :rule refl)
@@ -2838,7 +3493,7 @@
 (step t10.t6 (cl (= @p_23 (! (= veriT_vr13 @p_22) :named @p_24))) :rule cong :premises (t10.t1 t10.t5))
 (step t10 (cl (! (= @p_17 (! (forall ((veriT_vr12 B$) (veriT_vr13 A$)) @p_24) :named @p_26)) :named @p_25)) :rule bind)
 (step t11 (cl (not @p_25) (not @p_17) @p_26) :rule equiv_pos2)
-(step t12 (cl @p_26) :rule th_resolution :premises (axiom3 t10 t11))
+(step t12 (cl @p_26) :rule th_resolution :premises (a3 t10 t11))
 (anchor :step t13 :args ((:= (veriT_vr12 B$) veriT_vr14) (:= (veriT_vr13 A$) veriT_vr15)))
 (step t13.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_27)) :rule refl)
 (step t13.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
@@ -2853,7 +3508,7 @@
 (step t17 (cl (! (not @p_36) :named @p_40) (! (not @p_33) :named @p_38) @p_37) :rule equiv_pos2)
 (step t18 (cl (not @p_38) @p_39) :rule not_not)
 (step t19 (cl @p_40 @p_39 @p_37) :rule th_resolution :premises (t18 t17))
-(step t20 (cl @p_37) :rule th_resolution :premises (axiom4 t16 t19))
+(step t20 (cl @p_37) :rule th_resolution :premises (a4 t16 t19))
 (step t21 (cl (! (= @p_37 (! (and @p_41 @p_42 @p_43) :named @p_45)) :named @p_44)) :rule ac_simp)
 (step t22 (cl (not @p_44) (not @p_37) @p_45) :rule equiv_pos2)
 (step t23 (cl @p_45) :rule th_resolution :premises (t20 t21 t22))
@@ -2872,36 +3527,10 @@
 (step t36 (cl (! (not @p_41) :named @p_62) @p_61) :rule eq_congruent)
 (step t37 (cl @p_58 @p_59 @p_35 @p_60 @p_62) :rule th_resolution :premises (t35 t36))
 (step t38 (cl) :rule resolution :premises (t37 t24 t25 t26 t30 t32))
-d98294078e51b7d929ca2e2c002b0b435565488d 25 0
+323770b82ef8fd021b5433671b6c4077843fd9d7 97 0
 unsat
-(assume axiom0 (! (not (! (or (! (= (! (f$ g$ x$) :named @p_1) (! (and (! (fun_app$ g$ x$) :named @p_2) true) :named @p_13)) :named @p_4) (or (! (= @p_1 true) :named @p_5) (! (= @p_2 true) :named @p_6))) :named @p_3)) :named @p_7))
-(step t2 (cl (= @p_3 (! (or @p_4 @p_5 @p_6) :named @p_8))) :rule ac_simp)
-(step t3 (cl (! (= @p_7 (! (not @p_8) :named @p_10)) :named @p_9)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_9) :named @p_12) (! (not @p_7) :named @p_11) @p_10) :rule equiv_pos2)
-(step t5 (cl (not @p_11) @p_3) :rule not_not)
-(step t6 (cl @p_12 @p_3 @p_10) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_10) :rule th_resolution :premises (axiom0 t3 t6))
-(step t8 (cl (= @p_13 (! (and @p_2) :named @p_14))) :rule and_simplify)
-(step t9 (cl (= @p_14 @p_2)) :rule and_simplify)
-(step t10 (cl (= @p_13 @p_2)) :rule trans :premises (t8 t9))
-(step t11 (cl (= @p_4 (! (= @p_1 @p_2) :named @p_15))) :rule cong :premises (t10))
-(step t12 (cl (= @p_5 @p_1)) :rule equiv_simplify)
-(step t13 (cl (= @p_6 @p_2)) :rule equiv_simplify)
-(step t14 (cl (= @p_8 (! (or @p_15 @p_1 @p_2) :named @p_16))) :rule cong :premises (t11 t12 t13))
-(step t15 (cl (! (= @p_10 (! (not @p_16) :named @p_18)) :named @p_17)) :rule cong :premises (t14))
-(step t16 (cl (! (not @p_17) :named @p_20) (! (not @p_10) :named @p_19) @p_18) :rule equiv_pos2)
-(step t17 (cl (not @p_19) @p_8) :rule not_not)
-(step t18 (cl @p_20 @p_8 @p_18) :rule th_resolution :premises (t17 t16))
-(step t19 (cl @p_18) :rule th_resolution :premises (t7 t15 t18))
-(step t20 (cl (not @p_15)) :rule not_or :premises (t19))
-(step t21 (cl @p_1 @p_2) :rule not_equiv1 :premises (t20))
-(step t22 (cl (not @p_1)) :rule not_or :premises (t19))
-(step t23 (cl (not @p_2)) :rule not_or :premises (t19))
-(step t24 (cl) :rule resolution :premises (t21 t22 t23))
-a6d9c8f29a4df3b9eaa40764e38a8a41a8961f01 97 0
-unsat
-(assume axiom1 (! (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (! (= (! (fun_app$ (! (fun_upd$ ?v0 ?v1 ?v2) :named @p_2) ?v3) :named @p_4) (! (ite (! (= ?v1 ?v3) :named @p_8) ?v2 (! (fun_app$ ?v0 ?v3) :named @p_12)) :named @p_14)) :named @p_16)) :named @p_1))
-(assume axiom2 (! (not (! (=> (! (and (! (not (! (= i$ i1$) :named @p_62)) :named @p_40) (! (not (! (= i$ i2$) :named @p_46)) :named @p_41)) :named @p_33) (! (= (! (fun_app$ (fun_upd$ (! (fun_upd$ f$ i1$ v1$) :named @p_47) i2$ v2$) i$) :named @p_45) (! (fun_app$ f$ i$) :named @p_63)) :named @p_34)) :named @p_38)) :named @p_32))
+(assume a1 (! (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (! (= (! (fun_app$ (! (fun_upd$ ?v0 ?v1 ?v2) :named @p_2) ?v3) :named @p_4) (! (ite (! (= ?v1 ?v3) :named @p_8) ?v2 (! (fun_app$ ?v0 ?v3) :named @p_12)) :named @p_14)) :named @p_16)) :named @p_1))
+(assume a2 (! (not (! (=> (! (and (! (not (! (= i$ i1$) :named @p_62)) :named @p_40) (! (not (! (= i$ i2$) :named @p_46)) :named @p_41)) :named @p_33) (! (= (! (fun_app$ (fun_upd$ (! (fun_upd$ f$ i1$ v1$) :named @p_47) i2$ v2$) i$) :named @p_45) (! (fun_app$ f$ i$) :named @p_63)) :named @p_34)) :named @p_38)) :named @p_32))
 (anchor :step t3 :args ((:= (?v0 A_b_fun$) veriT_vr6) (:= (?v1 A$) veriT_vr7) (:= (?v2 B$) veriT_vr8) (:= (?v3 A$) veriT_vr9)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr6) :named @p_11)) :rule refl)
 (step t3.t2 (cl (! (= ?v1 veriT_vr7) :named @p_6)) :rule refl)
@@ -2920,7 +3549,7 @@
 (step t3.t15 (cl (= @p_16 (! (= @p_5 @p_15) :named @p_17))) :rule cong :premises (t3.t6 t3.t14))
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr6 A_b_fun$) (veriT_vr7 A$) (veriT_vr8 B$) (veriT_vr9 A$)) @p_17) :named @p_19)) :named @p_18)) :rule bind)
 (step t4 (cl (not @p_18) (not @p_1) @p_19) :rule equiv_pos2)
-(step t5 (cl @p_19) :rule th_resolution :premises (axiom1 t3 t4))
+(step t5 (cl @p_19) :rule th_resolution :premises (a1 t3 t4))
 (anchor :step t6 :args ((:= (veriT_vr6 A_b_fun$) veriT_vr10) (:= (veriT_vr7 A$) veriT_vr11) (:= (veriT_vr8 B$) veriT_vr12) (:= (veriT_vr9 A$) veriT_vr13)))
 (step t6.t1 (cl (! (= veriT_vr6 veriT_vr10) :named @p_26)) :rule refl)
 (step t6.t2 (cl (! (= veriT_vr7 veriT_vr11) :named @p_22)) :rule refl)
@@ -2944,7 +3573,7 @@
 (step t10 (cl (! (not @p_35) :named @p_39) (! (not @p_32) :named @p_37) @p_36) :rule equiv_pos2)
 (step t11 (cl (not @p_37) @p_38) :rule not_not)
 (step t12 (cl @p_39 @p_38 @p_36) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_36) :rule th_resolution :premises (axiom2 t9 t12))
+(step t13 (cl @p_36) :rule th_resolution :premises (a2 t9 t12))
 (step t14 (cl (! (= @p_36 (! (and @p_40 @p_41 @p_42) :named @p_44)) :named @p_43)) :rule ac_simp)
 (step t15 (cl (not @p_43) (not @p_36) @p_44) :rule equiv_pos2)
 (step t16 (cl @p_44) :rule th_resolution :premises (t13 t14 t15))
@@ -2996,12 +3625,38 @@
 (step t52 (cl @p_73) :rule resolution :premises (t48 t51))
 (step t53 (cl (not @p_58) (not @p_60) (not @p_71) (not @p_73) @p_34) :rule eq_transitive)
 (step t54 (cl) :rule resolution :premises (t53 t19 t34 t36 t50 t52))
-6c882ad63eb28539c511430af509d5d6577b2638 38 0
+5c8ad736381ed7e2bc55bcefd8a06994784b278f 25 0
 unsat
-(assume axiom0 (! (forall ((?v0 A$)) (! (= ?v0 (! (id$ ?v0) :named @p_4)) :named @p_6)) :named @p_2))
-(assume axiom1 (forall ((?v0 Bool)) (= (id$a ?v0) ?v0)))
-(assume axiom2 (! (not (! (and (! (= x$ (id$ x$)) :named @p_23) (! (= (! (id$a true) :named @p_17) true) :named @p_1)) :named @p_22)) :named @p_24))
-(step t4 (cl (! (and (! (= (! (id$a false) :named @p_16) false) :named @p_15) @p_1) :named @p_18)) :rule bfun_elim :premises (axiom1))
+(assume a0 (! (not (! (or (! (= (! (f$ g$ x$) :named @p_1) (! (and (! (fun_app$ g$ x$) :named @p_2) true) :named @p_13)) :named @p_4) (or (! (= @p_1 true) :named @p_5) (! (= @p_2 true) :named @p_6))) :named @p_3)) :named @p_7))
+(step t2 (cl (= @p_3 (! (or @p_4 @p_5 @p_6) :named @p_8))) :rule ac_simp)
+(step t3 (cl (! (= @p_7 (! (not @p_8) :named @p_10)) :named @p_9)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_9) :named @p_12) (! (not @p_7) :named @p_11) @p_10) :rule equiv_pos2)
+(step t5 (cl (not @p_11) @p_3) :rule not_not)
+(step t6 (cl @p_12 @p_3 @p_10) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_10) :rule th_resolution :premises (a0 t3 t6))
+(step t8 (cl (= @p_13 (! (and @p_2) :named @p_14))) :rule and_simplify)
+(step t9 (cl (= @p_14 @p_2)) :rule and_simplify)
+(step t10 (cl (= @p_13 @p_2)) :rule trans :premises (t8 t9))
+(step t11 (cl (= @p_4 (! (= @p_1 @p_2) :named @p_15))) :rule cong :premises (t10))
+(step t12 (cl (= @p_5 @p_1)) :rule equiv_simplify)
+(step t13 (cl (= @p_6 @p_2)) :rule equiv_simplify)
+(step t14 (cl (= @p_8 (! (or @p_15 @p_1 @p_2) :named @p_16))) :rule cong :premises (t11 t12 t13))
+(step t15 (cl (! (= @p_10 (! (not @p_16) :named @p_18)) :named @p_17)) :rule cong :premises (t14))
+(step t16 (cl (! (not @p_17) :named @p_20) (! (not @p_10) :named @p_19) @p_18) :rule equiv_pos2)
+(step t17 (cl (not @p_19) @p_8) :rule not_not)
+(step t18 (cl @p_20 @p_8 @p_18) :rule th_resolution :premises (t17 t16))
+(step t19 (cl @p_18) :rule th_resolution :premises (t7 t15 t18))
+(step t20 (cl (not @p_15)) :rule not_or :premises (t19))
+(step t21 (cl @p_1 @p_2) :rule not_equiv1 :premises (t20))
+(step t22 (cl (not @p_1)) :rule not_or :premises (t19))
+(step t23 (cl (not @p_2)) :rule not_or :premises (t19))
+(step t24 (cl) :rule resolution :premises (t21 t22 t23))
+866c42407f20d04dcdd5beace79be280ba36c916 38 0
+unsat
+(assume a0 (! (forall ((?v0 A$)) (! (= ?v0 (! (id$ ?v0) :named @p_4)) :named @p_6)) :named @p_2))
+(assume a1 (forall ((?v0 Bool)) (= (id$a ?v0) ?v0)))
+(assume a2 (! (not (! (and (! (= x$ (id$ x$)) :named @p_23) (! (= (! (id$a true) :named @p_17) true) :named @p_1)) :named @p_22)) :named @p_24))
+(step t4 (cl (! (and (! (= (! (id$a false) :named @p_16) false) :named @p_15) @p_1) :named @p_18)) :rule bfun_elim :premises (a1))
 (anchor :step t5 :args ((:= (?v0 A$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr0) :named @p_3)) :rule refl)
 (step t5.t2 (cl @p_3) :rule refl)
@@ -3009,7 +3664,7 @@
 (step t5.t4 (cl (= @p_6 (! (= veriT_vr0 @p_5) :named @p_7))) :rule cong :premises (t5.t1 t5.t3))
 (step t5 (cl (! (= @p_2 (! (forall ((veriT_vr0 A$)) @p_7) :named @p_9)) :named @p_8)) :rule bind)
 (step t6 (cl (not @p_8) (not @p_2) @p_9) :rule equiv_pos2)
-(step t7 (cl @p_9) :rule th_resolution :premises (axiom0 t5 t6))
+(step t7 (cl @p_9) :rule th_resolution :premises (a0 t5 t6))
 (anchor :step t8 :args ((:= (veriT_vr0 A$) veriT_vr1)))
 (step t8.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_10)) :rule refl)
 (step t8.t2 (cl @p_10) :rule refl)
@@ -3028,17 +3683,17 @@
 (step t18 (cl (! (not @p_26) :named @p_29) (! (not @p_24) :named @p_28) @p_27) :rule equiv_pos2)
 (step t19 (cl (not @p_28) @p_22) :rule not_not)
 (step t20 (cl @p_29 @p_22 @p_27) :rule th_resolution :premises (t19 t18))
-(step t21 (cl @p_27) :rule th_resolution :premises (axiom2 t17 t20))
+(step t21 (cl @p_27) :rule th_resolution :premises (a2 t17 t20))
 (step t22 (cl @p_17) :rule and :premises (t15))
 (step t23 (cl (! (not @p_23) :named @p_30) (not @p_17)) :rule not_and :premises (t21))
 (step t24 (cl @p_30) :rule resolution :premises (t23 t22))
 (step t25 (cl (or (! (not @p_14) :named @p_31) @p_23)) :rule forall_inst :args ((:= veriT_vr1 x$)))
 (step t26 (cl @p_31 @p_23) :rule or :premises (t25))
 (step t27 (cl) :rule resolution :premises (t26 t10 t24))
-395426c1e77b0b2b43dd37f4fdc5b1794b758773 27 0
+75683ef8683272f0e70a656b2aaeeba1b535ac8d 27 0
 unsat
-(assume axiom0 (not (=> (f$ (! (exists ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
-(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (axiom0))
+(assume a0 (not (=> (f$ (! (exists ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
+(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0))
 (anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
 (step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
 (step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
@@ -3063,10 +3718,38 @@
 (step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
 (step t22 (cl (not false)) :rule false)
 (step t23 (cl) :rule resolution :premises (t21 t22))
-2bbe312ac0bf24de2abf59ed85b8b3b02d04d4eb 60 0
+c16c43a541a3283a006315d4b74b5196ee73be5b 27 0
 unsat
-(assume axiom0 (! (forall ((?v0 Int) (?v1 Int)) (! (= (! (fun_app$ (! (fun_app$a uu$ ?v0) :named @p_2) ?v1) :named @p_4) (! (<= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_1))
-(assume axiom1 (! (not (! (=> (! (= uu$ le$) :named @p_23) (! (fun_app$ (! (fun_app$a le$ 3) :named @p_40) 42) :named @p_24)) :named @p_28)) :named @p_22))
+(assume a0 (not (=> (f$ (! (forall ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
+(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0))
+(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
+(step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
+(step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
+(step t3 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind)
+(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3))
+(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4))
+(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5))
+(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2)
+(step t8 (cl (not @p_14) @p_8) :rule not_not)
+(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7))
+(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9))
+(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify)
+(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2)
+(step t13 (cl (not @p_18) @p_11) :rule not_not)
+(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12))
+(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14))
+(step t16 (cl (= @p_20 false)) :rule not_simplify)
+(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16))
+(step t18 (cl (= @p_21 false)) :rule and_simplify)
+(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18))
+(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2)
+(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
+(step t22 (cl (not false)) :rule false)
+(step t23 (cl) :rule resolution :premises (t21 t22))
+bfe8d775ab64ce32fa8986be49dfdcae57d75099 60 0
+unsat
+(assume a0 (! (forall ((?v0 Int) (?v1 Int)) (! (= (! (fun_app$ (! (fun_app$a uu$ ?v0) :named @p_2) ?v1) :named @p_4) (! (<= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_1))
+(assume a1 (! (not (! (=> (! (= uu$ le$) :named @p_23) (! (fun_app$ (! (fun_app$a le$ 3) :named @p_40) 42) :named @p_24)) :named @p_28)) :named @p_22))
 (anchor :step t3 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
 (step t3.t2 (cl (= @p_2 (! (fun_app$a uu$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
@@ -3078,7 +3761,7 @@
 (step t3.t8 (cl (= @p_10 (! (= @p_5 @p_9) :named @p_11))) :rule cong :premises (t3.t4 t3.t7))
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_11) :named @p_13)) :named @p_12)) :rule bind)
 (step t4 (cl (not @p_12) (not @p_1) @p_13) :rule equiv_pos2)
-(step t5 (cl @p_13) :rule th_resolution :premises (axiom0 t3 t4))
+(step t5 (cl @p_13) :rule th_resolution :premises (a0 t3 t4))
 (anchor :step t6 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_16)) :rule refl)
 (step t6.t2 (cl (= @p_3 (! (fun_app$a uu$ veriT_vr2) :named @p_14))) :rule cong :premises (t6.t1))
@@ -3095,7 +3778,7 @@
 (step t10 (cl (! (not @p_25) :named @p_29) (! (not @p_22) :named @p_27) @p_26) :rule equiv_pos2)
 (step t11 (cl (not @p_27) @p_28) :rule not_not)
 (step t12 (cl @p_29 @p_28 @p_26) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_26) :rule th_resolution :premises (axiom1 t9 t12))
+(step t13 (cl @p_26) :rule th_resolution :premises (a1 t9 t12))
 (step t14 (cl @p_23) :rule and :premises (t13))
 (step t15 (cl @p_30) :rule and :premises (t13))
 (step t16 (cl (or (! (not @p_21) :named @p_37) (! (= (! (fun_app$ (! (fun_app$a uu$ 3) :named @p_41) 42) :named @p_32) (! (<= 3 42) :named @p_33)) :named @p_31))) :rule forall_inst :args ((:= veriT_vr2 3) (:= veriT_vr3 42)))
@@ -3124,40 +3807,12 @@
 (step t31 (cl @p_47) :rule eq_reflexive)
 (step t32 (cl @p_42 @p_24 @p_45) :rule th_resolution :premises (t30 t31))
 (step t33 (cl) :rule resolution :premises (t32 t14 t15 t25))
-cff62aa4cee92583faa1651c31b596d6853191d1 27 0
+2224e31ba45ff13284551d05730c64492fbe999c 125 0
 unsat
-(assume axiom0 (not (=> (f$ (! (forall ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
-(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (axiom0))
-(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
-(step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
-(step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
-(step t3 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind)
-(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3))
-(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2)
-(step t8 (cl (not @p_14) @p_8) :rule not_not)
-(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7))
-(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9))
-(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify)
-(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2)
-(step t13 (cl (not @p_18) @p_11) :rule not_not)
-(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12))
-(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14))
-(step t16 (cl (= @p_20 false)) :rule not_simplify)
-(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16))
-(step t18 (cl (= @p_21 false)) :rule and_simplify)
-(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18))
-(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2)
-(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
-(step t22 (cl (not false)) :rule false)
-(step t23 (cl) :rule resolution :premises (t21 t22))
-b98ce8490503b759ff8b992327f85a4088d1bb79 125 0
-unsat
-(assume axiom0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_2) (! (+ ?v0 1) :named @p_5)) :named @p_7)) :named @p_1))
-(assume axiom1 (! (forall ((?v0 Int_int_fun$)) (! (= nil$ (! (map$ ?v0 nil$) :named @p_22)) :named @p_24)) :named @p_21))
-(assume axiom2 (! (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$)) (! (= (! (map$ ?v0 (! (cons$ ?v1 ?v2) :named @p_33)) :named @p_35) (! (cons$ (! (fun_app$ ?v0 ?v1) :named @p_39) (! (map$ ?v0 ?v2) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_32))
-(assume axiom3 (not (! (= (! (map$ uu$ (cons$ 0 (! (cons$ 1 nil$) :named @p_62))) :named @p_61) (! (cons$ 1 (! (cons$ 2 nil$) :named @p_90)) :named @p_86)) :named @p_88)))
+(assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_2) (! (+ ?v0 1) :named @p_5)) :named @p_7)) :named @p_1))
+(assume a1 (! (forall ((?v0 Int_int_fun$)) (! (= nil$ (! (map$ ?v0 nil$) :named @p_22)) :named @p_24)) :named @p_21))
+(assume a2 (! (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$)) (! (= (! (map$ ?v0 (! (cons$ ?v1 ?v2) :named @p_33)) :named @p_35) (! (cons$ (! (fun_app$ ?v0 ?v1) :named @p_39) (! (map$ ?v0 ?v2) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_32))
+(assume a3 (not (! (= (! (map$ uu$ (cons$ 0 (! (cons$ 1 nil$) :named @p_62))) :named @p_61) (! (cons$ 1 (! (cons$ 2 nil$) :named @p_90)) :named @p_86)) :named @p_88)))
 (anchor :step t5 :args ((:= (?v0 Int) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t5.t2 (cl (= @p_2 (! (fun_app$ uu$ veriT_vr0) :named @p_3))) :rule cong :premises (t5.t1))
@@ -3166,7 +3821,7 @@
 (step t5.t5 (cl (= @p_7 (! (= @p_3 @p_6) :named @p_8))) :rule cong :premises (t5.t2 t5.t4))
 (step t5 (cl (! (= @p_1 (! (forall ((veriT_vr0 Int)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
 (step t6 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
-(step t7 (cl @p_10) :rule th_resolution :premises (axiom0 t5 t6))
+(step t7 (cl @p_10) :rule th_resolution :premises (a0 t5 t6))
 (anchor :step t8 :args ((veriT_vr0 Int)))
 (step t8.t1 (cl (= @p_6 (! (+ 1 veriT_vr0) :named @p_11))) :rule sum_simplify)
 (step t8.t2 (cl (= @p_8 (! (= @p_3 @p_11) :named @p_12))) :rule cong :premises (t8.t1))
@@ -3188,7 +3843,7 @@
 (step t14.t3 (cl (= @p_24 (! (= nil$ @p_23) :named @p_25))) :rule cong :premises (t14.t2))
 (step t14 (cl (! (= @p_21 (! (forall ((veriT_vr2 Int_int_fun$)) @p_25) :named @p_27)) :named @p_26)) :rule bind)
 (step t15 (cl (not @p_26) (not @p_21) @p_27) :rule equiv_pos2)
-(step t16 (cl @p_27) :rule th_resolution :premises (axiom1 t14 t15))
+(step t16 (cl @p_27) :rule th_resolution :premises (a1 t14 t15))
 (anchor :step t17 :args ((:= (veriT_vr2 Int_int_fun$) veriT_vr3)))
 (step t17.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl)
 (step t17.t2 (cl (= @p_23 (! (map$ veriT_vr3 nil$) :named @p_28))) :rule cong :premises (t17.t1))
@@ -3212,7 +3867,7 @@
 (step t20.t13 (cl (= @p_46 (! (= @p_36 @p_45) :named @p_47))) :rule cong :premises (t20.t5 t20.t12))
 (step t20 (cl (! (= @p_32 (! (forall ((veriT_vr4 Int_int_fun$) (veriT_vr5 Int) (veriT_vr6 Int_list$)) @p_47) :named @p_49)) :named @p_48)) :rule bind)
 (step t21 (cl (not @p_48) (not @p_32) @p_49) :rule equiv_pos2)
-(step t22 (cl @p_49) :rule th_resolution :premises (axiom2 t20 t21))
+(step t22 (cl @p_49) :rule th_resolution :premises (a2 t20 t21))
 (anchor :step t23 :args ((:= (veriT_vr4 Int_int_fun$) veriT_vr7) (:= (veriT_vr5 Int) veriT_vr8) (:= (veriT_vr6 Int_list$) veriT_vr9)))
 (step t23.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_52)) :rule refl)
 (step t23.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_53)) :rule refl)
@@ -3277,10 +3932,10 @@
 (step t58 (cl @p_96 @p_93 @p_94 @p_97) :rule th_resolution :premises (t56 t57))
 (step t59 (cl @p_89 @p_91 @p_96 @p_94 @p_97) :rule th_resolution :premises (t55 t58))
 (step t60 (cl @p_98 @p_88 @p_89 @p_96 @p_94 @p_97) :rule th_resolution :premises (t54 t59))
-(step t61 (cl) :rule resolution :premises (t60 axiom3 t28 t39 t41 t51 t53))
-4bfba84466bed875a9d6690636344a2452d6f312 23 0
+(step t61 (cl) :rule resolution :premises (t60 a3 t28 t39 t41 t51 t53))
+9bfeafd531163b7b5dc1f3e29f35b01c7ed668dc 23 0
 unsat
-(assume axiom0 (! (not (! (or (! (forall ((?v0 A$)) (! (p$ ?v0) :named @p_2)) :named @p_1) (! (not @p_1) :named @p_4)) :named @p_6)) :named @p_8))
+(assume a0 (! (not (! (or (! (forall ((?v0 A$)) (! (p$ ?v0) :named @p_2)) :named @p_1) (! (not @p_1) :named @p_4)) :named @p_6)) :named @p_8))
 (anchor :step t2 :args ((:= (?v0 A$) veriT_vr0)))
 (step t2.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (p$ veriT_vr0) :named @p_3))) :rule cong :premises (t2.t1))
@@ -3291,7 +3946,7 @@
 (step t6 (cl (! (not @p_10) :named @p_13) (! (not @p_8) :named @p_12) @p_11) :rule equiv_pos2)
 (step t7 (cl (not @p_12) @p_6) :rule not_not)
 (step t8 (cl @p_13 @p_6 @p_11) :rule th_resolution :premises (t7 t6))
-(step t9 (cl @p_11) :rule th_resolution :premises (axiom0 t5 t8))
+(step t9 (cl @p_11) :rule th_resolution :premises (a0 t5 t8))
 (step t10 (cl (= @p_9 true)) :rule or_simplify)
 (step t11 (cl (= @p_11 (! (not true) :named @p_14))) :rule cong :premises (t10))
 (step t12 (cl (= @p_14 false)) :rule not_simplify)
@@ -3302,59 +3957,10 @@
 (step t17 (cl false) :rule th_resolution :premises (t9 t13 t16))
 (step t18 (cl (not false)) :rule false)
 (step t19 (cl) :rule resolution :premises (t17 t18))
-2f429461f6d8832eb5f04c2d4afd47dfd1b769d9 48 0
+3fb3269903eddb271bcd0f8b72a806a38020c0d1 107 0
 unsat
-(assume axiom2 (! (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (! (=> (! (and (! (less_eq$ ?v0 ?v1) :named @p_4) (! (less_eq$ ?v1 ?v2) :named @p_7)) :named @p_9) (! (less_eq$ ?v0 ?v2) :named @p_13)) :named @p_15)) :named @p_3))
-(assume axiom3 (! (less_eq$ (! (sup$ (collect$ uu$)) :named @p_2) (! (sup$ (collect$ uua$)) :named @p_1)) :named @p_31))
-(assume axiom4 (! (less_eq$ @p_1 @p_2) :named @p_32))
-(assume axiom5 (not (! (less_eq$ @p_2 @p_2) :named @p_33)))
-(anchor :step t5 :args ((:= (?v0 A$) veriT_vr4) (:= (?v1 A$) veriT_vr5) (:= (?v2 A$) veriT_vr6)))
-(step t5.t1 (cl (! (= ?v0 veriT_vr4) :named @p_11)) :rule refl)
-(step t5.t2 (cl (! (= ?v1 veriT_vr5) :named @p_6)) :rule refl)
-(step t5.t3 (cl (= @p_4 (! (less_eq$ veriT_vr4 veriT_vr5) :named @p_5))) :rule cong :premises (t5.t1 t5.t2))
-(step t5.t4 (cl @p_6) :rule refl)
-(step t5.t5 (cl (! (= ?v2 veriT_vr6) :named @p_12)) :rule refl)
-(step t5.t6 (cl (= @p_7 (! (less_eq$ veriT_vr5 veriT_vr6) :named @p_8))) :rule cong :premises (t5.t4 t5.t5))
-(step t5.t7 (cl (= @p_9 (! (and @p_5 @p_8) :named @p_10))) :rule cong :premises (t5.t3 t5.t6))
-(step t5.t8 (cl @p_11) :rule refl)
-(step t5.t9 (cl @p_12) :rule refl)
-(step t5.t10 (cl (= @p_13 (! (less_eq$ veriT_vr4 veriT_vr6) :named @p_14))) :rule cong :premises (t5.t8 t5.t9))
-(step t5.t11 (cl (= @p_15 (! (=> @p_10 @p_14) :named @p_16))) :rule cong :premises (t5.t7 t5.t10))
-(step t5 (cl (! (= @p_3 (! (forall ((veriT_vr4 A$) (veriT_vr5 A$) (veriT_vr6 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
-(step t6 (cl (not @p_17) (not @p_3) @p_18) :rule equiv_pos2)
-(step t7 (cl @p_18) :rule th_resolution :premises (axiom2 t5 t6))
-(anchor :step t8 :args ((:= (veriT_vr4 A$) veriT_vr7) (:= (veriT_vr5 A$) veriT_vr8) (:= (veriT_vr6 A$) veriT_vr9)))
-(step t8.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_23)) :rule refl)
-(step t8.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_20)) :rule refl)
-(step t8.t3 (cl (= @p_5 (! (less_eq$ veriT_vr7 veriT_vr8) :named @p_19))) :rule cong :premises (t8.t1 t8.t2))
-(step t8.t4 (cl @p_20) :rule refl)
-(step t8.t5 (cl (! (= veriT_vr6 veriT_vr9) :named @p_24)) :rule refl)
-(step t8.t6 (cl (= @p_8 (! (less_eq$ veriT_vr8 veriT_vr9) :named @p_21))) :rule cong :premises (t8.t4 t8.t5))
-(step t8.t7 (cl (= @p_10 (! (and @p_19 @p_21) :named @p_22))) :rule cong :premises (t8.t3 t8.t6))
-(step t8.t8 (cl @p_23) :rule refl)
-(step t8.t9 (cl @p_24) :rule refl)
-(step t8.t10 (cl (= @p_14 (! (less_eq$ veriT_vr7 veriT_vr9) :named @p_25))) :rule cong :premises (t8.t8 t8.t9))
-(step t8.t11 (cl (= @p_16 (! (=> @p_22 @p_25) :named @p_26))) :rule cong :premises (t8.t7 t8.t10))
-(step t8 (cl (! (= @p_18 (! (forall ((veriT_vr7 A$) (veriT_vr8 A$) (veriT_vr9 A$)) @p_26) :named @p_28)) :named @p_27)) :rule bind)
-(step t9 (cl (not @p_27) (not @p_18) @p_28) :rule equiv_pos2)
-(step t10 (cl @p_28) :rule th_resolution :premises (t7 t8 t9))
-(step t11 (cl (or (! (not @p_28) :named @p_29) (! (forall ((veriT_vr7 A$) (veriT_vr8 A$) (veriT_vr9 A$)) (or (not @p_19) (not @p_21) @p_25)) :named @p_30))) :rule qnt_cnf)
-(step t12 (cl @p_29 @p_30) :rule or :premises (t11))
-(step t13 (cl (or (! (not @p_30) :named @p_34) (! (or (! (not @p_31) :named @p_39) (! (not @p_32) :named @p_40) @p_33) :named @p_35))) :rule forall_inst :args ((:= veriT_vr7 @p_2) (:= veriT_vr8 @p_1) (:= veriT_vr9 @p_2)))
-(step t14 (cl @p_34 @p_35) :rule or :premises (t13))
-(step t15 (cl (! (or @p_29 @p_35) :named @p_37) (! (not @p_29) :named @p_36)) :rule or_neg)
-(step t16 (cl (not @p_36) @p_28) :rule not_not)
-(step t17 (cl @p_37 @p_28) :rule th_resolution :premises (t16 t15))
-(step t18 (cl @p_37 (! (not @p_35) :named @p_38)) :rule or_neg)
-(step t19 (cl @p_37) :rule th_resolution :premises (t12 t14 t17 t18))
-(step t20 (cl @p_38 @p_39 @p_40 @p_33) :rule or_pos)
-(step t21 (cl @p_29 @p_35) :rule or :premises (t19))
-(step t22 (cl @p_38) :rule resolution :premises (t20 axiom3 axiom4 axiom5))
-(step t23 (cl) :rule resolution :premises (t21 t10 t22))
-8f4bf1893caa103dd59d38dee5686b501773527d 107 0
-unsat
-(assume axiom0 (! (forall ((?v0 Int)) (! (= (! (dec_10$ ?v0) :named @p_2) (! (ite (! (< ?v0 10) :named @p_5) ?v0 (! (dec_10$ (! (- ?v0 10) :named @p_7)) :named @p_9)) :named @p_11)) :named @p_13)) :named @p_1))
-(assume axiom1 (not (! (= (! (dec_10$ (! (* 4 (! (dec_10$ 4) :named @p_38)) :named @p_27)) :named @p_26) 6) :named @p_74)))
+(assume a0 (! (forall ((?v0 Int)) (! (= (! (dec_10$ ?v0) :named @p_2) (! (ite (! (< ?v0 10) :named @p_5) ?v0 (! (dec_10$ (! (- ?v0 10) :named @p_7)) :named @p_9)) :named @p_11)) :named @p_13)) :named @p_1))
+(assume a1 (not (! (= (! (dec_10$ (! (* 4 (! (dec_10$ 4) :named @p_38)) :named @p_27)) :named @p_26) 6) :named @p_74)))
 (anchor :step t3 :args ((:= (?v0 Int) veriT_vr0)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t3.t2 (cl (= @p_2 (! (dec_10$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
@@ -3368,7 +3974,7 @@
 (step t3.t10 (cl (= @p_13 (! (= @p_3 @p_12) :named @p_14))) :rule cong :premises (t3.t2 t3.t9))
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 Int)) @p_14) :named @p_16)) :named @p_15)) :rule bind)
 (step t4 (cl (not @p_15) (not @p_1) @p_16) :rule equiv_pos2)
-(step t5 (cl @p_16) :rule th_resolution :premises (axiom0 t3 t4))
+(step t5 (cl @p_16) :rule th_resolution :premises (a0 t3 t4))
 (anchor :step t6 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_18)) :rule refl)
 (step t6.t2 (cl (= @p_3 (! (dec_10$ veriT_vr1) :named @p_17))) :rule cong :premises (t6.t1))
@@ -3455,11 +4061,60 @@
 (step t57 (cl (! (not @p_64) :named @p_77) (! (not @p_66) :named @p_78) (! (not @p_68) :named @p_79) (! (= 6 @p_31) :named @p_73)) :rule eq_transitive)
 (step t58 (cl (not @p_73) (! (not @p_53) :named @p_75) (! (not @p_51) :named @p_76) @p_74) :rule eq_transitive)
 (step t59 (cl @p_75 @p_76 @p_74 @p_77 @p_78 @p_79) :rule th_resolution :premises (t58 t57))
-(step t60 (cl @p_75) :rule resolution :premises (t59 axiom1 t29 t45 t49 t56))
+(step t60 (cl @p_75) :rule resolution :premises (t59 a1 t29 t45 t49 t56))
 (step t61 (cl @p_30) :rule resolution :premises (t25 t60 t30))
 (step t62 (cl (not @p_30) @p_67) :rule la_generic :args (1 (- 4)))
 (step t63 (cl) :rule resolution :premises (t62 t61 t32))
-170ac60e28eef34728b56b5ef83cebdd5889b03f 1434 0
+21ed8993747dbe3d7fd900d61cf02456b0a38afa 48 0
+unsat
+(assume a2 (! (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (! (=> (! (and (! (less_eq$ ?v0 ?v1) :named @p_4) (! (less_eq$ ?v1 ?v2) :named @p_7)) :named @p_9) (! (less_eq$ ?v0 ?v2) :named @p_13)) :named @p_15)) :named @p_3))
+(assume a3 (! (less_eq$ (! (sup$ (collect$ uu$)) :named @p_2) (! (sup$ (collect$ uua$)) :named @p_1)) :named @p_31))
+(assume a4 (! (less_eq$ @p_1 @p_2) :named @p_32))
+(assume a5 (not (! (less_eq$ @p_2 @p_2) :named @p_33)))
+(anchor :step t5 :args ((:= (?v0 A$) veriT_vr4) (:= (?v1 A$) veriT_vr5) (:= (?v2 A$) veriT_vr6)))
+(step t5.t1 (cl (! (= ?v0 veriT_vr4) :named @p_11)) :rule refl)
+(step t5.t2 (cl (! (= ?v1 veriT_vr5) :named @p_6)) :rule refl)
+(step t5.t3 (cl (= @p_4 (! (less_eq$ veriT_vr4 veriT_vr5) :named @p_5))) :rule cong :premises (t5.t1 t5.t2))
+(step t5.t4 (cl @p_6) :rule refl)
+(step t5.t5 (cl (! (= ?v2 veriT_vr6) :named @p_12)) :rule refl)
+(step t5.t6 (cl (= @p_7 (! (less_eq$ veriT_vr5 veriT_vr6) :named @p_8))) :rule cong :premises (t5.t4 t5.t5))
+(step t5.t7 (cl (= @p_9 (! (and @p_5 @p_8) :named @p_10))) :rule cong :premises (t5.t3 t5.t6))
+(step t5.t8 (cl @p_11) :rule refl)
+(step t5.t9 (cl @p_12) :rule refl)
+(step t5.t10 (cl (= @p_13 (! (less_eq$ veriT_vr4 veriT_vr6) :named @p_14))) :rule cong :premises (t5.t8 t5.t9))
+(step t5.t11 (cl (= @p_15 (! (=> @p_10 @p_14) :named @p_16))) :rule cong :premises (t5.t7 t5.t10))
+(step t5 (cl (! (= @p_3 (! (forall ((veriT_vr4 A$) (veriT_vr5 A$) (veriT_vr6 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
+(step t6 (cl (not @p_17) (not @p_3) @p_18) :rule equiv_pos2)
+(step t7 (cl @p_18) :rule th_resolution :premises (a2 t5 t6))
+(anchor :step t8 :args ((:= (veriT_vr4 A$) veriT_vr7) (:= (veriT_vr5 A$) veriT_vr8) (:= (veriT_vr6 A$) veriT_vr9)))
+(step t8.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_23)) :rule refl)
+(step t8.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_20)) :rule refl)
+(step t8.t3 (cl (= @p_5 (! (less_eq$ veriT_vr7 veriT_vr8) :named @p_19))) :rule cong :premises (t8.t1 t8.t2))
+(step t8.t4 (cl @p_20) :rule refl)
+(step t8.t5 (cl (! (= veriT_vr6 veriT_vr9) :named @p_24)) :rule refl)
+(step t8.t6 (cl (= @p_8 (! (less_eq$ veriT_vr8 veriT_vr9) :named @p_21))) :rule cong :premises (t8.t4 t8.t5))
+(step t8.t7 (cl (= @p_10 (! (and @p_19 @p_21) :named @p_22))) :rule cong :premises (t8.t3 t8.t6))
+(step t8.t8 (cl @p_23) :rule refl)
+(step t8.t9 (cl @p_24) :rule refl)
+(step t8.t10 (cl (= @p_14 (! (less_eq$ veriT_vr7 veriT_vr9) :named @p_25))) :rule cong :premises (t8.t8 t8.t9))
+(step t8.t11 (cl (= @p_16 (! (=> @p_22 @p_25) :named @p_26))) :rule cong :premises (t8.t7 t8.t10))
+(step t8 (cl (! (= @p_18 (! (forall ((veriT_vr7 A$) (veriT_vr8 A$) (veriT_vr9 A$)) @p_26) :named @p_28)) :named @p_27)) :rule bind)
+(step t9 (cl (not @p_27) (not @p_18) @p_28) :rule equiv_pos2)
+(step t10 (cl @p_28) :rule th_resolution :premises (t7 t8 t9))
+(step t11 (cl (or (! (not @p_28) :named @p_29) (! (forall ((veriT_vr7 A$) (veriT_vr8 A$) (veriT_vr9 A$)) (or (not @p_19) (not @p_21) @p_25)) :named @p_30))) :rule qnt_cnf)
+(step t12 (cl @p_29 @p_30) :rule or :premises (t11))
+(step t13 (cl (or (! (not @p_30) :named @p_34) (! (or (! (not @p_31) :named @p_39) (! (not @p_32) :named @p_40) @p_33) :named @p_35))) :rule forall_inst :args ((:= veriT_vr7 @p_2) (:= veriT_vr8 @p_1) (:= veriT_vr9 @p_2)))
+(step t14 (cl @p_34 @p_35) :rule or :premises (t13))
+(step t15 (cl (! (or @p_29 @p_35) :named @p_37) (! (not @p_29) :named @p_36)) :rule or_neg)
+(step t16 (cl (not @p_36) @p_28) :rule not_not)
+(step t17 (cl @p_37 @p_28) :rule th_resolution :premises (t16 t15))
+(step t18 (cl @p_37 (! (not @p_35) :named @p_38)) :rule or_neg)
+(step t19 (cl @p_37) :rule th_resolution :premises (t12 t14 t17 t18))
+(step t20 (cl @p_38 @p_39 @p_40 @p_33) :rule or_pos)
+(step t21 (cl @p_29 @p_35) :rule or :premises (t19))
+(step t22 (cl @p_38) :rule resolution :premises (t20 a3 a4 a5))
+(step t23 (cl) :rule resolution :premises (t21 t10 t22))
+c14292db1124938af032dfdc907662d28ea67e96 1434 0
 unsat
 (define-fun veriT_sk0 () A$ (! (choice ((veriT_vr57 A$)) (not (! (=> (! (member$ veriT_vr57 (! (set$ (! (remdups$ xs$) :named @p_9)) :named @p_380)) :named @p_429) (! (not (! (member$ veriT_vr57 (! (set$ (! (remdups$ ys$) :named @p_10)) :named @p_381)) :named @p_431)) :named @p_432)) :named @p_433))) :named @p_449))
 (define-fun veriT_sk1 () A$ (! (choice ((veriT_vr58 A$)) (not (! (=> (! (member$ veriT_vr58 @p_381) :named @p_434) (! (not (! (member$ veriT_vr58 @p_380) :named @p_436)) :named @p_437)) :named @p_438))) :named @p_455))
@@ -3467,33 +4122,33 @@
 (define-fun veriT_sk6 () A$ (! (choice ((veriT_vr103 A$)) (not (! (=> (! (member$ veriT_vr103 @p_380) :named @p_879) (! (not (! (member$ veriT_vr103 @p_381) :named @p_881)) :named @p_882)) :named @p_878))) :named @p_857))
 (define-fun veriT_sk11 () A$ (! (choice ((veriT_vr117 A$)) (not (! (=> (! (member$ veriT_vr117 (! (coset$ xs$) :named @p_21)) :named @p_924) (! (member$ veriT_vr117 (! (set$ (! (append$ xs$ @p_10) :named @p_761)) :named @p_760)) :named @p_926)) :named @p_923))) :named @p_909))
 (define-fun veriT_sk14 () A$ (! (choice ((veriT_vr123 A$)) (not (! (=> (! (member$ veriT_vr123 @p_715) :named @p_969) (! (not (! (member$ veriT_vr123 @p_381) :named @p_971)) :named @p_972)) :named @p_968))) :named @p_943))
-(assume axiom0 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (= (! (fun_app$ (! (fun_app$a uu$ ?v0) :named @p_23) ?v1) :named @p_25) (! (= ?v0 ?v1) :named @p_13)) :named @p_30)) :named @p_22))
-(assume axiom1 (! (forall ((?v0 A_list$)) (! (= (! (fun_app$ (! (fun_app$a subset$ @p_21) :named @p_43) (! (set$ ?v0) :named @p_2)) :named @p_46) (! (and (! (less$ zero$ (! (fun_app$b card$ top$) :named @p_1)) :named @p_44) (! (= @p_1 (! (fun_app$b card$ (! (set$ (! (append$ xs$ ?v0) :named @p_49)) :named @p_51)) :named @p_53)) :named @p_55)) :named @p_57)) :named @p_59)) :named @p_42))
-(assume axiom2 (! (forall ((?v0 A$) (?v1 A_set$)) (! (=> (! (member$ ?v0 (! (uminus$ ?v1) :named @p_75)) :named @p_77) (! (not (! (member$ ?v0 ?v1) :named @p_81)) :named @p_83)) :named @p_85)) :named @p_74))
-(assume axiom3 (! (forall ((?v0 A_list$)) (! (= (! (fun_app$b card$ @p_2) :named @p_100) (! (size$ (! (remdups$ ?v0) :named @p_14)) :named @p_104)) :named @p_106)) :named @p_98))
-(assume axiom4 (! (forall ((?v0 A_list$)) (! (finite$ @p_2) :named @p_120)) :named @p_118))
-(assume axiom5 (! (forall ((?v0 A$)) (! (member$ ?v0 top$) :named @p_129)) :named @p_128))
-(assume axiom6 (not (! (= top$ bot$) :named @p_717)))
-(assume axiom9 (! (forall ((?v0 Nat$) (?v1 Nat$)) (! (= (! (= ?v0 (! (plus$ ?v0 ?v1) :named @p_138)) :named @p_140) (! (= zero$ ?v1) :named @p_143)) :named @p_145)) :named @p_136))
-(assume axiom10 (! (= (! (fun_app$b card$a @p_715) :named @p_1077) (! (size$ @p_9) :named @p_8)) :named @p_1076))
-(assume axiom11 (! (= card$ card$a) :named @p_1079))
-(assume axiom12 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> (! (and (! (finite$ ?v0) :named @p_4) (! (finite$ ?v1) :named @p_159)) :named @p_161) (! (= (! (plus$ (! (fun_app$b card$ ?v0) :named @p_3) (! (fun_app$b card$ ?v1) :named @p_166)) :named @p_168) (! (plus$ (! (fun_app$b card$ (! (sup$ ?v0 ?v1) :named @p_170)) :named @p_172) (! (fun_app$b card$ (! (inf$ ?v0 ?v1) :named @p_6)) :named @p_175)) :named @p_177)) :named @p_179)) :named @p_181)) :named @p_157))
-(assume axiom13 (! (forall ((?v0 A_set$)) (! (= (! (= zero$ @p_3) :named @p_204) (! (or (! (= ?v0 bot$) :named @p_207) (! (not @p_4) :named @p_210)) :named @p_212)) :named @p_214)) :named @p_202))
-(assume axiom14 (! (forall ((?v0 A_set$)) (! (=> (! (and (! (finite$ top$) :named @p_7) (! (= @p_1 @p_3) :named @p_230)) :named @p_232) (! (= ?v0 top$) :named @p_235)) :named @p_237)) :named @p_228))
-(assume axiom15 (! (forall ((?v0 A_list$)) (! (= @p_2 (! (uminus$ (! (coset$ ?v0) :named @p_5)) :named @p_253)) :named @p_255)) :named @p_249))
-(assume axiom16 (! (forall ((?v0 A_list$)) (! (= @p_5 (! (uminus$ @p_2) :named @p_270)) :named @p_272)) :named @p_266))
-(assume axiom17 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (= (! (= bot$ @p_6) :named @p_285) (! (forall ((?v2 A$)) (! (=> (! (member$ ?v2 ?v0) :named @p_15) (! (not (! (member$ ?v2 ?v1) :named @p_16)) :named @p_294)) :named @p_296)) :named @p_287)) :named @p_298)) :named @p_283))
-(assume axiom18 (! (= uu$ eq_set$) :named @p_1100))
-(assume axiom19 (! (forall ((?v0 A_set$)) (! (=> @p_4 (! (= (! (finite$ (! (uminus$ ?v0) :named @p_361)) :named @p_363) @p_7) :named @p_365)) :named @p_367)) :named @p_358))
-(assume axiom20 (! (= rhs$ (! (ite (! (= zero$ @p_1) :named @p_403) false (! (and (! (= @p_1 (! (plus$ @p_8 (! (size$ @p_10) :named @p_719)) :named @p_1056)) :named @p_400) (! (and (! (forall ((?v0 A$)) (! (=> (! (member$ ?v0 @p_380) :named @p_12) (! (not (! (member$ ?v0 @p_381) :named @p_11)) :named @p_385)) :named @p_387)) :named @p_379) (! (forall ((?v0 A$)) (! (=> @p_11 (! (not @p_12) :named @p_392)) :named @p_394)) :named @p_389)) :named @p_396)) :named @p_399)) :named @p_402)) :named @p_405))
-(assume axiom21 (! (forall ((?v0 A_list$) (?v1 A_list$)) (! (= (! (set$ (! (append$ ?v0 ?v1) :named @p_498)) :named @p_500) (! (sup$ @p_2 (! (set$ ?v1) :named @p_20)) :named @p_506)) :named @p_508)) :named @p_497))
-(assume axiom22 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (= @p_13 (! (and (! (fun_app$ (! (fun_app$a less_eq$ ?v0) :named @p_19) ?v1) :named @p_17) (! (fun_app$ (! (fun_app$a less_eq$ ?v1) :named @p_528) ?v0) :named @p_530)) :named @p_18)) :named @p_533)) :named @p_522))
-(assume axiom23 (! (forall ((?v0 A_list$)) (! (= @p_2 (! (set$ @p_14) :named @p_552)) :named @p_554)) :named @p_548))
-(assume axiom24 (! (= subset$ less_eq$) :named @p_1090))
-(assume axiom25 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> (! (forall ((?v2 A$)) (! (=> @p_15 @p_16) :named @p_571)) :named @p_566) @p_17) :named @p_577)) :named @p_565))
-(assume axiom26 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> @p_18 @p_13) :named @p_602)) :named @p_593))
-(assume axiom27 (! (forall ((?v0 A_set$) (?v1 A_list$)) (! (= (! (fun_app$ @p_19 (! (coset$ ?v1) :named @p_619)) :named @p_621) (! (forall ((?v2 A$)) (! (=> (! (member$ ?v2 @p_20) :named @p_627) (! (not @p_15) :named @p_632)) :named @p_634)) :named @p_623)) :named @p_636)) :named @p_617))
-(assume axiom28 (not (= (! (fun_app$ (! (fun_app$a eq_set$ @p_21) :named @p_1097) (! (set$ ys$) :named @p_713)) :named @p_711) rhs$)))
+(assume a0 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (= (! (fun_app$ (! (fun_app$a uu$ ?v0) :named @p_23) ?v1) :named @p_25) (! (= ?v0 ?v1) :named @p_13)) :named @p_30)) :named @p_22))
+(assume a1 (! (forall ((?v0 A_list$)) (! (= (! (fun_app$ (! (fun_app$a subset$ @p_21) :named @p_43) (! (set$ ?v0) :named @p_2)) :named @p_46) (! (and (! (less$ zero$ (! (fun_app$b card$ top$) :named @p_1)) :named @p_44) (! (= @p_1 (! (fun_app$b card$ (! (set$ (! (append$ xs$ ?v0) :named @p_49)) :named @p_51)) :named @p_53)) :named @p_55)) :named @p_57)) :named @p_59)) :named @p_42))
+(assume a2 (! (forall ((?v0 A$) (?v1 A_set$)) (! (=> (! (member$ ?v0 (! (uminus$ ?v1) :named @p_75)) :named @p_77) (! (not (! (member$ ?v0 ?v1) :named @p_81)) :named @p_83)) :named @p_85)) :named @p_74))
+(assume a3 (! (forall ((?v0 A_list$)) (! (= (! (fun_app$b card$ @p_2) :named @p_100) (! (size$ (! (remdups$ ?v0) :named @p_14)) :named @p_104)) :named @p_106)) :named @p_98))
+(assume a4 (! (forall ((?v0 A_list$)) (! (finite$ @p_2) :named @p_120)) :named @p_118))
+(assume a5 (! (forall ((?v0 A$)) (! (member$ ?v0 top$) :named @p_129)) :named @p_128))
+(assume a6 (not (! (= top$ bot$) :named @p_717)))
+(assume a9 (! (forall ((?v0 Nat$) (?v1 Nat$)) (! (= (! (= ?v0 (! (plus$ ?v0 ?v1) :named @p_138)) :named @p_140) (! (= zero$ ?v1) :named @p_143)) :named @p_145)) :named @p_136))
+(assume a10 (! (= (! (fun_app$b card$a @p_715) :named @p_1077) (! (size$ @p_9) :named @p_8)) :named @p_1076))
+(assume a11 (! (= card$ card$a) :named @p_1079))
+(assume a12 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> (! (and (! (finite$ ?v0) :named @p_4) (! (finite$ ?v1) :named @p_159)) :named @p_161) (! (= (! (plus$ (! (fun_app$b card$ ?v0) :named @p_3) (! (fun_app$b card$ ?v1) :named @p_166)) :named @p_168) (! (plus$ (! (fun_app$b card$ (! (sup$ ?v0 ?v1) :named @p_170)) :named @p_172) (! (fun_app$b card$ (! (inf$ ?v0 ?v1) :named @p_6)) :named @p_175)) :named @p_177)) :named @p_179)) :named @p_181)) :named @p_157))
+(assume a13 (! (forall ((?v0 A_set$)) (! (= (! (= zero$ @p_3) :named @p_204) (! (or (! (= ?v0 bot$) :named @p_207) (! (not @p_4) :named @p_210)) :named @p_212)) :named @p_214)) :named @p_202))
+(assume a14 (! (forall ((?v0 A_set$)) (! (=> (! (and (! (finite$ top$) :named @p_7) (! (= @p_1 @p_3) :named @p_230)) :named @p_232) (! (= ?v0 top$) :named @p_235)) :named @p_237)) :named @p_228))
+(assume a15 (! (forall ((?v0 A_list$)) (! (= @p_2 (! (uminus$ (! (coset$ ?v0) :named @p_5)) :named @p_253)) :named @p_255)) :named @p_249))
+(assume a16 (! (forall ((?v0 A_list$)) (! (= @p_5 (! (uminus$ @p_2) :named @p_270)) :named @p_272)) :named @p_266))
+(assume a17 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (= (! (= bot$ @p_6) :named @p_285) (! (forall ((?v2 A$)) (! (=> (! (member$ ?v2 ?v0) :named @p_15) (! (not (! (member$ ?v2 ?v1) :named @p_16)) :named @p_294)) :named @p_296)) :named @p_287)) :named @p_298)) :named @p_283))
+(assume a18 (! (= uu$ eq_set$) :named @p_1100))
+(assume a19 (! (forall ((?v0 A_set$)) (! (=> @p_4 (! (= (! (finite$ (! (uminus$ ?v0) :named @p_361)) :named @p_363) @p_7) :named @p_365)) :named @p_367)) :named @p_358))
+(assume a20 (! (= rhs$ (! (ite (! (= zero$ @p_1) :named @p_403) false (! (and (! (= @p_1 (! (plus$ @p_8 (! (size$ @p_10) :named @p_719)) :named @p_1056)) :named @p_400) (! (and (! (forall ((?v0 A$)) (! (=> (! (member$ ?v0 @p_380) :named @p_12) (! (not (! (member$ ?v0 @p_381) :named @p_11)) :named @p_385)) :named @p_387)) :named @p_379) (! (forall ((?v0 A$)) (! (=> @p_11 (! (not @p_12) :named @p_392)) :named @p_394)) :named @p_389)) :named @p_396)) :named @p_399)) :named @p_402)) :named @p_405))
+(assume a21 (! (forall ((?v0 A_list$) (?v1 A_list$)) (! (= (! (set$ (! (append$ ?v0 ?v1) :named @p_498)) :named @p_500) (! (sup$ @p_2 (! (set$ ?v1) :named @p_20)) :named @p_506)) :named @p_508)) :named @p_497))
+(assume a22 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (= @p_13 (! (and (! (fun_app$ (! (fun_app$a less_eq$ ?v0) :named @p_19) ?v1) :named @p_17) (! (fun_app$ (! (fun_app$a less_eq$ ?v1) :named @p_528) ?v0) :named @p_530)) :named @p_18)) :named @p_533)) :named @p_522))
+(assume a23 (! (forall ((?v0 A_list$)) (! (= @p_2 (! (set$ @p_14) :named @p_552)) :named @p_554)) :named @p_548))
+(assume a24 (! (= subset$ less_eq$) :named @p_1090))
+(assume a25 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> (! (forall ((?v2 A$)) (! (=> @p_15 @p_16) :named @p_571)) :named @p_566) @p_17) :named @p_577)) :named @p_565))
+(assume a26 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> @p_18 @p_13) :named @p_602)) :named @p_593))
+(assume a27 (! (forall ((?v0 A_set$) (?v1 A_list$)) (! (= (! (fun_app$ @p_19 (! (coset$ ?v1) :named @p_619)) :named @p_621) (! (forall ((?v2 A$)) (! (=> (! (member$ ?v2 @p_20) :named @p_627) (! (not @p_15) :named @p_632)) :named @p_634)) :named @p_623)) :named @p_636)) :named @p_617))
+(assume a28 (not (= (! (fun_app$ (! (fun_app$a eq_set$ @p_21) :named @p_1097) (! (set$ ys$) :named @p_713)) :named @p_711) rhs$)))
 (anchor :step t28 :args ((:= (?v0 A_set$) veriT_vr0) (:= (?v1 A_set$) veriT_vr1)))
 (step t28.t1 (cl (! (= ?v0 veriT_vr0) :named @p_27)) :rule refl)
 (step t28.t2 (cl (= @p_23 (! (fun_app$a uu$ veriT_vr0) :named @p_24))) :rule cong :premises (t28.t1))
@@ -3505,7 +4160,7 @@
 (step t28.t8 (cl (= @p_30 (! (= @p_26 @p_29) :named @p_31))) :rule cong :premises (t28.t4 t28.t7))
 (step t28 (cl (! (= @p_22 (! (forall ((veriT_vr0 A_set$) (veriT_vr1 A_set$)) @p_31) :named @p_33)) :named @p_32)) :rule bind)
 (step t29 (cl (not @p_32) (not @p_22) @p_33) :rule equiv_pos2)
-(step t30 (cl @p_33) :rule th_resolution :premises (axiom0 t28 t29))
+(step t30 (cl @p_33) :rule th_resolution :premises (a0 t28 t29))
 (anchor :step t31 :args ((:= (veriT_vr0 A_set$) veriT_vr2) (:= (veriT_vr1 A_set$) veriT_vr3)))
 (step t31.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_36)) :rule refl)
 (step t31.t2 (cl (= @p_24 (! (fun_app$a uu$ veriT_vr2) :named @p_34))) :rule cong :premises (t31.t1))
@@ -3531,7 +4186,7 @@
 (step t34.t10 (cl (= @p_59 (! (= @p_47 @p_58) :named @p_60))) :rule cong :premises (t34.t3 t34.t9))
 (step t34 (cl (! (= @p_42 (! (forall ((veriT_vr4 A_list$)) @p_60) :named @p_62)) :named @p_61)) :rule bind)
 (step t35 (cl (not @p_61) (not @p_42) @p_62) :rule equiv_pos2)
-(step t36 (cl @p_62) :rule th_resolution :premises (axiom1 t34 t35))
+(step t36 (cl @p_62) :rule th_resolution :premises (a1 t34 t35))
 (anchor :step t37 :args ((:= (veriT_vr4 A_list$) veriT_vr5)))
 (step t37.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_65)) :rule refl)
 (step t37.t2 (cl (= @p_45 (! (set$ veriT_vr5) :named @p_63))) :rule cong :premises (t37.t1))
@@ -3558,7 +4213,7 @@
 (step t40.t9 (cl (= @p_85 (! (=> @p_78 @p_84) :named @p_86))) :rule cong :premises (t40.t4 t40.t8))
 (step t40 (cl (! (= @p_74 (! (forall ((veriT_vr6 A$) (veriT_vr7 A_set$)) @p_86) :named @p_88)) :named @p_87)) :rule bind)
 (step t41 (cl (not @p_87) (not @p_74) @p_88) :rule equiv_pos2)
-(step t42 (cl @p_88) :rule th_resolution :premises (axiom2 t40 t41))
+(step t42 (cl @p_88) :rule th_resolution :premises (a2 t40 t41))
 (anchor :step t43 :args ((:= (veriT_vr6 A$) veriT_vr8) (:= (veriT_vr7 A_set$) veriT_vr9)))
 (step t43.t1 (cl (! (= veriT_vr6 veriT_vr8) :named @p_91)) :rule refl)
 (step t43.t2 (cl (! (= veriT_vr7 veriT_vr9) :named @p_92)) :rule refl)
@@ -3582,7 +4237,7 @@
 (step t46.t7 (cl (= @p_106 (! (= @p_101 @p_105) :named @p_107))) :rule cong :premises (t46.t3 t46.t6))
 (step t46 (cl (! (= @p_98 (! (forall ((veriT_vr10 A_list$)) @p_107) :named @p_109)) :named @p_108)) :rule bind)
 (step t47 (cl (not @p_108) (not @p_98) @p_109) :rule equiv_pos2)
-(step t48 (cl @p_109) :rule th_resolution :premises (axiom3 t46 t47))
+(step t48 (cl @p_109) :rule th_resolution :premises (a3 t46 t47))
 (anchor :step t49 :args ((:= (veriT_vr10 A_list$) veriT_vr11)))
 (step t49.t1 (cl (! (= veriT_vr10 veriT_vr11) :named @p_112)) :rule refl)
 (step t49.t2 (cl (= @p_99 (! (set$ veriT_vr11) :named @p_110))) :rule cong :premises (t49.t1))
@@ -3600,7 +4255,7 @@
 (step t52.t3 (cl (= @p_120 (! (finite$ @p_119) :named @p_121))) :rule cong :premises (t52.t2))
 (step t52 (cl (! (= @p_118 (! (forall ((veriT_vr12 A_list$)) @p_121) :named @p_123)) :named @p_122)) :rule bind)
 (step t53 (cl (not @p_122) (not @p_118) @p_123) :rule equiv_pos2)
-(step t54 (cl @p_123) :rule th_resolution :premises (axiom4 t52 t53))
+(step t54 (cl @p_123) :rule th_resolution :premises (a4 t52 t53))
 (anchor :step t55 :args ((:= (veriT_vr12 A_list$) veriT_vr13)))
 (step t55.t1 (cl (= veriT_vr12 veriT_vr13)) :rule refl)
 (step t55.t2 (cl (= @p_119 (! (set$ veriT_vr13) :named @p_124))) :rule cong :premises (t55.t1))
@@ -3613,7 +4268,7 @@
 (step t58.t2 (cl (= @p_129 (! (member$ veriT_vr14 top$) :named @p_130))) :rule cong :premises (t58.t1))
 (step t58 (cl (! (= @p_128 (! (forall ((veriT_vr14 A$)) @p_130) :named @p_132)) :named @p_131)) :rule bind)
 (step t59 (cl (not @p_131) (not @p_128) @p_132) :rule equiv_pos2)
-(step t60 (cl @p_132) :rule th_resolution :premises (axiom5 t58 t59))
+(step t60 (cl @p_132) :rule th_resolution :premises (a5 t58 t59))
 (anchor :step t61 :args ((:= (veriT_vr14 A$) veriT_vr15)))
 (step t61.t1 (cl (= veriT_vr14 veriT_vr15)) :rule refl)
 (step t61.t2 (cl (= @p_130 (! (member$ veriT_vr15 top$) :named @p_133))) :rule cong :premises (t61.t1))
@@ -3631,7 +4286,7 @@
 (step t64.t8 (cl (= @p_145 (! (= @p_141 @p_144) :named @p_146))) :rule cong :premises (t64.t5 t64.t7))
 (step t64 (cl (! (= @p_136 (! (forall ((veriT_vr26 Nat$) (veriT_vr27 Nat$)) @p_146) :named @p_148)) :named @p_147)) :rule bind)
 (step t65 (cl (not @p_147) (not @p_136) @p_148) :rule equiv_pos2)
-(step t66 (cl @p_148) :rule th_resolution :premises (axiom9 t64 t65))
+(step t66 (cl @p_148) :rule th_resolution :premises (a9 t64 t65))
 (anchor :step t67 :args ((:= (veriT_vr26 Nat$) veriT_vr28) (:= (veriT_vr27 Nat$) veriT_vr29)))
 (step t67.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_149)) :rule refl)
 (step t67.t2 (cl @p_149) :rule refl)
@@ -3668,7 +4323,7 @@
 (step t70.t21 (cl (= @p_181 (! (=> @p_162 @p_180) :named @p_182))) :rule cong :premises (t70.t5 t70.t20))
 (step t70 (cl (! (= @p_157 (! (forall ((veriT_vr30 A_set$) (veriT_vr31 A_set$)) @p_182) :named @p_184)) :named @p_183)) :rule bind)
 (step t71 (cl (not @p_183) (not @p_157) @p_184) :rule equiv_pos2)
-(step t72 (cl @p_184) :rule th_resolution :premises (axiom12 t70 t71))
+(step t72 (cl @p_184) :rule th_resolution :premises (a12 t70 t71))
 (anchor :step t73 :args ((:= (veriT_vr30 A_set$) veriT_vr32) (:= (veriT_vr31 A_set$) veriT_vr33)))
 (step t73.t1 (cl (! (= veriT_vr30 veriT_vr32) :named @p_188)) :rule refl)
 (step t73.t2 (cl (= @p_158 (! (finite$ veriT_vr32) :named @p_185))) :rule cong :premises (t73.t1))
@@ -3707,7 +4362,7 @@
 (step t76.t10 (cl (= @p_214 (! (= @p_205 @p_213) :named @p_215))) :rule cong :premises (t76.t3 t76.t9))
 (step t76 (cl (! (= @p_202 (! (forall ((veriT_vr34 A_set$)) @p_215) :named @p_217)) :named @p_216)) :rule bind)
 (step t77 (cl (not @p_216) (not @p_202) @p_217) :rule equiv_pos2)
-(step t78 (cl @p_217) :rule th_resolution :premises (axiom13 t76 t77))
+(step t78 (cl @p_217) :rule th_resolution :premises (a13 t76 t77))
 (anchor :step t79 :args ((:= (veriT_vr34 A_set$) veriT_vr35)))
 (step t79.t1 (cl (! (= veriT_vr34 veriT_vr35) :named @p_220)) :rule refl)
 (step t79.t2 (cl (= @p_203 (! (fun_app$b card$ veriT_vr35) :named @p_218))) :rule cong :premises (t79.t1))
@@ -3732,7 +4387,7 @@
 (step t82.t7 (cl (= @p_237 (! (=> @p_233 @p_236) :named @p_238))) :rule cong :premises (t82.t4 t82.t6))
 (step t82 (cl (! (= @p_228 (! (forall ((veriT_vr36 A_set$)) @p_238) :named @p_240)) :named @p_239)) :rule bind)
 (step t83 (cl (not @p_239) (not @p_228) @p_240) :rule equiv_pos2)
-(step t84 (cl @p_240) :rule th_resolution :premises (axiom14 t82 t83))
+(step t84 (cl @p_240) :rule th_resolution :premises (a14 t82 t83))
 (anchor :step t85 :args ((:= (veriT_vr36 A_set$) veriT_vr37)))
 (step t85.t1 (cl (! (= veriT_vr36 veriT_vr37) :named @p_244)) :rule refl)
 (step t85.t2 (cl (= @p_229 (! (fun_app$b card$ veriT_vr37) :named @p_241))) :rule cong :premises (t85.t1))
@@ -3753,7 +4408,7 @@
 (step t88.t6 (cl (= @p_255 (! (= @p_250 @p_254) :named @p_256))) :rule cong :premises (t88.t2 t88.t5))
 (step t88 (cl (! (= @p_249 (! (forall ((veriT_vr38 A_list$)) @p_256) :named @p_258)) :named @p_257)) :rule bind)
 (step t89 (cl (not @p_257) (not @p_249) @p_258) :rule equiv_pos2)
-(step t90 (cl @p_258) :rule th_resolution :premises (axiom15 t88 t89))
+(step t90 (cl @p_258) :rule th_resolution :premises (a15 t88 t89))
 (anchor :step t91 :args ((:= (veriT_vr38 A_list$) veriT_vr39)))
 (step t91.t1 (cl (! (= veriT_vr38 veriT_vr39) :named @p_260)) :rule refl)
 (step t91.t2 (cl (= @p_250 (! (set$ veriT_vr39) :named @p_259))) :rule cong :premises (t91.t1))
@@ -3773,7 +4428,7 @@
 (step t94.t6 (cl (= @p_272 (! (= @p_267 @p_271) :named @p_273))) :rule cong :premises (t94.t2 t94.t5))
 (step t94 (cl (! (= @p_266 (! (forall ((veriT_vr40 A_list$)) @p_273) :named @p_275)) :named @p_274)) :rule bind)
 (step t95 (cl (not @p_274) (not @p_266) @p_275) :rule equiv_pos2)
-(step t96 (cl @p_275) :rule th_resolution :premises (axiom16 t94 t95))
+(step t96 (cl @p_275) :rule th_resolution :premises (a16 t94 t95))
 (anchor :step t97 :args ((:= (veriT_vr40 A_list$) veriT_vr41)))
 (step t97.t1 (cl (! (= veriT_vr40 veriT_vr41) :named @p_277)) :rule refl)
 (step t97.t2 (cl (= @p_267 (! (coset$ veriT_vr41) :named @p_276))) :rule cong :premises (t97.t1))
@@ -3802,7 +4457,7 @@
 (step t100.t6 (cl (= @p_298 (! (= @p_286 @p_288) :named @p_299))) :rule cong :premises (t100.t4 t100.t5))
 (step t100 (cl (! (= @p_283 (! (forall ((veriT_vr42 A_set$) (veriT_vr43 A_set$)) @p_299) :named @p_301)) :named @p_300)) :rule bind)
 (step t101 (cl (not @p_300) (not @p_283) @p_301) :rule equiv_pos2)
-(step t102 (cl @p_301) :rule th_resolution :premises (axiom17 t100 t101))
+(step t102 (cl @p_301) :rule th_resolution :premises (a17 t100 t101))
 (anchor :step t103 :args ((veriT_vr42 A_set$) (veriT_vr43 A_set$)))
 (step t103.t1 (cl (= @p_299 (! (and (! (=> @p_286 @p_288) :named @p_315) (! (=> @p_288 @p_286) :named @p_325)) :named @p_302))) :rule connective_def)
 (step t103 (cl (! (= @p_301 (! (forall ((veriT_vr42 A_set$) (veriT_vr43 A_set$)) @p_302) :named @p_304)) :named @p_303)) :rule bind)
@@ -3902,7 +4557,7 @@
 (step t115.t7 (cl (= @p_367 (! (=> @p_359 @p_366) :named @p_368))) :rule cong :premises (t115.t2 t115.t6))
 (step t115 (cl (! (= @p_358 (! (forall ((veriT_vr53 A_set$)) @p_368) :named @p_370)) :named @p_369)) :rule bind)
 (step t116 (cl (not @p_369) (not @p_358) @p_370) :rule equiv_pos2)
-(step t117 (cl @p_370) :rule th_resolution :premises (axiom19 t115 t116))
+(step t117 (cl @p_370) :rule th_resolution :premises (a19 t115 t116))
 (anchor :step t118 :args ((:= (veriT_vr53 A_set$) veriT_vr54)))
 (step t118.t1 (cl (! (= veriT_vr53 veriT_vr54) :named @p_372)) :rule refl)
 (step t118.t2 (cl (= @p_359 (! (finite$ veriT_vr54) :named @p_371))) :rule cong :premises (t118.t1))
@@ -3935,7 +4590,7 @@
 (step t125 (cl (= @p_402 (! (ite @p_403 false @p_404) :named @p_406))) :rule cong :premises (t124))
 (step t126 (cl (! (= @p_405 (! (= rhs$ @p_406) :named @p_408)) :named @p_407)) :rule cong :premises (t125))
 (step t127 (cl (not @p_407) (not @p_405) @p_408) :rule equiv_pos2)
-(step t128 (cl @p_408) :rule th_resolution :premises (axiom20 t126 t127))
+(step t128 (cl @p_408) :rule th_resolution :premises (a20 t126 t127))
 (step t129 (cl (= @p_404 (! (and @p_400 @p_397 @p_398) :named @p_409))) :rule ac_simp)
 (step t130 (cl (= @p_406 (! (ite @p_403 false @p_409) :named @p_410))) :rule cong :premises (t129))
 (step t131 (cl (! (= @p_408 (! (= rhs$ @p_410) :named @p_412)) :named @p_411)) :rule cong :premises (t130))
@@ -4061,7 +4716,7 @@
 (step t185.t10 (cl (= @p_508 (! (= @p_501 @p_507) :named @p_509))) :rule cong :premises (t185.t4 t185.t9))
 (step t185 (cl (! (= @p_497 (! (forall ((veriT_vr61 A_list$) (veriT_vr62 A_list$)) @p_509) :named @p_511)) :named @p_510)) :rule bind)
 (step t186 (cl (not @p_510) (not @p_497) @p_511) :rule equiv_pos2)
-(step t187 (cl @p_511) :rule th_resolution :premises (axiom21 t185 t186))
+(step t187 (cl @p_511) :rule th_resolution :premises (a21 t185 t186))
 (anchor :step t188 :args ((:= (veriT_vr61 A_list$) veriT_vr63) (:= (veriT_vr62 A_list$) veriT_vr64)))
 (step t188.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_514)) :rule refl)
 (step t188.t2 (cl (! (= veriT_vr62 veriT_vr64) :named @p_516)) :rule refl)
@@ -4092,7 +4747,7 @@
 (step t191.t13 (cl (= @p_533 (! (= @p_523 @p_532) :named @p_534))) :rule cong :premises (t191.t3 t191.t12))
 (step t191 (cl (! (= @p_522 (! (forall ((veriT_vr65 A_set$) (veriT_vr66 A_set$)) @p_534) :named @p_536)) :named @p_535)) :rule bind)
 (step t192 (cl (not @p_535) (not @p_522) @p_536) :rule equiv_pos2)
-(step t193 (cl @p_536) :rule th_resolution :premises (axiom22 t191 t192))
+(step t193 (cl @p_536) :rule th_resolution :premises (a22 t191 t192))
 (anchor :step t194 :args ((:= (veriT_vr65 A_set$) veriT_vr67) (:= (veriT_vr66 A_set$) veriT_vr68)))
 (step t194.t1 (cl (! (= veriT_vr65 veriT_vr67) :named @p_538)) :rule refl)
 (step t194.t2 (cl (! (= veriT_vr66 veriT_vr68) :named @p_540)) :rule refl)
@@ -4119,7 +4774,7 @@
 (step t197.t6 (cl (= @p_554 (! (= @p_549 @p_553) :named @p_555))) :rule cong :premises (t197.t2 t197.t5))
 (step t197 (cl (! (= @p_548 (! (forall ((veriT_vr69 A_list$)) @p_555) :named @p_557)) :named @p_556)) :rule bind)
 (step t198 (cl (not @p_556) (not @p_548) @p_557) :rule equiv_pos2)
-(step t199 (cl @p_557) :rule th_resolution :premises (axiom23 t197 t198))
+(step t199 (cl @p_557) :rule th_resolution :premises (a23 t197 t198))
 (anchor :step t200 :args ((:= (veriT_vr69 A_list$) veriT_vr70)))
 (step t200.t1 (cl (! (= veriT_vr69 veriT_vr70) :named @p_559)) :rule refl)
 (step t200.t2 (cl (= @p_549 (! (set$ veriT_vr70) :named @p_558))) :rule cong :premises (t200.t1))
@@ -4147,7 +4802,7 @@
 (step t203.t6 (cl (= @p_577 (! (=> @p_567 @p_576) :named @p_578))) :rule cong :premises (t203.t1 t203.t5))
 (step t203 (cl (! (= @p_565 (! (forall ((veriT_vr71 A_set$) (veriT_vr72 A_set$)) @p_578) :named @p_580)) :named @p_579)) :rule bind)
 (step t204 (cl (not @p_579) (not @p_565) @p_580) :rule equiv_pos2)
-(step t205 (cl @p_580) :rule th_resolution :premises (axiom25 t203 t204))
+(step t205 (cl @p_580) :rule th_resolution :premises (a25 t203 t204))
 (anchor :step t206 :args ((:= (veriT_vr71 A_set$) veriT_vr74) (:= (veriT_vr72 A_set$) veriT_vr75)))
 (anchor :step t206.t1 :args ((:= (veriT_vr73 A$) veriT_vr76)))
 (step t206.t1.t1 (cl (! (= veriT_vr73 veriT_vr76) :named @p_583)) :rule refl)
@@ -4182,7 +4837,7 @@
 (step t209.t13 (cl (= @p_602 (! (=> @p_600 @p_601) :named @p_603))) :rule cong :premises (t209.t9 t209.t12))
 (step t209 (cl (! (= @p_593 (! (forall ((veriT_vr77 A_set$) (veriT_vr78 A_set$)) @p_603) :named @p_605)) :named @p_604)) :rule bind)
 (step t210 (cl (not @p_604) (not @p_593) @p_605) :rule equiv_pos2)
-(step t211 (cl @p_605) :rule th_resolution :premises (axiom26 t209 t210))
+(step t211 (cl @p_605) :rule th_resolution :premises (a26 t209 t210))
 (anchor :step t212 :args ((:= (veriT_vr77 A_set$) veriT_vr79) (:= (veriT_vr78 A_set$) veriT_vr80)))
 (step t212.t1 (cl (! (= veriT_vr77 veriT_vr79) :named @p_610)) :rule refl)
 (step t212.t2 (cl (= @p_594 (! (fun_app$a less_eq$ veriT_vr79) :named @p_606))) :rule cong :premises (t212.t1))
@@ -4220,7 +4875,7 @@
 (step t215.t7 (cl (= @p_636 (! (= @p_622 @p_624) :named @p_637))) :rule cong :premises (t215.t5 t215.t6))
 (step t215 (cl (! (= @p_617 (! (forall ((veriT_vr81 A_set$) (veriT_vr82 A_list$)) @p_637) :named @p_639)) :named @p_638)) :rule bind)
 (step t216 (cl (not @p_638) (not @p_617) @p_639) :rule equiv_pos2)
-(step t217 (cl @p_639) :rule th_resolution :premises (axiom27 t215 t216))
+(step t217 (cl @p_639) :rule th_resolution :premises (a27 t215 t216))
 (anchor :step t218 :args ((veriT_vr81 A_set$) (veriT_vr82 A_list$)))
 (step t218.t1 (cl (= @p_637 (! (and (! (=> @p_622 @p_624) :named @p_655) (! (=> @p_624 @p_622) :named @p_667)) :named @p_640))) :rule connective_def)
 (step t218 (cl (! (= @p_639 (! (forall ((veriT_vr81 A_set$) (veriT_vr82 A_list$)) @p_640) :named @p_642)) :named @p_641)) :rule bind)
@@ -4336,8 +4991,8 @@
 (step t245 (cl (not @p_707) @p_403) :rule not_not)
 (step t246 (cl @p_482 @p_403 @p_708 @p_709 @p_710) :rule th_resolution :premises (t245 t244))
 (step t247 (cl (not @p_482) rhs$) :rule implies :premises (t235))
-(step t248 (cl @p_711 rhs$) :rule not_equiv1 :premises (axiom28))
-(step t249 (cl (! (not @p_711) :named @p_1099) @p_712) :rule not_equiv2 :premises (axiom28))
+(step t248 (cl @p_711 rhs$) :rule not_equiv1 :premises (a28))
+(step t249 (cl (! (not @p_711) :named @p_1099) @p_712) :rule not_equiv2 :premises (a28))
 (step t250 (cl (or (! (not @p_474) :named @p_1028) (! (forall ((veriT_vr59 A$)) (or @p_472 @p_469)) :named @p_1029))) :rule qnt_cnf)
 (step t251 (cl (or (! (not @p_564) :named @p_714) (! (= @p_381 @p_713) :named @p_722))) :rule forall_inst :args ((:= veriT_vr70 ys$)))
 (step t252 (cl (or @p_714 (! (= @p_715 @p_380) :named @p_723))) :rule forall_inst :args ((:= veriT_vr70 xs$)))
@@ -4372,7 +5027,7 @@
 (step t281 (cl (! (not @p_732) :named @p_734) @p_403 @p_733) :rule equiv_pos1)
 (step t282 (cl @p_734 @p_422 @p_729) :rule equiv_pos2)
 (step t283 (cl @p_735 @p_732) :rule or :premises (t257))
-(step t284 (cl @p_733 @p_730) :rule resolution :premises (t277 axiom6))
+(step t284 (cl @p_733 @p_730) :rule resolution :premises (t277 a6))
 (step t285 (cl @p_732) :rule resolution :premises (t283 t81))
 (step t286 (cl @p_718 @p_736) :rule or :premises (t258))
 (step t287 (cl @p_736) :rule resolution :premises (t286 t57))
@@ -4797,7 +5452,7 @@
 (step t494 (cl @p_1089 @p_1086 @p_1043) :rule th_resolution :premises (t491 t493))
 (step t495 (cl @p_1075 @p_1083 @p_1082 @p_1089 @p_1043) :rule th_resolution :premises (t490 t494))
 (step t496 (cl @p_1054 @p_1070 @p_1071 @p_400 @p_1069 @p_1067 @p_1068 @p_1083 @p_1082 @p_1089 @p_1043) :rule th_resolution :premises (t484 t495))
-(step t497 (cl @p_1054 @p_1070 @p_400) :rule resolution :premises (t496 t270 axiom10 t319 t344 t405 t293 axiom11 t266))
+(step t497 (cl @p_1054 @p_1070 @p_400) :rule resolution :premises (t496 t270 a10 t319 t344 t405 t293 a11 t266))
 (step t498 (cl (not (! (= @p_43 @p_854) :named @p_1091)) (! (not (! (= @p_21 @p_939) :named @p_1094)) :named @p_1093) @p_1019 @p_1003) :rule eq_congruent_pred)
 (step t499 (cl (! (not @p_1090) :named @p_1092) @p_1051 @p_1091) :rule eq_congruent)
 (step t500 (cl @p_1092 @p_1091 @p_1040 @p_1043) :rule th_resolution :premises (t499 t453))
@@ -4805,7 +5460,7 @@
 (step t502 (cl @p_1040 @p_1043 @p_1067 @p_1068 @p_1094) :rule eq_transitive)
 (step t503 (cl @p_1019 @p_1003 @p_1092 @p_1040 @p_1043 @p_1040 @p_1043 @p_1067 @p_1068) :rule th_resolution :premises (t501 t502))
 (step t504 (cl @p_1019 @p_1003 @p_1092 @p_1040 @p_1043 @p_1067 @p_1068) :rule contraction :premises (t503))
-(step t505 (cl @p_1019 @p_1003 @p_1040) :rule resolution :premises (t504 axiom24 t266 t319 t270))
+(step t505 (cl @p_1019 @p_1003 @p_1040) :rule resolution :premises (t504 a24 t266 t319 t270))
 (step t506 (cl (not (! (= @p_713 @p_757) :named @p_1095)) @p_773 (! (not @p_736) :named @p_1096)) :rule eq_congruent_pred)
 (step t507 (cl @p_1040 @p_794 @p_1095) :rule eq_transitive)
 (step t508 (cl @p_773 @p_1096 @p_1040 @p_794) :rule th_resolution :premises (t506 t507))
@@ -4818,7 +5473,7 @@
 (step t515 (cl @p_1104 @p_748 @p_1099 @p_1103) :rule th_resolution :premises (t511 t514))
 (step t516 (cl @p_1105) :rule eq_reflexive)
 (step t517 (cl @p_748 @p_1099 @p_1103) :rule th_resolution :premises (t515 t516))
-(step t518 (cl @p_748 @p_1099) :rule resolution :premises (t517 axiom18))
+(step t518 (cl @p_748 @p_1099) :rule resolution :premises (t517 a18))
 (step t519 (cl rhs$) :rule resolution :premises (t471 t294 t243 t240 t246 t462 t497 t419 t416 t415 t410 t452 t422 t425 t505 t440 t282 t386 t284 t320 t328 t321 t509 t510 t301 t518 t248 t247 t296 t421 t418 t414 t427 t285 t390 t333 t323 t303))
 (step t520 (cl @p_493) :rule resolution :premises (t234 t519))
 (step t521 (cl @p_1099) :rule resolution :premises (t249 t519))
@@ -4833,7 +5488,7 @@
 (step t530 (cl @p_1106 @p_1104 @p_1107 @p_711) :rule eq_congruent_pred)
 (step t531 (cl @p_1104 @p_1107 @p_711 @p_1103) :rule th_resolution :premises (t530 t514))
 (step t532 (cl @p_1107 @p_711 @p_1103) :rule th_resolution :premises (t531 t516))
-(step t533 (cl @p_1107) :rule resolution :premises (t532 axiom18 t521))
+(step t533 (cl @p_1107) :rule resolution :premises (t532 a18 t521))
 (step t534 (cl (! (not (! (= @p_854 @p_854) :named @p_1110)) :named @p_1108) (not @p_796) @p_762 (! (not @p_855) :named @p_1109)) :rule eq_congruent_pred)
 (step t535 (cl @p_1108 @p_762 @p_1109 @p_794 @p_795 @p_797) :rule th_resolution :premises (t534 t351))
 (step t536 (cl @p_1110) :rule eq_reflexive)
@@ -4861,11 +5516,11 @@
 (step t558 (cl @p_708 @p_1072 @p_1071 @p_1070 @p_778 @p_1118 @p_1043) :rule th_resolution :premises (t550 t557))
 (step t559 (cl @p_708 @p_1071 @p_1070 @p_778 @p_1118 @p_1043 @p_1083 @p_1082 @p_1089 @p_1043) :rule th_resolution :premises (t558 t495))
 (step t560 (cl @p_708 @p_1071 @p_1070 @p_778 @p_1118 @p_1043 @p_1083 @p_1082 @p_1089) :rule contraction :premises (t559))
-(step t561 (cl @p_778) :rule resolution :premises (t560 axiom11 t523 t266 t293 t327 t344 axiom10 t546))
+(step t561 (cl @p_778) :rule resolution :premises (t560 a11 t523 t266 t293 t327 t344 a10 t546))
 (step t562 (cl @p_708 @p_1072 @p_1071 @p_1070 @p_1119 @p_1017) :rule eq_transitive)
 (step t563 (cl @p_708 @p_1072 @p_1071 @p_1070 @p_1017 @p_1069 @p_1067 @p_1068) :rule th_resolution :premises (t562 t483))
 (step t564 (cl @p_708 @p_1071 @p_1070 @p_1017 @p_1069 @p_1067 @p_1068 @p_1083 @p_1082 @p_1089 @p_1043) :rule th_resolution :premises (t563 t495))
-(step t565 (cl @p_1017) :rule resolution :premises (t564 axiom11 t523 t266 t270 axiom10 t319 t344 t405 t546 t293))
+(step t565 (cl @p_1017) :rule resolution :premises (t564 a11 t523 t266 t270 a10 t319 t344 t405 t546 t293))
 (step t566 (cl @p_767) :rule resolution :premises (t315 t549 t317))
 (step t567 (cl @p_777) :rule resolution :premises (t334 t561 t527))
 (step t568 (cl @p_1120) :rule resolution :premises (t314 t566 t538))
@@ -4875,7 +5530,7 @@
 (step t572 (cl @p_1092 @p_1111 @p_1123) :rule eq_congruent)
 (step t573 (cl @p_1092 @p_1123) :rule th_resolution :premises (t572 t513))
 (step t574 (cl @p_1121 @p_763 @p_1067 @p_1068 @p_1092) :rule th_resolution :premises (t571 t573))
-(step t575 (cl @p_1121) :rule resolution :premises (t574 axiom24 t270 t568 t319))
+(step t575 (cl @p_1121) :rule resolution :premises (t574 a24 t270 t568 t319))
 (step t576 (cl (not (! (= veriT_sk11 veriT_sk11) :named @p_1124)) (! (not (! (= top$ @p_760) :named @p_1128)) :named @p_1125) @p_933 (! (not @p_1039) :named @p_1126)) :rule eq_congruent_pred)
 (step t577 (cl @p_1124) :rule eq_reflexive)
 (step t578 (cl @p_1125 @p_933 @p_1126) :rule th_resolution :premises (t576 t577))
@@ -4893,680 +5548,76 @@
 (step t590 (cl @p_1134 @p_1135 @p_790 @p_1092) :rule th_resolution :premises (t589 t573))
 (step t591 (cl @p_1136) :rule eq_reflexive)
 (step t592 (cl @p_1135 @p_790 @p_1092) :rule th_resolution :premises (t590 t591))
-(step t593 (cl) :rule resolution :premises (t592 axiom24 t588 t586))
-d8bde960a6a2cb3d70d1b157d08487440b364301 654 0
+(step t593 (cl) :rule resolution :premises (t592 a24 t588 t586))
+7d1d28af77b48e47cf45f7abbbccb64bffffc3f9 6 0
+unsat
+(assume a0 (! (< 0.0 (+ x$ (! (* 2.0 y$) :named @p_1))) :named @p_2))
+(assume a1 (! (< 0.0 (- x$ @p_1)) :named @p_3))
+(assume a2 (! (< x$ 0.0) :named @p_4))
+(step t4 (cl (not @p_2) (not @p_3) (not @p_4)) :rule la_generic :args (1.0 1.0 2.0))
+(step t5 (cl) :rule resolution :premises (t4 a0 a1 a2))
[phone]c370281d48d21e99833e7ceba6103960 26 0
 unsat
-(assume axiom0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uua$ ?v0) :named @p_13) (! (line_integral_exists$ f$ (! (insert$ j$ bot$) :named @p_7)) :named @p_12)) :named @p_15)) :named @p_11))
-(assume axiom1 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_25) (! (line_integral_exists$ f$ (! (insert$ i$ bot$) :named @p_5)) :named @p_24)) :named @p_27)) :named @p_23))
-(assume axiom2 (! (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (! (= (! (case_prod$ ?v0 ?v1) :named @p_36) (! (fun_app$a (! (fun_app$ ?v0 (! (fst$ ?v1) :named @p_40)) :named @p_42) (! (snd$ ?v1) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
-(assume axiom3 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (! (=> (! (= (! (insert$ ?v0 bot$) :named @p_3) (! (insert$ ?v1 bot$) :named @p_64)) :named @p_66) (! (= ?v0 ?v1) :named @p_70)) :named @p_72)) :named @p_62))
-(assume axiom4 (! (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (! (= ?v1 (! (snd$ (! (pair$ ?v0 ?v1) :named @p_87)) :named @p_89)) :named @p_91)) :named @p_85))
-(assume axiom5 (! (forall ((?v0 Real) (?v1 Real)) (! (= ?v1 (! (snd$a (! (fun_app$b (! (pair$a ?v0) :named @p_102) ?v1) :named @p_105)) :named @p_107)) :named @p_109)) :named @p_101))
-(assume axiom6 (! (member$ (! (pair$ k$ g$) :named @p_403) one_chain_typeI$) :named @p_402))
-(assume axiom7 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (= bot$ (! (inf$ ?v0 (! (insert$ ?v1 ?v2) :named @p_1)) :named @p_122)) :named @p_124) (! (and (! (not (! (member$a ?v1 ?v0) :named @p_128)) :named @p_130) (! (= bot$ (! (inf$ ?v0 ?v2) :named @p_133)) :named @p_135)) :named @p_137)) :named @p_139)) :named @p_120))
-(assume axiom8 (! (finite$ bot$) :named @p_414))
-(assume axiom9 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (! (=> (! (finite$ ?v0) :named @p_4) (! (finite$ (! (insert$ ?v1 ?v0) :named @p_160)) :named @p_162)) :named @p_164)) :named @p_157))
-(assume axiom10 (! (= i$ (! (fun_app$b (pair$a 1.0) 0.0) :named @p_417)) :named @p_499))
-(assume axiom11 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (=> (! (member$a ?v0 ?v1) :named @p_176) (! (= ?v1 (! (insert$ ?v0 ?v1) :named @p_2)) :named @p_181)) :named @p_183)) :named @p_175))
-(assume axiom12 (! (= j$ (! (fun_app$b (pair$a 0.0) 1.0) :named @p_419)) :named @p_500))
-(assume axiom13 (! (forall ((?v0 Real_real_prod_set$)) (! (= bot$ (! (inf$ ?v0 bot$) :named @p_196)) :named @p_198)) :named @p_195))
-(assume axiom14 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (insert$ ?v0 @p_1) :named @p_208) (! (insert$ ?v1 (! (insert$ ?v0 ?v2) :named @p_213)) :named @p_215)) :named @p_217)) :named @p_206))
-(assume axiom15 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (= @p_2 (! (sup$ @p_3 ?v1) :named @p_236)) :named @p_238)) :named @p_231))
-(assume axiom16 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (! (=> (! (and @p_4 (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v2) :named @p_252) ?v3) :named @p_254) (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v4) :named @p_257) ?v3) :named @p_260) (! (and (! (= ?v0 (! (sup$ ?v2 ?v4) :named @p_265)) :named @p_267) (! (= bot$ (! (inf$ ?v2 ?v4) :named @p_269)) :named @p_271)) :named @p_273)) :named @p_275)) :named @p_277)) :named @p_279) (! (= (! (line_integral$ ?v1 ?v0 ?v3) :named @p_281) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_283) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_285)) :named @p_287)) :named @p_289)) :named @p_291)) :named @p_250))
-(assume axiom17 (! (and (! (= (one_chain_line_integral$ f$ @p_5 one_chain_typeI$) (one_chain_line_integral$ f$ @p_5 one_chain_typeII$)) :named @p_337) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeI$) :named @p_9) (! (case_prod$ uu$ ?v0) :named @p_6)) :named @p_326)) :named @p_322) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeII$) :named @p_8) @p_6) :named @p_331)) :named @p_328)) :named @p_333)) :named @p_336))
-(assume axiom18 (! (and (! (= (one_chain_line_integral$ f$ @p_7 one_chain_typeII$) (one_chain_line_integral$ f$ @p_7 one_chain_typeI$)) :named @p_377) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_8 (! (case_prod$ uua$ ?v0) :named @p_10)) :named @p_366)) :named @p_362) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_9 @p_10) :named @p_371)) :named @p_368)) :named @p_373)) :named @p_376))
-(assume axiom19 (not (! (= (! (line_integral$ f$ (! (insert$ i$ @p_7) :named @p_407) g$) :named @p_462) (! (+ (! (line_integral$ f$ @p_5 g$) :named @p_404) (! (line_integral$ f$ @p_7 g$) :named @p_405)) :named @p_463)) :named @p_410)))
-(anchor :step t21 :args ((:= (?v0 Int) veriT_vr0)))
-(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
-(step t21.t2 (cl (= @p_13 (! (fun_app$ uua$ veriT_vr0) :named @p_14))) :rule cong :premises (t21.t1))
-(step t21.t3 (cl (= @p_15 (! (= @p_12 @p_14) :named @p_16))) :rule cong :premises (t21.t2))
-(step t21 (cl (! (= @p_11 (! (forall ((veriT_vr0 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
-(step t22 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2)
-(step t23 (cl @p_18) :rule th_resolution :premises (axiom0 t21 t22))
-(anchor :step t24 :args ((:= (veriT_vr0 Int) veriT_vr1)))
-(step t24.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl)
-(step t24.t2 (cl (= @p_14 (! (fun_app$ uua$ veriT_vr1) :named @p_19))) :rule cong :premises (t24.t1))
-(step t24.t3 (cl (= @p_16 (! (= @p_12 @p_19) :named @p_20))) :rule cong :premises (t24.t2))
-(step t24 (cl (! (= @p_18 (! (forall ((veriT_vr1 Int)) @p_20) :named @p_22)) :named @p_21)) :rule bind)
-(step t25 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2)
-(step t26 (cl @p_22) :rule th_resolution :premises (t23 t24 t25))
-(anchor :step t27 :args ((:= (?v0 Int) veriT_vr2)))
-(step t27.t1 (cl (= ?v0 veriT_vr2)) :rule refl)
-(step t27.t2 (cl (= @p_25 (! (fun_app$ uu$ veriT_vr2) :named @p_26))) :rule cong :premises (t27.t1))
-(step t27.t3 (cl (= @p_27 (! (= @p_24 @p_26) :named @p_28))) :rule cong :premises (t27.t2))
-(step t27 (cl (! (= @p_23 (! (forall ((veriT_vr2 Int)) @p_28) :named @p_30)) :named @p_29)) :rule bind)
-(step t28 (cl (not @p_29) (not @p_23) @p_30) :rule equiv_pos2)
-(step t29 (cl @p_30) :rule th_resolution :premises (axiom1 t27 t28))
-(anchor :step t30 :args ((:= (veriT_vr2 Int) veriT_vr3)))
-(step t30.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl)
-(step t30.t2 (cl (= @p_26 (! (fun_app$ uu$ veriT_vr3) :named @p_31))) :rule cong :premises (t30.t1))
-(step t30.t3 (cl (= @p_28 (! (= @p_24 @p_31) :named @p_32))) :rule cong :premises (t30.t2))
-(step t30 (cl (! (= @p_30 (! (forall ((veriT_vr3 Int)) @p_32) :named @p_34)) :named @p_33)) :rule bind)
-(step t31 (cl (not @p_33) (not @p_30) @p_34) :rule equiv_pos2)
-(step t32 (cl @p_34) :rule th_resolution :premises (t29 t30 t31))
-(anchor :step t33 :args ((:= (?v0 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr4) (:= (?v1 Int_real_real_real_prod_fun_prod$) veriT_vr5)))
-(step t33.t1 (cl (! (= ?v0 veriT_vr4) :named @p_38)) :rule refl)
-(step t33.t2 (cl (! (= ?v1 veriT_vr5) :named @p_39)) :rule refl)
-(step t33.t3 (cl (= @p_36 (! (case_prod$ veriT_vr4 veriT_vr5) :named @p_37))) :rule cong :premises (t33.t1 t33.t2))
-(step t33.t4 (cl @p_38) :rule refl)
-(step t33.t5 (cl @p_39) :rule refl)
-(step t33.t6 (cl (= @p_40 (! (fst$ veriT_vr5) :named @p_41))) :rule cong :premises (t33.t5))
-(step t33.t7 (cl (= @p_42 (! (fun_app$ veriT_vr4 @p_41) :named @p_43))) :rule cong :premises (t33.t4 t33.t6))
-(step t33.t8 (cl @p_39) :rule refl)
-(step t33.t9 (cl (= @p_44 (! (snd$ veriT_vr5) :named @p_45))) :rule cong :premises (t33.t8))
-(step t33.t10 (cl (= @p_46 (! (fun_app$a @p_43 @p_45) :named @p_47))) :rule cong :premises (t33.t7 t33.t9))
-(step t33.t11 (cl (= @p_48 (! (= @p_37 @p_47) :named @p_49))) :rule cong :premises (t33.t3 t33.t10))
-(step t33 (cl (! (= @p_35 (! (forall ((veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr5 Int_real_real_real_prod_fun_prod$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
-(step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
-(step t35 (cl @p_51) :rule th_resolution :premises (axiom2 t33 t34))
-(anchor :step t36 :args ((:= (veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr6) (:= (veriT_vr5 Int_real_real_real_prod_fun_prod$) veriT_vr7)))
-(step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl)
-(step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl)
-(step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2))
-(step t36.t4 (cl @p_53) :rule refl)
-(step t36.t5 (cl @p_54) :rule refl)
-(step t36.t6 (cl (= @p_41 (! (fst$ veriT_vr7) :named @p_55))) :rule cong :premises (t36.t5))
-(step t36.t7 (cl (= @p_43 (! (fun_app$ veriT_vr6 @p_55) :named @p_56))) :rule cong :premises (t36.t4 t36.t6))
-(step t36.t8 (cl @p_54) :rule refl)
-(step t36.t9 (cl (= @p_45 (! (snd$ veriT_vr7) :named @p_57))) :rule cong :premises (t36.t8))
-(step t36.t10 (cl (= @p_47 (! (fun_app$a @p_56 @p_57) :named @p_58))) :rule cong :premises (t36.t7 t36.t9))
-(step t36.t11 (cl (= @p_49 (! (= @p_52 @p_58) :named @p_59))) :rule cong :premises (t36.t3 t36.t10))
-(step t36 (cl (! (= @p_51 (! (forall ((veriT_vr6 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr7 Int_real_real_real_prod_fun_prod$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
-(step t37 (cl (not @p_60) (not @p_51) @p_61) :rule equiv_pos2)
-(step t38 (cl @p_61) :rule th_resolution :premises (t35 t36 t37))
-(anchor :step t39 :args ((:= (?v0 Real_real_prod$) veriT_vr8) (:= (?v1 Real_real_prod$) veriT_vr9)))
-(step t39.t1 (cl (! (= ?v0 veriT_vr8) :named @p_68)) :rule refl)
-(step t39.t2 (cl (= @p_3 (! (insert$ veriT_vr8 bot$) :named @p_63))) :rule cong :premises (t39.t1))
-(step t39.t3 (cl (! (= ?v1 veriT_vr9) :named @p_69)) :rule refl)
-(step t39.t4 (cl (= @p_64 (! (insert$ veriT_vr9 bot$) :named @p_65))) :rule cong :premises (t39.t3))
-(step t39.t5 (cl (= @p_66 (! (= @p_63 @p_65) :named @p_67))) :rule cong :premises (t39.t2 t39.t4))
-(step t39.t6 (cl @p_68) :rule refl)
-(step t39.t7 (cl @p_69) :rule refl)
-(step t39.t8 (cl (= @p_70 (! (= veriT_vr8 veriT_vr9) :named @p_71))) :rule cong :premises (t39.t6 t39.t7))
-(step t39.t9 (cl (= @p_72 (! (=> @p_67 @p_71) :named @p_73))) :rule cong :premises (t39.t5 t39.t8))
-(step t39 (cl (! (= @p_62 (! (forall ((veriT_vr8 Real_real_prod$) (veriT_vr9 Real_real_prod$)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
-(step t40 (cl (not @p_74) (not @p_62) @p_75) :rule equiv_pos2)
-(step t41 (cl @p_75) :rule th_resolution :premises (axiom3 t39 t40))
-(anchor :step t42 :args ((:= (veriT_vr8 Real_real_prod$) veriT_vr10) (:= (veriT_vr9 Real_real_prod$) veriT_vr11)))
-(step t42.t1 (cl (! (= veriT_vr8 veriT_vr10) :named @p_79)) :rule refl)
-(step t42.t2 (cl (= @p_63 (! (insert$ veriT_vr10 bot$) :named @p_76))) :rule cong :premises (t42.t1))
-(step t42.t3 (cl (! (= veriT_vr9 veriT_vr11) :named @p_80)) :rule refl)
-(step t42.t4 (cl (= @p_65 (! (insert$ veriT_vr11 bot$) :named @p_77))) :rule cong :premises (t42.t3))
-(step t42.t5 (cl (= @p_67 (! (= @p_76 @p_77) :named @p_78))) :rule cong :premises (t42.t2 t42.t4))
-(step t42.t6 (cl @p_79) :rule refl)
-(step t42.t7 (cl @p_80) :rule refl)
-(step t42.t8 (cl (= @p_71 (! (= veriT_vr10 veriT_vr11) :named @p_81))) :rule cong :premises (t42.t6 t42.t7))
-(step t42.t9 (cl (= @p_73 (! (=> @p_78 @p_81) :named @p_82))) :rule cong :premises (t42.t5 t42.t8))
-(step t42 (cl (! (= @p_75 (! (forall ((veriT_vr10 Real_real_prod$) (veriT_vr11 Real_real_prod$)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
-(step t43 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
-(step t44 (cl @p_84) :rule th_resolution :premises (t41 t42 t43))
-(anchor :step t45 :args ((:= (?v0 Int) veriT_vr12) (:= (?v1 Real_real_real_prod_fun$) veriT_vr13)))
-(step t45.t1 (cl (! (= ?v1 veriT_vr13) :named @p_86)) :rule refl)
-(step t45.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
-(step t45.t3 (cl @p_86) :rule refl)
-(step t45.t4 (cl (= @p_87 (! (pair$ veriT_vr12 veriT_vr13) :named @p_88))) :rule cong :premises (t45.t2 t45.t3))
-(step t45.t5 (cl (= @p_89 (! (snd$ @p_88) :named @p_90))) :rule cong :premises (t45.t4))
-(step t45.t6 (cl (= @p_91 (! (= veriT_vr13 @p_90) :named @p_92))) :rule cong :premises (t45.t1 t45.t5))
-(step t45 (cl (! (= @p_85 (! (forall ((veriT_vr12 Int) (veriT_vr13 Real_real_real_prod_fun$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
-(step t46 (cl (not @p_93) (not @p_85) @p_94) :rule equiv_pos2)
-(step t47 (cl @p_94) :rule th_resolution :premises (axiom4 t45 t46))
-(anchor :step t48 :args ((:= (veriT_vr12 Int) veriT_vr14) (:= (veriT_vr13 Real_real_real_prod_fun$) veriT_vr15)))
-(step t48.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_95)) :rule refl)
-(step t48.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
-(step t48.t3 (cl @p_95) :rule refl)
-(step t48.t4 (cl (= @p_88 (! (pair$ veriT_vr14 veriT_vr15) :named @p_96))) :rule cong :premises (t48.t2 t48.t3))
-(step t48.t5 (cl (= @p_90 (! (snd$ @p_96) :named @p_97))) :rule cong :premises (t48.t4))
-(step t48.t6 (cl (= @p_92 (! (= veriT_vr15 @p_97) :named @p_98))) :rule cong :premises (t48.t1 t48.t5))
-(step t48 (cl (! (= @p_94 (! (forall ((veriT_vr14 Int) (veriT_vr15 Real_real_real_prod_fun$)) @p_98) :named @p_100)) :named @p_99)) :rule bind)
-(step t49 (cl (not @p_99) (not @p_94) @p_100) :rule equiv_pos2)
-(step t50 (cl @p_100) :rule th_resolution :premises (t47 t48 t49))
-(anchor :step t51 :args ((:= (?v0 Real) veriT_vr16) (:= (?v1 Real) veriT_vr17)))
-(step t51.t1 (cl (! (= ?v1 veriT_vr17) :named @p_104)) :rule refl)
-(step t51.t2 (cl (= ?v0 veriT_vr16)) :rule refl)
-(step t51.t3 (cl (= @p_102 (! (pair$a veriT_vr16) :named @p_103))) :rule cong :premises (t51.t2))
-(step t51.t4 (cl @p_104) :rule refl)
-(step t51.t5 (cl (= @p_105 (! (fun_app$b @p_103 veriT_vr17) :named @p_106))) :rule cong :premises (t51.t3 t51.t4))
-(step t51.t6 (cl (= @p_107 (! (snd$a @p_106) :named @p_108))) :rule cong :premises (t51.t5))
-(step t51.t7 (cl (= @p_109 (! (= veriT_vr17 @p_108) :named @p_110))) :rule cong :premises (t51.t1 t51.t6))
-(step t51 (cl (! (= @p_101 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_110) :named @p_112)) :named @p_111)) :rule bind)
-(step t52 (cl (not @p_111) (not @p_101) @p_112) :rule equiv_pos2)
-(step t53 (cl @p_112) :rule th_resolution :premises (axiom5 t51 t52))
-(anchor :step t54 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
-(step t54.t1 (cl (! (= veriT_vr17 veriT_vr19) :named @p_114)) :rule refl)
-(step t54.t2 (cl (= veriT_vr16 veriT_vr18)) :rule refl)
-(step t54.t3 (cl (= @p_103 (! (pair$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2))
-(step t54.t4 (cl @p_114) :rule refl)
-(step t54.t5 (cl (= @p_106 (! (fun_app$b @p_113 veriT_vr19) :named @p_115))) :rule cong :premises (t54.t3 t54.t4))
-(step t54.t6 (cl (= @p_108 (! (snd$a @p_115) :named @p_116))) :rule cong :premises (t54.t5))
-(step t54.t7 (cl (= @p_110 (! (= veriT_vr19 @p_116) :named @p_117))) :rule cong :premises (t54.t1 t54.t6))
-(step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind)
-(step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2)
-(step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55))
-(anchor :step t57 :args ((:= (?v0 Real_real_prod_set$) veriT_vr20) (:= (?v1 Real_real_prod$) veriT_vr21) (:= (?v2 Real_real_prod_set$) veriT_vr22)))
-(step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl)
-(step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl)
-(step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl)
-(step t57.t4 (cl (= @p_1 (! (insert$ veriT_vr21 veriT_vr22) :named @p_121))) :rule cong :premises (t57.t2 t57.t3))
-(step t57.t5 (cl (= @p_122 (! (inf$ veriT_vr20 @p_121) :named @p_123))) :rule cong :premises (t57.t1 t57.t4))
-(step t57.t6 (cl (= @p_124 (! (= bot$ @p_123) :named @p_125))) :rule cong :premises (t57.t5))
-(step t57.t7 (cl @p_126) :rule refl)
-(step t57.t8 (cl @p_127) :rule refl)
-(step t57.t9 (cl (= @p_128 (! (member$a veriT_vr21 veriT_vr20) :named @p_129))) :rule cong :premises (t57.t7 t57.t8))
-(step t57.t10 (cl (= @p_130 (! (not @p_129) :named @p_131))) :rule cong :premises (t57.t9))
-(step t57.t11 (cl @p_127) :rule refl)
-(step t57.t12 (cl @p_132) :rule refl)
-(step t57.t13 (cl (= @p_133 (! (inf$ veriT_vr20 veriT_vr22) :named @p_134))) :rule cong :premises (t57.t11 t57.t12))
-(step t57.t14 (cl (= @p_135 (! (= bot$ @p_134) :named @p_136))) :rule cong :premises (t57.t13))
-(step t57.t15 (cl (= @p_137 (! (and @p_131 @p_136) :named @p_138))) :rule cong :premises (t57.t10 t57.t14))
-(step t57.t16 (cl (= @p_139 (! (= @p_125 @p_138) :named @p_140))) :rule cong :premises (t57.t6 t57.t15))
-(step t57 (cl (! (= @p_120 (! (forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind)
-(step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2)
-(step t59 (cl @p_142) :rule th_resolution :premises (axiom7 t57 t58))
-(anchor :step t60 :args ((:= (veriT_vr20 Real_real_prod_set$) veriT_vr23) (:= (veriT_vr21 Real_real_prod$) veriT_vr24) (:= (veriT_vr22 Real_real_prod_set$) veriT_vr25)))
-(step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl)
-(step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl)
-(step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl)
-(step t60.t4 (cl (= @p_121 (! (insert$ veriT_vr24 veriT_vr25) :named @p_143))) :rule cong :premises (t60.t2 t60.t3))
-(step t60.t5 (cl (= @p_123 (! (inf$ veriT_vr23 @p_143) :named @p_144))) :rule cong :premises (t60.t1 t60.t4))
-(step t60.t6 (cl (= @p_125 (! (= bot$ @p_144) :named @p_145))) :rule cong :premises (t60.t5))
-(step t60.t7 (cl @p_146) :rule refl)
-(step t60.t8 (cl @p_147) :rule refl)
-(step t60.t9 (cl (= @p_129 (! (member$a veriT_vr24 veriT_vr23) :named @p_148))) :rule cong :premises (t60.t7 t60.t8))
-(step t60.t10 (cl (= @p_131 (! (not @p_148) :named @p_149))) :rule cong :premises (t60.t9))
-(step t60.t11 (cl @p_147) :rule refl)
-(step t60.t12 (cl @p_150) :rule refl)
-(step t60.t13 (cl (= @p_134 (! (inf$ veriT_vr23 veriT_vr25) :named @p_151))) :rule cong :premises (t60.t11 t60.t12))
-(step t60.t14 (cl (= @p_136 (! (= bot$ @p_151) :named @p_152))) :rule cong :premises (t60.t13))
-(step t60.t15 (cl (= @p_138 (! (and @p_149 @p_152) :named @p_153))) :rule cong :premises (t60.t10 t60.t14))
-(step t60.t16 (cl (= @p_140 (! (= @p_145 @p_153) :named @p_154))) :rule cong :premises (t60.t6 t60.t15))
-(step t60 (cl (! (= @p_142 (! (forall ((veriT_vr23 Real_real_prod_set$) (veriT_vr24 Real_real_prod$) (veriT_vr25 Real_real_prod_set$)) @p_154) :named @p_156)) :named @p_155)) :rule bind)
-(step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2)
-(step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61))
-(anchor :step t63 :args ((:= (?v0 Real_real_prod_set$) veriT_vr26) (:= (?v1 Real_real_prod$) veriT_vr27)))
-(step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl)
-(step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1))
-(step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl)
-(step t63.t4 (cl @p_159) :rule refl)
-(step t63.t5 (cl (= @p_160 (! (insert$ veriT_vr27 veriT_vr26) :named @p_161))) :rule cong :premises (t63.t3 t63.t4))
-(step t63.t6 (cl (= @p_162 (! (finite$ @p_161) :named @p_163))) :rule cong :premises (t63.t5))
-(step t63.t7 (cl (= @p_164 (! (=> @p_158 @p_163) :named @p_165))) :rule cong :premises (t63.t2 t63.t6))
-(step t63 (cl (! (= @p_157 (! (forall ((veriT_vr26 Real_real_prod_set$) (veriT_vr27 Real_real_prod$)) @p_165) :named @p_167)) :named @p_166)) :rule bind)
-(step t64 (cl (not @p_166) (not @p_157) @p_167) :rule equiv_pos2)
-(step t65 (cl @p_167) :rule th_resolution :premises (axiom9 t63 t64))
-(anchor :step t66 :args ((:= (veriT_vr26 Real_real_prod_set$) veriT_vr28) (:= (veriT_vr27 Real_real_prod$) veriT_vr29)))
-(step t66.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_169)) :rule refl)
-(step t66.t2 (cl (= @p_158 (! (finite$ veriT_vr28) :named @p_168))) :rule cong :premises (t66.t1))
-(step t66.t3 (cl (= veriT_vr27 veriT_vr29)) :rule refl)
-(step t66.t4 (cl @p_169) :rule refl)
-(step t66.t5 (cl (= @p_161 (! (insert$ veriT_vr29 veriT_vr28) :named @p_170))) :rule cong :premises (t66.t3 t66.t4))
-(step t66.t6 (cl (= @p_163 (! (finite$ @p_170) :named @p_171))) :rule cong :premises (t66.t5))
-(step t66.t7 (cl (= @p_165 (! (=> @p_168 @p_171) :named @p_172))) :rule cong :premises (t66.t2 t66.t6))
-(step t66 (cl (! (= @p_167 (! (forall ((veriT_vr28 Real_real_prod_set$) (veriT_vr29 Real_real_prod$)) @p_172) :named @p_174)) :named @p_173)) :rule bind)
-(step t67 (cl (not @p_173) (not @p_167) @p_174) :rule equiv_pos2)
-(step t68 (cl @p_174) :rule th_resolution :premises (t65 t66 t67))
-(anchor :step t69 :args ((:= (?v0 Real_real_prod$) veriT_vr30) (:= (?v1 Real_real_prod_set$) veriT_vr31)))
-(step t69.t1 (cl (! (= ?v0 veriT_vr30) :named @p_179)) :rule refl)
-(step t69.t2 (cl (! (= ?v1 veriT_vr31) :named @p_178)) :rule refl)
-(step t69.t3 (cl (= @p_176 (! (member$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2))
-(step t69.t4 (cl @p_178) :rule refl)
-(step t69.t5 (cl @p_179) :rule refl)
-(step t69.t6 (cl @p_178) :rule refl)
-(step t69.t7 (cl (= @p_2 (! (insert$ veriT_vr30 veriT_vr31) :named @p_180))) :rule cong :premises (t69.t5 t69.t6))
-(step t69.t8 (cl (= @p_181 (! (= veriT_vr31 @p_180) :named @p_182))) :rule cong :premises (t69.t4 t69.t7))
-(step t69.t9 (cl (= @p_183 (! (=> @p_177 @p_182) :named @p_184))) :rule cong :premises (t69.t3 t69.t8))
-(step t69 (cl (! (= @p_175 (! (forall ((veriT_vr30 Real_real_prod$) (veriT_vr31 Real_real_prod_set$)) @p_184) :named @p_186)) :named @p_185)) :rule bind)
-(step t70 (cl (not @p_185) (not @p_175) @p_186) :rule equiv_pos2)
-(step t71 (cl @p_186) :rule th_resolution :premises (axiom11 t69 t70))
-(anchor :step t72 :args ((:= (veriT_vr30 Real_real_prod$) veriT_vr32) (:= (veriT_vr31 Real_real_prod_set$) veriT_vr33)))
-(step t72.t1 (cl (! (= veriT_vr30 veriT_vr32) :named @p_189)) :rule refl)
-(step t72.t2 (cl (! (= veriT_vr31 veriT_vr33) :named @p_188)) :rule refl)
-(step t72.t3 (cl (= @p_177 (! (member$a veriT_vr32 veriT_vr33) :named @p_187))) :rule cong :premises (t72.t1 t72.t2))
-(step t72.t4 (cl @p_188) :rule refl)
-(step t72.t5 (cl @p_189) :rule refl)
-(step t72.t6 (cl @p_188) :rule refl)
-(step t72.t7 (cl (= @p_180 (! (insert$ veriT_vr32 veriT_vr33) :named @p_190))) :rule cong :premises (t72.t5 t72.t6))
-(step t72.t8 (cl (= @p_182 (! (= veriT_vr33 @p_190) :named @p_191))) :rule cong :premises (t72.t4 t72.t7))
-(step t72.t9 (cl (= @p_184 (! (=> @p_187 @p_191) :named @p_192))) :rule cong :premises (t72.t3 t72.t8))
-(step t72 (cl (! (= @p_186 (! (forall ((veriT_vr32 Real_real_prod$) (veriT_vr33 Real_real_prod_set$)) @p_192) :named @p_194)) :named @p_193)) :rule bind)
-(step t73 (cl (not @p_193) (not @p_186) @p_194) :rule equiv_pos2)
-(step t74 (cl @p_194) :rule th_resolution :premises (t71 t72 t73))
-(anchor :step t75 :args ((:= (?v0 Real_real_prod_set$) veriT_vr34)))
-(step t75.t1 (cl (= ?v0 veriT_vr34)) :rule refl)
-(step t75.t2 (cl (= @p_196 (! (inf$ veriT_vr34 bot$) :named @p_197))) :rule cong :premises (t75.t1))
-(step t75.t3 (cl (= @p_198 (! (= bot$ @p_197) :named @p_199))) :rule cong :premises (t75.t2))
-(step t75 (cl (! (= @p_195 (! (forall ((veriT_vr34 Real_real_prod_set$)) @p_199) :named @p_201)) :named @p_200)) :rule bind)
-(step t76 (cl (not @p_200) (not @p_195) @p_201) :rule equiv_pos2)
-(step t77 (cl @p_201) :rule th_resolution :premises (axiom13 t75 t76))
-(anchor :step t78 :args ((:= (veriT_vr34 Real_real_prod_set$) veriT_vr35)))
-(step t78.t1 (cl (= veriT_vr34 veriT_vr35)) :rule refl)
-(step t78.t2 (cl (= @p_197 (! (inf$ veriT_vr35 bot$) :named @p_202))) :rule cong :premises (t78.t1))
-(step t78.t3 (cl (= @p_199 (! (= bot$ @p_202) :named @p_203))) :rule cong :premises (t78.t2))
-(step t78 (cl (! (= @p_201 (! (forall ((veriT_vr35 Real_real_prod_set$)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
-(step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2)
-(step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79))
-(anchor :step t81 :args ((:= (?v0 Real_real_prod$) veriT_vr36) (:= (?v1 Real_real_prod$) veriT_vr37) (:= (?v2 Real_real_prod_set$) veriT_vr38)))
-(step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl)
-(step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl)
-(step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl)
-(step t81.t4 (cl (= @p_1 (! (insert$ veriT_vr37 veriT_vr38) :named @p_207))) :rule cong :premises (t81.t2 t81.t3))
-(step t81.t5 (cl (= @p_208 (! (insert$ veriT_vr36 @p_207) :named @p_209))) :rule cong :premises (t81.t1 t81.t4))
-(step t81.t6 (cl @p_210) :rule refl)
-(step t81.t7 (cl @p_211) :rule refl)
-(step t81.t8 (cl @p_212) :rule refl)
-(step t81.t9 (cl (= @p_213 (! (insert$ veriT_vr36 veriT_vr38) :named @p_214))) :rule cong :premises (t81.t7 t81.t8))
-(step t81.t10 (cl (= @p_215 (! (insert$ veriT_vr37 @p_214) :named @p_216))) :rule cong :premises (t81.t6 t81.t9))
-(step t81.t11 (cl (= @p_217 (! (= @p_209 @p_216) :named @p_218))) :rule cong :premises (t81.t5 t81.t10))
-(step t81 (cl (! (= @p_206 (! (forall ((veriT_vr36 Real_real_prod$) (veriT_vr37 Real_real_prod$) (veriT_vr38 Real_real_prod_set$)) @p_218) :named @p_220)) :named @p_219)) :rule bind)
-(step t82 (cl (not @p_219) (not @p_206) @p_220) :rule equiv_pos2)
-(step t83 (cl @p_220) :rule th_resolution :premises (axiom14 t81 t82))
-(anchor :step t84 :args ((:= (veriT_vr36 Real_real_prod$) veriT_vr39) (:= (veriT_vr37 Real_real_prod$) veriT_vr40) (:= (veriT_vr38 Real_real_prod_set$) veriT_vr41)))
-(step t84.t1 (cl (! (= veriT_vr36 veriT_vr39) :named @p_224)) :rule refl)
-(step t84.t2 (cl (! (= veriT_vr37 veriT_vr40) :named @p_223)) :rule refl)
-(step t84.t3 (cl (! (= veriT_vr38 veriT_vr41) :named @p_225)) :rule refl)
-(step t84.t4 (cl (= @p_207 (! (insert$ veriT_vr40 veriT_vr41) :named @p_221))) :rule cong :premises (t84.t2 t84.t3))
-(step t84.t5 (cl (= @p_209 (! (insert$ veriT_vr39 @p_221) :named @p_222))) :rule cong :premises (t84.t1 t84.t4))
-(step t84.t6 (cl @p_223) :rule refl)
-(step t84.t7 (cl @p_224) :rule refl)
-(step t84.t8 (cl @p_225) :rule refl)
-(step t84.t9 (cl (= @p_214 (! (insert$ veriT_vr39 veriT_vr41) :named @p_226))) :rule cong :premises (t84.t7 t84.t8))
-(step t84.t10 (cl (= @p_216 (! (insert$ veriT_vr40 @p_226) :named @p_227))) :rule cong :premises (t84.t6 t84.t9))
-(step t84.t11 (cl (= @p_218 (! (= @p_222 @p_227) :named @p_228))) :rule cong :premises (t84.t5 t84.t10))
-(step t84 (cl (! (= @p_220 (! (forall ((veriT_vr39 Real_real_prod$) (veriT_vr40 Real_real_prod$) (veriT_vr41 Real_real_prod_set$)) @p_228) :named @p_230)) :named @p_229)) :rule bind)
-(step t85 (cl (not @p_229) (not @p_220) @p_230) :rule equiv_pos2)
-(step t86 (cl @p_230) :rule th_resolution :premises (t83 t84 t85))
-(anchor :step t87 :args ((:= (?v0 Real_real_prod$) veriT_vr42) (:= (?v1 Real_real_prod_set$) veriT_vr43)))
-(step t87.t1 (cl (! (= ?v0 veriT_vr42) :named @p_233)) :rule refl)
-(step t87.t2 (cl (! (= ?v1 veriT_vr43) :named @p_235)) :rule refl)
-(step t87.t3 (cl (= @p_2 (! (insert$ veriT_vr42 veriT_vr43) :named @p_232))) :rule cong :premises (t87.t1 t87.t2))
-(step t87.t4 (cl @p_233) :rule refl)
-(step t87.t5 (cl (= @p_3 (! (insert$ veriT_vr42 bot$) :named @p_234))) :rule cong :premises (t87.t4))
-(step t87.t6 (cl @p_235) :rule refl)
-(step t87.t7 (cl (= @p_236 (! (sup$ @p_234 veriT_vr43) :named @p_237))) :rule cong :premises (t87.t5 t87.t6))
-(step t87.t8 (cl (= @p_238 (! (= @p_232 @p_237) :named @p_239))) :rule cong :premises (t87.t3 t87.t7))
-(step t87 (cl (! (= @p_231 (! (forall ((veriT_vr42 Real_real_prod$) (veriT_vr43 Real_real_prod_set$)) @p_239) :named @p_241)) :named @p_240)) :rule bind)
-(step t88 (cl (not @p_240) (not @p_231) @p_241) :rule equiv_pos2)
-(step t89 (cl @p_241) :rule th_resolution :premises (axiom15 t87 t88))
-(anchor :step t90 :args ((:= (veriT_vr42 Real_real_prod$) veriT_vr44) (:= (veriT_vr43 Real_real_prod_set$) veriT_vr45)))
-(step t90.t1 (cl (! (= veriT_vr42 veriT_vr44) :named @p_243)) :rule refl)
-(step t90.t2 (cl (! (= veriT_vr43 veriT_vr45) :named @p_245)) :rule refl)
-(step t90.t3 (cl (= @p_232 (! (insert$ veriT_vr44 veriT_vr45) :named @p_242))) :rule cong :premises (t90.t1 t90.t2))
-(step t90.t4 (cl @p_243) :rule refl)
-(step t90.t5 (cl (= @p_234 (! (insert$ veriT_vr44 bot$) :named @p_244))) :rule cong :premises (t90.t4))
-(step t90.t6 (cl @p_245) :rule refl)
-(step t90.t7 (cl (= @p_237 (! (sup$ @p_244 veriT_vr45) :named @p_246))) :rule cong :premises (t90.t5 t90.t6))
-(step t90.t8 (cl (= @p_239 (! (= @p_242 @p_246) :named @p_247))) :rule cong :premises (t90.t3 t90.t7))
-(step t90 (cl (! (= @p_241 (! (forall ((veriT_vr44 Real_real_prod$) (veriT_vr45 Real_real_prod_set$)) @p_247) :named @p_249)) :named @p_248)) :rule bind)
-(step t91 (cl (not @p_248) (not @p_241) @p_249) :rule equiv_pos2)
-(step t92 (cl @p_249) :rule th_resolution :premises (t89 t90 t91))
-(anchor :step t93 :args ((:= (?v0 Real_real_prod_set$) veriT_vr46) (:= (?v1 Real_real_prod_real_real_prod_fun$) veriT_vr47) (:= (?v2 Real_real_prod_set$) veriT_vr48) (:= (?v3 Real_real_real_prod_fun$) veriT_vr49) (:= (?v4 Real_real_prod_set$) veriT_vr50)))
-(step t93.t1 (cl (! (= ?v0 veriT_vr46) :named @p_262)) :rule refl)
-(step t93.t2 (cl (= @p_4 (! (finite$ veriT_vr46) :named @p_251))) :rule cong :premises (t93.t1))
-(step t93.t3 (cl (! (= ?v1 veriT_vr47) :named @p_256)) :rule refl)
-(step t93.t4 (cl (! (= ?v2 veriT_vr48) :named @p_263)) :rule refl)
-(step t93.t5 (cl (= @p_252 (! (line_integral_exists$ veriT_vr47 veriT_vr48) :named @p_253))) :rule cong :premises (t93.t3 t93.t4))
-(step t93.t6 (cl (! (= ?v3 veriT_vr49) :named @p_259)) :rule refl)
-(step t93.t7 (cl (= @p_254 (! (fun_app$a @p_253 veriT_vr49) :named @p_255))) :rule cong :premises (t93.t5 t93.t6))
-(step t93.t8 (cl @p_256) :rule refl)
-(step t93.t9 (cl (! (= ?v4 veriT_vr50) :named @p_264)) :rule refl)
-(step t93.t10 (cl (= @p_257 (! (line_integral_exists$ veriT_vr47 veriT_vr50) :named @p_258))) :rule cong :premises (t93.t8 t93.t9))
-(step t93.t11 (cl @p_259) :rule refl)
-(step t93.t12 (cl (= @p_260 (! (fun_app$a @p_258 veriT_vr49) :named @p_261))) :rule cong :premises (t93.t10 t93.t11))
-(step t93.t13 (cl @p_262) :rule refl)
-(step t93.t14 (cl @p_263) :rule refl)
-(step t93.t15 (cl @p_264) :rule refl)
-(step t93.t16 (cl (= @p_265 (! (sup$ veriT_vr48 veriT_vr50) :named @p_266))) :rule cong :premises (t93.t14 t93.t15))
-(step t93.t17 (cl (= @p_267 (! (= veriT_vr46 @p_266) :named @p_268))) :rule cong :premises (t93.t13 t93.t16))
-(step t93.t18 (cl @p_263) :rule refl)
-(step t93.t19 (cl @p_264) :rule refl)
-(step t93.t20 (cl (= @p_269 (! (inf$ veriT_vr48 veriT_vr50) :named @p_270))) :rule cong :premises (t93.t18 t93.t19))
-(step t93.t21 (cl (= @p_271 (! (= bot$ @p_270) :named @p_272))) :rule cong :premises (t93.t20))
-(step t93.t22 (cl (= @p_273 (! (and @p_268 @p_272) :named @p_274))) :rule cong :premises (t93.t17 t93.t21))
-(step t93.t23 (cl (= @p_275 (! (and @p_261 @p_274) :named @p_276))) :rule cong :premises (t93.t12 t93.t22))
-(step t93.t24 (cl (= @p_277 (! (and @p_255 @p_276) :named @p_278))) :rule cong :premises (t93.t7 t93.t23))
-(step t93.t25 (cl (= @p_279 (! (and @p_251 @p_278) :named @p_280))) :rule cong :premises (t93.t2 t93.t24))
-(step t93.t26 (cl @p_256) :rule refl)
-(step t93.t27 (cl @p_262) :rule refl)
-(step t93.t28 (cl @p_259) :rule refl)
-(step t93.t29 (cl (= @p_281 (! (line_integral$ veriT_vr47 veriT_vr46 veriT_vr49) :named @p_282))) :rule cong :premises (t93.t26 t93.t27 t93.t28))
-(step t93.t30 (cl @p_256) :rule refl)
-(step t93.t31 (cl @p_263) :rule refl)
-(step t93.t32 (cl @p_259) :rule refl)
-(step t93.t33 (cl (= @p_283 (! (line_integral$ veriT_vr47 veriT_vr48 veriT_vr49) :named @p_284))) :rule cong :premises (t93.t30 t93.t31 t93.t32))
-(step t93.t34 (cl @p_256) :rule refl)
-(step t93.t35 (cl @p_264) :rule refl)
-(step t93.t36 (cl @p_259) :rule refl)
-(step t93.t37 (cl (= @p_285 (! (line_integral$ veriT_vr47 veriT_vr50 veriT_vr49) :named @p_286))) :rule cong :premises (t93.t34 t93.t35 t93.t36))
-(step t93.t38 (cl (= @p_287 (! (+ @p_284 @p_286) :named @p_288))) :rule cong :premises (t93.t33 t93.t37))
-(step t93.t39 (cl (= @p_289 (! (= @p_282 @p_288) :named @p_290))) :rule cong :premises (t93.t29 t93.t38))
-(step t93.t40 (cl (= @p_291 (! (=> @p_280 @p_290) :named @p_292))) :rule cong :premises (t93.t25 t93.t39))
-(step t93 (cl (! (= @p_250 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_292) :named @p_294)) :named @p_293)) :rule bind)
-(step t94 (cl (not @p_293) (not @p_250) @p_294) :rule equiv_pos2)
-(step t95 (cl @p_294) :rule th_resolution :premises (axiom16 t93 t94))
-(anchor :step t96 :args ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)))
-(step t96.t1 (cl (= @p_280 (! (and @p_251 @p_255 @p_261 @p_268 @p_272) :named @p_295))) :rule ac_simp)
-(step t96.t2 (cl (= @p_292 (! (=> @p_295 @p_290) :named @p_296))) :rule cong :premises (t96.t1))
-(step t96 (cl (! (= @p_294 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_296) :named @p_298)) :named @p_297)) :rule bind)
-(step t97 (cl (not @p_297) (not @p_294) @p_298) :rule equiv_pos2)
-(step t98 (cl @p_298) :rule th_resolution :premises (t95 t96 t97))
-(anchor :step t99 :args ((:= (veriT_vr46 Real_real_prod_set$) veriT_vr51) (:= (veriT_vr47 Real_real_prod_real_real_prod_fun$) veriT_vr52) (:= (veriT_vr48 Real_real_prod_set$) veriT_vr53) (:= (veriT_vr49 Real_real_real_prod_fun$) veriT_vr54) (:= (veriT_vr50 Real_real_prod_set$) veriT_vr55)))
-(step t99.t1 (cl (! (= veriT_vr46 veriT_vr51) :named @p_306)) :rule refl)
-(step t99.t2 (cl (= @p_251 (! (finite$ veriT_vr51) :named @p_299))) :rule cong :premises (t99.t1))
-(step t99.t3 (cl (! (= veriT_vr47 veriT_vr52) :named @p_302)) :rule refl)
-(step t99.t4 (cl (! (= veriT_vr48 veriT_vr53) :named @p_307)) :rule refl)
-(step t99.t5 (cl (= @p_253 (! (line_integral_exists$ veriT_vr52 veriT_vr53) :named @p_300))) :rule cong :premises (t99.t3 t99.t4))
-(step t99.t6 (cl (! (= veriT_vr49 veriT_vr54) :named @p_304)) :rule refl)
-(step t99.t7 (cl (= @p_255 (! (fun_app$a @p_300 veriT_vr54) :named @p_301))) :rule cong :premises (t99.t5 t99.t6))
-(step t99.t8 (cl @p_302) :rule refl)
-(step t99.t9 (cl (! (= veriT_vr50 veriT_vr55) :named @p_308)) :rule refl)
-(step t99.t10 (cl (= @p_258 (! (line_integral_exists$ veriT_vr52 veriT_vr55) :named @p_303))) :rule cong :premises (t99.t8 t99.t9))
-(step t99.t11 (cl @p_304) :rule refl)
-(step t99.t12 (cl (= @p_261 (! (fun_app$a @p_303 veriT_vr54) :named @p_305))) :rule cong :premises (t99.t10 t99.t11))
-(step t99.t13 (cl @p_306) :rule refl)
-(step t99.t14 (cl @p_307) :rule refl)
-(step t99.t15 (cl @p_308) :rule refl)
-(step t99.t16 (cl (= @p_266 (! (sup$ veriT_vr53 veriT_vr55) :named @p_309))) :rule cong :premises (t99.t14 t99.t15))
-(step t99.t17 (cl (= @p_268 (! (= veriT_vr51 @p_309) :named @p_310))) :rule cong :premises (t99.t13 t99.t16))
-(step t99.t18 (cl @p_307) :rule refl)
-(step t99.t19 (cl @p_308) :rule refl)
-(step t99.t20 (cl (= @p_270 (! (inf$ veriT_vr53 veriT_vr55) :named @p_311))) :rule cong :premises (t99.t18 t99.t19))
-(step t99.t21 (cl (= @p_272 (! (= bot$ @p_311) :named @p_312))) :rule cong :premises (t99.t20))
-(step t99.t22 (cl (= @p_295 (! (and @p_299 @p_301 @p_305 @p_310 @p_312) :named @p_313))) :rule cong :premises (t99.t2 t99.t7 t99.t12 t99.t17 t99.t21))
-(step t99.t23 (cl @p_302) :rule refl)
-(step t99.t24 (cl @p_306) :rule refl)
-(step t99.t25 (cl @p_304) :rule refl)
-(step t99.t26 (cl (= @p_282 (! (line_integral$ veriT_vr52 veriT_vr51 veriT_vr54) :named @p_314))) :rule cong :premises (t99.t23 t99.t24 t99.t25))
-(step t99.t27 (cl @p_302) :rule refl)
-(step t99.t28 (cl @p_307) :rule refl)
-(step t99.t29 (cl @p_304) :rule refl)
-(step t99.t30 (cl (= @p_284 (! (line_integral$ veriT_vr52 veriT_vr53 veriT_vr54) :named @p_315))) :rule cong :premises (t99.t27 t99.t28 t99.t29))
-(step t99.t31 (cl @p_302) :rule refl)
-(step t99.t32 (cl @p_308) :rule refl)
-(step t99.t33 (cl @p_304) :rule refl)
-(step t99.t34 (cl (= @p_286 (! (line_integral$ veriT_vr52 veriT_vr55 veriT_vr54) :named @p_316))) :rule cong :premises (t99.t31 t99.t32 t99.t33))
-(step t99.t35 (cl (= @p_288 (! (+ @p_315 @p_316) :named @p_317))) :rule cong :premises (t99.t30 t99.t34))
-(step t99.t36 (cl (= @p_290 (! (= @p_314 @p_317) :named @p_318))) :rule cong :premises (t99.t26 t99.t35))
-(step t99.t37 (cl (= @p_296 (! (=> @p_313 @p_318) :named @p_319))) :rule cong :premises (t99.t22 t99.t36))
-(step t99 (cl (! (= @p_298 (! (forall ((veriT_vr51 Real_real_prod_set$) (veriT_vr52 Real_real_prod_real_real_prod_fun$) (veriT_vr53 Real_real_prod_set$) (veriT_vr54 Real_real_real_prod_fun$) (veriT_vr55 Real_real_prod_set$)) @p_319) :named @p_321)) :named @p_320)) :rule bind)
-(step t100 (cl (not @p_320) (not @p_298) @p_321) :rule equiv_pos2)
-(step t101 (cl @p_321) :rule th_resolution :premises (t98 t99 t100))
-(anchor :step t102 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr56)))
-(step t102.t1 (cl (! (= ?v0 veriT_vr56) :named @p_324)) :rule refl)
-(step t102.t2 (cl (= @p_9 (! (member$ veriT_vr56 one_chain_typeI$) :named @p_323))) :rule cong :premises (t102.t1))
-(step t102.t3 (cl @p_324) :rule refl)
-(step t102.t4 (cl (! (= @p_6 (! (case_prod$ uu$ veriT_vr56) :named @p_325)) :named @p_330)) :rule cong :premises (t102.t3))
-(step t102.t5 (cl (= @p_326 (! (=> @p_323 @p_325) :named @p_327))) :rule cong :premises (t102.t2 t102.t4))
-(step t102 (cl (= @p_322 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_327) :named @p_334))) :rule bind)
-(anchor :step t103 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr56)))
-(step t103.t1 (cl @p_324) :rule refl)
-(step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1))
-(step t103.t3 (cl @p_324) :rule refl)
-(step t103.t4 (cl @p_330) :rule cong :premises (t103.t3))
-(step t103.t5 (cl (= @p_331 (! (=> @p_329 @p_325) :named @p_332))) :rule cong :premises (t103.t2 t103.t4))
-(step t103 (cl (= @p_328 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_332) :named @p_335))) :rule bind)
-(step t104 (cl (= @p_333 (! (and @p_334 @p_335) :named @p_338))) :rule cong :premises (t102 t103))
-(step t105 (cl (! (= @p_336 (! (and @p_337 @p_338) :named @p_340)) :named @p_339)) :rule cong :premises (t104))
-(step t106 (cl (not @p_339) (not @p_336) @p_340) :rule equiv_pos2)
-(step t107 (cl @p_340) :rule th_resolution :premises (axiom17 t105 t106))
-(step t108 (cl (! (= @p_340 (! (and @p_337 @p_334 @p_335) :named @p_342)) :named @p_341)) :rule ac_simp)
-(step t109 (cl (not @p_341) (not @p_340) @p_342) :rule equiv_pos2)
-(step t110 (cl @p_342) :rule th_resolution :premises (t107 t108 t109))
-(anchor :step t111 :args ((:= (veriT_vr56 Int_real_real_real_prod_fun_prod$) veriT_vr57)))
-(step t111.t1 (cl (! (= veriT_vr56 veriT_vr57) :named @p_344)) :rule refl)
-(step t111.t2 (cl (= @p_329 (! (member$ veriT_vr57 one_chain_typeII$) :named @p_343))) :rule cong :premises (t111.t1))
-(step t111.t3 (cl @p_344) :rule refl)
-(step t111.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr57) :named @p_345))) :rule cong :premises (t111.t3))
-(step t111.t5 (cl (= @p_332 (! (=> @p_343 @p_345) :named @p_346))) :rule cong :premises (t111.t2 t111.t4))
-(step t111 (cl (= @p_335 (! (forall ((veriT_vr57 Int_real_real_real_prod_fun_prod$)) @p_346) :named @p_347))) :rule bind)
-(step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111))
-(step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2)
-(step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113))
-(anchor :step t115 :args ((:= (veriT_vr56 Int_real_real_real_prod_fun_prod$) veriT_vr58)))
-(step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl)
-(step t115.t2 (cl (= @p_323 (! (member$ veriT_vr58 one_chain_typeI$) :named @p_350))) :rule cong :premises (t115.t1))
-(step t115.t3 (cl @p_351) :rule refl)
-(step t115.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr58) :named @p_352))) :rule cong :premises (t115.t3))
-(step t115.t5 (cl (= @p_327 (! (=> @p_350 @p_352) :named @p_353))) :rule cong :premises (t115.t2 t115.t4))
-(step t115 (cl (= @p_334 (! (forall ((veriT_vr58 Int_real_real_real_prod_fun_prod$)) @p_353) :named @p_358))) :rule bind)
-(anchor :step t116 :args ((:= (veriT_vr57 Int_real_real_real_prod_fun_prod$) veriT_vr59)))
-(step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl)
-(step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1))
-(step t116.t3 (cl @p_355) :rule refl)
-(step t116.t4 (cl (= @p_345 (! (case_prod$ uu$ veriT_vr59) :named @p_356))) :rule cong :premises (t116.t3))
-(step t116.t5 (cl (= @p_346 (! (=> @p_354 @p_356) :named @p_357))) :rule cong :premises (t116.t2 t116.t4))
-(step t116 (cl (= @p_347 (! (forall ((veriT_vr59 Int_real_real_real_prod_fun_prod$)) @p_357) :named @p_359))) :rule bind)
-(step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116))
-(step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2)
-(step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118))
-(anchor :step t120 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr60)))
-(step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl)
-(step t120.t2 (cl (= @p_8 (! (member$ veriT_vr60 one_chain_typeII$) :named @p_363))) :rule cong :premises (t120.t1))
-(step t120.t3 (cl @p_364) :rule refl)
-(step t120.t4 (cl (! (= @p_10 (! (case_prod$ uua$ veriT_vr60) :named @p_365)) :named @p_370)) :rule cong :premises (t120.t3))
-(step t120.t5 (cl (= @p_366 (! (=> @p_363 @p_365) :named @p_367))) :rule cong :premises (t120.t2 t120.t4))
-(step t120 (cl (= @p_362 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_367) :named @p_374))) :rule bind)
-(anchor :step t121 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr60)))
-(step t121.t1 (cl @p_364) :rule refl)
-(step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1))
-(step t121.t3 (cl @p_364) :rule refl)
-(step t121.t4 (cl @p_370) :rule cong :premises (t121.t3))
-(step t121.t5 (cl (= @p_371 (! (=> @p_369 @p_365) :named @p_372))) :rule cong :premises (t121.t2 t121.t4))
-(step t121 (cl (= @p_368 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_372) :named @p_375))) :rule bind)
-(step t122 (cl (= @p_373 (! (and @p_374 @p_375) :named @p_378))) :rule cong :premises (t120 t121))
-(step t123 (cl (! (= @p_376 (! (and @p_377 @p_378) :named @p_380)) :named @p_379)) :rule cong :premises (t122))
-(step t124 (cl (not @p_379) (not @p_376) @p_380) :rule equiv_pos2)
-(step t125 (cl @p_380) :rule th_resolution :premises (axiom18 t123 t124))
-(step t126 (cl (! (= @p_380 (! (and @p_377 @p_374 @p_375) :named @p_382)) :named @p_381)) :rule ac_simp)
-(step t127 (cl (not @p_381) (not @p_380) @p_382) :rule equiv_pos2)
-(step t128 (cl @p_382) :rule th_resolution :premises (t125 t126 t127))
-(anchor :step t129 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr61)))
-(step t129.t1 (cl (! (= veriT_vr60 veriT_vr61) :named @p_384)) :rule refl)
-(step t129.t2 (cl (= @p_369 (! (member$ veriT_vr61 one_chain_typeI$) :named @p_383))) :rule cong :premises (t129.t1))
-(step t129.t3 (cl @p_384) :rule refl)
-(step t129.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr61) :named @p_385))) :rule cong :premises (t129.t3))
-(step t129.t5 (cl (= @p_372 (! (=> @p_383 @p_385) :named @p_386))) :rule cong :premises (t129.t2 t129.t4))
-(step t129 (cl (= @p_375 (! (forall ((veriT_vr61 Int_real_real_real_prod_fun_prod$)) @p_386) :named @p_387))) :rule bind)
-(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129))
-(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2)
-(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131))
-(anchor :step t133 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr62)))
-(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl)
-(step t133.t2 (cl (= @p_363 (! (member$ veriT_vr62 one_chain_typeII$) :named @p_390))) :rule cong :premises (t133.t1))
-(step t133.t3 (cl @p_391) :rule refl)
-(step t133.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr62) :named @p_392))) :rule cong :premises (t133.t3))
-(step t133.t5 (cl (= @p_367 (! (=> @p_390 @p_392) :named @p_393))) :rule cong :premises (t133.t2 t133.t4))
-(step t133 (cl (= @p_374 (! (forall ((veriT_vr62 Int_real_real_real_prod_fun_prod$)) @p_393) :named @p_398))) :rule bind)
-(anchor :step t134 :args ((:= (veriT_vr61 Int_real_real_real_prod_fun_prod$) veriT_vr63)))
-(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl)
-(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1))
-(step t134.t3 (cl @p_395) :rule refl)
-(step t134.t4 (cl (= @p_385 (! (case_prod$ uua$ veriT_vr63) :named @p_396))) :rule cong :premises (t134.t3))
-(step t134.t5 (cl (= @p_386 (! (=> @p_394 @p_396) :named @p_397))) :rule cong :premises (t134.t2 t134.t4))
-(step t134 (cl (= @p_387 (! (forall ((veriT_vr63 Int_real_real_real_prod_fun_prod$)) @p_397) :named @p_399))) :rule bind)
-(step t135 (cl (! (= @p_389 (! (and @p_377 @p_398 @p_399) :named @p_401)) :named @p_400)) :rule cong :premises (t133 t134))
-(step t136 (cl (not @p_400) (not @p_389) @p_401) :rule equiv_pos2)
-(step t137 (cl @p_401) :rule th_resolution :premises (t132 t135 t136))
-(step t138 (cl @p_358) :rule and :premises (t119))
-(step t139 (cl @p_399) :rule and :premises (t137))
-(step t140 (cl (or (! (not @p_399) :named @p_422) (! (=> @p_402 (! (case_prod$ uua$ @p_403) :named @p_421)) :named @p_420))) :rule forall_inst :args ((:= veriT_vr63 @p_403)))
-(step t141 (cl (or (! (not @p_358) :named @p_427) (! (=> @p_402 (! (case_prod$ uu$ @p_403) :named @p_426)) :named @p_424))) :rule forall_inst :args ((:= veriT_vr58 @p_403)))
-(step t142 (cl (or (! (not @p_321) :named @p_406) (! (=> (! (and (! (finite$ @p_5) :named @p_415) (! (fun_app$a @p_12 g$) :named @p_409) (! (fun_app$a @p_24 g$) :named @p_408) (! (= @p_5 (! (sup$ @p_7 @p_5) :named @p_466)) :named @p_430) (! (= bot$ (inf$ @p_7 @p_5)) :named @p_431)) :named @p_429) (! (= @p_404 (! (+ @p_405 @p_404) :named @p_528)) :named @p_433)) :named @p_432))) :rule forall_inst :args ((:= veriT_vr51 @p_5) (:= veriT_vr52 f$) (:= veriT_vr53 @p_7) (:= veriT_vr54 g$) (:= veriT_vr55 @p_5)))
-(step t143 (cl (or @p_406 (! (=> (! (and (! (finite$ @p_407) :named @p_412) @p_408 @p_409 (! (= @p_407 (sup$ @p_5 @p_7)) :named @p_411) (! (= bot$ (inf$ @p_5 @p_7)) :named @p_437)) :named @p_434) @p_410) :named @p_438))) :rule forall_inst :args ((:= veriT_vr51 @p_407) (:= veriT_vr52 f$) (:= veriT_vr53 @p_5) (:= veriT_vr54 g$) (:= veriT_vr55 @p_7)))
-(step t144 (cl (or (! (not @p_249) :named @p_441) @p_411)) :rule forall_inst :args ((:= veriT_vr44 i$) (:= veriT_vr45 @p_7)))
-(step t145 (cl (or (! (not @p_230) :named @p_442) (! (= @p_407 (! (insert$ j$ @p_5) :named @p_467)) :named @p_443))) :rule forall_inst :args ((:= veriT_vr39 j$) (:= veriT_vr40 i$) (:= veriT_vr41 bot$)))
-(step t146 (cl (or (! (not @p_194) :named @p_447) (! (=> (! (member$a i$ @p_7) :named @p_445) (! (= @p_7 @p_407) :named @p_446)) :named @p_444))) :rule forall_inst :args ((:= veriT_vr32 i$) (:= veriT_vr33 @p_7)))
-(step t147 (cl (or (! (not @p_174) :named @p_413) (! (=> (! (finite$ @p_7) :named @p_416) @p_412) :named @p_448))) :rule forall_inst :args ((:= veriT_vr28 @p_7) (:= veriT_vr29 i$)))
-(step t148 (cl (or @p_413 (! (=> @p_414 @p_415) :named @p_449))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 i$)))
-(step t149 (cl (or @p_413 (! (=> @p_414 @p_416) :named @p_451))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 j$)))
-(step t150 (cl (or (! (not @p_119) :named @p_418) (! (= 0.0 (! (snd$a @p_417) :named @p_495)) :named @p_454))) :rule forall_inst :args ((:= veriT_vr18 1.0) (:= veriT_vr19 0.0)))
-(step t151 (cl (or @p_418 (! (= 1.0 (! (snd$a @p_419) :named @p_496)) :named @p_455))) :rule forall_inst :args ((:= veriT_vr18 0.0) (:= veriT_vr19 1.0)))
-(step t152 (cl (or (! (not @p_100) :named @p_456) (! (= g$ (! (snd$ @p_403) :named @p_471)) :named @p_457))) :rule forall_inst :args ((:= veriT_vr14 k$) (:= veriT_vr15 g$)))
-(step t153 (cl (or (! (not @p_84) :named @p_461) (! (=> (! (= @p_7 @p_5) :named @p_459) (! (= j$ i$) :named @p_460)) :named @p_458))) :rule forall_inst :args ((:= veriT_vr10 i$) (:= veriT_vr11 j$)))
-(step t154 (cl (! (not @p_420) :named @p_423) (! (not @p_402) :named @p_425) @p_421) :rule implies_pos)
-(step t155 (cl @p_422 @p_420) :rule or :premises (t140))
-(step t156 (cl @p_423 @p_421) :rule resolution :premises (t154 axiom6))
-(step t157 (cl @p_420) :rule resolution :premises (t155 t139))
-(step t158 (cl @p_421) :rule resolution :premises (t156 t157))
-(step t159 (cl (! (not @p_424) :named @p_428) @p_425 @p_426) :rule implies_pos)
-(step t160 (cl @p_427 @p_424) :rule or :premises (t141))
-(step t161 (cl @p_428 @p_426) :rule resolution :premises (t159 axiom6))
-(step t162 (cl @p_424) :rule resolution :premises (t160 t138))
-(step t163 (cl @p_426) :rule resolution :premises (t161 t162))
-(step t164 (cl @p_429 (not @p_415) (! (not @p_409) :named @p_436) (! (not @p_408) :named @p_435) (not @p_430) (not @p_431)) :rule and_neg)
-(step t165 (cl (not @p_432) (not @p_429) @p_433) :rule implies_pos)
-(step t166 (cl @p_406 @p_432) :rule or :premises (t142))
-(step t167 (cl @p_432) :rule resolution :premises (t166 t101))
-(step t168 (cl @p_434 (not @p_412) @p_435 @p_436 (not @p_411) (! (not @p_437) :named @p_515)) :rule and_neg)
-(step t169 (cl (! (not @p_438) :named @p_439) (! (not @p_434) :named @p_440) @p_410) :rule implies_pos)
-(step t170 (cl @p_406 @p_438) :rule or :premises (t143))
-(step t171 (cl @p_439 @p_440) :rule resolution :premises (t169 axiom19))
-(step t172 (cl @p_438) :rule resolution :premises (t170 t101))
-(step t173 (cl @p_440) :rule resolution :premises (t171 t172))
-(step t174 (cl @p_441 @p_411) :rule or :premises (t144))
-(step t175 (cl @p_411) :rule resolution :premises (t174 t92))
-(step t176 (cl @p_442 @p_443) :rule or :premises (t145))
-(step t177 (cl @p_443) :rule resolution :premises (t176 t86))
-(step t178 (cl (not @p_444) (! (not @p_445) :named @p_470) @p_446) :rule implies_pos)
-(step t179 (cl @p_447 @p_444) :rule or :premises (t146))
-(step t180 (cl @p_444) :rule resolution :premises (t179 t74))
-(step t181 (cl (not @p_448) (not @p_416) @p_412) :rule implies_pos)
-(step t182 (cl @p_413 @p_448) :rule or :premises (t147))
-(step t183 (cl @p_448) :rule resolution :premises (t182 t68))
-(step t184 (cl (! (not @p_449) :named @p_450) (! (not @p_414) :named @p_452) @p_415) :rule implies_pos)
-(step t185 (cl @p_413 @p_449) :rule or :premises (t148))
-(step t186 (cl @p_450 @p_415) :rule resolution :premises (t184 axiom8))
-(step t187 (cl @p_449) :rule resolution :premises (t185 t68))
-(step t188 (cl @p_415) :rule resolution :premises (t186 t187))
-(step t189 (cl (! (not @p_451) :named @p_453) @p_452 @p_416) :rule implies_pos)
-(step t190 (cl @p_413 @p_451) :rule or :premises (t149))
-(step t191 (cl @p_453 @p_416) :rule resolution :premises (t189 axiom8))
-(step t192 (cl @p_451) :rule resolution :premises (t190 t68))
-(step t193 (cl @p_416) :rule resolution :premises (t191 t192))
-(step t194 (cl @p_412) :rule resolution :premises (t181 t193 t183))
-(step t195 (cl @p_418 @p_454) :rule or :premises (t150))
-(step t196 (cl @p_454) :rule resolution :premises (t195 t56))
-(step t197 (cl @p_418 @p_455) :rule or :premises (t151))
-(step t198 (cl @p_455) :rule resolution :premises (t197 t56))
-(step t199 (cl @p_456 @p_457) :rule or :premises (t152))
-(step t200 (cl @p_457) :rule resolution :premises (t199 t50))
-(step t201 (cl (not @p_458) (! (not @p_459) :named @p_507) @p_460) :rule implies_pos)
-(step t202 (cl @p_461 @p_458) :rule or :premises (t153))
-(step t203 (cl @p_458) :rule resolution :premises (t202 t44))
-(step t204 (cl (or @p_410 (! (not (! (<= @p_462 @p_463) :named @p_534)) :named @p_464) (! (not (! (<= @p_463 @p_462) :named @p_535)) :named @p_465))) :rule la_disequality)
-(step t205 (cl @p_410 @p_464 @p_465) :rule or :premises (t204))
-(step t206 (cl @p_464 @p_465) :rule resolution :premises (t205 axiom19))
-(step t207 (cl (or @p_441 (! (= @p_466 @p_467) :named @p_474))) :rule forall_inst :args ((:= veriT_vr44 j$) (:= veriT_vr45 @p_5)))
-(step t208 (cl (or @p_447 (! (=> (! (member$a j$ @p_5) :named @p_468) (! (= @p_5 @p_467) :named @p_477)) :named @p_475))) :rule forall_inst :args ((:= veriT_vr32 j$) (:= veriT_vr33 @p_5)))
-(step t209 (cl (or (! (not @p_156) :named @p_469) (! (= @p_437 (! (and (! (not @p_468) :named @p_476) (! (= bot$ (inf$ @p_5 bot$)) :named @p_479)) :named @p_478)) :named @p_482))) :rule forall_inst :args ((:= veriT_vr23 @p_5) (:= veriT_vr24 j$) (:= veriT_vr25 bot$)))
-(step t210 (cl (or @p_469 (! (= @p_431 (! (and @p_470 (! (= bot$ (inf$ @p_7 bot$)) :named @p_485)) :named @p_483)) :named @p_487))) :rule forall_inst :args ((:= veriT_vr23 @p_7) (:= veriT_vr24 i$) (:= veriT_vr25 bot$)))
-(step t211 (cl (or (! (not @p_61) :named @p_472) (! (= @p_426 (! (fun_app$a (! (fun_app$ uu$ (! (fst$ @p_403) :named @p_473)) :named @p_508) @p_471) :named @p_489)) :named @p_488))) :rule forall_inst :args ((:= veriT_vr6 uu$) (:= veriT_vr7 @p_403)))
-(step t212 (cl (or @p_472 (! (= @p_421 (! (fun_app$a (! (fun_app$ uua$ @p_473) :named @p_509) @p_471) :named @p_492)) :named @p_491))) :rule forall_inst :args ((:= veriT_vr6 uua$) (:= veriT_vr7 @p_403)))
-(step t213 (cl @p_441 @p_474) :rule or :premises (t207))
-(step t214 (cl @p_474) :rule resolution :premises (t213 t92))
-(step t215 (cl (not @p_475) @p_476 @p_477) :rule implies_pos)
-(step t216 (cl @p_447 @p_475) :rule or :premises (t208))
-(step t217 (cl @p_475) :rule resolution :premises (t216 t74))
-(step t218 (cl (not (! (not @p_470) :named @p_484)) @p_445) :rule not_not)
-(step t219 (cl @p_478 (! (not @p_476) :named @p_480) (! (not @p_479) :named @p_481)) :rule and_neg)
-(step t220 (cl (not @p_480) @p_468) :rule not_not)
-(step t221 (cl @p_478 @p_468 @p_481) :rule th_resolution :premises (t220 t219))
-(step t222 (cl (not @p_482) @p_437 (! (not @p_478) :named @p_516)) :rule equiv_pos1)
-(step t223 (cl @p_469 @p_482) :rule or :premises (t209))
-(step t224 (cl @p_482) :rule resolution :premises (t223 t62))
-(step t225 (cl @p_483 @p_484 (! (not @p_485) :named @p_486)) :rule and_neg)
-(step t226 (cl @p_483 @p_445 @p_486) :rule th_resolution :premises (t218 t225))
-(step t227 (cl (not @p_487) @p_431 (not @p_483)) :rule equiv_pos1)
-(step t228 (cl @p_469 @p_487) :rule or :premises (t210))
-(step t229 (cl @p_487) :rule resolution :premises (t228 t62))
-(step t230 (cl (! (not @p_488) :named @p_490) (not @p_426) @p_489) :rule equiv_pos2)
-(step t231 (cl @p_472 @p_488) :rule or :premises (t211))
-(step t232 (cl @p_490 @p_489) :rule resolution :premises (t230 t163))
-(step t233 (cl @p_488) :rule resolution :premises (t231 t38))
-(step t234 (cl @p_489) :rule resolution :premises (t232 t233))
-(step t235 (cl (! (not @p_491) :named @p_493) (not @p_421) @p_492) :rule equiv_pos2)
-(step t236 (cl @p_472 @p_491) :rule or :premises (t212))
-(step t237 (cl @p_493 @p_492) :rule resolution :premises (t235 t158))
-(step t238 (cl @p_491) :rule resolution :premises (t236 t38))
-(step t239 (cl @p_492) :rule resolution :premises (t237 t238))
-(step t240 (cl (or (! (not @p_205) :named @p_494) @p_479)) :rule forall_inst :args ((:= veriT_vr35 @p_5)))
-(step t241 (cl (or @p_494 @p_485)) :rule forall_inst :args ((:= veriT_vr35 @p_7)))
-(step t242 (cl @p_494 @p_479) :rule or :premises (t240))
-(step t243 (cl @p_479) :rule resolution :premises (t242 t80))
-(step t244 (cl @p_494 @p_485) :rule or :premises (t241))
-(step t245 (cl @p_485) :rule resolution :premises (t244 t80))
-(step t246 (cl (! (= @p_7 @p_7) :named @p_520)) :rule eq_reflexive)
-(step t247 (cl (not (! (= 1.0 0.0) :named @p_497))) :rule la_generic :args ((- 1)))
-(step t248 (cl (! (not @p_455) :named @p_505) (not (! (= @p_495 @p_496) :named @p_498)) (! (not @p_454) :named @p_506) @p_497) :rule eq_transitive)
-(step t249 (cl (not (! (= @p_417 @p_419) :named @p_501)) @p_498) :rule eq_congruent)
-(step t250 (cl (! (not @p_499) :named @p_502) (! (not @p_460) :named @p_503) (! (not @p_500) :named @p_504) @p_501) :rule eq_transitive)
-(step t251 (cl @p_498 @p_502 @p_503 @p_504) :rule th_resolution :premises (t249 t250))
-(step t252 (cl @p_505 @p_506 @p_497 @p_502 @p_503 @p_504) :rule th_resolution :premises (t248 t251))
-(step t253 (cl @p_505 @p_506 @p_502 @p_503 @p_504) :rule th_resolution :premises (t247 t252))
-(step t254 (cl @p_503) :rule resolution :premises (t253 axiom10 axiom12 t196 t198))
-(step t255 (cl @p_507) :rule resolution :premises (t201 t254 t203))
-(step t256 (cl (! (= f$ f$) :named @p_523)) :rule eq_reflexive)
-(step t257 (cl (! (= g$ g$) :named @p_524)) :rule eq_reflexive)
-(step t258 (cl (! (= @p_405 @p_405) :named @p_527)) :rule eq_reflexive)
-(step t259 (cl (or (! (not @p_34) :named @p_510) (! (= @p_24 @p_508) :named @p_511))) :rule forall_inst :args ((:= veriT_vr3 @p_473)))
-(step t260 (cl (or (! (not @p_22) :named @p_512) (! (= @p_12 @p_509) :named @p_513))) :rule forall_inst :args ((:= veriT_vr1 @p_473)))
-(step t261 (cl @p_510 @p_511) :rule or :premises (t259))
-(step t262 (cl @p_511) :rule resolution :premises (t261 t32))
-(step t263 (cl @p_512 @p_513) :rule or :premises (t260))
-(step t264 (cl @p_513) :rule resolution :premises (t263 t26))
-(step t265 (cl (not @p_511) (! (not @p_457) :named @p_514) @p_408 (not @p_489)) :rule eq_congruent_pred)
-(step t266 (cl @p_408) :rule resolution :premises (t265 t200 t234 t262))
-(step t267 (cl (not @p_513) @p_514 @p_409 (not @p_492)) :rule eq_congruent_pred)
-(step t268 (cl @p_409) :rule resolution :premises (t267 t200 t239 t264))
-(step t269 (cl @p_515) :rule resolution :premises (t168 t268 t194 t173 t175 t266))
-(step t270 (cl @p_516) :rule resolution :premises (t222 t269 t224))
-(step t271 (cl @p_468) :rule resolution :premises (t221 t270 t243))
-(step t272 (cl @p_477) :rule resolution :premises (t215 t271 t217))
-(step t273 (cl (! (not @p_477) :named @p_517) (not @p_474) @p_430) :rule eq_transitive)
-(step t274 (cl @p_430) :rule resolution :premises (t273 t214 t272))
-(step t275 (cl @p_517 (! (not @p_443) :named @p_518) (! (= @p_5 @p_407) :named @p_519)) :rule eq_transitive)
-(step t276 (cl @p_518 @p_517 @p_519) :rule eq_transitive)
-(step t277 (cl (not @p_520) (! (not @p_446) :named @p_521) (! (not @p_519) :named @p_522) @p_459) :rule eq_transitive)
-(step t278 (cl @p_521 @p_522 @p_459) :rule th_resolution :premises (t277 t246))
-(step t279 (cl @p_521 @p_459 @p_518 @p_517) :rule th_resolution :premises (t278 t276))
-(step t280 (cl @p_521) :rule resolution :premises (t279 t177 t255 t272))
-(step t281 (cl (not @p_523) @p_522 (! (not @p_524) :named @p_525) (! (= @p_462 @p_404) :named @p_526)) :rule eq_congruent)
-(step t282 (cl @p_522 @p_525 @p_526) :rule th_resolution :premises (t281 t256))
-(step t283 (cl @p_522 @p_526) :rule th_resolution :premises (t282 t257))
-(step t284 (cl @p_526 @p_517 @p_518) :rule th_resolution :premises (t283 t275))
-(step t285 (cl @p_470) :rule resolution :premises (t178 t280 t180))
-(step t286 (cl @p_483) :rule resolution :premises (t226 t285 t245))
-(step t287 (cl @p_431) :rule resolution :premises (t227 t286 t229))
-(step t288 (cl @p_429) :rule resolution :premises (t164 t287 t188 t266 t268 t274))
-(step t289 (cl @p_433) :rule resolution :premises (t165 t288 t167))
-(step t290 (cl (not @p_527) (! (not @p_526) :named @p_529) (! (= (! (+ @p_405 @p_462) :named @p_531) @p_528) :named @p_530)) :rule eq_congruent)
-(step t291 (cl @p_529 @p_530) :rule th_resolution :premises (t290 t258))
-(step t292 (cl @p_530 @p_517 @p_518) :rule th_resolution :premises (t291 t284))
-(step t293 (cl (! (not @p_433) :named @p_532) (not @p_530) (! (= @p_404 @p_531) :named @p_533)) :rule eq_transitive)
-(step t294 (cl @p_532 @p_533 @p_517 @p_518) :rule th_resolution :premises (t293 t292))
-(step t295 (cl @p_534 @p_529 (! (not @p_533) :named @p_536)) :rule la_generic :args (1.0 (- 2) (- 1)))
-(step t296 (cl @p_534 @p_517 @p_518 @p_532) :rule th_resolution :premises (t295 t284 t294))
-(step t297 (cl @p_534) :rule resolution :premises (t296 t289 t177 t272))
-(step t298 (cl @p_465) :rule resolution :premises (t206 t297))
-(step t299 (cl @p_535 @p_529 @p_536) :rule la_generic :args (1.0 2 1))
-(step t300 (cl @p_535 @p_517 @p_518 @p_532) :rule th_resolution :premises (t299 t284 t294))
-(step t301 (cl) :rule resolution :premises (t300 t289 t177 t298 t272))
-5fc0f54f0190d5b6a4967f69daa36736ef3d3325 6 0
+(assume a0 (! (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (! (p$ ?v0 ?v1) :named @p_2)) :named @p_1))
+(assume a1 (! (=> (! (p$ z$ y$) :named @p_12) false) :named @p_11))
+(step t3 (cl (! (= @p_1 (! (forall ((?v0 A$) (?v1 B$)) @p_2) :named @p_4)) :named @p_3)) :rule qnt_rm_unused)
+(step t4 (cl (not @p_3) (not @p_1) @p_4) :rule equiv_pos2)
+(step t5 (cl @p_4) :rule th_resolution :premises (a0 t3 t4))
+(anchor :step t6 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 B$) veriT_vr1)))
+(step t6.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
+(step t6.t2 (cl (= ?v1 veriT_vr1)) :rule refl)
+(step t6.t3 (cl (= @p_2 (! (p$ veriT_vr0 veriT_vr1) :named @p_5))) :rule cong :premises (t6.t1 t6.t2))
+(step t6 (cl (! (= @p_4 (! (forall ((veriT_vr0 A$) (veriT_vr1 B$)) @p_5) :named @p_7)) :named @p_6)) :rule bind)
+(step t7 (cl (not @p_6) (not @p_4) @p_7) :rule equiv_pos2)
+(step t8 (cl @p_7) :rule th_resolution :premises (t5 t6 t7))
+(anchor :step t9 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 B$) veriT_vr3)))
+(step t9.t1 (cl (= veriT_vr0 veriT_vr2)) :rule refl)
+(step t9.t2 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
+(step t9.t3 (cl (= @p_5 (! (p$ veriT_vr2 veriT_vr3) :named @p_8))) :rule cong :premises (t9.t1 t9.t2))
+(step t9 (cl (! (= @p_7 (! (forall ((veriT_vr2 A$) (veriT_vr3 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
+(step t10 (cl (not @p_9) (not @p_7) @p_10) :rule equiv_pos2)
+(step t11 (cl @p_10) :rule th_resolution :premises (t8 t9 t10))
+(step t12 (cl (! (= @p_11 (! (not @p_12) :named @p_14)) :named @p_13)) :rule implies_simplify)
+(step t13 (cl (not @p_13) (not @p_11) @p_14) :rule equiv_pos2)
+(step t14 (cl @p_14) :rule th_resolution :premises (a1 t12 t13))
+(step t15 (cl (or (! (not @p_10) :named @p_15) @p_12)) :rule forall_inst :args ((:= veriT_vr2 z$) (:= veriT_vr3 y$)))
+(step t16 (cl @p_15 @p_12) :rule or :premises (t15))
+(step t17 (cl) :rule resolution :premises (t16 t11 t14))
+732d0d825854417fe8b0c85959caf9624dd11670 23 0
 unsat
-(assume axiom0 (! (< 0.0 (+ x$ (! (* 2.0 y$) :named @p_1))) :named @p_2))
-(assume axiom1 (! (< 0.0 (- x$ @p_1)) :named @p_3))
-(assume axiom2 (! (< x$ 0.0) :named @p_4))
-(step t4 (cl (not @p_2) (not @p_3) (not @p_4)) :rule la_generic :args (1.0 1.0 2.0))
-(step t5 (cl) :rule resolution :premises (t4 axiom0 axiom1 axiom2))
-809cc2252f6f1da6c3a4347a531733952ab0b99f 467 0
+(assume a0 (! (not (! (<= y$ (! (ite (! (<= x$ y$) :named @p_3) y$ x$) :named @p_2)) :named @p_7)) :named @p_1))
+(step t2 (cl (! (= @p_1 (! (and (! (not (! (<= y$ @p_2) :named @p_13)) :named @p_9) (! (ite @p_3 (! (= y$ @p_2) :named @p_12) (! (= x$ @p_2) :named @p_11)) :named @p_10)) :named @p_5)) :named @p_4)) :rule ite_intro)
+(step t3 (cl (! (not @p_4) :named @p_8) (! (not @p_1) :named @p_6) @p_5) :rule equiv_pos2)
+(step t4 (cl (not @p_6) @p_7) :rule not_not)
+(step t5 (cl @p_8 @p_7 @p_5) :rule th_resolution :premises (t4 t3))
+(step t6 (cl @p_5) :rule th_resolution :premises (a0 t2 t5))
+(step t7 (cl @p_9) :rule and :premises (t6))
+(step t8 (cl @p_10) :rule and :premises (t6))
+(step t9 (cl @p_3 @p_11) :rule ite1 :premises (t8))
+(step t10 (cl (! (not @p_3) :named @p_15) @p_12) :rule ite2 :premises (t8))
+(step t11 (cl @p_13 @p_3 (! (not @p_11) :named @p_14)) :rule la_generic :args (1 1 (- 1)))
+(step t12 (cl @p_3 @p_14) :rule resolution :premises (t11 t7))
+(step t13 (cl (not (! (= y$ x$) :named @p_17)) (! (not @p_12) :named @p_16) @p_15 @p_13) :rule eq_congruent_pred)
+(step t14 (cl @p_16 @p_14 @p_17) :rule eq_transitive)
+(step t15 (cl @p_16 @p_15 @p_13 @p_16 @p_14) :rule th_resolution :premises (t13 t14))
+(step t16 (cl @p_16 @p_15 @p_13 @p_14) :rule contraction :premises (t15))
+(step t17 (cl @p_16 @p_15 @p_14) :rule resolution :premises (t16 t7))
+(step t18 (cl @p_14) :rule resolution :premises (t17 t10 t12))
+(step t19 (cl @p_3) :rule resolution :premises (t9 t18))
+(step t20 (cl @p_12) :rule resolution :premises (t10 t19))
+(step t21 (cl @p_13 @p_16) :rule la_generic :args (1 (- 1)))
+(step t22 (cl) :rule resolution :premises (t21 t7 t20))
+f17b9d0590c7cefc8013c1518981dc710a40e813 467 0
 unsat
-(assume axiom0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uuc$ ?v0) :named @p_9) (! (pair$ (! (times$ (! (- ?v0 (! (divide$ 1.0 2.0) :named @p_7)) :named @p_12) d$) :named @p_1) (! (diamond_y$ @p_1) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_6))
-(assume axiom3 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uub$ ?v0) :named @p_37) (! (pair$ (! (- (! (divide$ d$ 2.0) :named @p_3)) :named @p_2) (! (times$ (! (- (! (* 2.0 ?v0) :named @p_40) 1.0) :named @p_42) (! (diamond_y$ @p_2) :named @p_36)) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
-(assume axiom4 (! (< 0.0 d$) :named @p_257))
-(assume axiom5 (! (forall ((?v0 Real)) (! (= (! (diamond_y$ ?v0) :named @p_62) (! (- @p_3 (! (ite (! (< ?v0 0.0) :named @p_65) (! (- ?v0) :named @p_4) ?v0) :named @p_68)) :named @p_70)) :named @p_72)) :named @p_61))
-(assume axiom7 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (! (= (! (< (! (divide$ ?v0 ?v1) :named @p_5) (! (divide$ ?v2 ?v1) :named @p_88)) :named @p_90) (! (and (! (=> (! (< 0.0 ?v1) :named @p_92) (! (< ?v0 ?v2) :named @p_96)) :named @p_98) (! (and (! (=> (! (< ?v1 0.0) :named @p_100) (! (< ?v2 ?v0) :named @p_102)) :named @p_104) (! (not (! (= 0.0 ?v1) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_112)) :named @p_114)) :named @p_85))
-(assume axiom8 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (divide$ @p_4 ?v1) :named @p_142) (! (- @p_5) :named @p_147)) :named @p_149)) :named @p_140))
-(assume axiom9 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (times$ @p_4 ?v1) :named @p_164) (! (- (! (times$ ?v0 ?v1) :named @p_168)) :named @p_170)) :named @p_172)) :named @p_162))
-(assume axiom10 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (! (= (! (= (! (pair$ ?v0 ?v1) :named @p_186) (! (pair$ ?v2 ?v3) :named @p_188)) :named @p_190) (! (and (! (= ?v0 ?v2) :named @p_194) (! (= ?v1 ?v3) :named @p_198)) :named @p_200)) :named @p_202)) :named @p_185))
-(assume axiom11 (! (not (! (=> (! (and (! (not (= uua$ uu$)) :named @p_226) (! (= uuc$ uub$) :named @p_227)) :named @p_220) false) :named @p_224)) :named @p_219))
+(assume a0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uuc$ ?v0) :named @p_9) (! (pair$ (! (times$ (! (- ?v0 (! (divide$ 1.0 2.0) :named @p_7)) :named @p_12) d$) :named @p_1) (! (diamond_y$ @p_1) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_6))
+(assume a3 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uub$ ?v0) :named @p_37) (! (pair$ (! (- (! (divide$ d$ 2.0) :named @p_3)) :named @p_2) (! (times$ (! (- (! (* 2.0 ?v0) :named @p_40) 1.0) :named @p_42) (! (diamond_y$ @p_2) :named @p_36)) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
+(assume a4 (! (< 0.0 d$) :named @p_257))
+(assume a5 (! (forall ((?v0 Real)) (! (= (! (diamond_y$ ?v0) :named @p_62) (! (- @p_3 (! (ite (! (< ?v0 0.0) :named @p_65) (! (- ?v0) :named @p_4) ?v0) :named @p_68)) :named @p_70)) :named @p_72)) :named @p_61))
+(assume a7 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (! (= (! (< (! (divide$ ?v0 ?v1) :named @p_5) (! (divide$ ?v2 ?v1) :named @p_88)) :named @p_90) (! (and (! (=> (! (< 0.0 ?v1) :named @p_92) (! (< ?v0 ?v2) :named @p_96)) :named @p_98) (! (and (! (=> (! (< ?v1 0.0) :named @p_100) (! (< ?v2 ?v0) :named @p_102)) :named @p_104) (! (not (! (= 0.0 ?v1) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_112)) :named @p_114)) :named @p_85))
+(assume a8 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (divide$ @p_4 ?v1) :named @p_142) (! (- @p_5) :named @p_147)) :named @p_149)) :named @p_140))
+(assume a9 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (times$ @p_4 ?v1) :named @p_164) (! (- (! (times$ ?v0 ?v1) :named @p_168)) :named @p_170)) :named @p_172)) :named @p_162))
+(assume a10 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (! (= (! (= (! (pair$ ?v0 ?v1) :named @p_186) (! (pair$ ?v2 ?v3) :named @p_188)) :named @p_190) (! (and (! (= ?v0 ?v2) :named @p_194) (! (= ?v1 ?v3) :named @p_198)) :named @p_200)) :named @p_202)) :named @p_185))
+(assume a11 (! (not (! (=> (! (and (! (not (= uua$ uu$)) :named @p_226) (! (= uuc$ uub$) :named @p_227)) :named @p_220) false) :named @p_224)) :named @p_219))
 (anchor :step t10 :args ((:= (?v0 Real) veriT_vr0)))
 (step t10.t1 (cl (! (= ?v0 veriT_vr0) :named @p_11)) :rule refl)
 (step t10.t2 (cl (= @p_9 (! (fun_app$ uuc$ veriT_vr0) :named @p_10))) :rule cong :premises (t10.t1))
@@ -5581,7 +5632,7 @@
 (step t10.t11 (cl (= @p_20 (! (= @p_10 @p_19) :named @p_21))) :rule cong :premises (t10.t2 t10.t10))
 (step t10 (cl (! (= @p_6 (! (forall ((veriT_vr0 Real)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
 (step t11 (cl (not @p_22) (not @p_6) @p_23) :rule equiv_pos2)
-(step t12 (cl @p_23) :rule th_resolution :premises (axiom0 t10 t11))
+(step t12 (cl @p_23) :rule th_resolution :premises (a0 t10 t11))
 (anchor :step t13 :args ((:= (veriT_vr0 Real) veriT_vr1)))
 (step t13.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_26)) :rule refl)
 (step t13.t2 (cl (= @p_10 (! (fun_app$ uuc$ veriT_vr1) :named @p_25))) :rule cong :premises (t13.t1))
@@ -5608,7 +5659,7 @@
 (step t16.t8 (cl (= @p_48 (! (= @p_38 @p_47) :named @p_49))) :rule cong :premises (t16.t2 t16.t7))
 (step t16 (cl (! (= @p_35 (! (forall ((veriT_vr6 Real)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
 (step t17 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
-(step t18 (cl @p_51) :rule th_resolution :premises (axiom3 t16 t17))
+(step t18 (cl @p_51) :rule th_resolution :premises (a3 t16 t17))
 (anchor :step t19 :args ((:= (veriT_vr6 Real) veriT_vr7)))
 (step t19.t1 (cl (! (= veriT_vr6 veriT_vr7) :named @p_53)) :rule refl)
 (step t19.t2 (cl (= @p_38 (! (fun_app$ uub$ veriT_vr7) :named @p_52))) :rule cong :premises (t19.t1))
@@ -5634,7 +5685,7 @@
 (step t22.t10 (cl (= @p_72 (! (= @p_63 @p_71) :named @p_73))) :rule cong :premises (t22.t2 t22.t9))
 (step t22 (cl (! (= @p_61 (! (forall ((veriT_vr8 Real)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
 (step t23 (cl (not @p_74) (not @p_61) @p_75) :rule equiv_pos2)
-(step t24 (cl @p_75) :rule th_resolution :premises (axiom5 t22 t23))
+(step t24 (cl @p_75) :rule th_resolution :premises (a5 t22 t23))
 (anchor :step t25 :args ((:= (veriT_vr8 Real) veriT_vr9)))
 (step t25.t1 (cl (! (= veriT_vr8 veriT_vr9) :named @p_77)) :rule refl)
 (step t25.t2 (cl (= @p_63 (! (diamond_y$ veriT_vr9) :named @p_76))) :rule cong :premises (t25.t1))
@@ -5677,7 +5728,7 @@
 (step t28.t25 (cl (= @p_114 (! (= @p_91 @p_113) :named @p_115))) :rule cong :premises (t28.t7 t28.t24))
 (step t28 (cl (! (= @p_85 (! (forall ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)) @p_115) :named @p_117)) :named @p_116)) :rule bind)
 (step t29 (cl (not @p_116) (not @p_85) @p_117) :rule equiv_pos2)
-(step t30 (cl @p_117) :rule th_resolution :premises (axiom7 t28 t29))
+(step t30 (cl @p_117) :rule th_resolution :premises (a7 t28 t29))
 (anchor :step t31 :args ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)))
 (step t31.t1 (cl (= @p_113 (! (and @p_99 @p_105 @p_109) :named @p_118))) :rule ac_simp)
 (step t31.t2 (cl (= @p_115 (! (= @p_91 @p_118) :named @p_119))) :rule cong :premises (t31.t1))
@@ -5724,7 +5775,7 @@
 (step t37.t9 (cl (= @p_149 (! (= @p_143 @p_148) :named @p_150))) :rule cong :premises (t37.t4 t37.t8))
 (step t37 (cl (! (= @p_140 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_150) :named @p_152)) :named @p_151)) :rule bind)
 (step t38 (cl (not @p_151) (not @p_140) @p_152) :rule equiv_pos2)
-(step t39 (cl @p_152) :rule th_resolution :premises (axiom8 t37 t38))
+(step t39 (cl @p_152) :rule th_resolution :premises (a8 t37 t38))
 (anchor :step t40 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
 (step t40.t1 (cl (! (= veriT_vr16 veriT_vr18) :named @p_155)) :rule refl)
 (step t40.t2 (cl (= @p_141 (! (- veriT_vr18) :named @p_153))) :rule cong :premises (t40.t1))
@@ -5750,7 +5801,7 @@
 (step t43.t9 (cl (= @p_172 (! (= @p_165 @p_171) :named @p_173))) :rule cong :premises (t43.t4 t43.t8))
 (step t43 (cl (! (= @p_162 (! (forall ((veriT_vr20 Real) (veriT_vr21 Real)) @p_173) :named @p_175)) :named @p_174)) :rule bind)
 (step t44 (cl (not @p_174) (not @p_162) @p_175) :rule equiv_pos2)
-(step t45 (cl @p_175) :rule th_resolution :premises (axiom9 t43 t44))
+(step t45 (cl @p_175) :rule th_resolution :premises (a9 t43 t44))
 (anchor :step t46 :args ((:= (veriT_vr20 Real) veriT_vr22) (:= (veriT_vr21 Real) veriT_vr23)))
 (step t46.t1 (cl (! (= veriT_vr20 veriT_vr22) :named @p_178)) :rule refl)
 (step t46.t2 (cl (= @p_163 (! (- veriT_vr22) :named @p_176))) :rule cong :premises (t46.t1))
@@ -5782,7 +5833,7 @@
 (step t49.t15 (cl (= @p_202 (! (= @p_191 @p_201) :named @p_203))) :rule cong :premises (t49.t7 t49.t14))
 (step t49 (cl (! (= @p_185 (! (forall ((veriT_vr24 Real) (veriT_vr25 Real) (veriT_vr26 Real) (veriT_vr27 Real)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
 (step t50 (cl (not @p_204) (not @p_185) @p_205) :rule equiv_pos2)
-(step t51 (cl @p_205) :rule th_resolution :premises (axiom10 t49 t50))
+(step t51 (cl @p_205) :rule th_resolution :premises (a10 t49 t50))
 (anchor :step t52 :args ((:= (veriT_vr24 Real) veriT_vr28) (:= (veriT_vr25 Real) veriT_vr29) (:= (veriT_vr26 Real) veriT_vr30) (:= (veriT_vr27 Real) veriT_vr31)))
 (step t52.t1 (cl (! (= veriT_vr24 veriT_vr28) :named @p_209)) :rule refl)
 (step t52.t2 (cl (! (= veriT_vr25 veriT_vr29) :named @p_212)) :rule refl)
@@ -5806,7 +5857,7 @@
 (step t56 (cl (! (not @p_221) :named @p_225) (! (not @p_219) :named @p_223) @p_222) :rule equiv_pos2)
 (step t57 (cl (not @p_223) @p_224) :rule not_not)
 (step t58 (cl @p_225 @p_224 @p_222) :rule th_resolution :premises (t57 t56))
-(step t59 (cl @p_222) :rule th_resolution :premises (axiom11 t55 t58))
+(step t59 (cl @p_222) :rule th_resolution :premises (a11 t55 t58))
 (step t60 (cl (! (= @p_222 (! (and @p_226 @p_227 @p_228) :named @p_230)) :named @p_229)) :rule ac_simp)
 (step t61 (cl (not @p_229) (not @p_222) @p_230) :rule equiv_pos2)
 (step t62 (cl @p_230) :rule th_resolution :premises (t59 t60 t61))
@@ -5953,7 +6004,7 @@
 (step t130 (cl @p_251) :rule resolution :premises (t129 t42))
 (step t131 (cl @p_326 @p_259 (not @p_257)) :rule equiv_pos1)
 (step t132 (cl @p_256 @p_273) :rule or :premises (t95))
-(step t133 (cl @p_326 @p_259) :rule resolution :premises (t131 axiom4))
+(step t133 (cl @p_326 @p_259) :rule resolution :premises (t131 a4))
 (step t134 (cl @p_273) :rule resolution :premises (t132 t36))
 (step t135 (cl @p_259) :rule resolution :premises (t133 t134))
 (step t136 (cl @p_327 @p_328) :rule and_pos)
@@ -6024,636 +6075,17 @@
 (step t201 (cl @p_378 @p_381 @p_376 @p_344 @p_342 @p_378 @p_380) :rule th_resolution :premises (t197 t200))
 (step t202 (cl @p_378 @p_381 @p_376 @p_344 @p_342 @p_380) :rule contraction :premises (t201))
 (step t203 (cl) :rule resolution :premises (t202 t156 t165 t149 t173 t180 t196))
-42dfad143cfae67cfed01ebeb5997e53c8d08b98 26 0
-unsat
-(assume axiom0 (! (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (! (p$ ?v0 ?v1) :named @p_2)) :named @p_1))
-(assume axiom1 (! (=> (! (p$ z$ y$) :named @p_12) false) :named @p_11))
-(step t3 (cl (! (= @p_1 (! (forall ((?v0 A$) (?v1 B$)) @p_2) :named @p_4)) :named @p_3)) :rule qnt_rm_unused)
-(step t4 (cl (not @p_3) (not @p_1) @p_4) :rule equiv_pos2)
-(step t5 (cl @p_4) :rule th_resolution :premises (axiom0 t3 t4))
-(anchor :step t6 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 B$) veriT_vr1)))
-(step t6.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
-(step t6.t2 (cl (= ?v1 veriT_vr1)) :rule refl)
-(step t6.t3 (cl (= @p_2 (! (p$ veriT_vr0 veriT_vr1) :named @p_5))) :rule cong :premises (t6.t1 t6.t2))
-(step t6 (cl (! (= @p_4 (! (forall ((veriT_vr0 A$) (veriT_vr1 B$)) @p_5) :named @p_7)) :named @p_6)) :rule bind)
-(step t7 (cl (not @p_6) (not @p_4) @p_7) :rule equiv_pos2)
-(step t8 (cl @p_7) :rule th_resolution :premises (t5 t6 t7))
-(anchor :step t9 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 B$) veriT_vr3)))
-(step t9.t1 (cl (= veriT_vr0 veriT_vr2)) :rule refl)
-(step t9.t2 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
-(step t9.t3 (cl (= @p_5 (! (p$ veriT_vr2 veriT_vr3) :named @p_8))) :rule cong :premises (t9.t1 t9.t2))
-(step t9 (cl (! (= @p_7 (! (forall ((veriT_vr2 A$) (veriT_vr3 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
-(step t10 (cl (not @p_9) (not @p_7) @p_10) :rule equiv_pos2)
-(step t11 (cl @p_10) :rule th_resolution :premises (t8 t9 t10))
-(step t12 (cl (! (= @p_11 (! (not @p_12) :named @p_14)) :named @p_13)) :rule implies_simplify)
-(step t13 (cl (not @p_13) (not @p_11) @p_14) :rule equiv_pos2)
-(step t14 (cl @p_14) :rule th_resolution :premises (axiom1 t12 t13))
-(step t15 (cl (or (! (not @p_10) :named @p_15) @p_12)) :rule forall_inst :args ((:= veriT_vr2 z$) (:= veriT_vr3 y$)))
-(step t16 (cl @p_15 @p_12) :rule or :premises (t15))
-(step t17 (cl) :rule resolution :premises (t16 t11 t14))
-d91a4d59e816a47672957ce0be20acd9aa3eef3e 23 0
-unsat
-(assume axiom0 (! (not (! (<= y$ (! (ite (! (<= x$ y$) :named @p_3) y$ x$) :named @p_2)) :named @p_7)) :named @p_1))
-(step t2 (cl (! (= @p_1 (! (and (! (not (! (<= y$ @p_2) :named @p_13)) :named @p_9) (! (ite @p_3 (! (= y$ @p_2) :named @p_12) (! (= x$ @p_2) :named @p_11)) :named @p_10)) :named @p_5)) :named @p_4)) :rule ite_intro)
-(step t3 (cl (! (not @p_4) :named @p_8) (! (not @p_1) :named @p_6) @p_5) :rule equiv_pos2)
-(step t4 (cl (not @p_6) @p_7) :rule not_not)
-(step t5 (cl @p_8 @p_7 @p_5) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_5) :rule th_resolution :premises (axiom0 t2 t5))
-(step t7 (cl @p_9) :rule and :premises (t6))
-(step t8 (cl @p_10) :rule and :premises (t6))
-(step t9 (cl @p_3 @p_11) :rule ite1 :premises (t8))
-(step t10 (cl (! (not @p_3) :named @p_15) @p_12) :rule ite2 :premises (t8))
-(step t11 (cl @p_13 @p_3 (! (not @p_11) :named @p_14)) :rule la_generic :args (1 1 (- 1)))
-(step t12 (cl @p_3 @p_14) :rule resolution :premises (t11 t7))
-(step t13 (cl (not (! (= y$ x$) :named @p_17)) (! (not @p_12) :named @p_16) @p_15 @p_13) :rule eq_congruent_pred)
-(step t14 (cl @p_16 @p_14 @p_17) :rule eq_transitive)
-(step t15 (cl @p_16 @p_15 @p_13 @p_16 @p_14) :rule th_resolution :premises (t13 t14))
-(step t16 (cl @p_16 @p_15 @p_13 @p_14) :rule contraction :premises (t15))
-(step t17 (cl @p_16 @p_15 @p_14) :rule resolution :premises (t16 t7))
-(step t18 (cl @p_14) :rule resolution :premises (t17 t10 t12))
-(step t19 (cl @p_3) :rule resolution :premises (t9 t18))
-(step t20 (cl @p_12) :rule resolution :premises (t10 t19))
-(step t21 (cl @p_13 @p_16) :rule la_generic :args (1 (- 1)))
-(step t22 (cl) :rule resolution :premises (t21 t7 t20))
-47bc3239fb0fd8c5f8f4969f0c6c1996f0a21574 567 0
+268d7e42d22bc05b4bcc195eddbced079a39fedf 791 0
 unsat
-(define-fun veriT_sk0 () A$ (! (choice ((veriT_vr145 A$)) (not (! (not (! (and (! (= (! (arg_min_on$ f$ (! (image$b g$ b$) :named @p_6)) :named @p_336) (! (fun_app$b g$ veriT_vr145) :named @p_378)) :named @p_379) (! (member$a veriT_vr145 b$) :named @p_381)) :named @p_382)) :named @p_377))) :named @p_357))
-(assume axiom29 (! (forall ((?v0 B_set$) (?v1 B_c_fun$)) (! (=> (! (and (! (finite$ ?v0) :named @p_1) (! (not (! (= ?v0 bot$) :named @p_10)) :named @p_2)) :named @p_13) (! (member$ (! (arg_min_on$ ?v1 ?v0) :named @p_15) ?v0) :named @p_17)) :named @p_19)) :named @p_7))
-(assume axiom31 (! (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (! (=> (! (and @p_1 (! (and @p_2 (! (member$ ?v1 ?v0) :named @p_38)) :named @p_40)) :named @p_42) (! (less_eq$ (! (fun_app$ ?v2 (! (arg_min_on$ ?v2 ?v0) :named @p_45)) :named @p_47) (! (fun_app$ ?v2 ?v1) :named @p_50)) :named @p_52)) :named @p_54)) :named @p_33))
-(assume axiom33 (! (forall ((?v0 B_c_fun$) (?v1 A_b_fun$) (?v2 A$)) (! (= (! (fun_app$a (! (comp$ ?v0 ?v1) :named @p_78) ?v2) :named @p_80) (! (fun_app$ ?v0 (! (fun_app$b ?v1 ?v2) :named @p_3)) :named @p_86)) :named @p_88)) :named @p_77))
-(assume axiom36 (! (forall ((?v0 A_set$) (?v1 A_b_fun$)) (! (=> (! (finite$a ?v0) :named @p_103) (! (finite$ (! (image$b ?v1 ?v0) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_102))
-(assume axiom40 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (! (=> (! (and (! (member$ ?v0 (! (image$b ?v1 ?v2) :named @p_122)) :named @p_124) (! (forall ((?v3 A$)) (! (=> (! (and (! (= ?v0 (! (fun_app$b ?v1 ?v3) :named @p_130)) :named @p_132) (! (member$a ?v3 ?v2) :named @p_136)) :named @p_138) false) :named @p_140)) :named @p_126)) :named @p_142) false) :named @p_144)) :named @p_121))
-(assume axiom44 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (! (=> (! (and (! (= @p_3 ?v0) :named @p_173) (! (member$a ?v2 ?v3) :named @p_176)) :named @p_178) (! (member$ ?v0 (! (image$b ?v1 ?v3) :named @p_183)) :named @p_185)) :named @p_187)) :named @p_171))
-(assume axiom48 (! (forall ((?v0 A_b_fun$) (?v1 A_set$)) (! (= (! (= bot$ (! (image$b ?v0 ?v1) :named @p_205)) :named @p_207) (! (= bot$a ?v1) :named @p_210)) :named @p_212)) :named @p_204))
-(assume axiom50 (! (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (! (=> (! (and (! (inj_on$ ?v0 ?v1) :named @p_224) (! (and (! (= (! (fun_app$ ?v0 ?v2) :named @p_227) (! (fun_app$ ?v0 ?v3) :named @p_229)) :named @p_231) (! (and (! (member$ ?v2 ?v1) :named @p_235) (! (member$ ?v3 ?v1) :named @p_238)) :named @p_240)) :named @p_242)) :named @p_244) (! (= ?v3 ?v2) :named @p_246)) :named @p_248)) :named @p_223))
-(assume axiom51 (! (forall ((?v0 C$) (?v1 C$)) (! (= (! (less$ ?v0 ?v1) :named @p_272) (! (and (! (less_eq$ ?v0 ?v1) :named @p_276) (! (not (! (= ?v0 ?v1) :named @p_278)) :named @p_280)) :named @p_282)) :named @p_284)) :named @p_271))
-(assume axiom23 (! (inj_on$ f$ @p_6) :named @p_353))
-(assume axiom24 (! (finite$a b$) :named @p_332))
-(assume axiom25 (not (! (= bot$a b$) :named @p_331)))
-(assume axiom26 (! (member$a (! (arg_min_on$a (! (comp$ f$ g$) :named @p_4) b$) :named @p_5) b$) :named @p_423))
-(assume axiom27 (! (not (! (exists ((?v0 A$)) (! (and (! (member$a ?v0 b$) :named @p_300) (! (less$ (! (fun_app$a @p_4 ?v0) :named @p_303) (! (fun_app$a @p_4 @p_5) :named @p_299)) :named @p_305)) :named @p_307)) :named @p_298)) :named @p_309))
-(assume axiom52 (not (! (= @p_336 (! (fun_app$b g$ @p_5) :named @p_333)) :named @p_355)))
-(anchor :step t16 :args ((:= (?v0 B_set$) veriT_vr0) (:= (?v1 B_c_fun$) veriT_vr1)))
-(step t16.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
-(step t16.t2 (cl (= @p_1 (! (finite$ veriT_vr0) :named @p_8))) :rule cong :premises (t16.t1))
-(step t16.t3 (cl @p_9) :rule refl)
-(step t16.t4 (cl (= @p_10 (! (= bot$ veriT_vr0) :named @p_11))) :rule cong :premises (t16.t3))
-(step t16.t5 (cl (= @p_2 (! (not @p_11) :named @p_12))) :rule cong :premises (t16.t4))
-(step t16.t6 (cl (= @p_13 (! (and @p_8 @p_12) :named @p_14))) :rule cong :premises (t16.t2 t16.t5))
-(step t16.t7 (cl (= ?v1 veriT_vr1)) :rule refl)
-(step t16.t8 (cl @p_9) :rule refl)
-(step t16.t9 (cl (= @p_15 (! (arg_min_on$ veriT_vr1 veriT_vr0) :named @p_16))) :rule cong :premises (t16.t7 t16.t8))
-(step t16.t10 (cl @p_9) :rule refl)
-(step t16.t11 (cl (= @p_17 (! (member$ @p_16 veriT_vr0) :named @p_18))) :rule cong :premises (t16.t9 t16.t10))
-(step t16.t12 (cl (= @p_19 (! (=> @p_14 @p_18) :named @p_20))) :rule cong :premises (t16.t6 t16.t11))
-(step t16 (cl (! (= @p_7 (! (forall ((veriT_vr0 B_set$) (veriT_vr1 B_c_fun$)) @p_20) :named @p_22)) :named @p_21)) :rule bind)
-(step t17 (cl (not @p_21) (not @p_7) @p_22) :rule equiv_pos2)
-(step t18 (cl @p_22) :rule th_resolution :premises (axiom29 t16 t17))
-(anchor :step t19 :args ((:= (veriT_vr0 B_set$) veriT_vr2) (:= (veriT_vr1 B_c_fun$) veriT_vr3)))
-(step t19.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_24)) :rule refl)
-(step t19.t2 (cl (= @p_8 (! (finite$ veriT_vr2) :named @p_23))) :rule cong :premises (t19.t1))
-(step t19.t3 (cl @p_24) :rule refl)
-(step t19.t4 (cl (= @p_11 (! (= bot$ veriT_vr2) :named @p_25))) :rule cong :premises (t19.t3))
-(step t19.t5 (cl (= @p_12 (! (not @p_25) :named @p_26))) :rule cong :premises (t19.t4))
-(step t19.t6 (cl (= @p_14 (! (and @p_23 @p_26) :named @p_27))) :rule cong :premises (t19.t2 t19.t5))
-(step t19.t7 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
-(step t19.t8 (cl @p_24) :rule refl)
-(step t19.t9 (cl (= @p_16 (! (arg_min_on$ veriT_vr3 veriT_vr2) :named @p_28))) :rule cong :premises (t19.t7 t19.t8))
-(step t19.t10 (cl @p_24) :rule refl)
-(step t19.t11 (cl (= @p_18 (! (member$ @p_28 veriT_vr2) :named @p_29))) :rule cong :premises (t19.t9 t19.t10))
-(step t19.t12 (cl (= @p_20 (! (=> @p_27 @p_29) :named @p_30))) :rule cong :premises (t19.t6 t19.t11))
-(step t19 (cl (! (= @p_22 (! (forall ((veriT_vr2 B_set$) (veriT_vr3 B_c_fun$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
-(step t20 (cl (not @p_31) (not @p_22) @p_32) :rule equiv_pos2)
-(step t21 (cl @p_32) :rule th_resolution :premises (t18 t19 t20))
-(anchor :step t22 :args ((:= (?v0 B_set$) veriT_vr8) (:= (?v1 B$) veriT_vr9) (:= (?v2 B_c_fun$) veriT_vr10)))
-(step t22.t1 (cl (! (= ?v0 veriT_vr8) :named @p_35)) :rule refl)
-(step t22.t2 (cl (= @p_1 (! (finite$ veriT_vr8) :named @p_34))) :rule cong :premises (t22.t1))
-(step t22.t3 (cl @p_35) :rule refl)
-(step t22.t4 (cl (= @p_10 (! (= bot$ veriT_vr8) :named @p_36))) :rule cong :premises (t22.t3))
-(step t22.t5 (cl (= @p_2 (! (not @p_36) :named @p_37))) :rule cong :premises (t22.t4))
-(step t22.t6 (cl (! (= ?v1 veriT_vr9) :named @p_49)) :rule refl)
-(step t22.t7 (cl @p_35) :rule refl)
-(step t22.t8 (cl (= @p_38 (! (member$ veriT_vr9 veriT_vr8) :named @p_39))) :rule cong :premises (t22.t6 t22.t7))
-(step t22.t9 (cl (= @p_40 (! (and @p_37 @p_39) :named @p_41))) :rule cong :premises (t22.t5 t22.t8))
-(step t22.t10 (cl (= @p_42 (! (and @p_34 @p_41) :named @p_43))) :rule cong :premises (t22.t2 t22.t9))
-(step t22.t11 (cl (! (= ?v2 veriT_vr10) :named @p_44)) :rule refl)
-(step t22.t12 (cl @p_44) :rule refl)
-(step t22.t13 (cl @p_35) :rule refl)
-(step t22.t14 (cl (= @p_45 (! (arg_min_on$ veriT_vr10 veriT_vr8) :named @p_46))) :rule cong :premises (t22.t12 t22.t13))
-(step t22.t15 (cl (= @p_47 (! (fun_app$ veriT_vr10 @p_46) :named @p_48))) :rule cong :premises (t22.t11 t22.t14))
-(step t22.t16 (cl @p_44) :rule refl)
-(step t22.t17 (cl @p_49) :rule refl)
-(step t22.t18 (cl (= @p_50 (! (fun_app$ veriT_vr10 veriT_vr9) :named @p_51))) :rule cong :premises (t22.t16 t22.t17))
-(step t22.t19 (cl (= @p_52 (! (less_eq$ @p_48 @p_51) :named @p_53))) :rule cong :premises (t22.t15 t22.t18))
-(step t22.t20 (cl (= @p_54 (! (=> @p_43 @p_53) :named @p_55))) :rule cong :premises (t22.t10 t22.t19))
-(step t22 (cl (! (= @p_33 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_55) :named @p_57)) :named @p_56)) :rule bind)
-(step t23 (cl (not @p_56) (not @p_33) @p_57) :rule equiv_pos2)
-(step t24 (cl @p_57) :rule th_resolution :premises (axiom31 t22 t23))
-(anchor :step t25 :args ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)))
-(step t25.t1 (cl (= @p_43 (! (and @p_34 @p_37 @p_39) :named @p_58))) :rule ac_simp)
-(step t25.t2 (cl (= @p_55 (! (=> @p_58 @p_53) :named @p_59))) :rule cong :premises (t25.t1))
-(step t25 (cl (! (= @p_57 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
-(step t26 (cl (not @p_60) (not @p_57) @p_61) :rule equiv_pos2)
-(step t27 (cl @p_61) :rule th_resolution :premises (t24 t25 t26))
-(anchor :step t28 :args ((:= (veriT_vr8 B_set$) veriT_vr11) (:= (veriT_vr9 B$) veriT_vr12) (:= (veriT_vr10 B_c_fun$) veriT_vr13)))
-(step t28.t1 (cl (! (= veriT_vr8 veriT_vr11) :named @p_63)) :rule refl)
-(step t28.t2 (cl (= @p_34 (! (finite$ veriT_vr11) :named @p_62))) :rule cong :premises (t28.t1))
-(step t28.t3 (cl @p_63) :rule refl)
-(step t28.t4 (cl (= @p_36 (! (= bot$ veriT_vr11) :named @p_64))) :rule cong :premises (t28.t3))
-(step t28.t5 (cl (= @p_37 (! (not @p_64) :named @p_65))) :rule cong :premises (t28.t4))
-(step t28.t6 (cl (! (= veriT_vr9 veriT_vr12) :named @p_71)) :rule refl)
-(step t28.t7 (cl @p_63) :rule refl)
-(step t28.t8 (cl (= @p_39 (! (member$ veriT_vr12 veriT_vr11) :named @p_66))) :rule cong :premises (t28.t6 t28.t7))
-(step t28.t9 (cl (= @p_58 (! (and @p_62 @p_65 @p_66) :named @p_67))) :rule cong :premises (t28.t2 t28.t5 t28.t8))
-(step t28.t10 (cl (! (= veriT_vr10 veriT_vr13) :named @p_68)) :rule refl)
-(step t28.t11 (cl @p_68) :rule refl)
-(step t28.t12 (cl @p_63) :rule refl)
-(step t28.t13 (cl (= @p_46 (! (arg_min_on$ veriT_vr13 veriT_vr11) :named @p_69))) :rule cong :premises (t28.t11 t28.t12))
-(step t28.t14 (cl (= @p_48 (! (fun_app$ veriT_vr13 @p_69) :named @p_70))) :rule cong :premises (t28.t10 t28.t13))
-(step t28.t15 (cl @p_68) :rule refl)
-(step t28.t16 (cl @p_71) :rule refl)
-(step t28.t17 (cl (= @p_51 (! (fun_app$ veriT_vr13 veriT_vr12) :named @p_72))) :rule cong :premises (t28.t15 t28.t16))
-(step t28.t18 (cl (= @p_53 (! (less_eq$ @p_70 @p_72) :named @p_73))) :rule cong :premises (t28.t14 t28.t17))
-(step t28.t19 (cl (= @p_59 (! (=> @p_67 @p_73) :named @p_74))) :rule cong :premises (t28.t9 t28.t18))
-(step t28 (cl (! (= @p_61 (! (forall ((veriT_vr11 B_set$) (veriT_vr12 B$) (veriT_vr13 B_c_fun$)) @p_74) :named @p_76)) :named @p_75)) :rule bind)
-(step t29 (cl (not @p_75) (not @p_61) @p_76) :rule equiv_pos2)
-(step t30 (cl @p_76) :rule th_resolution :premises (t27 t28 t29))
-(anchor :step t31 :args ((:= (?v0 B_c_fun$) veriT_vr20) (:= (?v1 A_b_fun$) veriT_vr21) (:= (?v2 A$) veriT_vr22)))
-(step t31.t1 (cl (! (= ?v0 veriT_vr20) :named @p_82)) :rule refl)
-(step t31.t2 (cl (! (= ?v1 veriT_vr21) :named @p_83)) :rule refl)
-(step t31.t3 (cl (= @p_78 (! (comp$ veriT_vr20 veriT_vr21) :named @p_79))) :rule cong :premises (t31.t1 t31.t2))
-(step t31.t4 (cl (! (= ?v2 veriT_vr22) :named @p_84)) :rule refl)
-(step t31.t5 (cl (= @p_80 (! (fun_app$a @p_79 veriT_vr22) :named @p_81))) :rule cong :premises (t31.t3 t31.t4))
-(step t31.t6 (cl @p_82) :rule refl)
-(step t31.t7 (cl @p_83) :rule refl)
-(step t31.t8 (cl @p_84) :rule refl)
-(step t31.t9 (cl (= @p_3 (! (fun_app$b veriT_vr21 veriT_vr22) :named @p_85))) :rule cong :premises (t31.t7 t31.t8))
-(step t31.t10 (cl (= @p_86 (! (fun_app$ veriT_vr20 @p_85) :named @p_87))) :rule cong :premises (t31.t6 t31.t9))
-(step t31.t11 (cl (= @p_88 (! (= @p_81 @p_87) :named @p_89))) :rule cong :premises (t31.t5 t31.t10))
-(step t31 (cl (! (= @p_77 (! (forall ((veriT_vr20 B_c_fun$) (veriT_vr21 A_b_fun$) (veriT_vr22 A$)) @p_89) :named @p_91)) :named @p_90)) :rule bind)
-(step t32 (cl (not @p_90) (not @p_77) @p_91) :rule equiv_pos2)
-(step t33 (cl @p_91) :rule th_resolution :premises (axiom33 t31 t32))
-(anchor :step t34 :args ((:= (veriT_vr20 B_c_fun$) veriT_vr23) (:= (veriT_vr21 A_b_fun$) veriT_vr24) (:= (veriT_vr22 A$) veriT_vr25)))
-(step t34.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_94)) :rule refl)
-(step t34.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_95)) :rule refl)
-(step t34.t3 (cl (= @p_79 (! (comp$ veriT_vr23 veriT_vr24) :named @p_92))) :rule cong :premises (t34.t1 t34.t2))
-(step t34.t4 (cl (! (= veriT_vr22 veriT_vr25) :named @p_96)) :rule refl)
-(step t34.t5 (cl (= @p_81 (! (fun_app$a @p_92 veriT_vr25) :named @p_93))) :rule cong :premises (t34.t3 t34.t4))
-(step t34.t6 (cl @p_94) :rule refl)
-(step t34.t7 (cl @p_95) :rule refl)
-(step t34.t8 (cl @p_96) :rule refl)
-(step t34.t9 (cl (= @p_85 (! (fun_app$b veriT_vr24 veriT_vr25) :named @p_97))) :rule cong :premises (t34.t7 t34.t8))
-(step t34.t10 (cl (= @p_87 (! (fun_app$ veriT_vr23 @p_97) :named @p_98))) :rule cong :premises (t34.t6 t34.t9))
-(step t34.t11 (cl (= @p_89 (! (= @p_93 @p_98) :named @p_99))) :rule cong :premises (t34.t5 t34.t10))
-(step t34 (cl (! (= @p_91 (! (forall ((veriT_vr23 B_c_fun$) (veriT_vr24 A_b_fun$) (veriT_vr25 A$)) @p_99) :named @p_101)) :named @p_100)) :rule bind)
-(step t35 (cl (not @p_100) (not @p_91) @p_101) :rule equiv_pos2)
-(step t36 (cl @p_101) :rule th_resolution :premises (t33 t34 t35))
-(anchor :step t37 :args ((:= (?v0 A_set$) veriT_vr34) (:= (?v1 A_b_fun$) veriT_vr35)))
-(step t37.t1 (cl (! (= ?v0 veriT_vr34) :named @p_105)) :rule refl)
-(step t37.t2 (cl (= @p_103 (! (finite$a veriT_vr34) :named @p_104))) :rule cong :premises (t37.t1))
-(step t37.t3 (cl (= ?v1 veriT_vr35)) :rule refl)
-(step t37.t4 (cl @p_105) :rule refl)
-(step t37.t5 (cl (= @p_106 (! (image$b veriT_vr35 veriT_vr34) :named @p_107))) :rule cong :premises (t37.t3 t37.t4))
-(step t37.t6 (cl (= @p_108 (! (finite$ @p_107) :named @p_109))) :rule cong :premises (t37.t5))
-(step t37.t7 (cl (= @p_110 (! (=> @p_104 @p_109) :named @p_111))) :rule cong :premises (t37.t2 t37.t6))
-(step t37 (cl (! (= @p_102 (! (forall ((veriT_vr34 A_set$) (veriT_vr35 A_b_fun$)) @p_111) :named @p_113)) :named @p_112)) :rule bind)
-(step t38 (cl (not @p_112) (not @p_102) @p_113) :rule equiv_pos2)
-(step t39 (cl @p_113) :rule th_resolution :premises (axiom36 t37 t38))
-(anchor :step t40 :args ((:= (veriT_vr34 A_set$) veriT_vr36) (:= (veriT_vr35 A_b_fun$) veriT_vr37)))
-(step t40.t1 (cl (! (= veriT_vr34 veriT_vr36) :named @p_115)) :rule refl)
-(step t40.t2 (cl (= @p_104 (! (finite$a veriT_vr36) :named @p_114))) :rule cong :premises (t40.t1))
-(step t40.t3 (cl (= veriT_vr35 veriT_vr37)) :rule refl)
-(step t40.t4 (cl @p_115) :rule refl)
-(step t40.t5 (cl (= @p_107 (! (image$b veriT_vr37 veriT_vr36) :named @p_116))) :rule cong :premises (t40.t3 t40.t4))
-(step t40.t6 (cl (= @p_109 (! (finite$ @p_116) :named @p_117))) :rule cong :premises (t40.t5))
-(step t40.t7 (cl (= @p_111 (! (=> @p_114 @p_117) :named @p_118))) :rule cong :premises (t40.t2 t40.t6))
-(step t40 (cl (! (= @p_113 (! (forall ((veriT_vr36 A_set$) (veriT_vr37 A_b_fun$)) @p_118) :named @p_120)) :named @p_119)) :rule bind)
-(step t41 (cl (not @p_119) (not @p_113) @p_120) :rule equiv_pos2)
-(step t42 (cl @p_120) :rule th_resolution :premises (t39 t40 t41))
-(anchor :step t43 :args ((:= (?v0 B$) veriT_vr58) (:= (?v1 A_b_fun$) veriT_vr59) (:= (?v2 A_set$) veriT_vr60)))
-(step t43.t1 (cl (! (= ?v0 veriT_vr58) :named @p_128)) :rule refl)
-(step t43.t2 (cl (! (= ?v1 veriT_vr59) :named @p_129)) :rule refl)
-(step t43.t3 (cl (! (= ?v2 veriT_vr60) :named @p_135)) :rule refl)
-(step t43.t4 (cl (= @p_122 (! (image$b veriT_vr59 veriT_vr60) :named @p_123))) :rule cong :premises (t43.t2 t43.t3))
-(step t43.t5 (cl (= @p_124 (! (member$ veriT_vr58 @p_123) :named @p_125))) :rule cong :premises (t43.t1 t43.t4))
-(anchor :step t43.t6 :args ((:= (?v3 A$) veriT_vr61)))
-(step t43.t6.t1 (cl @p_128) :rule refl)
-(step t43.t6.t2 (cl @p_129) :rule refl)
-(step t43.t6.t3 (cl (! (= ?v3 veriT_vr61) :named @p_134)) :rule refl)
-(step t43.t6.t4 (cl (= @p_130 (! (fun_app$b veriT_vr59 veriT_vr61) :named @p_131))) :rule cong :premises (t43.t6.t2 t43.t6.t3))
-(step t43.t6.t5 (cl (= @p_132 (! (= veriT_vr58 @p_131) :named @p_133))) :rule cong :premises (t43.t6.t1 t43.t6.t4))
-(step t43.t6.t6 (cl @p_134) :rule refl)
-(step t43.t6.t7 (cl @p_135) :rule refl)
-(step t43.t6.t8 (cl (= @p_136 (! (member$a veriT_vr61 veriT_vr60) :named @p_137))) :rule cong :premises (t43.t6.t6 t43.t6.t7))
-(step t43.t6.t9 (cl (= @p_138 (! (and @p_133 @p_137) :named @p_139))) :rule cong :premises (t43.t6.t5 t43.t6.t8))
-(step t43.t6.t10 (cl (= @p_140 (! (=> @p_139 false) :named @p_141))) :rule cong :premises (t43.t6.t9))
-(step t43.t6 (cl (= @p_126 (! (forall ((veriT_vr61 A$)) @p_141) :named @p_127))) :rule bind)
-(step t43.t7 (cl (= @p_142 (! (and @p_125 @p_127) :named @p_143))) :rule cong :premises (t43.t5 t43.t6))
-(step t43.t8 (cl (= @p_144 (! (=> @p_143 false) :named @p_145))) :rule cong :premises (t43.t7))
-(step t43 (cl (! (= @p_121 (! (forall ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)) @p_145) :named @p_147)) :named @p_146)) :rule bind)
-(step t44 (cl (not @p_146) (not @p_121) @p_147) :rule equiv_pos2)
-(step t45 (cl @p_147) :rule th_resolution :premises (axiom40 t43 t44))
-(anchor :step t46 :args ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)))
-(anchor :step t46.t1 :args ((veriT_vr61 A$)))
-(step t46.t1.t1 (cl (= @p_141 (! (not @p_139) :named @p_149))) :rule implies_simplify)
-(step t46.t1 (cl (= @p_127 (! (forall ((veriT_vr61 A$)) @p_149) :named @p_148))) :rule bind)
-(step t46.t2 (cl (= @p_143 (! (and @p_125 @p_148) :named @p_150))) :rule cong :premises (t46.t1))
-(step t46.t3 (cl (= @p_145 (! (=> @p_150 false) :named @p_151))) :rule cong :premises (t46.t2))
-(step t46.t4 (cl (= @p_151 (! (not @p_150) :named @p_152))) :rule implies_simplify)
-(step t46.t5 (cl (= @p_145 @p_152)) :rule trans :premises (t46.t3 t46.t4))
-(step t46 (cl (! (= @p_147 (! (forall ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)) @p_152) :named @p_154)) :named @p_153)) :rule bind)
-(step t47 (cl (not @p_153) (not @p_147) @p_154) :rule equiv_pos2)
-(step t48 (cl @p_154) :rule th_resolution :premises (t45 t46 t47))
-(anchor :step t49 :args ((:= (veriT_vr58 B$) veriT_vr62) (:= (veriT_vr59 A_b_fun$) veriT_vr63) (:= (veriT_vr60 A_set$) veriT_vr64)))
-(step t49.t1 (cl (! (= veriT_vr58 veriT_vr62) :named @p_158)) :rule refl)
-(step t49.t2 (cl (! (= veriT_vr59 veriT_vr63) :named @p_159)) :rule refl)
-(step t49.t3 (cl (! (= veriT_vr60 veriT_vr64) :named @p_163)) :rule refl)
-(step t49.t4 (cl (= @p_123 (! (image$b veriT_vr63 veriT_vr64) :named @p_155))) :rule cong :premises (t49.t2 t49.t3))
-(step t49.t5 (cl (= @p_125 (! (member$ veriT_vr62 @p_155) :named @p_156))) :rule cong :premises (t49.t1 t49.t4))
-(anchor :step t49.t6 :args ((:= (veriT_vr61 A$) veriT_vr65)))
-(step t49.t6.t1 (cl @p_158) :rule refl)
-(step t49.t6.t2 (cl @p_159) :rule refl)
-(step t49.t6.t3 (cl (! (= veriT_vr61 veriT_vr65) :named @p_162)) :rule refl)
-(step t49.t6.t4 (cl (= @p_131 (! (fun_app$b veriT_vr63 veriT_vr65) :named @p_160))) :rule cong :premises (t49.t6.t2 t49.t6.t3))
-(step t49.t6.t5 (cl (= @p_133 (! (= veriT_vr62 @p_160) :named @p_161))) :rule cong :premises (t49.t6.t1 t49.t6.t4))
-(step t49.t6.t6 (cl @p_162) :rule refl)
-(step t49.t6.t7 (cl @p_163) :rule refl)
-(step t49.t6.t8 (cl (= @p_137 (! (member$a veriT_vr65 veriT_vr64) :named @p_164))) :rule cong :premises (t49.t6.t6 t49.t6.t7))
-(step t49.t6.t9 (cl (= @p_139 (! (and @p_161 @p_164) :named @p_165))) :rule cong :premises (t49.t6.t5 t49.t6.t8))
-(step t49.t6.t10 (cl (= @p_149 (! (not @p_165) :named @p_166))) :rule cong :premises (t49.t6.t9))
-(step t49.t6 (cl (= @p_148 (! (forall ((veriT_vr65 A$)) @p_166) :named @p_157))) :rule bind)
-(step t49.t7 (cl (= @p_150 (! (and @p_156 @p_157) :named @p_167))) :rule cong :premises (t49.t5 t49.t6))
-(step t49.t8 (cl (= @p_152 (! (not @p_167) :named @p_168))) :rule cong :premises (t49.t7))
-(step t49 (cl (! (= @p_154 (! (forall ((veriT_vr62 B$) (veriT_vr63 A_b_fun$) (veriT_vr64 A_set$)) @p_168) :named @p_170)) :named @p_169)) :rule bind)
-(step t50 (cl (not @p_169) (not @p_154) @p_170) :rule equiv_pos2)
-(step t51 (cl @p_170) :rule th_resolution :premises (t48 t49 t50))
-(anchor :step t52 :args ((:= (?v0 B$) veriT_vr90) (:= (?v1 A_b_fun$) veriT_vr91) (:= (?v2 A$) veriT_vr92) (:= (?v3 A_set$) veriT_vr93)))
-(step t52.t1 (cl (! (= ?v1 veriT_vr91) :named @p_181)) :rule refl)
-(step t52.t2 (cl (! (= ?v2 veriT_vr92) :named @p_175)) :rule refl)
-(step t52.t3 (cl (= @p_3 (! (fun_app$b veriT_vr91 veriT_vr92) :named @p_172))) :rule cong :premises (t52.t1 t52.t2))
-(step t52.t4 (cl (! (= ?v0 veriT_vr90) :named @p_180)) :rule refl)
-(step t52.t5 (cl (= @p_173 (! (= veriT_vr90 @p_172) :named @p_174))) :rule cong :premises (t52.t3 t52.t4))
-(step t52.t6 (cl @p_175) :rule refl)
-(step t52.t7 (cl (! (= ?v3 veriT_vr93) :named @p_182)) :rule refl)
-(step t52.t8 (cl (= @p_176 (! (member$a veriT_vr92 veriT_vr93) :named @p_177))) :rule cong :premises (t52.t6 t52.t7))
-(step t52.t9 (cl (= @p_178 (! (and @p_174 @p_177) :named @p_179))) :rule cong :premises (t52.t5 t52.t8))
-(step t52.t10 (cl @p_180) :rule refl)
-(step t52.t11 (cl @p_181) :rule refl)
-(step t52.t12 (cl @p_182) :rule refl)
-(step t52.t13 (cl (= @p_183 (! (image$b veriT_vr91 veriT_vr93) :named @p_184))) :rule cong :premises (t52.t11 t52.t12))
-(step t52.t14 (cl (= @p_185 (! (member$ veriT_vr90 @p_184) :named @p_186))) :rule cong :premises (t52.t10 t52.t13))
-(step t52.t15 (cl (= @p_187 (! (=> @p_179 @p_186) :named @p_188))) :rule cong :premises (t52.t9 t52.t14))
-(step t52 (cl (! (= @p_171 (! (forall ((veriT_vr90 B$) (veriT_vr91 A_b_fun$) (veriT_vr92 A$) (veriT_vr93 A_set$)) @p_188) :named @p_190)) :named @p_189)) :rule bind)
-(step t53 (cl (not @p_189) (not @p_171) @p_190) :rule equiv_pos2)
-(step t54 (cl @p_190) :rule th_resolution :premises (axiom44 t52 t53))
-(anchor :step t55 :args ((:= (veriT_vr90 B$) veriT_vr94) (:= (veriT_vr91 A_b_fun$) veriT_vr95) (:= (veriT_vr92 A$) veriT_vr96) (:= (veriT_vr93 A_set$) veriT_vr97)))
-(step t55.t1 (cl (! (= veriT_vr90 veriT_vr94) :named @p_196)) :rule refl)
-(step t55.t2 (cl (! (= veriT_vr91 veriT_vr95) :named @p_197)) :rule refl)
-(step t55.t3 (cl (! (= veriT_vr92 veriT_vr96) :named @p_193)) :rule refl)
-(step t55.t4 (cl (= @p_172 (! (fun_app$b veriT_vr95 veriT_vr96) :named @p_191))) :rule cong :premises (t55.t2 t55.t3))
-(step t55.t5 (cl (= @p_174 (! (= veriT_vr94 @p_191) :named @p_192))) :rule cong :premises (t55.t1 t55.t4))
-(step t55.t6 (cl @p_193) :rule refl)
-(step t55.t7 (cl (! (= veriT_vr93 veriT_vr97) :named @p_198)) :rule refl)
-(step t55.t8 (cl (= @p_177 (! (member$a veriT_vr96 veriT_vr97) :named @p_194))) :rule cong :premises (t55.t6 t55.t7))
-(step t55.t9 (cl (= @p_179 (! (and @p_192 @p_194) :named @p_195))) :rule cong :premises (t55.t5 t55.t8))
-(step t55.t10 (cl @p_196) :rule refl)
-(step t55.t11 (cl @p_197) :rule refl)
-(step t55.t12 (cl @p_198) :rule refl)
-(step t55.t13 (cl (= @p_184 (! (image$b veriT_vr95 veriT_vr97) :named @p_199))) :rule cong :premises (t55.t11 t55.t12))
-(step t55.t14 (cl (= @p_186 (! (member$ veriT_vr94 @p_199) :named @p_200))) :rule cong :premises (t55.t10 t55.t13))
-(step t55.t15 (cl (= @p_188 (! (=> @p_195 @p_200) :named @p_201))) :rule cong :premises (t55.t9 t55.t14))
-(step t55 (cl (! (= @p_190 (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) @p_201) :named @p_203)) :named @p_202)) :rule bind)
-(step t56 (cl (not @p_202) (not @p_190) @p_203) :rule equiv_pos2)
-(step t57 (cl @p_203) :rule th_resolution :premises (t54 t55 t56))
-(anchor :step t58 :args ((:= (?v0 A_b_fun$) veriT_vr114) (:= (?v1 A_set$) veriT_vr115)))
-(step t58.t1 (cl (= ?v0 veriT_vr114)) :rule refl)
-(step t58.t2 (cl (! (= ?v1 veriT_vr115) :named @p_209)) :rule refl)
-(step t58.t3 (cl (= @p_205 (! (image$b veriT_vr114 veriT_vr115) :named @p_206))) :rule cong :premises (t58.t1 t58.t2))
-(step t58.t4 (cl (= @p_207 (! (= bot$ @p_206) :named @p_208))) :rule cong :premises (t58.t3))
-(step t58.t5 (cl @p_209) :rule refl)
-(step t58.t6 (cl (= @p_210 (! (= bot$a veriT_vr115) :named @p_211))) :rule cong :premises (t58.t5))
-(step t58.t7 (cl (= @p_212 (! (= @p_208 @p_211) :named @p_213))) :rule cong :premises (t58.t4 t58.t6))
-(step t58 (cl (! (= @p_204 (! (forall ((veriT_vr114 A_b_fun$) (veriT_vr115 A_set$)) @p_213) :named @p_215)) :named @p_214)) :rule bind)
-(step t59 (cl (not @p_214) (not @p_204) @p_215) :rule equiv_pos2)
-(step t60 (cl @p_215) :rule th_resolution :premises (axiom48 t58 t59))
-(anchor :step t61 :args ((:= (veriT_vr114 A_b_fun$) veriT_vr116) (:= (veriT_vr115 A_set$) veriT_vr117)))
-(step t61.t1 (cl (= veriT_vr114 veriT_vr116)) :rule refl)
-(step t61.t2 (cl (! (= veriT_vr115 veriT_vr117) :named @p_218)) :rule refl)
-(step t61.t3 (cl (= @p_206 (! (image$b veriT_vr116 veriT_vr117) :named @p_216))) :rule cong :premises (t61.t1 t61.t2))
-(step t61.t4 (cl (= @p_208 (! (= bot$ @p_216) :named @p_217))) :rule cong :premises (t61.t3))
-(step t61.t5 (cl @p_218) :rule refl)
-(step t61.t6 (cl (= @p_211 (! (= bot$a veriT_vr117) :named @p_219))) :rule cong :premises (t61.t5))
-(step t61.t7 (cl (= @p_213 (! (= @p_217 @p_219) :named @p_220))) :rule cong :premises (t61.t4 t61.t6))
-(step t61 (cl (! (= @p_215 (! (forall ((veriT_vr116 A_b_fun$) (veriT_vr117 A_set$)) @p_220) :named @p_222)) :named @p_221)) :rule bind)
-(step t62 (cl (not @p_221) (not @p_215) @p_222) :rule equiv_pos2)
-(step t63 (cl @p_222) :rule th_resolution :premises (t60 t61 t62))
-(anchor :step t64 :args ((:= (?v0 B_c_fun$) veriT_vr122) (:= (?v1 B_set$) veriT_vr123) (:= (?v2 B$) veriT_vr124) (:= (?v3 B$) veriT_vr125)))
-(step t64.t1 (cl (! (= ?v0 veriT_vr122) :named @p_226)) :rule refl)
-(step t64.t2 (cl (! (= ?v1 veriT_vr123) :named @p_234)) :rule refl)
-(step t64.t3 (cl (= @p_224 (! (inj_on$ veriT_vr122 veriT_vr123) :named @p_225))) :rule cong :premises (t64.t1 t64.t2))
-(step t64.t4 (cl @p_226) :rule refl)
-(step t64.t5 (cl (! (= ?v2 veriT_vr124) :named @p_233)) :rule refl)
-(step t64.t6 (cl (= @p_227 (! (fun_app$ veriT_vr122 veriT_vr124) :named @p_228))) :rule cong :premises (t64.t4 t64.t5))
-(step t64.t7 (cl @p_226) :rule refl)
-(step t64.t8 (cl (! (= ?v3 veriT_vr125) :named @p_237)) :rule refl)
-(step t64.t9 (cl (= @p_229 (! (fun_app$ veriT_vr122 veriT_vr125) :named @p_230))) :rule cong :premises (t64.t7 t64.t8))
-(step t64.t10 (cl (= @p_231 (! (= @p_228 @p_230) :named @p_232))) :rule cong :premises (t64.t6 t64.t9))
-(step t64.t11 (cl @p_233) :rule refl)
-(step t64.t12 (cl @p_234) :rule refl)
-(step t64.t13 (cl (= @p_235 (! (member$ veriT_vr124 veriT_vr123) :named @p_236))) :rule cong :premises (t64.t11 t64.t12))
-(step t64.t14 (cl @p_237) :rule refl)
-(step t64.t15 (cl @p_234) :rule refl)
-(step t64.t16 (cl (= @p_238 (! (member$ veriT_vr125 veriT_vr123) :named @p_239))) :rule cong :premises (t64.t14 t64.t15))
-(step t64.t17 (cl (= @p_240 (! (and @p_236 @p_239) :named @p_241))) :rule cong :premises (t64.t13 t64.t16))
-(step t64.t18 (cl (= @p_242 (! (and @p_232 @p_241) :named @p_243))) :rule cong :premises (t64.t10 t64.t17))
-(step t64.t19 (cl (= @p_244 (! (and @p_225 @p_243) :named @p_245))) :rule cong :premises (t64.t3 t64.t18))
-(step t64.t20 (cl @p_237) :rule refl)
-(step t64.t21 (cl @p_233) :rule refl)
-(step t64.t22 (cl (= @p_246 (! (= veriT_vr124 veriT_vr125) :named @p_247))) :rule cong :premises (t64.t20 t64.t21))
-(step t64.t23 (cl (= @p_248 (! (=> @p_245 @p_247) :named @p_249))) :rule cong :premises (t64.t19 t64.t22))
-(step t64 (cl (! (= @p_223 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_249) :named @p_251)) :named @p_250)) :rule bind)
-(step t65 (cl (not @p_250) (not @p_223) @p_251) :rule equiv_pos2)
-(step t66 (cl @p_251) :rule th_resolution :premises (axiom50 t64 t65))
-(anchor :step t67 :args ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)))
-(step t67.t1 (cl (= @p_245 (! (and @p_225 @p_232 @p_236 @p_239) :named @p_252))) :rule ac_simp)
-(step t67.t2 (cl (= @p_249 (! (=> @p_252 @p_247) :named @p_253))) :rule cong :premises (t67.t1))
-(step t67 (cl (! (= @p_251 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_253) :named @p_255)) :named @p_254)) :rule bind)
-(step t68 (cl (not @p_254) (not @p_251) @p_255) :rule equiv_pos2)
-(step t69 (cl @p_255) :rule th_resolution :premises (t66 t67 t68))
-(anchor :step t70 :args ((:= (veriT_vr122 B_c_fun$) veriT_vr126) (:= (veriT_vr123 B_set$) veriT_vr127) (:= (veriT_vr124 B$) veriT_vr128) (:= (veriT_vr125 B$) veriT_vr129)))
-(step t70.t1 (cl (! (= veriT_vr122 veriT_vr126) :named @p_257)) :rule refl)
-(step t70.t2 (cl (! (= veriT_vr123 veriT_vr127) :named @p_262)) :rule refl)
-(step t70.t3 (cl (= @p_225 (! (inj_on$ veriT_vr126 veriT_vr127) :named @p_256))) :rule cong :premises (t70.t1 t70.t2))
-(step t70.t4 (cl @p_257) :rule refl)
-(step t70.t5 (cl (! (= veriT_vr124 veriT_vr128) :named @p_261)) :rule refl)
-(step t70.t6 (cl (= @p_228 (! (fun_app$ veriT_vr126 veriT_vr128) :named @p_258))) :rule cong :premises (t70.t4 t70.t5))
-(step t70.t7 (cl @p_257) :rule refl)
-(step t70.t8 (cl (! (= veriT_vr125 veriT_vr129) :named @p_264)) :rule refl)
-(step t70.t9 (cl (= @p_230 (! (fun_app$ veriT_vr126 veriT_vr129) :named @p_259))) :rule cong :premises (t70.t7 t70.t8))
-(step t70.t10 (cl (= @p_232 (! (= @p_258 @p_259) :named @p_260))) :rule cong :premises (t70.t6 t70.t9))
-(step t70.t11 (cl @p_261) :rule refl)
-(step t70.t12 (cl @p_262) :rule refl)
-(step t70.t13 (cl (= @p_236 (! (member$ veriT_vr128 veriT_vr127) :named @p_263))) :rule cong :premises (t70.t11 t70.t12))
-(step t70.t14 (cl @p_264) :rule refl)
-(step t70.t15 (cl @p_262) :rule refl)
-(step t70.t16 (cl (= @p_239 (! (member$ veriT_vr129 veriT_vr127) :named @p_265))) :rule cong :premises (t70.t14 t70.t15))
-(step t70.t17 (cl (= @p_252 (! (and @p_256 @p_260 @p_263 @p_265) :named @p_266))) :rule cong :premises (t70.t3 t70.t10 t70.t13 t70.t16))
-(step t70.t18 (cl @p_261) :rule refl)
-(step t70.t19 (cl @p_264) :rule refl)
-(step t70.t20 (cl (= @p_247 (! (= veriT_vr128 veriT_vr129) :named @p_267))) :rule cong :premises (t70.t18 t70.t19))
-(step t70.t21 (cl (= @p_253 (! (=> @p_266 @p_267) :named @p_268))) :rule cong :premises (t70.t17 t70.t20))
-(step t70 (cl (! (= @p_255 (! (forall ((veriT_vr126 B_c_fun$) (veriT_vr127 B_set$) (veriT_vr128 B$) (veriT_vr129 B$)) @p_268) :named @p_270)) :named @p_269)) :rule bind)
-(step t71 (cl (not @p_269) (not @p_255) @p_270) :rule equiv_pos2)
-(step t72 (cl @p_270) :rule th_resolution :premises (t69 t70 t71))
-(anchor :step t73 :args ((:= (?v0 C$) veriT_vr130) (:= (?v1 C$) veriT_vr131)))
-(step t73.t1 (cl (! (= ?v0 veriT_vr130) :named @p_274)) :rule refl)
-(step t73.t2 (cl (! (= ?v1 veriT_vr131) :named @p_275)) :rule refl)
-(step t73.t3 (cl (= @p_272 (! (less$ veriT_vr130 veriT_vr131) :named @p_273))) :rule cong :premises (t73.t1 t73.t2))
-(step t73.t4 (cl @p_274) :rule refl)
-(step t73.t5 (cl @p_275) :rule refl)
-(step t73.t6 (cl (= @p_276 (! (less_eq$ veriT_vr130 veriT_vr131) :named @p_277))) :rule cong :premises (t73.t4 t73.t5))
-(step t73.t7 (cl @p_274) :rule refl)
-(step t73.t8 (cl @p_275) :rule refl)
-(step t73.t9 (cl (= @p_278 (! (= veriT_vr130 veriT_vr131) :named @p_279))) :rule cong :premises (t73.t7 t73.t8))
-(step t73.t10 (cl (= @p_280 (! (not @p_279) :named @p_281))) :rule cong :premises (t73.t9))
-(step t73.t11 (cl (= @p_282 (! (and @p_277 @p_281) :named @p_283))) :rule cong :premises (t73.t6 t73.t10))
-(step t73.t12 (cl (= @p_284 (! (= @p_273 @p_283) :named @p_285))) :rule cong :premises (t73.t3 t73.t11))
-(step t73 (cl (! (= @p_271 (! (forall ((veriT_vr130 C$) (veriT_vr131 C$)) @p_285) :named @p_287)) :named @p_286)) :rule bind)
-(step t74 (cl (not @p_286) (not @p_271) @p_287) :rule equiv_pos2)
-(step t75 (cl @p_287) :rule th_resolution :premises (axiom51 t73 t74))
-(anchor :step t76 :args ((:= (veriT_vr130 C$) veriT_vr132) (:= (veriT_vr131 C$) veriT_vr133)))
-(step t76.t1 (cl (! (= veriT_vr130 veriT_vr132) :named @p_289)) :rule refl)
-(step t76.t2 (cl (! (= veriT_vr131 veriT_vr133) :named @p_290)) :rule refl)
-(step t76.t3 (cl (= @p_273 (! (less$ veriT_vr132 veriT_vr133) :named @p_288))) :rule cong :premises (t76.t1 t76.t2))
-(step t76.t4 (cl @p_289) :rule refl)
-(step t76.t5 (cl @p_290) :rule refl)
-(step t76.t6 (cl (= @p_277 (! (less_eq$ veriT_vr132 veriT_vr133) :named @p_291))) :rule cong :premises (t76.t4 t76.t5))
-(step t76.t7 (cl @p_289) :rule refl)
-(step t76.t8 (cl @p_290) :rule refl)
-(step t76.t9 (cl (= @p_279 (! (= veriT_vr132 veriT_vr133) :named @p_292))) :rule cong :premises (t76.t7 t76.t8))
-(step t76.t10 (cl (= @p_281 (! (not @p_292) :named @p_293))) :rule cong :premises (t76.t9))
-(step t76.t11 (cl (= @p_283 (! (and @p_291 @p_293) :named @p_294))) :rule cong :premises (t76.t6 t76.t10))
-(step t76.t12 (cl (= @p_285 (! (= @p_288 @p_294) :named @p_295))) :rule cong :premises (t76.t3 t76.t11))
-(step t76 (cl (! (= @p_287 (! (forall ((veriT_vr132 C$) (veriT_vr133 C$)) @p_295) :named @p_297)) :named @p_296)) :rule bind)
-(step t77 (cl (not @p_296) (not @p_287) @p_297) :rule equiv_pos2)
-(step t78 (cl @p_297) :rule th_resolution :premises (t75 t76 t77))
-(anchor :step t79 :args ((:= (?v0 A$) veriT_vr134)))
-(step t79.t1 (cl (! (= ?v0 veriT_vr134) :named @p_302)) :rule refl)
-(step t79.t2 (cl (= @p_300 (! (member$a veriT_vr134 b$) :named @p_301))) :rule cong :premises (t79.t1))
-(step t79.t3 (cl @p_302) :rule refl)
-(step t79.t4 (cl (= @p_303 (! (fun_app$a @p_4 veriT_vr134) :named @p_304))) :rule cong :premises (t79.t3))
-(step t79.t5 (cl (= @p_305 (! (less$ @p_304 @p_299) :named @p_306))) :rule cong :premises (t79.t4))
-(step t79.t6 (cl (= @p_307 (! (and @p_301 @p_306) :named @p_308))) :rule cong :premises (t79.t2 t79.t5))
-(step t79 (cl (= @p_298 (! (exists ((veriT_vr134 A$)) @p_308) :named @p_310))) :rule bind)
-(step t80 (cl (! (= @p_309 (! (not @p_310) :named @p_312)) :named @p_311)) :rule cong :premises (t79))
-(step t81 (cl (! (not @p_311) :named @p_314) (! (not @p_309) :named @p_313) @p_312) :rule equiv_pos2)
-(step t82 (cl (not @p_313) @p_298) :rule not_not)
-(step t83 (cl @p_314 @p_298 @p_312) :rule th_resolution :premises (t82 t81))
-(step t84 (cl @p_312) :rule th_resolution :premises (axiom27 t80 t83))
-(anchor :step t85 :args ((:= (veriT_vr134 A$) veriT_vr135)))
-(step t85.t1 (cl (! (= veriT_vr134 veriT_vr135) :named @p_316)) :rule refl)
-(step t85.t2 (cl (= @p_301 (! (member$a veriT_vr135 b$) :named @p_315))) :rule cong :premises (t85.t1))
-(step t85.t3 (cl @p_316) :rule refl)
-(step t85.t4 (cl (= @p_304 (! (fun_app$a @p_4 veriT_vr135) :named @p_317))) :rule cong :premises (t85.t3))
-(step t85.t5 (cl (= @p_306 (! (less$ @p_317 @p_299) :named @p_318))) :rule cong :premises (t85.t4))
-(step t85.t6 (cl (= @p_308 (! (and @p_315 @p_318) :named @p_319))) :rule cong :premises (t85.t2 t85.t5))
-(step t85 (cl (= @p_310 (! (exists ((veriT_vr135 A$)) @p_319) :named @p_320))) :rule bind)
-(step t86 (cl (! (= @p_312 (! (not @p_320) :named @p_322)) :named @p_321)) :rule cong :premises (t85))
-(step t87 (cl (! (not @p_321) :named @p_324) (! (not @p_312) :named @p_323) @p_322) :rule equiv_pos2)
-(step t88 (cl (not @p_323) @p_310) :rule not_not)
-(step t89 (cl @p_324 @p_310 @p_322) :rule th_resolution :premises (t88 t87))
-(step t90 (cl @p_322) :rule th_resolution :premises (t84 t86 t89))
-(step t91 (cl (= @p_320 (! (not (! (forall ((veriT_vr135 A$)) (not @p_319)) :named @p_330)) :named @p_325))) :rule connective_def)
-(step t92 (cl (! (= @p_322 (! (not @p_325) :named @p_327)) :named @p_326)) :rule cong :premises (t91))
-(step t93 (cl (! (not @p_326) :named @p_329) (! (not @p_322) :named @p_328) @p_327) :rule equiv_pos2)
-(step t94 (cl (not @p_328) @p_320) :rule not_not)
-(step t95 (cl @p_329 @p_320 @p_327) :rule th_resolution :premises (t94 t93))
-(step t96 (cl (not @p_327) @p_330) :rule not_not)
-(step t97 (cl @p_329 @p_320 @p_330) :rule th_resolution :premises (t96 t95))
-(step t98 (cl @p_327) :rule th_resolution :premises (t90 t92 t97))
-(step t99 (cl @p_330) :rule th_resolution :premises (t96 t98))
-(step t100 (cl (or (! (not @p_203) :named @p_421) (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) (or (not @p_192) (not @p_194) @p_200)) :named @p_422))) :rule qnt_cnf)
-(step t101 (cl (or (! (not @p_222) :named @p_339) (! (= (! (= bot$ @p_6) :named @p_335) @p_331) :named @p_337))) :rule forall_inst :args ((:= veriT_vr116 g$) (:= veriT_vr117 b$)))
-(step t102 (cl (or (! (not @p_120) :named @p_342) (! (=> @p_332 (! (finite$ @p_6) :named @p_334)) :named @p_341))) :rule forall_inst :args ((:= veriT_vr36 b$) (:= veriT_vr37 g$)))
-(step t103 (cl (or (! (not @p_101) :named @p_344) (! (= @p_299 (! (fun_app$ f$ @p_333) :named @p_354)) :named @p_345))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 @p_5)))
-(step t104 (cl (or (! (not @p_32) :named @p_351) (! (=> (! (and @p_334 (! (not @p_335) :named @p_338)) :named @p_346) (! (member$ @p_336 @p_6) :named @p_350)) :named @p_349))) :rule forall_inst :args ((:= veriT_vr2 @p_6) (:= veriT_vr3 f$)))
-(step t105 (cl (! (not @p_337) :named @p_340) @p_338 @p_331) :rule equiv_pos2)
-(step t106 (cl @p_339 @p_337) :rule or :premises (t101))
-(step t107 (cl @p_340 @p_338) :rule resolution :premises (t105 axiom25))
-(step t108 (cl @p_337) :rule resolution :premises (t106 t63))
-(step t109 (cl @p_338) :rule resolution :premises (t107 t108))
-(step t110 (cl (! (not @p_341) :named @p_343) (not @p_332) @p_334) :rule implies_pos)
-(step t111 (cl @p_342 @p_341) :rule or :premises (t102))
-(step t112 (cl @p_343 @p_334) :rule resolution :premises (t110 axiom24))
-(step t113 (cl @p_341) :rule resolution :premises (t111 t42))
-(step t114 (cl @p_334) :rule resolution :premises (t112 t113))
-(step t115 (cl @p_344 @p_345) :rule or :premises (t103))
-(step t116 (cl @p_345) :rule resolution :premises (t115 t36))
-(step t117 (cl @p_346 (! (not @p_334) :named @p_348) (! (not @p_338) :named @p_347)) :rule and_neg)
-(step t118 (cl (not @p_347) @p_335) :rule not_not)
-(step t119 (cl @p_346 @p_348 @p_335) :rule th_resolution :premises (t118 t117))
-(step t120 (cl (! (not @p_349) :named @p_352) (not @p_346) @p_350) :rule implies_pos)
-(step t121 (cl @p_351 @p_349) :rule or :premises (t104))
-(step t122 (cl @p_346) :rule resolution :premises (t119 t109 t114))
-(step t123 (cl @p_352 @p_350) :rule resolution :premises (t120 t122))
-(step t124 (cl @p_349) :rule resolution :premises (t121 t21))
-(step t125 (cl @p_350) :rule resolution :premises (t123 t124))
-(step t126 (cl (or (! (not @p_270) :named @p_410) (! (=> (! (and @p_353 (! (= @p_354 (! (fun_app$ f$ @p_336) :named @p_406)) :named @p_408) @p_350 (! (member$ @p_333 @p_6) :named @p_405)) :named @p_407) @p_355) :named @p_409))) :rule forall_inst :args ((:= veriT_vr126 f$) (:= veriT_vr127 @p_6) (:= veriT_vr128 @p_336) (:= veriT_vr129 @p_333)))
-(step t127 (cl (or (! (not @p_170) :named @p_401) (! (not (! (and @p_350 (! (forall ((veriT_vr65 A$)) (! (not (! (and (! (= @p_336 (! (fun_app$b g$ veriT_vr65) :named @p_359)) :named @p_361) (! (member$a veriT_vr65 b$) :named @p_364)) :named @p_366)) :named @p_368)) :named @p_358)) :named @p_370)) :named @p_356))) :rule forall_inst :args ((:= veriT_vr62 @p_336) (:= veriT_vr63 g$) (:= veriT_vr64 b$)))
-(anchor :step t128)
-(assume t128.h1 @p_356)
-(anchor :step t128.t2 :args ((:= (veriT_vr65 A$) veriT_vr144)))
-(step t128.t2.t1 (cl (! (= veriT_vr65 veriT_vr144) :named @p_363)) :rule refl)
-(step t128.t2.t2 (cl (= @p_359 (! (fun_app$b g$ veriT_vr144) :named @p_360))) :rule cong :premises (t128.t2.t1))
-(step t128.t2.t3 (cl (= @p_361 (! (= @p_336 @p_360) :named @p_362))) :rule cong :premises (t128.t2.t2))
-(step t128.t2.t4 (cl @p_363) :rule refl)
-(step t128.t2.t5 (cl (= @p_364 (! (member$a veriT_vr144 b$) :named @p_365))) :rule cong :premises (t128.t2.t4))
-(step t128.t2.t6 (cl (= @p_366 (! (and @p_362 @p_365) :named @p_367))) :rule cong :premises (t128.t2.t3 t128.t2.t5))
-(step t128.t2.t7 (cl (= @p_368 (! (not @p_367) :named @p_369))) :rule cong :premises (t128.t2.t6))
-(step t128.t2 (cl (= @p_358 (! (forall ((veriT_vr144 A$)) @p_369) :named @p_371))) :rule bind)
-(step t128.t3 (cl (= @p_370 (! (and @p_350 @p_371) :named @p_372))) :rule cong :premises (t128.t2))
-(step t128.t4 (cl (! (= @p_356 (! (not @p_372) :named @p_375)) :named @p_373)) :rule cong :premises (t128.t3))
-(step t128.t5 (cl (! (not @p_373) :named @p_376) (! (not @p_356) :named @p_374) @p_375) :rule equiv_pos2)
-(step t128.t6 (cl (! (not @p_374) :named @p_400) @p_370) :rule not_not)
-(step t128.t7 (cl @p_376 @p_370 @p_375) :rule th_resolution :premises (t128.t6 t128.t5))
-(step t128.t8 (cl @p_375) :rule th_resolution :premises (t128.h1 t128.t4 t128.t7))
-(anchor :step t128.t9 :args ((:= (veriT_vr144 A$) veriT_vr145)))
-(step t128.t9.t1 (cl (! (= veriT_vr144 veriT_vr145) :named @p_380)) :rule refl)
-(step t128.t9.t2 (cl (= @p_360 @p_378)) :rule cong :premises (t128.t9.t1))
-(step t128.t9.t3 (cl (= @p_362 @p_379)) :rule cong :premises (t128.t9.t2))
-(step t128.t9.t4 (cl @p_380) :rule refl)
-(step t128.t9.t5 (cl (= @p_365 @p_381)) :rule cong :premises (t128.t9.t4))
-(step t128.t9.t6 (cl (= @p_367 @p_382)) :rule cong :premises (t128.t9.t3 t128.t9.t5))
-(step t128.t9.t7 (cl (= @p_369 @p_377)) :rule cong :premises (t128.t9.t6))
-(step t128.t9 (cl (= @p_371 (! (forall ((veriT_vr145 A$)) @p_377) :named @p_383))) :rule bind)
-(step t128.t10 (cl (= @p_372 (! (and @p_350 @p_383) :named @p_384))) :rule cong :premises (t128.t9))
-(step t128.t11 (cl (! (= @p_375 (! (not @p_384) :named @p_386)) :named @p_385)) :rule cong :premises (t128.t10))
-(step t128.t12 (cl (! (not @p_385) :named @p_388) (! (not @p_375) :named @p_387) @p_386) :rule equiv_pos2)
-(step t128.t13 (cl (not @p_387) @p_372) :rule not_not)
-(step t128.t14 (cl @p_388 @p_372 @p_386) :rule th_resolution :premises (t128.t13 t128.t12))
-(step t128.t15 (cl @p_386) :rule th_resolution :premises (t128.t8 t128.t11 t128.t14))
-(anchor :step t128.t16 :args ((:= (veriT_vr145 A$) veriT_sk0)))
-(step t128.t16.t1 (cl (! (= veriT_vr145 veriT_sk0) :named @p_392)) :rule refl)
-(step t128.t16.t2 (cl (= @p_378 (! (fun_app$b g$ veriT_sk0) :named @p_390))) :rule cong :premises (t128.t16.t1))
-(step t128.t16.t3 (cl (= @p_379 (! (= @p_336 @p_390) :named @p_391))) :rule cong :premises (t128.t16.t2))
-(step t128.t16.t4 (cl @p_392) :rule refl)
-(step t128.t16.t5 (cl (= @p_381 (! (member$a veriT_sk0 b$) :named @p_393))) :rule cong :premises (t128.t16.t4))
-(step t128.t16.t6 (cl (= @p_382 (! (and @p_391 @p_393) :named @p_394))) :rule cong :premises (t128.t16.t3 t128.t16.t5))
-(step t128.t16.t7 (cl (= @p_377 (! (not @p_394) :named @p_389))) :rule cong :premises (t128.t16.t6))
-(step t128.t16 (cl (= @p_383 @p_389)) :rule sko_forall)
-(step t128.t17 (cl (= @p_384 (! (and @p_350 @p_389) :named @p_395))) :rule cong :premises (t128.t16))
-(step t128.t18 (cl (! (= @p_386 (! (not @p_395) :named @p_396)) :named @p_397)) :rule cong :premises (t128.t17))
-(step t128.t19 (cl (! (not @p_397) :named @p_399) (! (not @p_386) :named @p_398) @p_396) :rule equiv_pos2)
-(step t128.t20 (cl (not @p_398) @p_384) :rule not_not)
-(step t128.t21 (cl @p_399 @p_384 @p_396) :rule th_resolution :premises (t128.t20 t128.t19))
-(step t128.t22 (cl @p_396) :rule th_resolution :premises (t128.t15 t128.t18 t128.t21))
-(step t128 (cl @p_374 @p_396) :rule subproof :discharge (h1))
-(step t129 (cl @p_400 @p_370) :rule not_not)
-(step t130 (cl @p_370 @p_396) :rule th_resolution :premises (t129 t128))
-(step t131 (cl @p_401 @p_356) :rule or :premises (t127))
-(step t132 (cl (! (or @p_401 @p_396) :named @p_403) (! (not @p_401) :named @p_402)) :rule or_neg)
-(step t133 (cl (not @p_402) @p_170) :rule not_not)
-(step t134 (cl @p_403 @p_170) :rule th_resolution :premises (t133 t132))
-(step t135 (cl @p_403 (! (not @p_396) :named @p_404)) :rule or_neg)
-(step t136 (cl (not @p_404) @p_395) :rule not_not)
-(step t137 (cl @p_403 @p_395) :rule th_resolution :premises (t136 t135))
-(step t138 (cl @p_403) :rule th_resolution :premises (t131 t130 t134 t137))
-(step t139 (cl (or (! (not @p_76) :named @p_420) (! (=> (! (and @p_334 @p_338 @p_405) :named @p_417) (! (less_eq$ @p_406 @p_354) :named @p_419)) :named @p_418))) :rule forall_inst :args ((:= veriT_vr11 @p_6) (:= veriT_vr12 @p_333) (:= veriT_vr13 f$)))
-(step t140 (cl @p_407 (not @p_353) (! (not @p_408) :named @p_411) (! (not @p_350) :named @p_415) (! (not @p_405) :named @p_412)) :rule and_neg)
-(step t141 (cl (! (not @p_409) :named @p_413) (! (not @p_407) :named @p_414) @p_355) :rule implies_pos)
-(step t142 (cl @p_410 @p_409) :rule or :premises (t126))
-(step t143 (cl @p_407 @p_411 @p_412) :rule resolution :premises (t140 axiom23 t125))
-(step t144 (cl @p_413 @p_414) :rule resolution :premises (t141 axiom52))
-(step t145 (cl @p_409) :rule resolution :premises (t142 t72))
-(step t146 (cl @p_414) :rule resolution :premises (t144 t145))
-(step t147 (cl @p_389 @p_391) :rule and_pos)
-(step t148 (cl @p_389 @p_393) :rule and_pos)
-(step t149 (cl @p_395 @p_415 (! (not @p_389) :named @p_416)) :rule and_neg)
-(step t150 (cl (not @p_416) @p_394) :rule not_not)
-(step t151 (cl @p_395 @p_415 @p_394) :rule th_resolution :premises (t150 t149))
-(step t152 (cl @p_401 @p_396) :rule or :premises (t138))
-(step t153 (cl @p_395 @p_394) :rule resolution :premises (t151 t125))
-(step t154 (cl @p_396) :rule resolution :premises (t152 t51))
-(step t155 (cl @p_394) :rule resolution :premises (t153 t154))
-(step t156 (cl @p_391) :rule resolution :premises (t147 t155))
-(step t157 (cl @p_393) :rule resolution :premises (t148 t155))
-(step t158 (cl @p_417 @p_348 @p_347 @p_412) :rule and_neg)
-(step t159 (cl @p_417 @p_348 @p_335 @p_412) :rule th_resolution :premises (t118 t158))
-(step t160 (cl (not @p_418) (not @p_417) @p_419) :rule implies_pos)
-(step t161 (cl @p_420 @p_418) :rule or :premises (t139))
-(step t162 (cl @p_417 @p_412) :rule resolution :premises (t159 t109 t114))
-(step t163 (cl @p_418) :rule resolution :premises (t161 t30))
-(step t164 (cl @p_421 @p_422) :rule or :premises (t100))
-(step t165 (cl (or (! (not @p_422) :named @p_424) (! (or (! (not (! (= @p_333 @p_333) :named @p_430)) :named @p_431) (! (not @p_423) :named @p_429) @p_405) :named @p_425))) :rule forall_inst :args ((:= veriT_vr94 @p_333) (:= veriT_vr95 g$) (:= veriT_vr96 @p_5) (:= veriT_vr97 b$)))
-(step t166 (cl @p_424 @p_425) :rule or :premises (t165))
-(step t167 (cl (! (or @p_421 @p_425) :named @p_427) (! (not @p_421) :named @p_426)) :rule or_neg)
-(step t168 (cl (not @p_426) @p_203) :rule not_not)
-(step t169 (cl @p_427 @p_203) :rule th_resolution :premises (t168 t167))
-(step t170 (cl @p_427 (! (not @p_425) :named @p_428)) :rule or_neg)
-(step t171 (cl @p_427) :rule th_resolution :premises (t164 t166 t169 t170))
-(anchor :step t172)
-(assume t172.h1 @p_425)
-(step t172.t2 (cl (= @p_430 true)) :rule eq_simplify)
-(step t172.t3 (cl (= @p_431 (! (not true) :named @p_432))) :rule cong :premises (t172.t2))
-(step t172.t4 (cl (= @p_432 false)) :rule not_simplify)
-(step t172.t5 (cl (= @p_431 false)) :rule trans :premises (t172.t3 t172.t4))
-(step t172.t6 (cl (= @p_425 (! (or false @p_429 @p_405) :named @p_433))) :rule cong :premises (t172.t5))
-(step t172.t7 (cl (= @p_433 (! (or @p_429 @p_405) :named @p_434))) :rule or_simplify)
-(step t172.t8 (cl (! (= @p_425 @p_434) :named @p_435)) :rule trans :premises (t172.t6 t172.t7))
-(step t172.t9 (cl (not @p_435) @p_428 @p_434) :rule equiv_pos2)
-(step t172.t10 (cl @p_434) :rule th_resolution :premises (t172.h1 t172.t8 t172.t9))
-(step t172 (cl @p_428 @p_434) :rule subproof :discharge (h1))
-(step t173 (cl @p_421 @p_425) :rule or :premises (t171))
-(step t174 (cl (! (or @p_421 @p_434) :named @p_436) @p_426) :rule or_neg)
-(step t175 (cl @p_436 @p_203) :rule th_resolution :premises (t168 t174))
-(step t176 (cl @p_436 (! (not @p_434) :named @p_437)) :rule or_neg)
-(step t177 (cl @p_436) :rule th_resolution :premises (t173 t172 t175 t176))
-(step t178 (cl @p_437 @p_429 @p_405) :rule or_pos)
-(step t179 (cl @p_421 @p_434) :rule or :premises (t177))
-(step t180 (cl @p_437 @p_405) :rule resolution :premises (t178 axiom26))
-(step t181 (cl @p_434) :rule resolution :premises (t179 t57))
-(step t182 (cl @p_405) :rule resolution :premises (t180 t181))
-(step t183 (cl @p_411) :rule resolution :premises (t143 t182 t146))
-(step t184 (cl @p_417) :rule resolution :premises (t162 t182))
-(step t185 (cl @p_419) :rule resolution :premises (t160 t184 t163))
-(step t186 (cl (or @p_325 (! (not (! (and @p_393 (! (less$ (! (fun_app$a @p_4 veriT_sk0) :named @p_438) @p_299) :named @p_440)) :named @p_439)) :named @p_441))) :rule forall_inst :args ((:= veriT_vr135 veriT_sk0)))
-(step t187 (cl (or (! (not @p_297) :named @p_448) (! (= (! (less$ @p_406 @p_354) :named @p_447) (! (and @p_419 @p_411) :named @p_443)) :named @p_446))) :rule forall_inst :args ((:= veriT_vr132 @p_406) (:= veriT_vr133 @p_354)))
-(step t188 (cl (or @p_344 (! (= @p_438 (! (fun_app$ f$ @p_390) :named @p_451)) :named @p_450))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 veriT_sk0)))
-(step t189 (cl @p_439 (not @p_393) (! (not @p_440) :named @p_442)) :rule and_neg)
-(step t190 (cl @p_325 @p_441) :rule or :premises (t186))
-(step t191 (cl @p_439 @p_442) :rule resolution :premises (t189 t157))
-(step t192 (cl @p_441) :rule resolution :premises (t190 t99))
-(step t193 (cl @p_442) :rule resolution :premises (t191 t192))
-(step t194 (cl @p_443 (! (not @p_419) :named @p_445) (! (not @p_411) :named @p_444)) :rule and_neg)
-(step t195 (cl (not @p_444) @p_408) :rule not_not)
-(step t196 (cl @p_443 @p_445 @p_408) :rule th_resolution :premises (t195 t194))
-(step t197 (cl (! (not @p_446) :named @p_449) @p_447 (not @p_443)) :rule equiv_pos1)
-(step t198 (cl @p_448 @p_446) :rule or :premises (t187))
-(step t199 (cl @p_443) :rule resolution :premises (t196 t183 t185))
-(step t200 (cl @p_449 @p_447) :rule resolution :premises (t197 t199))
-(step t201 (cl @p_446) :rule resolution :premises (t198 t78))
-(step t202 (cl @p_447) :rule resolution :premises (t200 t201))
-(step t203 (cl @p_344 @p_450) :rule or :premises (t188))
-(step t204 (cl @p_450) :rule resolution :premises (t203 t36))
-(step t205 (cl (not (! (= @p_406 @p_438) :named @p_452)) (! (not @p_345) :named @p_457) (! (not @p_447) :named @p_458) @p_440) :rule eq_congruent_pred)
-(step t206 (cl (not (! (= @p_406 @p_451) :named @p_453)) (! (not @p_450) :named @p_456) @p_452) :rule eq_transitive)
-(step t207 (cl (not (! (= f$ f$) :named @p_454)) (! (not @p_391) :named @p_455) @p_453) :rule eq_congruent)
-(step t208 (cl @p_454) :rule eq_reflexive)
-(step t209 (cl @p_455 @p_453) :rule th_resolution :premises (t207 t208))
-(step t210 (cl @p_456 @p_452 @p_455) :rule th_resolution :premises (t206 t209))
-(step t211 (cl @p_457 @p_458 @p_440 @p_456 @p_455) :rule th_resolution :premises (t205 t210))
-(step t212 (cl) :rule resolution :premises (t211 t116 t156 t193 t202 t204))
-2c004ebfd8457fdbede51bb75b1997f1f1e2bc6d 791 0
-unsat
-(assume axiom0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uuc$ ?v0) :named @p_9) (! (pair$ (! (times$ (! (- ?v0 (! (divide$ 1.0 2.0) :named @p_7)) :named @p_12) d$) :named @p_1) (! (diamond_y$ @p_1) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_6))
-(assume axiom3 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uub$ ?v0) :named @p_37) (! (pair$ (! (- (! (divide$ d$ 2.0) :named @p_3)) :named @p_2) (! (times$ (! (- (! (* 2.0 ?v0) :named @p_40) 1.0) :named @p_42) (! (diamond_y$ @p_2) :named @p_36)) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
-(assume axiom4 (! (< 0.0 d$) :named @p_453))
-(assume axiom5 (! (forall ((?v0 Real)) (! (= (! (diamond_y$ ?v0) :named @p_62) (! (- @p_3 (! (ite (! (< ?v0 0.0) :named @p_65) (! (- ?v0) :named @p_4) ?v0) :named @p_68)) :named @p_70)) :named @p_72)) :named @p_61))
-(assume axiom7 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (! (= (! (< (! (divide$ ?v0 ?v1) :named @p_5) (! (divide$ ?v2 ?v1) :named @p_88)) :named @p_90) (! (and (! (=> (! (< 0.0 ?v1) :named @p_92) (! (< ?v0 ?v2) :named @p_96)) :named @p_98) (! (and (! (=> (! (< ?v1 0.0) :named @p_100) (! (< ?v2 ?v0) :named @p_102)) :named @p_104) (! (not (! (= 0.0 ?v1) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_112)) :named @p_114)) :named @p_85))
-(assume axiom8 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (divide$ @p_4 ?v1) :named @p_142) (! (- @p_5) :named @p_147)) :named @p_149)) :named @p_140))
-(assume axiom9 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (times$ @p_4 ?v1) :named @p_164) (! (- (! (times$ ?v0 ?v1) :named @p_168)) :named @p_170)) :named @p_172)) :named @p_162))
-(assume axiom10 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (! (= (! (= (! (pair$ ?v0 ?v1) :named @p_186) (! (pair$ ?v2 ?v3) :named @p_188)) :named @p_190) (! (and (! (= ?v0 ?v2) :named @p_194) (! (= ?v1 ?v3) :named @p_198)) :named @p_200)) :named @p_202)) :named @p_185))
-(assume axiom11 (! (not (! (=> (! (and (! (not (= uua$ uu$)) :named @p_226) (! (= uuc$ uub$) :named @p_227)) :named @p_220) false) :named @p_224)) :named @p_219))
+(assume a0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uuc$ ?v0) :named @p_9) (! (pair$ (! (times$ (! (- ?v0 (! (divide$ 1.0 2.0) :named @p_7)) :named @p_12) d$) :named @p_1) (! (diamond_y$ @p_1) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_6))
+(assume a3 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uub$ ?v0) :named @p_37) (! (pair$ (! (- (! (divide$ d$ 2.0) :named @p_3)) :named @p_2) (! (times$ (! (- (! (* 2.0 ?v0) :named @p_40) 1.0) :named @p_42) (! (diamond_y$ @p_2) :named @p_36)) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
+(assume a4 (! (< 0.0 d$) :named @p_453))
+(assume a5 (! (forall ((?v0 Real)) (! (= (! (diamond_y$ ?v0) :named @p_62) (! (- @p_3 (! (ite (! (< ?v0 0.0) :named @p_65) (! (- ?v0) :named @p_4) ?v0) :named @p_68)) :named @p_70)) :named @p_72)) :named @p_61))
+(assume a7 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (! (= (! (< (! (divide$ ?v0 ?v1) :named @p_5) (! (divide$ ?v2 ?v1) :named @p_88)) :named @p_90) (! (and (! (=> (! (< 0.0 ?v1) :named @p_92) (! (< ?v0 ?v2) :named @p_96)) :named @p_98) (! (and (! (=> (! (< ?v1 0.0) :named @p_100) (! (< ?v2 ?v0) :named @p_102)) :named @p_104) (! (not (! (= 0.0 ?v1) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_112)) :named @p_114)) :named @p_85))
+(assume a8 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (divide$ @p_4 ?v1) :named @p_142) (! (- @p_5) :named @p_147)) :named @p_149)) :named @p_140))
+(assume a9 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (times$ @p_4 ?v1) :named @p_164) (! (- (! (times$ ?v0 ?v1) :named @p_168)) :named @p_170)) :named @p_172)) :named @p_162))
+(assume a10 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (! (= (! (= (! (pair$ ?v0 ?v1) :named @p_186) (! (pair$ ?v2 ?v3) :named @p_188)) :named @p_190) (! (and (! (= ?v0 ?v2) :named @p_194) (! (= ?v1 ?v3) :named @p_198)) :named @p_200)) :named @p_202)) :named @p_185))
+(assume a11 (! (not (! (=> (! (and (! (not (= uua$ uu$)) :named @p_226) (! (= uuc$ uub$) :named @p_227)) :named @p_220) false) :named @p_224)) :named @p_219))
 (anchor :step t10 :args ((:= (?v0 Real) veriT_vr0)))
 (step t10.t1 (cl (! (= ?v0 veriT_vr0) :named @p_11)) :rule refl)
 (step t10.t2 (cl (= @p_9 (! (fun_app$ uuc$ veriT_vr0) :named @p_10))) :rule cong :premises (t10.t1))
@@ -6668,7 +6100,7 @@
 (step t10.t11 (cl (= @p_20 (! (= @p_10 @p_19) :named @p_21))) :rule cong :premises (t10.t2 t10.t10))
 (step t10 (cl (! (= @p_6 (! (forall ((veriT_vr0 Real)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
 (step t11 (cl (not @p_22) (not @p_6) @p_23) :rule equiv_pos2)
-(step t12 (cl @p_23) :rule th_resolution :premises (axiom0 t10 t11))
+(step t12 (cl @p_23) :rule th_resolution :premises (a0 t10 t11))
 (anchor :step t13 :args ((:= (veriT_vr0 Real) veriT_vr1)))
 (step t13.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_26)) :rule refl)
 (step t13.t2 (cl (= @p_10 (! (fun_app$ uuc$ veriT_vr1) :named @p_25))) :rule cong :premises (t13.t1))
@@ -6695,7 +6127,7 @@
 (step t16.t8 (cl (= @p_48 (! (= @p_38 @p_47) :named @p_49))) :rule cong :premises (t16.t2 t16.t7))
 (step t16 (cl (! (= @p_35 (! (forall ((veriT_vr6 Real)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
 (step t17 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
-(step t18 (cl @p_51) :rule th_resolution :premises (axiom3 t16 t17))
+(step t18 (cl @p_51) :rule th_resolution :premises (a3 t16 t17))
 (anchor :step t19 :args ((:= (veriT_vr6 Real) veriT_vr7)))
 (step t19.t1 (cl (! (= veriT_vr6 veriT_vr7) :named @p_53)) :rule refl)
 (step t19.t2 (cl (= @p_38 (! (fun_app$ uub$ veriT_vr7) :named @p_52))) :rule cong :premises (t19.t1))
@@ -6721,7 +6153,7 @@
 (step t22.t10 (cl (= @p_72 (! (= @p_63 @p_71) :named @p_73))) :rule cong :premises (t22.t2 t22.t9))
 (step t22 (cl (! (= @p_61 (! (forall ((veriT_vr8 Real)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
 (step t23 (cl (not @p_74) (not @p_61) @p_75) :rule equiv_pos2)
-(step t24 (cl @p_75) :rule th_resolution :premises (axiom5 t22 t23))
+(step t24 (cl @p_75) :rule th_resolution :premises (a5 t22 t23))
 (anchor :step t25 :args ((:= (veriT_vr8 Real) veriT_vr9)))
 (step t25.t1 (cl (! (= veriT_vr8 veriT_vr9) :named @p_77)) :rule refl)
 (step t25.t2 (cl (= @p_63 (! (diamond_y$ veriT_vr9) :named @p_76))) :rule cong :premises (t25.t1))
@@ -6764,7 +6196,7 @@
 (step t28.t25 (cl (= @p_114 (! (= @p_91 @p_113) :named @p_115))) :rule cong :premises (t28.t7 t28.t24))
 (step t28 (cl (! (= @p_85 (! (forall ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)) @p_115) :named @p_117)) :named @p_116)) :rule bind)
 (step t29 (cl (not @p_116) (not @p_85) @p_117) :rule equiv_pos2)
-(step t30 (cl @p_117) :rule th_resolution :premises (axiom7 t28 t29))
+(step t30 (cl @p_117) :rule th_resolution :premises (a7 t28 t29))
 (anchor :step t31 :args ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)))
 (step t31.t1 (cl (= @p_113 (! (and @p_99 @p_105 @p_109) :named @p_118))) :rule ac_simp)
 (step t31.t2 (cl (= @p_115 (! (= @p_91 @p_118) :named @p_119))) :rule cong :premises (t31.t1))
@@ -6811,7 +6243,7 @@
 (step t37.t9 (cl (= @p_149 (! (= @p_143 @p_148) :named @p_150))) :rule cong :premises (t37.t4 t37.t8))
 (step t37 (cl (! (= @p_140 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_150) :named @p_152)) :named @p_151)) :rule bind)
 (step t38 (cl (not @p_151) (not @p_140) @p_152) :rule equiv_pos2)
-(step t39 (cl @p_152) :rule th_resolution :premises (axiom8 t37 t38))
+(step t39 (cl @p_152) :rule th_resolution :premises (a8 t37 t38))
 (anchor :step t40 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
 (step t40.t1 (cl (! (= veriT_vr16 veriT_vr18) :named @p_155)) :rule refl)
 (step t40.t2 (cl (= @p_141 (! (- veriT_vr18) :named @p_153))) :rule cong :premises (t40.t1))
@@ -6837,7 +6269,7 @@
 (step t43.t9 (cl (= @p_172 (! (= @p_165 @p_171) :named @p_173))) :rule cong :premises (t43.t4 t43.t8))
 (step t43 (cl (! (= @p_162 (! (forall ((veriT_vr20 Real) (veriT_vr21 Real)) @p_173) :named @p_175)) :named @p_174)) :rule bind)
 (step t44 (cl (not @p_174) (not @p_162) @p_175) :rule equiv_pos2)
-(step t45 (cl @p_175) :rule th_resolution :premises (axiom9 t43 t44))
+(step t45 (cl @p_175) :rule th_resolution :premises (a9 t43 t44))
 (anchor :step t46 :args ((:= (veriT_vr20 Real) veriT_vr22) (:= (veriT_vr21 Real) veriT_vr23)))
 (step t46.t1 (cl (! (= veriT_vr20 veriT_vr22) :named @p_178)) :rule refl)
 (step t46.t2 (cl (= @p_163 (! (- veriT_vr22) :named @p_176))) :rule cong :premises (t46.t1))
@@ -6869,7 +6301,7 @@
 (step t49.t15 (cl (= @p_202 (! (= @p_191 @p_201) :named @p_203))) :rule cong :premises (t49.t7 t49.t14))
 (step t49 (cl (! (= @p_185 (! (forall ((veriT_vr24 Real) (veriT_vr25 Real) (veriT_vr26 Real) (veriT_vr27 Real)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
 (step t50 (cl (not @p_204) (not @p_185) @p_205) :rule equiv_pos2)
-(step t51 (cl @p_205) :rule th_resolution :premises (axiom10 t49 t50))
+(step t51 (cl @p_205) :rule th_resolution :premises (a10 t49 t50))
 (anchor :step t52 :args ((:= (veriT_vr24 Real) veriT_vr28) (:= (veriT_vr25 Real) veriT_vr29) (:= (veriT_vr26 Real) veriT_vr30) (:= (veriT_vr27 Real) veriT_vr31)))
 (step t52.t1 (cl (! (= veriT_vr24 veriT_vr28) :named @p_209)) :rule refl)
 (step t52.t2 (cl (! (= veriT_vr25 veriT_vr29) :named @p_212)) :rule refl)
@@ -6893,7 +6325,7 @@
 (step t56 (cl (! (not @p_221) :named @p_225) (! (not @p_219) :named @p_223) @p_222) :rule equiv_pos2)
 (step t57 (cl (not @p_223) @p_224) :rule not_not)
 (step t58 (cl @p_225 @p_224 @p_222) :rule th_resolution :premises (t57 t56))
-(step t59 (cl @p_222) :rule th_resolution :premises (axiom11 t55 t58))
+(step t59 (cl @p_222) :rule th_resolution :premises (a11 t55 t58))
 (step t60 (cl (! (= @p_222 (! (and @p_226 @p_227 @p_228) :named @p_230)) :named @p_229)) :rule ac_simp)
 (step t61 (cl (not @p_229) (not @p_222) @p_230) :rule equiv_pos2)
 (step t62 (cl @p_230) :rule th_resolution :premises (t59 t60 t61))
@@ -7353,7 +6785,7 @@
 (step t250 (cl @p_448) :rule resolution :premises (t249 t36))
 (step t251 (cl @p_502 @p_455 (not @p_453)) :rule equiv_pos1)
 (step t252 (cl @p_282 @p_464) :rule or :premises (t196))
-(step t253 (cl @p_502 @p_455) :rule resolution :premises (t251 axiom4))
+(step t253 (cl @p_502 @p_455) :rule resolution :premises (t251 a4))
 (step t254 (cl @p_464) :rule resolution :premises (t252 t36))
 (step t255 (cl @p_455) :rule resolution :premises (t253 t254))
 (step t256 (cl @p_503 @p_504) :rule and_pos)
@@ -7435,9 +6867,577 @@
 (step t332 (cl @p_568 @p_563 @p_564 @p_555 @p_556 @p_557 @p_527) :rule contraction :premises (t331))
 (step t333 (cl @p_561 @p_403 @p_288 @p_568 @p_563 @p_555 @p_556 @p_557 @p_527) :rule th_resolution :premises (t325 t332))
 (step t334 (cl) :rule resolution :premises (t333 t81 t217 t221 t277 t270 t286 t295 t300 t316))
-6120eaf40c2621e298051bc401bc258d4c6ef4d6 323 0
+f79704028180f39e90d9e958e4416fd1e60a60df 567 0
 unsat
-(assume axiom1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_2)) :named @p_9)) :named @p_6) (! (= ?v0 (! (joinpaths$ @p_1 (! (rec_join$ @p_2) :named @p_95)) :named @p_7)) :named @p_97)) :named @p_99) false) :named @p_101)) :named @p_88)) :named @p_103)) :named @p_105)) :named @p_107) false) :named @p_109) (! (=> (! (and (! (= @p_3 @p_3) :named @p_112) (! (and (! (=> (! (and @p_4 (! (= uu$ @p_3) :named @p_115)) :named @p_117) false) :named @p_119) (! (and (! (forall ((?v2 B$)) (! (=> (! (and @p_5 (! (= @p_3 @p_1) :named @p_125)) :named @p_127) false) :named @p_129)) :named @p_121) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and @p_6 (! (= @p_3 @p_7) :named @p_137)) :named @p_139) false) :named @p_141)) :named @p_131)) :named @p_143)) :named @p_145)) :named @p_147) false) :named @p_149)) :named @p_151)) :named @p_53) (! (= (! (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (! (=> (! (and (! (= (! (rec_join$ ?v0) :named @p_10) ?v1) :named @p_19) (! (and (! (=> (! (and (! (= nil$ ?v0) :named @p_11) (! (= uu$ ?v1) :named @p_20)) :named @p_22) false) :named @p_24) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= @p_8 ?v0) :named @p_17) (! (= @p_1 ?v1) :named @p_27)) :named @p_29) false) :named @p_31)) :named @p_25) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= @p_9 ?v0) :named @p_18) (! (= @p_7 ?v1) :named @p_35)) :named @p_37) false) :named @p_39)) :named @p_33)) :named @p_41)) :named @p_43)) :named @p_45) false) :named @p_47)) :named @p_14) (! (forall ((?v0 B_list$)) (! (=> (! (and (! (= @p_10 @p_10) :named @p_15) (! (and (! (=> (! (and @p_11 (! (= uu$ @p_10) :named @p_21)) :named @p_23) false) :named @p_16) (! (and (! (forall ((?v1 B$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 nil$) :named @p_162)) :named @p_163) (! (= @p_10 (! (coeff_cube_to_path$ ?v1) :named @p_12)) :named @p_165)) :named @p_166) false) :named @p_167)) :named @p_161) (! (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_13)) :named @p_169)) :named @p_170) (! (= @p_10 (! (joinpaths$ @p_12 (! (rec_join$ @p_13) :named @p_175)) :named @p_176)) :named @p_177)) :named @p_178) false) :named @p_179)) :named @p_168)) :named @p_180)) :named @p_181)) :named @p_182) false) :named @p_183)) :named @p_51)) :named @p_49)) :named @p_52)) :named @p_55))
+(define-fun veriT_sk0 () A$ (! (choice ((veriT_vr145 A$)) (not (! (not (! (and (! (= (! (arg_min_on$ f$ (! (image$b g$ b$) :named @p_6)) :named @p_336) (! (fun_app$b g$ veriT_vr145) :named @p_378)) :named @p_379) (! (member$a veriT_vr145 b$) :named @p_381)) :named @p_382)) :named @p_377))) :named @p_357))
+(assume a29 (! (forall ((?v0 B_set$) (?v1 B_c_fun$)) (! (=> (! (and (! (finite$ ?v0) :named @p_1) (! (not (! (= ?v0 bot$) :named @p_10)) :named @p_2)) :named @p_13) (! (member$ (! (arg_min_on$ ?v1 ?v0) :named @p_15) ?v0) :named @p_17)) :named @p_19)) :named @p_7))
+(assume a31 (! (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (! (=> (! (and @p_1 (! (and @p_2 (! (member$ ?v1 ?v0) :named @p_38)) :named @p_40)) :named @p_42) (! (less_eq$ (! (fun_app$ ?v2 (! (arg_min_on$ ?v2 ?v0) :named @p_45)) :named @p_47) (! (fun_app$ ?v2 ?v1) :named @p_50)) :named @p_52)) :named @p_54)) :named @p_33))
+(assume a33 (! (forall ((?v0 B_c_fun$) (?v1 A_b_fun$) (?v2 A$)) (! (= (! (fun_app$a (! (comp$ ?v0 ?v1) :named @p_78) ?v2) :named @p_80) (! (fun_app$ ?v0 (! (fun_app$b ?v1 ?v2) :named @p_3)) :named @p_86)) :named @p_88)) :named @p_77))
+(assume a36 (! (forall ((?v0 A_set$) (?v1 A_b_fun$)) (! (=> (! (finite$a ?v0) :named @p_103) (! (finite$ (! (image$b ?v1 ?v0) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_102))
+(assume a40 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (! (=> (! (and (! (member$ ?v0 (! (image$b ?v1 ?v2) :named @p_122)) :named @p_124) (! (forall ((?v3 A$)) (! (=> (! (and (! (= ?v0 (! (fun_app$b ?v1 ?v3) :named @p_130)) :named @p_132) (! (member$a ?v3 ?v2) :named @p_136)) :named @p_138) false) :named @p_140)) :named @p_126)) :named @p_142) false) :named @p_144)) :named @p_121))
+(assume a44 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (! (=> (! (and (! (= @p_3 ?v0) :named @p_173) (! (member$a ?v2 ?v3) :named @p_176)) :named @p_178) (! (member$ ?v0 (! (image$b ?v1 ?v3) :named @p_183)) :named @p_185)) :named @p_187)) :named @p_171))
+(assume a48 (! (forall ((?v0 A_b_fun$) (?v1 A_set$)) (! (= (! (= bot$ (! (image$b ?v0 ?v1) :named @p_205)) :named @p_207) (! (= bot$a ?v1) :named @p_210)) :named @p_212)) :named @p_204))
+(assume a50 (! (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (! (=> (! (and (! (inj_on$ ?v0 ?v1) :named @p_224) (! (and (! (= (! (fun_app$ ?v0 ?v2) :named @p_227) (! (fun_app$ ?v0 ?v3) :named @p_229)) :named @p_231) (! (and (! (member$ ?v2 ?v1) :named @p_235) (! (member$ ?v3 ?v1) :named @p_238)) :named @p_240)) :named @p_242)) :named @p_244) (! (= ?v3 ?v2) :named @p_246)) :named @p_248)) :named @p_223))
+(assume a51 (! (forall ((?v0 C$) (?v1 C$)) (! (= (! (less$ ?v0 ?v1) :named @p_272) (! (and (! (less_eq$ ?v0 ?v1) :named @p_276) (! (not (! (= ?v0 ?v1) :named @p_278)) :named @p_280)) :named @p_282)) :named @p_284)) :named @p_271))
+(assume a23 (! (inj_on$ f$ @p_6) :named @p_353))
+(assume a24 (! (finite$a b$) :named @p_332))
+(assume a25 (not (! (= bot$a b$) :named @p_331)))
+(assume a26 (! (member$a (! (arg_min_on$a (! (comp$ f$ g$) :named @p_4) b$) :named @p_5) b$) :named @p_423))
+(assume a27 (! (not (! (exists ((?v0 A$)) (! (and (! (member$a ?v0 b$) :named @p_300) (! (less$ (! (fun_app$a @p_4 ?v0) :named @p_303) (! (fun_app$a @p_4 @p_5) :named @p_299)) :named @p_305)) :named @p_307)) :named @p_298)) :named @p_309))
+(assume a52 (not (! (= @p_336 (! (fun_app$b g$ @p_5) :named @p_333)) :named @p_355)))
+(anchor :step t16 :args ((:= (?v0 B_set$) veriT_vr0) (:= (?v1 B_c_fun$) veriT_vr1)))
+(step t16.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
+(step t16.t2 (cl (= @p_1 (! (finite$ veriT_vr0) :named @p_8))) :rule cong :premises (t16.t1))
+(step t16.t3 (cl @p_9) :rule refl)
+(step t16.t4 (cl (= @p_10 (! (= bot$ veriT_vr0) :named @p_11))) :rule cong :premises (t16.t3))
+(step t16.t5 (cl (= @p_2 (! (not @p_11) :named @p_12))) :rule cong :premises (t16.t4))
+(step t16.t6 (cl (= @p_13 (! (and @p_8 @p_12) :named @p_14))) :rule cong :premises (t16.t2 t16.t5))
+(step t16.t7 (cl (= ?v1 veriT_vr1)) :rule refl)
+(step t16.t8 (cl @p_9) :rule refl)
+(step t16.t9 (cl (= @p_15 (! (arg_min_on$ veriT_vr1 veriT_vr0) :named @p_16))) :rule cong :premises (t16.t7 t16.t8))
+(step t16.t10 (cl @p_9) :rule refl)
+(step t16.t11 (cl (= @p_17 (! (member$ @p_16 veriT_vr0) :named @p_18))) :rule cong :premises (t16.t9 t16.t10))
+(step t16.t12 (cl (= @p_19 (! (=> @p_14 @p_18) :named @p_20))) :rule cong :premises (t16.t6 t16.t11))
+(step t16 (cl (! (= @p_7 (! (forall ((veriT_vr0 B_set$) (veriT_vr1 B_c_fun$)) @p_20) :named @p_22)) :named @p_21)) :rule bind)
+(step t17 (cl (not @p_21) (not @p_7) @p_22) :rule equiv_pos2)
+(step t18 (cl @p_22) :rule th_resolution :premises (a29 t16 t17))
+(anchor :step t19 :args ((:= (veriT_vr0 B_set$) veriT_vr2) (:= (veriT_vr1 B_c_fun$) veriT_vr3)))
+(step t19.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_24)) :rule refl)
+(step t19.t2 (cl (= @p_8 (! (finite$ veriT_vr2) :named @p_23))) :rule cong :premises (t19.t1))
+(step t19.t3 (cl @p_24) :rule refl)
+(step t19.t4 (cl (= @p_11 (! (= bot$ veriT_vr2) :named @p_25))) :rule cong :premises (t19.t3))
+(step t19.t5 (cl (= @p_12 (! (not @p_25) :named @p_26))) :rule cong :premises (t19.t4))
+(step t19.t6 (cl (= @p_14 (! (and @p_23 @p_26) :named @p_27))) :rule cong :premises (t19.t2 t19.t5))
+(step t19.t7 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
+(step t19.t8 (cl @p_24) :rule refl)
+(step t19.t9 (cl (= @p_16 (! (arg_min_on$ veriT_vr3 veriT_vr2) :named @p_28))) :rule cong :premises (t19.t7 t19.t8))
+(step t19.t10 (cl @p_24) :rule refl)
+(step t19.t11 (cl (= @p_18 (! (member$ @p_28 veriT_vr2) :named @p_29))) :rule cong :premises (t19.t9 t19.t10))
+(step t19.t12 (cl (= @p_20 (! (=> @p_27 @p_29) :named @p_30))) :rule cong :premises (t19.t6 t19.t11))
+(step t19 (cl (! (= @p_22 (! (forall ((veriT_vr2 B_set$) (veriT_vr3 B_c_fun$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
+(step t20 (cl (not @p_31) (not @p_22) @p_32) :rule equiv_pos2)
+(step t21 (cl @p_32) :rule th_resolution :premises (t18 t19 t20))
+(anchor :step t22 :args ((:= (?v0 B_set$) veriT_vr8) (:= (?v1 B$) veriT_vr9) (:= (?v2 B_c_fun$) veriT_vr10)))
+(step t22.t1 (cl (! (= ?v0 veriT_vr8) :named @p_35)) :rule refl)
+(step t22.t2 (cl (= @p_1 (! (finite$ veriT_vr8) :named @p_34))) :rule cong :premises (t22.t1))
+(step t22.t3 (cl @p_35) :rule refl)
+(step t22.t4 (cl (= @p_10 (! (= bot$ veriT_vr8) :named @p_36))) :rule cong :premises (t22.t3))
+(step t22.t5 (cl (= @p_2 (! (not @p_36) :named @p_37))) :rule cong :premises (t22.t4))
+(step t22.t6 (cl (! (= ?v1 veriT_vr9) :named @p_49)) :rule refl)
+(step t22.t7 (cl @p_35) :rule refl)
+(step t22.t8 (cl (= @p_38 (! (member$ veriT_vr9 veriT_vr8) :named @p_39))) :rule cong :premises (t22.t6 t22.t7))
+(step t22.t9 (cl (= @p_40 (! (and @p_37 @p_39) :named @p_41))) :rule cong :premises (t22.t5 t22.t8))
+(step t22.t10 (cl (= @p_42 (! (and @p_34 @p_41) :named @p_43))) :rule cong :premises (t22.t2 t22.t9))
+(step t22.t11 (cl (! (= ?v2 veriT_vr10) :named @p_44)) :rule refl)
+(step t22.t12 (cl @p_44) :rule refl)
+(step t22.t13 (cl @p_35) :rule refl)
+(step t22.t14 (cl (= @p_45 (! (arg_min_on$ veriT_vr10 veriT_vr8) :named @p_46))) :rule cong :premises (t22.t12 t22.t13))
+(step t22.t15 (cl (= @p_47 (! (fun_app$ veriT_vr10 @p_46) :named @p_48))) :rule cong :premises (t22.t11 t22.t14))
+(step t22.t16 (cl @p_44) :rule refl)
+(step t22.t17 (cl @p_49) :rule refl)
+(step t22.t18 (cl (= @p_50 (! (fun_app$ veriT_vr10 veriT_vr9) :named @p_51))) :rule cong :premises (t22.t16 t22.t17))
+(step t22.t19 (cl (= @p_52 (! (less_eq$ @p_48 @p_51) :named @p_53))) :rule cong :premises (t22.t15 t22.t18))
+(step t22.t20 (cl (= @p_54 (! (=> @p_43 @p_53) :named @p_55))) :rule cong :premises (t22.t10 t22.t19))
+(step t22 (cl (! (= @p_33 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_55) :named @p_57)) :named @p_56)) :rule bind)
+(step t23 (cl (not @p_56) (not @p_33) @p_57) :rule equiv_pos2)
+(step t24 (cl @p_57) :rule th_resolution :premises (a31 t22 t23))
+(anchor :step t25 :args ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)))
+(step t25.t1 (cl (= @p_43 (! (and @p_34 @p_37 @p_39) :named @p_58))) :rule ac_simp)
+(step t25.t2 (cl (= @p_55 (! (=> @p_58 @p_53) :named @p_59))) :rule cong :premises (t25.t1))
+(step t25 (cl (! (= @p_57 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
+(step t26 (cl (not @p_60) (not @p_57) @p_61) :rule equiv_pos2)
+(step t27 (cl @p_61) :rule th_resolution :premises (t24 t25 t26))
+(anchor :step t28 :args ((:= (veriT_vr8 B_set$) veriT_vr11) (:= (veriT_vr9 B$) veriT_vr12) (:= (veriT_vr10 B_c_fun$) veriT_vr13)))
+(step t28.t1 (cl (! (= veriT_vr8 veriT_vr11) :named @p_63)) :rule refl)
+(step t28.t2 (cl (= @p_34 (! (finite$ veriT_vr11) :named @p_62))) :rule cong :premises (t28.t1))
+(step t28.t3 (cl @p_63) :rule refl)
+(step t28.t4 (cl (= @p_36 (! (= bot$ veriT_vr11) :named @p_64))) :rule cong :premises (t28.t3))
+(step t28.t5 (cl (= @p_37 (! (not @p_64) :named @p_65))) :rule cong :premises (t28.t4))
+(step t28.t6 (cl (! (= veriT_vr9 veriT_vr12) :named @p_71)) :rule refl)
+(step t28.t7 (cl @p_63) :rule refl)
+(step t28.t8 (cl (= @p_39 (! (member$ veriT_vr12 veriT_vr11) :named @p_66))) :rule cong :premises (t28.t6 t28.t7))
+(step t28.t9 (cl (= @p_58 (! (and @p_62 @p_65 @p_66) :named @p_67))) :rule cong :premises (t28.t2 t28.t5 t28.t8))
+(step t28.t10 (cl (! (= veriT_vr10 veriT_vr13) :named @p_68)) :rule refl)
+(step t28.t11 (cl @p_68) :rule refl)
+(step t28.t12 (cl @p_63) :rule refl)
+(step t28.t13 (cl (= @p_46 (! (arg_min_on$ veriT_vr13 veriT_vr11) :named @p_69))) :rule cong :premises (t28.t11 t28.t12))
+(step t28.t14 (cl (= @p_48 (! (fun_app$ veriT_vr13 @p_69) :named @p_70))) :rule cong :premises (t28.t10 t28.t13))
+(step t28.t15 (cl @p_68) :rule refl)
+(step t28.t16 (cl @p_71) :rule refl)
+(step t28.t17 (cl (= @p_51 (! (fun_app$ veriT_vr13 veriT_vr12) :named @p_72))) :rule cong :premises (t28.t15 t28.t16))
+(step t28.t18 (cl (= @p_53 (! (less_eq$ @p_70 @p_72) :named @p_73))) :rule cong :premises (t28.t14 t28.t17))
+(step t28.t19 (cl (= @p_59 (! (=> @p_67 @p_73) :named @p_74))) :rule cong :premises (t28.t9 t28.t18))
+(step t28 (cl (! (= @p_61 (! (forall ((veriT_vr11 B_set$) (veriT_vr12 B$) (veriT_vr13 B_c_fun$)) @p_74) :named @p_76)) :named @p_75)) :rule bind)
+(step t29 (cl (not @p_75) (not @p_61) @p_76) :rule equiv_pos2)
+(step t30 (cl @p_76) :rule th_resolution :premises (t27 t28 t29))
+(anchor :step t31 :args ((:= (?v0 B_c_fun$) veriT_vr20) (:= (?v1 A_b_fun$) veriT_vr21) (:= (?v2 A$) veriT_vr22)))
+(step t31.t1 (cl (! (= ?v0 veriT_vr20) :named @p_82)) :rule refl)
+(step t31.t2 (cl (! (= ?v1 veriT_vr21) :named @p_83)) :rule refl)
+(step t31.t3 (cl (= @p_78 (! (comp$ veriT_vr20 veriT_vr21) :named @p_79))) :rule cong :premises (t31.t1 t31.t2))
+(step t31.t4 (cl (! (= ?v2 veriT_vr22) :named @p_84)) :rule refl)
+(step t31.t5 (cl (= @p_80 (! (fun_app$a @p_79 veriT_vr22) :named @p_81))) :rule cong :premises (t31.t3 t31.t4))
+(step t31.t6 (cl @p_82) :rule refl)
+(step t31.t7 (cl @p_83) :rule refl)
+(step t31.t8 (cl @p_84) :rule refl)
+(step t31.t9 (cl (= @p_3 (! (fun_app$b veriT_vr21 veriT_vr22) :named @p_85))) :rule cong :premises (t31.t7 t31.t8))
+(step t31.t10 (cl (= @p_86 (! (fun_app$ veriT_vr20 @p_85) :named @p_87))) :rule cong :premises (t31.t6 t31.t9))
+(step t31.t11 (cl (= @p_88 (! (= @p_81 @p_87) :named @p_89))) :rule cong :premises (t31.t5 t31.t10))
+(step t31 (cl (! (= @p_77 (! (forall ((veriT_vr20 B_c_fun$) (veriT_vr21 A_b_fun$) (veriT_vr22 A$)) @p_89) :named @p_91)) :named @p_90)) :rule bind)
+(step t32 (cl (not @p_90) (not @p_77) @p_91) :rule equiv_pos2)
+(step t33 (cl @p_91) :rule th_resolution :premises (a33 t31 t32))
+(anchor :step t34 :args ((:= (veriT_vr20 B_c_fun$) veriT_vr23) (:= (veriT_vr21 A_b_fun$) veriT_vr24) (:= (veriT_vr22 A$) veriT_vr25)))
+(step t34.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_94)) :rule refl)
+(step t34.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_95)) :rule refl)
+(step t34.t3 (cl (= @p_79 (! (comp$ veriT_vr23 veriT_vr24) :named @p_92))) :rule cong :premises (t34.t1 t34.t2))
+(step t34.t4 (cl (! (= veriT_vr22 veriT_vr25) :named @p_96)) :rule refl)
+(step t34.t5 (cl (= @p_81 (! (fun_app$a @p_92 veriT_vr25) :named @p_93))) :rule cong :premises (t34.t3 t34.t4))
+(step t34.t6 (cl @p_94) :rule refl)
+(step t34.t7 (cl @p_95) :rule refl)
+(step t34.t8 (cl @p_96) :rule refl)
+(step t34.t9 (cl (= @p_85 (! (fun_app$b veriT_vr24 veriT_vr25) :named @p_97))) :rule cong :premises (t34.t7 t34.t8))
+(step t34.t10 (cl (= @p_87 (! (fun_app$ veriT_vr23 @p_97) :named @p_98))) :rule cong :premises (t34.t6 t34.t9))
+(step t34.t11 (cl (= @p_89 (! (= @p_93 @p_98) :named @p_99))) :rule cong :premises (t34.t5 t34.t10))
+(step t34 (cl (! (= @p_91 (! (forall ((veriT_vr23 B_c_fun$) (veriT_vr24 A_b_fun$) (veriT_vr25 A$)) @p_99) :named @p_101)) :named @p_100)) :rule bind)
+(step t35 (cl (not @p_100) (not @p_91) @p_101) :rule equiv_pos2)
+(step t36 (cl @p_101) :rule th_resolution :premises (t33 t34 t35))
+(anchor :step t37 :args ((:= (?v0 A_set$) veriT_vr34) (:= (?v1 A_b_fun$) veriT_vr35)))
+(step t37.t1 (cl (! (= ?v0 veriT_vr34) :named @p_105)) :rule refl)
+(step t37.t2 (cl (= @p_103 (! (finite$a veriT_vr34) :named @p_104))) :rule cong :premises (t37.t1))
+(step t37.t3 (cl (= ?v1 veriT_vr35)) :rule refl)
+(step t37.t4 (cl @p_105) :rule refl)
+(step t37.t5 (cl (= @p_106 (! (image$b veriT_vr35 veriT_vr34) :named @p_107))) :rule cong :premises (t37.t3 t37.t4))
+(step t37.t6 (cl (= @p_108 (! (finite$ @p_107) :named @p_109))) :rule cong :premises (t37.t5))
+(step t37.t7 (cl (= @p_110 (! (=> @p_104 @p_109) :named @p_111))) :rule cong :premises (t37.t2 t37.t6))
+(step t37 (cl (! (= @p_102 (! (forall ((veriT_vr34 A_set$) (veriT_vr35 A_b_fun$)) @p_111) :named @p_113)) :named @p_112)) :rule bind)
+(step t38 (cl (not @p_112) (not @p_102) @p_113) :rule equiv_pos2)
+(step t39 (cl @p_113) :rule th_resolution :premises (a36 t37 t38))
+(anchor :step t40 :args ((:= (veriT_vr34 A_set$) veriT_vr36) (:= (veriT_vr35 A_b_fun$) veriT_vr37)))
+(step t40.t1 (cl (! (= veriT_vr34 veriT_vr36) :named @p_115)) :rule refl)
+(step t40.t2 (cl (= @p_104 (! (finite$a veriT_vr36) :named @p_114))) :rule cong :premises (t40.t1))
+(step t40.t3 (cl (= veriT_vr35 veriT_vr37)) :rule refl)
+(step t40.t4 (cl @p_115) :rule refl)
+(step t40.t5 (cl (= @p_107 (! (image$b veriT_vr37 veriT_vr36) :named @p_116))) :rule cong :premises (t40.t3 t40.t4))
+(step t40.t6 (cl (= @p_109 (! (finite$ @p_116) :named @p_117))) :rule cong :premises (t40.t5))
+(step t40.t7 (cl (= @p_111 (! (=> @p_114 @p_117) :named @p_118))) :rule cong :premises (t40.t2 t40.t6))
+(step t40 (cl (! (= @p_113 (! (forall ((veriT_vr36 A_set$) (veriT_vr37 A_b_fun$)) @p_118) :named @p_120)) :named @p_119)) :rule bind)
+(step t41 (cl (not @p_119) (not @p_113) @p_120) :rule equiv_pos2)
+(step t42 (cl @p_120) :rule th_resolution :premises (t39 t40 t41))
+(anchor :step t43 :args ((:= (?v0 B$) veriT_vr58) (:= (?v1 A_b_fun$) veriT_vr59) (:= (?v2 A_set$) veriT_vr60)))
+(step t43.t1 (cl (! (= ?v0 veriT_vr58) :named @p_128)) :rule refl)
+(step t43.t2 (cl (! (= ?v1 veriT_vr59) :named @p_129)) :rule refl)
+(step t43.t3 (cl (! (= ?v2 veriT_vr60) :named @p_135)) :rule refl)
+(step t43.t4 (cl (= @p_122 (! (image$b veriT_vr59 veriT_vr60) :named @p_123))) :rule cong :premises (t43.t2 t43.t3))
+(step t43.t5 (cl (= @p_124 (! (member$ veriT_vr58 @p_123) :named @p_125))) :rule cong :premises (t43.t1 t43.t4))
+(anchor :step t43.t6 :args ((:= (?v3 A$) veriT_vr61)))
+(step t43.t6.t1 (cl @p_128) :rule refl)
+(step t43.t6.t2 (cl @p_129) :rule refl)
+(step t43.t6.t3 (cl (! (= ?v3 veriT_vr61) :named @p_134)) :rule refl)
+(step t43.t6.t4 (cl (= @p_130 (! (fun_app$b veriT_vr59 veriT_vr61) :named @p_131))) :rule cong :premises (t43.t6.t2 t43.t6.t3))
+(step t43.t6.t5 (cl (= @p_132 (! (= veriT_vr58 @p_131) :named @p_133))) :rule cong :premises (t43.t6.t1 t43.t6.t4))
+(step t43.t6.t6 (cl @p_134) :rule refl)
+(step t43.t6.t7 (cl @p_135) :rule refl)
+(step t43.t6.t8 (cl (= @p_136 (! (member$a veriT_vr61 veriT_vr60) :named @p_137))) :rule cong :premises (t43.t6.t6 t43.t6.t7))
+(step t43.t6.t9 (cl (= @p_138 (! (and @p_133 @p_137) :named @p_139))) :rule cong :premises (t43.t6.t5 t43.t6.t8))
+(step t43.t6.t10 (cl (= @p_140 (! (=> @p_139 false) :named @p_141))) :rule cong :premises (t43.t6.t9))
+(step t43.t6 (cl (= @p_126 (! (forall ((veriT_vr61 A$)) @p_141) :named @p_127))) :rule bind)
+(step t43.t7 (cl (= @p_142 (! (and @p_125 @p_127) :named @p_143))) :rule cong :premises (t43.t5 t43.t6))
+(step t43.t8 (cl (= @p_144 (! (=> @p_143 false) :named @p_145))) :rule cong :premises (t43.t7))
+(step t43 (cl (! (= @p_121 (! (forall ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)) @p_145) :named @p_147)) :named @p_146)) :rule bind)
+(step t44 (cl (not @p_146) (not @p_121) @p_147) :rule equiv_pos2)
+(step t45 (cl @p_147) :rule th_resolution :premises (a40 t43 t44))
+(anchor :step t46 :args ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)))
+(anchor :step t46.t1 :args ((veriT_vr61 A$)))
+(step t46.t1.t1 (cl (= @p_141 (! (not @p_139) :named @p_149))) :rule implies_simplify)
+(step t46.t1 (cl (= @p_127 (! (forall ((veriT_vr61 A$)) @p_149) :named @p_148))) :rule bind)
+(step t46.t2 (cl (= @p_143 (! (and @p_125 @p_148) :named @p_150))) :rule cong :premises (t46.t1))
+(step t46.t3 (cl (= @p_145 (! (=> @p_150 false) :named @p_151))) :rule cong :premises (t46.t2))
+(step t46.t4 (cl (= @p_151 (! (not @p_150) :named @p_152))) :rule implies_simplify)
+(step t46.t5 (cl (= @p_145 @p_152)) :rule trans :premises (t46.t3 t46.t4))
+(step t46 (cl (! (= @p_147 (! (forall ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)) @p_152) :named @p_154)) :named @p_153)) :rule bind)
+(step t47 (cl (not @p_153) (not @p_147) @p_154) :rule equiv_pos2)
+(step t48 (cl @p_154) :rule th_resolution :premises (t45 t46 t47))
+(anchor :step t49 :args ((:= (veriT_vr58 B$) veriT_vr62) (:= (veriT_vr59 A_b_fun$) veriT_vr63) (:= (veriT_vr60 A_set$) veriT_vr64)))
+(step t49.t1 (cl (! (= veriT_vr58 veriT_vr62) :named @p_158)) :rule refl)
+(step t49.t2 (cl (! (= veriT_vr59 veriT_vr63) :named @p_159)) :rule refl)
+(step t49.t3 (cl (! (= veriT_vr60 veriT_vr64) :named @p_163)) :rule refl)
+(step t49.t4 (cl (= @p_123 (! (image$b veriT_vr63 veriT_vr64) :named @p_155))) :rule cong :premises (t49.t2 t49.t3))
+(step t49.t5 (cl (= @p_125 (! (member$ veriT_vr62 @p_155) :named @p_156))) :rule cong :premises (t49.t1 t49.t4))
+(anchor :step t49.t6 :args ((:= (veriT_vr61 A$) veriT_vr65)))
+(step t49.t6.t1 (cl @p_158) :rule refl)
+(step t49.t6.t2 (cl @p_159) :rule refl)
+(step t49.t6.t3 (cl (! (= veriT_vr61 veriT_vr65) :named @p_162)) :rule refl)
+(step t49.t6.t4 (cl (= @p_131 (! (fun_app$b veriT_vr63 veriT_vr65) :named @p_160))) :rule cong :premises (t49.t6.t2 t49.t6.t3))
+(step t49.t6.t5 (cl (= @p_133 (! (= veriT_vr62 @p_160) :named @p_161))) :rule cong :premises (t49.t6.t1 t49.t6.t4))
+(step t49.t6.t6 (cl @p_162) :rule refl)
+(step t49.t6.t7 (cl @p_163) :rule refl)
+(step t49.t6.t8 (cl (= @p_137 (! (member$a veriT_vr65 veriT_vr64) :named @p_164))) :rule cong :premises (t49.t6.t6 t49.t6.t7))
+(step t49.t6.t9 (cl (= @p_139 (! (and @p_161 @p_164) :named @p_165))) :rule cong :premises (t49.t6.t5 t49.t6.t8))
+(step t49.t6.t10 (cl (= @p_149 (! (not @p_165) :named @p_166))) :rule cong :premises (t49.t6.t9))
+(step t49.t6 (cl (= @p_148 (! (forall ((veriT_vr65 A$)) @p_166) :named @p_157))) :rule bind)
+(step t49.t7 (cl (= @p_150 (! (and @p_156 @p_157) :named @p_167))) :rule cong :premises (t49.t5 t49.t6))
+(step t49.t8 (cl (= @p_152 (! (not @p_167) :named @p_168))) :rule cong :premises (t49.t7))
+(step t49 (cl (! (= @p_154 (! (forall ((veriT_vr62 B$) (veriT_vr63 A_b_fun$) (veriT_vr64 A_set$)) @p_168) :named @p_170)) :named @p_169)) :rule bind)
+(step t50 (cl (not @p_169) (not @p_154) @p_170) :rule equiv_pos2)
+(step t51 (cl @p_170) :rule th_resolution :premises (t48 t49 t50))
+(anchor :step t52 :args ((:= (?v0 B$) veriT_vr90) (:= (?v1 A_b_fun$) veriT_vr91) (:= (?v2 A$) veriT_vr92) (:= (?v3 A_set$) veriT_vr93)))
+(step t52.t1 (cl (! (= ?v1 veriT_vr91) :named @p_181)) :rule refl)
+(step t52.t2 (cl (! (= ?v2 veriT_vr92) :named @p_175)) :rule refl)
+(step t52.t3 (cl (= @p_3 (! (fun_app$b veriT_vr91 veriT_vr92) :named @p_172))) :rule cong :premises (t52.t1 t52.t2))
+(step t52.t4 (cl (! (= ?v0 veriT_vr90) :named @p_180)) :rule refl)
+(step t52.t5 (cl (= @p_173 (! (= veriT_vr90 @p_172) :named @p_174))) :rule cong :premises (t52.t3 t52.t4))
+(step t52.t6 (cl @p_175) :rule refl)
+(step t52.t7 (cl (! (= ?v3 veriT_vr93) :named @p_182)) :rule refl)
+(step t52.t8 (cl (= @p_176 (! (member$a veriT_vr92 veriT_vr93) :named @p_177))) :rule cong :premises (t52.t6 t52.t7))
+(step t52.t9 (cl (= @p_178 (! (and @p_174 @p_177) :named @p_179))) :rule cong :premises (t52.t5 t52.t8))
+(step t52.t10 (cl @p_180) :rule refl)
+(step t52.t11 (cl @p_181) :rule refl)
+(step t52.t12 (cl @p_182) :rule refl)
+(step t52.t13 (cl (= @p_183 (! (image$b veriT_vr91 veriT_vr93) :named @p_184))) :rule cong :premises (t52.t11 t52.t12))
+(step t52.t14 (cl (= @p_185 (! (member$ veriT_vr90 @p_184) :named @p_186))) :rule cong :premises (t52.t10 t52.t13))
+(step t52.t15 (cl (= @p_187 (! (=> @p_179 @p_186) :named @p_188))) :rule cong :premises (t52.t9 t52.t14))
+(step t52 (cl (! (= @p_171 (! (forall ((veriT_vr90 B$) (veriT_vr91 A_b_fun$) (veriT_vr92 A$) (veriT_vr93 A_set$)) @p_188) :named @p_190)) :named @p_189)) :rule bind)
+(step t53 (cl (not @p_189) (not @p_171) @p_190) :rule equiv_pos2)
+(step t54 (cl @p_190) :rule th_resolution :premises (a44 t52 t53))
+(anchor :step t55 :args ((:= (veriT_vr90 B$) veriT_vr94) (:= (veriT_vr91 A_b_fun$) veriT_vr95) (:= (veriT_vr92 A$) veriT_vr96) (:= (veriT_vr93 A_set$) veriT_vr97)))
+(step t55.t1 (cl (! (= veriT_vr90 veriT_vr94) :named @p_196)) :rule refl)
+(step t55.t2 (cl (! (= veriT_vr91 veriT_vr95) :named @p_197)) :rule refl)
+(step t55.t3 (cl (! (= veriT_vr92 veriT_vr96) :named @p_193)) :rule refl)
+(step t55.t4 (cl (= @p_172 (! (fun_app$b veriT_vr95 veriT_vr96) :named @p_191))) :rule cong :premises (t55.t2 t55.t3))
+(step t55.t5 (cl (= @p_174 (! (= veriT_vr94 @p_191) :named @p_192))) :rule cong :premises (t55.t1 t55.t4))
+(step t55.t6 (cl @p_193) :rule refl)
+(step t55.t7 (cl (! (= veriT_vr93 veriT_vr97) :named @p_198)) :rule refl)
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+(step t55.t9 (cl (= @p_179 (! (and @p_192 @p_194) :named @p_195))) :rule cong :premises (t55.t5 t55.t8))
+(step t55.t10 (cl @p_196) :rule refl)
+(step t55.t11 (cl @p_197) :rule refl)
+(step t55.t12 (cl @p_198) :rule refl)
+(step t55.t13 (cl (= @p_184 (! (image$b veriT_vr95 veriT_vr97) :named @p_199))) :rule cong :premises (t55.t11 t55.t12))
+(step t55.t14 (cl (= @p_186 (! (member$ veriT_vr94 @p_199) :named @p_200))) :rule cong :premises (t55.t10 t55.t13))
+(step t55.t15 (cl (= @p_188 (! (=> @p_195 @p_200) :named @p_201))) :rule cong :premises (t55.t9 t55.t14))
+(step t55 (cl (! (= @p_190 (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) @p_201) :named @p_203)) :named @p_202)) :rule bind)
+(step t56 (cl (not @p_202) (not @p_190) @p_203) :rule equiv_pos2)
+(step t57 (cl @p_203) :rule th_resolution :premises (t54 t55 t56))
+(anchor :step t58 :args ((:= (?v0 A_b_fun$) veriT_vr114) (:= (?v1 A_set$) veriT_vr115)))
+(step t58.t1 (cl (= ?v0 veriT_vr114)) :rule refl)
+(step t58.t2 (cl (! (= ?v1 veriT_vr115) :named @p_209)) :rule refl)
+(step t58.t3 (cl (= @p_205 (! (image$b veriT_vr114 veriT_vr115) :named @p_206))) :rule cong :premises (t58.t1 t58.t2))
+(step t58.t4 (cl (= @p_207 (! (= bot$ @p_206) :named @p_208))) :rule cong :premises (t58.t3))
+(step t58.t5 (cl @p_209) :rule refl)
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+(step t58.t7 (cl (= @p_212 (! (= @p_208 @p_211) :named @p_213))) :rule cong :premises (t58.t4 t58.t6))
+(step t58 (cl (! (= @p_204 (! (forall ((veriT_vr114 A_b_fun$) (veriT_vr115 A_set$)) @p_213) :named @p_215)) :named @p_214)) :rule bind)
+(step t59 (cl (not @p_214) (not @p_204) @p_215) :rule equiv_pos2)
+(step t60 (cl @p_215) :rule th_resolution :premises (a48 t58 t59))
+(anchor :step t61 :args ((:= (veriT_vr114 A_b_fun$) veriT_vr116) (:= (veriT_vr115 A_set$) veriT_vr117)))
+(step t61.t1 (cl (= veriT_vr114 veriT_vr116)) :rule refl)
+(step t61.t2 (cl (! (= veriT_vr115 veriT_vr117) :named @p_218)) :rule refl)
+(step t61.t3 (cl (= @p_206 (! (image$b veriT_vr116 veriT_vr117) :named @p_216))) :rule cong :premises (t61.t1 t61.t2))
+(step t61.t4 (cl (= @p_208 (! (= bot$ @p_216) :named @p_217))) :rule cong :premises (t61.t3))
+(step t61.t5 (cl @p_218) :rule refl)
+(step t61.t6 (cl (= @p_211 (! (= bot$a veriT_vr117) :named @p_219))) :rule cong :premises (t61.t5))
+(step t61.t7 (cl (= @p_213 (! (= @p_217 @p_219) :named @p_220))) :rule cong :premises (t61.t4 t61.t6))
+(step t61 (cl (! (= @p_215 (! (forall ((veriT_vr116 A_b_fun$) (veriT_vr117 A_set$)) @p_220) :named @p_222)) :named @p_221)) :rule bind)
+(step t62 (cl (not @p_221) (not @p_215) @p_222) :rule equiv_pos2)
+(step t63 (cl @p_222) :rule th_resolution :premises (t60 t61 t62))
+(anchor :step t64 :args ((:= (?v0 B_c_fun$) veriT_vr122) (:= (?v1 B_set$) veriT_vr123) (:= (?v2 B$) veriT_vr124) (:= (?v3 B$) veriT_vr125)))
+(step t64.t1 (cl (! (= ?v0 veriT_vr122) :named @p_226)) :rule refl)
+(step t64.t2 (cl (! (= ?v1 veriT_vr123) :named @p_234)) :rule refl)
+(step t64.t3 (cl (= @p_224 (! (inj_on$ veriT_vr122 veriT_vr123) :named @p_225))) :rule cong :premises (t64.t1 t64.t2))
+(step t64.t4 (cl @p_226) :rule refl)
+(step t64.t5 (cl (! (= ?v2 veriT_vr124) :named @p_233)) :rule refl)
+(step t64.t6 (cl (= @p_227 (! (fun_app$ veriT_vr122 veriT_vr124) :named @p_228))) :rule cong :premises (t64.t4 t64.t5))
+(step t64.t7 (cl @p_226) :rule refl)
+(step t64.t8 (cl (! (= ?v3 veriT_vr125) :named @p_237)) :rule refl)
+(step t64.t9 (cl (= @p_229 (! (fun_app$ veriT_vr122 veriT_vr125) :named @p_230))) :rule cong :premises (t64.t7 t64.t8))
+(step t64.t10 (cl (= @p_231 (! (= @p_228 @p_230) :named @p_232))) :rule cong :premises (t64.t6 t64.t9))
+(step t64.t11 (cl @p_233) :rule refl)
+(step t64.t12 (cl @p_234) :rule refl)
+(step t64.t13 (cl (= @p_235 (! (member$ veriT_vr124 veriT_vr123) :named @p_236))) :rule cong :premises (t64.t11 t64.t12))
+(step t64.t14 (cl @p_237) :rule refl)
+(step t64.t15 (cl @p_234) :rule refl)
+(step t64.t16 (cl (= @p_238 (! (member$ veriT_vr125 veriT_vr123) :named @p_239))) :rule cong :premises (t64.t14 t64.t15))
+(step t64.t17 (cl (= @p_240 (! (and @p_236 @p_239) :named @p_241))) :rule cong :premises (t64.t13 t64.t16))
+(step t64.t18 (cl (= @p_242 (! (and @p_232 @p_241) :named @p_243))) :rule cong :premises (t64.t10 t64.t17))
+(step t64.t19 (cl (= @p_244 (! (and @p_225 @p_243) :named @p_245))) :rule cong :premises (t64.t3 t64.t18))
+(step t64.t20 (cl @p_237) :rule refl)
+(step t64.t21 (cl @p_233) :rule refl)
+(step t64.t22 (cl (= @p_246 (! (= veriT_vr124 veriT_vr125) :named @p_247))) :rule cong :premises (t64.t20 t64.t21))
+(step t64.t23 (cl (= @p_248 (! (=> @p_245 @p_247) :named @p_249))) :rule cong :premises (t64.t19 t64.t22))
+(step t64 (cl (! (= @p_223 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_249) :named @p_251)) :named @p_250)) :rule bind)
+(step t65 (cl (not @p_250) (not @p_223) @p_251) :rule equiv_pos2)
+(step t66 (cl @p_251) :rule th_resolution :premises (a50 t64 t65))
+(anchor :step t67 :args ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)))
+(step t67.t1 (cl (= @p_245 (! (and @p_225 @p_232 @p_236 @p_239) :named @p_252))) :rule ac_simp)
+(step t67.t2 (cl (= @p_249 (! (=> @p_252 @p_247) :named @p_253))) :rule cong :premises (t67.t1))
+(step t67 (cl (! (= @p_251 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_253) :named @p_255)) :named @p_254)) :rule bind)
+(step t68 (cl (not @p_254) (not @p_251) @p_255) :rule equiv_pos2)
+(step t69 (cl @p_255) :rule th_resolution :premises (t66 t67 t68))
+(anchor :step t70 :args ((:= (veriT_vr122 B_c_fun$) veriT_vr126) (:= (veriT_vr123 B_set$) veriT_vr127) (:= (veriT_vr124 B$) veriT_vr128) (:= (veriT_vr125 B$) veriT_vr129)))
+(step t70.t1 (cl (! (= veriT_vr122 veriT_vr126) :named @p_257)) :rule refl)
+(step t70.t2 (cl (! (= veriT_vr123 veriT_vr127) :named @p_262)) :rule refl)
+(step t70.t3 (cl (= @p_225 (! (inj_on$ veriT_vr126 veriT_vr127) :named @p_256))) :rule cong :premises (t70.t1 t70.t2))
+(step t70.t4 (cl @p_257) :rule refl)
+(step t70.t5 (cl (! (= veriT_vr124 veriT_vr128) :named @p_261)) :rule refl)
+(step t70.t6 (cl (= @p_228 (! (fun_app$ veriT_vr126 veriT_vr128) :named @p_258))) :rule cong :premises (t70.t4 t70.t5))
+(step t70.t7 (cl @p_257) :rule refl)
+(step t70.t8 (cl (! (= veriT_vr125 veriT_vr129) :named @p_264)) :rule refl)
+(step t70.t9 (cl (= @p_230 (! (fun_app$ veriT_vr126 veriT_vr129) :named @p_259))) :rule cong :premises (t70.t7 t70.t8))
+(step t70.t10 (cl (= @p_232 (! (= @p_258 @p_259) :named @p_260))) :rule cong :premises (t70.t6 t70.t9))
+(step t70.t11 (cl @p_261) :rule refl)
+(step t70.t12 (cl @p_262) :rule refl)
+(step t70.t13 (cl (= @p_236 (! (member$ veriT_vr128 veriT_vr127) :named @p_263))) :rule cong :premises (t70.t11 t70.t12))
+(step t70.t14 (cl @p_264) :rule refl)
+(step t70.t15 (cl @p_262) :rule refl)
+(step t70.t16 (cl (= @p_239 (! (member$ veriT_vr129 veriT_vr127) :named @p_265))) :rule cong :premises (t70.t14 t70.t15))
+(step t70.t17 (cl (= @p_252 (! (and @p_256 @p_260 @p_263 @p_265) :named @p_266))) :rule cong :premises (t70.t3 t70.t10 t70.t13 t70.t16))
+(step t70.t18 (cl @p_261) :rule refl)
+(step t70.t19 (cl @p_264) :rule refl)
+(step t70.t20 (cl (= @p_247 (! (= veriT_vr128 veriT_vr129) :named @p_267))) :rule cong :premises (t70.t18 t70.t19))
+(step t70.t21 (cl (= @p_253 (! (=> @p_266 @p_267) :named @p_268))) :rule cong :premises (t70.t17 t70.t20))
+(step t70 (cl (! (= @p_255 (! (forall ((veriT_vr126 B_c_fun$) (veriT_vr127 B_set$) (veriT_vr128 B$) (veriT_vr129 B$)) @p_268) :named @p_270)) :named @p_269)) :rule bind)
+(step t71 (cl (not @p_269) (not @p_255) @p_270) :rule equiv_pos2)
+(step t72 (cl @p_270) :rule th_resolution :premises (t69 t70 t71))
+(anchor :step t73 :args ((:= (?v0 C$) veriT_vr130) (:= (?v1 C$) veriT_vr131)))
+(step t73.t1 (cl (! (= ?v0 veriT_vr130) :named @p_274)) :rule refl)
+(step t73.t2 (cl (! (= ?v1 veriT_vr131) :named @p_275)) :rule refl)
+(step t73.t3 (cl (= @p_272 (! (less$ veriT_vr130 veriT_vr131) :named @p_273))) :rule cong :premises (t73.t1 t73.t2))
+(step t73.t4 (cl @p_274) :rule refl)
+(step t73.t5 (cl @p_275) :rule refl)
+(step t73.t6 (cl (= @p_276 (! (less_eq$ veriT_vr130 veriT_vr131) :named @p_277))) :rule cong :premises (t73.t4 t73.t5))
+(step t73.t7 (cl @p_274) :rule refl)
+(step t73.t8 (cl @p_275) :rule refl)
+(step t73.t9 (cl (= @p_278 (! (= veriT_vr130 veriT_vr131) :named @p_279))) :rule cong :premises (t73.t7 t73.t8))
+(step t73.t10 (cl (= @p_280 (! (not @p_279) :named @p_281))) :rule cong :premises (t73.t9))
+(step t73.t11 (cl (= @p_282 (! (and @p_277 @p_281) :named @p_283))) :rule cong :premises (t73.t6 t73.t10))
+(step t73.t12 (cl (= @p_284 (! (= @p_273 @p_283) :named @p_285))) :rule cong :premises (t73.t3 t73.t11))
+(step t73 (cl (! (= @p_271 (! (forall ((veriT_vr130 C$) (veriT_vr131 C$)) @p_285) :named @p_287)) :named @p_286)) :rule bind)
+(step t74 (cl (not @p_286) (not @p_271) @p_287) :rule equiv_pos2)
+(step t75 (cl @p_287) :rule th_resolution :premises (a51 t73 t74))
+(anchor :step t76 :args ((:= (veriT_vr130 C$) veriT_vr132) (:= (veriT_vr131 C$) veriT_vr133)))
+(step t76.t1 (cl (! (= veriT_vr130 veriT_vr132) :named @p_289)) :rule refl)
+(step t76.t2 (cl (! (= veriT_vr131 veriT_vr133) :named @p_290)) :rule refl)
+(step t76.t3 (cl (= @p_273 (! (less$ veriT_vr132 veriT_vr133) :named @p_288))) :rule cong :premises (t76.t1 t76.t2))
+(step t76.t4 (cl @p_289) :rule refl)
+(step t76.t5 (cl @p_290) :rule refl)
+(step t76.t6 (cl (= @p_277 (! (less_eq$ veriT_vr132 veriT_vr133) :named @p_291))) :rule cong :premises (t76.t4 t76.t5))
+(step t76.t7 (cl @p_289) :rule refl)
+(step t76.t8 (cl @p_290) :rule refl)
+(step t76.t9 (cl (= @p_279 (! (= veriT_vr132 veriT_vr133) :named @p_292))) :rule cong :premises (t76.t7 t76.t8))
+(step t76.t10 (cl (= @p_281 (! (not @p_292) :named @p_293))) :rule cong :premises (t76.t9))
+(step t76.t11 (cl (= @p_283 (! (and @p_291 @p_293) :named @p_294))) :rule cong :premises (t76.t6 t76.t10))
+(step t76.t12 (cl (= @p_285 (! (= @p_288 @p_294) :named @p_295))) :rule cong :premises (t76.t3 t76.t11))
+(step t76 (cl (! (= @p_287 (! (forall ((veriT_vr132 C$) (veriT_vr133 C$)) @p_295) :named @p_297)) :named @p_296)) :rule bind)
+(step t77 (cl (not @p_296) (not @p_287) @p_297) :rule equiv_pos2)
+(step t78 (cl @p_297) :rule th_resolution :premises (t75 t76 t77))
+(anchor :step t79 :args ((:= (?v0 A$) veriT_vr134)))
+(step t79.t1 (cl (! (= ?v0 veriT_vr134) :named @p_302)) :rule refl)
+(step t79.t2 (cl (= @p_300 (! (member$a veriT_vr134 b$) :named @p_301))) :rule cong :premises (t79.t1))
+(step t79.t3 (cl @p_302) :rule refl)
+(step t79.t4 (cl (= @p_303 (! (fun_app$a @p_4 veriT_vr134) :named @p_304))) :rule cong :premises (t79.t3))
+(step t79.t5 (cl (= @p_305 (! (less$ @p_304 @p_299) :named @p_306))) :rule cong :premises (t79.t4))
+(step t79.t6 (cl (= @p_307 (! (and @p_301 @p_306) :named @p_308))) :rule cong :premises (t79.t2 t79.t5))
+(step t79 (cl (= @p_298 (! (exists ((veriT_vr134 A$)) @p_308) :named @p_310))) :rule bind)
+(step t80 (cl (! (= @p_309 (! (not @p_310) :named @p_312)) :named @p_311)) :rule cong :premises (t79))
+(step t81 (cl (! (not @p_311) :named @p_314) (! (not @p_309) :named @p_313) @p_312) :rule equiv_pos2)
+(step t82 (cl (not @p_313) @p_298) :rule not_not)
+(step t83 (cl @p_314 @p_298 @p_312) :rule th_resolution :premises (t82 t81))
+(step t84 (cl @p_312) :rule th_resolution :premises (a27 t80 t83))
+(anchor :step t85 :args ((:= (veriT_vr134 A$) veriT_vr135)))
+(step t85.t1 (cl (! (= veriT_vr134 veriT_vr135) :named @p_316)) :rule refl)
+(step t85.t2 (cl (= @p_301 (! (member$a veriT_vr135 b$) :named @p_315))) :rule cong :premises (t85.t1))
+(step t85.t3 (cl @p_316) :rule refl)
+(step t85.t4 (cl (= @p_304 (! (fun_app$a @p_4 veriT_vr135) :named @p_317))) :rule cong :premises (t85.t3))
+(step t85.t5 (cl (= @p_306 (! (less$ @p_317 @p_299) :named @p_318))) :rule cong :premises (t85.t4))
+(step t85.t6 (cl (= @p_308 (! (and @p_315 @p_318) :named @p_319))) :rule cong :premises (t85.t2 t85.t5))
+(step t85 (cl (= @p_310 (! (exists ((veriT_vr135 A$)) @p_319) :named @p_320))) :rule bind)
+(step t86 (cl (! (= @p_312 (! (not @p_320) :named @p_322)) :named @p_321)) :rule cong :premises (t85))
+(step t87 (cl (! (not @p_321) :named @p_324) (! (not @p_312) :named @p_323) @p_322) :rule equiv_pos2)
+(step t88 (cl (not @p_323) @p_310) :rule not_not)
+(step t89 (cl @p_324 @p_310 @p_322) :rule th_resolution :premises (t88 t87))
+(step t90 (cl @p_322) :rule th_resolution :premises (t84 t86 t89))
+(step t91 (cl (= @p_320 (! (not (! (forall ((veriT_vr135 A$)) (not @p_319)) :named @p_330)) :named @p_325))) :rule connective_def)
+(step t92 (cl (! (= @p_322 (! (not @p_325) :named @p_327)) :named @p_326)) :rule cong :premises (t91))
+(step t93 (cl (! (not @p_326) :named @p_329) (! (not @p_322) :named @p_328) @p_327) :rule equiv_pos2)
+(step t94 (cl (not @p_328) @p_320) :rule not_not)
+(step t95 (cl @p_329 @p_320 @p_327) :rule th_resolution :premises (t94 t93))
+(step t96 (cl (not @p_327) @p_330) :rule not_not)
+(step t97 (cl @p_329 @p_320 @p_330) :rule th_resolution :premises (t96 t95))
+(step t98 (cl @p_327) :rule th_resolution :premises (t90 t92 t97))
+(step t99 (cl @p_330) :rule th_resolution :premises (t96 t98))
+(step t100 (cl (or (! (not @p_203) :named @p_421) (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) (or (not @p_192) (not @p_194) @p_200)) :named @p_422))) :rule qnt_cnf)
+(step t101 (cl (or (! (not @p_222) :named @p_339) (! (= (! (= bot$ @p_6) :named @p_335) @p_331) :named @p_337))) :rule forall_inst :args ((:= veriT_vr116 g$) (:= veriT_vr117 b$)))
+(step t102 (cl (or (! (not @p_120) :named @p_342) (! (=> @p_332 (! (finite$ @p_6) :named @p_334)) :named @p_341))) :rule forall_inst :args ((:= veriT_vr36 b$) (:= veriT_vr37 g$)))
+(step t103 (cl (or (! (not @p_101) :named @p_344) (! (= @p_299 (! (fun_app$ f$ @p_333) :named @p_354)) :named @p_345))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 @p_5)))
+(step t104 (cl (or (! (not @p_32) :named @p_351) (! (=> (! (and @p_334 (! (not @p_335) :named @p_338)) :named @p_346) (! (member$ @p_336 @p_6) :named @p_350)) :named @p_349))) :rule forall_inst :args ((:= veriT_vr2 @p_6) (:= veriT_vr3 f$)))
+(step t105 (cl (! (not @p_337) :named @p_340) @p_338 @p_331) :rule equiv_pos2)
+(step t106 (cl @p_339 @p_337) :rule or :premises (t101))
+(step t107 (cl @p_340 @p_338) :rule resolution :premises (t105 a25))
+(step t108 (cl @p_337) :rule resolution :premises (t106 t63))
+(step t109 (cl @p_338) :rule resolution :premises (t107 t108))
+(step t110 (cl (! (not @p_341) :named @p_343) (not @p_332) @p_334) :rule implies_pos)
+(step t111 (cl @p_342 @p_341) :rule or :premises (t102))
+(step t112 (cl @p_343 @p_334) :rule resolution :premises (t110 a24))
+(step t113 (cl @p_341) :rule resolution :premises (t111 t42))
+(step t114 (cl @p_334) :rule resolution :premises (t112 t113))
+(step t115 (cl @p_344 @p_345) :rule or :premises (t103))
+(step t116 (cl @p_345) :rule resolution :premises (t115 t36))
+(step t117 (cl @p_346 (! (not @p_334) :named @p_348) (! (not @p_338) :named @p_347)) :rule and_neg)
+(step t118 (cl (not @p_347) @p_335) :rule not_not)
+(step t119 (cl @p_346 @p_348 @p_335) :rule th_resolution :premises (t118 t117))
+(step t120 (cl (! (not @p_349) :named @p_352) (not @p_346) @p_350) :rule implies_pos)
+(step t121 (cl @p_351 @p_349) :rule or :premises (t104))
+(step t122 (cl @p_346) :rule resolution :premises (t119 t109 t114))
+(step t123 (cl @p_352 @p_350) :rule resolution :premises (t120 t122))
+(step t124 (cl @p_349) :rule resolution :premises (t121 t21))
+(step t125 (cl @p_350) :rule resolution :premises (t123 t124))
+(step t126 (cl (or (! (not @p_270) :named @p_410) (! (=> (! (and @p_353 (! (= @p_354 (! (fun_app$ f$ @p_336) :named @p_406)) :named @p_408) @p_350 (! (member$ @p_333 @p_6) :named @p_405)) :named @p_407) @p_355) :named @p_409))) :rule forall_inst :args ((:= veriT_vr126 f$) (:= veriT_vr127 @p_6) (:= veriT_vr128 @p_336) (:= veriT_vr129 @p_333)))
+(step t127 (cl (or (! (not @p_170) :named @p_401) (! (not (! (and @p_350 (! (forall ((veriT_vr65 A$)) (! (not (! (and (! (= @p_336 (! (fun_app$b g$ veriT_vr65) :named @p_359)) :named @p_361) (! (member$a veriT_vr65 b$) :named @p_364)) :named @p_366)) :named @p_368)) :named @p_358)) :named @p_370)) :named @p_356))) :rule forall_inst :args ((:= veriT_vr62 @p_336) (:= veriT_vr63 g$) (:= veriT_vr64 b$)))
+(anchor :step t128)
+(assume t128.h1 @p_356)
+(anchor :step t128.t2 :args ((:= (veriT_vr65 A$) veriT_vr144)))
+(step t128.t2.t1 (cl (! (= veriT_vr65 veriT_vr144) :named @p_363)) :rule refl)
+(step t128.t2.t2 (cl (= @p_359 (! (fun_app$b g$ veriT_vr144) :named @p_360))) :rule cong :premises (t128.t2.t1))
+(step t128.t2.t3 (cl (= @p_361 (! (= @p_336 @p_360) :named @p_362))) :rule cong :premises (t128.t2.t2))
+(step t128.t2.t4 (cl @p_363) :rule refl)
+(step t128.t2.t5 (cl (= @p_364 (! (member$a veriT_vr144 b$) :named @p_365))) :rule cong :premises (t128.t2.t4))
+(step t128.t2.t6 (cl (= @p_366 (! (and @p_362 @p_365) :named @p_367))) :rule cong :premises (t128.t2.t3 t128.t2.t5))
+(step t128.t2.t7 (cl (= @p_368 (! (not @p_367) :named @p_369))) :rule cong :premises (t128.t2.t6))
+(step t128.t2 (cl (= @p_358 (! (forall ((veriT_vr144 A$)) @p_369) :named @p_371))) :rule bind)
+(step t128.t3 (cl (= @p_370 (! (and @p_350 @p_371) :named @p_372))) :rule cong :premises (t128.t2))
+(step t128.t4 (cl (! (= @p_356 (! (not @p_372) :named @p_375)) :named @p_373)) :rule cong :premises (t128.t3))
+(step t128.t5 (cl (! (not @p_373) :named @p_376) (! (not @p_356) :named @p_374) @p_375) :rule equiv_pos2)
+(step t128.t6 (cl (! (not @p_374) :named @p_400) @p_370) :rule not_not)
+(step t128.t7 (cl @p_376 @p_370 @p_375) :rule th_resolution :premises (t128.t6 t128.t5))
+(step t128.t8 (cl @p_375) :rule th_resolution :premises (t128.h1 t128.t4 t128.t7))
+(anchor :step t128.t9 :args ((:= (veriT_vr144 A$) veriT_vr145)))
+(step t128.t9.t1 (cl (! (= veriT_vr144 veriT_vr145) :named @p_380)) :rule refl)
+(step t128.t9.t2 (cl (= @p_360 @p_378)) :rule cong :premises (t128.t9.t1))
+(step t128.t9.t3 (cl (= @p_362 @p_379)) :rule cong :premises (t128.t9.t2))
+(step t128.t9.t4 (cl @p_380) :rule refl)
+(step t128.t9.t5 (cl (= @p_365 @p_381)) :rule cong :premises (t128.t9.t4))
+(step t128.t9.t6 (cl (= @p_367 @p_382)) :rule cong :premises (t128.t9.t3 t128.t9.t5))
+(step t128.t9.t7 (cl (= @p_369 @p_377)) :rule cong :premises (t128.t9.t6))
+(step t128.t9 (cl (= @p_371 (! (forall ((veriT_vr145 A$)) @p_377) :named @p_383))) :rule bind)
+(step t128.t10 (cl (= @p_372 (! (and @p_350 @p_383) :named @p_384))) :rule cong :premises (t128.t9))
+(step t128.t11 (cl (! (= @p_375 (! (not @p_384) :named @p_386)) :named @p_385)) :rule cong :premises (t128.t10))
+(step t128.t12 (cl (! (not @p_385) :named @p_388) (! (not @p_375) :named @p_387) @p_386) :rule equiv_pos2)
+(step t128.t13 (cl (not @p_387) @p_372) :rule not_not)
+(step t128.t14 (cl @p_388 @p_372 @p_386) :rule th_resolution :premises (t128.t13 t128.t12))
+(step t128.t15 (cl @p_386) :rule th_resolution :premises (t128.t8 t128.t11 t128.t14))
+(anchor :step t128.t16 :args ((:= (veriT_vr145 A$) veriT_sk0)))
+(step t128.t16.t1 (cl (! (= veriT_vr145 veriT_sk0) :named @p_392)) :rule refl)
+(step t128.t16.t2 (cl (= @p_378 (! (fun_app$b g$ veriT_sk0) :named @p_390))) :rule cong :premises (t128.t16.t1))
+(step t128.t16.t3 (cl (= @p_379 (! (= @p_336 @p_390) :named @p_391))) :rule cong :premises (t128.t16.t2))
+(step t128.t16.t4 (cl @p_392) :rule refl)
+(step t128.t16.t5 (cl (= @p_381 (! (member$a veriT_sk0 b$) :named @p_393))) :rule cong :premises (t128.t16.t4))
+(step t128.t16.t6 (cl (= @p_382 (! (and @p_391 @p_393) :named @p_394))) :rule cong :premises (t128.t16.t3 t128.t16.t5))
+(step t128.t16.t7 (cl (= @p_377 (! (not @p_394) :named @p_389))) :rule cong :premises (t128.t16.t6))
+(step t128.t16 (cl (= @p_383 @p_389)) :rule sko_forall)
+(step t128.t17 (cl (= @p_384 (! (and @p_350 @p_389) :named @p_395))) :rule cong :premises (t128.t16))
+(step t128.t18 (cl (! (= @p_386 (! (not @p_395) :named @p_396)) :named @p_397)) :rule cong :premises (t128.t17))
+(step t128.t19 (cl (! (not @p_397) :named @p_399) (! (not @p_386) :named @p_398) @p_396) :rule equiv_pos2)
+(step t128.t20 (cl (not @p_398) @p_384) :rule not_not)
+(step t128.t21 (cl @p_399 @p_384 @p_396) :rule th_resolution :premises (t128.t20 t128.t19))
+(step t128.t22 (cl @p_396) :rule th_resolution :premises (t128.t15 t128.t18 t128.t21))
+(step t128 (cl @p_374 @p_396) :rule subproof :discharge (h1))
+(step t129 (cl @p_400 @p_370) :rule not_not)
+(step t130 (cl @p_370 @p_396) :rule th_resolution :premises (t129 t128))
+(step t131 (cl @p_401 @p_356) :rule or :premises (t127))
+(step t132 (cl (! (or @p_401 @p_396) :named @p_403) (! (not @p_401) :named @p_402)) :rule or_neg)
+(step t133 (cl (not @p_402) @p_170) :rule not_not)
+(step t134 (cl @p_403 @p_170) :rule th_resolution :premises (t133 t132))
+(step t135 (cl @p_403 (! (not @p_396) :named @p_404)) :rule or_neg)
+(step t136 (cl (not @p_404) @p_395) :rule not_not)
+(step t137 (cl @p_403 @p_395) :rule th_resolution :premises (t136 t135))
+(step t138 (cl @p_403) :rule th_resolution :premises (t131 t130 t134 t137))
+(step t139 (cl (or (! (not @p_76) :named @p_420) (! (=> (! (and @p_334 @p_338 @p_405) :named @p_417) (! (less_eq$ @p_406 @p_354) :named @p_419)) :named @p_418))) :rule forall_inst :args ((:= veriT_vr11 @p_6) (:= veriT_vr12 @p_333) (:= veriT_vr13 f$)))
+(step t140 (cl @p_407 (not @p_353) (! (not @p_408) :named @p_411) (! (not @p_350) :named @p_415) (! (not @p_405) :named @p_412)) :rule and_neg)
+(step t141 (cl (! (not @p_409) :named @p_413) (! (not @p_407) :named @p_414) @p_355) :rule implies_pos)
+(step t142 (cl @p_410 @p_409) :rule or :premises (t126))
+(step t143 (cl @p_407 @p_411 @p_412) :rule resolution :premises (t140 a23 t125))
+(step t144 (cl @p_413 @p_414) :rule resolution :premises (t141 a52))
+(step t145 (cl @p_409) :rule resolution :premises (t142 t72))
+(step t146 (cl @p_414) :rule resolution :premises (t144 t145))
+(step t147 (cl @p_389 @p_391) :rule and_pos)
+(step t148 (cl @p_389 @p_393) :rule and_pos)
+(step t149 (cl @p_395 @p_415 (! (not @p_389) :named @p_416)) :rule and_neg)
+(step t150 (cl (not @p_416) @p_394) :rule not_not)
+(step t151 (cl @p_395 @p_415 @p_394) :rule th_resolution :premises (t150 t149))
+(step t152 (cl @p_401 @p_396) :rule or :premises (t138))
+(step t153 (cl @p_395 @p_394) :rule resolution :premises (t151 t125))
+(step t154 (cl @p_396) :rule resolution :premises (t152 t51))
+(step t155 (cl @p_394) :rule resolution :premises (t153 t154))
+(step t156 (cl @p_391) :rule resolution :premises (t147 t155))
+(step t157 (cl @p_393) :rule resolution :premises (t148 t155))
+(step t158 (cl @p_417 @p_348 @p_347 @p_412) :rule and_neg)
+(step t159 (cl @p_417 @p_348 @p_335 @p_412) :rule th_resolution :premises (t118 t158))
+(step t160 (cl (not @p_418) (not @p_417) @p_419) :rule implies_pos)
+(step t161 (cl @p_420 @p_418) :rule or :premises (t139))
+(step t162 (cl @p_417 @p_412) :rule resolution :premises (t159 t109 t114))
+(step t163 (cl @p_418) :rule resolution :premises (t161 t30))
+(step t164 (cl @p_421 @p_422) :rule or :premises (t100))
+(step t165 (cl (or (! (not @p_422) :named @p_424) (! (or (! (not (! (= @p_333 @p_333) :named @p_430)) :named @p_431) (! (not @p_423) :named @p_429) @p_405) :named @p_425))) :rule forall_inst :args ((:= veriT_vr94 @p_333) (:= veriT_vr95 g$) (:= veriT_vr96 @p_5) (:= veriT_vr97 b$)))
+(step t166 (cl @p_424 @p_425) :rule or :premises (t165))
+(step t167 (cl (! (or @p_421 @p_425) :named @p_427) (! (not @p_421) :named @p_426)) :rule or_neg)
+(step t168 (cl (not @p_426) @p_203) :rule not_not)
+(step t169 (cl @p_427 @p_203) :rule th_resolution :premises (t168 t167))
+(step t170 (cl @p_427 (! (not @p_425) :named @p_428)) :rule or_neg)
+(step t171 (cl @p_427) :rule th_resolution :premises (t164 t166 t169 t170))
+(anchor :step t172)
+(assume t172.h1 @p_425)
+(step t172.t2 (cl (= @p_430 true)) :rule eq_simplify)
+(step t172.t3 (cl (= @p_431 (! (not true) :named @p_432))) :rule cong :premises (t172.t2))
+(step t172.t4 (cl (= @p_432 false)) :rule not_simplify)
+(step t172.t5 (cl (= @p_431 false)) :rule trans :premises (t172.t3 t172.t4))
+(step t172.t6 (cl (= @p_425 (! (or false @p_429 @p_405) :named @p_433))) :rule cong :premises (t172.t5))
+(step t172.t7 (cl (= @p_433 (! (or @p_429 @p_405) :named @p_434))) :rule or_simplify)
+(step t172.t8 (cl (! (= @p_425 @p_434) :named @p_435)) :rule trans :premises (t172.t6 t172.t7))
+(step t172.t9 (cl (not @p_435) @p_428 @p_434) :rule equiv_pos2)
+(step t172.t10 (cl @p_434) :rule th_resolution :premises (t172.h1 t172.t8 t172.t9))
+(step t172 (cl @p_428 @p_434) :rule subproof :discharge (h1))
+(step t173 (cl @p_421 @p_425) :rule or :premises (t171))
+(step t174 (cl (! (or @p_421 @p_434) :named @p_436) @p_426) :rule or_neg)
+(step t175 (cl @p_436 @p_203) :rule th_resolution :premises (t168 t174))
+(step t176 (cl @p_436 (! (not @p_434) :named @p_437)) :rule or_neg)
+(step t177 (cl @p_436) :rule th_resolution :premises (t173 t172 t175 t176))
+(step t178 (cl @p_437 @p_429 @p_405) :rule or_pos)
+(step t179 (cl @p_421 @p_434) :rule or :premises (t177))
+(step t180 (cl @p_437 @p_405) :rule resolution :premises (t178 a26))
+(step t181 (cl @p_434) :rule resolution :premises (t179 t57))
+(step t182 (cl @p_405) :rule resolution :premises (t180 t181))
+(step t183 (cl @p_411) :rule resolution :premises (t143 t182 t146))
+(step t184 (cl @p_417) :rule resolution :premises (t162 t182))
+(step t185 (cl @p_419) :rule resolution :premises (t160 t184 t163))
+(step t186 (cl (or @p_325 (! (not (! (and @p_393 (! (less$ (! (fun_app$a @p_4 veriT_sk0) :named @p_438) @p_299) :named @p_440)) :named @p_439)) :named @p_441))) :rule forall_inst :args ((:= veriT_vr135 veriT_sk0)))
+(step t187 (cl (or (! (not @p_297) :named @p_448) (! (= (! (less$ @p_406 @p_354) :named @p_447) (! (and @p_419 @p_411) :named @p_443)) :named @p_446))) :rule forall_inst :args ((:= veriT_vr132 @p_406) (:= veriT_vr133 @p_354)))
+(step t188 (cl (or @p_344 (! (= @p_438 (! (fun_app$ f$ @p_390) :named @p_451)) :named @p_450))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 veriT_sk0)))
+(step t189 (cl @p_439 (not @p_393) (! (not @p_440) :named @p_442)) :rule and_neg)
+(step t190 (cl @p_325 @p_441) :rule or :premises (t186))
+(step t191 (cl @p_439 @p_442) :rule resolution :premises (t189 t157))
+(step t192 (cl @p_441) :rule resolution :premises (t190 t99))
+(step t193 (cl @p_442) :rule resolution :premises (t191 t192))
+(step t194 (cl @p_443 (! (not @p_419) :named @p_445) (! (not @p_411) :named @p_444)) :rule and_neg)
+(step t195 (cl (not @p_444) @p_408) :rule not_not)
+(step t196 (cl @p_443 @p_445 @p_408) :rule th_resolution :premises (t195 t194))
+(step t197 (cl (! (not @p_446) :named @p_449) @p_447 (not @p_443)) :rule equiv_pos1)
+(step t198 (cl @p_448 @p_446) :rule or :premises (t187))
+(step t199 (cl @p_443) :rule resolution :premises (t196 t183 t185))
+(step t200 (cl @p_449 @p_447) :rule resolution :premises (t197 t199))
+(step t201 (cl @p_446) :rule resolution :premises (t198 t78))
+(step t202 (cl @p_447) :rule resolution :premises (t200 t201))
+(step t203 (cl @p_344 @p_450) :rule or :premises (t188))
+(step t204 (cl @p_450) :rule resolution :premises (t203 t36))
+(step t205 (cl (not (! (= @p_406 @p_438) :named @p_452)) (! (not @p_345) :named @p_457) (! (not @p_447) :named @p_458) @p_440) :rule eq_congruent_pred)
+(step t206 (cl (not (! (= @p_406 @p_451) :named @p_453)) (! (not @p_450) :named @p_456) @p_452) :rule eq_transitive)
+(step t207 (cl (not (! (= f$ f$) :named @p_454)) (! (not @p_391) :named @p_455) @p_453) :rule eq_congruent)
+(step t208 (cl @p_454) :rule eq_reflexive)
+(step t209 (cl @p_455 @p_453) :rule th_resolution :premises (t207 t208))
+(step t210 (cl @p_456 @p_452 @p_455) :rule th_resolution :premises (t206 t209))
+(step t211 (cl @p_457 @p_458 @p_440 @p_456 @p_455) :rule th_resolution :premises (t205 t210))
+(step t212 (cl) :rule resolution :premises (t211 t116 t156 t193 t202 t204))
+ba9da4ba7350e0a8fc453119da89963e8ee28018 323 0
+unsat
+(assume a1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_2)) :named @p_9)) :named @p_6) (! (= ?v0 (! (joinpaths$ @p_1 (! (rec_join$ @p_2) :named @p_95)) :named @p_7)) :named @p_97)) :named @p_99) false) :named @p_101)) :named @p_88)) :named @p_103)) :named @p_105)) :named @p_107) false) :named @p_109) (! (=> (! (and (! (= @p_3 @p_3) :named @p_112) (! (and (! (=> (! (and @p_4 (! (= uu$ @p_3) :named @p_115)) :named @p_117) false) :named @p_119) (! (and (! (forall ((?v2 B$)) (! (=> (! (and @p_5 (! (= @p_3 @p_1) :named @p_125)) :named @p_127) false) :named @p_129)) :named @p_121) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and @p_6 (! (= @p_3 @p_7) :named @p_137)) :named @p_139) false) :named @p_141)) :named @p_131)) :named @p_143)) :named @p_145)) :named @p_147) false) :named @p_149)) :named @p_151)) :named @p_53) (! (= (! (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (! (=> (! (and (! (= (! (rec_join$ ?v0) :named @p_10) ?v1) :named @p_19) (! (and (! (=> (! (and (! (= nil$ ?v0) :named @p_11) (! (= uu$ ?v1) :named @p_20)) :named @p_22) false) :named @p_24) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= @p_8 ?v0) :named @p_17) (! (= @p_1 ?v1) :named @p_27)) :named @p_29) false) :named @p_31)) :named @p_25) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= @p_9 ?v0) :named @p_18) (! (= @p_7 ?v1) :named @p_35)) :named @p_37) false) :named @p_39)) :named @p_33)) :named @p_41)) :named @p_43)) :named @p_45) false) :named @p_47)) :named @p_14) (! (forall ((?v0 B_list$)) (! (=> (! (and (! (= @p_10 @p_10) :named @p_15) (! (and (! (=> (! (and @p_11 (! (= uu$ @p_10) :named @p_21)) :named @p_23) false) :named @p_16) (! (and (! (forall ((?v1 B$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 nil$) :named @p_162)) :named @p_163) (! (= @p_10 (! (coeff_cube_to_path$ ?v1) :named @p_12)) :named @p_165)) :named @p_166) false) :named @p_167)) :named @p_161) (! (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_13)) :named @p_169)) :named @p_170) (! (= @p_10 (! (joinpaths$ @p_12 (! (rec_join$ @p_13) :named @p_175)) :named @p_176)) :named @p_177)) :named @p_178) false) :named @p_179)) :named @p_168)) :named @p_180)) :named @p_181)) :named @p_182) false) :named @p_183)) :named @p_51)) :named @p_49)) :named @p_52)) :named @p_55))
 (anchor :step t2 :args ((?v0 B_list$) (:= (?v1 Real_a_fun$) @p_10)))
 (step t2.t1 (cl @p_19) :rule refl)
 (step t2.t2 (cl (= @p_19 @p_15)) :rule cong :premises (t2.t1))
@@ -7468,7 +7468,7 @@
 (step t6 (cl (! (not @p_57) :named @p_60) (! (not @p_55) :named @p_59) @p_58) :rule equiv_pos2)
 (step t7 (cl (not @p_59) @p_52) :rule not_not)
 (step t8 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t7 t6))
-(step t9 (cl @p_58) :rule th_resolution :premises (axiom1 t5 t8))
+(step t9 (cl @p_58) :rule th_resolution :premises (a1 t5 t8))
 (anchor :step t10 :args ((:= (?v0 Real_a_fun$) veriT_vr2) (:= (?v1 B_list$) veriT_vr3)))
 (step t10.t1 (cl (! (= ?v1 veriT_vr3) :named @p_70)) :rule refl)
 (step t10.t2 (cl (! (= @p_3 (! (rec_join$ veriT_vr3) :named @p_63)) :named @p_111)) :rule cong :premises (t10.t1))
@@ -7759,10 +7759,10 @@
 (step t44 (cl false) :rule th_resolution :premises (t31 t42 t43))
 (step t45 (cl (not false)) :rule false)
 (step t46 (cl) :rule resolution :premises (t44 t45))
-f76f257aace4d1c925379d3446177d02a43e00b9 36 0
+2da165964e2359aec5a20e66969cc8494006e9ba 36 0
 unsat
-(assume axiom4 (! (forall ((?v0 Int)) (! (and (! (pred$e ?v0) :named @p_4) (! (or (! (pred$d (! (cons$d ?v0 nil$d) :named @p_7)) :named @p_1) (! (not @p_1) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2))
-(assume axiom5 (not (! (pred$e 1) :named @p_26)))
+(assume a4 (! (forall ((?v0 Int)) (! (and (! (pred$e ?v0) :named @p_4) (! (or (! (pred$d (! (cons$d ?v0 nil$d) :named @p_7)) :named @p_1) (! (not @p_1) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2))
+(assume a5 (not (! (pred$e 1) :named @p_26)))
 (anchor :step t3 :args ((:= (?v0 Int) veriT_vr8)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr8) :named @p_6)) :rule refl)
 (step t3.t2 (cl (= @p_4 (! (pred$e veriT_vr8) :named @p_5))) :rule cong :premises (t3.t1))
@@ -7777,7 +7777,7 @@
 (step t3.t11 (cl (= @p_15 (! (and @p_5 @p_14) :named @p_16))) :rule cong :premises (t3.t2 t3.t10))
 (step t3 (cl (! (= @p_2 (! (forall ((veriT_vr8 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
 (step t4 (cl (not @p_17) (not @p_2) @p_18) :rule equiv_pos2)
-(step t5 (cl @p_18) :rule th_resolution :premises (axiom4 t3 t4))
+(step t5 (cl @p_18) :rule th_resolution :premises (a4 t3 t4))
 (anchor :step t6 :args ((veriT_vr8 Int)))
 (step t6.t1 (cl (= @p_14 true)) :rule or_simplify)
 (step t6.t2 (cl (= @p_16 (! (and @p_5 true) :named @p_19))) :rule cong :premises (t6.t1))
@@ -7795,20 +7795,20 @@
 (step t11 (cl @p_25) :rule th_resolution :premises (t8 t9 t10))
 (step t12 (cl (or (! (not @p_25) :named @p_27) @p_26)) :rule forall_inst :args ((:= veriT_vr9 1)))
 (step t13 (cl @p_27 @p_26) :rule or :premises (t12))
-(step t14 (cl) :rule resolution :premises (t13 t11 axiom5))
-9aecf5ce2acf5c9a6a97abe747fcd03e35b92209 158 0
+(step t14 (cl) :rule resolution :premises (t13 t11 a5))
+f9bb7f97f8819ceceaefe0cdf934d0eda3431a5b 158 0
 unsat
-(assume axiom0 (! (forall ((?v0 Int)) (! (= (! (g$ (! (some$ ?v0) :named @p_5)) :named @p_7) (! (g$a (! (cons$ ?v0 nil$) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_4))
-(assume axiom1 (forall ((?v0 Bool)) (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a)))))
-(assume axiom6 (! (forall ((?v0 Bool_list$)) (! (= (! (g$c ?v0) :named @p_27) (! (size$ ?v0) :named @p_30)) :named @p_32)) :named @p_26))
-(assume axiom7 (! (forall ((?v0 Int_list$)) (! (= (! (g$a ?v0) :named @p_43) (! (size$a ?v0) :named @p_46)) :named @p_48)) :named @p_42))
-(assume axiom12 (! (= zero$ (! (size$ nil$a) :named @p_118)) :named @p_143))
-(assume axiom13 (! (= zero$ (! (size$a nil$) :named @p_133)) :named @p_144))
-(assume axiom14 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (size$ (cons$a ?v0 ?v1)) (! (plus$ (! (size$ ?v1) :named @p_60) (! (suc$ zero$) :named @p_1)) :named @p_3))))
-(assume axiom15 (! (forall ((?v0 Int) (?v1 Int_list$)) (! (= (! (size$a (! (cons$ ?v0 ?v1) :named @p_96)) :named @p_98) (! (plus$ (! (size$a ?v1) :named @p_101) @p_1) :named @p_103)) :named @p_105)) :named @p_95))
-(assume axiom16 (not (! (= (! (g$ (some$ 3)) :named @p_124) (! (g$b (some$a true)) :named @p_2)) :named @p_141)))
-(step t10 (cl (and (= (g$b (some$a false)) (g$c (! (cons$a false nil$a) :named @p_119))) (! (= @p_2 (! (g$c (! (cons$a true nil$a) :named @p_121)) :named @p_122)) :named @p_117))) :rule bfun_elim :premises (axiom1))
-(step t11 (cl (! (forall ((?v1 Bool_list$)) (! (and (! (= @p_3 (! (size$ (! (cons$a false ?v1) :named @p_63)) :named @p_65)) :named @p_67) (! (= @p_3 (! (size$ (! (cons$a true ?v1) :named @p_71)) :named @p_73)) :named @p_75)) :named @p_77)) :named @p_58)) :rule bfun_elim :premises (axiom14))
+(assume a0 (! (forall ((?v0 Int)) (! (= (! (g$ (! (some$ ?v0) :named @p_5)) :named @p_7) (! (g$a (! (cons$ ?v0 nil$) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_4))
+(assume a1 (forall ((?v0 Bool)) (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a)))))
+(assume a6 (! (forall ((?v0 Bool_list$)) (! (= (! (g$c ?v0) :named @p_27) (! (size$ ?v0) :named @p_30)) :named @p_32)) :named @p_26))
+(assume a7 (! (forall ((?v0 Int_list$)) (! (= (! (g$a ?v0) :named @p_43) (! (size$a ?v0) :named @p_46)) :named @p_48)) :named @p_42))
+(assume a12 (! (= zero$ (! (size$ nil$a) :named @p_118)) :named @p_143))
+(assume a13 (! (= zero$ (! (size$a nil$) :named @p_133)) :named @p_144))
+(assume a14 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (size$ (cons$a ?v0 ?v1)) (! (plus$ (! (size$ ?v1) :named @p_60) (! (suc$ zero$) :named @p_1)) :named @p_3))))
+(assume a15 (! (forall ((?v0 Int) (?v1 Int_list$)) (! (= (! (size$a (! (cons$ ?v0 ?v1) :named @p_96)) :named @p_98) (! (plus$ (! (size$a ?v1) :named @p_101) @p_1) :named @p_103)) :named @p_105)) :named @p_95))
+(assume a16 (not (! (= (! (g$ (some$ 3)) :named @p_124) (! (g$b (some$a true)) :named @p_2)) :named @p_141)))
+(step t10 (cl (and (= (g$b (some$a false)) (g$c (! (cons$a false nil$a) :named @p_119))) (! (= @p_2 (! (g$c (! (cons$a true nil$a) :named @p_121)) :named @p_122)) :named @p_117))) :rule bfun_elim :premises (a1))
+(step t11 (cl (! (forall ((?v1 Bool_list$)) (! (and (! (= @p_3 (! (size$ (! (cons$a false ?v1) :named @p_63)) :named @p_65)) :named @p_67) (! (= @p_3 (! (size$ (! (cons$a true ?v1) :named @p_71)) :named @p_73)) :named @p_75)) :named @p_77)) :named @p_58)) :rule bfun_elim :premises (a14))
 (anchor :step t12 :args ((:= (?v0 Int) veriT_vr0)))
 (step t12.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
 (step t12.t2 (cl (= @p_5 (! (some$ veriT_vr0) :named @p_6))) :rule cong :premises (t12.t1))
@@ -7819,7 +7819,7 @@
 (step t12.t7 (cl (= @p_14 (! (= @p_8 @p_13) :named @p_15))) :rule cong :premises (t12.t3 t12.t6))
 (step t12 (cl (! (= @p_4 (! (forall ((veriT_vr0 Int)) @p_15) :named @p_17)) :named @p_16)) :rule bind)
 (step t13 (cl (not @p_16) (not @p_4) @p_17) :rule equiv_pos2)
-(step t14 (cl @p_17) :rule th_resolution :premises (axiom0 t12 t13))
+(step t14 (cl @p_17) :rule th_resolution :premises (a0 t12 t13))
 (anchor :step t15 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t15.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_20)) :rule refl)
 (step t15.t2 (cl (= @p_6 (! (some$ veriT_vr1) :named @p_18))) :rule cong :premises (t15.t1))
@@ -7839,7 +7839,7 @@
 (step t18.t5 (cl (= @p_32 (! (= @p_28 @p_31) :named @p_33))) :rule cong :premises (t18.t2 t18.t4))
 (step t18 (cl (! (= @p_26 (! (forall ((veriT_vr2 Bool_list$)) @p_33) :named @p_35)) :named @p_34)) :rule bind)
 (step t19 (cl (not @p_34) (not @p_26) @p_35) :rule equiv_pos2)
-(step t20 (cl @p_35) :rule th_resolution :premises (axiom6 t18 t19))
+(step t20 (cl @p_35) :rule th_resolution :premises (a6 t18 t19))
 (anchor :step t21 :args ((:= (veriT_vr2 Bool_list$) veriT_vr3)))
 (step t21.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_37)) :rule refl)
 (step t21.t2 (cl (= @p_28 (! (g$c veriT_vr3) :named @p_36))) :rule cong :premises (t21.t1))
@@ -7857,7 +7857,7 @@
 (step t24.t5 (cl (= @p_48 (! (= @p_44 @p_47) :named @p_49))) :rule cong :premises (t24.t2 t24.t4))
 (step t24 (cl (! (= @p_42 (! (forall ((veriT_vr4 Int_list$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
 (step t25 (cl (not @p_50) (not @p_42) @p_51) :rule equiv_pos2)
-(step t26 (cl @p_51) :rule th_resolution :premises (axiom7 t24 t25))
+(step t26 (cl @p_51) :rule th_resolution :premises (a7 t24 t25))
 (anchor :step t27 :args ((:= (veriT_vr4 Int_list$) veriT_vr5)))
 (step t27.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_53)) :rule refl)
 (step t27.t2 (cl (= @p_44 (! (g$a veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1))
@@ -7916,7 +7916,7 @@
 (step t36.t8 (cl (= @p_105 (! (= @p_99 @p_104) :named @p_106))) :rule cong :premises (t36.t4 t36.t7))
 (step t36 (cl (! (= @p_95 (! (forall ((veriT_vr22 Int) (veriT_vr23 Int_list$)) @p_106) :named @p_108)) :named @p_107)) :rule bind)
 (step t37 (cl (not @p_107) (not @p_95) @p_108) :rule equiv_pos2)
-(step t38 (cl @p_108) :rule th_resolution :premises (axiom15 t36 t37))
+(step t38 (cl @p_108) :rule th_resolution :premises (a15 t36 t37))
 (anchor :step t39 :args ((:= (veriT_vr22 Int) veriT_vr24) (:= (veriT_vr23 Int_list$) veriT_vr25)))
 (step t39.t1 (cl (= veriT_vr22 veriT_vr24)) :rule refl)
 (step t39.t2 (cl (! (= veriT_vr23 veriT_vr25) :named @p_111)) :rule refl)
@@ -7954,919 +7954,552 @@
 (step t64 (cl @p_149) :rule eq_reflexive)
 (step t65 (cl @p_142 @p_147 @p_148) :rule th_resolution :premises (t63 t64))
 (step t66 (cl @p_150 @p_151 @p_152 @p_153 @p_154 @p_155 @p_141 @p_147 @p_148) :rule th_resolution :premises (t60 t65))
-(step t67 (cl) :rule resolution :premises (t66 t42 axiom12 axiom13 axiom16 t49 t51 t53 t57 t59))
-1a2d4d1ee4565edc7b401dfc82d8d10a78382c1c 910 0
+(step t67 (cl) :rule resolution :premises (t66 t42 a12 a13 a16 t49 t51 t53 t57 t59))
+79bb70ff288db1936aaccee9c58bb4c098292b28 543 0
 unsat
-(define-fun veriT_sk0 () V$ (! (choice ((veriT_vr65 V$)) (not (! (not (! (= x2$ (! (rraise$ veriT_vr65) :named @p_401)) :named @p_402)) :named @p_400))) :named @p_414))
-(define-fun veriT_sk1 () Abort$ (! (choice ((veriT_vr66 Abort$)) (not (! (not (! (= x2$ (! (rabort$ veriT_vr66) :named @p_404)) :named @p_405)) :named @p_403))) :named @p_418))
-(define-fun veriT_sk3 () V_list_v_result$ (! (choice ((veriT_vr73 V_list_v_result$)) (! (= (! (fun_evaluate$ st$a env$ (cons$ e$ nil$)) :named @p_3) (! (pair$ (! (fst$ @p_3) :named @p_378) veriT_vr73) :named @p_461)) :named @p_460)) :named @p_465))
-(define-fun veriT_sk11 () V_list_v_result$ (! (choice ((veriT_vr108 V_list_v_result$)) (! (= (! (fix_clock$ st$a @p_3) :named @p_470) (! (pair$ st$ veriT_vr108) :named @p_503)) :named @p_502)) :named @p_515))
-(assume axiom0 (! (forall ((?v0 V$)) (! (= (! (fun_app$ uua$ ?v0) :named @p_9) (! (fun_app$ (! (fun_evaluate_match$ st$ env$ ?v0 pes$) :named @p_12) ?v0) :named @p_14)) :named @p_16)) :named @p_8))
-(assume axiom1 (! (forall ((?v0 Abort$)) (! (= (! (fun_app$a uub$ ?v0) :named @p_28) (! (pair$ st$ (! (rerr$ (! (rabort$ ?v0) :named @p_31)) :named @p_33)) :named @p_35)) :named @p_37)) :named @p_27))
-(assume axiom2 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 Nat$)) (! (= (! (fun_app$b (! (uu$ ?v0 ?v1) :named @p_5) ?v2) :named @p_53) (! (ite (! (less_eq$ (! (clock$ ?v1) :named @p_1) (! (clock$ ?v0) :named @p_2)) :named @p_57) @p_1 @p_2) :named @p_61)) :named @p_63)) :named @p_49))
-(assume axiom3 (! (= @p_470 (! (pair$ st$ r$) :named @p_609)) :named @p_628))
-(assume axiom4 (! (less_eq$ (! (clock$ @p_378) :named @p_371) (! (clock$ st$a) :named @p_7)) :named @p_369))
-(assume axiom5 (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (! (=> (! (and (! (less_eq$ ?v0 ?v1) :named @p_81) (! (less_eq$ ?v2 ?v0) :named @p_84)) :named @p_86) (! (less_eq$ ?v2 ?v1) :named @p_90)) :named @p_92)) :named @p_80))
-(assume axiom6 (! (forall ((?v0 Astate$) (?v1 Astate_v_list_v_result_prod$)) (! (= (! (= ?v0 (! (fst$ ?v1) :named @p_107)) :named @p_109) (! (exists ((?v2 V_list_v_result$)) (! (= ?v1 (! (pair$ ?v0 ?v2) :named @p_115)) :named @p_117)) :named @p_111)) :named @p_119)) :named @p_106))
-(assume axiom7 (! (forall ((?v0 V_error_result$)) (! (=> (! (and (! (forall ((?v1 V$)) (! (=> (! (= ?v0 (! (rraise$ ?v1) :named @p_174)) :named @p_6) false) :named @p_177)) :named @p_172) (! (forall ((?v1 Abort$)) (! (=> (! (= ?v0 (! (rabort$ ?v1) :named @p_182)) :named @p_184) false) :named @p_186)) :named @p_179)) :named @p_188) false) :named @p_190)) :named @p_171))
-(assume axiom8 (! (forall ((?v0 V_astate_v_list_v_result_prod_fun$) (?v1 Abort_astate_v_list_v_result_prod_fun$) (?v2 V$)) (! (= (! (case_error_result$ ?v0 ?v1 (! (rraise$ ?v2) :named @p_217)) :named @p_219) (! (fun_app$ ?v0 ?v2) :named @p_223)) :named @p_225)) :named @p_216))
-(assume axiom9 (! (forall ((?v0 V_astate_v_list_v_result_prod_fun$) (?v1 Abort_astate_v_list_v_result_prod_fun$) (?v2 Abort$)) (! (= (! (case_error_result$ ?v0 ?v1 (! (rabort$ ?v2) :named @p_238)) :named @p_240) (! (fun_app$a ?v1 ?v2) :named @p_244)) :named @p_246)) :named @p_237))
-(assume axiom10 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 V_list_v_result$) (?v3 Astate$)) (! (=> (! (= (! (fix_clock$ ?v0 (! (pair$ ?v1 ?v2) :named @p_259)) :named @p_4) (! (pair$ ?v3 ?v2) :named @p_263)) :named @p_265) (! (less_eq$ (! (clock$ ?v3) :named @p_268) @p_1) :named @p_272)) :named @p_274)) :named @p_258))
-(assume axiom11 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 V_list_v_result$)) (! (= @p_4 (! (pair$ (! (update_clock$ @p_5 ?v1) :named @p_297) ?v2) :named @p_300)) :named @p_302)) :named @p_291))
-(assume axiom12 (! (forall ((?v0 V_error_result$) (?v1 V$)) (! (=> (! (and (! (= r$ (! (rerr$ ?v0) :named @p_319)) :named @p_321) @p_6) :named @p_326) (! (less_eq$ (! (clock$ (! (fst$ (! (fun_app$ (! (fun_evaluate_match$ st$ env$ ?v1 pes$) :named @p_329) ?v1) :named @p_331)) :named @p_333)) :named @p_335) (! (clock$ st$) :named @p_318)) :named @p_337)) :named @p_339)) :named @p_317))
-(assume axiom13 (! (not (! (=> (! (= r$ (! (rerr$ x2$) :named @p_615)) :named @p_359) (! (less_eq$ (! (clock$ (! (fst$ (! (case_error_result$ uua$ uub$ x2$) :named @p_602)) :named @p_530)) :named @p_370) @p_7) :named @p_360)) :named @p_364)) :named @p_358))
-(anchor :step t15 :args ((:= (?v0 V$) veriT_vr0)))
-(step t15.t1 (cl (! (= ?v0 veriT_vr0) :named @p_11)) :rule refl)
-(step t15.t2 (cl (= @p_9 (! (fun_app$ uua$ veriT_vr0) :named @p_10))) :rule cong :premises (t15.t1))
-(step t15.t3 (cl @p_11) :rule refl)
-(step t15.t4 (cl (= @p_12 (! (fun_evaluate_match$ st$ env$ veriT_vr0 pes$) :named @p_13))) :rule cong :premises (t15.t3))
-(step t15.t5 (cl @p_11) :rule refl)
-(step t15.t6 (cl (= @p_14 (! (fun_app$ @p_13 veriT_vr0) :named @p_15))) :rule cong :premises (t15.t4 t15.t5))
-(step t15.t7 (cl (= @p_16 (! (= @p_10 @p_15) :named @p_17))) :rule cong :premises (t15.t2 t15.t6))
-(step t15 (cl (! (= @p_8 (! (forall ((veriT_vr0 V$)) @p_17) :named @p_19)) :named @p_18)) :rule bind)
-(step t16 (cl (not @p_18) (not @p_8) @p_19) :rule equiv_pos2)
-(step t17 (cl @p_19) :rule th_resolution :premises (axiom0 t15 t16))
-(anchor :step t18 :args ((:= (veriT_vr0 V$) veriT_vr1)))
-(step t18.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_21)) :rule refl)
-(step t18.t2 (cl (= @p_10 (! (fun_app$ uua$ veriT_vr1) :named @p_20))) :rule cong :premises (t18.t1))
-(step t18.t3 (cl @p_21) :rule refl)
-(step t18.t4 (cl (= @p_13 (! (fun_evaluate_match$ st$ env$ veriT_vr1 pes$) :named @p_22))) :rule cong :premises (t18.t3))
-(step t18.t5 (cl @p_21) :rule refl)
-(step t18.t6 (cl (= @p_15 (! (fun_app$ @p_22 veriT_vr1) :named @p_23))) :rule cong :premises (t18.t4 t18.t5))
-(step t18.t7 (cl (= @p_17 (! (= @p_20 @p_23) :named @p_24))) :rule cong :premises (t18.t2 t18.t6))
-(step t18 (cl (! (= @p_19 (! (forall ((veriT_vr1 V$)) @p_24) :named @p_26)) :named @p_25)) :rule bind)
-(step t19 (cl (not @p_25) (not @p_19) @p_26) :rule equiv_pos2)
-(step t20 (cl @p_26) :rule th_resolution :premises (t17 t18 t19))
-(anchor :step t21 :args ((:= (?v0 Abort$) veriT_vr2)))
-(step t21.t1 (cl (! (= ?v0 veriT_vr2) :named @p_30)) :rule refl)
-(step t21.t2 (cl (= @p_28 (! (fun_app$a uub$ veriT_vr2) :named @p_29))) :rule cong :premises (t21.t1))
-(step t21.t3 (cl @p_30) :rule refl)
-(step t21.t4 (cl (= @p_31 (! (rabort$ veriT_vr2) :named @p_32))) :rule cong :premises (t21.t3))
-(step t21.t5 (cl (= @p_33 (! (rerr$ @p_32) :named @p_34))) :rule cong :premises (t21.t4))
-(step t21.t6 (cl (= @p_35 (! (pair$ st$ @p_34) :named @p_36))) :rule cong :premises (t21.t5))
-(step t21.t7 (cl (= @p_37 (! (= @p_29 @p_36) :named @p_38))) :rule cong :premises (t21.t2 t21.t6))
-(step t21 (cl (! (= @p_27 (! (forall ((veriT_vr2 Abort$)) @p_38) :named @p_40)) :named @p_39)) :rule bind)
-(step t22 (cl (not @p_39) (not @p_27) @p_40) :rule equiv_pos2)
-(step t23 (cl @p_40) :rule th_resolution :premises (axiom1 t21 t22))
-(anchor :step t24 :args ((:= (veriT_vr2 Abort$) veriT_vr3)))
-(step t24.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_42)) :rule refl)
-(step t24.t2 (cl (= @p_29 (! (fun_app$a uub$ veriT_vr3) :named @p_41))) :rule cong :premises (t24.t1))
-(step t24.t3 (cl @p_42) :rule refl)
-(step t24.t4 (cl (= @p_32 (! (rabort$ veriT_vr3) :named @p_43))) :rule cong :premises (t24.t3))
-(step t24.t5 (cl (= @p_34 (! (rerr$ @p_43) :named @p_44))) :rule cong :premises (t24.t4))
-(step t24.t6 (cl (= @p_36 (! (pair$ st$ @p_44) :named @p_45))) :rule cong :premises (t24.t5))
-(step t24.t7 (cl (= @p_38 (! (= @p_41 @p_45) :named @p_46))) :rule cong :premises (t24.t2 t24.t6))
-(step t24 (cl (! (= @p_40 (! (forall ((veriT_vr3 Abort$)) @p_46) :named @p_48)) :named @p_47)) :rule bind)
-(step t25 (cl (not @p_47) (not @p_40) @p_48) :rule equiv_pos2)
-(step t26 (cl @p_48) :rule th_resolution :premises (t23 t24 t25))
-(anchor :step t27 :args ((:= (?v0 Astate$) veriT_vr4) (:= (?v1 Astate$) veriT_vr5) (:= (?v2 Nat$) veriT_vr6)))
-(step t27.t1 (cl (! (= ?v0 veriT_vr4) :named @p_56)) :rule refl)
-(step t27.t2 (cl (! (= ?v1 veriT_vr5) :named @p_55)) :rule refl)
-(step t27.t3 (cl (= @p_5 (! (uu$ veriT_vr4 veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1 t27.t2))
-(step t27.t4 (cl (= ?v2 veriT_vr6)) :rule refl)
-(step t27.t5 (cl (= @p_53 (! (fun_app$b @p_52 veriT_vr6) :named @p_54))) :rule cong :premises (t27.t3 t27.t4))
-(step t27.t6 (cl @p_55) :rule refl)
-(step t27.t7 (cl (! (= @p_1 (! (clock$ veriT_vr5) :named @p_50)) :named @p_59)) :rule cong :premises (t27.t6))
-(step t27.t8 (cl @p_56) :rule refl)
-(step t27.t9 (cl (! (= @p_2 (! (clock$ veriT_vr4) :named @p_51)) :named @p_60)) :rule cong :premises (t27.t8))
-(step t27.t10 (cl (= @p_57 (! (less_eq$ @p_50 @p_51) :named @p_58))) :rule cong :premises (t27.t7 t27.t9))
-(step t27.t11 (cl @p_55) :rule refl)
-(step t27.t12 (cl @p_59) :rule cong :premises (t27.t11))
-(step t27.t13 (cl @p_56) :rule refl)
-(step t27.t14 (cl @p_60) :rule cong :premises (t27.t13))
-(step t27.t15 (cl (= @p_61 (! (ite @p_58 @p_50 @p_51) :named @p_62))) :rule cong :premises (t27.t10 t27.t12 t27.t14))
-(step t27.t16 (cl (= @p_63 (! (= @p_54 @p_62) :named @p_64))) :rule cong :premises (t27.t5 t27.t15))
-(step t27 (cl (! (= @p_49 (! (forall ((veriT_vr4 Astate$) (veriT_vr5 Astate$) (veriT_vr6 Nat$)) @p_64) :named @p_66)) :named @p_65)) :rule bind)
-(step t28 (cl (not @p_65) (not @p_49) @p_66) :rule equiv_pos2)
-(step t29 (cl @p_66) :rule th_resolution :premises (axiom2 t27 t28))
-(anchor :step t30 :args ((:= (veriT_vr4 Astate$) veriT_vr7) (:= (veriT_vr5 Astate$) veriT_vr8) (:= (veriT_vr6 Nat$) veriT_vr9)))
-(step t30.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_72)) :rule refl)
-(step t30.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_71)) :rule refl)
-(step t30.t3 (cl (= @p_52 (! (uu$ veriT_vr7 veriT_vr8) :named @p_69))) :rule cong :premises (t30.t1 t30.t2))
-(step t30.t4 (cl (= veriT_vr6 veriT_vr9)) :rule refl)
-(step t30.t5 (cl (= @p_54 (! (fun_app$b @p_69 veriT_vr9) :named @p_70))) :rule cong :premises (t30.t3 t30.t4))
-(step t30.t6 (cl @p_71) :rule refl)
-(step t30.t7 (cl (! (= @p_50 (! (clock$ veriT_vr8) :named @p_67)) :named @p_74)) :rule cong :premises (t30.t6))
-(step t30.t8 (cl @p_72) :rule refl)
-(step t30.t9 (cl (! (= @p_51 (! (clock$ veriT_vr7) :named @p_68)) :named @p_75)) :rule cong :premises (t30.t8))
-(step t30.t10 (cl (= @p_58 (! (less_eq$ @p_67 @p_68) :named @p_73))) :rule cong :premises (t30.t7 t30.t9))
-(step t30.t11 (cl @p_71) :rule refl)
-(step t30.t12 (cl @p_74) :rule cong :premises (t30.t11))
-(step t30.t13 (cl @p_72) :rule refl)
-(step t30.t14 (cl @p_75) :rule cong :premises (t30.t13))
-(step t30.t15 (cl (= @p_62 (! (ite @p_73 @p_67 @p_68) :named @p_76))) :rule cong :premises (t30.t10 t30.t12 t30.t14))
-(step t30.t16 (cl (= @p_64 (! (= @p_70 @p_76) :named @p_77))) :rule cong :premises (t30.t5 t30.t15))
-(step t30 (cl (! (= @p_66 (! (forall ((veriT_vr7 Astate$) (veriT_vr8 Astate$) (veriT_vr9 Nat$)) @p_77) :named @p_79)) :named @p_78)) :rule bind)
-(step t31 (cl (not @p_78) (not @p_66) @p_79) :rule equiv_pos2)
-(step t32 (cl @p_79) :rule th_resolution :premises (t29 t30 t31))
-(anchor :step t33 :args ((:= (?v0 Nat$) veriT_vr10) (:= (?v1 Nat$) veriT_vr11) (:= (?v2 Nat$) veriT_vr12)))
-(step t33.t1 (cl (! (= ?v0 veriT_vr10) :named @p_83)) :rule refl)
-(step t33.t2 (cl (! (= ?v1 veriT_vr11) :named @p_89)) :rule refl)
-(step t33.t3 (cl (= @p_81 (! (less_eq$ veriT_vr10 veriT_vr11) :named @p_82))) :rule cong :premises (t33.t1 t33.t2))
-(step t33.t4 (cl (! (= ?v2 veriT_vr12) :named @p_88)) :rule refl)
-(step t33.t5 (cl @p_83) :rule refl)
-(step t33.t6 (cl (= @p_84 (! (less_eq$ veriT_vr12 veriT_vr10) :named @p_85))) :rule cong :premises (t33.t4 t33.t5))
-(step t33.t7 (cl (= @p_86 (! (and @p_82 @p_85) :named @p_87))) :rule cong :premises (t33.t3 t33.t6))
-(step t33.t8 (cl @p_88) :rule refl)
-(step t33.t9 (cl @p_89) :rule refl)
-(step t33.t10 (cl (= @p_90 (! (less_eq$ veriT_vr12 veriT_vr11) :named @p_91))) :rule cong :premises (t33.t8 t33.t9))
-(step t33.t11 (cl (= @p_92 (! (=> @p_87 @p_91) :named @p_93))) :rule cong :premises (t33.t7 t33.t10))
-(step t33 (cl (! (= @p_80 (! (forall ((veriT_vr10 Nat$) (veriT_vr11 Nat$) (veriT_vr12 Nat$)) @p_93) :named @p_95)) :named @p_94)) :rule bind)
-(step t34 (cl (not @p_94) (not @p_80) @p_95) :rule equiv_pos2)
-(step t35 (cl @p_95) :rule th_resolution :premises (axiom5 t33 t34))
-(anchor :step t36 :args ((:= (veriT_vr10 Nat$) veriT_vr13) (:= (veriT_vr11 Nat$) veriT_vr14) (:= (veriT_vr12 Nat$) veriT_vr15)))
-(step t36.t1 (cl (! (= veriT_vr10 veriT_vr13) :named @p_97)) :rule refl)
-(step t36.t2 (cl (! (= veriT_vr11 veriT_vr14) :named @p_101)) :rule refl)
-(step t36.t3 (cl (= @p_82 (! (less_eq$ veriT_vr13 veriT_vr14) :named @p_96))) :rule cong :premises (t36.t1 t36.t2))
-(step t36.t4 (cl (! (= veriT_vr12 veriT_vr15) :named @p_100)) :rule refl)
-(step t36.t5 (cl @p_97) :rule refl)
-(step t36.t6 (cl (= @p_85 (! (less_eq$ veriT_vr15 veriT_vr13) :named @p_98))) :rule cong :premises (t36.t4 t36.t5))
-(step t36.t7 (cl (= @p_87 (! (and @p_96 @p_98) :named @p_99))) :rule cong :premises (t36.t3 t36.t6))
-(step t36.t8 (cl @p_100) :rule refl)
-(step t36.t9 (cl @p_101) :rule refl)
-(step t36.t10 (cl (= @p_91 (! (less_eq$ veriT_vr15 veriT_vr14) :named @p_102))) :rule cong :premises (t36.t8 t36.t9))
-(step t36.t11 (cl (= @p_93 (! (=> @p_99 @p_102) :named @p_103))) :rule cong :premises (t36.t7 t36.t10))
-(step t36 (cl (! (= @p_95 (! (forall ((veriT_vr13 Nat$) (veriT_vr14 Nat$) (veriT_vr15 Nat$)) @p_103) :named @p_105)) :named @p_104)) :rule bind)
-(step t37 (cl (not @p_104) (not @p_95) @p_105) :rule equiv_pos2)
-(step t38 (cl @p_105) :rule th_resolution :premises (t35 t36 t37))
-(anchor :step t39 :args ((:= (?v0 Astate$) veriT_vr16) (:= (?v1 Astate_v_list_v_result_prod$) veriT_vr17)))
-(step t39.t1 (cl (! (= ?v0 veriT_vr16) :named @p_114)) :rule refl)
-(step t39.t2 (cl (! (= ?v1 veriT_vr17) :named @p_113)) :rule refl)
-(step t39.t3 (cl (= @p_107 (! (fst$ veriT_vr17) :named @p_108))) :rule cong :premises (t39.t2))
-(step t39.t4 (cl (= @p_109 (! (= veriT_vr16 @p_108) :named @p_110))) :rule cong :premises (t39.t1 t39.t3))
-(anchor :step t39.t5 :args ((:= (?v2 V_list_v_result$) veriT_vr18)))
-(step t39.t5.t1 (cl @p_113) :rule refl)
-(step t39.t5.t2 (cl @p_114) :rule refl)
-(step t39.t5.t3 (cl (= ?v2 veriT_vr18)) :rule refl)
-(step t39.t5.t4 (cl (= @p_115 (! (pair$ veriT_vr16 veriT_vr18) :named @p_116))) :rule cong :premises (t39.t5.t2 t39.t5.t3))
-(step t39.t5.t5 (cl (= @p_117 (! (= veriT_vr17 @p_116) :named @p_118))) :rule cong :premises (t39.t5.t1 t39.t5.t4))
-(step t39.t5 (cl (= @p_111 (! (exists ((veriT_vr18 V_list_v_result$)) @p_118) :named @p_112))) :rule bind)
-(step t39.t6 (cl (= @p_119 (! (= @p_110 @p_112) :named @p_120))) :rule cong :premises (t39.t4 t39.t5))
-(step t39 (cl (! (= @p_106 (! (forall ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)) @p_120) :named @p_122)) :named @p_121)) :rule bind)
-(step t40 (cl (not @p_121) (not @p_106) @p_122) :rule equiv_pos2)
-(step t41 (cl @p_122) :rule th_resolution :premises (axiom6 t39 t40))
-(anchor :step t42 :args ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)))
-(step t42.t1 (cl (= @p_120 (! (and (! (=> @p_110 @p_112) :named @p_133) (! (=> @p_112 @p_110) :named @p_140)) :named @p_123))) :rule connective_def)
-(step t42 (cl (! (= @p_122 (! (forall ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)) @p_123) :named @p_125)) :named @p_124)) :rule bind)
-(step t43 (cl (not @p_124) (not @p_122) @p_125) :rule equiv_pos2)
-(step t44 (cl @p_125) :rule th_resolution :premises (t41 t42 t43))
-(anchor :step t45 :args ((:= (veriT_vr16 Astate$) veriT_vr19) (:= (veriT_vr17 Astate_v_list_v_result_prod$) veriT_vr20)))
-(step t45.t1 (cl (! (= veriT_vr16 veriT_vr19) :named @p_130)) :rule refl)
-(step t45.t2 (cl (! (= veriT_vr17 veriT_vr20) :named @p_129)) :rule refl)
-(step t45.t3 (cl (! (= @p_108 (! (fst$ veriT_vr20) :named @p_127)) :named @p_138)) :rule cong :premises (t45.t2))
-(step t45.t4 (cl (! (= @p_110 (! (= veriT_vr19 @p_127) :named @p_126)) :named @p_139)) :rule cong :premises (t45.t1 t45.t3))
-(anchor :step t45.t5 :args ((:= (veriT_vr18 V_list_v_result$) veriT_vr21)))
-(step t45.t5.t1 (cl @p_129) :rule refl)
-(step t45.t5.t2 (cl @p_130) :rule refl)
-(step t45.t5.t3 (cl (= veriT_vr18 veriT_vr21)) :rule refl)
-(step t45.t5.t4 (cl (= @p_116 (! (pair$ veriT_vr19 veriT_vr21) :named @p_131))) :rule cong :premises (t45.t5.t2 t45.t5.t3))
-(step t45.t5.t5 (cl (= @p_118 (! (= veriT_vr20 @p_131) :named @p_132))) :rule cong :premises (t45.t5.t1 t45.t5.t4))
-(step t45.t5 (cl (= @p_112 (! (exists ((veriT_vr21 V_list_v_result$)) @p_132) :named @p_128))) :rule bind)
-(step t45.t6 (cl (= @p_133 (! (=> @p_126 @p_128) :named @p_134))) :rule cong :premises (t45.t4 t45.t5))
-(anchor :step t45.t7 :args ((:= (veriT_vr18 V_list_v_result$) veriT_vr22)))
-(step t45.t7.t1 (cl @p_129) :rule refl)
-(step t45.t7.t2 (cl @p_130) :rule refl)
-(step t45.t7.t3 (cl (= veriT_vr18 veriT_vr22)) :rule refl)
-(step t45.t7.t4 (cl (= @p_116 (! (pair$ veriT_vr19 veriT_vr22) :named @p_136))) :rule cong :premises (t45.t7.t2 t45.t7.t3))
-(step t45.t7.t5 (cl (= @p_118 (! (= veriT_vr20 @p_136) :named @p_137))) :rule cong :premises (t45.t7.t1 t45.t7.t4))
-(step t45.t7 (cl (= @p_112 (! (exists ((veriT_vr22 V_list_v_result$)) @p_137) :named @p_135))) :rule bind)
-(step t45.t8 (cl @p_130) :rule refl)
-(step t45.t9 (cl @p_129) :rule refl)
-(step t45.t10 (cl @p_138) :rule cong :premises (t45.t9))
-(step t45.t11 (cl @p_139) :rule cong :premises (t45.t8 t45.t10))
-(step t45.t12 (cl (= @p_140 (! (=> @p_135 @p_126) :named @p_141))) :rule cong :premises (t45.t7 t45.t11))
-(step t45.t13 (cl (= @p_123 (! (and @p_134 @p_141) :named @p_142))) :rule cong :premises (t45.t6 t45.t12))
-(step t45 (cl (! (= @p_125 (! (forall ((veriT_vr19 Astate$) (veriT_vr20 Astate_v_list_v_result_prod$)) @p_142) :named @p_144)) :named @p_143)) :rule bind)
-(step t46 (cl (not @p_143) (not @p_125) @p_144) :rule equiv_pos2)
-(step t47 (cl @p_144) :rule th_resolution :premises (t44 t45 t46))
-(anchor :step t48 :args ((:= (veriT_vr19 Astate$) veriT_vr23) (:= (veriT_vr20 Astate_v_list_v_result_prod$) veriT_vr24)))
-(step t48.t1 (cl (! (= veriT_vr19 veriT_vr23) :named @p_149)) :rule refl)
-(step t48.t2 (cl (! (= veriT_vr20 veriT_vr24) :named @p_148)) :rule refl)
-(step t48.t3 (cl (! (= @p_127 (! (fst$ veriT_vr24) :named @p_147)) :named @p_153)) :rule cong :premises (t48.t2))
-(step t48.t4 (cl (! (= @p_126 (! (= veriT_vr23 @p_147) :named @p_146)) :named @p_154)) :rule cong :premises (t48.t1 t48.t3))
-(anchor :step t48.t5 :args ((:= (veriT_vr21 V_list_v_result$) veriT_vr25)))
-(step t48.t5.t1 (cl @p_148) :rule refl)
-(step t48.t5.t2 (cl @p_149) :rule refl)
-(step t48.t5.t3 (cl (= veriT_vr21 veriT_vr25)) :rule refl)
-(step t48.t5.t4 (cl (= @p_131 (! (pair$ veriT_vr23 veriT_vr25) :named @p_150))) :rule cong :premises (t48.t5.t2 t48.t5.t3))
-(step t48.t5.t5 (cl (= @p_132 (! (= veriT_vr24 @p_150) :named @p_151))) :rule cong :premises (t48.t5.t1 t48.t5.t4))
-(step t48.t5 (cl (= @p_128 (! (exists ((veriT_vr25 V_list_v_result$)) @p_151) :named @p_145))) :rule bind)
-(step t48.t6 (cl (= @p_134 (! (=> @p_146 @p_145) :named @p_152))) :rule cong :premises (t48.t4 t48.t5))
-(anchor :step t48.t7 :args ((:= (veriT_vr22 V_list_v_result$) veriT_vr25)))
-(step t48.t7.t1 (cl @p_148) :rule refl)
-(step t48.t7.t2 (cl @p_149) :rule refl)
-(step t48.t7.t3 (cl (= veriT_vr22 veriT_vr25)) :rule refl)
-(step t48.t7.t4 (cl (= @p_136 @p_150)) :rule cong :premises (t48.t7.t2 t48.t7.t3))
-(step t48.t7.t5 (cl (= @p_137 @p_151)) :rule cong :premises (t48.t7.t1 t48.t7.t4))
-(step t48.t7 (cl (= @p_135 @p_145)) :rule bind)
-(step t48.t8 (cl @p_149) :rule refl)
-(step t48.t9 (cl @p_148) :rule refl)
-(step t48.t10 (cl @p_153) :rule cong :premises (t48.t9))
-(step t48.t11 (cl @p_154) :rule cong :premises (t48.t8 t48.t10))
-(step t48.t12 (cl (= @p_141 (! (=> @p_145 @p_146) :named @p_155))) :rule cong :premises (t48.t7 t48.t11))
-(step t48.t13 (cl (= @p_142 (! (and @p_152 @p_155) :named @p_156))) :rule cong :premises (t48.t6 t48.t12))
-(step t48 (cl (! (= @p_144 (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)) @p_156) :named @p_158)) :named @p_157)) :rule bind)
-(step t49 (cl (not @p_157) (not @p_144) @p_158) :rule equiv_pos2)
-(step t50 (cl @p_158) :rule th_resolution :premises (t47 t48 t49))
-(anchor :step t51 :args ((:= (veriT_vr23 Astate$) veriT_vr23) (:= (veriT_vr24 Astate_v_list_v_result_prod$) veriT_vr24)))
-(anchor :step t51.t1 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr26)))
-(step t51.t1.t1 (cl (= veriT_vr25 veriT_vr26)) :rule refl)
-(step t51.t1.t2 (cl (= @p_150 (! (pair$ veriT_vr23 veriT_vr26) :named @p_160))) :rule cong :premises (t51.t1.t1))
-(step t51.t1.t3 (cl (= @p_151 (! (= veriT_vr24 @p_160) :named @p_161))) :rule cong :premises (t51.t1.t2))
-(step t51.t1 (cl (= @p_145 (! (exists ((veriT_vr26 V_list_v_result$)) @p_161) :named @p_159))) :rule bind)
-(step t51.t2 (cl (= @p_155 (! (=> @p_159 @p_146) :named @p_162))) :rule cong :premises (t51.t1))
-(step t51.t3 (cl (= @p_156 (! (and @p_152 @p_162) :named @p_163))) :rule cong :premises (t51.t2))
-(step t51 (cl (! (= @p_158 (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)) @p_163) :named @p_165)) :named @p_164)) :rule bind)
-(step t52 (cl (not @p_164) (not @p_158) @p_165) :rule equiv_pos2)
-(step t53 (cl @p_165) :rule th_resolution :premises (t50 t51 t52))
-(anchor :step t54 :args ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)))
-(step t54.t1 (cl (= @p_159 (! (not (forall ((veriT_vr26 V_list_v_result$)) (! (not @p_161) :named @p_367))) :named @p_166))) :rule connective_def)
-(step t54.t2 (cl (= @p_162 (! (=> @p_166 @p_146) :named @p_167))) :rule cong :premises (t54.t1))
-(step t54.t3 (cl (= @p_163 (! (and @p_152 @p_167) :named @p_168))) :rule cong :premises (t54.t2))
-(step t54 (cl (! (= @p_165 (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)) @p_168) :named @p_170)) :named @p_169)) :rule bind)
-(step t55 (cl (not @p_169) (not @p_165) @p_170) :rule equiv_pos2)
-(step t56 (cl @p_170) :rule th_resolution :premises (t53 t54 t55))
-(anchor :step t57 :args ((:= (?v0 V_error_result$) veriT_vr27)))
-(anchor :step t57.t1 :args ((:= (?v1 V$) veriT_vr28)))
-(step t57.t1.t1 (cl (! (= ?v0 veriT_vr27) :named @p_181)) :rule refl)
-(step t57.t1.t2 (cl (= ?v1 veriT_vr28)) :rule refl)
-(step t57.t1.t3 (cl (= @p_174 (! (rraise$ veriT_vr28) :named @p_175))) :rule cong :premises (t57.t1.t2))
-(step t57.t1.t4 (cl (= @p_6 (! (= veriT_vr27 @p_175) :named @p_176))) :rule cong :premises (t57.t1.t1 t57.t1.t3))
-(step t57.t1.t5 (cl (= @p_177 (! (=> @p_176 false) :named @p_178))) :rule cong :premises (t57.t1.t4))
-(step t57.t1 (cl (= @p_172 (! (forall ((veriT_vr28 V$)) @p_178) :named @p_173))) :rule bind)
-(anchor :step t57.t2 :args ((:= (?v1 Abort$) veriT_vr29)))
-(step t57.t2.t1 (cl @p_181) :rule refl)
-(step t57.t2.t2 (cl (= ?v1 veriT_vr29)) :rule refl)
-(step t57.t2.t3 (cl (= @p_182 (! (rabort$ veriT_vr29) :named @p_183))) :rule cong :premises (t57.t2.t2))
-(step t57.t2.t4 (cl (= @p_184 (! (= veriT_vr27 @p_183) :named @p_185))) :rule cong :premises (t57.t2.t1 t57.t2.t3))
-(step t57.t2.t5 (cl (= @p_186 (! (=> @p_185 false) :named @p_187))) :rule cong :premises (t57.t2.t4))
-(step t57.t2 (cl (= @p_179 (! (forall ((veriT_vr29 Abort$)) @p_187) :named @p_180))) :rule bind)
-(step t57.t3 (cl (= @p_188 (! (and @p_173 @p_180) :named @p_189))) :rule cong :premises (t57.t1 t57.t2))
-(step t57.t4 (cl (= @p_190 (! (=> @p_189 false) :named @p_191))) :rule cong :premises (t57.t3))
-(step t57 (cl (! (= @p_171 (! (forall ((veriT_vr27 V_error_result$)) @p_191) :named @p_193)) :named @p_192)) :rule bind)
-(step t58 (cl (not @p_192) (not @p_171) @p_193) :rule equiv_pos2)
-(step t59 (cl @p_193) :rule th_resolution :premises (axiom7 t57 t58))
-(anchor :step t60 :args ((veriT_vr27 V_error_result$)))
-(anchor :step t60.t1 :args ((veriT_vr28 V$)))
-(step t60.t1.t1 (cl (= @p_178 (! (not @p_176) :named @p_195))) :rule implies_simplify)
-(step t60.t1 (cl (= @p_173 (! (forall ((veriT_vr28 V$)) @p_195) :named @p_194))) :rule bind)
-(anchor :step t60.t2 :args ((veriT_vr29 Abort$)))
-(step t60.t2.t1 (cl (= @p_187 (! (not @p_185) :named @p_197))) :rule implies_simplify)
-(step t60.t2 (cl (= @p_180 (! (forall ((veriT_vr29 Abort$)) @p_197) :named @p_196))) :rule bind)
-(step t60.t3 (cl (= @p_189 (! (and @p_194 @p_196) :named @p_198))) :rule cong :premises (t60.t1 t60.t2))
-(step t60.t4 (cl (= @p_191 (! (=> @p_198 false) :named @p_199))) :rule cong :premises (t60.t3))
-(step t60.t5 (cl (= @p_199 (! (not @p_198) :named @p_200))) :rule implies_simplify)
-(step t60.t6 (cl (= @p_191 @p_200)) :rule trans :premises (t60.t4 t60.t5))
-(step t60 (cl (! (= @p_193 (! (forall ((veriT_vr27 V_error_result$)) @p_200) :named @p_202)) :named @p_201)) :rule bind)
-(step t61 (cl (not @p_201) (not @p_193) @p_202) :rule equiv_pos2)
-(step t62 (cl @p_202) :rule th_resolution :premises (t59 t60 t61))
-(anchor :step t63 :args ((:= (veriT_vr27 V_error_result$) veriT_vr30)))
-(anchor :step t63.t1 :args ((:= (veriT_vr28 V$) veriT_vr31)))
-(step t63.t1.t1 (cl (! (= veriT_vr27 veriT_vr30) :named @p_208)) :rule refl)
-(step t63.t1.t2 (cl (= veriT_vr28 veriT_vr31)) :rule refl)
-(step t63.t1.t3 (cl (= @p_175 (! (rraise$ veriT_vr31) :named @p_204))) :rule cong :premises (t63.t1.t2))
-(step t63.t1.t4 (cl (= @p_176 (! (= veriT_vr30 @p_204) :named @p_205))) :rule cong :premises (t63.t1.t1 t63.t1.t3))
-(step t63.t1.t5 (cl (= @p_195 (! (not @p_205) :named @p_206))) :rule cong :premises (t63.t1.t4))
-(step t63.t1 (cl (= @p_194 (! (forall ((veriT_vr31 V$)) @p_206) :named @p_203))) :rule bind)
-(anchor :step t63.t2 :args ((:= (veriT_vr29 Abort$) veriT_vr32)))
-(step t63.t2.t1 (cl @p_208) :rule refl)
-(step t63.t2.t2 (cl (= veriT_vr29 veriT_vr32)) :rule refl)
-(step t63.t2.t3 (cl (= @p_183 (! (rabort$ veriT_vr32) :named @p_209))) :rule cong :premises (t63.t2.t2))
-(step t63.t2.t4 (cl (= @p_185 (! (= veriT_vr30 @p_209) :named @p_210))) :rule cong :premises (t63.t2.t1 t63.t2.t3))
-(step t63.t2.t5 (cl (= @p_197 (! (not @p_210) :named @p_211))) :rule cong :premises (t63.t2.t4))
-(step t63.t2 (cl (= @p_196 (! (forall ((veriT_vr32 Abort$)) @p_211) :named @p_207))) :rule bind)
-(step t63.t3 (cl (= @p_198 (! (and @p_203 @p_207) :named @p_212))) :rule cong :premises (t63.t1 t63.t2))
-(step t63.t4 (cl (= @p_200 (! (not @p_212) :named @p_213))) :rule cong :premises (t63.t3))
-(step t63 (cl (! (= @p_202 (! (forall ((veriT_vr30 V_error_result$)) @p_213) :named @p_215)) :named @p_214)) :rule bind)
-(step t64 (cl (not @p_214) (not @p_202) @p_215) :rule equiv_pos2)
-(step t65 (cl @p_215) :rule th_resolution :premises (t62 t63 t64))
-(anchor :step t66 :args ((:= (?v0 V_astate_v_list_v_result_prod_fun$) veriT_vr33) (:= (?v1 Abort_astate_v_list_v_result_prod_fun$) veriT_vr34) (:= (?v2 V$) veriT_vr35)))
-(step t66.t1 (cl (! (= ?v0 veriT_vr33) :named @p_221)) :rule refl)
-(step t66.t2 (cl (= ?v1 veriT_vr34)) :rule refl)
-(step t66.t3 (cl (! (= ?v2 veriT_vr35) :named @p_222)) :rule refl)
-(step t66.t4 (cl (= @p_217 (! (rraise$ veriT_vr35) :named @p_218))) :rule cong :premises (t66.t3))
-(step t66.t5 (cl (= @p_219 (! (case_error_result$ veriT_vr33 veriT_vr34 @p_218) :named @p_220))) :rule cong :premises (t66.t1 t66.t2 t66.t4))
-(step t66.t6 (cl @p_221) :rule refl)
-(step t66.t7 (cl @p_222) :rule refl)
-(step t66.t8 (cl (= @p_223 (! (fun_app$ veriT_vr33 veriT_vr35) :named @p_224))) :rule cong :premises (t66.t6 t66.t7))
-(step t66.t9 (cl (= @p_225 (! (= @p_220 @p_224) :named @p_226))) :rule cong :premises (t66.t5 t66.t8))
-(step t66 (cl (! (= @p_216 (! (forall ((veriT_vr33 V_astate_v_list_v_result_prod_fun$) (veriT_vr34 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr35 V$)) @p_226) :named @p_228)) :named @p_227)) :rule bind)
-(step t67 (cl (not @p_227) (not @p_216) @p_228) :rule equiv_pos2)
-(step t68 (cl @p_228) :rule th_resolution :premises (axiom8 t66 t67))
-(anchor :step t69 :args ((:= (veriT_vr33 V_astate_v_list_v_result_prod_fun$) veriT_vr36) (:= (veriT_vr34 Abort_astate_v_list_v_result_prod_fun$) veriT_vr37) (:= (veriT_vr35 V$) veriT_vr38)))
-(step t69.t1 (cl (! (= veriT_vr33 veriT_vr36) :named @p_231)) :rule refl)
-(step t69.t2 (cl (= veriT_vr34 veriT_vr37)) :rule refl)
-(step t69.t3 (cl (! (= veriT_vr35 veriT_vr38) :named @p_232)) :rule refl)
-(step t69.t4 (cl (= @p_218 (! (rraise$ veriT_vr38) :named @p_229))) :rule cong :premises (t69.t3))
-(step t69.t5 (cl (= @p_220 (! (case_error_result$ veriT_vr36 veriT_vr37 @p_229) :named @p_230))) :rule cong :premises (t69.t1 t69.t2 t69.t4))
-(step t69.t6 (cl @p_231) :rule refl)
-(step t69.t7 (cl @p_232) :rule refl)
-(step t69.t8 (cl (= @p_224 (! (fun_app$ veriT_vr36 veriT_vr38) :named @p_233))) :rule cong :premises (t69.t6 t69.t7))
-(step t69.t9 (cl (= @p_226 (! (= @p_230 @p_233) :named @p_234))) :rule cong :premises (t69.t5 t69.t8))
-(step t69 (cl (! (= @p_228 (! (forall ((veriT_vr36 V_astate_v_list_v_result_prod_fun$) (veriT_vr37 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr38 V$)) @p_234) :named @p_236)) :named @p_235)) :rule bind)
-(step t70 (cl (not @p_235) (not @p_228) @p_236) :rule equiv_pos2)
-(step t71 (cl @p_236) :rule th_resolution :premises (t68 t69 t70))
-(anchor :step t72 :args ((:= (?v0 V_astate_v_list_v_result_prod_fun$) veriT_vr39) (:= (?v1 Abort_astate_v_list_v_result_prod_fun$) veriT_vr40) (:= (?v2 Abort$) veriT_vr41)))
-(step t72.t1 (cl (= ?v0 veriT_vr39)) :rule refl)
-(step t72.t2 (cl (! (= ?v1 veriT_vr40) :named @p_242)) :rule refl)
-(step t72.t3 (cl (! (= ?v2 veriT_vr41) :named @p_243)) :rule refl)
-(step t72.t4 (cl (= @p_238 (! (rabort$ veriT_vr41) :named @p_239))) :rule cong :premises (t72.t3))
-(step t72.t5 (cl (= @p_240 (! (case_error_result$ veriT_vr39 veriT_vr40 @p_239) :named @p_241))) :rule cong :premises (t72.t1 t72.t2 t72.t4))
-(step t72.t6 (cl @p_242) :rule refl)
-(step t72.t7 (cl @p_243) :rule refl)
-(step t72.t8 (cl (= @p_244 (! (fun_app$a veriT_vr40 veriT_vr41) :named @p_245))) :rule cong :premises (t72.t6 t72.t7))
-(step t72.t9 (cl (= @p_246 (! (= @p_241 @p_245) :named @p_247))) :rule cong :premises (t72.t5 t72.t8))
-(step t72 (cl (! (= @p_237 (! (forall ((veriT_vr39 V_astate_v_list_v_result_prod_fun$) (veriT_vr40 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr41 Abort$)) @p_247) :named @p_249)) :named @p_248)) :rule bind)
-(step t73 (cl (not @p_248) (not @p_237) @p_249) :rule equiv_pos2)
-(step t74 (cl @p_249) :rule th_resolution :premises (axiom9 t72 t73))
-(anchor :step t75 :args ((:= (veriT_vr39 V_astate_v_list_v_result_prod_fun$) veriT_vr42) (:= (veriT_vr40 Abort_astate_v_list_v_result_prod_fun$) veriT_vr43) (:= (veriT_vr41 Abort$) veriT_vr44)))
-(step t75.t1 (cl (= veriT_vr39 veriT_vr42)) :rule refl)
-(step t75.t2 (cl (! (= veriT_vr40 veriT_vr43) :named @p_252)) :rule refl)
-(step t75.t3 (cl (! (= veriT_vr41 veriT_vr44) :named @p_253)) :rule refl)
-(step t75.t4 (cl (= @p_239 (! (rabort$ veriT_vr44) :named @p_250))) :rule cong :premises (t75.t3))
-(step t75.t5 (cl (= @p_241 (! (case_error_result$ veriT_vr42 veriT_vr43 @p_250) :named @p_251))) :rule cong :premises (t75.t1 t75.t2 t75.t4))
-(step t75.t6 (cl @p_252) :rule refl)
-(step t75.t7 (cl @p_253) :rule refl)
-(step t75.t8 (cl (= @p_245 (! (fun_app$a veriT_vr43 veriT_vr44) :named @p_254))) :rule cong :premises (t75.t6 t75.t7))
-(step t75.t9 (cl (= @p_247 (! (= @p_251 @p_254) :named @p_255))) :rule cong :premises (t75.t5 t75.t8))
-(step t75 (cl (! (= @p_249 (! (forall ((veriT_vr42 V_astate_v_list_v_result_prod_fun$) (veriT_vr43 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr44 Abort$)) @p_255) :named @p_257)) :named @p_256)) :rule bind)
-(step t76 (cl (not @p_256) (not @p_249) @p_257) :rule equiv_pos2)
-(step t77 (cl @p_257) :rule th_resolution :premises (t74 t75 t76))
-(anchor :step t78 :args ((:= (?v0 Astate$) veriT_vr45) (:= (?v1 Astate$) veriT_vr46) (:= (?v2 V_list_v_result$) veriT_vr47) (:= (?v3 Astate$) veriT_vr48)))
-(step t78.t1 (cl (= ?v0 veriT_vr45)) :rule refl)
-(step t78.t2 (cl (! (= ?v1 veriT_vr46) :named @p_270)) :rule refl)
-(step t78.t3 (cl (! (= ?v2 veriT_vr47) :named @p_262)) :rule refl)
-(step t78.t4 (cl (= @p_259 (! (pair$ veriT_vr46 veriT_vr47) :named @p_260))) :rule cong :premises (t78.t2 t78.t3))
-(step t78.t5 (cl (= @p_4 (! (fix_clock$ veriT_vr45 @p_260) :named @p_261))) :rule cong :premises (t78.t1 t78.t4))
-(step t78.t6 (cl (! (= ?v3 veriT_vr48) :named @p_267)) :rule refl)
-(step t78.t7 (cl @p_262) :rule refl)
-(step t78.t8 (cl (= @p_263 (! (pair$ veriT_vr48 veriT_vr47) :named @p_264))) :rule cong :premises (t78.t6 t78.t7))
-(step t78.t9 (cl (= @p_265 (! (= @p_261 @p_264) :named @p_266))) :rule cong :premises (t78.t5 t78.t8))
-(step t78.t10 (cl @p_267) :rule refl)
-(step t78.t11 (cl (= @p_268 (! (clock$ veriT_vr48) :named @p_269))) :rule cong :premises (t78.t10))
-(step t78.t12 (cl @p_270) :rule refl)
-(step t78.t13 (cl (= @p_1 (! (clock$ veriT_vr46) :named @p_271))) :rule cong :premises (t78.t12))
-(step t78.t14 (cl (= @p_272 (! (less_eq$ @p_269 @p_271) :named @p_273))) :rule cong :premises (t78.t11 t78.t13))
-(step t78.t15 (cl (= @p_274 (! (=> @p_266 @p_273) :named @p_275))) :rule cong :premises (t78.t9 t78.t14))
-(step t78 (cl (! (= @p_258 (! (forall ((veriT_vr45 Astate$) (veriT_vr46 Astate$) (veriT_vr47 V_list_v_result$) (veriT_vr48 Astate$)) @p_275) :named @p_277)) :named @p_276)) :rule bind)
-(step t79 (cl (not @p_276) (not @p_258) @p_277) :rule equiv_pos2)
-(step t80 (cl @p_277) :rule th_resolution :premises (axiom10 t78 t79))
-(anchor :step t81 :args ((:= (veriT_vr45 Astate$) veriT_vr49) (:= (veriT_vr46 Astate$) veriT_vr50) (:= (veriT_vr47 V_list_v_result$) veriT_vr51) (:= (veriT_vr48 Astate$) veriT_vr52)))
-(step t81.t1 (cl (= veriT_vr45 veriT_vr49)) :rule refl)
-(step t81.t2 (cl (! (= veriT_vr46 veriT_vr50) :named @p_285)) :rule refl)
-(step t81.t3 (cl (! (= veriT_vr47 veriT_vr51) :named @p_280)) :rule refl)
-(step t81.t4 (cl (= @p_260 (! (pair$ veriT_vr50 veriT_vr51) :named @p_278))) :rule cong :premises (t81.t2 t81.t3))
-(step t81.t5 (cl (= @p_261 (! (fix_clock$ veriT_vr49 @p_278) :named @p_279))) :rule cong :premises (t81.t1 t81.t4))
-(step t81.t6 (cl (! (= veriT_vr48 veriT_vr52) :named @p_283)) :rule refl)
-(step t81.t7 (cl @p_280) :rule refl)
-(step t81.t8 (cl (= @p_264 (! (pair$ veriT_vr52 veriT_vr51) :named @p_281))) :rule cong :premises (t81.t6 t81.t7))
-(step t81.t9 (cl (= @p_266 (! (= @p_279 @p_281) :named @p_282))) :rule cong :premises (t81.t5 t81.t8))
-(step t81.t10 (cl @p_283) :rule refl)
-(step t81.t11 (cl (= @p_269 (! (clock$ veriT_vr52) :named @p_284))) :rule cong :premises (t81.t10))
-(step t81.t12 (cl @p_285) :rule refl)
-(step t81.t13 (cl (= @p_271 (! (clock$ veriT_vr50) :named @p_286))) :rule cong :premises (t81.t12))
-(step t81.t14 (cl (= @p_273 (! (less_eq$ @p_284 @p_286) :named @p_287))) :rule cong :premises (t81.t11 t81.t13))
-(step t81.t15 (cl (= @p_275 (! (=> @p_282 @p_287) :named @p_288))) :rule cong :premises (t81.t9 t81.t14))
-(step t81 (cl (! (= @p_277 (! (forall ((veriT_vr49 Astate$) (veriT_vr50 Astate$) (veriT_vr51 V_list_v_result$) (veriT_vr52 Astate$)) @p_288) :named @p_290)) :named @p_289)) :rule bind)
-(step t82 (cl (not @p_289) (not @p_277) @p_290) :rule equiv_pos2)
-(step t83 (cl @p_290) :rule th_resolution :premises (t80 t81 t82))
-(anchor :step t84 :args ((:= (?v0 Astate$) veriT_vr53) (:= (?v1 Astate$) veriT_vr54) (:= (?v2 V_list_v_result$) veriT_vr55)))
-(step t84.t1 (cl (! (= ?v0 veriT_vr53) :named @p_294)) :rule refl)
-(step t84.t2 (cl (! (= ?v1 veriT_vr54) :named @p_295)) :rule refl)
-(step t84.t3 (cl (! (= ?v2 veriT_vr55) :named @p_299)) :rule refl)
-(step t84.t4 (cl (= @p_259 (! (pair$ veriT_vr54 veriT_vr55) :named @p_292))) :rule cong :premises (t84.t2 t84.t3))
-(step t84.t5 (cl (= @p_4 (! (fix_clock$ veriT_vr53 @p_292) :named @p_293))) :rule cong :premises (t84.t1 t84.t4))
-(step t84.t6 (cl @p_294) :rule refl)
-(step t84.t7 (cl @p_295) :rule refl)
-(step t84.t8 (cl (= @p_5 (! (uu$ veriT_vr53 veriT_vr54) :named @p_296))) :rule cong :premises (t84.t6 t84.t7))
-(step t84.t9 (cl @p_295) :rule refl)
-(step t84.t10 (cl (= @p_297 (! (update_clock$ @p_296 veriT_vr54) :named @p_298))) :rule cong :premises (t84.t8 t84.t9))
-(step t84.t11 (cl @p_299) :rule refl)
-(step t84.t12 (cl (= @p_300 (! (pair$ @p_298 veriT_vr55) :named @p_301))) :rule cong :premises (t84.t10 t84.t11))
-(step t84.t13 (cl (= @p_302 (! (= @p_293 @p_301) :named @p_303))) :rule cong :premises (t84.t5 t84.t12))
-(step t84 (cl (! (= @p_291 (! (forall ((veriT_vr53 Astate$) (veriT_vr54 Astate$) (veriT_vr55 V_list_v_result$)) @p_303) :named @p_305)) :named @p_304)) :rule bind)
-(step t85 (cl (not @p_304) (not @p_291) @p_305) :rule equiv_pos2)
-(step t86 (cl @p_305) :rule th_resolution :premises (axiom11 t84 t85))
-(anchor :step t87 :args ((:= (veriT_vr53 Astate$) veriT_vr56) (:= (veriT_vr54 Astate$) veriT_vr57) (:= (veriT_vr55 V_list_v_result$) veriT_vr58)))
-(step t87.t1 (cl (! (= veriT_vr53 veriT_vr56) :named @p_308)) :rule refl)
-(step t87.t2 (cl (! (= veriT_vr54 veriT_vr57) :named @p_309)) :rule refl)
-(step t87.t3 (cl (! (= veriT_vr55 veriT_vr58) :named @p_312)) :rule refl)
-(step t87.t4 (cl (= @p_292 (! (pair$ veriT_vr57 veriT_vr58) :named @p_306))) :rule cong :premises (t87.t2 t87.t3))
-(step t87.t5 (cl (= @p_293 (! (fix_clock$ veriT_vr56 @p_306) :named @p_307))) :rule cong :premises (t87.t1 t87.t4))
-(step t87.t6 (cl @p_308) :rule refl)
-(step t87.t7 (cl @p_309) :rule refl)
-(step t87.t8 (cl (= @p_296 (! (uu$ veriT_vr56 veriT_vr57) :named @p_310))) :rule cong :premises (t87.t6 t87.t7))
-(step t87.t9 (cl @p_309) :rule refl)
-(step t87.t10 (cl (= @p_298 (! (update_clock$ @p_310 veriT_vr57) :named @p_311))) :rule cong :premises (t87.t8 t87.t9))
-(step t87.t11 (cl @p_312) :rule refl)
-(step t87.t12 (cl (= @p_301 (! (pair$ @p_311 veriT_vr58) :named @p_313))) :rule cong :premises (t87.t10 t87.t11))
-(step t87.t13 (cl (= @p_303 (! (= @p_307 @p_313) :named @p_314))) :rule cong :premises (t87.t5 t87.t12))
-(step t87 (cl (! (= @p_305 (! (forall ((veriT_vr56 Astate$) (veriT_vr57 Astate$) (veriT_vr58 V_list_v_result$)) @p_314) :named @p_316)) :named @p_315)) :rule bind)
-(step t88 (cl (not @p_315) (not @p_305) @p_316) :rule equiv_pos2)
-(step t89 (cl @p_316) :rule th_resolution :premises (t86 t87 t88))
-(anchor :step t90 :args ((:= (?v0 V_error_result$) veriT_vr59) (:= (?v1 V$) veriT_vr60)))
-(step t90.t1 (cl (! (= ?v0 veriT_vr59) :named @p_323)) :rule refl)
-(step t90.t2 (cl (= @p_319 (! (rerr$ veriT_vr59) :named @p_320))) :rule cong :premises (t90.t1))
-(step t90.t3 (cl (= @p_321 (! (= r$ @p_320) :named @p_322))) :rule cong :premises (t90.t2))
-(step t90.t4 (cl @p_323) :rule refl)
-(step t90.t5 (cl (! (= ?v1 veriT_vr60) :named @p_328)) :rule refl)
-(step t90.t6 (cl (= @p_174 (! (rraise$ veriT_vr60) :named @p_324))) :rule cong :premises (t90.t5))
-(step t90.t7 (cl (= @p_6 (! (= veriT_vr59 @p_324) :named @p_325))) :rule cong :premises (t90.t4 t90.t6))
-(step t90.t8 (cl (= @p_326 (! (and @p_322 @p_325) :named @p_327))) :rule cong :premises (t90.t3 t90.t7))
-(step t90.t9 (cl @p_328) :rule refl)
-(step t90.t10 (cl (= @p_329 (! (fun_evaluate_match$ st$ env$ veriT_vr60 pes$) :named @p_330))) :rule cong :premises (t90.t9))
-(step t90.t11 (cl @p_328) :rule refl)
-(step t90.t12 (cl (= @p_331 (! (fun_app$ @p_330 veriT_vr60) :named @p_332))) :rule cong :premises (t90.t10 t90.t11))
-(step t90.t13 (cl (= @p_333 (! (fst$ @p_332) :named @p_334))) :rule cong :premises (t90.t12))
-(step t90.t14 (cl (= @p_335 (! (clock$ @p_334) :named @p_336))) :rule cong :premises (t90.t13))
-(step t90.t15 (cl (= @p_337 (! (less_eq$ @p_336 @p_318) :named @p_338))) :rule cong :premises (t90.t14))
-(step t90.t16 (cl (= @p_339 (! (=> @p_327 @p_338) :named @p_340))) :rule cong :premises (t90.t8 t90.t15))
-(step t90 (cl (! (= @p_317 (! (forall ((veriT_vr59 V_error_result$) (veriT_vr60 V$)) @p_340) :named @p_342)) :named @p_341)) :rule bind)
-(step t91 (cl (not @p_341) (not @p_317) @p_342) :rule equiv_pos2)
-(step t92 (cl @p_342) :rule th_resolution :premises (axiom12 t90 t91))
-(anchor :step t93 :args ((:= (veriT_vr59 V_error_result$) veriT_vr61) (:= (veriT_vr60 V$) veriT_vr62)))
-(step t93.t1 (cl (! (= veriT_vr59 veriT_vr61) :named @p_345)) :rule refl)
-(step t93.t2 (cl (= @p_320 (! (rerr$ veriT_vr61) :named @p_343))) :rule cong :premises (t93.t1))
-(step t93.t3 (cl (= @p_322 (! (= r$ @p_343) :named @p_344))) :rule cong :premises (t93.t2))
-(step t93.t4 (cl @p_345) :rule refl)
-(step t93.t5 (cl (! (= veriT_vr60 veriT_vr62) :named @p_349)) :rule refl)
-(step t93.t6 (cl (= @p_324 (! (rraise$ veriT_vr62) :named @p_346))) :rule cong :premises (t93.t5))
-(step t93.t7 (cl (= @p_325 (! (= veriT_vr61 @p_346) :named @p_347))) :rule cong :premises (t93.t4 t93.t6))
-(step t93.t8 (cl (= @p_327 (! (and @p_344 @p_347) :named @p_348))) :rule cong :premises (t93.t3 t93.t7))
-(step t93.t9 (cl @p_349) :rule refl)
-(step t93.t10 (cl (= @p_330 (! (fun_evaluate_match$ st$ env$ veriT_vr62 pes$) :named @p_350))) :rule cong :premises (t93.t9))
-(step t93.t11 (cl @p_349) :rule refl)
-(step t93.t12 (cl (= @p_332 (! (fun_app$ @p_350 veriT_vr62) :named @p_351))) :rule cong :premises (t93.t10 t93.t11))
-(step t93.t13 (cl (= @p_334 (! (fst$ @p_351) :named @p_352))) :rule cong :premises (t93.t12))
-(step t93.t14 (cl (= @p_336 (! (clock$ @p_352) :named @p_353))) :rule cong :premises (t93.t13))
-(step t93.t15 (cl (= @p_338 (! (less_eq$ @p_353 @p_318) :named @p_354))) :rule cong :premises (t93.t14))
-(step t93.t16 (cl (= @p_340 (! (=> @p_348 @p_354) :named @p_355))) :rule cong :premises (t93.t8 t93.t15))
-(step t93 (cl (! (= @p_342 (! (forall ((veriT_vr61 V_error_result$) (veriT_vr62 V$)) @p_355) :named @p_357)) :named @p_356)) :rule bind)
-(step t94 (cl (not @p_356) (not @p_342) @p_357) :rule equiv_pos2)
-(step t95 (cl @p_357) :rule th_resolution :premises (t92 t93 t94))
-(step t96 (cl (! (= @p_358 (! (and @p_359 (! (not @p_360) :named @p_366)) :named @p_362)) :named @p_361)) :rule bool_simplify)
-(step t97 (cl (! (not @p_361) :named @p_365) (! (not @p_358) :named @p_363) @p_362) :rule equiv_pos2)
-(step t98 (cl (not @p_363) @p_364) :rule not_not)
-(step t99 (cl @p_365 @p_364 @p_362) :rule th_resolution :premises (t98 t97))
-(step t100 (cl @p_362) :rule th_resolution :premises (axiom13 t96 t99))
-(step t101 (cl @p_359) :rule and :premises (t100))
-(step t102 (cl @p_366) :rule and :premises (t100))
-(step t103 (cl (or (! (not @p_105) :named @p_368) (! (forall ((veriT_vr13 Nat$) (veriT_vr14 Nat$) (veriT_vr15 Nat$)) (or (not @p_96) (not @p_98) @p_102)) :named @p_573))) :rule qnt_cnf)
-(step t104 (cl (or (! (not @p_170) :named @p_431) (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$) (veriT_vr26 V_list_v_result$)) (or @p_367 @p_146)) :named @p_629))) :rule qnt_cnf)
-(step t105 (cl (or @p_368 (! (=> (! (and @p_369 (! (less_eq$ @p_370 @p_371) :named @p_373)) :named @p_372) @p_360) :named @p_374))) :rule forall_inst :args ((:= veriT_vr13 @p_371) (:= veriT_vr14 @p_7) (:= veriT_vr15 @p_370)))
-(step t106 (cl @p_372 (! (not @p_369) :named @p_574) (! (not @p_373) :named @p_375)) :rule and_neg)
-(step t107 (cl (! (not @p_374) :named @p_376) (! (not @p_372) :named @p_377) @p_360) :rule implies_pos)
-(step t108 (cl @p_368 @p_374) :rule or :premises (t105))
-(step t109 (cl @p_372 @p_375) :rule resolution :premises (t106 axiom4))
-(step t110 (cl @p_376 @p_377) :rule resolution :premises (t107 t102))
-(step t111 (cl @p_374) :rule resolution :premises (t108 t38))
-(step t112 (cl @p_377) :rule resolution :premises (t110 t111))
-(step t113 (cl @p_375) :rule resolution :premises (t109 t112))
-(step t114 (cl (not (! (not @p_368) :named @p_578)) @p_105) :rule not_not)
-(step t115 (cl (or (! (not @p_316) :named @p_547) (! (= (fix_clock$ st$a (pair$ @p_378 r$)) (pair$ (! (update_clock$ (uu$ st$a @p_378) @p_378) :named @p_561) r$)) :named @p_548))) :rule forall_inst :args ((:= veriT_vr56 st$a) (:= veriT_vr57 @p_378) (:= veriT_vr58 r$)))
-(step t116 (cl (or (! (not @p_215) :named @p_427) (! (not (! (and (! (forall ((veriT_vr31 V$)) (! (not (! (= x2$ @p_204) :named @p_382)) :named @p_384)) :named @p_380) (! (forall ((veriT_vr32 Abort$)) (! (not (! (= x2$ @p_209) :named @p_388)) :named @p_390)) :named @p_386)) :named @p_392)) :named @p_379))) :rule forall_inst :args ((:= veriT_vr30 x2$)))
-(anchor :step t117)
-(assume t117.h1 @p_379)
-(anchor :step t117.t2 :args ((:= (veriT_vr31 V$) veriT_vr63)))
-(step t117.t2.t1 (cl (= veriT_vr31 veriT_vr63)) :rule refl)
-(step t117.t2.t2 (cl (= @p_204 (! (rraise$ veriT_vr63) :named @p_381))) :rule cong :premises (t117.t2.t1))
-(step t117.t2.t3 (cl (= @p_382 (! (= x2$ @p_381) :named @p_383))) :rule cong :premises (t117.t2.t2))
-(step t117.t2.t4 (cl (= @p_384 (! (not @p_383) :named @p_385))) :rule cong :premises (t117.t2.t3))
-(step t117.t2 (cl (= @p_380 (! (forall ((veriT_vr63 V$)) @p_385) :named @p_393))) :rule bind)
-(anchor :step t117.t3 :args ((:= (veriT_vr32 Abort$) veriT_vr64)))
-(step t117.t3.t1 (cl (= veriT_vr32 veriT_vr64)) :rule refl)
-(step t117.t3.t2 (cl (= @p_209 (! (rabort$ veriT_vr64) :named @p_387))) :rule cong :premises (t117.t3.t1))
-(step t117.t3.t3 (cl (= @p_388 (! (= x2$ @p_387) :named @p_389))) :rule cong :premises (t117.t3.t2))
-(step t117.t3.t4 (cl (= @p_390 (! (not @p_389) :named @p_391))) :rule cong :premises (t117.t3.t3))
-(step t117.t3 (cl (= @p_386 (! (forall ((veriT_vr64 Abort$)) @p_391) :named @p_394))) :rule bind)
-(step t117.t4 (cl (= @p_392 (! (and @p_393 @p_394) :named @p_395))) :rule cong :premises (t117.t2 t117.t3))
-(step t117.t5 (cl (! (= @p_379 (! (not @p_395) :named @p_398)) :named @p_396)) :rule cong :premises (t117.t4))
-(step t117.t6 (cl (! (not @p_396) :named @p_399) (! (not @p_379) :named @p_397) @p_398) :rule equiv_pos2)
-(step t117.t7 (cl (! (not @p_397) :named @p_426) @p_392) :rule not_not)
-(step t117.t8 (cl @p_399 @p_392 @p_398) :rule th_resolution :premises (t117.t7 t117.t6))
-(step t117.t9 (cl @p_398) :rule th_resolution :premises (t117.h1 t117.t5 t117.t8))
-(anchor :step t117.t10 :args ((:= (veriT_vr63 V$) veriT_vr65)))
-(step t117.t10.t1 (cl (= veriT_vr63 veriT_vr65)) :rule refl)
-(step t117.t10.t2 (cl (= @p_381 @p_401)) :rule cong :premises (t117.t10.t1))
-(step t117.t10.t3 (cl (= @p_383 @p_402)) :rule cong :premises (t117.t10.t2))
-(step t117.t10.t4 (cl (= @p_385 @p_400)) :rule cong :premises (t117.t10.t3))
-(step t117.t10 (cl (= @p_393 (! (forall ((veriT_vr65 V$)) @p_400) :named @p_406))) :rule bind)
-(anchor :step t117.t11 :args ((:= (veriT_vr64 Abort$) veriT_vr66)))
-(step t117.t11.t1 (cl (= veriT_vr64 veriT_vr66)) :rule refl)
-(step t117.t11.t2 (cl (= @p_387 @p_404)) :rule cong :premises (t117.t11.t1))
-(step t117.t11.t3 (cl (= @p_389 @p_405)) :rule cong :premises (t117.t11.t2))
-(step t117.t11.t4 (cl (= @p_391 @p_403)) :rule cong :premises (t117.t11.t3))
-(step t117.t11 (cl (= @p_394 (! (forall ((veriT_vr66 Abort$)) @p_403) :named @p_407))) :rule bind)
-(step t117.t12 (cl (= @p_395 (! (and @p_406 @p_407) :named @p_408))) :rule cong :premises (t117.t10 t117.t11))
-(step t117.t13 (cl (! (= @p_398 (! (not @p_408) :named @p_410)) :named @p_409)) :rule cong :premises (t117.t12))
-(step t117.t14 (cl (! (not @p_409) :named @p_412) (! (not @p_398) :named @p_411) @p_410) :rule equiv_pos2)
-(step t117.t15 (cl (not @p_411) @p_395) :rule not_not)
-(step t117.t16 (cl @p_412 @p_395 @p_410) :rule th_resolution :premises (t117.t15 t117.t14))
-(step t117.t17 (cl @p_410) :rule th_resolution :premises (t117.t9 t117.t13 t117.t16))
-(anchor :step t117.t18 :args ((:= (veriT_vr65 V$) veriT_sk0)))
-(step t117.t18.t1 (cl (= veriT_vr65 veriT_sk0)) :rule refl)
-(step t117.t18.t2 (cl (= @p_401 (! (rraise$ veriT_sk0) :named @p_415))) :rule cong :premises (t117.t18.t1))
-(step t117.t18.t3 (cl (= @p_402 (! (= x2$ @p_415) :named @p_416))) :rule cong :premises (t117.t18.t2))
-(step t117.t18.t4 (cl (= @p_400 (! (not @p_416) :named @p_413))) :rule cong :premises (t117.t18.t3))
-(step t117.t18 (cl (= @p_406 @p_413)) :rule sko_forall)
-(anchor :step t117.t19 :args ((:= (veriT_vr66 Abort$) veriT_sk1)))
-(step t117.t19.t1 (cl (= veriT_vr66 veriT_sk1)) :rule refl)
-(step t117.t19.t2 (cl (= @p_404 (! (rabort$ veriT_sk1) :named @p_419))) :rule cong :premises (t117.t19.t1))
-(step t117.t19.t3 (cl (= @p_405 (! (= x2$ @p_419) :named @p_420))) :rule cong :premises (t117.t19.t2))
-(step t117.t19.t4 (cl (= @p_403 (! (not @p_420) :named @p_417))) :rule cong :premises (t117.t19.t3))
-(step t117.t19 (cl (= @p_407 @p_417)) :rule sko_forall)
-(step t117.t20 (cl (= @p_408 (! (and @p_413 @p_417) :named @p_421))) :rule cong :premises (t117.t18 t117.t19))
-(step t117.t21 (cl (! (= @p_410 (! (not @p_421) :named @p_422)) :named @p_423)) :rule cong :premises (t117.t20))
-(step t117.t22 (cl (! (not @p_423) :named @p_425) (! (not @p_410) :named @p_424) @p_422) :rule equiv_pos2)
-(step t117.t23 (cl (not @p_424) @p_408) :rule not_not)
-(step t117.t24 (cl @p_425 @p_408 @p_422) :rule th_resolution :premises (t117.t23 t117.t22))
-(step t117.t25 (cl @p_422) :rule th_resolution :premises (t117.t17 t117.t21 t117.t24))
-(step t117 (cl @p_397 @p_422) :rule subproof :discharge (h1))
-(step t118 (cl @p_426 @p_392) :rule not_not)
-(step t119 (cl @p_392 @p_422) :rule th_resolution :premises (t118 t117))
-(step t120 (cl @p_427 @p_379) :rule or :premises (t116))
-(step t121 (cl (! (or @p_427 @p_422) :named @p_429) (! (not @p_427) :named @p_428)) :rule or_neg)
-(step t122 (cl (not @p_428) @p_215) :rule not_not)
-(step t123 (cl @p_429 @p_215) :rule th_resolution :premises (t122 t121))
-(step t124 (cl @p_429 (! (not @p_422) :named @p_430)) :rule or_neg)
-(step t125 (cl (not @p_430) @p_421) :rule not_not)
-(step t126 (cl @p_429 @p_421) :rule th_resolution :premises (t125 t124))
-(step t127 (cl @p_429) :rule th_resolution :premises (t120 t119 t123 t126))
-(step t128 (cl (not (! (not @p_431) :named @p_468)) @p_170) :rule not_not)
-(step t129 (cl (or @p_431 (! (and (! (=> (! (= @p_378 @p_378) :named @p_432) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_3 (! (pair$ @p_378 veriT_vr25) :named @p_435)) :named @p_437)) :named @p_434)) :named @p_439) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_3 (! (pair$ @p_378 veriT_vr26) :named @p_442)) :named @p_443)) :named @p_444)) :named @p_441)) :named @p_446) @p_432) :named @p_448)) :named @p_433))) :rule forall_inst :args ((:= veriT_vr23 @p_378) (:= veriT_vr24 @p_3)))
-(anchor :step t130)
-(assume t130.h1 @p_433)
-(anchor :step t130.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr72)))
-(step t130.t2.t1 (cl (= veriT_vr25 veriT_vr72)) :rule refl)
-(step t130.t2.t2 (cl (= @p_435 (! (pair$ @p_378 veriT_vr72) :named @p_436))) :rule cong :premises (t130.t2.t1))
-(step t130.t2.t3 (cl (= @p_437 (! (= @p_3 @p_436) :named @p_438))) :rule cong :premises (t130.t2.t2))
-(step t130.t2 (cl (= @p_434 (! (exists ((veriT_vr72 V_list_v_result$)) @p_438) :named @p_440))) :rule bind)
-(step t130.t3 (cl (= @p_439 (! (=> @p_432 @p_440) :named @p_450))) :rule cong :premises (t130.t2))
-(anchor :step t130.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr72)))
-(step t130.t4.t1 (cl (= veriT_vr26 veriT_vr72)) :rule refl)
-(step t130.t4.t2 (cl (= @p_442 @p_436)) :rule cong :premises (t130.t4.t1))
-(step t130.t4.t3 (cl (= @p_443 @p_438)) :rule cong :premises (t130.t4.t2))
-(step t130.t4.t4 (cl (= @p_444 (! (not @p_438) :named @p_445))) :rule cong :premises (t130.t4.t3))
-(step t130.t4 (cl (= @p_441 (! (forall ((veriT_vr72 V_list_v_result$)) @p_445) :named @p_447))) :rule bind)
-(step t130.t5 (cl (= @p_446 (! (not @p_447) :named @p_449))) :rule cong :premises (t130.t4))
-(step t130.t6 (cl (= @p_448 (! (=> @p_449 @p_432) :named @p_451))) :rule cong :premises (t130.t5))
-(step t130.t7 (cl (! (= @p_433 (! (and @p_450 @p_451) :named @p_454)) :named @p_452)) :rule cong :premises (t130.t3 t130.t6))
-(step t130.t8 (cl (not @p_452) (! (not @p_433) :named @p_453) @p_454) :rule equiv_pos2)
-(step t130.t9 (cl @p_454) :rule th_resolution :premises (t130.h1 t130.t7 t130.t8))
-(step t130.t10 (cl (= @p_432 true)) :rule eq_simplify)
-(step t130.t11 (cl (= @p_450 (! (=> true @p_440) :named @p_455))) :rule cong :premises (t130.t10))
-(step t130.t12 (cl (= @p_455 @p_440)) :rule implies_simplify)
-(step t130.t13 (cl (= @p_450 @p_440)) :rule trans :premises (t130.t11 t130.t12))
-(step t130.t14 (cl (= @p_451 (! (=> @p_449 true) :named @p_456))) :rule cong :premises (t130.t10))
-(step t130.t15 (cl (= @p_456 true)) :rule implies_simplify)
-(step t130.t16 (cl (= @p_451 true)) :rule trans :premises (t130.t14 t130.t15))
-(step t130.t17 (cl (= @p_454 (! (and @p_440 true) :named @p_457))) :rule cong :premises (t130.t13 t130.t16))
-(step t130.t18 (cl (= @p_457 (! (and @p_440) :named @p_458))) :rule and_simplify)
-(step t130.t19 (cl (= @p_458 @p_440)) :rule and_simplify)
-(step t130.t20 (cl (! (= @p_454 @p_440) :named @p_459)) :rule trans :premises (t130.t17 t130.t18 t130.t19))
-(step t130.t21 (cl (not @p_459) (not @p_454) @p_440) :rule equiv_pos2)
-(step t130.t22 (cl @p_440) :rule th_resolution :premises (t130.t9 t130.t20 t130.t21))
-(anchor :step t130.t23 :args ((:= (veriT_vr72 V_list_v_result$) veriT_vr73)))
-(step t130.t23.t1 (cl (= veriT_vr72 veriT_vr73)) :rule refl)
-(step t130.t23.t2 (cl (= @p_436 @p_461)) :rule cong :premises (t130.t23.t1))
-(step t130.t23.t3 (cl (= @p_438 @p_460)) :rule cong :premises (t130.t23.t2))
-(step t130.t23 (cl (! (= @p_440 (! (exists ((veriT_vr73 V_list_v_result$)) @p_460) :named @p_463)) :named @p_462)) :rule bind)
-(step t130.t24 (cl (not @p_462) (not @p_440) @p_463) :rule equiv_pos2)
-(step t130.t25 (cl @p_463) :rule th_resolution :premises (t130.t22 t130.t23 t130.t24))
-(anchor :step t130.t26 :args ((:= (veriT_vr73 V_list_v_result$) veriT_sk3)))
-(step t130.t26.t1 (cl (= veriT_vr73 veriT_sk3)) :rule refl)
-(step t130.t26.t2 (cl (= @p_461 (! (pair$ @p_378 veriT_sk3) :named @p_466))) :rule cong :premises (t130.t26.t1))
-(step t130.t26.t3 (cl (= @p_460 (! (= @p_3 @p_466) :named @p_464))) :rule cong :premises (t130.t26.t2))
-(step t130.t26 (cl (! (= @p_463 @p_464) :named @p_467)) :rule sko_ex)
-(step t130.t27 (cl (not @p_467) (not @p_463) @p_464) :rule equiv_pos2)
-(step t130.t28 (cl @p_464) :rule th_resolution :premises (t130.t25 t130.t26 t130.t27))
-(step t130 (cl @p_453 @p_464) :rule subproof :discharge (h1))
-(step t131 (cl @p_431 @p_433) :rule or :premises (t129))
-(step t132 (cl (! (or @p_431 @p_464) :named @p_469) @p_468) :rule or_neg)
-(step t133 (cl @p_469 @p_170) :rule th_resolution :premises (t128 t132))
-(step t134 (cl @p_469 (! (not @p_464) :named @p_595)) :rule or_neg)
-(step t135 (cl @p_469) :rule th_resolution :premises (t131 t130 t133 t134))
-(step t136 (cl (or @p_431 (! (and (! (=> (! (= st$ (! (fst$ @p_470) :named @p_650)) :named @p_471) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_470 (! (pair$ st$ veriT_vr25) :named @p_474)) :named @p_476)) :named @p_473)) :named @p_478) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_470 (! (pair$ st$ veriT_vr26) :named @p_481)) :named @p_482)) :named @p_483)) :named @p_480)) :named @p_485) @p_471) :named @p_487)) :named @p_472))) :rule forall_inst :args ((:= veriT_vr23 st$) (:= veriT_vr24 @p_470)))
-(anchor :step t137)
-(assume t137.h1 @p_472)
-(anchor :step t137.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr106)))
-(step t137.t2.t1 (cl (= veriT_vr25 veriT_vr106)) :rule refl)
-(step t137.t2.t2 (cl (= @p_474 (! (pair$ st$ veriT_vr106) :named @p_475))) :rule cong :premises (t137.t2.t1))
-(step t137.t2.t3 (cl (= @p_476 (! (= @p_470 @p_475) :named @p_477))) :rule cong :premises (t137.t2.t2))
-(step t137.t2 (cl (= @p_473 (! (exists ((veriT_vr106 V_list_v_result$)) @p_477) :named @p_479))) :rule bind)
-(step t137.t3 (cl (= @p_478 (! (=> @p_471 @p_479) :named @p_489))) :rule cong :premises (t137.t2))
-(anchor :step t137.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr106)))
-(step t137.t4.t1 (cl (= veriT_vr26 veriT_vr106)) :rule refl)
-(step t137.t4.t2 (cl (= @p_481 @p_475)) :rule cong :premises (t137.t4.t1))
-(step t137.t4.t3 (cl (= @p_482 @p_477)) :rule cong :premises (t137.t4.t2))
-(step t137.t4.t4 (cl (= @p_483 (! (not @p_477) :named @p_484))) :rule cong :premises (t137.t4.t3))
-(step t137.t4 (cl (= @p_480 (! (forall ((veriT_vr106 V_list_v_result$)) @p_484) :named @p_486))) :rule bind)
-(step t137.t5 (cl (= @p_485 (! (not @p_486) :named @p_488))) :rule cong :premises (t137.t4))
-(step t137.t6 (cl (= @p_487 (! (=> @p_488 @p_471) :named @p_490))) :rule cong :premises (t137.t5))
-(step t137.t7 (cl (! (= @p_472 (! (and @p_489 @p_490) :named @p_493)) :named @p_491)) :rule cong :premises (t137.t3 t137.t6))
-(step t137.t8 (cl (not @p_491) (! (not @p_472) :named @p_492) @p_493) :rule equiv_pos2)
-(step t137.t9 (cl @p_493) :rule th_resolution :premises (t137.h1 t137.t7 t137.t8))
-(anchor :step t137.t10 :args ((:= (veriT_vr106 V_list_v_result$) veriT_vr107)))
-(step t137.t10.t1 (cl (= veriT_vr106 veriT_vr107)) :rule refl)
-(step t137.t10.t2 (cl (= @p_475 (! (pair$ st$ veriT_vr107) :named @p_494))) :rule cong :premises (t137.t10.t1))
-(step t137.t10.t3 (cl (= @p_477 (! (= @p_470 @p_494) :named @p_495))) :rule cong :premises (t137.t10.t2))
-(step t137.t10.t4 (cl (= @p_484 (! (not @p_495) :named @p_496))) :rule cong :premises (t137.t10.t3))
-(step t137.t10 (cl (= @p_486 (! (forall ((veriT_vr107 V_list_v_result$)) @p_496) :named @p_497))) :rule bind)
-(step t137.t11 (cl (= @p_488 (! (not @p_497) :named @p_498))) :rule cong :premises (t137.t10))
-(step t137.t12 (cl (= @p_490 (! (=> @p_498 @p_471) :named @p_499))) :rule cong :premises (t137.t11))
-(step t137.t13 (cl (! (= @p_493 (! (and @p_489 @p_499) :named @p_501)) :named @p_500)) :rule cong :premises (t137.t12))
-(step t137.t14 (cl (not @p_500) (not @p_493) @p_501) :rule equiv_pos2)
-(step t137.t15 (cl @p_501) :rule th_resolution :premises (t137.t9 t137.t13 t137.t14))
-(anchor :step t137.t16 :args ((:= (veriT_vr106 V_list_v_result$) veriT_vr108)))
-(step t137.t16.t1 (cl (= veriT_vr106 veriT_vr108)) :rule refl)
-(step t137.t16.t2 (cl (= @p_475 @p_503)) :rule cong :premises (t137.t16.t1))
-(step t137.t16.t3 (cl (= @p_477 @p_502)) :rule cong :premises (t137.t16.t2))
-(step t137.t16 (cl (= @p_479 (! (exists ((veriT_vr108 V_list_v_result$)) @p_502) :named @p_504))) :rule bind)
-(step t137.t17 (cl (= @p_489 (! (=> @p_471 @p_504) :named @p_510))) :rule cong :premises (t137.t16))
-(anchor :step t137.t18 :args ((:= (veriT_vr107 V_list_v_result$) veriT_vr109)))
-(step t137.t18.t1 (cl (= veriT_vr107 veriT_vr109)) :rule refl)
-(step t137.t18.t2 (cl (= @p_494 (! (pair$ st$ veriT_vr109) :named @p_505))) :rule cong :premises (t137.t18.t1))
-(step t137.t18.t3 (cl (= @p_495 (! (= @p_470 @p_505) :named @p_506))) :rule cong :premises (t137.t18.t2))
-(step t137.t18.t4 (cl (= @p_496 (! (not @p_506) :named @p_507))) :rule cong :premises (t137.t18.t3))
-(step t137.t18 (cl (= @p_497 (! (forall ((veriT_vr109 V_list_v_result$)) @p_507) :named @p_508))) :rule bind)
-(step t137.t19 (cl (= @p_498 (! (not @p_508) :named @p_509))) :rule cong :premises (t137.t18))
-(step t137.t20 (cl (= @p_499 (! (=> @p_509 @p_471) :named @p_511))) :rule cong :premises (t137.t19))
-(step t137.t21 (cl (! (= @p_501 (! (and @p_510 @p_511) :named @p_513)) :named @p_512)) :rule cong :premises (t137.t17 t137.t20))
-(step t137.t22 (cl (not @p_512) (not @p_501) @p_513) :rule equiv_pos2)
-(step t137.t23 (cl @p_513) :rule th_resolution :premises (t137.t15 t137.t21 t137.t22))
-(anchor :step t137.t24 :args ((:= (veriT_vr108 V_list_v_result$) veriT_sk11)))
-(step t137.t24.t1 (cl (= veriT_vr108 veriT_sk11)) :rule refl)
-(step t137.t24.t2 (cl (= @p_503 (! (pair$ st$ veriT_sk11) :named @p_516))) :rule cong :premises (t137.t24.t1))
-(step t137.t24.t3 (cl (= @p_502 (! (= @p_470 @p_516) :named @p_514))) :rule cong :premises (t137.t24.t2))
-(step t137.t24 (cl (= @p_504 @p_514)) :rule sko_ex)
-(step t137.t25 (cl (= @p_510 (! (=> @p_471 @p_514) :named @p_517))) :rule cong :premises (t137.t24))
-(step t137.t26 (cl (! (= @p_513 (! (and @p_517 @p_511) :named @p_519)) :named @p_518)) :rule cong :premises (t137.t25))
-(step t137.t27 (cl (not @p_518) (not @p_513) @p_519) :rule equiv_pos2)
-(step t137.t28 (cl @p_519) :rule th_resolution :premises (t137.t23 t137.t26 t137.t27))
-(anchor :step t137.t29 :args ((:= (veriT_vr109 V_list_v_result$) veriT_vr110)))
-(step t137.t29.t1 (cl (= veriT_vr109 veriT_vr110)) :rule refl)
-(step t137.t29.t2 (cl (= @p_505 (! (pair$ st$ veriT_vr110) :named @p_521))) :rule cong :premises (t137.t29.t1))
-(step t137.t29.t3 (cl (= @p_506 (! (= @p_470 @p_521) :named @p_522))) :rule cong :premises (t137.t29.t2))
-(step t137.t29.t4 (cl (= @p_507 (! (not @p_522) :named @p_523))) :rule cong :premises (t137.t29.t3))
-(step t137.t29 (cl (= @p_508 (! (forall ((veriT_vr110 V_list_v_result$)) @p_523) :named @p_520))) :rule bind)
-(step t137.t30 (cl (= @p_509 (! (not @p_520) :named @p_524))) :rule cong :premises (t137.t29))
-(step t137.t31 (cl (= @p_511 (! (=> @p_524 @p_471) :named @p_525))) :rule cong :premises (t137.t30))
-(step t137.t32 (cl (! (= @p_519 (! (and @p_517 @p_525) :named @p_526)) :named @p_527)) :rule cong :premises (t137.t31))
-(step t137.t33 (cl (not @p_527) (not @p_519) @p_526) :rule equiv_pos2)
-(step t137.t34 (cl @p_526) :rule th_resolution :premises (t137.t28 t137.t32 t137.t33))
-(step t137 (cl @p_492 @p_526) :rule subproof :discharge (h1))
-(step t138 (cl @p_431 @p_472) :rule or :premises (t136))
-(step t139 (cl (! (or @p_431 @p_526) :named @p_528) @p_468) :rule or_neg)
-(step t140 (cl @p_528 @p_170) :rule th_resolution :premises (t128 t139))
-(step t141 (cl @p_528 (! (not @p_526) :named @p_553)) :rule or_neg)
-(step t142 (cl @p_528) :rule th_resolution :premises (t138 t137 t140 t141))
-(step t143 (cl (not (! (not (! (not @p_79) :named @p_529)) :named @p_537)) @p_79) :rule not_not)
-(step t144 (cl (or @p_529 (! (= (! (fun_app$b (! (uu$ @p_378 @p_530) :named @p_655) @p_371) :named @p_532) (! (ite @p_373 @p_370 @p_371) :named @p_533)) :named @p_531))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 @p_530) (:= veriT_vr9 @p_371)))
-(anchor :step t145)
-(assume t145.h1 @p_531)
-(step t145.t2 (cl (! (= @p_531 (! (and (! (= @p_532 @p_533) :named @p_555) (! (ite @p_373 (= @p_370 @p_533) (! (= @p_371 @p_533) :named @p_557)) :named @p_556)) :named @p_534)) :named @p_535)) :rule ite_intro)
-(step t145.t3 (cl (not @p_535) (! (not @p_531) :named @p_536) @p_534) :rule equiv_pos2)
-(step t145.t4 (cl @p_534) :rule th_resolution :premises (t145.h1 t145.t2 t145.t3))
-(step t145 (cl @p_536 @p_534) :rule subproof :discharge (h1))
-(step t146 (cl @p_529 @p_531) :rule or :premises (t144))
-(step t147 (cl (! (or @p_529 @p_534) :named @p_538) @p_537) :rule or_neg)
-(step t148 (cl @p_538 @p_79) :rule th_resolution :premises (t143 t147))
-(step t149 (cl @p_538 (! (not @p_534) :named @p_554)) :rule or_neg)
-(step t150 (cl @p_538) :rule th_resolution :premises (t146 t145 t148 t149))
-(step t151 (cl (or @p_529 (! (= (! (fun_app$b (! (uu$ @p_378 st$) :named @p_656) @p_371) :named @p_540) (! (ite (! (less_eq$ @p_318 @p_371) :named @p_542) @p_318 @p_371) :named @p_541)) :named @p_539))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 st$) (:= veriT_vr9 @p_371)))
-(anchor :step t152)
-(assume t152.h1 @p_539)
-(step t152.t2 (cl (! (= @p_539 (! (and (! (= @p_540 @p_541) :named @p_560) (ite @p_542 (! (= @p_318 @p_541) :named @p_662) (= @p_371 @p_541))) :named @p_543)) :named @p_544)) :rule ite_intro)
-(step t152.t3 (cl (not @p_544) (! (not @p_539) :named @p_545) @p_543) :rule equiv_pos2)
-(step t152.t4 (cl @p_543) :rule th_resolution :premises (t152.h1 t152.t2 t152.t3))
-(step t152 (cl @p_545 @p_543) :rule subproof :discharge (h1))
-(step t153 (cl @p_529 @p_539) :rule or :premises (t151))
-(step t154 (cl (! (or @p_529 @p_543) :named @p_546) @p_537) :rule or_neg)
-(step t155 (cl @p_546 @p_79) :rule th_resolution :premises (t143 t154))
-(step t156 (cl @p_546 (! (not @p_543) :named @p_559)) :rule or_neg)
-(step t157 (cl @p_546) :rule th_resolution :premises (t153 t152 t155 t156))
-(step t158 (cl @p_547 @p_548) :rule or :premises (t115))
-(step t159 (cl @p_548) :rule resolution :premises (t158 t89))
-(step t160 (cl @p_421 (! (not @p_413) :named @p_549) (! (not @p_417) :named @p_550)) :rule and_neg)
-(step t161 (cl (not @p_549) @p_416) :rule not_not)
-(step t162 (cl @p_421 @p_416 @p_550) :rule th_resolution :premises (t161 t160))
-(step t163 (cl (not @p_550) @p_420) :rule not_not)
-(step t164 (cl @p_421 @p_416 @p_420) :rule th_resolution :premises (t163 t162))
-(step t165 (cl @p_427 @p_422) :rule or :premises (t127))
-(step t166 (cl @p_422) :rule resolution :premises (t165 t65))
-(step t167 (cl @p_431 @p_464) :rule or :premises (t135))
-(step t168 (cl @p_464) :rule resolution :premises (t167 t56))
-(step t169 (cl (! (not @p_525) :named @p_552) (! (not @p_524) :named @p_551) @p_471) :rule implies_pos)
-(step t170 (cl (not @p_551) @p_520) :rule not_not)
-(step t171 (cl @p_552 @p_520 @p_471) :rule th_resolution :premises (t170 t169))
-(step t172 (cl @p_553 @p_525) :rule and_pos)
-(step t173 (cl @p_431 @p_526) :rule or :premises (t142))
-(step t174 (cl @p_526) :rule resolution :premises (t173 t56))
-(step t175 (cl @p_525) :rule resolution :premises (t172 t174))
-(step t176 (cl @p_554 @p_555) :rule and_pos)
-(step t177 (cl (! (not @p_556) :named @p_558) @p_373 @p_557) :rule ite_pos1)
-(step t178 (cl @p_554 @p_556) :rule and_pos)
-(step t179 (cl @p_529 @p_534) :rule or :premises (t150))
-(step t180 (cl @p_558 @p_557) :rule resolution :premises (t177 t113))
-(step t181 (cl @p_534) :rule resolution :premises (t179 t32))
-(step t182 (cl @p_555) :rule resolution :premises (t176 t181))
-(step t183 (cl @p_556) :rule resolution :premises (t178 t181))
-(step t184 (cl @p_557) :rule resolution :premises (t180 t183))
-(step t185 (cl @p_559 @p_560) :rule and_pos)
-(step t186 (cl @p_529 @p_543) :rule or :premises (t157))
-(step t187 (cl @p_543) :rule resolution :premises (t186 t32))
-(step t188 (cl @p_560) :rule resolution :premises (t185 t187))
-(step t189 (cl (! (not (! (= st$ @p_530) :named @p_651)) :named @p_654) (! (= @p_318 @p_370) :named @p_663)) :rule eq_congruent)
-(step t190 (cl (or (! (not @p_357) :named @p_565) (! (=> (! (and @p_359 @p_416) :named @p_562) (! (less_eq$ (! (clock$ (! (fst$ (! (fun_app$ (fun_evaluate_match$ st$ env$ veriT_sk0 pes$) veriT_sk0) :named @p_583)) :named @p_618)) :named @p_619) @p_318) :named @p_564)) :named @p_563))) :rule forall_inst :args ((:= veriT_vr61 x2$) (:= veriT_vr62 veriT_sk0)))
-(step t191 (cl (or @p_547 (! (= (! (fix_clock$ st$a @p_466) :named @p_596) (! (pair$ @p_561 veriT_sk3) :named @p_676)) :named @p_566))) :rule forall_inst :args ((:= veriT_vr56 st$a) (:= veriT_vr57 @p_378) (:= veriT_vr58 veriT_sk3)))
-(step t192 (cl (or (! (not @p_290) :named @p_569) (! (=> @p_548 (! (less_eq$ (! (clock$ @p_561) :named @p_575) @p_371) :named @p_568)) :named @p_567))) :rule forall_inst :args ((:= veriT_vr49 st$a) (:= veriT_vr50 @p_378) (:= veriT_vr51 r$) (:= veriT_vr52 @p_561)))
-(step t193 (cl (or (! (not @p_236) :named @p_571) (! (= (! (case_error_result$ uua$ uub$ @p_415) :named @p_621) (! (fun_app$ uua$ veriT_sk0) :named @p_584)) :named @p_572))) :rule forall_inst :args ((:= veriT_vr36 uua$) (:= veriT_vr37 uub$) (:= veriT_vr38 veriT_sk0)))
-(step t194 (cl @p_562 (! (not @p_359) :named @p_614) @p_413) :rule and_neg)
-(step t195 (cl (not @p_563) (not @p_562) @p_564) :rule implies_pos)
-(step t196 (cl @p_565 @p_563) :rule or :premises (t190))
-(step t197 (cl @p_562 @p_413) :rule resolution :premises (t194 t101))
-(step t198 (cl @p_563) :rule resolution :premises (t196 t95))
-(step t199 (cl @p_547 @p_566) :rule or :premises (t191))
-(step t200 (cl @p_566) :rule resolution :premises (t199 t89))
-(step t201 (cl (! (not @p_567) :named @p_570) (not @p_548) @p_568) :rule implies_pos)
-(step t202 (cl @p_569 @p_567) :rule or :premises (t192))
-(step t203 (cl @p_570 @p_568) :rule resolution :premises (t201 t159))
-(step t204 (cl @p_567) :rule resolution :premises (t202 t83))
-(step t205 (cl @p_568) :rule resolution :premises (t203 t204))
-(step t206 (cl @p_571 @p_572) :rule or :premises (t193))
-(step t207 (cl @p_572) :rule resolution :premises (t206 t71))
-(step t208 (cl @p_368 @p_573) :rule or :premises (t103))
-(step t209 (cl (or (! (not @p_573) :named @p_576) (! (or @p_574 (! (not @p_568) :named @p_581) (! (less_eq$ @p_575 @p_7) :named @p_582)) :named @p_577))) :rule forall_inst :args ((:= veriT_vr13 @p_371) (:= veriT_vr14 @p_7) (:= veriT_vr15 @p_575)))
-(step t210 (cl @p_576 @p_577) :rule or :premises (t209))
-(step t211 (cl (! (or @p_368 @p_577) :named @p_579) @p_578) :rule or_neg)
-(step t212 (cl @p_579 @p_105) :rule th_resolution :premises (t114 t211))
-(step t213 (cl @p_579 (! (not @p_577) :named @p_580)) :rule or_neg)
-(step t214 (cl @p_579) :rule th_resolution :premises (t208 t210 t212 t213))
-(step t215 (cl @p_580 @p_574 @p_581 @p_582) :rule or_pos)
-(step t216 (cl @p_368 @p_577) :rule or :premises (t214))
-(step t217 (cl @p_580 @p_582) :rule resolution :premises (t215 axiom4 t205))
-(step t218 (cl @p_577) :rule resolution :premises (t216 t38))
-(step t219 (cl @p_582) :rule resolution :premises (t217 t218))
-(step t220 (cl (or (! (not @p_257) :named @p_585) (! (= (! (case_error_result$ uua$ uub$ @p_419) :named @p_603) (! (fun_app$a uub$ veriT_sk1) :named @p_599)) :named @p_586))) :rule forall_inst :args ((:= veriT_vr42 uua$) (:= veriT_vr43 uub$) (:= veriT_vr44 veriT_sk1)))
-(step t221 (cl (or @p_368 (! (=> (! (and @p_582 (! (less_eq$ @p_370 @p_575) :named @p_588)) :named @p_587) @p_360) :named @p_589))) :rule forall_inst :args ((:= veriT_vr13 @p_575) (:= veriT_vr14 @p_7) (:= veriT_vr15 @p_370)))
-(step t222 (cl (or (! (not @p_26) :named @p_593) (! (= @p_583 @p_584) :named @p_594))) :rule forall_inst :args ((:= veriT_vr1 veriT_sk0)))
-(step t223 (cl @p_585 @p_586) :rule or :premises (t220))
-(step t224 (cl @p_586) :rule resolution :premises (t223 t77))
-(step t225 (cl @p_587 (not @p_582) (! (not @p_588) :named @p_590)) :rule and_neg)
-(step t226 (cl (! (not @p_589) :named @p_591) (! (not @p_587) :named @p_592) @p_360) :rule implies_pos)
-(step t227 (cl @p_368 @p_589) :rule or :premises (t221))
-(step t228 (cl @p_587 @p_590) :rule resolution :premises (t225 t219))
-(step t229 (cl @p_591 @p_592) :rule resolution :premises (t226 t102))
-(step t230 (cl @p_589) :rule resolution :premises (t227 t38))
-(step t231 (cl @p_592) :rule resolution :premises (t229 t230))
-(step t232 (cl @p_590) :rule resolution :premises (t228 t231))
-(step t233 (cl @p_593 @p_594) :rule or :premises (t222))
-(step t234 (cl @p_594) :rule resolution :premises (t233 t20))
-(step t235 (cl (not (! (= st$a st$a) :named @p_597)) @p_595 (! (= @p_470 @p_596) :named @p_598)) :rule eq_congruent)
-(step t236 (cl @p_597) :rule eq_reflexive)
-(step t237 (cl @p_595 @p_598) :rule th_resolution :premises (t235 t236))
-(step t238 (cl (or (! (not @p_48) :named @p_600) (! (= @p_599 (! (pair$ st$ (! (rerr$ @p_419) :named @p_608)) :named @p_610)) :named @p_601))) :rule forall_inst :args ((:= veriT_vr3 veriT_sk1)))
-(step t239 (cl @p_600 @p_601) :rule or :premises (t238))
-(step t240 (cl @p_601) :rule resolution :premises (t239 t26))
-(step t241 (cl (! (not (! (= uua$ uua$) :named @p_604)) :named @p_623) (! (not (! (= uub$ uub$) :named @p_607)) :named @p_605) @p_417 (! (= @p_602 @p_603) :named @p_606)) :rule eq_congruent)
-(step t242 (cl @p_604) :rule eq_reflexive)
-(step t243 (cl @p_605 @p_417 @p_606) :rule th_resolution :premises (t241 t242))
-(step t244 (cl @p_607) :rule eq_reflexive)
-(step t245 (cl @p_417 @p_606) :rule th_resolution :premises (t243 t244))
-(step t246 (cl (not (! (= st$ st$) :named @p_611)) (! (not (! (= r$ @p_608) :named @p_616)) :named @p_612) (! (= @p_609 @p_610) :named @p_613)) :rule eq_congruent)
-(step t247 (cl @p_611) :rule eq_reflexive)
-(step t248 (cl @p_612 @p_613) :rule th_resolution :premises (t246 t247))
-(step t249 (cl @p_614 (not (! (= @p_615 @p_608) :named @p_617)) @p_616) :rule eq_transitive)
-(step t250 (cl @p_417 @p_617) :rule eq_congruent)
-(step t251 (cl @p_614 @p_616 @p_417) :rule th_resolution :premises (t249 t250))
-(step t252 (cl @p_613 @p_614 @p_417) :rule th_resolution :premises (t248 t251))
-(step t253 (cl (not (! (= @p_530 @p_618) :named @p_620)) (! (= @p_370 @p_619) :named @p_627)) :rule eq_congruent)
-(step t254 (cl (not (! (= @p_602 @p_583) :named @p_622)) @p_620) :rule eq_congruent)
-(step t255 (cl (not (! (= @p_602 @p_621) :named @p_624)) (! (not @p_572) :named @p_625) (! (not @p_594) :named @p_626) @p_622) :rule eq_transitive)
-(step t256 (cl @p_623 @p_605 @p_413 @p_624) :rule eq_congruent)
-(step t257 (cl @p_605 @p_413 @p_624) :rule th_resolution :premises (t256 t242))
-(step t258 (cl @p_413 @p_624) :rule th_resolution :premises (t257 t244))
-(step t259 (cl @p_625 @p_626 @p_622 @p_413) :rule th_resolution :premises (t255 t258))
-(step t260 (cl @p_620 @p_625 @p_626 @p_413) :rule th_resolution :premises (t254 t259))
-(step t261 (cl @p_627 @p_625 @p_626 @p_413) :rule th_resolution :premises (t253 t260))
-(step t262 (cl (or @p_524 (! (not @p_628) :named @p_630))) :rule forall_inst :args ((:= veriT_vr110 r$)))
-(step t263 (cl @p_431 @p_629) :rule or :premises (t104))
-(step t264 (cl @p_524 @p_630) :rule or :premises (t262))
-(step t265 (cl @p_524) :rule resolution :premises (t264 axiom3))
-(step t266 (cl @p_471) :rule resolution :premises (t171 t265 t175))
-(step t267 (cl (or @p_529 (! (= (! (fun_app$b (! (uu$ @p_378 @p_561) :named @p_631) (! (clock$ (update_clock$ @p_631 @p_561)) :named @p_632)) :named @p_634) (! (ite @p_568 @p_575 @p_371) :named @p_635)) :named @p_633))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 @p_561) (:= veriT_vr9 @p_632)))
-(anchor :step t268)
-(assume t268.h1 @p_633)
-(step t268.t2 (cl (! (= @p_633 (! (and (= @p_634 @p_635) (! (ite @p_568 (! (= @p_575 @p_635) :named @p_647) (= @p_371 @p_635)) :named @p_646)) :named @p_636)) :named @p_637)) :rule ite_intro)
-(step t268.t3 (cl (not @p_637) (! (not @p_633) :named @p_638) @p_636) :rule equiv_pos2)
-(step t268.t4 (cl @p_636) :rule th_resolution :premises (t268.h1 t268.t2 t268.t3))
-(step t268 (cl @p_638 @p_636) :rule subproof :discharge (h1))
-(step t269 (cl @p_529 @p_633) :rule or :premises (t267))
-(step t270 (cl (! (or @p_529 @p_636) :named @p_639) @p_537) :rule or_neg)
-(step t271 (cl @p_639 @p_79) :rule th_resolution :premises (t143 t270))
-(step t272 (cl @p_639 (! (not @p_636) :named @p_648)) :rule or_neg)
-(step t273 (cl @p_639) :rule th_resolution :premises (t269 t268 t271 t272))
-(step t274 (cl (or @p_529 (! (= @p_635 (! (fun_app$b @p_631 @p_371) :named @p_641)) :named @p_640))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 @p_561) (:= veriT_vr9 @p_371)))
-(anchor :step t275)
-(assume t275.h1 @p_640)
-(step t275.t2 (cl (! (= @p_640 (! (= @p_635 @p_641) :named @p_642)) :named @p_643)) :rule ite_intro)
-(step t275.t3 (cl (not @p_643) (! (not @p_640) :named @p_644) @p_642) :rule equiv_pos2)
-(step t275.t4 (cl @p_642) :rule th_resolution :premises (t275.h1 t275.t2 t275.t3))
-(step t275 (cl @p_644 @p_642) :rule subproof :discharge (h1))
-(step t276 (cl @p_529 @p_640) :rule or :premises (t274))
-(step t277 (cl (! (or @p_529 @p_642) :named @p_645) @p_537) :rule or_neg)
-(step t278 (cl @p_645 @p_79) :rule th_resolution :premises (t143 t277))
-(step t279 (cl @p_645 (! (not @p_642) :named @p_696)) :rule or_neg)
-(step t280 (cl @p_645) :rule th_resolution :premises (t276 t275 t278 t279))
-(step t281 (cl (! (not @p_646) :named @p_649) @p_581 @p_647) :rule ite_pos2)
-(step t282 (cl @p_648 @p_646) :rule and_pos)
-(step t283 (cl @p_529 @p_636) :rule or :premises (t273))
-(step t284 (cl @p_649 @p_647) :rule resolution :premises (t281 t205))
-(step t285 (cl @p_636) :rule resolution :premises (t283 t32))
-(step t286 (cl @p_646) :rule resolution :premises (t282 t285))
-(step t287 (cl @p_647) :rule resolution :premises (t284 t286))
-(step t288 (cl @p_529 @p_642) :rule or :premises (t280))
-(step t289 (cl @p_642) :rule resolution :premises (t288 t32))
-(step t290 (cl (! (= @p_371 @p_371) :named @p_671)) :rule eq_reflexive)
-(step t291 (cl (! (not @p_471) :named @p_661) (not (! (= @p_530 @p_650) :named @p_652)) @p_651) :rule eq_transitive)
-(step t292 (cl (not (! (= @p_470 @p_602) :named @p_653)) @p_652) :rule eq_congruent)
-(step t293 (cl @p_630 (not @p_613) (! (not @p_601) :named @p_657) (! (not @p_586) :named @p_658) (! (not @p_606) :named @p_659) @p_653) :rule eq_transitive)
-(step t294 (cl (! (not @p_432) :named @p_674) @p_654 (! (= @p_655 @p_656) :named @p_670)) :rule eq_congruent)
-(step t295 (cl @p_432) :rule eq_reflexive)
-(step t296 (cl @p_630 @p_657 @p_658 @p_659 @p_653 @p_614 @p_417) :rule th_resolution :premises (t293 t252))
-(step t297 (cl @p_630 @p_657 @p_658 @p_653 @p_614 @p_417 @p_417) :rule th_resolution :premises (t296 t245))
-(step t298 (cl @p_630 @p_657 @p_658 @p_653 @p_614 @p_417) :rule contraction :premises (t297))
-(step t299 (cl @p_652 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t292 t298))
-(step t300 (cl (not (! (= @p_371 @p_370) :named @p_664)) (! (not (! (= @p_7 @p_7) :named @p_660)) :named @p_675) @p_574 @p_360) :rule eq_congruent_pred)
-(step t301 (cl @p_660) :rule eq_reflexive)
-(step t302 (cl @p_661 @p_651 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t291 t299))
-(step t303 (cl (! (not @p_557) :named @p_665) (! (not @p_555) :named @p_666) (! (not (! (= @p_532 @p_540) :named @p_672)) :named @p_667) (! (not @p_560) :named @p_668) (! (not @p_662) :named @p_669) (not @p_663) @p_664) :rule eq_transitive)
-(step t304 (cl @p_663 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t189 t302))
-(step t305 (cl @p_665 @p_666 @p_667 @p_668 @p_669 @p_664 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t303 t304))
-(step t306 (cl (! (not @p_670) :named @p_673) (! (not @p_671) :named @p_699) @p_672) :rule eq_congruent)
-(step t307 (cl @p_673 @p_672) :rule th_resolution :premises (t306 t290))
-(step t308 (cl @p_674 @p_670 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t294 t302))
-(step t309 (cl @p_670 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t308 t295))
-(step t310 (cl @p_672 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t307 t309))
-(step t311 (cl @p_665 @p_666 @p_668 @p_669 @p_664 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t305 t310))
-(step t312 (cl @p_665 @p_666 @p_668 @p_669 @p_664 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule contraction :premises (t311))
-(step t313 (cl @p_675 @p_574 @p_360 @p_665 @p_666 @p_668 @p_669 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t300 t312))
-(step t314 (cl @p_574 @p_360 @p_665 @p_666 @p_668 @p_669 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t313 t301))
-(step t315 (cl @p_669 @p_417) :rule resolution :premises (t314 axiom3 axiom4 t101 t102 t266 t182 t184 t188 t224 t240))
-(step t316 (cl (or (! (not @p_629) :named @p_677) (! (or (! (not (! (= @p_676 @p_676) :named @p_682)) :named @p_683) (! (= @p_561 (! (fst$ @p_676) :named @p_691)) :named @p_681)) :named @p_678))) :rule forall_inst :args ((:= veriT_vr23 @p_561) (:= veriT_vr24 @p_676) (:= veriT_vr26 veriT_sk3)))
-(step t317 (cl @p_677 @p_678) :rule or :premises (t316))
-(step t318 (cl (! (or @p_431 @p_678) :named @p_679) @p_468) :rule or_neg)
-(step t319 (cl @p_679 @p_170) :rule th_resolution :premises (t128 t318))
-(step t320 (cl @p_679 (! (not @p_678) :named @p_680)) :rule or_neg)
-(step t321 (cl @p_679) :rule th_resolution :premises (t263 t317 t319 t320))
-(anchor :step t322)
-(assume t322.h1 @p_678)
-(step t322.t2 (cl (= @p_682 true)) :rule eq_simplify)
-(step t322.t3 (cl (= @p_683 (! (not true) :named @p_684))) :rule cong :premises (t322.t2))
-(step t322.t4 (cl (= @p_684 false)) :rule not_simplify)
-(step t322.t5 (cl (= @p_683 false)) :rule trans :premises (t322.t3 t322.t4))
-(step t322.t6 (cl (= @p_678 (! (or false @p_681) :named @p_685))) :rule cong :premises (t322.t5))
-(step t322.t7 (cl (= @p_685 (! (or @p_681) :named @p_686))) :rule or_simplify)
-(step t322.t8 (cl (= @p_686 @p_681)) :rule or_simplify)
-(step t322.t9 (cl (! (= @p_678 @p_681) :named @p_687)) :rule trans :premises (t322.t6 t322.t7 t322.t8))
-(step t322.t10 (cl (not @p_687) @p_680 @p_681) :rule equiv_pos2)
-(step t322.t11 (cl @p_681) :rule th_resolution :premises (t322.h1 t322.t9 t322.t10))
-(step t322 (cl @p_680 @p_681) :rule subproof :discharge (h1))
-(step t323 (cl @p_431 @p_678) :rule or :premises (t321))
-(step t324 (cl (! (or @p_431 @p_681) :named @p_688) @p_468) :rule or_neg)
-(step t325 (cl @p_688 @p_170) :rule th_resolution :premises (t128 t324))
-(step t326 (cl @p_688 (! (not @p_681) :named @p_693)) :rule or_neg)
-(step t327 (cl @p_688) :rule th_resolution :premises (t323 t322 t325 t326))
-(step t328 (cl @p_431 @p_681) :rule or :premises (t327))
-(step t329 (cl @p_681) :rule resolution :premises (t328 t56))
-(step t330 (cl (not @p_598) (! (not @p_566) :named @p_689) (! (= @p_470 @p_676) :named @p_690)) :rule eq_transitive)
-(step t331 (cl @p_689 @p_690 @p_595) :rule th_resolution :premises (t330 t237))
-(step t332 (cl (not @p_690) (! (= @p_650 @p_691) :named @p_692)) :rule eq_congruent)
-(step t333 (cl @p_692 @p_689 @p_595) :rule th_resolution :premises (t332 t331))
-(step t334 (cl @p_661 (not @p_692) @p_693 (! (= st$ @p_561) :named @p_694)) :rule eq_transitive)
-(step t335 (cl @p_661 @p_693 @p_694 @p_689 @p_595) :rule th_resolution :premises (t334 t333))
-(step t336 (cl (! (not @p_694) :named @p_702) (! (= @p_318 @p_575) :named @p_695)) :rule eq_congruent)
-(step t337 (cl @p_695 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t336 t335))
-(step t338 (cl (! (not @p_695) :named @p_704) (! (not @p_647) :named @p_697) @p_696 (! (not (! (= @p_540 @p_641) :named @p_700)) :named @p_698) @p_668 @p_662) :rule eq_transitive)
-(step t339 (cl @p_697 @p_696 @p_698 @p_668 @p_662 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t338 t337))
-(step t340 (cl (! (not (! (= @p_656 @p_631) :named @p_703)) :named @p_701) @p_699 @p_700) :rule eq_congruent)
-(step t341 (cl @p_701 @p_700) :rule th_resolution :premises (t340 t290))
-(step t342 (cl @p_674 @p_702 @p_703) :rule eq_congruent)
-(step t343 (cl @p_702 @p_703) :rule th_resolution :premises (t342 t295))
-(step t344 (cl @p_703 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t343 t335))
-(step t345 (cl @p_700 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t341 t344))
-(step t346 (cl @p_697 @p_696 @p_668 @p_662 @p_661 @p_693 @p_689 @p_595 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t339 t345))
-(step t347 (cl @p_697 @p_696 @p_668 @p_662 @p_661 @p_693 @p_689 @p_595) :rule contraction :premises (t346))
-(step t348 (cl @p_662) :rule resolution :premises (t347 t266 t188 t200 t287 t289 t168 t329))
-(step t349 (cl @p_417) :rule resolution :premises (t315 t348))
-(step t350 (cl @p_416) :rule resolution :premises (t164 t349 t166))
-(step t351 (cl @p_562) :rule resolution :premises (t197 t350))
-(step t352 (cl @p_564) :rule resolution :premises (t195 t351 t198))
-(step t353 (cl (not @p_627) @p_704 (! (not @p_564) :named @p_705) @p_588) :rule eq_congruent_pred)
-(step t354 (cl @p_704 @p_705 @p_588 @p_625 @p_626 @p_413) :rule th_resolution :premises (t353 t261))
-(step t355 (cl @p_705 @p_588 @p_625 @p_626 @p_413 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t354 t337))
-(step t356 (cl) :rule resolution :premises (t355 t350 t168 t266 t352 t200 t207 t232 t234 t329))
-eae55ce4deb2476399eb5222073e987ca2cc4536 3015 0
+(define-fun veriT_sk0 () Exp$ (! (choice ((veriT_vr40 Exp$)) (not (! (=> (! (member$ veriT_vr40 (! (myset$ z$) :named @p_199)) :named @p_278) (! (not (! (forall ((veriT_vr41 FreeExp$)) (! (not (! (= veriT_vr40 (! (fun_app$ uu$ veriT_vr41) :named @p_281)) :named @p_282)) :named @p_283)) :named @p_279)) :named @p_284)) :named @p_277))) :named @p_201))
+(define-fun veriT_sk1 () FreeExp_list$ (! (choice ((veriT_vr42 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr42) :named @p_286)) :named @p_285)) :named @p_301))
+(define-fun veriT_sk2 () FreeExp$ (! (choice ((veriT_vr48 FreeExp$)) (not (! (not (! (= veriT_sk0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ veriT_vr48 bot$) :named @p_356)) :named @p_357)) :named @p_358)) :named @p_359)) :named @p_355))) :named @p_366))
+(assume a0 (! (forall ((?v0 FreeExp$)) (! (= (! (fun_app$ uu$ ?v0) :named @p_3) (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v0 bot$) :named @p_6)) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_2))
+(assume a1 (! (forall ((?v0 FreeExp_list$)) (! (= (! (abs_ExpList$ ?v0) :named @p_1) (! (map2$ uu$ ?v0) :named @p_27)) :named @p_29)) :named @p_24))
+(assume a2 (! (forall ((?v0 Exp$)) (! (=> (! (forall ((?v1 FreeExp$)) (! (=> (! (= ?v0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v1 bot$) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_48) false) :named @p_50)) :named @p_40) false) :named @p_52)) :named @p_39))
+(assume a3 (! (forall ((?v0 Exp_list$) (?v1 FreeExp_exp_fun$)) (! (= (! (exists ((?v2 FreeExp_list$)) (! (= ?v0 (! (map2$ ?v1 ?v2) :named @p_74)) :named @p_76)) :named @p_72) (! (forall ((?v2 Exp$)) (! (=> (! (member$ ?v2 (! (myset$ ?v0) :named @p_81)) :named @p_83) (! (exists ((?v3 FreeExp$)) (! (= ?v2 (! (fun_app$ ?v1 ?v3) :named @p_89)) :named @p_91)) :named @p_85)) :named @p_93)) :named @p_78)) :named @p_95)) :named @p_71))
+(assume a4 (! (not (! (exists ((?v0 FreeExp_list$)) (! (= @p_1 z$) :named @p_178)) :named @p_176)) :named @p_180))
+(anchor :step t6 :args ((:= (?v0 FreeExp$) veriT_vr0)))
+(step t6.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl)
+(step t6.t2 (cl (= @p_3 (! (fun_app$ uu$ veriT_vr0) :named @p_4))) :rule cong :premises (t6.t1))
+(step t6.t3 (cl @p_5) :rule refl)
+(step t6.t4 (cl (= @p_6 (! (insert$ veriT_vr0 bot$) :named @p_7))) :rule cong :premises (t6.t3))
+(step t6.t5 (cl (= @p_8 (! (myImage$ exprel$ @p_7) :named @p_9))) :rule cong :premises (t6.t4))
+(step t6.t6 (cl (= @p_10 (! (abs_Exp$ @p_9) :named @p_11))) :rule cong :premises (t6.t5))
+(step t6.t7 (cl (= @p_12 (! (= @p_4 @p_11) :named @p_13))) :rule cong :premises (t6.t2 t6.t6))
+(step t6 (cl (! (= @p_2 (! (forall ((veriT_vr0 FreeExp$)) @p_13) :named @p_15)) :named @p_14)) :rule bind)
+(step t7 (cl (not @p_14) (not @p_2) @p_15) :rule equiv_pos2)
+(step t8 (cl @p_15) :rule th_resolution :premises (a0 t6 t7))
+(anchor :step t9 :args ((:= (veriT_vr0 FreeExp$) veriT_vr1)))
+(step t9.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_17)) :rule refl)
+(step t9.t2 (cl (= @p_4 (! (fun_app$ uu$ veriT_vr1) :named @p_16))) :rule cong :premises (t9.t1))
+(step t9.t3 (cl @p_17) :rule refl)
+(step t9.t4 (cl (= @p_7 (! (insert$ veriT_vr1 bot$) :named @p_18))) :rule cong :premises (t9.t3))
+(step t9.t5 (cl (= @p_9 (! (myImage$ exprel$ @p_18) :named @p_19))) :rule cong :premises (t9.t4))
+(step t9.t6 (cl (= @p_11 (! (abs_Exp$ @p_19) :named @p_20))) :rule cong :premises (t9.t5))
+(step t9.t7 (cl (= @p_13 (! (= @p_16 @p_20) :named @p_21))) :rule cong :premises (t9.t2 t9.t6))
+(step t9 (cl (! (= @p_15 (! (forall ((veriT_vr1 FreeExp$)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
+(step t10 (cl (not @p_22) (not @p_15) @p_23) :rule equiv_pos2)
+(step t11 (cl @p_23) :rule th_resolution :premises (t8 t9 t10))
+(anchor :step t12 :args ((:= (?v0 FreeExp_list$) veriT_vr2)))
+(step t12.t1 (cl (! (= ?v0 veriT_vr2) :named @p_26)) :rule refl)
+(step t12.t2 (cl (= @p_1 (! (abs_ExpList$ veriT_vr2) :named @p_25))) :rule cong :premises (t12.t1))
+(step t12.t3 (cl @p_26) :rule refl)
+(step t12.t4 (cl (= @p_27 (! (map2$ uu$ veriT_vr2) :named @p_28))) :rule cong :premises (t12.t3))
+(step t12.t5 (cl (= @p_29 (! (= @p_25 @p_28) :named @p_30))) :rule cong :premises (t12.t2 t12.t4))
+(step t12 (cl (! (= @p_24 (! (forall ((veriT_vr2 FreeExp_list$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
+(step t13 (cl (not @p_31) (not @p_24) @p_32) :rule equiv_pos2)
+(step t14 (cl @p_32) :rule th_resolution :premises (a1 t12 t13))
+(anchor :step t15 :args ((:= (veriT_vr2 FreeExp_list$) veriT_vr3)))
+(step t15.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_34)) :rule refl)
+(step t15.t2 (cl (= @p_25 (! (abs_ExpList$ veriT_vr3) :named @p_33))) :rule cong :premises (t15.t1))
+(step t15.t3 (cl @p_34) :rule refl)
+(step t15.t4 (cl (= @p_28 (! (map2$ uu$ veriT_vr3) :named @p_35))) :rule cong :premises (t15.t3))
+(step t15.t5 (cl (= @p_30 (! (= @p_33 @p_35) :named @p_36))) :rule cong :premises (t15.t2 t15.t4))
+(step t15 (cl (! (= @p_32 (! (forall ((veriT_vr3 FreeExp_list$)) @p_36) :named @p_38)) :named @p_37)) :rule bind)
+(step t16 (cl (not @p_37) (not @p_32) @p_38) :rule equiv_pos2)
+(step t17 (cl @p_38) :rule th_resolution :premises (t14 t15 t16))
+(anchor :step t18 :args ((:= (?v0 Exp$) veriT_vr4)))
+(anchor :step t18.t1 :args ((:= (?v1 FreeExp$) veriT_vr5)))
+(step t18.t1.t1 (cl (= ?v0 veriT_vr4)) :rule refl)
+(step t18.t1.t2 (cl (= ?v1 veriT_vr5)) :rule refl)
+(step t18.t1.t3 (cl (= @p_42 (! (insert$ veriT_vr5 bot$) :named @p_43))) :rule cong :premises (t18.t1.t2))
+(step t18.t1.t4 (cl (= @p_44 (! (myImage$ exprel$ @p_43) :named @p_45))) :rule cong :premises (t18.t1.t3))
+(step t18.t1.t5 (cl (= @p_46 (! (abs_Exp$ @p_45) :named @p_47))) :rule cong :premises (t18.t1.t4))
+(step t18.t1.t6 (cl (= @p_48 (! (= veriT_vr4 @p_47) :named @p_49))) :rule cong :premises (t18.t1.t1 t18.t1.t5))
+(step t18.t1.t7 (cl (= @p_50 (! (=> @p_49 false) :named @p_51))) :rule cong :premises (t18.t1.t6))
+(step t18.t1 (cl (= @p_40 (! (forall ((veriT_vr5 FreeExp$)) @p_51) :named @p_41))) :rule bind)
+(step t18.t2 (cl (= @p_52 (! (=> @p_41 false) :named @p_53))) :rule cong :premises (t18.t1))
+(step t18 (cl (! (= @p_39 (! (forall ((veriT_vr4 Exp$)) @p_53) :named @p_55)) :named @p_54)) :rule bind)
+(step t19 (cl (not @p_54) (not @p_39) @p_55) :rule equiv_pos2)
+(step t20 (cl @p_55) :rule th_resolution :premises (a2 t18 t19))
+(anchor :step t21 :args ((veriT_vr4 Exp$)))
+(anchor :step t21.t1 :args ((veriT_vr5 FreeExp$)))
+(step t21.t1.t1 (cl (= @p_51 (! (not @p_49) :named @p_57))) :rule implies_simplify)
+(step t21.t1 (cl (= @p_41 (! (forall ((veriT_vr5 FreeExp$)) @p_57) :named @p_56))) :rule bind)
+(step t21.t2 (cl (= @p_53 (! (=> @p_56 false) :named @p_58))) :rule cong :premises (t21.t1))
+(step t21.t3 (cl (= @p_58 (! (not @p_56) :named @p_59))) :rule implies_simplify)
+(step t21.t4 (cl (= @p_53 @p_59)) :rule trans :premises (t21.t2 t21.t3))
+(step t21 (cl (! (= @p_55 (! (forall ((veriT_vr4 Exp$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
+(step t22 (cl (not @p_60) (not @p_55) @p_61) :rule equiv_pos2)
+(step t23 (cl @p_61) :rule th_resolution :premises (t20 t21 t22))
+(anchor :step t24 :args ((:= (veriT_vr4 Exp$) veriT_vr6)))
+(anchor :step t24.t1 :args ((:= (veriT_vr5 FreeExp$) veriT_vr7)))
+(step t24.t1.t1 (cl (= veriT_vr4 veriT_vr6)) :rule refl)
+(step t24.t1.t2 (cl (= veriT_vr5 veriT_vr7)) :rule refl)
+(step t24.t1.t3 (cl (= @p_43 (! (insert$ veriT_vr7 bot$) :named @p_63))) :rule cong :premises (t24.t1.t2))
+(step t24.t1.t4 (cl (= @p_45 (! (myImage$ exprel$ @p_63) :named @p_64))) :rule cong :premises (t24.t1.t3))
+(step t24.t1.t5 (cl (= @p_47 (! (abs_Exp$ @p_64) :named @p_65))) :rule cong :premises (t24.t1.t4))
+(step t24.t1.t6 (cl (= @p_49 (! (= veriT_vr6 @p_65) :named @p_66))) :rule cong :premises (t24.t1.t1 t24.t1.t5))
+(step t24.t1.t7 (cl (= @p_57 (! (not @p_66) :named @p_67))) :rule cong :premises (t24.t1.t6))
+(step t24.t1 (cl (= @p_56 (! (forall ((veriT_vr7 FreeExp$)) @p_67) :named @p_62))) :rule bind)
+(step t24.t2 (cl (= @p_59 (! (not @p_62) :named @p_68))) :rule cong :premises (t24.t1))
+(step t24 (cl (! (= @p_61 (! (forall ((veriT_vr6 Exp$)) @p_68) :named @p_70)) :named @p_69)) :rule bind)
+(step t25 (cl (not @p_69) (not @p_61) @p_70) :rule equiv_pos2)
+(step t26 (cl @p_70) :rule th_resolution :premises (t23 t24 t25))
+(anchor :step t27 :args ((:= (?v0 Exp_list$) veriT_vr8) (:= (?v1 FreeExp_exp_fun$) veriT_vr9)))
+(anchor :step t27.t1 :args ((:= (?v2 FreeExp_list$) veriT_vr10)))
+(step t27.t1.t1 (cl (! (= ?v0 veriT_vr8) :named @p_80)) :rule refl)
+(step t27.t1.t2 (cl (! (= ?v1 veriT_vr9) :named @p_88)) :rule refl)
+(step t27.t1.t3 (cl (= ?v2 veriT_vr10)) :rule refl)
+(step t27.t1.t4 (cl (= @p_74 (! (map2$ veriT_vr9 veriT_vr10) :named @p_75))) :rule cong :premises (t27.t1.t2 t27.t1.t3))
+(step t27.t1.t5 (cl (= @p_76 (! (= veriT_vr8 @p_75) :named @p_77))) :rule cong :premises (t27.t1.t1 t27.t1.t4))
+(step t27.t1 (cl (= @p_72 (! (exists ((veriT_vr10 FreeExp_list$)) @p_77) :named @p_73))) :rule bind)
+(anchor :step t27.t2 :args ((:= (?v2 Exp$) veriT_vr11)))
+(step t27.t2.t1 (cl (! (= ?v2 veriT_vr11) :named @p_87)) :rule refl)
+(step t27.t2.t2 (cl @p_80) :rule refl)
+(step t27.t2.t3 (cl (= @p_81 (! (myset$ veriT_vr8) :named @p_82))) :rule cong :premises (t27.t2.t2))
+(step t27.t2.t4 (cl (= @p_83 (! (member$ veriT_vr11 @p_82) :named @p_84))) :rule cong :premises (t27.t2.t1 t27.t2.t3))
+(anchor :step t27.t2.t5 :args ((:= (?v3 FreeExp$) veriT_vr12)))
+(step t27.t2.t5.t1 (cl @p_87) :rule refl)
+(step t27.t2.t5.t2 (cl @p_88) :rule refl)
+(step t27.t2.t5.t3 (cl (= ?v3 veriT_vr12)) :rule refl)
+(step t27.t2.t5.t4 (cl (= @p_89 (! (fun_app$ veriT_vr9 veriT_vr12) :named @p_90))) :rule cong :premises (t27.t2.t5.t2 t27.t2.t5.t3))
+(step t27.t2.t5.t5 (cl (= @p_91 (! (= veriT_vr11 @p_90) :named @p_92))) :rule cong :premises (t27.t2.t5.t1 t27.t2.t5.t4))
+(step t27.t2.t5 (cl (= @p_85 (! (exists ((veriT_vr12 FreeExp$)) @p_92) :named @p_86))) :rule bind)
+(step t27.t2.t6 (cl (= @p_93 (! (=> @p_84 @p_86) :named @p_94))) :rule cong :premises (t27.t2.t4 t27.t2.t5))
+(step t27.t2 (cl (= @p_78 (! (forall ((veriT_vr11 Exp$)) @p_94) :named @p_79))) :rule bind)
+(step t27.t3 (cl (= @p_95 (! (= @p_73 @p_79) :named @p_96))) :rule cong :premises (t27.t1 t27.t2))
+(step t27 (cl (! (= @p_71 (! (forall ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)) @p_96) :named @p_98)) :named @p_97)) :rule bind)
+(step t28 (cl (not @p_97) (not @p_71) @p_98) :rule equiv_pos2)
+(step t29 (cl @p_98) :rule th_resolution :premises (a3 t27 t28))
+(anchor :step t30 :args ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)))
+(step t30.t1 (cl (= @p_96 (! (and (! (=> @p_73 @p_79) :named @p_115) (! (=> @p_79 @p_73) :named @p_128)) :named @p_99))) :rule connective_def)
+(step t30 (cl (! (= @p_98 (! (forall ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)) @p_99) :named @p_101)) :named @p_100)) :rule bind)
+(step t31 (cl (not @p_100) (not @p_98) @p_101) :rule equiv_pos2)
+(step t32 (cl @p_101) :rule th_resolution :premises (t29 t30 t31))
+(anchor :step t33 :args ((:= (veriT_vr8 Exp_list$) veriT_vr13) (:= (veriT_vr9 FreeExp_exp_fun$) veriT_vr14)))
+(anchor :step t33.t1 :args ((:= (veriT_vr10 FreeExp_list$) veriT_vr15)))
+(step t33.t1.t1 (cl (! (= veriT_vr8 veriT_vr13) :named @p_107)) :rule refl)
+(step t33.t1.t2 (cl (! (= veriT_vr9 veriT_vr14) :named @p_111)) :rule refl)
+(step t33.t1.t3 (cl (= veriT_vr10 veriT_vr15)) :rule refl)
+(step t33.t1.t4 (cl (= @p_75 (! (map2$ veriT_vr14 veriT_vr15) :named @p_104))) :rule cong :premises (t33.t1.t2 t33.t1.t3))
+(step t33.t1.t5 (cl (= @p_77 (! (= veriT_vr13 @p_104) :named @p_105))) :rule cong :premises (t33.t1.t1 t33.t1.t4))
+(step t33.t1 (cl (= @p_73 (! (exists ((veriT_vr15 FreeExp_list$)) @p_105) :named @p_103))) :rule bind)
+(anchor :step t33.t2 :args ((:= (veriT_vr11 Exp$) veriT_vr16)))
+(step t33.t2.t1 (cl (! (= veriT_vr11 veriT_vr16) :named @p_110)) :rule refl)
+(step t33.t2.t2 (cl @p_107) :rule refl)
+(step t33.t2.t3 (cl (! (= @p_82 (! (myset$ veriT_vr13) :named @p_102)) :named @p_118)) :rule cong :premises (t33.t2.t2))
+(step t33.t2.t4 (cl (= @p_84 (! (member$ veriT_vr16 @p_102) :named @p_108))) :rule cong :premises (t33.t2.t1 t33.t2.t3))
+(anchor :step t33.t2.t5 :args ((:= (veriT_vr12 FreeExp$) veriT_vr17)))
+(step t33.t2.t5.t1 (cl @p_110) :rule refl)
+(step t33.t2.t5.t2 (cl @p_111) :rule refl)
+(step t33.t2.t5.t3 (cl (= veriT_vr12 veriT_vr17)) :rule refl)
+(step t33.t2.t5.t4 (cl (= @p_90 (! (fun_app$ veriT_vr14 veriT_vr17) :named @p_112))) :rule cong :premises (t33.t2.t5.t2 t33.t2.t5.t3))
+(step t33.t2.t5.t5 (cl (= @p_92 (! (= veriT_vr16 @p_112) :named @p_113))) :rule cong :premises (t33.t2.t5.t1 t33.t2.t5.t4))
+(step t33.t2.t5 (cl (= @p_86 (! (exists ((veriT_vr17 FreeExp$)) @p_113) :named @p_109))) :rule bind)
+(step t33.t2.t6 (cl (= @p_94 (! (=> @p_108 @p_109) :named @p_114))) :rule cong :premises (t33.t2.t4 t33.t2.t5))
+(step t33.t2 (cl (= @p_79 (! (forall ((veriT_vr16 Exp$)) @p_114) :named @p_106))) :rule bind)
+(step t33.t3 (cl (= @p_115 (! (=> @p_103 @p_106) :named @p_116))) :rule cong :premises (t33.t1 t33.t2))
+(anchor :step t33.t4 :args ((:= (veriT_vr11 Exp$) veriT_vr18)))
+(step t33.t4.t1 (cl (! (= veriT_vr11 veriT_vr18) :named @p_121)) :rule refl)
+(step t33.t4.t2 (cl @p_107) :rule refl)
+(step t33.t4.t3 (cl @p_118) :rule cong :premises (t33.t4.t2))
+(step t33.t4.t4 (cl (= @p_84 (! (member$ veriT_vr18 @p_102) :named @p_119))) :rule cong :premises (t33.t4.t1 t33.t4.t3))
+(anchor :step t33.t4.t5 :args ((:= (veriT_vr12 FreeExp$) veriT_vr19)))
+(step t33.t4.t5.t1 (cl @p_121) :rule refl)
+(step t33.t4.t5.t2 (cl @p_111) :rule refl)
+(step t33.t4.t5.t3 (cl (= veriT_vr12 veriT_vr19)) :rule refl)
+(step t33.t4.t5.t4 (cl (= @p_90 (! (fun_app$ veriT_vr14 veriT_vr19) :named @p_122))) :rule cong :premises (t33.t4.t5.t2 t33.t4.t5.t3))
+(step t33.t4.t5.t5 (cl (= @p_92 (! (= veriT_vr18 @p_122) :named @p_123))) :rule cong :premises (t33.t4.t5.t1 t33.t4.t5.t4))
+(step t33.t4.t5 (cl (= @p_86 (! (exists ((veriT_vr19 FreeExp$)) @p_123) :named @p_120))) :rule bind)
+(step t33.t4.t6 (cl (= @p_94 (! (=> @p_119 @p_120) :named @p_124))) :rule cong :premises (t33.t4.t4 t33.t4.t5))
+(step t33.t4 (cl (= @p_79 (! (forall ((veriT_vr18 Exp$)) @p_124) :named @p_117))) :rule bind)
+(anchor :step t33.t5 :args ((:= (veriT_vr10 FreeExp_list$) veriT_vr20)))
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+(step t40 (cl (not @p_165) (not @p_152) @p_166) :rule equiv_pos2)
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+(step t47 (cl (! (not @p_182) :named @p_185) (! (not @p_180) :named @p_184) @p_183) :rule equiv_pos2)
+(step t48 (cl (not @p_184) @p_176) :rule not_not)
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+(step t51.t1 (cl (= veriT_vr29 veriT_vr30)) :rule refl)
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+(step t58 (cl (! (= @p_190 (! (not @p_193) :named @p_195)) :named @p_194)) :rule cong :premises (t57))
+(step t59 (cl (! (not @p_194) :named @p_197) (! (not @p_190) :named @p_196) @p_195) :rule equiv_pos2)
+(step t60 (cl (not @p_196) @p_188) :rule not_not)
+(step t61 (cl @p_197 @p_188 @p_195) :rule th_resolution :premises (t60 t59))
+(step t62 (cl (not @p_195) @p_198) :rule not_not)
+(step t63 (cl @p_197 @p_188 @p_198) :rule th_resolution :premises (t62 t61))
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+(step t66 (cl (or (! (not @p_175) :named @p_336) (! (and (! (=> (! (not (! (forall ((veriT_vr23 FreeExp_list$)) (! (not (! (= z$ (! (map2$ uu$ veriT_vr23) :named @p_203)) :named @p_205)) :named @p_207)) :named @p_202)) :named @p_209) (! (forall ((veriT_vr24 Exp$)) (! (=> (! (member$ veriT_vr24 @p_199) :named @p_212) (! (exists ((veriT_vr25 FreeExp$)) (! (= veriT_vr24 (! (fun_app$ uu$ veriT_vr25) :named @p_217)) :named @p_219)) :named @p_214)) :named @p_221)) :named @p_211)) :named @p_223) (! (=> (! (forall ((veriT_vr26 Exp$)) (! (=> (! (member$ veriT_vr26 @p_199) :named @p_227) (! (not (! (forall ((veriT_vr27 FreeExp$)) (! (not (! (= veriT_vr26 (! (fun_app$ uu$ veriT_vr27) :named @p_231)) :named @p_232)) :named @p_233)) :named @p_228)) :named @p_235)) :named @p_237)) :named @p_226) (! (exists ((veriT_vr28 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr28) :named @p_240)) :named @p_241)) :named @p_239)) :named @p_242)) :named @p_200))) :rule forall_inst :args ((:= veriT_vr21 z$) (:= veriT_vr22 uu$)))
+(anchor :step t67)
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+(anchor :step t67.t4.t3 :args ((:= (veriT_vr25 FreeExp$) veriT_vr33)))
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+(anchor :step t67.t6.t3 :args ((:= (veriT_vr27 FreeExp$) veriT_vr33)))
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+(anchor :step t67.t7 :args ((:= (veriT_vr28 FreeExp_list$) veriT_vr31)))
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+(step t67.t7.t3 (cl (= @p_241 @p_206)) :rule cong :premises (t67.t7.t2))
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+(step t67.t9 (cl (! (= @p_200 (! (and @p_245 @p_246) :named @p_249)) :named @p_247)) :rule cong :premises (t67.t5 t67.t8))
+(step t67.t10 (cl (not @p_247) (! (not @p_200) :named @p_248) @p_249) :rule equiv_pos2)
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+(anchor :step t67.t12 :args ((:= (veriT_vr32 Exp$) veriT_vr34)))
+(step t67.t12.t1 (cl (! (= veriT_vr32 veriT_vr34) :named @p_252)) :rule refl)
+(step t67.t12.t2 (cl (= @p_213 (! (member$ veriT_vr34 @p_199) :named @p_250))) :rule cong :premises (t67.t12.t1))
+(anchor :step t67.t12.t3 :args ((:= (veriT_vr33 FreeExp$) veriT_vr35)))
+(step t67.t12.t3.t1 (cl @p_252) :rule refl)
+(step t67.t12.t3.t2 (cl (= veriT_vr33 veriT_vr35)) :rule refl)
+(step t67.t12.t3.t3 (cl (= @p_218 (! (fun_app$ uu$ veriT_vr35) :named @p_253))) :rule cong :premises (t67.t12.t3.t2))
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+(step t87 (cl (! (or @p_377 @p_365) :named @p_379) (! (not @p_377) :named @p_378)) :rule or_neg)
+(step t88 (cl (not @p_378) @p_70) :rule not_not)
+(step t89 (cl @p_379 @p_70) :rule th_resolution :premises (t88 t87))
+(step t90 (cl @p_379 @p_370) :rule or_neg)
+(step t91 (cl @p_379) :rule th_resolution :premises (t86 t85 t89 t90))
+(step t92 (cl @p_377 @p_365) :rule or :premises (t91))
+(step t93 (cl @p_365) :rule resolution :premises (t92 t26))
+(step t94 (cl (or @p_331 (! (not (! (= veriT_sk0 (! (fun_app$ uu$ veriT_sk2) :named @p_381)) :named @p_392)) :named @p_382))) :rule forall_inst :args ((:= veriT_vr46 veriT_sk2)))
+(step t95 (cl (or @p_193 (! (not (! (= z$ (! (abs_ExpList$ veriT_sk1) :named @p_380)) :named @p_389)) :named @p_383))) :rule forall_inst :args ((:= veriT_vr30 veriT_sk1)))
+(step t96 (cl (or (! (not @p_38) :named @p_384) (! (= @p_302 @p_380) :named @p_385))) :rule forall_inst :args ((:= veriT_vr3 veriT_sk1)))
+(step t97 (cl (or (! (not @p_23) :named @p_386) (! (= @p_369 @p_381) :named @p_387))) :rule forall_inst :args ((:= veriT_vr1 veriT_sk2)))
+(step t98 (cl @p_331 @p_382) :rule or :premises (t94))
+(step t99 (cl @p_193 @p_383) :rule or :premises (t95))
+(step t100 (cl @p_383) :rule resolution :premises (t99 t65))
+(step t101 (cl @p_384 @p_385) :rule or :premises (t96))
+(step t102 (cl @p_385) :rule resolution :premises (t101 t17))
+(step t103 (cl @p_386 @p_387) :rule or :premises (t97))
+(step t104 (cl @p_387) :rule resolution :premises (t103 t11))
+(step t105 (cl (! (= z$ z$) :named @p_388)) :rule eq_reflexive)
+(step t106 (cl (not @p_388) (! (not @p_300) :named @p_390) (! (not @p_385) :named @p_391) @p_389) :rule eq_transitive)
+(step t107 (cl @p_390 @p_391 @p_389) :rule th_resolution :premises (t106 t105))
+(step t108 (cl @p_390) :rule resolution :premises (t107 t100 t102))
+(step t109 (cl @p_370 (not @p_387) @p_392) :rule eq_transitive)
+(step t110 (cl @p_392) :rule resolution :premises (t109 t93 t104))
+(step t111 (cl @p_393) :rule resolution :premises (t77 t108 t81))
+(step t112 (cl @p_331) :rule resolution :premises (t98 t110))
+(step t113 (cl) :rule resolution :premises (t76 t111 t112))
+40b27e0a4a8779ad293f698e9d6f54d1b11a66ce 3015 0
 unsat
 (define-fun veriT_sk0 () A_b_c_M_state_fun$ (! (choice ((veriT_vr57 A_b_c_M_state_fun$)) (not (forall ((veriT_vr58 A_b_c_M_state_fun$)) (! (=> (! (forall ((veriT_vr59 A$) (veriT_vr60 C$)) (! (or (! (is_fail$ (! (run$ (! (fun_app$ veriT_vr57 veriT_vr59) :named @p_552) veriT_vr60) :named @p_544)) :named @p_542) (! (and (! (= (! (is_fail$ (! (run$ (! (fun_app$ veriT_vr58 veriT_vr59) :named @p_554) veriT_vr60) :named @p_543)) :named @p_556) @p_542) :named @p_561) (! (forall ((veriT_vr61 B$) (veriT_vr62 C$)) (! (= (! (is_res$ @p_543 (! (pair$ veriT_vr61 veriT_vr62) :named @p_545)) :named @p_566) (! (is_res$ @p_544 @p_545) :named @p_570)) :named @p_571)) :named @p_562)) :named @p_572)) :named @p_573)) :named @p_551) (! (forall ((veriT_vr63 D$)) (! (or (! (is_fail$a (! (run$a (! (b$ veriT_vr57) :named @p_575) veriT_vr63) :named @p_546)) :named @p_548) (! (exists ((veriT_vr64 E$) (veriT_vr65 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr64 veriT_vr65) :named @p_580)) :named @p_581) (! (is_fail$b (! (run$b (! (c$ veriT_vr64 veriT_vr57) :named @p_583) veriT_vr65) :named @p_585)) :named @p_586)) :named @p_587)) :named @p_576) (! (and (! (and (! (=> (! (or (! (is_fail$a (! (run$a (! (b$ veriT_vr58) :named @p_588) veriT_vr63) :named @p_547)) :named @p_549) (! (exists ((veriT_vr66 E$) (veriT_vr67 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr66 veriT_vr67) :named @p_592)) :named @p_593) (! (is_fail$b (! (run$b (! (c$ veriT_vr66 veriT_vr58) :named @p_595) veriT_vr67) :named @p_597)) :named @p_598)) :named @p_599)) :named @p_589)) :named @p_600) (! (or @p_548 (! (exists ((veriT_vr68 E$) (veriT_vr69 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr68 veriT_vr69) :named @p_603)) :named @p_604) (! (is_fail$b (! (run$b (! (c$ veriT_vr68 veriT_vr57) :named @p_606) veriT_vr69) :named @p_608)) :named @p_609)) :named @p_610)) :named @p_602)) :named @p_611)) :named @p_613) (! (=> (! (or @p_548 (! (exists ((veriT_vr70 E$) (veriT_vr71 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr70 veriT_vr71) :named @p_615)) :named @p_616) (! (is_fail$b (! (run$b (! (c$ veriT_vr70 veriT_vr57) :named @p_618) veriT_vr71) :named @p_620)) :named @p_621)) :named @p_622)) :named @p_614)) :named @p_623) (! (or @p_549 (! (exists ((veriT_vr72 E$) (veriT_vr73 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr72 veriT_vr73) :named @p_626)) :named @p_627) (! (is_fail$b (! (run$b (! (c$ veriT_vr72 veriT_vr58) :named @p_629) veriT_vr73) :named @p_631)) :named @p_632)) :named @p_633)) :named @p_625)) :named @p_634)) :named @p_636)) :named @p_637) (! (forall ((veriT_vr74 F$) (veriT_vr75 D$)) (! (and (! (=> (! (or @p_549 (! (exists ((veriT_vr76 E$) (veriT_vr77 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr76 veriT_vr77) :named @p_640)) :named @p_641) (! (is_res$b (! (run$b (! (c$ veriT_vr76 veriT_vr58) :named @p_643) veriT_vr77) :named @p_645) (! (pair$b veriT_vr74 veriT_vr75) :named @p_550)) :named @p_646)) :named @p_647)) :named @p_639)) :named @p_648) (! (or @p_548 (! (exists ((veriT_vr78 E$) (veriT_vr79 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr78 veriT_vr79) :named @p_650)) :named @p_651) (! (is_res$b (! (run$b (! (c$ veriT_vr78 veriT_vr57) :named @p_653) veriT_vr79) :named @p_655) @p_550) :named @p_659)) :named @p_660)) :named @p_649)) :named @p_661)) :named @p_663) (! (=> (! (or @p_548 (! (exists ((veriT_vr80 E$) (veriT_vr81 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr80 veriT_vr81) :named @p_665)) :named @p_666) (! (is_res$b (! (run$b (! (c$ veriT_vr80 veriT_vr57) :named @p_668) veriT_vr81) :named @p_670) @p_550) :named @p_671)) :named @p_672)) :named @p_664)) :named @p_673) (! (or @p_549 (! (exists ((veriT_vr82 E$) (veriT_vr83 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr82 veriT_vr83) :named @p_675)) :named @p_676) (! (is_res$b (! (run$b (! (c$ veriT_vr82 veriT_vr58) :named @p_678) veriT_vr83) :named @p_680) @p_550) :named @p_681)) :named @p_682)) :named @p_674)) :named @p_683)) :named @p_685)) :named @p_686)) :named @p_638)) :named @p_687)) :named @p_688)) :named @p_574)) :named @p_689)))) :named @p_696))
 (define-fun veriT_sk1 () A_b_c_M_state_fun$ (! (choice ((veriT_vr58 A_b_c_M_state_fun$)) (not (=> (forall ((veriT_vr59 A$) (veriT_vr60 C$)) (or (! (is_fail$ (! (run$ (fun_app$ @p_696 veriT_vr59) veriT_vr60) :named @p_698)) :named @p_697) (and (= @p_556 @p_697) (forall ((veriT_vr61 B$) (veriT_vr62 C$)) (= @p_566 (is_res$ @p_698 @p_545)))))) (forall ((veriT_vr63 D$)) (or (! (is_fail$a (! (run$a (! (b$ @p_696) :named @p_721) veriT_vr63) :named @p_699)) :named @p_700) (! (exists ((veriT_vr64 E$) (veriT_vr65 D$)) (and (is_res$a @p_699 @p_580) (is_fail$b (run$b (c$ veriT_vr64 @p_696) veriT_vr65)))) :named @p_704) (and (and (=> @p_600 (! (or @p_700 (exists ((veriT_vr68 E$) (veriT_vr69 D$)) (and (is_res$a @p_699 @p_603) (is_fail$b (run$b (c$ veriT_vr68 @p_696) veriT_vr69))))) :named @p_707)) (=> (! (or @p_700 (exists ((veriT_vr70 E$) (veriT_vr71 D$)) (and (is_res$a @p_699 @p_615) (! (is_fail$b (run$b (c$ veriT_vr70 @p_696) veriT_vr71)) :named @p_722)))) :named @p_708) @p_634)) (forall ((veriT_vr74 F$) (veriT_vr75 D$)) (and (=> @p_648 (! (or @p_700 (exists ((veriT_vr78 E$) (veriT_vr79 D$)) (and (is_res$a @p_699 @p_650) (! (is_res$b (! (run$b (c$ veriT_vr78 @p_696) veriT_vr79) :named @p_737) @p_550) :named @p_730)))) :named @p_710)) (=> (! (or @p_700 (exists ((veriT_vr80 E$) (veriT_vr81 D$)) (and (is_res$a @p_699 @p_665) (! (is_res$b (! (run$b (c$ veriT_vr80 @p_696) veriT_vr81) :named @p_740) @p_550) :named @p_732)))) :named @p_711) @p_683))))))))) :named @p_705))
@@ -8897,7 +8530,7 @@
 (define-fun veriT_sk42 () C$ (! (choice ((veriT_vr244 C$)) (not (or (! (is_fail$ (! (run$ (! (fun_app$ veriT_sk0 @p_1763) :named @p_1771) veriT_vr244) :named @p_1766)) :named @p_1764) (and (= (is_fail$ (! (run$ (! (fun_app$ veriT_sk1 @p_1763) :named @p_1770) veriT_vr244) :named @p_1765)) @p_1764) (forall ((veriT_vr245 B$) (veriT_vr246 C$)) (= (is_res$ @p_1765 @p_1762) (is_res$ @p_1766 @p_1762))))))) :named @p_1767))
 (define-fun veriT_sk43 () B$ (! (choice ((veriT_vr245 B$)) (not (forall ((veriT_vr246 C$)) (= (is_res$ (! (run$ @p_1770 @p_1767) :named @p_1772) @p_1762) (is_res$ (! (run$ @p_1771 @p_1767) :named @p_1774) @p_1762))))) :named @p_1773))
 (define-fun veriT_sk44 () C$ (! (choice ((veriT_vr246 C$)) (not (= (is_res$ @p_1772 (! (pair$ @p_1773 veriT_vr246) :named @p_1775)) (is_res$ @p_1774 @p_1775)))) :named @p_1870))
-(assume axiom0 (! (not (! (=> (! (and (! (forall ((?v0 A_b_c_M_state_fun$) (?v1 A_b_c_M_state_fun$)) (! (=> (! (forall ((?v2 A$) (?v3 C$)) (! (or (! (is_fail$ (! (run$ (! (fun_app$ ?v0 ?v2) :named @p_34) ?v3) :named @p_3)) :named @p_1) (! (and (! (= (! (is_fail$ (! (run$ (! (fun_app$ ?v1 ?v2) :named @p_37) ?v3) :named @p_2)) :named @p_40) @p_1) :named @p_46) (! (forall ((?v4 B$) (?v5 C$)) (! (= (! (is_res$ @p_2 (! (pair$ ?v4 ?v5) :named @p_4)) :named @p_53) (! (is_res$ @p_3 @p_4) :named @p_58)) :named @p_60)) :named @p_48)) :named @p_62)) :named @p_64)) :named @p_17) (! (forall ((?v2 D$)) (! (or (! (is_fail$a (! (run$a (! (b$ ?v0) :named @p_68) ?v2) :named @p_7)) :named @p_5) (! (and (! (= (! (is_fail$a (! (run$a (! (b$ ?v1) :named @p_70) ?v2) :named @p_6)) :named @p_19) @p_5) :named @p_77) (! (forall ((?v3 E$) (?v4 D$)) (! (= (! (is_res$a @p_6 (! (pair$a ?v3 ?v4) :named @p_8)) :named @p_20) (! (is_res$a @p_7 @p_8) :named @p_18)) :named @p_88)) :named @p_79)) :named @p_90)) :named @p_92)) :named @p_66)) :named @p_94)) :named @p_24) (! (forall ((?v0 E$) (?v1 A_b_c_M_state_fun$) (?v2 A_b_c_M_state_fun$)) (! (=> (! (forall ((?v3 A$) (?v4 C$)) (! (or (! (is_fail$ (! (run$ (! (fun_app$ ?v1 ?v3) :named @p_102) ?v4) :named @p_11)) :named @p_9) (! (and (! (= (! (is_fail$ (! (run$ (! (fun_app$ ?v2 ?v3) :named @p_104) ?v4) :named @p_10)) :named @p_106) @p_9) :named @p_111) (! (forall ((?v5 B$) (?v6 C$)) (! (= (! (is_res$ @p_10 (! (pair$ ?v5 ?v6) :named @p_12)) :named @p_116) (! (is_res$ @p_11 @p_12) :named @p_120)) :named @p_121)) :named @p_112)) :named @p_122)) :named @p_123)) :named @p_101) (! (forall ((?v3 D$)) (! (or (! (is_fail$b (! (run$b (! (c$ ?v0 ?v1) :named @p_126) ?v3) :named @p_15)) :named @p_13) (! (and (! (= (! (is_fail$b (! (run$b (! (c$ ?v0 ?v2) :named @p_129) ?v3) :named @p_14)) :named @p_132) @p_13) :named @p_137) (! (forall ((?v4 F$) (?v5 D$)) (! (= (! (is_res$b @p_14 (! (pair$b ?v4 ?v5) :named @p_16)) :named @p_143) (! (is_res$b @p_15 @p_16) :named @p_148)) :named @p_150)) :named @p_139)) :named @p_152)) :named @p_154)) :named @p_124)) :named @p_156)) :named @p_96)) :named @p_158) (! (forall ((?v0 A_b_c_M_state_fun$) (?v1 A_b_c_M_state_fun$)) (! (=> @p_17 (! (forall ((?v2 D$)) (! (or @p_5 (! (or (! (exists ((?v3 E$) (?v4 D$)) (! (and @p_18 (! (is_fail$b (! (run$b (! (c$ ?v3 ?v0) :named @p_176) ?v4) :named @p_177)) :named @p_179)) :named @p_181)) :named @p_21) (! (and (! (= (! (or @p_19 (! (exists ((?v3 E$) (?v4 D$)) (! (and @p_20 (! (is_fail$b (! (run$b (! (c$ ?v3 ?v1) :named @p_187) ?v4) :named @p_188)) :named @p_190)) :named @p_192)) :named @p_184)) :named @p_194) (! (or @p_5 @p_21) :named @p_201)) :named @p_203) (! (forall ((?v3 F$) (?v4 D$)) (! (= (! (or @p_19 (! (exists ((?v5 E$) (?v6 D$)) (! (and (! (is_res$a @p_6 (! (pair$a ?v5 ?v6) :named @p_22)) :named @p_209) (! (is_res$b (! (run$b (! (c$ ?v5 ?v1) :named @p_212) ?v6) :named @p_214) (! (pair$b ?v3 ?v4) :named @p_23)) :named @p_216)) :named @p_218)) :named @p_207)) :named @p_220) (! (or @p_5 (! (exists ((?v5 E$) (?v6 D$)) (! (and (! (is_res$a @p_7 @p_22) :named @p_225) (! (is_res$b (! (run$b (! (c$ ?v5 ?v0) :named @p_227) ?v6) :named @p_228) @p_23) :named @p_232)) :named @p_234)) :named @p_222)) :named @p_236)) :named @p_238)) :named @p_205)) :named @p_240)) :named @p_242)) :named @p_244)) :named @p_173)) :named @p_246)) :named @p_161)) :named @p_248)) :named @p_251))
+(assume a0 (! (not (! (=> (! (and (! (forall ((?v0 A_b_c_M_state_fun$) (?v1 A_b_c_M_state_fun$)) (! (=> (! (forall ((?v2 A$) (?v3 C$)) (! (or (! (is_fail$ (! (run$ (! (fun_app$ ?v0 ?v2) :named @p_34) ?v3) :named @p_3)) :named @p_1) (! (and (! (= (! (is_fail$ (! (run$ (! (fun_app$ ?v1 ?v2) :named @p_37) ?v3) :named @p_2)) :named @p_40) @p_1) :named @p_46) (! (forall ((?v4 B$) (?v5 C$)) (! (= (! (is_res$ @p_2 (! (pair$ ?v4 ?v5) :named @p_4)) :named @p_53) (! (is_res$ @p_3 @p_4) :named @p_58)) :named @p_60)) :named @p_48)) :named @p_62)) :named @p_64)) :named @p_17) (! (forall ((?v2 D$)) (! (or (! (is_fail$a (! (run$a (! (b$ ?v0) :named @p_68) ?v2) :named @p_7)) :named @p_5) (! (and (! (= (! (is_fail$a (! (run$a (! (b$ ?v1) :named @p_70) ?v2) :named @p_6)) :named @p_19) @p_5) :named @p_77) (! (forall ((?v3 E$) (?v4 D$)) (! (= (! (is_res$a @p_6 (! (pair$a ?v3 ?v4) :named @p_8)) :named @p_20) (! (is_res$a @p_7 @p_8) :named @p_18)) :named @p_88)) :named @p_79)) :named @p_90)) :named @p_92)) :named @p_66)) :named @p_94)) :named @p_24) (! (forall ((?v0 E$) (?v1 A_b_c_M_state_fun$) (?v2 A_b_c_M_state_fun$)) (! (=> (! (forall ((?v3 A$) (?v4 C$)) (! (or (! (is_fail$ (! (run$ (! (fun_app$ ?v1 ?v3) :named @p_102) ?v4) :named @p_11)) :named @p_9) (! (and (! (= (! (is_fail$ (! (run$ (! (fun_app$ ?v2 ?v3) :named @p_104) ?v4) :named @p_10)) :named @p_106) @p_9) :named @p_111) (! (forall ((?v5 B$) (?v6 C$)) (! (= (! (is_res$ @p_10 (! (pair$ ?v5 ?v6) :named @p_12)) :named @p_116) (! (is_res$ @p_11 @p_12) :named @p_120)) :named @p_121)) :named @p_112)) :named @p_122)) :named @p_123)) :named @p_101) (! (forall ((?v3 D$)) (! (or (! (is_fail$b (! (run$b (! (c$ ?v0 ?v1) :named @p_126) ?v3) :named @p_15)) :named @p_13) (! (and (! (= (! (is_fail$b (! (run$b (! (c$ ?v0 ?v2) :named @p_129) ?v3) :named @p_14)) :named @p_132) @p_13) :named @p_137) (! (forall ((?v4 F$) (?v5 D$)) (! (= (! (is_res$b @p_14 (! (pair$b ?v4 ?v5) :named @p_16)) :named @p_143) (! (is_res$b @p_15 @p_16) :named @p_148)) :named @p_150)) :named @p_139)) :named @p_152)) :named @p_154)) :named @p_124)) :named @p_156)) :named @p_96)) :named @p_158) (! (forall ((?v0 A_b_c_M_state_fun$) (?v1 A_b_c_M_state_fun$)) (! (=> @p_17 (! (forall ((?v2 D$)) (! (or @p_5 (! (or (! (exists ((?v3 E$) (?v4 D$)) (! (and @p_18 (! (is_fail$b (! (run$b (! (c$ ?v3 ?v0) :named @p_176) ?v4) :named @p_177)) :named @p_179)) :named @p_181)) :named @p_21) (! (and (! (= (! (or @p_19 (! (exists ((?v3 E$) (?v4 D$)) (! (and @p_20 (! (is_fail$b (! (run$b (! (c$ ?v3 ?v1) :named @p_187) ?v4) :named @p_188)) :named @p_190)) :named @p_192)) :named @p_184)) :named @p_194) (! (or @p_5 @p_21) :named @p_201)) :named @p_203) (! (forall ((?v3 F$) (?v4 D$)) (! (= (! (or @p_19 (! (exists ((?v5 E$) (?v6 D$)) (! (and (! (is_res$a @p_6 (! (pair$a ?v5 ?v6) :named @p_22)) :named @p_209) (! (is_res$b (! (run$b (! (c$ ?v5 ?v1) :named @p_212) ?v6) :named @p_214) (! (pair$b ?v3 ?v4) :named @p_23)) :named @p_216)) :named @p_218)) :named @p_207)) :named @p_220) (! (or @p_5 (! (exists ((?v5 E$) (?v6 D$)) (! (and (! (is_res$a @p_7 @p_22) :named @p_225) (! (is_res$b (! (run$b (! (c$ ?v5 ?v0) :named @p_227) ?v6) :named @p_228) @p_23) :named @p_232)) :named @p_234)) :named @p_222)) :named @p_236)) :named @p_238)) :named @p_205)) :named @p_240)) :named @p_242)) :named @p_244)) :named @p_173)) :named @p_246)) :named @p_161)) :named @p_248)) :named @p_251))
 (anchor :step t2 :args ((:= (?v0 A_b_c_M_state_fun$) veriT_vr0) (:= (?v1 A_b_c_M_state_fun$) veriT_vr1)))
 (anchor :step t2.t1 :args ((:= (?v2 A$) veriT_vr2) (:= (?v3 C$) veriT_vr3)))
 (step t2.t1.t1 (cl (! (= ?v0 veriT_vr0) :named @p_42)) :rule refl)
@@ -9257,7 +8890,7 @@
 (step t8 (cl (! (not @p_253) :named @p_256) (! (not @p_251) :named @p_255) @p_254) :rule equiv_pos2)
 (step t9 (cl (not @p_255) @p_248) :rule not_not)
 (step t10 (cl @p_256 @p_248 @p_254) :rule th_resolution :premises (t9 t8))
-(step t11 (cl @p_254) :rule th_resolution :premises (axiom0 t7 t10))
+(step t11 (cl @p_254) :rule th_resolution :premises (a0 t7 t10))
 (step t12 (cl (! (= @p_254 (! (and @p_249 (! (not @p_250) :named @p_264)) :named @p_258)) :named @p_257)) :rule bool_simplify)
 (step t13 (cl (! (not @p_257) :named @p_260) (! (not @p_254) :named @p_259) @p_258) :rule equiv_pos2)
 (step t14 (cl (not @p_259) @p_252) :rule not_not)
@@ -11882,550 +11515,914 @@
 (step t468 (cl @p_1652) :rule resolution :premises (t321 t467 t463))
 (step t469 (cl @p_1700) :rule resolution :premises (t264 t468 t467))
 (step t470 (cl) :rule resolution :premises (t328 t468 t463 t330 t469))
-a352c3d2d258129c9c0fa30de525ad6ea4644748 543 0
+672f5a048dc0215d5adebfbf2f0a3a36f69e286e 910 0
 unsat
-(define-fun veriT_sk0 () Exp$ (! (choice ((veriT_vr40 Exp$)) (not (! (=> (! (member$ veriT_vr40 (! (myset$ z$) :named @p_199)) :named @p_278) (! (not (! (forall ((veriT_vr41 FreeExp$)) (! (not (! (= veriT_vr40 (! (fun_app$ uu$ veriT_vr41) :named @p_281)) :named @p_282)) :named @p_283)) :named @p_279)) :named @p_284)) :named @p_277))) :named @p_201))
-(define-fun veriT_sk1 () FreeExp_list$ (! (choice ((veriT_vr42 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr42) :named @p_286)) :named @p_285)) :named @p_301))
-(define-fun veriT_sk2 () FreeExp$ (! (choice ((veriT_vr48 FreeExp$)) (not (! (not (! (= veriT_sk0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ veriT_vr48 bot$) :named @p_356)) :named @p_357)) :named @p_358)) :named @p_359)) :named @p_355))) :named @p_366))
-(assume axiom0 (! (forall ((?v0 FreeExp$)) (! (= (! (fun_app$ uu$ ?v0) :named @p_3) (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v0 bot$) :named @p_6)) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_2))
-(assume axiom1 (! (forall ((?v0 FreeExp_list$)) (! (= (! (abs_ExpList$ ?v0) :named @p_1) (! (map2$ uu$ ?v0) :named @p_27)) :named @p_29)) :named @p_24))
-(assume axiom2 (! (forall ((?v0 Exp$)) (! (=> (! (forall ((?v1 FreeExp$)) (! (=> (! (= ?v0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v1 bot$) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_48) false) :named @p_50)) :named @p_40) false) :named @p_52)) :named @p_39))
-(assume axiom3 (! (forall ((?v0 Exp_list$) (?v1 FreeExp_exp_fun$)) (! (= (! (exists ((?v2 FreeExp_list$)) (! (= ?v0 (! (map2$ ?v1 ?v2) :named @p_74)) :named @p_76)) :named @p_72) (! (forall ((?v2 Exp$)) (! (=> (! (member$ ?v2 (! (myset$ ?v0) :named @p_81)) :named @p_83) (! (exists ((?v3 FreeExp$)) (! (= ?v2 (! (fun_app$ ?v1 ?v3) :named @p_89)) :named @p_91)) :named @p_85)) :named @p_93)) :named @p_78)) :named @p_95)) :named @p_71))
-(assume axiom4 (! (not (! (exists ((?v0 FreeExp_list$)) (! (= @p_1 z$) :named @p_178)) :named @p_176)) :named @p_180))
-(anchor :step t6 :args ((:= (?v0 FreeExp$) veriT_vr0)))
-(step t6.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl)
-(step t6.t2 (cl (= @p_3 (! (fun_app$ uu$ veriT_vr0) :named @p_4))) :rule cong :premises (t6.t1))
-(step t6.t3 (cl @p_5) :rule refl)
-(step t6.t4 (cl (= @p_6 (! (insert$ veriT_vr0 bot$) :named @p_7))) :rule cong :premises (t6.t3))
-(step t6.t5 (cl (= @p_8 (! (myImage$ exprel$ @p_7) :named @p_9))) :rule cong :premises (t6.t4))
-(step t6.t6 (cl (= @p_10 (! (abs_Exp$ @p_9) :named @p_11))) :rule cong :premises (t6.t5))
-(step t6.t7 (cl (= @p_12 (! (= @p_4 @p_11) :named @p_13))) :rule cong :premises (t6.t2 t6.t6))
-(step t6 (cl (! (= @p_2 (! (forall ((veriT_vr0 FreeExp$)) @p_13) :named @p_15)) :named @p_14)) :rule bind)
-(step t7 (cl (not @p_14) (not @p_2) @p_15) :rule equiv_pos2)
-(step t8 (cl @p_15) :rule th_resolution :premises (axiom0 t6 t7))
-(anchor :step t9 :args ((:= (veriT_vr0 FreeExp$) veriT_vr1)))
-(step t9.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_17)) :rule refl)
-(step t9.t2 (cl (= @p_4 (! (fun_app$ uu$ veriT_vr1) :named @p_16))) :rule cong :premises (t9.t1))
-(step t9.t3 (cl @p_17) :rule refl)
-(step t9.t4 (cl (= @p_7 (! (insert$ veriT_vr1 bot$) :named @p_18))) :rule cong :premises (t9.t3))
-(step t9.t5 (cl (= @p_9 (! (myImage$ exprel$ @p_18) :named @p_19))) :rule cong :premises (t9.t4))
-(step t9.t6 (cl (= @p_11 (! (abs_Exp$ @p_19) :named @p_20))) :rule cong :premises (t9.t5))
-(step t9.t7 (cl (= @p_13 (! (= @p_16 @p_20) :named @p_21))) :rule cong :premises (t9.t2 t9.t6))
-(step t9 (cl (! (= @p_15 (! (forall ((veriT_vr1 FreeExp$)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
-(step t10 (cl (not @p_22) (not @p_15) @p_23) :rule equiv_pos2)
-(step t11 (cl @p_23) :rule th_resolution :premises (t8 t9 t10))
-(anchor :step t12 :args ((:= (?v0 FreeExp_list$) veriT_vr2)))
-(step t12.t1 (cl (! (= ?v0 veriT_vr2) :named @p_26)) :rule refl)
-(step t12.t2 (cl (= @p_1 (! (abs_ExpList$ veriT_vr2) :named @p_25))) :rule cong :premises (t12.t1))
-(step t12.t3 (cl @p_26) :rule refl)
-(step t12.t4 (cl (= @p_27 (! (map2$ uu$ veriT_vr2) :named @p_28))) :rule cong :premises (t12.t3))
-(step t12.t5 (cl (= @p_29 (! (= @p_25 @p_28) :named @p_30))) :rule cong :premises (t12.t2 t12.t4))
-(step t12 (cl (! (= @p_24 (! (forall ((veriT_vr2 FreeExp_list$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
-(step t13 (cl (not @p_31) (not @p_24) @p_32) :rule equiv_pos2)
-(step t14 (cl @p_32) :rule th_resolution :premises (axiom1 t12 t13))
-(anchor :step t15 :args ((:= (veriT_vr2 FreeExp_list$) veriT_vr3)))
-(step t15.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_34)) :rule refl)
-(step t15.t2 (cl (= @p_25 (! (abs_ExpList$ veriT_vr3) :named @p_33))) :rule cong :premises (t15.t1))
-(step t15.t3 (cl @p_34) :rule refl)
-(step t15.t4 (cl (= @p_28 (! (map2$ uu$ veriT_vr3) :named @p_35))) :rule cong :premises (t15.t3))
-(step t15.t5 (cl (= @p_30 (! (= @p_33 @p_35) :named @p_36))) :rule cong :premises (t15.t2 t15.t4))
-(step t15 (cl (! (= @p_32 (! (forall ((veriT_vr3 FreeExp_list$)) @p_36) :named @p_38)) :named @p_37)) :rule bind)
-(step t16 (cl (not @p_37) (not @p_32) @p_38) :rule equiv_pos2)
-(step t17 (cl @p_38) :rule th_resolution :premises (t14 t15 t16))
-(anchor :step t18 :args ((:= (?v0 Exp$) veriT_vr4)))
-(anchor :step t18.t1 :args ((:= (?v1 FreeExp$) veriT_vr5)))
-(step t18.t1.t1 (cl (= ?v0 veriT_vr4)) :rule refl)
-(step t18.t1.t2 (cl (= ?v1 veriT_vr5)) :rule refl)
-(step t18.t1.t3 (cl (= @p_42 (! (insert$ veriT_vr5 bot$) :named @p_43))) :rule cong :premises (t18.t1.t2))
-(step t18.t1.t4 (cl (= @p_44 (! (myImage$ exprel$ @p_43) :named @p_45))) :rule cong :premises (t18.t1.t3))
-(step t18.t1.t5 (cl (= @p_46 (! (abs_Exp$ @p_45) :named @p_47))) :rule cong :premises (t18.t1.t4))
-(step t18.t1.t6 (cl (= @p_48 (! (= veriT_vr4 @p_47) :named @p_49))) :rule cong :premises (t18.t1.t1 t18.t1.t5))
-(step t18.t1.t7 (cl (= @p_50 (! (=> @p_49 false) :named @p_51))) :rule cong :premises (t18.t1.t6))
-(step t18.t1 (cl (= @p_40 (! (forall ((veriT_vr5 FreeExp$)) @p_51) :named @p_41))) :rule bind)
-(step t18.t2 (cl (= @p_52 (! (=> @p_41 false) :named @p_53))) :rule cong :premises (t18.t1))
-(step t18 (cl (! (= @p_39 (! (forall ((veriT_vr4 Exp$)) @p_53) :named @p_55)) :named @p_54)) :rule bind)
-(step t19 (cl (not @p_54) (not @p_39) @p_55) :rule equiv_pos2)
-(step t20 (cl @p_55) :rule th_resolution :premises (axiom2 t18 t19))
-(anchor :step t21 :args ((veriT_vr4 Exp$)))
-(anchor :step t21.t1 :args ((veriT_vr5 FreeExp$)))
-(step t21.t1.t1 (cl (= @p_51 (! (not @p_49) :named @p_57))) :rule implies_simplify)
-(step t21.t1 (cl (= @p_41 (! (forall ((veriT_vr5 FreeExp$)) @p_57) :named @p_56))) :rule bind)
-(step t21.t2 (cl (= @p_53 (! (=> @p_56 false) :named @p_58))) :rule cong :premises (t21.t1))
-(step t21.t3 (cl (= @p_58 (! (not @p_56) :named @p_59))) :rule implies_simplify)
-(step t21.t4 (cl (= @p_53 @p_59)) :rule trans :premises (t21.t2 t21.t3))
-(step t21 (cl (! (= @p_55 (! (forall ((veriT_vr4 Exp$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
-(step t22 (cl (not @p_60) (not @p_55) @p_61) :rule equiv_pos2)
-(step t23 (cl @p_61) :rule th_resolution :premises (t20 t21 t22))
-(anchor :step t24 :args ((:= (veriT_vr4 Exp$) veriT_vr6)))
-(anchor :step t24.t1 :args ((:= (veriT_vr5 FreeExp$) veriT_vr7)))
-(step t24.t1.t1 (cl (= veriT_vr4 veriT_vr6)) :rule refl)
-(step t24.t1.t2 (cl (= veriT_vr5 veriT_vr7)) :rule refl)
-(step t24.t1.t3 (cl (= @p_43 (! (insert$ veriT_vr7 bot$) :named @p_63))) :rule cong :premises (t24.t1.t2))
-(step t24.t1.t4 (cl (= @p_45 (! (myImage$ exprel$ @p_63) :named @p_64))) :rule cong :premises (t24.t1.t3))
-(step t24.t1.t5 (cl (= @p_47 (! (abs_Exp$ @p_64) :named @p_65))) :rule cong :premises (t24.t1.t4))
-(step t24.t1.t6 (cl (= @p_49 (! (= veriT_vr6 @p_65) :named @p_66))) :rule cong :premises (t24.t1.t1 t24.t1.t5))
-(step t24.t1.t7 (cl (= @p_57 (! (not @p_66) :named @p_67))) :rule cong :premises (t24.t1.t6))
-(step t24.t1 (cl (= @p_56 (! (forall ((veriT_vr7 FreeExp$)) @p_67) :named @p_62))) :rule bind)
-(step t24.t2 (cl (= @p_59 (! (not @p_62) :named @p_68))) :rule cong :premises (t24.t1))
-(step t24 (cl (! (= @p_61 (! (forall ((veriT_vr6 Exp$)) @p_68) :named @p_70)) :named @p_69)) :rule bind)
-(step t25 (cl (not @p_69) (not @p_61) @p_70) :rule equiv_pos2)
-(step t26 (cl @p_70) :rule th_resolution :premises (t23 t24 t25))
-(anchor :step t27 :args ((:= (?v0 Exp_list$) veriT_vr8) (:= (?v1 FreeExp_exp_fun$) veriT_vr9)))
-(anchor :step t27.t1 :args ((:= (?v2 FreeExp_list$) veriT_vr10)))
-(step t27.t1.t1 (cl (! (= ?v0 veriT_vr8) :named @p_80)) :rule refl)
-(step t27.t1.t2 (cl (! (= ?v1 veriT_vr9) :named @p_88)) :rule refl)
-(step t27.t1.t3 (cl (= ?v2 veriT_vr10)) :rule refl)
-(step t27.t1.t4 (cl (= @p_74 (! (map2$ veriT_vr9 veriT_vr10) :named @p_75))) :rule cong :premises (t27.t1.t2 t27.t1.t3))
-(step t27.t1.t5 (cl (= @p_76 (! (= veriT_vr8 @p_75) :named @p_77))) :rule cong :premises (t27.t1.t1 t27.t1.t4))
-(step t27.t1 (cl (= @p_72 (! (exists ((veriT_vr10 FreeExp_list$)) @p_77) :named @p_73))) :rule bind)
-(anchor :step t27.t2 :args ((:= (?v2 Exp$) veriT_vr11)))
-(step t27.t2.t1 (cl (! (= ?v2 veriT_vr11) :named @p_87)) :rule refl)
-(step t27.t2.t2 (cl @p_80) :rule refl)
-(step t27.t2.t3 (cl (= @p_81 (! (myset$ veriT_vr8) :named @p_82))) :rule cong :premises (t27.t2.t2))
-(step t27.t2.t4 (cl (= @p_83 (! (member$ veriT_vr11 @p_82) :named @p_84))) :rule cong :premises (t27.t2.t1 t27.t2.t3))
-(anchor :step t27.t2.t5 :args ((:= (?v3 FreeExp$) veriT_vr12)))
-(step t27.t2.t5.t1 (cl @p_87) :rule refl)
-(step t27.t2.t5.t2 (cl @p_88) :rule refl)
-(step t27.t2.t5.t3 (cl (= ?v3 veriT_vr12)) :rule refl)
-(step t27.t2.t5.t4 (cl (= @p_89 (! (fun_app$ veriT_vr9 veriT_vr12) :named @p_90))) :rule cong :premises (t27.t2.t5.t2 t27.t2.t5.t3))
-(step t27.t2.t5.t5 (cl (= @p_91 (! (= veriT_vr11 @p_90) :named @p_92))) :rule cong :premises (t27.t2.t5.t1 t27.t2.t5.t4))
-(step t27.t2.t5 (cl (= @p_85 (! (exists ((veriT_vr12 FreeExp$)) @p_92) :named @p_86))) :rule bind)
-(step t27.t2.t6 (cl (= @p_93 (! (=> @p_84 @p_86) :named @p_94))) :rule cong :premises (t27.t2.t4 t27.t2.t5))
-(step t27.t2 (cl (= @p_78 (! (forall ((veriT_vr11 Exp$)) @p_94) :named @p_79))) :rule bind)
-(step t27.t3 (cl (= @p_95 (! (= @p_73 @p_79) :named @p_96))) :rule cong :premises (t27.t1 t27.t2))
-(step t27 (cl (! (= @p_71 (! (forall ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)) @p_96) :named @p_98)) :named @p_97)) :rule bind)
-(step t28 (cl (not @p_97) (not @p_71) @p_98) :rule equiv_pos2)
-(step t29 (cl @p_98) :rule th_resolution :premises (axiom3 t27 t28))
-(anchor :step t30 :args ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)))
-(step t30.t1 (cl (= @p_96 (! (and (! (=> @p_73 @p_79) :named @p_115) (! (=> @p_79 @p_73) :named @p_128)) :named @p_99))) :rule connective_def)
-(step t30 (cl (! (= @p_98 (! (forall ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)) @p_99) :named @p_101)) :named @p_100)) :rule bind)
-(step t31 (cl (not @p_100) (not @p_98) @p_101) :rule equiv_pos2)
-(step t32 (cl @p_101) :rule th_resolution :premises (t29 t30 t31))
-(anchor :step t33 :args ((:= (veriT_vr8 Exp_list$) veriT_vr13) (:= (veriT_vr9 FreeExp_exp_fun$) veriT_vr14)))
-(anchor :step t33.t1 :args ((:= (veriT_vr10 FreeExp_list$) veriT_vr15)))
-(step t33.t1.t1 (cl (! (= veriT_vr8 veriT_vr13) :named @p_107)) :rule refl)
-(step t33.t1.t2 (cl (! (= veriT_vr9 veriT_vr14) :named @p_111)) :rule refl)
-(step t33.t1.t3 (cl (= veriT_vr10 veriT_vr15)) :rule refl)
-(step t33.t1.t4 (cl (= @p_75 (! (map2$ veriT_vr14 veriT_vr15) :named @p_104))) :rule cong :premises (t33.t1.t2 t33.t1.t3))
-(step t33.t1.t5 (cl (= @p_77 (! (= veriT_vr13 @p_104) :named @p_105))) :rule cong :premises (t33.t1.t1 t33.t1.t4))
-(step t33.t1 (cl (= @p_73 (! (exists ((veriT_vr15 FreeExp_list$)) @p_105) :named @p_103))) :rule bind)
-(anchor :step t33.t2 :args ((:= (veriT_vr11 Exp$) veriT_vr16)))
-(step t33.t2.t1 (cl (! (= veriT_vr11 veriT_vr16) :named @p_110)) :rule refl)
-(step t33.t2.t2 (cl @p_107) :rule refl)
-(step t33.t2.t3 (cl (! (= @p_82 (! (myset$ veriT_vr13) :named @p_102)) :named @p_118)) :rule cong :premises (t33.t2.t2))
-(step t33.t2.t4 (cl (= @p_84 (! (member$ veriT_vr16 @p_102) :named @p_108))) :rule cong :premises (t33.t2.t1 t33.t2.t3))
-(anchor :step t33.t2.t5 :args ((:= (veriT_vr12 FreeExp$) veriT_vr17)))
-(step t33.t2.t5.t1 (cl @p_110) :rule refl)
-(step t33.t2.t5.t2 (cl @p_111) :rule refl)
-(step t33.t2.t5.t3 (cl (= veriT_vr12 veriT_vr17)) :rule refl)
-(step t33.t2.t5.t4 (cl (= @p_90 (! (fun_app$ veriT_vr14 veriT_vr17) :named @p_112))) :rule cong :premises (t33.t2.t5.t2 t33.t2.t5.t3))
-(step t33.t2.t5.t5 (cl (= @p_92 (! (= veriT_vr16 @p_112) :named @p_113))) :rule cong :premises (t33.t2.t5.t1 t33.t2.t5.t4))
-(step t33.t2.t5 (cl (= @p_86 (! (exists ((veriT_vr17 FreeExp$)) @p_113) :named @p_109))) :rule bind)
-(step t33.t2.t6 (cl (= @p_94 (! (=> @p_108 @p_109) :named @p_114))) :rule cong :premises (t33.t2.t4 t33.t2.t5))
-(step t33.t2 (cl (= @p_79 (! (forall ((veriT_vr16 Exp$)) @p_114) :named @p_106))) :rule bind)
-(step t33.t3 (cl (= @p_115 (! (=> @p_103 @p_106) :named @p_116))) :rule cong :premises (t33.t1 t33.t2))
-(anchor :step t33.t4 :args ((:= (veriT_vr11 Exp$) veriT_vr18)))
-(step t33.t4.t1 (cl (! (= veriT_vr11 veriT_vr18) :named @p_121)) :rule refl)
-(step t33.t4.t2 (cl @p_107) :rule refl)
-(step t33.t4.t3 (cl @p_118) :rule cong :premises (t33.t4.t2))
-(step t33.t4.t4 (cl (= @p_84 (! (member$ veriT_vr18 @p_102) :named @p_119))) :rule cong :premises (t33.t4.t1 t33.t4.t3))
-(anchor :step t33.t4.t5 :args ((:= (veriT_vr12 FreeExp$) veriT_vr19)))
-(step t33.t4.t5.t1 (cl @p_121) :rule refl)
-(step t33.t4.t5.t2 (cl @p_111) :rule refl)
-(step t33.t4.t5.t3 (cl (= veriT_vr12 veriT_vr19)) :rule refl)
-(step t33.t4.t5.t4 (cl (= @p_90 (! (fun_app$ veriT_vr14 veriT_vr19) :named @p_122))) :rule cong :premises (t33.t4.t5.t2 t33.t4.t5.t3))
-(step t33.t4.t5.t5 (cl (= @p_92 (! (= veriT_vr18 @p_122) :named @p_123))) :rule cong :premises (t33.t4.t5.t1 t33.t4.t5.t4))
-(step t33.t4.t5 (cl (= @p_86 (! (exists ((veriT_vr19 FreeExp$)) @p_123) :named @p_120))) :rule bind)
-(step t33.t4.t6 (cl (= @p_94 (! (=> @p_119 @p_120) :named @p_124))) :rule cong :premises (t33.t4.t4 t33.t4.t5))
-(step t33.t4 (cl (= @p_79 (! (forall ((veriT_vr18 Exp$)) @p_124) :named @p_117))) :rule bind)
-(anchor :step t33.t5 :args ((:= (veriT_vr10 FreeExp_list$) veriT_vr20)))
-(step t33.t5.t1 (cl @p_107) :rule refl)
-(step t33.t5.t2 (cl @p_111) :rule refl)
-(step t33.t5.t3 (cl (= veriT_vr10 veriT_vr20)) :rule refl)
-(step t33.t5.t4 (cl (= @p_75 (! (map2$ veriT_vr14 veriT_vr20) :named @p_126))) :rule cong :premises (t33.t5.t2 t33.t5.t3))
-(step t33.t5.t5 (cl (= @p_77 (! (= veriT_vr13 @p_126) :named @p_127))) :rule cong :premises (t33.t5.t1 t33.t5.t4))
-(step t33.t5 (cl (= @p_73 (! (exists ((veriT_vr20 FreeExp_list$)) @p_127) :named @p_125))) :rule bind)
-(step t33.t6 (cl (= @p_128 (! (=> @p_117 @p_125) :named @p_129))) :rule cong :premises (t33.t4 t33.t5))
-(step t33.t7 (cl (= @p_99 (! (and @p_116 @p_129) :named @p_130))) :rule cong :premises (t33.t3 t33.t6))
-(step t33 (cl (! (= @p_101 (! (forall ((veriT_vr13 Exp_list$) (veriT_vr14 FreeExp_exp_fun$)) @p_130) :named @p_132)) :named @p_131)) :rule bind)
-(step t34 (cl (not @p_131) (not @p_101) @p_132) :rule equiv_pos2)
-(step t35 (cl @p_132) :rule th_resolution :premises (t32 t33 t34))
-(anchor :step t36 :args ((:= (veriT_vr13 Exp_list$) veriT_vr21) (:= (veriT_vr14 FreeExp_exp_fun$) veriT_vr22)))
-(anchor :step t36.t1 :args ((:= (veriT_vr15 FreeExp_list$) veriT_vr23)))
-(step t36.t1.t1 (cl (! (= veriT_vr13 veriT_vr21) :named @p_137)) :rule refl)
-(step t36.t1.t2 (cl (! (= veriT_vr14 veriT_vr22) :named @p_142)) :rule refl)
-(step t36.t1.t3 (cl (= veriT_vr15 veriT_vr23)) :rule refl)
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-(step t36.t2.t2 (cl @p_137) :rule refl)
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-(step t36.t2.t4 (cl (= @p_108 (! (member$ veriT_vr24 @p_138) :named @p_139))) :rule cong :premises (t36.t2.t1 t36.t2.t3))
-(anchor :step t36.t2.t5 :args ((:= (veriT_vr17 FreeExp$) veriT_vr25)))
-(step t36.t2.t5.t1 (cl @p_141) :rule refl)
-(step t36.t2.t5.t2 (cl @p_142) :rule refl)
-(step t36.t2.t5.t3 (cl (= veriT_vr17 veriT_vr25)) :rule refl)
-(step t36.t2.t5.t4 (cl (= @p_112 (! (fun_app$ veriT_vr22 veriT_vr25) :named @p_143))) :rule cong :premises (t36.t2.t5.t2 t36.t2.t5.t3))
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-(anchor :step t36.t4 :args ((:= (veriT_vr18 Exp$) veriT_vr24)))
-(step t36.t4.t1 (cl (! (= veriT_vr18 veriT_vr24) :named @p_148)) :rule refl)
-(step t36.t4.t2 (cl @p_137) :rule refl)
-(step t36.t4.t3 (cl @p_147) :rule cong :premises (t36.t4.t2))
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-(anchor :step t36.t4.t5 :args ((:= (veriT_vr19 FreeExp$) veriT_vr25)))
-(step t36.t4.t5.t1 (cl @p_148) :rule refl)
-(step t36.t4.t5.t2 (cl @p_142) :rule refl)
-(step t36.t4.t5.t3 (cl (= veriT_vr19 veriT_vr25)) :rule refl)
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-(step t36.t5.t2 (cl @p_142) :rule refl)
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-(anchor :step t39.t1 :args ((:= (veriT_vr24 Exp$) veriT_vr26)))
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-(anchor :step t39.t1.t3 :args ((:= (veriT_vr25 FreeExp$) veriT_vr27)))
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-(step t39.t2.t2 (cl (= @p_135 (! (map2$ veriT_vr22 veriT_vr28) :named @p_161))) :rule cong :premises (t39.t2.t1))
-(step t39.t2.t3 (cl (= @p_136 (! (= veriT_vr21 @p_161) :named @p_162))) :rule cong :premises (t39.t2.t2))
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-(step t42.t5 (cl (= @p_164 (! (and @p_168 @p_172) :named @p_173))) :rule cong :premises (t42.t2 t42.t4))
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-(step t43 (cl (not @p_174) (not @p_166) @p_175) :rule equiv_pos2)
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-(step t48 (cl (not @p_184) @p_176) :rule not_not)
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-(step t50 (cl @p_183) :rule th_resolution :premises (axiom4 t46 t49))
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-(step t51.t1 (cl (= veriT_vr29 veriT_vr30)) :rule refl)
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-(step t51 (cl (= @p_181 (! (exists ((veriT_vr30 FreeExp_list$)) @p_187) :named @p_188))) :rule bind)
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-(step t54 (cl (not @p_191) @p_181) :rule not_not)
-(step t55 (cl @p_192 @p_181 @p_190) :rule th_resolution :premises (t54 t53))
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-(step t58 (cl (! (= @p_190 (! (not @p_193) :named @p_195)) :named @p_194)) :rule cong :premises (t57))
-(step t59 (cl (! (not @p_194) :named @p_197) (! (not @p_190) :named @p_196) @p_195) :rule equiv_pos2)
-(step t60 (cl (not @p_196) @p_188) :rule not_not)
-(step t61 (cl @p_197 @p_188 @p_195) :rule th_resolution :premises (t60 t59))
-(step t62 (cl (not @p_195) @p_198) :rule not_not)
-(step t63 (cl @p_197 @p_188 @p_198) :rule th_resolution :premises (t62 t61))
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-(step t66 (cl (or (! (not @p_175) :named @p_336) (! (and (! (=> (! (not (! (forall ((veriT_vr23 FreeExp_list$)) (! (not (! (= z$ (! (map2$ uu$ veriT_vr23) :named @p_203)) :named @p_205)) :named @p_207)) :named @p_202)) :named @p_209) (! (forall ((veriT_vr24 Exp$)) (! (=> (! (member$ veriT_vr24 @p_199) :named @p_212) (! (exists ((veriT_vr25 FreeExp$)) (! (= veriT_vr24 (! (fun_app$ uu$ veriT_vr25) :named @p_217)) :named @p_219)) :named @p_214)) :named @p_221)) :named @p_211)) :named @p_223) (! (=> (! (forall ((veriT_vr26 Exp$)) (! (=> (! (member$ veriT_vr26 @p_199) :named @p_227) (! (not (! (forall ((veriT_vr27 FreeExp$)) (! (not (! (= veriT_vr26 (! (fun_app$ uu$ veriT_vr27) :named @p_231)) :named @p_232)) :named @p_233)) :named @p_228)) :named @p_235)) :named @p_237)) :named @p_226) (! (exists ((veriT_vr28 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr28) :named @p_240)) :named @p_241)) :named @p_239)) :named @p_242)) :named @p_200))) :rule forall_inst :args ((:= veriT_vr21 z$) (:= veriT_vr22 uu$)))
-(anchor :step t67)
-(assume t67.h1 @p_200)
-(anchor :step t67.t2 :args ((:= (veriT_vr23 FreeExp_list$) veriT_vr31)))
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-(step t67.t2.t2 (cl (= @p_203 (! (map2$ uu$ veriT_vr31) :named @p_204))) :rule cong :premises (t67.t2.t1))
-(step t67.t2.t3 (cl (= @p_205 (! (= z$ @p_204) :named @p_206))) :rule cong :premises (t67.t2.t2))
-(step t67.t2.t4 (cl (= @p_207 (! (not @p_206) :named @p_208))) :rule cong :premises (t67.t2.t3))
-(step t67.t2 (cl (= @p_202 (! (forall ((veriT_vr31 FreeExp_list$)) @p_208) :named @p_210))) :rule bind)
-(step t67.t3 (cl (= @p_209 (! (not @p_210) :named @p_224))) :rule cong :premises (t67.t2))
-(anchor :step t67.t4 :args ((:= (veriT_vr24 Exp$) veriT_vr32)))
-(step t67.t4.t1 (cl (! (= veriT_vr24 veriT_vr32) :named @p_216)) :rule refl)
-(step t67.t4.t2 (cl (= @p_212 (! (member$ veriT_vr32 @p_199) :named @p_213))) :rule cong :premises (t67.t4.t1))
-(anchor :step t67.t4.t3 :args ((:= (veriT_vr25 FreeExp$) veriT_vr33)))
-(step t67.t4.t3.t1 (cl @p_216) :rule refl)
-(step t67.t4.t3.t2 (cl (= veriT_vr25 veriT_vr33)) :rule refl)
-(step t67.t4.t3.t3 (cl (= @p_217 (! (fun_app$ uu$ veriT_vr33) :named @p_218))) :rule cong :premises (t67.t4.t3.t2))
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-(anchor :step t67.t6 :args ((:= (veriT_vr26 Exp$) veriT_vr32)))
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-(step t67.t6.t2 (cl (= @p_227 @p_213)) :rule cong :premises (t67.t6.t1))
-(anchor :step t67.t6.t3 :args ((:= (veriT_vr27 FreeExp$) veriT_vr33)))
-(step t67.t6.t3.t1 (cl @p_230) :rule refl)
-(step t67.t6.t3.t2 (cl (= veriT_vr27 veriT_vr33)) :rule refl)
-(step t67.t6.t3.t3 (cl (= @p_231 @p_218)) :rule cong :premises (t67.t6.t3.t2))
-(step t67.t6.t3.t4 (cl (= @p_232 @p_220)) :rule cong :premises (t67.t6.t3.t1 t67.t6.t3.t3))
-(step t67.t6.t3.t5 (cl (= @p_233 (! (not @p_220) :named @p_234))) :rule cong :premises (t67.t6.t3.t4))
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-(step t67.t6.t5 (cl (= @p_237 (! (=> @p_213 @p_236) :named @p_238))) :rule cong :premises (t67.t6.t2 t67.t6.t4))
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-(anchor :step t67.t7 :args ((:= (veriT_vr28 FreeExp_list$) veriT_vr31)))
-(step t67.t7.t1 (cl (= veriT_vr28 veriT_vr31)) :rule refl)
-(step t67.t7.t2 (cl (= @p_240 @p_204)) :rule cong :premises (t67.t7.t1))
-(step t67.t7.t3 (cl (= @p_241 @p_206)) :rule cong :premises (t67.t7.t2))
-(step t67.t7 (cl (= @p_239 (! (exists ((veriT_vr31 FreeExp_list$)) @p_206) :named @p_244))) :rule bind)
-(step t67.t8 (cl (= @p_242 (! (=> @p_243 @p_244) :named @p_246))) :rule cong :premises (t67.t6 t67.t7))
-(step t67.t9 (cl (! (= @p_200 (! (and @p_245 @p_246) :named @p_249)) :named @p_247)) :rule cong :premises (t67.t5 t67.t8))
-(step t67.t10 (cl (not @p_247) (! (not @p_200) :named @p_248) @p_249) :rule equiv_pos2)
-(step t67.t11 (cl @p_249) :rule th_resolution :premises (t67.h1 t67.t9 t67.t10))
-(anchor :step t67.t12 :args ((:= (veriT_vr32 Exp$) veriT_vr34)))
-(step t67.t12.t1 (cl (! (= veriT_vr32 veriT_vr34) :named @p_252)) :rule refl)
-(step t67.t12.t2 (cl (= @p_213 (! (member$ veriT_vr34 @p_199) :named @p_250))) :rule cong :premises (t67.t12.t1))
-(anchor :step t67.t12.t3 :args ((:= (veriT_vr33 FreeExp$) veriT_vr35)))
-(step t67.t12.t3.t1 (cl @p_252) :rule refl)
-(step t67.t12.t3.t2 (cl (= veriT_vr33 veriT_vr35)) :rule refl)
-(step t67.t12.t3.t3 (cl (= @p_218 (! (fun_app$ uu$ veriT_vr35) :named @p_253))) :rule cong :premises (t67.t12.t3.t2))
-(step t67.t12.t3.t4 (cl (= @p_220 (! (= veriT_vr34 @p_253) :named @p_254))) :rule cong :premises (t67.t12.t3.t1 t67.t12.t3.t3))
-(step t67.t12.t3.t5 (cl (= @p_234 (! (not @p_254) :named @p_255))) :rule cong :premises (t67.t12.t3.t4))
-(step t67.t12.t3 (cl (= @p_229 (! (forall ((veriT_vr35 FreeExp$)) @p_255) :named @p_251))) :rule bind)
-(step t67.t12.t4 (cl (= @p_236 (! (not @p_251) :named @p_256))) :rule cong :premises (t67.t12.t3))
-(step t67.t12.t5 (cl (= @p_238 (! (=> @p_250 @p_256) :named @p_257))) :rule cong :premises (t67.t12.t2 t67.t12.t4))
-(step t67.t12 (cl (= @p_243 (! (forall ((veriT_vr34 Exp$)) @p_257) :named @p_260))) :rule bind)
-(anchor :step t67.t13 :args ((:= (veriT_vr31 FreeExp_list$) veriT_vr36)))
-(step t67.t13.t1 (cl (= veriT_vr31 veriT_vr36)) :rule refl)
-(step t67.t13.t2 (cl (= @p_204 (! (map2$ uu$ veriT_vr36) :named @p_258))) :rule cong :premises (t67.t13.t1))
-(step t67.t13.t3 (cl (= @p_206 (! (= z$ @p_258) :named @p_259))) :rule cong :premises (t67.t13.t2))
-(step t67.t13 (cl (= @p_244 (! (exists ((veriT_vr36 FreeExp_list$)) @p_259) :named @p_261))) :rule bind)
-(step t67.t14 (cl (= @p_246 (! (=> @p_260 @p_261) :named @p_262))) :rule cong :premises (t67.t12 t67.t13))
-(step t67.t15 (cl (! (= @p_249 (! (and @p_245 @p_262) :named @p_264)) :named @p_263)) :rule cong :premises (t67.t14))
-(step t67.t16 (cl (not @p_263) (not @p_249) @p_264) :rule equiv_pos2)
-(step t67.t17 (cl @p_264) :rule th_resolution :premises (t67.t11 t67.t15 t67.t16))
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-(step t98 (cl @p_331 @p_382) :rule or :premises (t94))
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-(step t103 (cl @p_386 @p_387) :rule or :premises (t97))
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-(step t107 (cl @p_390 @p_391 @p_389) :rule th_resolution :premises (t106 t105))
-(step t108 (cl @p_390) :rule resolution :premises (t107 t100 t102))
-(step t109 (cl @p_370 (not @p_387) @p_392) :rule eq_transitive)
-(step t110 (cl @p_392) :rule resolution :premises (t109 t93 t104))
-(step t111 (cl @p_393) :rule resolution :premises (t77 t108 t81))
-(step t112 (cl @p_331) :rule resolution :premises (t98 t110))
-(step t113 (cl) :rule resolution :premises (t76 t111 t112))
-c24fc06f55d92aed7783d8234aedb7ced3e99be7 2 0
-(error "status is not unsat.")
-unknown
+(define-fun veriT_sk0 () V$ (! (choice ((veriT_vr65 V$)) (not (! (not (! (= x2$ (! (rraise$ veriT_vr65) :named @p_401)) :named @p_402)) :named @p_400))) :named @p_414))
+(define-fun veriT_sk1 () Abort$ (! (choice ((veriT_vr66 Abort$)) (not (! (not (! (= x2$ (! (rabort$ veriT_vr66) :named @p_404)) :named @p_405)) :named @p_403))) :named @p_418))
+(define-fun veriT_sk3 () V_list_v_result$ (! (choice ((veriT_vr73 V_list_v_result$)) (! (= (! (fun_evaluate$ st$a env$ (cons$ e$ nil$)) :named @p_3) (! (pair$ (! (fst$ @p_3) :named @p_378) veriT_vr73) :named @p_461)) :named @p_460)) :named @p_465))
+(define-fun veriT_sk11 () V_list_v_result$ (! (choice ((veriT_vr108 V_list_v_result$)) (! (= (! (fix_clock$ st$a @p_3) :named @p_470) (! (pair$ st$ veriT_vr108) :named @p_503)) :named @p_502)) :named @p_515))
+(assume a0 (! (forall ((?v0 V$)) (! (= (! (fun_app$ uua$ ?v0) :named @p_9) (! (fun_app$ (! (fun_evaluate_match$ st$ env$ ?v0 pes$) :named @p_12) ?v0) :named @p_14)) :named @p_16)) :named @p_8))
+(assume a1 (! (forall ((?v0 Abort$)) (! (= (! (fun_app$a uub$ ?v0) :named @p_28) (! (pair$ st$ (! (rerr$ (! (rabort$ ?v0) :named @p_31)) :named @p_33)) :named @p_35)) :named @p_37)) :named @p_27))
+(assume a2 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 Nat$)) (! (= (! (fun_app$b (! (uu$ ?v0 ?v1) :named @p_5) ?v2) :named @p_53) (! (ite (! (less_eq$ (! (clock$ ?v1) :named @p_1) (! (clock$ ?v0) :named @p_2)) :named @p_57) @p_1 @p_2) :named @p_61)) :named @p_63)) :named @p_49))
+(assume a3 (! (= @p_470 (! (pair$ st$ r$) :named @p_609)) :named @p_628))
+(assume a4 (! (less_eq$ (! (clock$ @p_378) :named @p_371) (! (clock$ st$a) :named @p_7)) :named @p_369))
+(assume a5 (! (forall ((?v0 Nat$) (?v1 Nat$) (?v2 Nat$)) (! (=> (! (and (! (less_eq$ ?v0 ?v1) :named @p_81) (! (less_eq$ ?v2 ?v0) :named @p_84)) :named @p_86) (! (less_eq$ ?v2 ?v1) :named @p_90)) :named @p_92)) :named @p_80))
+(assume a6 (! (forall ((?v0 Astate$) (?v1 Astate_v_list_v_result_prod$)) (! (= (! (= ?v0 (! (fst$ ?v1) :named @p_107)) :named @p_109) (! (exists ((?v2 V_list_v_result$)) (! (= ?v1 (! (pair$ ?v0 ?v2) :named @p_115)) :named @p_117)) :named @p_111)) :named @p_119)) :named @p_106))
+(assume a7 (! (forall ((?v0 V_error_result$)) (! (=> (! (and (! (forall ((?v1 V$)) (! (=> (! (= ?v0 (! (rraise$ ?v1) :named @p_174)) :named @p_6) false) :named @p_177)) :named @p_172) (! (forall ((?v1 Abort$)) (! (=> (! (= ?v0 (! (rabort$ ?v1) :named @p_182)) :named @p_184) false) :named @p_186)) :named @p_179)) :named @p_188) false) :named @p_190)) :named @p_171))
+(assume a8 (! (forall ((?v0 V_astate_v_list_v_result_prod_fun$) (?v1 Abort_astate_v_list_v_result_prod_fun$) (?v2 V$)) (! (= (! (case_error_result$ ?v0 ?v1 (! (rraise$ ?v2) :named @p_217)) :named @p_219) (! (fun_app$ ?v0 ?v2) :named @p_223)) :named @p_225)) :named @p_216))
+(assume a9 (! (forall ((?v0 V_astate_v_list_v_result_prod_fun$) (?v1 Abort_astate_v_list_v_result_prod_fun$) (?v2 Abort$)) (! (= (! (case_error_result$ ?v0 ?v1 (! (rabort$ ?v2) :named @p_238)) :named @p_240) (! (fun_app$a ?v1 ?v2) :named @p_244)) :named @p_246)) :named @p_237))
+(assume a10 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 V_list_v_result$) (?v3 Astate$)) (! (=> (! (= (! (fix_clock$ ?v0 (! (pair$ ?v1 ?v2) :named @p_259)) :named @p_4) (! (pair$ ?v3 ?v2) :named @p_263)) :named @p_265) (! (less_eq$ (! (clock$ ?v3) :named @p_268) @p_1) :named @p_272)) :named @p_274)) :named @p_258))
+(assume a11 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 V_list_v_result$)) (! (= @p_4 (! (pair$ (! (update_clock$ @p_5 ?v1) :named @p_297) ?v2) :named @p_300)) :named @p_302)) :named @p_291))
+(assume a12 (! (forall ((?v0 V_error_result$) (?v1 V$)) (! (=> (! (and (! (= r$ (! (rerr$ ?v0) :named @p_319)) :named @p_321) @p_6) :named @p_326) (! (less_eq$ (! (clock$ (! (fst$ (! (fun_app$ (! (fun_evaluate_match$ st$ env$ ?v1 pes$) :named @p_329) ?v1) :named @p_331)) :named @p_333)) :named @p_335) (! (clock$ st$) :named @p_318)) :named @p_337)) :named @p_339)) :named @p_317))
+(assume a13 (! (not (! (=> (! (= r$ (! (rerr$ x2$) :named @p_615)) :named @p_359) (! (less_eq$ (! (clock$ (! (fst$ (! (case_error_result$ uua$ uub$ x2$) :named @p_602)) :named @p_530)) :named @p_370) @p_7) :named @p_360)) :named @p_364)) :named @p_358))
+(anchor :step t15 :args ((:= (?v0 V$) veriT_vr0)))
+(step t15.t1 (cl (! (= ?v0 veriT_vr0) :named @p_11)) :rule refl)
+(step t15.t2 (cl (= @p_9 (! (fun_app$ uua$ veriT_vr0) :named @p_10))) :rule cong :premises (t15.t1))
+(step t15.t3 (cl @p_11) :rule refl)
+(step t15.t4 (cl (= @p_12 (! (fun_evaluate_match$ st$ env$ veriT_vr0 pes$) :named @p_13))) :rule cong :premises (t15.t3))
+(step t15.t5 (cl @p_11) :rule refl)
+(step t15.t6 (cl (= @p_14 (! (fun_app$ @p_13 veriT_vr0) :named @p_15))) :rule cong :premises (t15.t4 t15.t5))
+(step t15.t7 (cl (= @p_16 (! (= @p_10 @p_15) :named @p_17))) :rule cong :premises (t15.t2 t15.t6))
+(step t15 (cl (! (= @p_8 (! (forall ((veriT_vr0 V$)) @p_17) :named @p_19)) :named @p_18)) :rule bind)
+(step t16 (cl (not @p_18) (not @p_8) @p_19) :rule equiv_pos2)
+(step t17 (cl @p_19) :rule th_resolution :premises (a0 t15 t16))
+(anchor :step t18 :args ((:= (veriT_vr0 V$) veriT_vr1)))
+(step t18.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_21)) :rule refl)
+(step t18.t2 (cl (= @p_10 (! (fun_app$ uua$ veriT_vr1) :named @p_20))) :rule cong :premises (t18.t1))
+(step t18.t3 (cl @p_21) :rule refl)
+(step t18.t4 (cl (= @p_13 (! (fun_evaluate_match$ st$ env$ veriT_vr1 pes$) :named @p_22))) :rule cong :premises (t18.t3))
+(step t18.t5 (cl @p_21) :rule refl)
+(step t18.t6 (cl (= @p_15 (! (fun_app$ @p_22 veriT_vr1) :named @p_23))) :rule cong :premises (t18.t4 t18.t5))
+(step t18.t7 (cl (= @p_17 (! (= @p_20 @p_23) :named @p_24))) :rule cong :premises (t18.t2 t18.t6))
+(step t18 (cl (! (= @p_19 (! (forall ((veriT_vr1 V$)) @p_24) :named @p_26)) :named @p_25)) :rule bind)
+(step t19 (cl (not @p_25) (not @p_19) @p_26) :rule equiv_pos2)
+(step t20 (cl @p_26) :rule th_resolution :premises (t17 t18 t19))
+(anchor :step t21 :args ((:= (?v0 Abort$) veriT_vr2)))
+(step t21.t1 (cl (! (= ?v0 veriT_vr2) :named @p_30)) :rule refl)
+(step t21.t2 (cl (= @p_28 (! (fun_app$a uub$ veriT_vr2) :named @p_29))) :rule cong :premises (t21.t1))
+(step t21.t3 (cl @p_30) :rule refl)
+(step t21.t4 (cl (= @p_31 (! (rabort$ veriT_vr2) :named @p_32))) :rule cong :premises (t21.t3))
+(step t21.t5 (cl (= @p_33 (! (rerr$ @p_32) :named @p_34))) :rule cong :premises (t21.t4))
+(step t21.t6 (cl (= @p_35 (! (pair$ st$ @p_34) :named @p_36))) :rule cong :premises (t21.t5))
+(step t21.t7 (cl (= @p_37 (! (= @p_29 @p_36) :named @p_38))) :rule cong :premises (t21.t2 t21.t6))
+(step t21 (cl (! (= @p_27 (! (forall ((veriT_vr2 Abort$)) @p_38) :named @p_40)) :named @p_39)) :rule bind)
+(step t22 (cl (not @p_39) (not @p_27) @p_40) :rule equiv_pos2)
+(step t23 (cl @p_40) :rule th_resolution :premises (a1 t21 t22))
+(anchor :step t24 :args ((:= (veriT_vr2 Abort$) veriT_vr3)))
+(step t24.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_42)) :rule refl)
+(step t24.t2 (cl (= @p_29 (! (fun_app$a uub$ veriT_vr3) :named @p_41))) :rule cong :premises (t24.t1))
+(step t24.t3 (cl @p_42) :rule refl)
+(step t24.t4 (cl (= @p_32 (! (rabort$ veriT_vr3) :named @p_43))) :rule cong :premises (t24.t3))
+(step t24.t5 (cl (= @p_34 (! (rerr$ @p_43) :named @p_44))) :rule cong :premises (t24.t4))
+(step t24.t6 (cl (= @p_36 (! (pair$ st$ @p_44) :named @p_45))) :rule cong :premises (t24.t5))
+(step t24.t7 (cl (= @p_38 (! (= @p_41 @p_45) :named @p_46))) :rule cong :premises (t24.t2 t24.t6))
+(step t24 (cl (! (= @p_40 (! (forall ((veriT_vr3 Abort$)) @p_46) :named @p_48)) :named @p_47)) :rule bind)
+(step t25 (cl (not @p_47) (not @p_40) @p_48) :rule equiv_pos2)
+(step t26 (cl @p_48) :rule th_resolution :premises (t23 t24 t25))
+(anchor :step t27 :args ((:= (?v0 Astate$) veriT_vr4) (:= (?v1 Astate$) veriT_vr5) (:= (?v2 Nat$) veriT_vr6)))
+(step t27.t1 (cl (! (= ?v0 veriT_vr4) :named @p_56)) :rule refl)
+(step t27.t2 (cl (! (= ?v1 veriT_vr5) :named @p_55)) :rule refl)
+(step t27.t3 (cl (= @p_5 (! (uu$ veriT_vr4 veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1 t27.t2))
+(step t27.t4 (cl (= ?v2 veriT_vr6)) :rule refl)
+(step t27.t5 (cl (= @p_53 (! (fun_app$b @p_52 veriT_vr6) :named @p_54))) :rule cong :premises (t27.t3 t27.t4))
+(step t27.t6 (cl @p_55) :rule refl)
+(step t27.t7 (cl (! (= @p_1 (! (clock$ veriT_vr5) :named @p_50)) :named @p_59)) :rule cong :premises (t27.t6))
+(step t27.t8 (cl @p_56) :rule refl)
+(step t27.t9 (cl (! (= @p_2 (! (clock$ veriT_vr4) :named @p_51)) :named @p_60)) :rule cong :premises (t27.t8))
+(step t27.t10 (cl (= @p_57 (! (less_eq$ @p_50 @p_51) :named @p_58))) :rule cong :premises (t27.t7 t27.t9))
+(step t27.t11 (cl @p_55) :rule refl)
+(step t27.t12 (cl @p_59) :rule cong :premises (t27.t11))
+(step t27.t13 (cl @p_56) :rule refl)
+(step t27.t14 (cl @p_60) :rule cong :premises (t27.t13))
+(step t27.t15 (cl (= @p_61 (! (ite @p_58 @p_50 @p_51) :named @p_62))) :rule cong :premises (t27.t10 t27.t12 t27.t14))
+(step t27.t16 (cl (= @p_63 (! (= @p_54 @p_62) :named @p_64))) :rule cong :premises (t27.t5 t27.t15))
+(step t27 (cl (! (= @p_49 (! (forall ((veriT_vr4 Astate$) (veriT_vr5 Astate$) (veriT_vr6 Nat$)) @p_64) :named @p_66)) :named @p_65)) :rule bind)
+(step t28 (cl (not @p_65) (not @p_49) @p_66) :rule equiv_pos2)
+(step t29 (cl @p_66) :rule th_resolution :premises (a2 t27 t28))
+(anchor :step t30 :args ((:= (veriT_vr4 Astate$) veriT_vr7) (:= (veriT_vr5 Astate$) veriT_vr8) (:= (veriT_vr6 Nat$) veriT_vr9)))
+(step t30.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_72)) :rule refl)
+(step t30.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_71)) :rule refl)
+(step t30.t3 (cl (= @p_52 (! (uu$ veriT_vr7 veriT_vr8) :named @p_69))) :rule cong :premises (t30.t1 t30.t2))
+(step t30.t4 (cl (= veriT_vr6 veriT_vr9)) :rule refl)
+(step t30.t5 (cl (= @p_54 (! (fun_app$b @p_69 veriT_vr9) :named @p_70))) :rule cong :premises (t30.t3 t30.t4))
+(step t30.t6 (cl @p_71) :rule refl)
+(step t30.t7 (cl (! (= @p_50 (! (clock$ veriT_vr8) :named @p_67)) :named @p_74)) :rule cong :premises (t30.t6))
+(step t30.t8 (cl @p_72) :rule refl)
+(step t30.t9 (cl (! (= @p_51 (! (clock$ veriT_vr7) :named @p_68)) :named @p_75)) :rule cong :premises (t30.t8))
+(step t30.t10 (cl (= @p_58 (! (less_eq$ @p_67 @p_68) :named @p_73))) :rule cong :premises (t30.t7 t30.t9))
+(step t30.t11 (cl @p_71) :rule refl)
+(step t30.t12 (cl @p_74) :rule cong :premises (t30.t11))
+(step t30.t13 (cl @p_72) :rule refl)
+(step t30.t14 (cl @p_75) :rule cong :premises (t30.t13))
+(step t30.t15 (cl (= @p_62 (! (ite @p_73 @p_67 @p_68) :named @p_76))) :rule cong :premises (t30.t10 t30.t12 t30.t14))
+(step t30.t16 (cl (= @p_64 (! (= @p_70 @p_76) :named @p_77))) :rule cong :premises (t30.t5 t30.t15))
+(step t30 (cl (! (= @p_66 (! (forall ((veriT_vr7 Astate$) (veriT_vr8 Astate$) (veriT_vr9 Nat$)) @p_77) :named @p_79)) :named @p_78)) :rule bind)
+(step t31 (cl (not @p_78) (not @p_66) @p_79) :rule equiv_pos2)
+(step t32 (cl @p_79) :rule th_resolution :premises (t29 t30 t31))
+(anchor :step t33 :args ((:= (?v0 Nat$) veriT_vr10) (:= (?v1 Nat$) veriT_vr11) (:= (?v2 Nat$) veriT_vr12)))
+(step t33.t1 (cl (! (= ?v0 veriT_vr10) :named @p_83)) :rule refl)
+(step t33.t2 (cl (! (= ?v1 veriT_vr11) :named @p_89)) :rule refl)
+(step t33.t3 (cl (= @p_81 (! (less_eq$ veriT_vr10 veriT_vr11) :named @p_82))) :rule cong :premises (t33.t1 t33.t2))
+(step t33.t4 (cl (! (= ?v2 veriT_vr12) :named @p_88)) :rule refl)
+(step t33.t5 (cl @p_83) :rule refl)
+(step t33.t6 (cl (= @p_84 (! (less_eq$ veriT_vr12 veriT_vr10) :named @p_85))) :rule cong :premises (t33.t4 t33.t5))
+(step t33.t7 (cl (= @p_86 (! (and @p_82 @p_85) :named @p_87))) :rule cong :premises (t33.t3 t33.t6))
+(step t33.t8 (cl @p_88) :rule refl)
+(step t33.t9 (cl @p_89) :rule refl)
+(step t33.t10 (cl (= @p_90 (! (less_eq$ veriT_vr12 veriT_vr11) :named @p_91))) :rule cong :premises (t33.t8 t33.t9))
+(step t33.t11 (cl (= @p_92 (! (=> @p_87 @p_91) :named @p_93))) :rule cong :premises (t33.t7 t33.t10))
+(step t33 (cl (! (= @p_80 (! (forall ((veriT_vr10 Nat$) (veriT_vr11 Nat$) (veriT_vr12 Nat$)) @p_93) :named @p_95)) :named @p_94)) :rule bind)
+(step t34 (cl (not @p_94) (not @p_80) @p_95) :rule equiv_pos2)
+(step t35 (cl @p_95) :rule th_resolution :premises (a5 t33 t34))
+(anchor :step t36 :args ((:= (veriT_vr10 Nat$) veriT_vr13) (:= (veriT_vr11 Nat$) veriT_vr14) (:= (veriT_vr12 Nat$) veriT_vr15)))
+(step t36.t1 (cl (! (= veriT_vr10 veriT_vr13) :named @p_97)) :rule refl)
+(step t36.t2 (cl (! (= veriT_vr11 veriT_vr14) :named @p_101)) :rule refl)
+(step t36.t3 (cl (= @p_82 (! (less_eq$ veriT_vr13 veriT_vr14) :named @p_96))) :rule cong :premises (t36.t1 t36.t2))
+(step t36.t4 (cl (! (= veriT_vr12 veriT_vr15) :named @p_100)) :rule refl)
+(step t36.t5 (cl @p_97) :rule refl)
+(step t36.t6 (cl (= @p_85 (! (less_eq$ veriT_vr15 veriT_vr13) :named @p_98))) :rule cong :premises (t36.t4 t36.t5))
+(step t36.t7 (cl (= @p_87 (! (and @p_96 @p_98) :named @p_99))) :rule cong :premises (t36.t3 t36.t6))
+(step t36.t8 (cl @p_100) :rule refl)
+(step t36.t9 (cl @p_101) :rule refl)
+(step t36.t10 (cl (= @p_91 (! (less_eq$ veriT_vr15 veriT_vr14) :named @p_102))) :rule cong :premises (t36.t8 t36.t9))
+(step t36.t11 (cl (= @p_93 (! (=> @p_99 @p_102) :named @p_103))) :rule cong :premises (t36.t7 t36.t10))
+(step t36 (cl (! (= @p_95 (! (forall ((veriT_vr13 Nat$) (veriT_vr14 Nat$) (veriT_vr15 Nat$)) @p_103) :named @p_105)) :named @p_104)) :rule bind)
+(step t37 (cl (not @p_104) (not @p_95) @p_105) :rule equiv_pos2)
+(step t38 (cl @p_105) :rule th_resolution :premises (t35 t36 t37))
+(anchor :step t39 :args ((:= (?v0 Astate$) veriT_vr16) (:= (?v1 Astate_v_list_v_result_prod$) veriT_vr17)))
+(step t39.t1 (cl (! (= ?v0 veriT_vr16) :named @p_114)) :rule refl)
+(step t39.t2 (cl (! (= ?v1 veriT_vr17) :named @p_113)) :rule refl)
+(step t39.t3 (cl (= @p_107 (! (fst$ veriT_vr17) :named @p_108))) :rule cong :premises (t39.t2))
+(step t39.t4 (cl (= @p_109 (! (= veriT_vr16 @p_108) :named @p_110))) :rule cong :premises (t39.t1 t39.t3))
+(anchor :step t39.t5 :args ((:= (?v2 V_list_v_result$) veriT_vr18)))
+(step t39.t5.t1 (cl @p_113) :rule refl)
+(step t39.t5.t2 (cl @p_114) :rule refl)
+(step t39.t5.t3 (cl (= ?v2 veriT_vr18)) :rule refl)
+(step t39.t5.t4 (cl (= @p_115 (! (pair$ veriT_vr16 veriT_vr18) :named @p_116))) :rule cong :premises (t39.t5.t2 t39.t5.t3))
+(step t39.t5.t5 (cl (= @p_117 (! (= veriT_vr17 @p_116) :named @p_118))) :rule cong :premises (t39.t5.t1 t39.t5.t4))
+(step t39.t5 (cl (= @p_111 (! (exists ((veriT_vr18 V_list_v_result$)) @p_118) :named @p_112))) :rule bind)
+(step t39.t6 (cl (= @p_119 (! (= @p_110 @p_112) :named @p_120))) :rule cong :premises (t39.t4 t39.t5))
+(step t39 (cl (! (= @p_106 (! (forall ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)) @p_120) :named @p_122)) :named @p_121)) :rule bind)
+(step t40 (cl (not @p_121) (not @p_106) @p_122) :rule equiv_pos2)
+(step t41 (cl @p_122) :rule th_resolution :premises (a6 t39 t40))
+(anchor :step t42 :args ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)))
+(step t42.t1 (cl (= @p_120 (! (and (! (=> @p_110 @p_112) :named @p_133) (! (=> @p_112 @p_110) :named @p_140)) :named @p_123))) :rule connective_def)
+(step t42 (cl (! (= @p_122 (! (forall ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)) @p_123) :named @p_125)) :named @p_124)) :rule bind)
+(step t43 (cl (not @p_124) (not @p_122) @p_125) :rule equiv_pos2)
+(step t44 (cl @p_125) :rule th_resolution :premises (t41 t42 t43))
+(anchor :step t45 :args ((:= (veriT_vr16 Astate$) veriT_vr19) (:= (veriT_vr17 Astate_v_list_v_result_prod$) veriT_vr20)))
+(step t45.t1 (cl (! (= veriT_vr16 veriT_vr19) :named @p_130)) :rule refl)
+(step t45.t2 (cl (! (= veriT_vr17 veriT_vr20) :named @p_129)) :rule refl)
+(step t45.t3 (cl (! (= @p_108 (! (fst$ veriT_vr20) :named @p_127)) :named @p_138)) :rule cong :premises (t45.t2))
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+(step t78.t1 (cl (= ?v0 veriT_vr45)) :rule refl)
+(step t78.t2 (cl (! (= ?v1 veriT_vr46) :named @p_270)) :rule refl)
+(step t78.t3 (cl (! (= ?v2 veriT_vr47) :named @p_262)) :rule refl)
+(step t78.t4 (cl (= @p_259 (! (pair$ veriT_vr46 veriT_vr47) :named @p_260))) :rule cong :premises (t78.t2 t78.t3))
+(step t78.t5 (cl (= @p_4 (! (fix_clock$ veriT_vr45 @p_260) :named @p_261))) :rule cong :premises (t78.t1 t78.t4))
+(step t78.t6 (cl (! (= ?v3 veriT_vr48) :named @p_267)) :rule refl)
+(step t78.t7 (cl @p_262) :rule refl)
+(step t78.t8 (cl (= @p_263 (! (pair$ veriT_vr48 veriT_vr47) :named @p_264))) :rule cong :premises (t78.t6 t78.t7))
+(step t78.t9 (cl (= @p_265 (! (= @p_261 @p_264) :named @p_266))) :rule cong :premises (t78.t5 t78.t8))
+(step t78.t10 (cl @p_267) :rule refl)
+(step t78.t11 (cl (= @p_268 (! (clock$ veriT_vr48) :named @p_269))) :rule cong :premises (t78.t10))
+(step t78.t12 (cl @p_270) :rule refl)
+(step t78.t13 (cl (= @p_1 (! (clock$ veriT_vr46) :named @p_271))) :rule cong :premises (t78.t12))
+(step t78.t14 (cl (= @p_272 (! (less_eq$ @p_269 @p_271) :named @p_273))) :rule cong :premises (t78.t11 t78.t13))
+(step t78.t15 (cl (= @p_274 (! (=> @p_266 @p_273) :named @p_275))) :rule cong :premises (t78.t9 t78.t14))
+(step t78 (cl (! (= @p_258 (! (forall ((veriT_vr45 Astate$) (veriT_vr46 Astate$) (veriT_vr47 V_list_v_result$) (veriT_vr48 Astate$)) @p_275) :named @p_277)) :named @p_276)) :rule bind)
+(step t79 (cl (not @p_276) (not @p_258) @p_277) :rule equiv_pos2)
+(step t80 (cl @p_277) :rule th_resolution :premises (a10 t78 t79))
+(anchor :step t81 :args ((:= (veriT_vr45 Astate$) veriT_vr49) (:= (veriT_vr46 Astate$) veriT_vr50) (:= (veriT_vr47 V_list_v_result$) veriT_vr51) (:= (veriT_vr48 Astate$) veriT_vr52)))
+(step t81.t1 (cl (= veriT_vr45 veriT_vr49)) :rule refl)
+(step t81.t2 (cl (! (= veriT_vr46 veriT_vr50) :named @p_285)) :rule refl)
+(step t81.t3 (cl (! (= veriT_vr47 veriT_vr51) :named @p_280)) :rule refl)
+(step t81.t4 (cl (= @p_260 (! (pair$ veriT_vr50 veriT_vr51) :named @p_278))) :rule cong :premises (t81.t2 t81.t3))
+(step t81.t5 (cl (= @p_261 (! (fix_clock$ veriT_vr49 @p_278) :named @p_279))) :rule cong :premises (t81.t1 t81.t4))
+(step t81.t6 (cl (! (= veriT_vr48 veriT_vr52) :named @p_283)) :rule refl)
+(step t81.t7 (cl @p_280) :rule refl)
+(step t81.t8 (cl (= @p_264 (! (pair$ veriT_vr52 veriT_vr51) :named @p_281))) :rule cong :premises (t81.t6 t81.t7))
+(step t81.t9 (cl (= @p_266 (! (= @p_279 @p_281) :named @p_282))) :rule cong :premises (t81.t5 t81.t8))
+(step t81.t10 (cl @p_283) :rule refl)
+(step t81.t11 (cl (= @p_269 (! (clock$ veriT_vr52) :named @p_284))) :rule cong :premises (t81.t10))
+(step t81.t12 (cl @p_285) :rule refl)
+(step t81.t13 (cl (= @p_271 (! (clock$ veriT_vr50) :named @p_286))) :rule cong :premises (t81.t12))
+(step t81.t14 (cl (= @p_273 (! (less_eq$ @p_284 @p_286) :named @p_287))) :rule cong :premises (t81.t11 t81.t13))
+(step t81.t15 (cl (= @p_275 (! (=> @p_282 @p_287) :named @p_288))) :rule cong :premises (t81.t9 t81.t14))
+(step t81 (cl (! (= @p_277 (! (forall ((veriT_vr49 Astate$) (veriT_vr50 Astate$) (veriT_vr51 V_list_v_result$) (veriT_vr52 Astate$)) @p_288) :named @p_290)) :named @p_289)) :rule bind)
+(step t82 (cl (not @p_289) (not @p_277) @p_290) :rule equiv_pos2)
+(step t83 (cl @p_290) :rule th_resolution :premises (t80 t81 t82))
+(anchor :step t84 :args ((:= (?v0 Astate$) veriT_vr53) (:= (?v1 Astate$) veriT_vr54) (:= (?v2 V_list_v_result$) veriT_vr55)))
+(step t84.t1 (cl (! (= ?v0 veriT_vr53) :named @p_294)) :rule refl)
+(step t84.t2 (cl (! (= ?v1 veriT_vr54) :named @p_295)) :rule refl)
+(step t84.t3 (cl (! (= ?v2 veriT_vr55) :named @p_299)) :rule refl)
+(step t84.t4 (cl (= @p_259 (! (pair$ veriT_vr54 veriT_vr55) :named @p_292))) :rule cong :premises (t84.t2 t84.t3))
+(step t84.t5 (cl (= @p_4 (! (fix_clock$ veriT_vr53 @p_292) :named @p_293))) :rule cong :premises (t84.t1 t84.t4))
+(step t84.t6 (cl @p_294) :rule refl)
+(step t84.t7 (cl @p_295) :rule refl)
+(step t84.t8 (cl (= @p_5 (! (uu$ veriT_vr53 veriT_vr54) :named @p_296))) :rule cong :premises (t84.t6 t84.t7))
+(step t84.t9 (cl @p_295) :rule refl)
+(step t84.t10 (cl (= @p_297 (! (update_clock$ @p_296 veriT_vr54) :named @p_298))) :rule cong :premises (t84.t8 t84.t9))
+(step t84.t11 (cl @p_299) :rule refl)
+(step t84.t12 (cl (= @p_300 (! (pair$ @p_298 veriT_vr55) :named @p_301))) :rule cong :premises (t84.t10 t84.t11))
+(step t84.t13 (cl (= @p_302 (! (= @p_293 @p_301) :named @p_303))) :rule cong :premises (t84.t5 t84.t12))
+(step t84 (cl (! (= @p_291 (! (forall ((veriT_vr53 Astate$) (veriT_vr54 Astate$) (veriT_vr55 V_list_v_result$)) @p_303) :named @p_305)) :named @p_304)) :rule bind)
+(step t85 (cl (not @p_304) (not @p_291) @p_305) :rule equiv_pos2)
+(step t86 (cl @p_305) :rule th_resolution :premises (a11 t84 t85))
+(anchor :step t87 :args ((:= (veriT_vr53 Astate$) veriT_vr56) (:= (veriT_vr54 Astate$) veriT_vr57) (:= (veriT_vr55 V_list_v_result$) veriT_vr58)))
+(step t87.t1 (cl (! (= veriT_vr53 veriT_vr56) :named @p_308)) :rule refl)
+(step t87.t2 (cl (! (= veriT_vr54 veriT_vr57) :named @p_309)) :rule refl)
+(step t87.t3 (cl (! (= veriT_vr55 veriT_vr58) :named @p_312)) :rule refl)
+(step t87.t4 (cl (= @p_292 (! (pair$ veriT_vr57 veriT_vr58) :named @p_306))) :rule cong :premises (t87.t2 t87.t3))
+(step t87.t5 (cl (= @p_293 (! (fix_clock$ veriT_vr56 @p_306) :named @p_307))) :rule cong :premises (t87.t1 t87.t4))
+(step t87.t6 (cl @p_308) :rule refl)
+(step t87.t7 (cl @p_309) :rule refl)
+(step t87.t8 (cl (= @p_296 (! (uu$ veriT_vr56 veriT_vr57) :named @p_310))) :rule cong :premises (t87.t6 t87.t7))
+(step t87.t9 (cl @p_309) :rule refl)
+(step t87.t10 (cl (= @p_298 (! (update_clock$ @p_310 veriT_vr57) :named @p_311))) :rule cong :premises (t87.t8 t87.t9))
+(step t87.t11 (cl @p_312) :rule refl)
+(step t87.t12 (cl (= @p_301 (! (pair$ @p_311 veriT_vr58) :named @p_313))) :rule cong :premises (t87.t10 t87.t11))
+(step t87.t13 (cl (= @p_303 (! (= @p_307 @p_313) :named @p_314))) :rule cong :premises (t87.t5 t87.t12))
+(step t87 (cl (! (= @p_305 (! (forall ((veriT_vr56 Astate$) (veriT_vr57 Astate$) (veriT_vr58 V_list_v_result$)) @p_314) :named @p_316)) :named @p_315)) :rule bind)
+(step t88 (cl (not @p_315) (not @p_305) @p_316) :rule equiv_pos2)
+(step t89 (cl @p_316) :rule th_resolution :premises (t86 t87 t88))
+(anchor :step t90 :args ((:= (?v0 V_error_result$) veriT_vr59) (:= (?v1 V$) veriT_vr60)))
+(step t90.t1 (cl (! (= ?v0 veriT_vr59) :named @p_323)) :rule refl)
+(step t90.t2 (cl (= @p_319 (! (rerr$ veriT_vr59) :named @p_320))) :rule cong :premises (t90.t1))
+(step t90.t3 (cl (= @p_321 (! (= r$ @p_320) :named @p_322))) :rule cong :premises (t90.t2))
+(step t90.t4 (cl @p_323) :rule refl)
+(step t90.t5 (cl (! (= ?v1 veriT_vr60) :named @p_328)) :rule refl)
+(step t90.t6 (cl (= @p_174 (! (rraise$ veriT_vr60) :named @p_324))) :rule cong :premises (t90.t5))
+(step t90.t7 (cl (= @p_6 (! (= veriT_vr59 @p_324) :named @p_325))) :rule cong :premises (t90.t4 t90.t6))
+(step t90.t8 (cl (= @p_326 (! (and @p_322 @p_325) :named @p_327))) :rule cong :premises (t90.t3 t90.t7))
+(step t90.t9 (cl @p_328) :rule refl)
+(step t90.t10 (cl (= @p_329 (! (fun_evaluate_match$ st$ env$ veriT_vr60 pes$) :named @p_330))) :rule cong :premises (t90.t9))
+(step t90.t11 (cl @p_328) :rule refl)
+(step t90.t12 (cl (= @p_331 (! (fun_app$ @p_330 veriT_vr60) :named @p_332))) :rule cong :premises (t90.t10 t90.t11))
+(step t90.t13 (cl (= @p_333 (! (fst$ @p_332) :named @p_334))) :rule cong :premises (t90.t12))
+(step t90.t14 (cl (= @p_335 (! (clock$ @p_334) :named @p_336))) :rule cong :premises (t90.t13))
+(step t90.t15 (cl (= @p_337 (! (less_eq$ @p_336 @p_318) :named @p_338))) :rule cong :premises (t90.t14))
+(step t90.t16 (cl (= @p_339 (! (=> @p_327 @p_338) :named @p_340))) :rule cong :premises (t90.t8 t90.t15))
+(step t90 (cl (! (= @p_317 (! (forall ((veriT_vr59 V_error_result$) (veriT_vr60 V$)) @p_340) :named @p_342)) :named @p_341)) :rule bind)
+(step t91 (cl (not @p_341) (not @p_317) @p_342) :rule equiv_pos2)
+(step t92 (cl @p_342) :rule th_resolution :premises (a12 t90 t91))
+(anchor :step t93 :args ((:= (veriT_vr59 V_error_result$) veriT_vr61) (:= (veriT_vr60 V$) veriT_vr62)))
+(step t93.t1 (cl (! (= veriT_vr59 veriT_vr61) :named @p_345)) :rule refl)
+(step t93.t2 (cl (= @p_320 (! (rerr$ veriT_vr61) :named @p_343))) :rule cong :premises (t93.t1))
+(step t93.t3 (cl (= @p_322 (! (= r$ @p_343) :named @p_344))) :rule cong :premises (t93.t2))
+(step t93.t4 (cl @p_345) :rule refl)
+(step t93.t5 (cl (! (= veriT_vr60 veriT_vr62) :named @p_349)) :rule refl)
+(step t93.t6 (cl (= @p_324 (! (rraise$ veriT_vr62) :named @p_346))) :rule cong :premises (t93.t5))
+(step t93.t7 (cl (= @p_325 (! (= veriT_vr61 @p_346) :named @p_347))) :rule cong :premises (t93.t4 t93.t6))
+(step t93.t8 (cl (= @p_327 (! (and @p_344 @p_347) :named @p_348))) :rule cong :premises (t93.t3 t93.t7))
+(step t93.t9 (cl @p_349) :rule refl)
+(step t93.t10 (cl (= @p_330 (! (fun_evaluate_match$ st$ env$ veriT_vr62 pes$) :named @p_350))) :rule cong :premises (t93.t9))
+(step t93.t11 (cl @p_349) :rule refl)
+(step t93.t12 (cl (= @p_332 (! (fun_app$ @p_350 veriT_vr62) :named @p_351))) :rule cong :premises (t93.t10 t93.t11))
+(step t93.t13 (cl (= @p_334 (! (fst$ @p_351) :named @p_352))) :rule cong :premises (t93.t12))
+(step t93.t14 (cl (= @p_336 (! (clock$ @p_352) :named @p_353))) :rule cong :premises (t93.t13))
+(step t93.t15 (cl (= @p_338 (! (less_eq$ @p_353 @p_318) :named @p_354))) :rule cong :premises (t93.t14))
+(step t93.t16 (cl (= @p_340 (! (=> @p_348 @p_354) :named @p_355))) :rule cong :premises (t93.t8 t93.t15))
+(step t93 (cl (! (= @p_342 (! (forall ((veriT_vr61 V_error_result$) (veriT_vr62 V$)) @p_355) :named @p_357)) :named @p_356)) :rule bind)
+(step t94 (cl (not @p_356) (not @p_342) @p_357) :rule equiv_pos2)
+(step t95 (cl @p_357) :rule th_resolution :premises (t92 t93 t94))
+(step t96 (cl (! (= @p_358 (! (and @p_359 (! (not @p_360) :named @p_366)) :named @p_362)) :named @p_361)) :rule bool_simplify)
+(step t97 (cl (! (not @p_361) :named @p_365) (! (not @p_358) :named @p_363) @p_362) :rule equiv_pos2)
+(step t98 (cl (not @p_363) @p_364) :rule not_not)
+(step t99 (cl @p_365 @p_364 @p_362) :rule th_resolution :premises (t98 t97))
+(step t100 (cl @p_362) :rule th_resolution :premises (a13 t96 t99))
+(step t101 (cl @p_359) :rule and :premises (t100))
+(step t102 (cl @p_366) :rule and :premises (t100))
+(step t103 (cl (or (! (not @p_105) :named @p_368) (! (forall ((veriT_vr13 Nat$) (veriT_vr14 Nat$) (veriT_vr15 Nat$)) (or (not @p_96) (not @p_98) @p_102)) :named @p_573))) :rule qnt_cnf)
+(step t104 (cl (or (! (not @p_170) :named @p_431) (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$) (veriT_vr26 V_list_v_result$)) (or @p_367 @p_146)) :named @p_629))) :rule qnt_cnf)
+(step t105 (cl (or @p_368 (! (=> (! (and @p_369 (! (less_eq$ @p_370 @p_371) :named @p_373)) :named @p_372) @p_360) :named @p_374))) :rule forall_inst :args ((:= veriT_vr13 @p_371) (:= veriT_vr14 @p_7) (:= veriT_vr15 @p_370)))
+(step t106 (cl @p_372 (! (not @p_369) :named @p_574) (! (not @p_373) :named @p_375)) :rule and_neg)
+(step t107 (cl (! (not @p_374) :named @p_376) (! (not @p_372) :named @p_377) @p_360) :rule implies_pos)
+(step t108 (cl @p_368 @p_374) :rule or :premises (t105))
+(step t109 (cl @p_372 @p_375) :rule resolution :premises (t106 a4))
+(step t110 (cl @p_376 @p_377) :rule resolution :premises (t107 t102))
+(step t111 (cl @p_374) :rule resolution :premises (t108 t38))
+(step t112 (cl @p_377) :rule resolution :premises (t110 t111))
+(step t113 (cl @p_375) :rule resolution :premises (t109 t112))
+(step t114 (cl (not (! (not @p_368) :named @p_578)) @p_105) :rule not_not)
+(step t115 (cl (or (! (not @p_316) :named @p_547) (! (= (fix_clock$ st$a (pair$ @p_378 r$)) (pair$ (! (update_clock$ (uu$ st$a @p_378) @p_378) :named @p_561) r$)) :named @p_548))) :rule forall_inst :args ((:= veriT_vr56 st$a) (:= veriT_vr57 @p_378) (:= veriT_vr58 r$)))
+(step t116 (cl (or (! (not @p_215) :named @p_427) (! (not (! (and (! (forall ((veriT_vr31 V$)) (! (not (! (= x2$ @p_204) :named @p_382)) :named @p_384)) :named @p_380) (! (forall ((veriT_vr32 Abort$)) (! (not (! (= x2$ @p_209) :named @p_388)) :named @p_390)) :named @p_386)) :named @p_392)) :named @p_379))) :rule forall_inst :args ((:= veriT_vr30 x2$)))
+(anchor :step t117)
+(assume t117.h1 @p_379)
+(anchor :step t117.t2 :args ((:= (veriT_vr31 V$) veriT_vr63)))
+(step t117.t2.t1 (cl (= veriT_vr31 veriT_vr63)) :rule refl)
+(step t117.t2.t2 (cl (= @p_204 (! (rraise$ veriT_vr63) :named @p_381))) :rule cong :premises (t117.t2.t1))
+(step t117.t2.t3 (cl (= @p_382 (! (= x2$ @p_381) :named @p_383))) :rule cong :premises (t117.t2.t2))
+(step t117.t2.t4 (cl (= @p_384 (! (not @p_383) :named @p_385))) :rule cong :premises (t117.t2.t3))
+(step t117.t2 (cl (= @p_380 (! (forall ((veriT_vr63 V$)) @p_385) :named @p_393))) :rule bind)
+(anchor :step t117.t3 :args ((:= (veriT_vr32 Abort$) veriT_vr64)))
+(step t117.t3.t1 (cl (= veriT_vr32 veriT_vr64)) :rule refl)
+(step t117.t3.t2 (cl (= @p_209 (! (rabort$ veriT_vr64) :named @p_387))) :rule cong :premises (t117.t3.t1))
+(step t117.t3.t3 (cl (= @p_388 (! (= x2$ @p_387) :named @p_389))) :rule cong :premises (t117.t3.t2))
+(step t117.t3.t4 (cl (= @p_390 (! (not @p_389) :named @p_391))) :rule cong :premises (t117.t3.t3))
+(step t117.t3 (cl (= @p_386 (! (forall ((veriT_vr64 Abort$)) @p_391) :named @p_394))) :rule bind)
+(step t117.t4 (cl (= @p_392 (! (and @p_393 @p_394) :named @p_395))) :rule cong :premises (t117.t2 t117.t3))
+(step t117.t5 (cl (! (= @p_379 (! (not @p_395) :named @p_398)) :named @p_396)) :rule cong :premises (t117.t4))
+(step t117.t6 (cl (! (not @p_396) :named @p_399) (! (not @p_379) :named @p_397) @p_398) :rule equiv_pos2)
+(step t117.t7 (cl (! (not @p_397) :named @p_426) @p_392) :rule not_not)
+(step t117.t8 (cl @p_399 @p_392 @p_398) :rule th_resolution :premises (t117.t7 t117.t6))
+(step t117.t9 (cl @p_398) :rule th_resolution :premises (t117.h1 t117.t5 t117.t8))
+(anchor :step t117.t10 :args ((:= (veriT_vr63 V$) veriT_vr65)))
+(step t117.t10.t1 (cl (= veriT_vr63 veriT_vr65)) :rule refl)
+(step t117.t10.t2 (cl (= @p_381 @p_401)) :rule cong :premises (t117.t10.t1))
+(step t117.t10.t3 (cl (= @p_383 @p_402)) :rule cong :premises (t117.t10.t2))
+(step t117.t10.t4 (cl (= @p_385 @p_400)) :rule cong :premises (t117.t10.t3))
+(step t117.t10 (cl (= @p_393 (! (forall ((veriT_vr65 V$)) @p_400) :named @p_406))) :rule bind)
+(anchor :step t117.t11 :args ((:= (veriT_vr64 Abort$) veriT_vr66)))
+(step t117.t11.t1 (cl (= veriT_vr64 veriT_vr66)) :rule refl)
+(step t117.t11.t2 (cl (= @p_387 @p_404)) :rule cong :premises (t117.t11.t1))
+(step t117.t11.t3 (cl (= @p_389 @p_405)) :rule cong :premises (t117.t11.t2))
+(step t117.t11.t4 (cl (= @p_391 @p_403)) :rule cong :premises (t117.t11.t3))
+(step t117.t11 (cl (= @p_394 (! (forall ((veriT_vr66 Abort$)) @p_403) :named @p_407))) :rule bind)
+(step t117.t12 (cl (= @p_395 (! (and @p_406 @p_407) :named @p_408))) :rule cong :premises (t117.t10 t117.t11))
+(step t117.t13 (cl (! (= @p_398 (! (not @p_408) :named @p_410)) :named @p_409)) :rule cong :premises (t117.t12))
+(step t117.t14 (cl (! (not @p_409) :named @p_412) (! (not @p_398) :named @p_411) @p_410) :rule equiv_pos2)
+(step t117.t15 (cl (not @p_411) @p_395) :rule not_not)
+(step t117.t16 (cl @p_412 @p_395 @p_410) :rule th_resolution :premises (t117.t15 t117.t14))
+(step t117.t17 (cl @p_410) :rule th_resolution :premises (t117.t9 t117.t13 t117.t16))
+(anchor :step t117.t18 :args ((:= (veriT_vr65 V$) veriT_sk0)))
+(step t117.t18.t1 (cl (= veriT_vr65 veriT_sk0)) :rule refl)
+(step t117.t18.t2 (cl (= @p_401 (! (rraise$ veriT_sk0) :named @p_415))) :rule cong :premises (t117.t18.t1))
+(step t117.t18.t3 (cl (= @p_402 (! (= x2$ @p_415) :named @p_416))) :rule cong :premises (t117.t18.t2))
+(step t117.t18.t4 (cl (= @p_400 (! (not @p_416) :named @p_413))) :rule cong :premises (t117.t18.t3))
+(step t117.t18 (cl (= @p_406 @p_413)) :rule sko_forall)
+(anchor :step t117.t19 :args ((:= (veriT_vr66 Abort$) veriT_sk1)))
+(step t117.t19.t1 (cl (= veriT_vr66 veriT_sk1)) :rule refl)
+(step t117.t19.t2 (cl (= @p_404 (! (rabort$ veriT_sk1) :named @p_419))) :rule cong :premises (t117.t19.t1))
+(step t117.t19.t3 (cl (= @p_405 (! (= x2$ @p_419) :named @p_420))) :rule cong :premises (t117.t19.t2))
+(step t117.t19.t4 (cl (= @p_403 (! (not @p_420) :named @p_417))) :rule cong :premises (t117.t19.t3))
+(step t117.t19 (cl (= @p_407 @p_417)) :rule sko_forall)
+(step t117.t20 (cl (= @p_408 (! (and @p_413 @p_417) :named @p_421))) :rule cong :premises (t117.t18 t117.t19))
+(step t117.t21 (cl (! (= @p_410 (! (not @p_421) :named @p_422)) :named @p_423)) :rule cong :premises (t117.t20))
+(step t117.t22 (cl (! (not @p_423) :named @p_425) (! (not @p_410) :named @p_424) @p_422) :rule equiv_pos2)
+(step t117.t23 (cl (not @p_424) @p_408) :rule not_not)
+(step t117.t24 (cl @p_425 @p_408 @p_422) :rule th_resolution :premises (t117.t23 t117.t22))
+(step t117.t25 (cl @p_422) :rule th_resolution :premises (t117.t17 t117.t21 t117.t24))
+(step t117 (cl @p_397 @p_422) :rule subproof :discharge (h1))
+(step t118 (cl @p_426 @p_392) :rule not_not)
+(step t119 (cl @p_392 @p_422) :rule th_resolution :premises (t118 t117))
+(step t120 (cl @p_427 @p_379) :rule or :premises (t116))
+(step t121 (cl (! (or @p_427 @p_422) :named @p_429) (! (not @p_427) :named @p_428)) :rule or_neg)
+(step t122 (cl (not @p_428) @p_215) :rule not_not)
+(step t123 (cl @p_429 @p_215) :rule th_resolution :premises (t122 t121))
+(step t124 (cl @p_429 (! (not @p_422) :named @p_430)) :rule or_neg)
+(step t125 (cl (not @p_430) @p_421) :rule not_not)
+(step t126 (cl @p_429 @p_421) :rule th_resolution :premises (t125 t124))
+(step t127 (cl @p_429) :rule th_resolution :premises (t120 t119 t123 t126))
+(step t128 (cl (not (! (not @p_431) :named @p_468)) @p_170) :rule not_not)
+(step t129 (cl (or @p_431 (! (and (! (=> (! (= @p_378 @p_378) :named @p_432) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_3 (! (pair$ @p_378 veriT_vr25) :named @p_435)) :named @p_437)) :named @p_434)) :named @p_439) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_3 (! (pair$ @p_378 veriT_vr26) :named @p_442)) :named @p_443)) :named @p_444)) :named @p_441)) :named @p_446) @p_432) :named @p_448)) :named @p_433))) :rule forall_inst :args ((:= veriT_vr23 @p_378) (:= veriT_vr24 @p_3)))
+(anchor :step t130)
+(assume t130.h1 @p_433)
+(anchor :step t130.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr72)))
+(step t130.t2.t1 (cl (= veriT_vr25 veriT_vr72)) :rule refl)
+(step t130.t2.t2 (cl (= @p_435 (! (pair$ @p_378 veriT_vr72) :named @p_436))) :rule cong :premises (t130.t2.t1))
+(step t130.t2.t3 (cl (= @p_437 (! (= @p_3 @p_436) :named @p_438))) :rule cong :premises (t130.t2.t2))
+(step t130.t2 (cl (= @p_434 (! (exists ((veriT_vr72 V_list_v_result$)) @p_438) :named @p_440))) :rule bind)
+(step t130.t3 (cl (= @p_439 (! (=> @p_432 @p_440) :named @p_450))) :rule cong :premises (t130.t2))
+(anchor :step t130.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr72)))
+(step t130.t4.t1 (cl (= veriT_vr26 veriT_vr72)) :rule refl)
+(step t130.t4.t2 (cl (= @p_442 @p_436)) :rule cong :premises (t130.t4.t1))
+(step t130.t4.t3 (cl (= @p_443 @p_438)) :rule cong :premises (t130.t4.t2))
+(step t130.t4.t4 (cl (= @p_444 (! (not @p_438) :named @p_445))) :rule cong :premises (t130.t4.t3))
+(step t130.t4 (cl (= @p_441 (! (forall ((veriT_vr72 V_list_v_result$)) @p_445) :named @p_447))) :rule bind)
+(step t130.t5 (cl (= @p_446 (! (not @p_447) :named @p_449))) :rule cong :premises (t130.t4))
+(step t130.t6 (cl (= @p_448 (! (=> @p_449 @p_432) :named @p_451))) :rule cong :premises (t130.t5))
+(step t130.t7 (cl (! (= @p_433 (! (and @p_450 @p_451) :named @p_454)) :named @p_452)) :rule cong :premises (t130.t3 t130.t6))
+(step t130.t8 (cl (not @p_452) (! (not @p_433) :named @p_453) @p_454) :rule equiv_pos2)
+(step t130.t9 (cl @p_454) :rule th_resolution :premises (t130.h1 t130.t7 t130.t8))
+(step t130.t10 (cl (= @p_432 true)) :rule eq_simplify)
+(step t130.t11 (cl (= @p_450 (! (=> true @p_440) :named @p_455))) :rule cong :premises (t130.t10))
+(step t130.t12 (cl (= @p_455 @p_440)) :rule implies_simplify)
+(step t130.t13 (cl (= @p_450 @p_440)) :rule trans :premises (t130.t11 t130.t12))
+(step t130.t14 (cl (= @p_451 (! (=> @p_449 true) :named @p_456))) :rule cong :premises (t130.t10))
+(step t130.t15 (cl (= @p_456 true)) :rule implies_simplify)
+(step t130.t16 (cl (= @p_451 true)) :rule trans :premises (t130.t14 t130.t15))
+(step t130.t17 (cl (= @p_454 (! (and @p_440 true) :named @p_457))) :rule cong :premises (t130.t13 t130.t16))
+(step t130.t18 (cl (= @p_457 (! (and @p_440) :named @p_458))) :rule and_simplify)
+(step t130.t19 (cl (= @p_458 @p_440)) :rule and_simplify)
+(step t130.t20 (cl (! (= @p_454 @p_440) :named @p_459)) :rule trans :premises (t130.t17 t130.t18 t130.t19))
+(step t130.t21 (cl (not @p_459) (not @p_454) @p_440) :rule equiv_pos2)
+(step t130.t22 (cl @p_440) :rule th_resolution :premises (t130.t9 t130.t20 t130.t21))
+(anchor :step t130.t23 :args ((:= (veriT_vr72 V_list_v_result$) veriT_vr73)))
+(step t130.t23.t1 (cl (= veriT_vr72 veriT_vr73)) :rule refl)
+(step t130.t23.t2 (cl (= @p_436 @p_461)) :rule cong :premises (t130.t23.t1))
+(step t130.t23.t3 (cl (= @p_438 @p_460)) :rule cong :premises (t130.t23.t2))
+(step t130.t23 (cl (! (= @p_440 (! (exists ((veriT_vr73 V_list_v_result$)) @p_460) :named @p_463)) :named @p_462)) :rule bind)
+(step t130.t24 (cl (not @p_462) (not @p_440) @p_463) :rule equiv_pos2)
+(step t130.t25 (cl @p_463) :rule th_resolution :premises (t130.t22 t130.t23 t130.t24))
+(anchor :step t130.t26 :args ((:= (veriT_vr73 V_list_v_result$) veriT_sk3)))
+(step t130.t26.t1 (cl (= veriT_vr73 veriT_sk3)) :rule refl)
+(step t130.t26.t2 (cl (= @p_461 (! (pair$ @p_378 veriT_sk3) :named @p_466))) :rule cong :premises (t130.t26.t1))
+(step t130.t26.t3 (cl (= @p_460 (! (= @p_3 @p_466) :named @p_464))) :rule cong :premises (t130.t26.t2))
+(step t130.t26 (cl (! (= @p_463 @p_464) :named @p_467)) :rule sko_ex)
+(step t130.t27 (cl (not @p_467) (not @p_463) @p_464) :rule equiv_pos2)
+(step t130.t28 (cl @p_464) :rule th_resolution :premises (t130.t25 t130.t26 t130.t27))
+(step t130 (cl @p_453 @p_464) :rule subproof :discharge (h1))
+(step t131 (cl @p_431 @p_433) :rule or :premises (t129))
+(step t132 (cl (! (or @p_431 @p_464) :named @p_469) @p_468) :rule or_neg)
+(step t133 (cl @p_469 @p_170) :rule th_resolution :premises (t128 t132))
+(step t134 (cl @p_469 (! (not @p_464) :named @p_595)) :rule or_neg)
+(step t135 (cl @p_469) :rule th_resolution :premises (t131 t130 t133 t134))
+(step t136 (cl (or @p_431 (! (and (! (=> (! (= st$ (! (fst$ @p_470) :named @p_650)) :named @p_471) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_470 (! (pair$ st$ veriT_vr25) :named @p_474)) :named @p_476)) :named @p_473)) :named @p_478) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_470 (! (pair$ st$ veriT_vr26) :named @p_481)) :named @p_482)) :named @p_483)) :named @p_480)) :named @p_485) @p_471) :named @p_487)) :named @p_472))) :rule forall_inst :args ((:= veriT_vr23 st$) (:= veriT_vr24 @p_470)))
+(anchor :step t137)
+(assume t137.h1 @p_472)
+(anchor :step t137.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr106)))
+(step t137.t2.t1 (cl (= veriT_vr25 veriT_vr106)) :rule refl)
+(step t137.t2.t2 (cl (= @p_474 (! (pair$ st$ veriT_vr106) :named @p_475))) :rule cong :premises (t137.t2.t1))
+(step t137.t2.t3 (cl (= @p_476 (! (= @p_470 @p_475) :named @p_477))) :rule cong :premises (t137.t2.t2))
+(step t137.t2 (cl (= @p_473 (! (exists ((veriT_vr106 V_list_v_result$)) @p_477) :named @p_479))) :rule bind)
+(step t137.t3 (cl (= @p_478 (! (=> @p_471 @p_479) :named @p_489))) :rule cong :premises (t137.t2))
+(anchor :step t137.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr106)))
+(step t137.t4.t1 (cl (= veriT_vr26 veriT_vr106)) :rule refl)
+(step t137.t4.t2 (cl (= @p_481 @p_475)) :rule cong :premises (t137.t4.t1))
+(step t137.t4.t3 (cl (= @p_482 @p_477)) :rule cong :premises (t137.t4.t2))
+(step t137.t4.t4 (cl (= @p_483 (! (not @p_477) :named @p_484))) :rule cong :premises (t137.t4.t3))
+(step t137.t4 (cl (= @p_480 (! (forall ((veriT_vr106 V_list_v_result$)) @p_484) :named @p_486))) :rule bind)
+(step t137.t5 (cl (= @p_485 (! (not @p_486) :named @p_488))) :rule cong :premises (t137.t4))
+(step t137.t6 (cl (= @p_487 (! (=> @p_488 @p_471) :named @p_490))) :rule cong :premises (t137.t5))
+(step t137.t7 (cl (! (= @p_472 (! (and @p_489 @p_490) :named @p_493)) :named @p_491)) :rule cong :premises (t137.t3 t137.t6))
+(step t137.t8 (cl (not @p_491) (! (not @p_472) :named @p_492) @p_493) :rule equiv_pos2)
+(step t137.t9 (cl @p_493) :rule th_resolution :premises (t137.h1 t137.t7 t137.t8))
+(anchor :step t137.t10 :args ((:= (veriT_vr106 V_list_v_result$) veriT_vr107)))
+(step t137.t10.t1 (cl (= veriT_vr106 veriT_vr107)) :rule refl)
+(step t137.t10.t2 (cl (= @p_475 (! (pair$ st$ veriT_vr107) :named @p_494))) :rule cong :premises (t137.t10.t1))
+(step t137.t10.t3 (cl (= @p_477 (! (= @p_470 @p_494) :named @p_495))) :rule cong :premises (t137.t10.t2))
+(step t137.t10.t4 (cl (= @p_484 (! (not @p_495) :named @p_496))) :rule cong :premises (t137.t10.t3))
+(step t137.t10 (cl (= @p_486 (! (forall ((veriT_vr107 V_list_v_result$)) @p_496) :named @p_497))) :rule bind)
+(step t137.t11 (cl (= @p_488 (! (not @p_497) :named @p_498))) :rule cong :premises (t137.t10))
+(step t137.t12 (cl (= @p_490 (! (=> @p_498 @p_471) :named @p_499))) :rule cong :premises (t137.t11))
+(step t137.t13 (cl (! (= @p_493 (! (and @p_489 @p_499) :named @p_501)) :named @p_500)) :rule cong :premises (t137.t12))
+(step t137.t14 (cl (not @p_500) (not @p_493) @p_501) :rule equiv_pos2)
+(step t137.t15 (cl @p_501) :rule th_resolution :premises (t137.t9 t137.t13 t137.t14))
+(anchor :step t137.t16 :args ((:= (veriT_vr106 V_list_v_result$) veriT_vr108)))
+(step t137.t16.t1 (cl (= veriT_vr106 veriT_vr108)) :rule refl)
+(step t137.t16.t2 (cl (= @p_475 @p_503)) :rule cong :premises (t137.t16.t1))
+(step t137.t16.t3 (cl (= @p_477 @p_502)) :rule cong :premises (t137.t16.t2))
+(step t137.t16 (cl (= @p_479 (! (exists ((veriT_vr108 V_list_v_result$)) @p_502) :named @p_504))) :rule bind)
+(step t137.t17 (cl (= @p_489 (! (=> @p_471 @p_504) :named @p_510))) :rule cong :premises (t137.t16))
+(anchor :step t137.t18 :args ((:= (veriT_vr107 V_list_v_result$) veriT_vr109)))
+(step t137.t18.t1 (cl (= veriT_vr107 veriT_vr109)) :rule refl)
+(step t137.t18.t2 (cl (= @p_494 (! (pair$ st$ veriT_vr109) :named @p_505))) :rule cong :premises (t137.t18.t1))
+(step t137.t18.t3 (cl (= @p_495 (! (= @p_470 @p_505) :named @p_506))) :rule cong :premises (t137.t18.t2))
+(step t137.t18.t4 (cl (= @p_496 (! (not @p_506) :named @p_507))) :rule cong :premises (t137.t18.t3))
+(step t137.t18 (cl (= @p_497 (! (forall ((veriT_vr109 V_list_v_result$)) @p_507) :named @p_508))) :rule bind)
+(step t137.t19 (cl (= @p_498 (! (not @p_508) :named @p_509))) :rule cong :premises (t137.t18))
+(step t137.t20 (cl (= @p_499 (! (=> @p_509 @p_471) :named @p_511))) :rule cong :premises (t137.t19))
+(step t137.t21 (cl (! (= @p_501 (! (and @p_510 @p_511) :named @p_513)) :named @p_512)) :rule cong :premises (t137.t17 t137.t20))
+(step t137.t22 (cl (not @p_512) (not @p_501) @p_513) :rule equiv_pos2)
+(step t137.t23 (cl @p_513) :rule th_resolution :premises (t137.t15 t137.t21 t137.t22))
+(anchor :step t137.t24 :args ((:= (veriT_vr108 V_list_v_result$) veriT_sk11)))
+(step t137.t24.t1 (cl (= veriT_vr108 veriT_sk11)) :rule refl)
+(step t137.t24.t2 (cl (= @p_503 (! (pair$ st$ veriT_sk11) :named @p_516))) :rule cong :premises (t137.t24.t1))
+(step t137.t24.t3 (cl (= @p_502 (! (= @p_470 @p_516) :named @p_514))) :rule cong :premises (t137.t24.t2))
+(step t137.t24 (cl (= @p_504 @p_514)) :rule sko_ex)
+(step t137.t25 (cl (= @p_510 (! (=> @p_471 @p_514) :named @p_517))) :rule cong :premises (t137.t24))
+(step t137.t26 (cl (! (= @p_513 (! (and @p_517 @p_511) :named @p_519)) :named @p_518)) :rule cong :premises (t137.t25))
+(step t137.t27 (cl (not @p_518) (not @p_513) @p_519) :rule equiv_pos2)
+(step t137.t28 (cl @p_519) :rule th_resolution :premises (t137.t23 t137.t26 t137.t27))
+(anchor :step t137.t29 :args ((:= (veriT_vr109 V_list_v_result$) veriT_vr110)))
+(step t137.t29.t1 (cl (= veriT_vr109 veriT_vr110)) :rule refl)
+(step t137.t29.t2 (cl (= @p_505 (! (pair$ st$ veriT_vr110) :named @p_521))) :rule cong :premises (t137.t29.t1))
+(step t137.t29.t3 (cl (= @p_506 (! (= @p_470 @p_521) :named @p_522))) :rule cong :premises (t137.t29.t2))
+(step t137.t29.t4 (cl (= @p_507 (! (not @p_522) :named @p_523))) :rule cong :premises (t137.t29.t3))
+(step t137.t29 (cl (= @p_508 (! (forall ((veriT_vr110 V_list_v_result$)) @p_523) :named @p_520))) :rule bind)
+(step t137.t30 (cl (= @p_509 (! (not @p_520) :named @p_524))) :rule cong :premises (t137.t29))
+(step t137.t31 (cl (= @p_511 (! (=> @p_524 @p_471) :named @p_525))) :rule cong :premises (t137.t30))
+(step t137.t32 (cl (! (= @p_519 (! (and @p_517 @p_525) :named @p_526)) :named @p_527)) :rule cong :premises (t137.t31))
+(step t137.t33 (cl (not @p_527) (not @p_519) @p_526) :rule equiv_pos2)
+(step t137.t34 (cl @p_526) :rule th_resolution :premises (t137.t28 t137.t32 t137.t33))
+(step t137 (cl @p_492 @p_526) :rule subproof :discharge (h1))
+(step t138 (cl @p_431 @p_472) :rule or :premises (t136))
+(step t139 (cl (! (or @p_431 @p_526) :named @p_528) @p_468) :rule or_neg)
+(step t140 (cl @p_528 @p_170) :rule th_resolution :premises (t128 t139))
+(step t141 (cl @p_528 (! (not @p_526) :named @p_553)) :rule or_neg)
+(step t142 (cl @p_528) :rule th_resolution :premises (t138 t137 t140 t141))
+(step t143 (cl (not (! (not (! (not @p_79) :named @p_529)) :named @p_537)) @p_79) :rule not_not)
+(step t144 (cl (or @p_529 (! (= (! (fun_app$b (! (uu$ @p_378 @p_530) :named @p_655) @p_371) :named @p_532) (! (ite @p_373 @p_370 @p_371) :named @p_533)) :named @p_531))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 @p_530) (:= veriT_vr9 @p_371)))
+(anchor :step t145)
+(assume t145.h1 @p_531)
+(step t145.t2 (cl (! (= @p_531 (! (and (! (= @p_532 @p_533) :named @p_555) (! (ite @p_373 (= @p_370 @p_533) (! (= @p_371 @p_533) :named @p_557)) :named @p_556)) :named @p_534)) :named @p_535)) :rule ite_intro)
+(step t145.t3 (cl (not @p_535) (! (not @p_531) :named @p_536) @p_534) :rule equiv_pos2)
+(step t145.t4 (cl @p_534) :rule th_resolution :premises (t145.h1 t145.t2 t145.t3))
+(step t145 (cl @p_536 @p_534) :rule subproof :discharge (h1))
+(step t146 (cl @p_529 @p_531) :rule or :premises (t144))
+(step t147 (cl (! (or @p_529 @p_534) :named @p_538) @p_537) :rule or_neg)
+(step t148 (cl @p_538 @p_79) :rule th_resolution :premises (t143 t147))
+(step t149 (cl @p_538 (! (not @p_534) :named @p_554)) :rule or_neg)
+(step t150 (cl @p_538) :rule th_resolution :premises (t146 t145 t148 t149))
+(step t151 (cl (or @p_529 (! (= (! (fun_app$b (! (uu$ @p_378 st$) :named @p_656) @p_371) :named @p_540) (! (ite (! (less_eq$ @p_318 @p_371) :named @p_542) @p_318 @p_371) :named @p_541)) :named @p_539))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 st$) (:= veriT_vr9 @p_371)))
+(anchor :step t152)
+(assume t152.h1 @p_539)
+(step t152.t2 (cl (! (= @p_539 (! (and (! (= @p_540 @p_541) :named @p_560) (ite @p_542 (! (= @p_318 @p_541) :named @p_662) (= @p_371 @p_541))) :named @p_543)) :named @p_544)) :rule ite_intro)
+(step t152.t3 (cl (not @p_544) (! (not @p_539) :named @p_545) @p_543) :rule equiv_pos2)
+(step t152.t4 (cl @p_543) :rule th_resolution :premises (t152.h1 t152.t2 t152.t3))
+(step t152 (cl @p_545 @p_543) :rule subproof :discharge (h1))
+(step t153 (cl @p_529 @p_539) :rule or :premises (t151))
+(step t154 (cl (! (or @p_529 @p_543) :named @p_546) @p_537) :rule or_neg)
+(step t155 (cl @p_546 @p_79) :rule th_resolution :premises (t143 t154))
+(step t156 (cl @p_546 (! (not @p_543) :named @p_559)) :rule or_neg)
+(step t157 (cl @p_546) :rule th_resolution :premises (t153 t152 t155 t156))
+(step t158 (cl @p_547 @p_548) :rule or :premises (t115))
+(step t159 (cl @p_548) :rule resolution :premises (t158 t89))
+(step t160 (cl @p_421 (! (not @p_413) :named @p_549) (! (not @p_417) :named @p_550)) :rule and_neg)
+(step t161 (cl (not @p_549) @p_416) :rule not_not)
+(step t162 (cl @p_421 @p_416 @p_550) :rule th_resolution :premises (t161 t160))
+(step t163 (cl (not @p_550) @p_420) :rule not_not)
+(step t164 (cl @p_421 @p_416 @p_420) :rule th_resolution :premises (t163 t162))
+(step t165 (cl @p_427 @p_422) :rule or :premises (t127))
+(step t166 (cl @p_422) :rule resolution :premises (t165 t65))
+(step t167 (cl @p_431 @p_464) :rule or :premises (t135))
+(step t168 (cl @p_464) :rule resolution :premises (t167 t56))
+(step t169 (cl (! (not @p_525) :named @p_552) (! (not @p_524) :named @p_551) @p_471) :rule implies_pos)
+(step t170 (cl (not @p_551) @p_520) :rule not_not)
+(step t171 (cl @p_552 @p_520 @p_471) :rule th_resolution :premises (t170 t169))
+(step t172 (cl @p_553 @p_525) :rule and_pos)
+(step t173 (cl @p_431 @p_526) :rule or :premises (t142))
+(step t174 (cl @p_526) :rule resolution :premises (t173 t56))
+(step t175 (cl @p_525) :rule resolution :premises (t172 t174))
+(step t176 (cl @p_554 @p_555) :rule and_pos)
+(step t177 (cl (! (not @p_556) :named @p_558) @p_373 @p_557) :rule ite_pos1)
+(step t178 (cl @p_554 @p_556) :rule and_pos)
+(step t179 (cl @p_529 @p_534) :rule or :premises (t150))
+(step t180 (cl @p_558 @p_557) :rule resolution :premises (t177 t113))
+(step t181 (cl @p_534) :rule resolution :premises (t179 t32))
+(step t182 (cl @p_555) :rule resolution :premises (t176 t181))
+(step t183 (cl @p_556) :rule resolution :premises (t178 t181))
+(step t184 (cl @p_557) :rule resolution :premises (t180 t183))
+(step t185 (cl @p_559 @p_560) :rule and_pos)
+(step t186 (cl @p_529 @p_543) :rule or :premises (t157))
+(step t187 (cl @p_543) :rule resolution :premises (t186 t32))
+(step t188 (cl @p_560) :rule resolution :premises (t185 t187))
+(step t189 (cl (! (not (! (= st$ @p_530) :named @p_651)) :named @p_654) (! (= @p_318 @p_370) :named @p_663)) :rule eq_congruent)
+(step t190 (cl (or (! (not @p_357) :named @p_565) (! (=> (! (and @p_359 @p_416) :named @p_562) (! (less_eq$ (! (clock$ (! (fst$ (! (fun_app$ (fun_evaluate_match$ st$ env$ veriT_sk0 pes$) veriT_sk0) :named @p_583)) :named @p_618)) :named @p_619) @p_318) :named @p_564)) :named @p_563))) :rule forall_inst :args ((:= veriT_vr61 x2$) (:= veriT_vr62 veriT_sk0)))
+(step t191 (cl (or @p_547 (! (= (! (fix_clock$ st$a @p_466) :named @p_596) (! (pair$ @p_561 veriT_sk3) :named @p_676)) :named @p_566))) :rule forall_inst :args ((:= veriT_vr56 st$a) (:= veriT_vr57 @p_378) (:= veriT_vr58 veriT_sk3)))
+(step t192 (cl (or (! (not @p_290) :named @p_569) (! (=> @p_548 (! (less_eq$ (! (clock$ @p_561) :named @p_575) @p_371) :named @p_568)) :named @p_567))) :rule forall_inst :args ((:= veriT_vr49 st$a) (:= veriT_vr50 @p_378) (:= veriT_vr51 r$) (:= veriT_vr52 @p_561)))
+(step t193 (cl (or (! (not @p_236) :named @p_571) (! (= (! (case_error_result$ uua$ uub$ @p_415) :named @p_621) (! (fun_app$ uua$ veriT_sk0) :named @p_584)) :named @p_572))) :rule forall_inst :args ((:= veriT_vr36 uua$) (:= veriT_vr37 uub$) (:= veriT_vr38 veriT_sk0)))
+(step t194 (cl @p_562 (! (not @p_359) :named @p_614) @p_413) :rule and_neg)
+(step t195 (cl (not @p_563) (not @p_562) @p_564) :rule implies_pos)
+(step t196 (cl @p_565 @p_563) :rule or :premises (t190))
+(step t197 (cl @p_562 @p_413) :rule resolution :premises (t194 t101))
+(step t198 (cl @p_563) :rule resolution :premises (t196 t95))
+(step t199 (cl @p_547 @p_566) :rule or :premises (t191))
+(step t200 (cl @p_566) :rule resolution :premises (t199 t89))
+(step t201 (cl (! (not @p_567) :named @p_570) (not @p_548) @p_568) :rule implies_pos)
+(step t202 (cl @p_569 @p_567) :rule or :premises (t192))
+(step t203 (cl @p_570 @p_568) :rule resolution :premises (t201 t159))
+(step t204 (cl @p_567) :rule resolution :premises (t202 t83))
+(step t205 (cl @p_568) :rule resolution :premises (t203 t204))
+(step t206 (cl @p_571 @p_572) :rule or :premises (t193))
+(step t207 (cl @p_572) :rule resolution :premises (t206 t71))
+(step t208 (cl @p_368 @p_573) :rule or :premises (t103))
+(step t209 (cl (or (! (not @p_573) :named @p_576) (! (or @p_574 (! (not @p_568) :named @p_581) (! (less_eq$ @p_575 @p_7) :named @p_582)) :named @p_577))) :rule forall_inst :args ((:= veriT_vr13 @p_371) (:= veriT_vr14 @p_7) (:= veriT_vr15 @p_575)))
+(step t210 (cl @p_576 @p_577) :rule or :premises (t209))
+(step t211 (cl (! (or @p_368 @p_577) :named @p_579) @p_578) :rule or_neg)
+(step t212 (cl @p_579 @p_105) :rule th_resolution :premises (t114 t211))
+(step t213 (cl @p_579 (! (not @p_577) :named @p_580)) :rule or_neg)
+(step t214 (cl @p_579) :rule th_resolution :premises (t208 t210 t212 t213))
+(step t215 (cl @p_580 @p_574 @p_581 @p_582) :rule or_pos)
+(step t216 (cl @p_368 @p_577) :rule or :premises (t214))
+(step t217 (cl @p_580 @p_582) :rule resolution :premises (t215 a4 t205))
+(step t218 (cl @p_577) :rule resolution :premises (t216 t38))
+(step t219 (cl @p_582) :rule resolution :premises (t217 t218))
+(step t220 (cl (or (! (not @p_257) :named @p_585) (! (= (! (case_error_result$ uua$ uub$ @p_419) :named @p_603) (! (fun_app$a uub$ veriT_sk1) :named @p_599)) :named @p_586))) :rule forall_inst :args ((:= veriT_vr42 uua$) (:= veriT_vr43 uub$) (:= veriT_vr44 veriT_sk1)))
+(step t221 (cl (or @p_368 (! (=> (! (and @p_582 (! (less_eq$ @p_370 @p_575) :named @p_588)) :named @p_587) @p_360) :named @p_589))) :rule forall_inst :args ((:= veriT_vr13 @p_575) (:= veriT_vr14 @p_7) (:= veriT_vr15 @p_370)))
+(step t222 (cl (or (! (not @p_26) :named @p_593) (! (= @p_583 @p_584) :named @p_594))) :rule forall_inst :args ((:= veriT_vr1 veriT_sk0)))
+(step t223 (cl @p_585 @p_586) :rule or :premises (t220))
+(step t224 (cl @p_586) :rule resolution :premises (t223 t77))
+(step t225 (cl @p_587 (not @p_582) (! (not @p_588) :named @p_590)) :rule and_neg)
+(step t226 (cl (! (not @p_589) :named @p_591) (! (not @p_587) :named @p_592) @p_360) :rule implies_pos)
+(step t227 (cl @p_368 @p_589) :rule or :premises (t221))
+(step t228 (cl @p_587 @p_590) :rule resolution :premises (t225 t219))
+(step t229 (cl @p_591 @p_592) :rule resolution :premises (t226 t102))
+(step t230 (cl @p_589) :rule resolution :premises (t227 t38))
+(step t231 (cl @p_592) :rule resolution :premises (t229 t230))
+(step t232 (cl @p_590) :rule resolution :premises (t228 t231))
+(step t233 (cl @p_593 @p_594) :rule or :premises (t222))
+(step t234 (cl @p_594) :rule resolution :premises (t233 t20))
+(step t235 (cl (not (! (= st$a st$a) :named @p_597)) @p_595 (! (= @p_470 @p_596) :named @p_598)) :rule eq_congruent)
+(step t236 (cl @p_597) :rule eq_reflexive)
+(step t237 (cl @p_595 @p_598) :rule th_resolution :premises (t235 t236))
+(step t238 (cl (or (! (not @p_48) :named @p_600) (! (= @p_599 (! (pair$ st$ (! (rerr$ @p_419) :named @p_608)) :named @p_610)) :named @p_601))) :rule forall_inst :args ((:= veriT_vr3 veriT_sk1)))
+(step t239 (cl @p_600 @p_601) :rule or :premises (t238))
+(step t240 (cl @p_601) :rule resolution :premises (t239 t26))
+(step t241 (cl (! (not (! (= uua$ uua$) :named @p_604)) :named @p_623) (! (not (! (= uub$ uub$) :named @p_607)) :named @p_605) @p_417 (! (= @p_602 @p_603) :named @p_606)) :rule eq_congruent)
+(step t242 (cl @p_604) :rule eq_reflexive)
+(step t243 (cl @p_605 @p_417 @p_606) :rule th_resolution :premises (t241 t242))
+(step t244 (cl @p_607) :rule eq_reflexive)
+(step t245 (cl @p_417 @p_606) :rule th_resolution :premises (t243 t244))
+(step t246 (cl (not (! (= st$ st$) :named @p_611)) (! (not (! (= r$ @p_608) :named @p_616)) :named @p_612) (! (= @p_609 @p_610) :named @p_613)) :rule eq_congruent)
+(step t247 (cl @p_611) :rule eq_reflexive)
+(step t248 (cl @p_612 @p_613) :rule th_resolution :premises (t246 t247))
+(step t249 (cl @p_614 (not (! (= @p_615 @p_608) :named @p_617)) @p_616) :rule eq_transitive)
+(step t250 (cl @p_417 @p_617) :rule eq_congruent)
+(step t251 (cl @p_614 @p_616 @p_417) :rule th_resolution :premises (t249 t250))
+(step t252 (cl @p_613 @p_614 @p_417) :rule th_resolution :premises (t248 t251))
+(step t253 (cl (not (! (= @p_530 @p_618) :named @p_620)) (! (= @p_370 @p_619) :named @p_627)) :rule eq_congruent)
+(step t254 (cl (not (! (= @p_602 @p_583) :named @p_622)) @p_620) :rule eq_congruent)
+(step t255 (cl (not (! (= @p_602 @p_621) :named @p_624)) (! (not @p_572) :named @p_625) (! (not @p_594) :named @p_626) @p_622) :rule eq_transitive)
+(step t256 (cl @p_623 @p_605 @p_413 @p_624) :rule eq_congruent)
+(step t257 (cl @p_605 @p_413 @p_624) :rule th_resolution :premises (t256 t242))
+(step t258 (cl @p_413 @p_624) :rule th_resolution :premises (t257 t244))
+(step t259 (cl @p_625 @p_626 @p_622 @p_413) :rule th_resolution :premises (t255 t258))
+(step t260 (cl @p_620 @p_625 @p_626 @p_413) :rule th_resolution :premises (t254 t259))
+(step t261 (cl @p_627 @p_625 @p_626 @p_413) :rule th_resolution :premises (t253 t260))
+(step t262 (cl (or @p_524 (! (not @p_628) :named @p_630))) :rule forall_inst :args ((:= veriT_vr110 r$)))
+(step t263 (cl @p_431 @p_629) :rule or :premises (t104))
+(step t264 (cl @p_524 @p_630) :rule or :premises (t262))
+(step t265 (cl @p_524) :rule resolution :premises (t264 a3))
+(step t266 (cl @p_471) :rule resolution :premises (t171 t265 t175))
+(step t267 (cl (or @p_529 (! (= (! (fun_app$b (! (uu$ @p_378 @p_561) :named @p_631) (! (clock$ (update_clock$ @p_631 @p_561)) :named @p_632)) :named @p_634) (! (ite @p_568 @p_575 @p_371) :named @p_635)) :named @p_633))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 @p_561) (:= veriT_vr9 @p_632)))
+(anchor :step t268)
+(assume t268.h1 @p_633)
+(step t268.t2 (cl (! (= @p_633 (! (and (= @p_634 @p_635) (! (ite @p_568 (! (= @p_575 @p_635) :named @p_647) (= @p_371 @p_635)) :named @p_646)) :named @p_636)) :named @p_637)) :rule ite_intro)
+(step t268.t3 (cl (not @p_637) (! (not @p_633) :named @p_638) @p_636) :rule equiv_pos2)
+(step t268.t4 (cl @p_636) :rule th_resolution :premises (t268.h1 t268.t2 t268.t3))
+(step t268 (cl @p_638 @p_636) :rule subproof :discharge (h1))
+(step t269 (cl @p_529 @p_633) :rule or :premises (t267))
+(step t270 (cl (! (or @p_529 @p_636) :named @p_639) @p_537) :rule or_neg)
+(step t271 (cl @p_639 @p_79) :rule th_resolution :premises (t143 t270))
+(step t272 (cl @p_639 (! (not @p_636) :named @p_648)) :rule or_neg)
+(step t273 (cl @p_639) :rule th_resolution :premises (t269 t268 t271 t272))
+(step t274 (cl (or @p_529 (! (= @p_635 (! (fun_app$b @p_631 @p_371) :named @p_641)) :named @p_640))) :rule forall_inst :args ((:= veriT_vr7 @p_378) (:= veriT_vr8 @p_561) (:= veriT_vr9 @p_371)))
+(anchor :step t275)
+(assume t275.h1 @p_640)
+(step t275.t2 (cl (! (= @p_640 (! (= @p_635 @p_641) :named @p_642)) :named @p_643)) :rule ite_intro)
+(step t275.t3 (cl (not @p_643) (! (not @p_640) :named @p_644) @p_642) :rule equiv_pos2)
+(step t275.t4 (cl @p_642) :rule th_resolution :premises (t275.h1 t275.t2 t275.t3))
+(step t275 (cl @p_644 @p_642) :rule subproof :discharge (h1))
+(step t276 (cl @p_529 @p_640) :rule or :premises (t274))
+(step t277 (cl (! (or @p_529 @p_642) :named @p_645) @p_537) :rule or_neg)
+(step t278 (cl @p_645 @p_79) :rule th_resolution :premises (t143 t277))
+(step t279 (cl @p_645 (! (not @p_642) :named @p_696)) :rule or_neg)
+(step t280 (cl @p_645) :rule th_resolution :premises (t276 t275 t278 t279))
+(step t281 (cl (! (not @p_646) :named @p_649) @p_581 @p_647) :rule ite_pos2)
+(step t282 (cl @p_648 @p_646) :rule and_pos)
+(step t283 (cl @p_529 @p_636) :rule or :premises (t273))
+(step t284 (cl @p_649 @p_647) :rule resolution :premises (t281 t205))
+(step t285 (cl @p_636) :rule resolution :premises (t283 t32))
+(step t286 (cl @p_646) :rule resolution :premises (t282 t285))
+(step t287 (cl @p_647) :rule resolution :premises (t284 t286))
+(step t288 (cl @p_529 @p_642) :rule or :premises (t280))
+(step t289 (cl @p_642) :rule resolution :premises (t288 t32))
+(step t290 (cl (! (= @p_371 @p_371) :named @p_671)) :rule eq_reflexive)
+(step t291 (cl (! (not @p_471) :named @p_661) (not (! (= @p_530 @p_650) :named @p_652)) @p_651) :rule eq_transitive)
+(step t292 (cl (not (! (= @p_470 @p_602) :named @p_653)) @p_652) :rule eq_congruent)
+(step t293 (cl @p_630 (not @p_613) (! (not @p_601) :named @p_657) (! (not @p_586) :named @p_658) (! (not @p_606) :named @p_659) @p_653) :rule eq_transitive)
+(step t294 (cl (! (not @p_432) :named @p_674) @p_654 (! (= @p_655 @p_656) :named @p_670)) :rule eq_congruent)
+(step t295 (cl @p_432) :rule eq_reflexive)
+(step t296 (cl @p_630 @p_657 @p_658 @p_659 @p_653 @p_614 @p_417) :rule th_resolution :premises (t293 t252))
+(step t297 (cl @p_630 @p_657 @p_658 @p_653 @p_614 @p_417 @p_417) :rule th_resolution :premises (t296 t245))
+(step t298 (cl @p_630 @p_657 @p_658 @p_653 @p_614 @p_417) :rule contraction :premises (t297))
+(step t299 (cl @p_652 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t292 t298))
+(step t300 (cl (not (! (= @p_371 @p_370) :named @p_664)) (! (not (! (= @p_7 @p_7) :named @p_660)) :named @p_675) @p_574 @p_360) :rule eq_congruent_pred)
+(step t301 (cl @p_660) :rule eq_reflexive)
+(step t302 (cl @p_661 @p_651 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t291 t299))
+(step t303 (cl (! (not @p_557) :named @p_665) (! (not @p_555) :named @p_666) (! (not (! (= @p_532 @p_540) :named @p_672)) :named @p_667) (! (not @p_560) :named @p_668) (! (not @p_662) :named @p_669) (not @p_663) @p_664) :rule eq_transitive)
+(step t304 (cl @p_663 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t189 t302))
+(step t305 (cl @p_665 @p_666 @p_667 @p_668 @p_669 @p_664 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t303 t304))
+(step t306 (cl (! (not @p_670) :named @p_673) (! (not @p_671) :named @p_699) @p_672) :rule eq_congruent)
+(step t307 (cl @p_673 @p_672) :rule th_resolution :premises (t306 t290))
+(step t308 (cl @p_674 @p_670 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t294 t302))
+(step t309 (cl @p_670 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t308 t295))
+(step t310 (cl @p_672 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t307 t309))
+(step t311 (cl @p_665 @p_666 @p_668 @p_669 @p_664 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t305 t310))
+(step t312 (cl @p_665 @p_666 @p_668 @p_669 @p_664 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule contraction :premises (t311))
+(step t313 (cl @p_675 @p_574 @p_360 @p_665 @p_666 @p_668 @p_669 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t300 t312))
+(step t314 (cl @p_574 @p_360 @p_665 @p_666 @p_668 @p_669 @p_661 @p_630 @p_657 @p_658 @p_614 @p_417) :rule th_resolution :premises (t313 t301))
+(step t315 (cl @p_669 @p_417) :rule resolution :premises (t314 a3 a4 t101 t102 t266 t182 t184 t188 t224 t240))
+(step t316 (cl (or (! (not @p_629) :named @p_677) (! (or (! (not (! (= @p_676 @p_676) :named @p_682)) :named @p_683) (! (= @p_561 (! (fst$ @p_676) :named @p_691)) :named @p_681)) :named @p_678))) :rule forall_inst :args ((:= veriT_vr23 @p_561) (:= veriT_vr24 @p_676) (:= veriT_vr26 veriT_sk3)))
+(step t317 (cl @p_677 @p_678) :rule or :premises (t316))
+(step t318 (cl (! (or @p_431 @p_678) :named @p_679) @p_468) :rule or_neg)
+(step t319 (cl @p_679 @p_170) :rule th_resolution :premises (t128 t318))
+(step t320 (cl @p_679 (! (not @p_678) :named @p_680)) :rule or_neg)
+(step t321 (cl @p_679) :rule th_resolution :premises (t263 t317 t319 t320))
+(anchor :step t322)
+(assume t322.h1 @p_678)
+(step t322.t2 (cl (= @p_682 true)) :rule eq_simplify)
+(step t322.t3 (cl (= @p_683 (! (not true) :named @p_684))) :rule cong :premises (t322.t2))
+(step t322.t4 (cl (= @p_684 false)) :rule not_simplify)
+(step t322.t5 (cl (= @p_683 false)) :rule trans :premises (t322.t3 t322.t4))
+(step t322.t6 (cl (= @p_678 (! (or false @p_681) :named @p_685))) :rule cong :premises (t322.t5))
+(step t322.t7 (cl (= @p_685 (! (or @p_681) :named @p_686))) :rule or_simplify)
+(step t322.t8 (cl (= @p_686 @p_681)) :rule or_simplify)
+(step t322.t9 (cl (! (= @p_678 @p_681) :named @p_687)) :rule trans :premises (t322.t6 t322.t7 t322.t8))
+(step t322.t10 (cl (not @p_687) @p_680 @p_681) :rule equiv_pos2)
+(step t322.t11 (cl @p_681) :rule th_resolution :premises (t322.h1 t322.t9 t322.t10))
+(step t322 (cl @p_680 @p_681) :rule subproof :discharge (h1))
+(step t323 (cl @p_431 @p_678) :rule or :premises (t321))
+(step t324 (cl (! (or @p_431 @p_681) :named @p_688) @p_468) :rule or_neg)
+(step t325 (cl @p_688 @p_170) :rule th_resolution :premises (t128 t324))
+(step t326 (cl @p_688 (! (not @p_681) :named @p_693)) :rule or_neg)
+(step t327 (cl @p_688) :rule th_resolution :premises (t323 t322 t325 t326))
+(step t328 (cl @p_431 @p_681) :rule or :premises (t327))
+(step t329 (cl @p_681) :rule resolution :premises (t328 t56))
+(step t330 (cl (not @p_598) (! (not @p_566) :named @p_689) (! (= @p_470 @p_676) :named @p_690)) :rule eq_transitive)
+(step t331 (cl @p_689 @p_690 @p_595) :rule th_resolution :premises (t330 t237))
+(step t332 (cl (not @p_690) (! (= @p_650 @p_691) :named @p_692)) :rule eq_congruent)
+(step t333 (cl @p_692 @p_689 @p_595) :rule th_resolution :premises (t332 t331))
+(step t334 (cl @p_661 (not @p_692) @p_693 (! (= st$ @p_561) :named @p_694)) :rule eq_transitive)
+(step t335 (cl @p_661 @p_693 @p_694 @p_689 @p_595) :rule th_resolution :premises (t334 t333))
+(step t336 (cl (! (not @p_694) :named @p_702) (! (= @p_318 @p_575) :named @p_695)) :rule eq_congruent)
+(step t337 (cl @p_695 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t336 t335))
+(step t338 (cl (! (not @p_695) :named @p_704) (! (not @p_647) :named @p_697) @p_696 (! (not (! (= @p_540 @p_641) :named @p_700)) :named @p_698) @p_668 @p_662) :rule eq_transitive)
+(step t339 (cl @p_697 @p_696 @p_698 @p_668 @p_662 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t338 t337))
+(step t340 (cl (! (not (! (= @p_656 @p_631) :named @p_703)) :named @p_701) @p_699 @p_700) :rule eq_congruent)
+(step t341 (cl @p_701 @p_700) :rule th_resolution :premises (t340 t290))
+(step t342 (cl @p_674 @p_702 @p_703) :rule eq_congruent)
+(step t343 (cl @p_702 @p_703) :rule th_resolution :premises (t342 t295))
+(step t344 (cl @p_703 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t343 t335))
+(step t345 (cl @p_700 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t341 t344))
+(step t346 (cl @p_697 @p_696 @p_668 @p_662 @p_661 @p_693 @p_689 @p_595 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t339 t345))
+(step t347 (cl @p_697 @p_696 @p_668 @p_662 @p_661 @p_693 @p_689 @p_595) :rule contraction :premises (t346))
+(step t348 (cl @p_662) :rule resolution :premises (t347 t266 t188 t200 t287 t289 t168 t329))
+(step t349 (cl @p_417) :rule resolution :premises (t315 t348))
+(step t350 (cl @p_416) :rule resolution :premises (t164 t349 t166))
+(step t351 (cl @p_562) :rule resolution :premises (t197 t350))
+(step t352 (cl @p_564) :rule resolution :premises (t195 t351 t198))
+(step t353 (cl (not @p_627) @p_704 (! (not @p_564) :named @p_705) @p_588) :rule eq_congruent_pred)
+(step t354 (cl @p_704 @p_705 @p_588 @p_625 @p_626 @p_413) :rule th_resolution :premises (t353 t261))
+(step t355 (cl @p_705 @p_588 @p_625 @p_626 @p_413 @p_661 @p_693 @p_689 @p_595) :rule th_resolution :premises (t354 t337))
+(step t356 (cl) :rule resolution :premises (t355 t350 t168 t266 t352 t200 t207 t232 t234 t329))

--- a/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.certs	Mon Jun 19 22:28:09 2023 +0200
@@ -1,4 +1,4 @@
-e165589be66542b081eba62a2be2f8d39e278f08 8 0
+a5d69231f52771aee13986f9557d0f15deceb578 8 0
 unsat
 ((set-logic <null>)
 (proof
@@ -7,7 +7,7 @@
 (let ((@x49 (trans (monotonicity @x42 (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) false))))
 (mp (asserted (not (= (_ bv11 4) (bvneg (_ bv5 4))))) @x49 false))))))
 
-20e2d38b51f6dc863f10c42423e9f6f7a33f7e4b 7 0
+ce29313a11444a23d27ac32aa304904b58c5ef48 7 0
 unsat
 ((set-logic <null>)
 (proof
@@ -15,7 +15,7 @@
 (let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (_ bv11 4))) false))))
 (mp (asserted (not (= (_ bv11 4) (_ bv11 4)))) @x39 false)))))
 
-d8ead1987eeaf8dcad77816c2da275e02790bc36 7 0
+bb95b2d5c073512432c61cceeaca86ea168b5973 7 0
 unsat
 ((set-logic <null>)
 (proof
@@ -23,7 +23,7 @@
 (let ((@x42 (trans @x38 (rewrite (= (not true) false)) (= (not (bvult (_ bv23 8) (_ bv27 8))) false))))
 (mp (asserted (not (bvult (_ bv23 8) (_ bv27 8)))) @x42 false)))))
 
-4eecaa07b1c9316924af400458f2703dd8953c87 9 0
+26bb2ac93ef8c385bfbf217919bbafac305e5636 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -33,7 +33,17 @@
 (let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) false))))
 (mp (asserted (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)))) @x49 false)))))))
 
-61ca0ebc9b9c8beef8d244b430a042b2d7554237 9 0
+9cf93e929e27dc04c30894bd14ced90c3cc565db 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x43 (monotonicity (rewrite (= (bvsub (_ bv11 8) (_ bv27 8)) (_ bv240 8))) (rewrite (= (bvneg (_ bv16 8)) (_ bv240 8))) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) (= (_ bv240 8) (_ bv240 8))))))
+(let ((@x47 (trans @x43 (rewrite (= (= (_ bv240 8) (_ bv240 8)) true)) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) true))))
+(let ((@x50 (monotonicity @x47 (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) (not true)))))
+(let ((@x54 (trans @x50 (rewrite (= (not true) false)) (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) false))))
+(mp (asserted (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))))) @x54 false)))))))
+
+0e3ec4ac7c67aebfff2a5df85b922b50d3602563 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -43,25 +53,7 @@
 (let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) false))))
 (mp (asserted (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)))) @x49 false)))))))
 
-cb45ce1f17edce2b3b3ad244b6b8eceaf9ddbf50 7 0
-unsat
-((set-logic <null>)
-(proof
-(let ((@x35 (monotonicity (rewrite (= (= (_ bv11 5) (_ bv11 5)) true)) (= (not (= (_ bv11 5) (_ bv11 5))) (not true)))))
-(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 5) (_ bv11 5))) false))))
-(mp (asserted (not (= (_ bv11 5) (_ bv11 5)))) @x39 false)))))
-
-b4a0da18f94642970a0d035b1b57fe43e92d2c57 9 0
-unsat
-((set-logic <null>)
-(proof
-(let ((@x43 (monotonicity (rewrite (= (bvsub (_ bv11 8) (_ bv27 8)) (_ bv240 8))) (rewrite (= (bvneg (_ bv16 8)) (_ bv240 8))) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) (= (_ bv240 8) (_ bv240 8))))))
-(let ((@x47 (trans @x43 (rewrite (= (= (_ bv240 8) (_ bv240 8)) true)) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) true))))
-(let ((@x50 (monotonicity @x47 (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) (not true)))))
-(let ((@x54 (trans @x50 (rewrite (= (not true) false)) (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) false))))
-(mp (asserted (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))))) @x54 false)))))))
-
-78c274ff0caaa3763fad0db197f0c2134d9f5f9e 11 0
+faad761e2741d8b647fa62db13d8b0e649fb03d0 11 0
 unsat
 ((set-logic <null>)
 (proof
@@ -73,7 +65,34 @@
 (let ((@x63 (trans @x59 (rewrite (= (not true) false)) (= (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7)))) false))))
 (mp (asserted (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))))) @x63 false)))))))))
 
-7fcdb48d651781a0ed801bb738bfeb88ce1a3408 19 0
+4bf6f825855790123eb3af10c0a8ece72a2696c0 7 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x35 (monotonicity (rewrite (= (= (_ bv11 5) (_ bv11 5)) true)) (= (not (= (_ bv11 5) (_ bv11 5))) (not true)))))
+(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 5) (_ bv11 5))) false))))
+(mp (asserted (not (= (_ bv11 5) (_ bv11 5)))) @x39 false)))))
+
+a481dcd4c078eb4bbc4578997c1becc3d0588892 18 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x31 (bvmul (_ bv4 4) x$)))
+(let (($x32 (= ?x31 (_ bv4 4))))
+(let (($x43 (= (_ bv5 4) x$)))
+(let (($x56 (not (or (not $x43) (= (_ bv4 4) ?x31)))))
+(let ((@x48 (monotonicity (rewrite (= (= x$ (_ bv5 4)) $x43)) (= (not (= x$ (_ bv5 4))) (not $x43)))))
+(let ((@x55 (monotonicity @x48 (rewrite (= $x32 (= (_ bv4 4) ?x31))) (= (or (not (= x$ (_ bv5 4))) $x32) (or (not $x43) (= (_ bv4 4) ?x31))))))
+(let (($x34 (not (=> (= x$ (_ bv5 4)) $x32))))
+(let ((@x39 (rewrite (= (=> (= x$ (_ bv5 4)) $x32) (or (not (= x$ (_ bv5 4))) $x32)))))
+(let ((@x60 (trans (monotonicity @x39 (= $x34 (not (or (not (= x$ (_ bv5 4))) $x32)))) (monotonicity @x55 (= (not (or (not (= x$ (_ bv5 4))) $x32)) $x56)) (= $x34 $x56))))
+(let ((@x67 (monotonicity (not-or-elim (mp (asserted $x34) @x60 $x56) $x43) (= ?x31 (bvmul (_ bv4 4) (_ bv5 4))))))
+(let ((@x73 (monotonicity (trans @x67 (rewrite (= (bvmul (_ bv4 4) (_ bv5 4)) (_ bv4 4))) $x32) (= (= (_ bv4 4) ?x31) (= (_ bv4 4) (_ bv4 4))))))
+(let ((@x77 (trans @x73 (rewrite (= (= (_ bv4 4) (_ bv4 4)) true)) (= (= (_ bv4 4) ?x31) true))))
+(let ((@x84 (trans (monotonicity @x77 (= (not (= (_ bv4 4) ?x31)) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv4 4) ?x31)) false))))
+(mp (not-or-elim (mp (asserted $x34) @x60 $x56) (not (= (_ bv4 4) ?x31))) @x84 false))))))))))))))))
+
+e913ddebe8fd3723faed676f00550d0f85717e48 19 0
 unsat
 ((set-logic <null>)
 (proof
@@ -93,26 +112,7 @@
 (let ((@x67 (trans @x63 (rewrite (= (not true) false)) (= $x38 false))))
 (mp (asserted $x38) @x67 false)))))))))))))))))
 
-6a1e9b1374089d298641f80da7dba5f13c400a0b 18 0
-unsat
-((set-logic <null>)
-(proof
-(let ((?x31 (bvmul (_ bv4 4) x$)))
-(let (($x32 (= ?x31 (_ bv4 4))))
-(let (($x43 (= (_ bv5 4) x$)))
-(let (($x56 (not (or (not $x43) (= (_ bv4 4) ?x31)))))
-(let ((@x48 (monotonicity (rewrite (= (= x$ (_ bv5 4)) $x43)) (= (not (= x$ (_ bv5 4))) (not $x43)))))
-(let ((@x55 (monotonicity @x48 (rewrite (= $x32 (= (_ bv4 4) ?x31))) (= (or (not (= x$ (_ bv5 4))) $x32) (or (not $x43) (= (_ bv4 4) ?x31))))))
-(let (($x34 (not (=> (= x$ (_ bv5 4)) $x32))))
-(let ((@x39 (rewrite (= (=> (= x$ (_ bv5 4)) $x32) (or (not (= x$ (_ bv5 4))) $x32)))))
-(let ((@x60 (trans (monotonicity @x39 (= $x34 (not (or (not (= x$ (_ bv5 4))) $x32)))) (monotonicity @x55 (= (not (or (not (= x$ (_ bv5 4))) $x32)) $x56)) (= $x34 $x56))))
-(let ((@x67 (monotonicity (not-or-elim (mp (asserted $x34) @x60 $x56) $x43) (= ?x31 (bvmul (_ bv4 4) (_ bv5 4))))))
-(let ((@x73 (monotonicity (trans @x67 (rewrite (= (bvmul (_ bv4 4) (_ bv5 4)) (_ bv4 4))) $x32) (= (= (_ bv4 4) ?x31) (= (_ bv4 4) (_ bv4 4))))))
-(let ((@x77 (trans @x73 (rewrite (= (= (_ bv4 4) (_ bv4 4)) true)) (= (= (_ bv4 4) ?x31) true))))
-(let ((@x84 (trans (monotonicity @x77 (= (not (= (_ bv4 4) ?x31)) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv4 4) ?x31)) false))))
-(mp (not-or-elim (mp (asserted $x34) @x60 $x56) (not (= (_ bv4 4) ?x31))) @x84 false))))))))))))))))
-
-c5fc4af7c2aedc018a219b1ff9f416d7b65f5a31 9 0
+1cd4bc28651d39e32aab684ecfdd3be7c1dd0a2c 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -122,7 +122,7 @@
 (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) false))))
 (mp (asserted (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)))) @x48 false)))))))
 
-1c20d52cf12e17a84c100be59093e532b3bb68be 9 0
+178251ca0606b596bae71a7cf9b656088f51af57 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -132,7 +132,16 @@
 (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) false))))
 (mp (asserted (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)))) @x48 false)))))))
 
-e3b7b6c3b5d69c891a955965789259491afe936e 9 0
+c2fb3d6f1f3f3e6dd3836f7f610e92c43dd7dfff 8 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= (bvnot (_ bv240 16)) (_ bv65295 16))) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) (= (_ bv65295 16) (_ bv65295 16))))))
+(let ((@x40 (trans @x36 (rewrite (= (= (_ bv65295 16) (_ bv65295 16)) true)) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) true))))
+(let ((@x47 (trans (monotonicity @x40 (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) (not true))) (rewrite (= (not true) false)) (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) false))))
+(mp (asserted (not (= (bvnot (_ bv240 16)) (_ bv65295 16)))) @x47 false))))))
+
+769bdf70860c69df30d176b7eb677294e426fc4b 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -142,16 +151,26 @@
 (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) false))))
 (mp (asserted (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)))) @x48 false)))))))
 
-28cf5c7c114782c55ace89ae60a8c9590a1fe7fa 8 0
+584cf4e60989598a0043c67a2cbfb9786830972b 9 0
 unsat
 ((set-logic <null>)
 (proof
-(let ((@x36 (monotonicity (rewrite (= (bvnot (_ bv240 16)) (_ bv65295 16))) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) (= (_ bv65295 16) (_ bv65295 16))))))
-(let ((@x40 (trans @x36 (rewrite (= (= (_ bv65295 16) (_ bv65295 16)) true)) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) true))))
-(let ((@x47 (trans (monotonicity @x40 (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) (not true))) (rewrite (= (not true) false)) (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) false))))
-(mp (asserted (not (= (bvnot (_ bv240 16)) (_ bv65295 16)))) @x47 false))))))
+(let ((@x37 (monotonicity (rewrite (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) (= (_ bv207 10) (_ bv207 10))))))
+(let ((@x41 (trans @x37 (rewrite (= (= (_ bv207 10) (_ bv207 10)) true)) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) true))))
+(let ((@x44 (monotonicity @x41 (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (not true)))))
+(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) false))))
+(mp (asserted (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)))) @x48 false)))))))
 
-d8191fbbb76dcd44809576b51b6eff8251b75359 9 0
+c4ba99a31bff950f61b48e2df91d0092a4605b5b 8 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) (= (_ bv3 2) (_ bv3 2))))))
+(let ((@x40 (trans @x36 (rewrite (= (= (_ bv3 2) (_ bv3 2)) true)) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) true))))
+(let ((@x47 (trans (monotonicity @x40 (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (not true))) (rewrite (= (not true) false)) (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) false))))
+(mp (asserted (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)))) @x47 false))))))
+
+62fc6678382dfb5f2112f46aac810939a87814fd 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -161,26 +180,7 @@
 (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) false))))
 (mp (asserted (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)))) @x48 false)))))))
 
-eda0203202a2208597ba357936c7f6397472d9e3 9 0
-unsat
-((set-logic <null>)
-(proof
-(let ((@x37 (monotonicity (rewrite (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) (= (_ bv207 10) (_ bv207 10))))))
-(let ((@x41 (trans @x37 (rewrite (= (= (_ bv207 10) (_ bv207 10)) true)) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) true))))
-(let ((@x44 (monotonicity @x41 (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (not true)))))
-(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) false))))
-(mp (asserted (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)))) @x48 false)))))))
-
-347626e8b074207fa00db1a5481c346ae674c0ef 8 0
-unsat
-((set-logic <null>)
-(proof
-(let ((@x36 (monotonicity (rewrite (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) (= (_ bv3 2) (_ bv3 2))))))
-(let ((@x40 (trans @x36 (rewrite (= (= (_ bv3 2) (_ bv3 2)) true)) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) true))))
-(let ((@x47 (trans (monotonicity @x40 (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (not true))) (rewrite (= (not true) false)) (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) false))))
-(mp (asserted (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)))) @x47 false))))))
-
-41cbd3386ab2afabe3429a5ba3bb3dba0a63fdda 9 0
+597573e2f4fd839e604ae52ba364ae11700dace1 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -190,7 +190,17 @@
 (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) false))))
 (mp (asserted (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)))) @x47 false)))))))
 
-4840a0f1cb5ba7cadf4e893f0809e950d55d606f 9 0
+9db301365e8ecb55d7eee63724f390087c022cac 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x37 (monotonicity (rewrite (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) (= (_ bv76 8) (_ bv76 8))))))
+(let ((@x41 (trans @x37 (rewrite (= (= (_ bv76 8) (_ bv76 8)) true)) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) true))))
+(let ((@x44 (monotonicity @x41 (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (not true)))))
+(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) false))))
+(mp (asserted (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)))) @x48 false)))))))
+
[phone]f4de43526d88d4ecd79c12df4bdb4825 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -200,17 +210,17 @@
 (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) false))))
 (mp (asserted (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)))) @x47 false)))))))
 
-d128f083f8e89abf5c4703b8c8d009ea3df30435 9 0
+f043e921c4475109c2fdff12856bf28a46f470e8 9 0
 unsat
 ((set-logic <null>)
 (proof
-(let ((@x37 (monotonicity (rewrite (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) (= (_ bv76 8) (_ bv76 8))))))
-(let ((@x41 (trans @x37 (rewrite (= (= (_ bv76 8) (_ bv76 8)) true)) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) true))))
-(let ((@x44 (monotonicity @x41 (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (not true)))))
-(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) false))))
-(mp (asserted (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)))) @x48 false)))))))
+(let ((@x37 (monotonicity (rewrite (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) (= (_ bv4 8) (_ bv4 8))))))
+(let ((@x41 (trans @x37 (rewrite (= (= (_ bv4 8) (_ bv4 8)) true)) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) true))))
+(let ((@x44 (monotonicity @x41 (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (not true)))))
+(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) false))))
+(mp (asserted (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)))) @x48 false)))))))
 
-1d784062d38bcd3aadcf27beee2ff21ad647962d 9 0
+a14cf81020b4c017a44794d9f507892fc994a0aa 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -220,17 +230,7 @@
 (let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) false))))
 (mp (asserted (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)))) @x48 false)))))))
 
-0ee5cedc38e1172399f1a0c82d9e80da55776724 9 0
-unsat
-((set-logic <null>)
-(proof
-(let ((@x37 (monotonicity (rewrite (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) (= (_ bv4 8) (_ bv4 8))))))
-(let ((@x41 (trans @x37 (rewrite (= (= (_ bv4 8) (_ bv4 8)) true)) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) true))))
-(let ((@x44 (monotonicity @x41 (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (not true)))))
-(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) false))))
-(mp (asserted (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)))) @x48 false)))))))
-
-954b050a7dd5950a1db7cf22773ed0f960e848cf 9 0
+1737667dcdf52add3cf7ec23188f82da46dd2b0a 9 0
 unsat
 ((set-logic <null>)
 (proof
@@ -240,7 +240,17 @@
 (let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) false))))
 (mp (asserted (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)))) @x47 false)))))))
 
-adcab1ed49379d48decf485ff9b3a574acbba42e 17 0
+4c62aea85c861b1e65021c56cee22174328eedc0 9 0
+unsat
+((set-logic <null>)
+(proof
+(let ((@x36 (monotonicity (rewrite (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) (= (_ bv13 4) (_ bv13 4))))))
+(let ((@x40 (trans @x36 (rewrite (= (= (_ bv13 4) (_ bv13 4)) true)) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) true))))
+(let ((@x43 (monotonicity @x40 (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (not true)))))
+(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) false))))
+(mp (asserted (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)))) @x47 false)))))))
+
+dfec96be9ace458cbe9ee12898f33db7192c335c 17 0
 unsat
 ((set-logic <null>)
 (proof
@@ -258,17 +268,7 @@
 (let ((@x55 (unit-resolution ((_ th-lemma bv) $x53) @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 $x52)))
 (unit-resolution @x55 @x63 false)))))))))))))))
 
-9ed6f1c7a48e735be777f66302217a85b3126246 9 0
-unsat
-((set-logic <null>)
-(proof
-(let ((@x36 (monotonicity (rewrite (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) (= (_ bv13 4) (_ bv13 4))))))
-(let ((@x40 (trans @x36 (rewrite (= (= (_ bv13 4) (_ bv13 4)) true)) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) true))))
-(let ((@x43 (monotonicity @x40 (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (not true)))))
-(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) false))))
-(mp (asserted (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)))) @x47 false)))))))
-
-a287f607ed00218feee9de1c2a188887f4e4fe7f 51 0
+73db5e04efabac69390d8eaa510230b30d68aff6 51 0
 unsat
 ((set-logic <null>)
 (proof
@@ -320,7 +320,20 @@
 (let ((@x314 (unit-resolution ((_ th-lemma bv) $x312) @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 (unit-resolution (def-axiom (or $x95 (not $x74))) @x303 (not $x74)) (unit-resolution (def-axiom (or $x95 (not $x75))) @x303 (not $x75)) (unit-resolution (def-axiom (or $x95 (not $x76))) @x303 (not $x76)) (unit-resolution (def-axiom (or $x95 (not $x77))) @x303 (not $x77)) (unit-resolution (def-axiom (or $x95 (not $x78))) @x303 (not $x78)) (unit-resolution (def-axiom (or $x95 (not $x79))) @x303 (not $x79)) (unit-resolution (def-axiom (or $x95 (not $x80))) @x303 (not $x80)) (unit-resolution (def-axiom (or $x95 $x264)) @x303 $x264) $x300)))
 (unit-resolution @x314 @x322 false)))))))))))))))))))))))))))))))))))))))))))))))))
 
-38254797dc481377c1b43bd5f27caf2ac4b4f09e 29 0
+ed93cefa9922cae76b281457731fa49405ea5f1e 12 0
+unsat
+((set-logic <null>)
+(proof
+(let ((?x31 (p$ true)))
+(let (($x29 (bvule (_ bv0 4) a$)))
+(let ((?x30 (p$ $x29)))
+(let (($x32 (= ?x30 ?x31)))
+(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
+(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
+(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
+(mp (asserted (not $x32)) @x53 false))))))))))
+
+7378269c0bf8c864db559557bebcaf1734a4d5b0 29 0
 unsat
 ((set-logic <null>)
 (proof
@@ -350,16 +363,3 @@
 (let ((@x30 (asserted $x29)))
 (unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x29) $x183)) @x30 (unit-resolution @x189 @x180 $x184) false)))))))))))))))))))
 
-73a07817344b4149f448226a2110372c08f215f6 12 0
-unsat
-((set-logic <null>)
-(proof
-(let ((?x31 (p$ true)))
-(let (($x29 (bvule (_ bv0 4) a$)))
-(let ((?x30 (p$ $x29)))
-(let (($x32 (= ?x30 ?x31)))
-(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
-(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
-(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
-(mp (asserted (not $x32)) @x53 false))))))))))
-

--- a/src/HOL/SMT_Examples/VCC_Max.certs	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/SMT_Examples/VCC_Max.certs	Mon Jun 19 22:28:09 2023 +0200
@@ -1,4 +1,4 @@
-49e1416aaa3d82d5c60160b24fb878147b44ee17 2924 0
+bb3039fa3c51c2ff1e3d9c4077fcbaf0fc7ae1b5 2924 0
 unsat
 ((set-logic <null>)
 (declare-fun ?v0!15 () Int)

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/cvc5_replay.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -0,0 +1,386 @@
+(*  Title:      HOL/Tools/SMT/cvc4_replay.ML
+    Author:     Mathias Fleury, JKU
+    Author:     Hanna Lachnitt, Stanford University
+
+CVC4 proof parsing and replay.
+*)
+
+signature CVC5_REPLAY =
+sig
+  val replay: Proof.context -> SMT_Translate.replay_data -> string list -> thm
+end;
+
+structure CVC5_Replay: CVC5_REPLAY =
+struct
+
+fun subst_only_free pairs =
+  let
+     fun substf u =
+        (case Termtab.lookup pairs u of
+          SOME u' => u'
+        | NONE =>
+          (case u of
+            (Abs(a,T,t)) => Abs(a, T, substf t)
+          | (t$u') => substf t $ substf u'
+          | u => u))
+  in substf end;
+
+
+fun under_fixes f unchanged_prems (prems, nthms) names args insts decls (concl, ctxt) =
+  let
+    val thms1 = unchanged_prems @ map (SMT_Replay.varify ctxt) prems
+    val thms2 = map snd nthms
+  in (f ctxt (thms1 @ thms2) args insts decls concl) end
+
+
+(** Replaying **)
+
+fun replay_thm method_for rewrite_rules ll_defs ctxt assumed unchanged_prems prems nthms
+    concl_transformation global_transformation args insts
+    (Lethe_Proof.Lethe_Replay_Node {id, rule, concl, bounds, declarations = decls, ...}) =
+  let
+    val rewrite = let val thy = Proof_Context.theory_of (empty_simpset ctxt) in
+        Raw_Simplifier.rewrite_term thy rewrite_rules []
+        #> not (null ll_defs andalso Lethe_Proof.keep_raw_lifting rule) ? SMTLIB_Isar.unlift_term ll_defs
+      end
+    val rewrite_concl = if Lethe_Proof.keep_app_symbols rule then
+          filter (curry Term.could_unify (Thm.concl_of @{thm SMT.fun_app_def}) o Thm.concl_of) rewrite_rules
+        else rewrite_rules
+    val post = let val thy = Proof_Context.theory_of (empty_simpset ctxt) in
+        Raw_Simplifier.rewrite_term thy rewrite_concl []
+        #> Object_Logic.atomize_term ctxt
+        #> not (null ll_defs) ? SMTLIB_Isar.unlift_term ll_defs
+        #> SMTLIB_Isar.unskolemize_names ctxt
+        #> HOLogic.mk_Trueprop
+      end
+    val concl = concl
+      |> Term.subst_free concl_transformation
+      |> subst_only_free global_transformation
+      |> post
+  in
+    if rule = Lethe_Proof.input_rule then
+      (case Symtab.lookup assumed id of
+        SOME (_, thm) => thm
+      | _ => raise Fail ("assumption " ^ @{make_string} id ^ " not found"))
+    else
+      under_fixes (method_for rule) unchanged_prems
+        (prems, nthms) (map fst bounds)
+        (map rewrite args)
+        (Symtab.map (K rewrite) insts)
+        decls
+        (concl, ctxt)
+      |> Simplifier.simplify (empty_simpset ctxt addsimps rewrite_rules)
+  end
+
+fun add_used_asserts_in_step (Lethe_Proof.Lethe_Replay_Node {prems,
+    subproof = (_, _, _, subproof), concl, ...}) =
+  let fun f x = (case try (snd o SMTLIB_Interface.role_and_index_of_assert_name) x of
+        NONE => NONE
+      | SOME a => SOME (a, concl))
+  in
+  union (op =) (map_filter f prems @
+     flat (map (fn x => add_used_asserts_in_step x []) subproof))
+  end
+
+fun remove_rewrite_rules_from_rules n =
+  (fn (step as Lethe_Proof.Lethe_Replay_Node {id, ...}) =>
+    (case try (snd o SMTLIB_Interface.role_and_index_of_assert_name) id of
+      NONE => SOME step
+    | SOME a => if a < n then NONE else SOME step))
+
+
+fun replay_theorem_step rewrite_rules ll_defs assumed inputs proof_prems
+  (step as Lethe_Proof.Lethe_Replay_Node {id, rule, prems, bounds, args, insts,
+     subproof = (fixes, assms, input, subproof), concl, ...}) state =
+  let
+   (* val _ = @{print}("replay_theorem_step rule", rule)
+    val _ = @{print}("replay_theorem_step id", id)
+
+    val _ = @{print}("replay_theorem_step args", args)
+    val _ = @{print}("replay_theorem_step inputs", inputs)
+    val _ = @{print}("replay_theorem_step assumed", assumed)
+    val _ = @{print}("replay_theorem_step proof_prems", proof_prems)*)
+
+    val (proofs, stats, ctxt, concl_tranformation, global_transformation) = state
+    val (_, ctxt) = Variable.variant_fixes (map fst bounds) ctxt
+      |> (fn (names, ctxt) => (names,
+        fold Variable.declare_term [SMTLIB_Isar.unskolemize_names ctxt concl] ctxt))
+
+    val (names, sub_ctxt) = Variable.variant_fixes (map fst fixes) ctxt
+       ||> fold Variable.declare_term (map Free fixes)
+    val export_vars = concl_tranformation @
+       (ListPair.zip (map Free fixes, map Free (ListPair.zip (names, map snd fixes))))
+
+    val post = let val thy = Proof_Context.theory_of (empty_simpset ctxt) in
+        Raw_Simplifier.rewrite_term thy ((if Lethe_Proof.keep_raw_lifting rule andalso not (null rewrite_rules) then tl rewrite_rules else rewrite_rules)) []
+        #> Object_Logic.atomize_term ctxt
+        #> not (null ll_defs andalso Lethe_Proof.keep_raw_lifting rule) ? SMTLIB_Isar.unlift_term ll_defs
+        #> SMTLIB_Isar.unskolemize_names ctxt
+        #> HOLogic.mk_Trueprop
+      end
+
+    val assms = map (subst_only_free global_transformation o Term.subst_free (export_vars) o post) assms
+    val input = map (subst_only_free global_transformation o Term.subst_free (export_vars) o post) input
+
+    val (all_proof_prems', sub_ctxt2) = Assumption.add_assumes (map (Thm.cterm_of sub_ctxt) (assms @ input))
+      sub_ctxt
+    fun is_refl thm = Thm.concl_of thm |> (fn (_ $ t) => t) |> HOLogic.dest_eq |> (op =) handle TERM _=> false
+    val all_proof_prems' =
+        all_proof_prems'
+        |> filter_out is_refl
+    val proof_prems' = take (length assms) all_proof_prems'
+
+    val input = drop (length assms) all_proof_prems'
+    val all_proof_prems = proof_prems @ proof_prems'
+
+    val replay = replay_theorem_step rewrite_rules ll_defs assumed (input @ inputs) all_proof_prems
+    val (proofs', stats, _, _, sub_global_rew) =
+       fold replay subproof (proofs, stats, sub_ctxt2, export_vars, global_transformation)
+
+    val export_thm = singleton (Proof_Context.export sub_ctxt2 ctxt)
+
+    (*for sko_ex and sko_forall, assumptions are in proofs',  but the definition of the skolem
+       function is in proofs *)
+    val nthms =
+      prems
+      |> map (apsnd export_thm) o map_filter (Symtab.lookup (if (null subproof) then proofs else proofs'))
+
+    val nthms' = (if Lethe_Proof.is_skolemization rule
+         then prems else [])
+      |> map_filter (Symtab.lookup proofs)
+    val args = map (Term.subst_free concl_tranformation o subst_only_free global_transformation) args
+    val insts = Symtab.map (K (Term.subst_free concl_tranformation o subst_only_free global_transformation)) insts
+    val proof_prems =
+       if Lethe_Replay_Methods.requires_subproof_assms prems rule then proof_prems else []
+    val local_inputs =
+       if Lethe_Replay_Methods.requires_local_input prems rule then input @ inputs else []
+
+
+    val replay = (Timing.timing (replay_thm CVC5_Replay_Methods.method_for rewrite_rules ll_defs
+       ctxt assumed [] (proof_prems @ local_inputs) (nthms @ nthms') concl_tranformation
+       global_transformation args insts))
+
+    val ({elapsed, ...}, thm) =
+      SMT_Config.with_time_limit ctxt SMT_Config.reconstruction_step_timeout replay step
+        handle Timeout.TIMEOUT _ => raise SMT_Failure.SMT SMT_Failure.Time_Out
+    (*TODO: Maybe add flag so this is only output when checking an external proof, although I feel
+      it would be useful even when not*)
+    val _ = (SMT_Config.verbose_msg ctxt (K ("Successfully checked step " ^ id)) ())
+
+    val stats' = Symtab.cons_list (rule, Time.toNanoseconds elapsed) stats
+    val proofs = Symtab.update (id, (map fst bounds, thm)) proofs
+  in (proofs, stats', ctxt,
+       concl_tranformation, sub_global_rew) end
+
+fun replay_definition_step rewrite_rules ll_defs _ _ _
+  (Lethe_Proof.Lethe_Replay_Node {id, declarations = raw_declarations, subproof = (_, _, _, subproof), ...}) state =
+  let
+    val _ = if null subproof then ()
+          else raise (Fail ("unrecognized cvc5 proof, definition has a subproof"))
+    val (proofs, stats, ctxt, concl_tranformation, global_transformation) = state
+    val global_transformer = subst_only_free global_transformation
+    val rewrite = let val thy = Proof_Context.theory_of ctxt in
+        Raw_Simplifier.rewrite_term thy (rewrite_rules) []
+        #> not (null ll_defs) ? SMTLIB_Isar.unlift_term ll_defs
+      end
+    val start0 = Timing.start ()
+    val declaration = map (apsnd (rewrite o global_transformer)) raw_declarations
+    val (names, ctxt) = Variable.variant_fixes (map fst declaration) ctxt
+       ||> fold Variable.declare_term (map Free (map (apsnd fastype_of) declaration))
+    val old_names = map Free (map (fn (a, b) => (a, fastype_of b)) declaration)
+    val new_names = map Free (ListPair.zip (names, map (fastype_of o snd) declaration))
+    fun update_mapping (a, b) tab =
+          if a <> b andalso Termtab.lookup tab a = NONE
+          then Termtab.update_new (a, b) tab else tab
+    val global_transformation = global_transformation
+     |> fold update_mapping (ListPair.zip (old_names, new_names))
+    val global_transformer = subst_only_free global_transformation
+
+    val generate_definition =
+      (fn (name, term) => (HOLogic.mk_Trueprop
+        (Const(\<^const_name>\<open>HOL.eq\<close>, fastype_of term --> fastype_of term --> @{typ bool}) $
+            Free (name, fastype_of term) $ term)))
+      #> global_transformer
+      #> Thm.cterm_of ctxt
+    val decls = map generate_definition declaration
+    val (defs, ctxt) = Assumption.add_assumes decls ctxt
+    val thms_with_old_name = ListPair.zip (map fst declaration, defs)
+    val proofs = fold
+      (fn (name, thm) => Symtab.update (id, ([name], @{thm sym} OF [thm])))
+      thms_with_old_name proofs
+    val total = Time.toNanoseconds (#elapsed (Timing.result start0))
+    val stats = Symtab.cons_list ("choice", total) stats
+  in (proofs, stats, ctxt, concl_tranformation, global_transformation) end
+
+
+fun replay_assumed assms ll_defs rewrite_rules stats ctxt term =
+  let
+    val rewrite = let val thy = Proof_Context.theory_of (empty_simpset ctxt) in
+        Raw_Simplifier.rewrite_term thy rewrite_rules []
+        #> not (null ll_defs) ? SMTLIB_Isar.unlift_term ll_defs
+      end
+    val replay = Timing.timing (SMT_Replay_Methods.prove ctxt (rewrite term))
+    val ({elapsed, ...}, thm) =
+      SMT_Config.with_time_limit ctxt SMT_Config.reconstruction_step_timeout replay
+         (fn _ => Method.insert_tac ctxt (map snd assms) THEN' Classical.fast_tac ctxt)
+        handle Timeout.TIMEOUT _ => raise SMT_Failure.SMT SMT_Failure.Time_Out
+    val stats' = Symtab.cons_list (Lethe_Proof.input_rule, Time.toNanoseconds elapsed) stats
+  in
+    (thm, stats')
+  end
+
+val cvc_assms_prefix = "__repeated_assms_" (*FUDGE*)
+(*The index k is not unique for monomorphised theorems.*)
+fun cvc_assms_name l k = cvc_assms_prefix ^ SMTLIB_Interface.assert_name_of_role_and_index SMT_Util.Axiom k ^ "_" ^ l
+
+fun add_correct_assms_deps ctxt rewrite_rules ll_defs assms steps =
+  let
+    fun add_correct_assms_deps (st as Lethe_Proof.Lethe_Replay_Node {id, rule, args, prems, proof_ctxt,
+        concl, bounds, insts, declarations, subproof}) =
+     (case try (snd o SMTLIB_Interface.role_and_index_of_assert_name) id of
+       NONE => st
+     | SOME _ =>
+       (case List.find (fn (_, th') =>  CVC_Proof_Parse.cvc_matching_assms ctxt rewrite_rules ll_defs concl th') assms of
+         NONE => st
+       | SOME ((k,_), _) =>
+       let
+          val assms_prem = cvc_assms_name id k
+       in
+        Lethe_Proof.mk_replay_node id rule args (assms_prem :: prems) proof_ctxt concl bounds insts declarations
+         subproof
+       end))
+  in
+    map add_correct_assms_deps steps
+  end
+
+fun replay_step rewrite_rules ll_defs assumed inputs proof_prems
+  (step as Lethe_Proof.Lethe_Replay_Node {rule, ...}) state =
+  if rule = Lethe_Proof.lethe_def
+  then replay_definition_step rewrite_rules ll_defs assumed inputs proof_prems step state
+  else replay_theorem_step rewrite_rules ll_defs assumed inputs proof_prems step state
+
+
+fun replay outer_ctxt
+    ({context = ctxt, typs, terms, rewrite_rules, assms, ll_defs, ...} : SMT_Translate.replay_data)
+     output =
+  let
+    val _ = if not (SMT_Config.use_lethe_proof_from_cvc ctxt)
+       then (raise SMT_Failure.SMT (SMT_Failure.Other_Failure ("reconstruction with CVC is experimental.\n" ^
+         "You must activate it with [[smt_cvc_lethe = true]] and use cvc5 (not included as component) .")))
+       else ()
+
+    val rewrite_rules =
+      filter_out (fn thm => Term.could_unify (Thm.prop_of @{thm verit_eq_true_simplify},
+          Thm.prop_of thm))
+        rewrite_rules
+    val num_ll_defs = length ll_defs
+    val index_of_id = Integer.add (~ num_ll_defs)
+    val id_of_index = Integer.add num_ll_defs
+
+    val start0 = Timing.start ()
+
+(*Here the premise should still be in the assumption*)
+    val (actual_steps, ctxt2) =
+      Lethe_Proof.parse_replay typs terms output ctxt
+    val parsing_time = Time.toNanoseconds (#elapsed (Timing.result start0))
+
+    fun step_of_assume (i, th) =
+      let
+        fun matching (_, th') = CVC_Proof_Parse.cvc_matching_assms ctxt rewrite_rules ll_defs th th'
+      in
+        case List.find matching assms of
+          NONE => []
+        | SOME ((k, role), th') =>
+
+            Lethe_Proof.Lethe_Replay_Node {
+              id = cvc_assms_name (SMTLIB_Interface.assert_name_of_role_and_index role (id_of_index i)) k,
+              rule = Lethe_Proof.input_rule,
+              args = [],
+              prems = [],
+              proof_ctxt = [],
+              concl = Thm.prop_of th'
+                |> Raw_Simplifier.rewrite_term (Proof_Context.theory_of
+                     (empty_simpset ctxt addsimps rewrite_rules)) rewrite_rules [],
+              bounds = [],
+              insts = Symtab.empty,
+              declarations = [],
+              subproof = ([], [], [], [])}
+            |> single
+      end
+
+    val used_assert_ids = fold add_used_asserts_in_step actual_steps []
+    fun normalize_tac ctxt = let val thy = Proof_Context.theory_of (empty_simpset ctxt) in
+      Raw_Simplifier.rewrite_term thy rewrite_rules [] end
+    val used_assm_js =
+      map_filter (fn (id, th) => let val i = index_of_id id in if i >= 0 then SOME (i, th)
+          else NONE end)
+        used_assert_ids
+
+    val assm_steps = map step_of_assume used_assm_js
+        |> flat
+    fun extract (Lethe_Proof.Lethe_Replay_Node {id, rule, concl, bounds, ...}) =
+         (id, rule, concl, map fst bounds)
+    fun cond rule = rule = Lethe_Proof.input_rule
+    val add_asssert = SMT_Replay.add_asserted Symtab.update Symtab.empty extract cond
+
+    val ((_, _), (ctxt3, assumed)) =
+      add_asssert outer_ctxt rewrite_rules (map (apfst fst) assms)
+        (map_filter (remove_rewrite_rules_from_rules num_ll_defs) assm_steps) ctxt2
+
+     val used_rew_js =
+      map_filter (fn (id, th) => let val i = index_of_id id in if i < 0
+          then SOME (id, normalize_tac ctxt (nth ll_defs id)) else NONE end)
+        used_assert_ids
+
+    val (assumed, stats) = fold (fn ((id, thm)) => fn (assumed, stats) =>
+      let
+        val (thm, stats) = replay_assumed assms ll_defs rewrite_rules stats ctxt thm
+        val name = SMTLIB_Interface.assert_name_of_role_and_index SMT_Util.Axiom id
+      in
+        (Symtab.update (name, ([], thm)) assumed, stats)
+      end)
+      used_rew_js (assumed, Symtab.cons_list ("parsing", parsing_time) Symtab.empty)
+
+
+    val actual_steps = actual_steps
+      |> add_correct_assms_deps ctxt rewrite_rules ll_defs assms
+
+    val ctxt4 =
+      ctxt3
+      |> put_simpset (SMT_Replay.make_simpset ctxt3 [])
+      |> Config.put SAT.solver (Config.get ctxt3 SMT_Config.sat_solver)
+    val len = Lethe_Proof.number_of_steps actual_steps
+    fun steps_with_depth _ [] = []
+      | steps_with_depth i (p :: ps) = (i +  Lethe_Proof.number_of_steps [p], p) ::
+          steps_with_depth (i +  Lethe_Proof.number_of_steps [p]) ps
+    val actual_steps = steps_with_depth 0 actual_steps
+    val start = Timing.start ()
+    val print_runtime_statistics = SMT_Replay.intermediate_statistics ctxt4 start len
+    fun blockwise f (i, x) (next, y) =
+      (if i > next then print_runtime_statistics i else ();
+       (if i > next then i + 10 else next, f x y))
+
+    val global_transformation : term Termtab.table = Termtab.empty
+
+    val (_, (proofs, stats, ctxt5, _, _)) =
+      fold (blockwise (replay_step rewrite_rules ll_defs assumed [] [])) actual_steps
+        (1, (assumed, stats, ctxt4, [], global_transformation))
+
+    val total = Time.toMilliseconds (#elapsed (Timing.result start))
+
+    val (_, (_, Lethe_Proof.Lethe_Replay_Node {id, ...})) = split_last actual_steps
+
+    val _ = print_runtime_statistics len
+
+    val thm_with_defs = Symtab.lookup proofs id |> the |> snd
+      |> singleton (Proof_Context.export ctxt5 outer_ctxt)
+    val _ = SMT_Config.statistics_msg ctxt5
+      (Pretty.string_of o SMT_Replay.pretty_statistics "cvc" total) stats
+    val _ = SMT_Replay.spying (SMT_Config.spy_verit ctxt) ctxt
+      (fn () => SMT_Replay.print_stats (Symtab.dest stats)) "spy_cvc"
+
+  in
+    CVC5_Replay_Methods.discharge ctxt [thm_with_defs] @{term False}
+  end
+
+end

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/cvc5_replay_methods.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -0,0 +1,261 @@
+(*  Title:      HOL/Tools/SMT/cvc4_replay_methods.ML
+    Author:     Mathias Fleury, JKU, Uni Freiburg
+    Author:     Hanna Lachnitt, Stanford University
+
+Proof method for replaying veriT proofs.
+*)
+
+signature CVC5_REPLAY_METHODS =
+sig
+  (*methods for verit proof rules*)
+  val method_for: string -> Proof.context -> thm list -> term list -> term Symtab.table ->
+     (string * term) list -> term -> thm
+
+  val discharge: Proof.context -> thm list -> term -> thm
+end;
+
+
+structure CVC5_Replay_Methods: CVC5_REPLAY_METHODS =
+struct
+
+open Lethe_Replay_Methods
+
+fun cvc5_rule_of "bind" = Bind
+  | cvc5_rule_of "cong" = Cong
+  | cvc5_rule_of "refl" = Refl
+  | cvc5_rule_of "equiv1" = Equiv1
+  | cvc5_rule_of "equiv2" = Equiv2
+  | cvc5_rule_of "equiv_pos1" = Equiv_pos1
+   (*Equiv_pos2 covered below*)
+  | cvc5_rule_of "equiv_neg1" = Equiv_neg1
+  | cvc5_rule_of "equiv_neg2" = Equiv_neg2
+  | cvc5_rule_of "sko_forall" = Skolem_Forall
+  | cvc5_rule_of "sko_ex" = Skolem_Ex
+  | cvc5_rule_of "eq_reflexive" = Eq_Reflexive
+  | cvc5_rule_of "forall_inst" = Forall_Inst
+  | cvc5_rule_of "implies_pos" = Implies_Pos
+  | cvc5_rule_of "or" = Or
+  | cvc5_rule_of "not_or" = Not_Or
+  | cvc5_rule_of "resolution" = Resolution
+  | cvc5_rule_of "trans" = Trans
+  | cvc5_rule_of "false" = False
+  | cvc5_rule_of "ac_simp" = AC_Simp
+  | cvc5_rule_of "and" = And
+  | cvc5_rule_of "not_and" = Not_And
+  | cvc5_rule_of "and_pos" = And_Pos
+  | cvc5_rule_of "and_neg" = And_Neg
+  | cvc5_rule_of "or_pos" = Or_Pos
+  | cvc5_rule_of "or_neg" = Or_Neg
+  | cvc5_rule_of "not_equiv1" = Not_Equiv1
+  | cvc5_rule_of "not_equiv2" = Not_Equiv2
+  | cvc5_rule_of "not_implies1" = Not_Implies1
+  | cvc5_rule_of "not_implies2" = Not_Implies2
+  | cvc5_rule_of "implies_neg1" = Implies_Neg1
+  | cvc5_rule_of "implies_neg2" = Implies_Neg2
+  | cvc5_rule_of "implies" = Implies
+  | cvc5_rule_of "bfun_elim" = Bfun_Elim
+  | cvc5_rule_of "ite1" = ITE1
+  | cvc5_rule_of "ite2" = ITE2
+  | cvc5_rule_of "not_ite1" = Not_ITE1
+  | cvc5_rule_of "not_ite2" = Not_ITE2
+  | cvc5_rule_of "ite_pos1" = ITE_Pos1
+  | cvc5_rule_of "ite_pos2" = ITE_Pos2
+  | cvc5_rule_of "ite_neg1" = ITE_Neg1
+  | cvc5_rule_of "ite_neg2" = ITE_Neg2
+  | cvc5_rule_of "la_disequality" = LA_Disequality
+  | cvc5_rule_of "lia_generic" = LIA_Generic
+  | cvc5_rule_of "la_generic" = LA_Generic
+  | cvc5_rule_of "la_tautology" = LA_Tautology
+  | cvc5_rule_of "la_totality" = LA_Totality
+  | cvc5_rule_of "la_rw_eq"= LA_RW_Eq
+  | cvc5_rule_of "nla_generic"= NLA_Generic
+  | cvc5_rule_of "eq_transitive" = Eq_Transitive
+  | cvc5_rule_of "qnt_rm_unused" = Qnt_Rm_Unused
+  | cvc5_rule_of "onepoint" = Onepoint
+  | cvc5_rule_of "qnt_join" = Qnt_Join
+  | cvc5_rule_of "subproof" = Subproof
+  | cvc5_rule_of "bool_simplify" = Bool_Simplify
+  | cvc5_rule_of "or_simplify" = Or_Simplify
+  | cvc5_rule_of "ite_simplify" = ITE_Simplify
+  | cvc5_rule_of "and_simplify" = And_Simplify
+  | cvc5_rule_of "not_simplify" = Not_Simplify
+  | cvc5_rule_of "equiv_simplify" = Equiv_Simplify
+  | cvc5_rule_of "eq_simplify" = Eq_Simplify
+  | cvc5_rule_of "implies_simplify" = Implies_Simplify
+  | cvc5_rule_of "connective_def" = Connective_Def
+  | cvc5_rule_of "minus_simplify" = Minus_Simplify
+  | cvc5_rule_of "sum_simplify" = Sum_Simplify
+  | cvc5_rule_of "prod_simplify" = Prod_Simplify
+  | cvc5_rule_of "comp_simplify" = Comp_Simplify
+  | cvc5_rule_of "qnt_simplify" = Qnt_Simplify
+  | cvc5_rule_of "tautology" = Tautological_Clause
+  | cvc5_rule_of "qnt_cnf" = Qnt_CNF
+  | cvc5_rule_of "symm" = Symm
+  | cvc5_rule_of "not_symm" = Not_Symm
+  | cvc5_rule_of "reordering" = Reordering
+  | cvc5_rule_of "unary_minus_simplify" = Minus_Simplify
+  | cvc5_rule_of "quantifier_simplify" = Tmp_Quantifier_Simplify (*TODO Remove*)
+  | cvc5_rule_of r =
+     if r = Lethe_Proof.normalized_input_rule then Normalized_Input
+     else if r = Lethe_Proof.local_input_rule then Local_Input
+     else if r = Lethe_Proof.lethe_def then Definition
+     else if r = Lethe_Proof.not_not_rule then Not_Not
+     else if r = Lethe_Proof.contract_rule orelse r = "duplicate_literals" then Duplicate_Literals
+     else if r = Lethe_Proof.ite_intro_rule then ITE_Intro
+     else if r = Lethe_Proof.eq_congruent_rule then Eq_Congruent
+     else if r = Lethe_Proof.eq_congruent_pred_rule then Eq_Congruent_Pred
+     else if r = Lethe_Proof.theory_resolution2_rule then Theory_Resolution2
+     else if r = Lethe_Proof.th_resolution_rule then Theory_Resolution
+     else if r = Lethe_Proof.equiv_pos2_rule then Equiv_pos2
+     else if r = Lethe_Proof.hole orelse r = "undefined" then Hole
+     else (@{print} ("maybe unsupported rule", r); Other_Rule r)
+
+fun normalized_input ctxt prems t = SMT_Replay_Methods.prove ctxt t (fn _ =>
+let
+    val _ = (SMT_Config.verit_msg ctxt) (fn () => \<^print> ("normalized input t =",t))
+    val _ = (SMT_Config.verit_msg ctxt) (fn () => \<^print> ("normalized ipput prems =",prems))
+
+in
+  resolve_tac ctxt prems
+    (*TODO: should only be used for lambda encoding*)
+    ORELSE' Clasimp.force_tac ctxt
+end)
+
+fun qnt_simplify ctxt _ t = SMT_Replay_Methods.prove ctxt t (fn _ =>
+      K (Clasimp.auto_tac ctxt))
+
+
+fun hole ctxt prems t = SMT_Replay_Methods.prove ctxt t (fn _ =>
+  K (print_tac ctxt "stuff")
+    THEN' Method.insert_tac ctxt prems
+    (*TODO: should only be used for lambda encoding*)
+THEN' K (print_tac ctxt "stuff")
+    THEN' Clasimp.force_tac ctxt
+THEN' K (print_tac ctxt "stuff")
+)
+
+(*
+Example:
+lemma \<open>(\<forall>x y. P x = Q y) \<Longrightarrow> (\<forall> y z. Q y = R z) \<Longrightarrow> (\<forall>x z. P x = R z)\<close>
+*)
+fun trans ctxt prems t =
+  SMT_Replay_Methods.prove ctxt t (fn _ =>
+    Method.insert_tac ctxt prems
+    THEN' (REPEAT_CHANGED (resolve_tac ctxt @{thms trans} THEN' assume_tac ctxt))
+    THEN' (resolve_tac ctxt @{thms refl}))
+
+
+(* Combining all together *)
+
+fun unsupported rule ctxt thms _ _ _ = SMT_Replay_Methods.replay_error ctxt "Unsupported verit rule"
+  rule thms
+
+fun ignore_args  f ctxt thm _    _     _ t = f ctxt thm t
+fun ignore_decls f ctxt thm args insts _ t = f ctxt thm args insts t
+fun ignore_insts f ctxt thm args  _    _ t = f ctxt thm args t
+
+fun choose _ And = ignore_args and_rule
+  | choose _ And_Neg = ignore_args and_neg_rule
+  | choose _ And_Pos = ignore_args and_pos
+  | choose _ And_Simplify = ignore_args rewrite_and_simplify
+  | choose _ Bind = ignore_insts bind
+  | choose _ Bool_Simplify = ignore_args rewrite_bool_simplify
+  | choose _ Comp_Simplify = ignore_args rewrite_comp_simplify
+  | choose _ Cong = ignore_args (cong "cvc5")
+  | choose _ Connective_Def = ignore_args rewrite_connective_def
+  | choose _ Duplicate_Literals = ignore_args duplicate_literals
+  | choose _ Eq_Congruent = ignore_args eq_congruent
+  | choose _ Eq_Congruent_Pred = ignore_args eq_congruent_pred
+  | choose _ Eq_Reflexive = ignore_args eq_reflexive
+  | choose _ Eq_Simplify = ignore_args rewrite_eq_simplify
+  | choose _ Eq_Transitive = ignore_args eq_transitive
+  | choose _ Equiv1 = ignore_args equiv1
+  | choose _ Equiv2 = ignore_args equiv2
+  | choose _ Equiv_neg1 = ignore_args equiv_neg1
+  | choose _ Equiv_neg2 = ignore_args equiv_neg2
+  | choose _ Equiv_pos1 = ignore_args equiv_pos1
+  | choose _ Equiv_pos2 = ignore_args equiv_pos2
+  | choose _ Equiv_Simplify = ignore_args rewrite_equiv_simplify
+  | choose _ False = ignore_args false_rule
+  | choose _ Forall_Inst = ignore_decls forall_inst
+  | choose _ Implies = ignore_args implies_rules
+  | choose _ Implies_Neg1 = ignore_args implies_neg1
+  | choose _ Implies_Neg2 = ignore_args implies_neg2
+  | choose _ Implies_Pos = ignore_args implies_pos
+  | choose _ Implies_Simplify = ignore_args rewrite_implies_simplify
+  | choose _ ITE1 = ignore_args ite1
+  | choose _ ITE2 = ignore_args ite2
+  | choose _ ITE_Intro = ignore_args ite_intro
+  | choose _ ITE_Neg1 = ignore_args ite_neg1
+  | choose _ ITE_Neg2 = ignore_args ite_neg2
+  | choose _ ITE_Pos1 = ignore_args ite_pos1
+  | choose _ ITE_Pos2 = ignore_args ite_pos2
+  | choose _ ITE_Simplify = ignore_args rewrite_ite_simplify
+  | choose _ LA_Disequality = ignore_args la_disequality
+  | choose _ LA_Generic = ignore_insts la_generic
+  | choose _ LA_RW_Eq = ignore_args la_rw_eq
+  | choose _ LA_Tautology = ignore_args SMT_Replay_Methods.arith_th_lemma_wo_shallow
+  | choose _ LA_Totality = ignore_args SMT_Replay_Methods.arith_th_lemma_wo_shallow
+  | choose _ LIA_Generic = ignore_args lia_generic
+  | choose _ Local_Input = ignore_args (refl "cvc5")
+  | choose _ Minus_Simplify = ignore_args rewrite_minus_simplify
+  | choose _ NLA_Generic = ignore_args SMT_Replay_Methods.arith_th_lemma_wo_shallow
+  | choose _ Normalized_Input = ignore_args normalized_input
+  | choose _ Not_And = ignore_args not_and_rule
+  | choose _ Not_Equiv1 = ignore_args not_equiv1
+  | choose _ Not_Equiv2 = ignore_args not_equiv2
+  | choose _ Not_Implies1 = ignore_args not_implies1
+  | choose _ Not_Implies2 = ignore_args not_implies2
+  | choose _ Not_ITE1 = ignore_args not_ite1
+  | choose _ Not_ITE2 = ignore_args not_ite2
+  | choose _ Not_Not = ignore_args not_not
+  | choose _ Not_Or = ignore_args not_or_rule
+  | choose _ Not_Simplify = ignore_args rewrite_not_simplify
+  | choose _ Or = ignore_args or
+  | choose _ Or_Neg = ignore_args or_neg_rule
+  | choose _ Or_Pos = ignore_args or_pos_rule
+  | choose _ Or_Simplify = ignore_args rewrite_or_simplify
+  | choose _ Theory_Resolution2 = ignore_args theory_resolution2
+  | choose _ Prod_Simplify = ignore_args prod_simplify
+  | choose _ Qnt_Join = ignore_args qnt_join
+  | choose _ Qnt_Rm_Unused = ignore_args qnt_rm_unused
+  | choose _ Onepoint = ignore_args onepoint
+  | choose _ Qnt_Simplify = ignore_args qnt_simplify
+  | choose _ Refl = ignore_args (refl "cvc5")
+  | choose _ Resolution = ignore_args unit_res
+  | choose _ Skolem_Ex = ignore_args skolem_ex
+  | choose _ Skolem_Forall = ignore_args skolem_forall
+  | choose _ Subproof = ignore_args subproof
+  | choose _ Sum_Simplify = ignore_args sum_simplify
+  | choose _ Tautological_Clause = ignore_args tautological_clause
+  | choose _ Theory_Resolution = ignore_args unit_res
+  | choose _ AC_Simp = ignore_args tmp_AC_rule
+  | choose _ Bfun_Elim = ignore_args bfun_elim
+  | choose _ Qnt_CNF = ignore_args qnt_cnf
+  | choose _ Trans = ignore_args trans
+  | choose _ Symm = ignore_args symm
+  | choose _ Not_Symm = ignore_args not_symm
+  | choose _ Reordering = ignore_args reordering
+  | choose _ Tmp_Quantifier_Simplify = ignore_args qnt_simplify
+  | choose ctxt (x as Other_Rule r) =
+    (case get_alethe_tac r ctxt of
+      NONE => unsupported (string_of_verit_rule x)
+    | SOME a => ignore_insts a)
+  | choose _ Hole = ignore_args hole
+  | choose _ r = (@{print} ("unknown rule, using hole", r); ignore_args hole)
+(*unsupported (string_of_verit_rule r)*)
+
+type verit_method = Proof.context -> thm list -> term -> thm
+type abs_context = int * term Termtab.table
+
+fun with_tracing rule method ctxt thms args insts decls t =
+  let val _ = SMT_Replay_Methods.trace_goal ctxt rule thms t
+  in method ctxt thms args insts decls t end
+
+fun method_for rule ctxt = with_tracing rule (choose (Context.Proof ctxt) (cvc5_rule_of rule)) ctxt
+
+fun discharge ctxt [thm] t =
+  SMT_Replay_Methods.prove ctxt t (fn _ =>
+    resolve_tac ctxt [thm] THEN_ALL_NEW (resolve_tac ctxt @{thms refl}))
+
+end;

--- a/src/HOL/Tools/SMT/cvc_proof_parse.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/cvc_proof_parse.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -9,12 +9,49 @@
   val parse_proof: SMT_Translate.replay_data ->
     ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
     SMT_Solver.parsed_proof
+  val parse_proof_lethe: SMT_Translate.replay_data ->
+    ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
+    SMT_Solver.parsed_proof
+  val cvc_matching_assms: Proof.context -> thm list -> term list -> term -> thm -> bool
+
 end;
 
 structure CVC_Proof_Parse: CVC_PROOF_PARSE =
 struct
 
-fun parse_proof ({ll_defs, assms, ...} : SMT_Translate.replay_data) xfacts prems _ output =
+open ATP_Util
+open ATP_Problem
+open ATP_Proof
+open ATP_Proof_Reconstruct
+open Lethe_Isar
+open Lethe_Proof
+
+(*taken from verit*)
+fun add_used_asserts_in_step (Lethe_Proof.Lethe_Step {prems, ...}) =
+  union (op =) (map_filter (try (snd o SMTLIB_Interface.role_and_index_of_assert_name)) prems)
+
+fun cvc_matching_assms ctxt rewrite_rules ll_defs th th' =
+  let
+    val expand =
+       not (null ll_defs) ? SMTLIB_Isar.unlift_term ll_defs
+       #> Object_Logic.dest_judgment ctxt o (Thm.cterm_of ctxt)
+       #> Thm.eta_long_conversion
+       #> Thm.prop_of
+       #> snd o Logic.dest_equals
+       #> Raw_Simplifier.rewrite_term (Proof_Context.theory_of
+          (empty_simpset ctxt addsimps rewrite_rules (*@ @{thms eq_True} still useful?*))) rewrite_rules []
+
+
+    val normalize = 
+       Object_Logic.dest_judgment ctxt o (Thm.cprop_of)
+       #> Thm.eta_long_conversion
+       #> Thm.prop_of
+       #> snd o Logic.dest_equals
+       #> Raw_Simplifier.rewrite_term (Proof_Context.theory_of
+          (empty_simpset ctxt addsimps rewrite_rules @ @{thms eq_True})) rewrite_rules []
+  in (expand th) aconv (normalize th') end
+
+fun parse_proof_unsatcore ({ll_defs, assms, ...} : SMT_Translate.replay_data) xfacts prems _ output =
   if exists (String.isPrefix "(error \"This build of CVC4 doesn't have proof support") output then
     {outcome = NONE, fact_ids = NONE, atp_proof = K []}
   else
@@ -44,4 +81,73 @@
       {outcome = NONE, fact_ids = SOME fact_ids', atp_proof = K []}
     end
 
+
+fun parse_proof_lethe
+    ({context = ctxt, typs, terms, ll_defs, rewrite_rules, assms} : SMT_Translate.replay_data)
+    xfacts prems concl output =
+   if exists (String.isPrefix "(error \"This build of CVC4 doesn't have proof support") output then
+     {outcome = NONE, fact_ids = NONE, atp_proof = K []}
+   else
+     let
+    val num_ll_defs = length ll_defs
+    val id_of_index = Integer.add num_ll_defs
+    val index_of_id = Integer.add (~ num_ll_defs)
+
+    fun step_of_assume i ((_, role), th) =
+      let
+        val th = Thm.prop_of th
+        fun matching (_, th') = cvc_matching_assms ctxt rewrite_rules ll_defs th th'
+      in
+        case List.find matching assms of
+          NONE => []
+        | SOME (k, _) =>
+          Lethe_Proof.Lethe_Step 
+           {id = SMTLIB_Interface.assert_name_of_role_and_index role (id_of_index i),
+            rule = input_rule, prems = [], proof_ctxt = [], concl = th, fixes = []}
+          |> single
+      end
+
+    val (actual_steps, _) = Lethe_Proof.parse typs terms output ctxt
+    val used_assert_ids = fold add_used_asserts_in_step actual_steps []
+    val used_assm_js =
+      map_filter (fn id => let val i = index_of_id id in if i >= 0 then SOME i else NONE end)
+        used_assert_ids
+    val used_assms = map (nth assms) used_assm_js
+    val assm_steps = map2 step_of_assume used_assm_js used_assms
+        |> flat
+    val steps = assm_steps @ actual_steps
+
+    val conjecture_i = 0
+    val prems_i = conjecture_i + 1
+    val num_prems = length prems
+    val facts_i = prems_i + num_prems
+    val num_facts = length xfacts
+    val helpers_i = facts_i + num_facts
+
+    val conjecture_id = id_of_index conjecture_i
+    val prem_ids = map id_of_index (prems_i upto prems_i + num_prems - 1)
+    val fact_ids' =
+      map_filter (fn j =>
+        let val ((i, _), _) = nth assms j in
+          try (apsnd (nth xfacts)) (id_of_index j, i - facts_i)
+        end) used_assm_js
+    val helper_ids' =
+      map_filter (fn ((i, _), thm) => if i >= helpers_i then SOME (i, thm) else NONE) used_assms
+
+    val fact_helper_ts =
+      map (fn (_, th) => (ATP_Util.short_thm_name ctxt th, Thm.prop_of th)) helper_ids' @
+      map (fn (_, ((s, _), th)) => (s, Thm.prop_of th)) fact_ids'
+    val fact_helper_ids' =
+      map (apsnd (ATP_Util.short_thm_name ctxt)) helper_ids' @ map (apsnd (fst o fst)) fact_ids'
+  in
+    {outcome = NONE, fact_ids = SOME fact_ids',
+     atp_proof = fn () => atp_proof_of_veriT_proof ctxt ll_defs rewrite_rules prems concl
+       fact_helper_ts prem_ids conjecture_id fact_helper_ids' steps}
+  end
+
+fun parse_proof (rep as {context = ctxt, ...}) =
+  if SMT_Config.use_lethe_proof_from_cvc ctxt
+  then parse_proof_unsatcore rep
+  else parse_proof_unsatcore rep
+
 end;

--- a/src/HOL/Tools/SMT/lethe_proof.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/lethe_proof.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -32,6 +32,17 @@
      term -> (string * typ) list -> term Symtab.table -> (string * term) list ->
      (string * typ) list * term list * term list * lethe_replay_node list -> lethe_replay_node
 
+datatype raw_lethe_node = Raw_Lethe_Node of {
+  id: string,
+  rule: string,
+  args: SMTLIB.tree,
+  prems: string list,
+  concl: SMTLIB.tree,
+  declarations: (string * SMTLIB.tree) list,
+  subproof: raw_lethe_node list}
+ val parse_raw_proof_steps: string option -> SMTLIB.tree list -> SMTLIB_Proof.name_bindings -> int ->
+ raw_lethe_node list * SMTLIB.tree list * SMTLIB_Proof.name_bindings
+
   (*proof parser*)
   val parse: typ Symtab.table -> term Symtab.table -> string list ->
     Proof.context -> lethe_step list * Proof.context
@@ -60,6 +71,7 @@
   val theory_resolution2_rule: string
   val equiv_pos2_rule: string
   val and_pos_rule: string
+  val hole: string
   val th_resolution_rule: string
 
   val is_skolemization: string -> bool
@@ -145,6 +157,7 @@
 val equiv_pos2_rule = "equiv_pos2"
 val th_resolution_rule = "th_resolution"
 val and_pos_rule = "and_pos"
+val hole = "hole"
 
 val is_lethe_def = String.isSuffix lethe_def
 val skolemization_steps = ["sko_forall", "sko_ex"]
@@ -202,6 +215,7 @@
                 (case node_of (SMTLIB.Sym y) cx of
                   ((_, []), _) => [([x], typ)]
                 | _ => [([x, y], typ)])
+             | (SMTLIB.S (SMTLIB.Sym "=" :: SMTLIB.S [SMTLIB.Sym x, typ] :: SMTLIB.Sym y :: []), _) => [([x, y], SOME typ)]
              | (SMTLIB.S (SMTLIB.Sym "=" :: SMTLIB.Sym x :: _), typ) => [([x], typ)]
              |  t => raise (Fail ("match error " ^ @{make_string} t)))
     |> flat
@@ -220,7 +234,7 @@
   fold (fn (SMTLIB.S [SMTLIB.Sym "=", _, SMTLIB.Sym y]) => curry (op ::) y) bds []
 
 (*FIXME there is probably a way to use the information given by onepoint*)
-fun bound_vars_by_rule _ "bind" (bds) = extract_symbols bds
+fun bound_vars_by_rule _ "bind" bds = extract_symbols bds
   | bound_vars_by_rule cx "onepoint" bds = extract_qnt_symbols cx bds
   | bound_vars_by_rule _ "sko_forall" bds = extract_symbols_map bds
   | bound_vars_by_rule _ "sko_ex" bds = extract_symbols_map bds
@@ -243,17 +257,19 @@
 
 end
 
-datatype step_kind = ASSUME | ANCHOR | NO_STEP | NORMAL_STEP | SKOLEM
+datatype step_kind = ASSUME | ASSERT | ANCHOR | NO_STEP | NORMAL_STEP | SKOLEM
 
-fun parse_raw_proof_steps (limit : string option) (ls : SMTLIB.tree list) (cx : name_bindings) :
+fun parse_raw_proof_steps (limit : string option) (ls : SMTLIB.tree list) (cx : name_bindings) (assms_nbr : int):
      (raw_lethe_node list * SMTLIB.tree list * name_bindings) =
   let
     fun rotate_pair (a, (b, c)) = ((a, b), c)
     fun step_kind [] = (NO_STEP, SMTLIB.S [], [])
       | step_kind ((p as SMTLIB.S (SMTLIB.Sym "anchor" :: _)) :: l) = (ANCHOR, p, l)
       | step_kind ((p as SMTLIB.S (SMTLIB.Sym "assume" :: _)) :: l) = (ASSUME, p, l)
+      | step_kind ((p as SMTLIB.S (SMTLIB.Sym "assert" :: _)) :: l) = (ASSERT, p, l)
       | step_kind ((p as SMTLIB.S (SMTLIB.Sym "step" :: _)) :: l) = (NORMAL_STEP, p, l)
       | step_kind ((p as SMTLIB.S (SMTLIB.Sym "define-fun" :: _)) :: l) = (SKOLEM, p, l)
+      | step_kind ((p as SMTLIB.S (SMTLIB.Sym "declare-fun" :: _)) :: l) = (SKOLEM, p, l)
       | step_kind p = raise (Fail ("step_kind unrec: " ^ @{make_string} p))
     fun parse_skolem (SMTLIB.S [SMTLIB.Sym "define-fun", SMTLIB.Sym id,  _, typ,
            SMTLIB.S (SMTLIB.Sym "!" :: t :: [SMTLIB.Key _, SMTLIB.Sym name])]) cx =
@@ -266,11 +282,19 @@
               (SMTLIB.S [SMTLIB.Sym "=", SMTLIB.Sym id, l]) [], cx)
          end
       | parse_skolem (SMTLIB.S [SMTLIB.Sym "define-fun", SMTLIB.Sym id,  _, typ, SMTLIB.S l]) cx =
-         let val (l, cx) = (fst oo SMTLIB_Proof.extract_and_update_name_bindings) (SMTLIB.S l ) cx
+         let val (l, cx) = (fst oo SMTLIB_Proof.extract_and_update_name_bindings) (SMTLIB.S l) cx
          in
            (mk_raw_node (id ^ lethe_def) lethe_def (SMTLIB.S [SMTLIB.Sym id, typ, l]) [] []
               (SMTLIB.S [SMTLIB.Sym "=", SMTLIB.Sym id, l]) [], cx)
          end
+      | parse_skolem (SMTLIB.S [SMTLIB.Sym "declare-fun", SMTLIB.Sym id, typ, def]) cx =
+         (*replace the name binding by the constant instead of the full term in order to reduce
+           the size of the generated terms and therefore the reconstruction time*)
+         let val (l, cx) = (fst oo SMTLIB_Proof.extract_and_update_name_bindings) def cx
+         in
+           (mk_raw_node (id ^ lethe_def) lethe_def (SMTLIB.S [SMTLIB.Sym id, typ, l]) [] []
+              (SMTLIB.S [SMTLIB.Sym "=", SMTLIB.Sym id, def]) [], cx)
+         end
       | parse_skolem t _ = raise Fail ("unrecognized Lethe proof " ^ \<^make_string> t)
     fun get_id_cx (SMTLIB.S ((SMTLIB.Sym _) :: (SMTLIB.Sym id) :: l), cx) = (id, (l, cx))
       | get_id_cx t = raise Fail ("unrecognized Lethe proof " ^ \<^make_string> t)
@@ -318,28 +342,41 @@
               val (s, (_, cx)) =  (p, cx)
                 |> parse_normal_step
                 |>>  (to_raw_node [])
-              val (rp, rl, cx) = parse_raw_proof_steps limit l cx
+              val (rp, rl, cx) = parse_raw_proof_steps limit l cx assms_nbr
           in (s :: rp, rl, cx) end
       | (ASSUME, p, l) =>
           let
             val (id, t :: []) = p
               |> get_id
+
             val ((t, cx), _) = SMTLIB_Proof.extract_and_update_name_bindings t cx
             val s = mk_raw_node id input_rule (SMTLIB.S []) [] [] t []
-            val (rp, rl, cx) = parse_raw_proof_steps limit l cx
+            (*Recursive call to parse rest of the steps.*)
+            val (rp, rl, cx) = parse_raw_proof_steps limit l cx (assms_nbr + 1)
+          in (s :: rp, rl, cx) end
+      | (ASSERT, p, l) => 
+          let
+            val (id, term) = (case p of
+                SMTLIB.S [SMTLIB.Sym "assert", SMTLIB.S [SMTLIB.Sym "!", term, SMTLIB.Key "named", SMTLIB.Sym id]] => (id, term)
+              | SMTLIB.S [SMTLIB.Sym "assert", term] => (Int.toString assms_nbr, term))
+
+            val ((t, cx), _) = SMTLIB_Proof.extract_and_update_name_bindings term cx
+            val s = mk_raw_node id input_rule (SMTLIB.S []) [] [] t []
+            (*Recursive call to parse rest of the steps.*)
+            val (rp, rl, cx) = parse_raw_proof_steps limit l cx (assms_nbr+1)
           in (s :: rp, rl, cx) end
       | (ANCHOR, p, l) =>
           let
             val (anchor_id, (anchor_args, (_, cx))) = (p, cx) |> (parse_anchor_step ##> parse_args)
-            val (subproof, discharge_step :: remaining_proof, cx) = parse_raw_proof_steps (SOME anchor_id) l cx
+            val (subproof, discharge_step :: remaining_proof, cx) = parse_raw_proof_steps (SOME anchor_id) l cx assms_nbr
             val (curss, (_, cx)) = parse_normal_step (discharge_step, cx)
             val s = to_raw_node subproof (fst curss, anchor_args)
-            val (rp, rl, cx) = parse_raw_proof_steps limit remaining_proof cx
+            val (rp, rl, cx) = parse_raw_proof_steps limit remaining_proof cx assms_nbr
           in (s :: rp, rl, cx) end
       | (SKOLEM, p, l) =>
           let
             val (s, cx) = parse_skolem p cx
-            val (rp, rl, cx) = parse_raw_proof_steps limit l cx
+            val (rp, rl, cx) = parse_raw_proof_steps limit l cx (assms_nbr)
           in (s :: rp, rl, cx) end
   end
 
@@ -352,6 +389,7 @@
 
 fun args_of_rule "bind" t = t
   | args_of_rule "la_generic" t = t
+  | args_of_rule "all_simplify" t = t
   | args_of_rule _ _ = []
 
 fun insts_of_forall_inst "forall_inst" t = map (fn SMTLIB.S [_, SMTLIB.Sym x, a] => (x, a)) t
@@ -389,6 +427,13 @@
   let
     fun expand_assms cs =
       map (fn t => case AList.lookup (op =) cs t of NONE => t | SOME a => a)
+    fun match_typing_arguments (SMTLIB.S [SMTLIB.Sym var, typ as SMTLIB.Sym _] :: SMTLIB.S [SMTLIB.Sym "=", SMTLIB.Sym x1, x2] :: xs) =
+       if var = x1 then (*CVC5*)
+         SMTLIB.S [SMTLIB.Sym "=", SMTLIB.S [SMTLIB.Sym x1, typ], x2] :: match_typing_arguments xs
+       else
+         SMTLIB.S [SMTLIB.Sym var, typ] :: match_typing_arguments (SMTLIB.S [SMTLIB.Sym "=", SMTLIB.Sym x1, x2] :: xs)
+     | match_typing_arguments (a :: xs) = a :: match_typing_arguments xs
+     | match_typing_arguments [] = []
     fun expand_lonely_arguments (args as SMTLIB.S [SMTLIB.Sym "=", _, _]) = [args]
       | expand_lonely_arguments (x as SMTLIB.S [SMTLIB.Sym var, _]) = [SMTLIB.S [SMTLIB.Sym "=", x, SMTLIB.Sym var]]
 
@@ -399,7 +444,7 @@
           |> map
               (fn SMTLIB.S [SMTLIB.Key "=", x, y] => SMTLIB.S [SMTLIB.Sym "=", x, y]
               | x => x)
-          |> (rule = "bind" orelse rule = "onepoint") ? flat o (map expand_lonely_arguments)
+          |> (rule = "bind" orelse rule = "onepoint") ? flat o (map expand_lonely_arguments) o match_typing_arguments
           |> `(if rule = lethe_def then single o extract_skolem else K [])
           ||> SMTLIB.S
 
@@ -428,7 +473,7 @@
     |> single
  | extract_types_of_args (SMTLIB.S t) =
   let
-    fun extract_types_of_arg (SMTLIB.S [eq, SMTLIB.S [var, typ], t]) = (SMTLIB.S [eq, var, t], SOME typ)
+    fun extract_types_of_arg (SMTLIB.S [eq as SMTLIB.Sym "=", SMTLIB.S [var, typ], t]) = (SMTLIB.S [eq, var, t], SOME typ)
       | extract_types_of_arg t = (t, NONE)
   in
     t
@@ -439,6 +484,8 @@
   (if is_skolemization rule then map (fn id => id ^ lethe_def) (skolems_introduced_by_rule args) else []) @
   flat (map collect_skolem_defs subproof)
 
+val desymbolize = Name.desymbolize (SOME false) o perhaps (try (unprefix "?"))
+
 (*The postprocessing does:
   1. translate the terms to Isabelle syntax, taking care of free variables
   2. remove the ambiguity in the proof terms:
@@ -453,8 +500,6 @@
   let
     fun postprocess (Raw_Lethe_Node {id, rule, args, prems, declarations, concl, subproof}) (cx, rew) =
     let
-      val _ = (SMT_Config.verit_msg ctxt) (fn () => @{print} ("id =", id, "concl =", concl))
-
       val args = extract_types_of_args args
       val globally_bound_vars = declared_csts cx rule args
       val cx = fold (update_binding o (fn (s, typ) => (s, Term (Free (s, type_of cx typ)))))
@@ -486,13 +531,9 @@
       (* postprocess conclusion *)
       val concl = SMTLIB_Isar.unskolemize_names ctxt (subproof_rewriter concl)
 
-      val _ = (SMT_Config.verit_msg ctxt) (fn () => \<^print> ("id =", id, "concl =", concl))
-      val _ = (SMT_Config.verit_msg ctxt) (fn () => \<^print> ("id =", id, "cx' =", cx',
-        "bound_vars =", bound_vars))
-
-      val bound_tvars =
-          map (fn (s, SOME typ) => (s, type_of cx typ))
-            (shadowing_vars @ new_lhs_vars)
+      fun give_proper_type (s, SOME typ) = (s, type_of cx typ)
+       | give_proper_type (s, NONE) = raise (Fail ("could not find type of var " ^ @{make_string} s ^ " in step " ^ id ^ " in " ^  @{make_string} concl))
+      val bound_tvars = map give_proper_type (shadowing_vars @ new_lhs_vars)
       val subproof_cx =
          add_bound_variables_to_ctxt cx (shadowing_vars @ new_lhs_vars) cx
 
@@ -531,15 +572,18 @@
 
       (* postprocess arguments *)
       val rule_args = args_of_rule rule stripped_args
+
       val (termified_args, _) = fold_map term_of rule_args subproof_cx
       val normalized_args = map unsk_and_rewrite termified_args
+
       val rule_args = map subproof_rewriter normalized_args
 
       val raw_insts = insts_of_forall_inst rule stripped_args
       fun termify_term (x, t) cx = let val (t, cx) = term_of t cx in ((x, t), cx) end
       val (termified_args, _) = fold_map termify_term raw_insts subproof_cx
+
       val insts = Symtab.empty
-        |> fold (fn (x, t) => fn insts => Symtab.update_new (x, t) insts) termified_args
+        |> fold (fn (x, t) => fn insts => Symtab.update_new (desymbolize x, t) insts) termified_args
         |> Symtab.map (K unsk_and_rewrite)
 
       (* declarations *)
@@ -742,14 +786,16 @@
   fun import_proof_and_post_process typs funs lines ctxt =
     let
       val compress = SMT_Config.compress_verit_proofs ctxt
+
       val smtlib_lines_without_qm =
         lines
+        |> filter_out (fn x => x = "")
         |> map single
         |> map SMTLIB.parse
         |> map remove_all_qm2
         |> map remove_pattern
       val (raw_steps, _, _) =
-        parse_raw_proof_steps NONE smtlib_lines_without_qm SMTLIB_Proof.empty_name_binding
+        parse_raw_proof_steps NONE smtlib_lines_without_qm SMTLIB_Proof.empty_name_binding 0
 
       fun process step (cx, cx') =
         let fun postprocess step (cx, cx') =
@@ -779,7 +825,6 @@
 fun parse_replay typs funs lines ctxt =
   let
     val (u, env) = import_proof_and_post_process typs funs lines ctxt
-    val _ = (SMT_Config.verit_msg ctxt) (fn () => \<^print> u)
   in
     (u, ctxt_of env)
   end

--- a/src/HOL/Tools/SMT/lethe_replay_methods.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/lethe_replay_methods.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -50,7 +50,10 @@
      (*For compression*)
      Theory_Resolution2 |
      (*Extended rules*)
-     Symm | Not_Symm | Reordering | Tmp_Quantifier_Simplify
+     Symm | Not_Symm | Reordering | Tmp_Quantifier_Simplify |
+     (*CVC5 to support new rules declared later (like BV rules)*)
+     Other_Rule of string |
+     Hole
 
   val requires_subproof_assms : string list -> string -> bool
   val requires_local_input: string list -> string -> bool
@@ -73,7 +76,7 @@
   val rewrite_equiv_simplify: lethe_tac
   val rewrite_implies_simplify: lethe_tac
   val rewrite_or_simplify: lethe_tac
-  val cong: lethe_tac
+  val cong: string -> lethe_tac
   val rewrite_connective_def: lethe_tac
   val duplicate_literals: lethe_tac
   val eq_congruent: lethe_tac
@@ -104,7 +107,7 @@
   val la_generic: lethe_tac_args
   val la_rw_eq: lethe_tac
   val lia_generic: lethe_tac
-  val refl: lethe_tac
+  val refl: string -> lethe_tac
   val normalized_input: lethe_tac
   val not_and_rule: lethe_tac
   val not_equiv1: lethe_tac
@@ -139,12 +142,20 @@
   val not_symm: lethe_tac
   val reordering: lethe_tac
 
-(*
-  val : lethe_tac
-*)
+
+  (*Extension to declare new alethe rules*)
+  val declare_alethe_rule:  string -> lethe_tac_args -> Context.generic -> Context.generic
+  val rm_alethe_rule: string -> Context.generic -> Context.generic
+  val get_alethe_tac: string -> Context.generic -> lethe_tac_args option
+  val print_alethe_tac: Context.generic -> Pretty.T
+
+  (*Useful lifting of tactics*)
   val REPEAT_CHANGED: ('a -> tactic) -> 'a -> tactic
   val TRY': ('a -> tactic) -> 'a -> tactic
 
+  val simplify_tac: Proof.context -> thm list -> int -> tactic
+  val replay_error: Proof.context -> string -> verit_rule -> thm list -> term -> 'a
+
 end;
 
 
@@ -213,7 +224,10 @@
    (*For compression*)
    Theory_Resolution2 |
    (*Extended rules*)
-   Symm | Not_Symm | Reordering | Tmp_Quantifier_Simplify
+   Symm | Not_Symm | Reordering | Tmp_Quantifier_Simplify |
+   (*CVC5*)
+   Other_Rule of string |
+   Hole
 
 fun string_of_verit_rule Bind = "Bind"
   | string_of_verit_rule Cong = "Cong"
@@ -297,8 +311,67 @@
   | string_of_verit_rule Tautological_Clause = "tautology"
   | string_of_verit_rule Duplicate_Literals = Lethe_Proof.contract_rule
   | string_of_verit_rule Qnt_CNF = "qnt_cnf"
+  | string_of_verit_rule (Other_Rule r) = r
   | string_of_verit_rule r = "Unknown rule: " ^ \<^make_string> r
 
+(** Context Extension for Rules **)
+(*We currently do not distinguish between the extension required for each solver. Maybe later
+it will be needed.*)
+type alethe_rule_ext = {rules: (string * lethe_tac_args) list}
+
+fun mk_alethe_rule_ext rules : alethe_rule_ext = 
+   {rules=rules}
+
+val empty_data = mk_alethe_rule_ext []
+
+fun merge_data ({rules=rules1}:alethe_rule_ext, {rules=rules2}:alethe_rule_ext) : alethe_rule_ext =
+  mk_alethe_rule_ext (AList.merge (op =) (fn _ => true) (rules1, rules2))
+
+structure Data = Generic_Data
+(
+  type T = alethe_rule_ext
+  val empty = empty_data
+  val merge = merge_data
+)
+
+fun declare_alethe_rule rule tac context =
+  let
+    val {rules} = Data.get context
+  in
+    Data.map
+      (K (mk_alethe_rule_ext (AList.update (op =) (rule, tac) rules)))
+      context
+  end
+
+fun rm_alethe_rule stgy context =
+  let
+    val {rules} = Data.get context
+  in
+    Data.map
+      (K (mk_alethe_rule_ext (AList.delete (op =) stgy rules)))
+      context
+  end
+
+fun get_alethe_tac rule context =
+  let
+    val {rules} = Data.get context
+  in
+    AList.lookup (op =) rules rule
+  end
+
+fun print_alethe_tac context =
+  let
+    val {rules} = Data.get context
+  in
+    rules
+    |> map (fn (a, b) => a ^ "->" ^ @{make_string} b)
+    |> map Pretty.str
+    |> Pretty.big_list "Declared alethe rules:\n"
+  end
+
+
+(** Tactics for Reconstruction **)
+(**)
 fun replay_error ctxt msg rule thms t =
   SMT_Replay_Methods.replay_error ctxt msg (string_of_verit_rule rule) thms t
 
@@ -331,7 +404,7 @@
   |> (fn ctxt => ctxt addsimps @{thms simp_thms} addsimps thms)
   |> Simplifier.full_simp_tac
 
-val try_provers = SMT_Replay_Methods.try_provers "verit"
+val try_provers = SMT_Replay_Methods.try_provers
 
 fun TRY' tac = fn i => TRY (tac i)
 fun REPEAT' tac = fn i => REPEAT (tac i)
@@ -446,19 +519,19 @@
 
 (* Congruence/Refl *)
 
-fun cong ctxt thms = try_provers ctxt
+fun cong name ctxt thms = try_provers name ctxt
     (string_of_verit_rule Cong) [
   ("basic", SMT_Replay_Methods.cong_basic ctxt thms),
   ("unfolding then reflexivity", SMT_Replay_Methods.cong_unfolding_trivial ctxt thms),
   ("unfolding then auto", SMT_Replay_Methods.cong_unfolding_first ctxt thms),
   ("full", SMT_Replay_Methods.cong_full ctxt thms)] thms
 
-fun refl ctxt thm t =
+fun refl name ctxt thm t =
   (case find_first (fn thm => t = Thm.full_prop_of thm) thm of
       SOME thm => thm
     | NONE =>
         (case try (fn t => SMT_Replay_Methods.match_instantiate ctxt t @{thm refl}) t of
-          NONE => cong ctxt thm t
+          NONE => cong name ctxt thm t
         | SOME thm => thm))
 
 (* Instantiation *)

--- a/src/HOL/Tools/SMT/smt_config.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/smt_config.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -55,6 +55,7 @@
   val verit_arith_msg: Proof.context -> (unit -> 'a) -> unit
   val spy_verit: Proof.context -> bool
   val spy_Z3: Proof.context -> bool
+  val use_lethe_proof_from_cvc: Proof.context -> bool
 
   (*certificates*)
   val select_certificates: string -> Context.generic -> Context.generic
@@ -201,6 +202,7 @@
 val infer_triggers = Attrib.setup_config_bool \<^binding>\<open>smt_infer_triggers\<close> (K false)
 val debug_files = Attrib.setup_config_string \<^binding>\<open>smt_debug_files\<close> (K "")
 val sat_solver = Attrib.setup_config_string \<^binding>\<open>smt_sat_solver\<close> (K "cdclite")
+val cvc_experimental_lethe = Attrib.setup_config_bool \<^binding>\<open>smt_cvc_lethe\<close> (K false)
 
 
 (* diagnostics *)
@@ -218,6 +220,8 @@
 fun spy_Z3 ctxt  = Config.get ctxt spy_z3
 fun compress_verit_proofs ctxt  = Config.get ctxt trace_verit_compression
 
+fun use_lethe_proof_from_cvc ctxt  = Config.get ctxt cvc_experimental_lethe
+
 
 (* tools *)
 

--- a/src/HOL/Tools/SMT/smt_real.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/smt_real.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -30,6 +30,28 @@
   fun times _ _ ts = if is_linear ts then SOME ("*", 2, ts, mk_times) else NONE
 in
 
+fun real_type_parser (SMTLIB.Sym "Real", []) = SOME \<^typ>\<open>Real.real\<close>
+  | real_type_parser _ = NONE
+
+fun real_term_parser (SMTLIB.Dec (i, 0), []) = SOME (HOLogic.mk_number \<^typ>\<open>Real.real\<close> i)
+  | real_term_parser (SMTLIB.Sym "/", [t1, t2]) =
+      SOME (\<^term>\<open>Rings.divide :: real => _\<close> $ t1 $ t2)
+  | real_term_parser (SMTLIB.Sym "to_real", [t]) = SOME (\<^term>\<open>Int.of_int :: int => _\<close> $ t)
+  | real_term_parser _ = NONE
+
+fun abstract abs t =
+  (case t of
+    (c as \<^term>\<open>Rings.divide :: real => _\<close>) $ t1 $ t2 =>
+      abs t1 ##>> abs t2 #>> (fn (u1, u2) => SOME (c $ u1 $ u2))
+  | (c as \<^term>\<open>Int.of_int :: int => _\<close>) $ t =>
+      abs t #>> (fn u => SOME (c $ u))
+  | _ => pair NONE)
+
+val _ = Theory.setup (Context.theory_map (
+  SMTLIB_Proof.add_type_parser real_type_parser #>
+  SMTLIB_Proof.add_term_parser real_term_parser #>
+  SMT_Replay_Methods.add_arith_abstracter abstract))
+
 val setup_builtins =
   SMT_Builtin.add_builtin_typ SMTLIB_Interface.smtlibC
     (\<^typ>\<open>real\<close>, K (SOME ("Real", [])), real_num) #>
@@ -40,11 +62,7 @@
     (\<^Const>\<open>plus \<^Type>\<open>real\<close>\<close>, "+"),
     (\<^Const>\<open>minus \<^Type>\<open>real\<close>\<close>, "-") ] #>
   SMT_Builtin.add_builtin_fun SMTLIB_Interface.smtlibC
-    (Term.dest_Const \<^Const>\<open>times \<^Type>\<open>real\<close>\<close>, times) #>
-  SMT_Builtin.add_builtin_fun' Z3_Interface.smtlib_z3C
-    (\<^Const>\<open>times \<^Type>\<open>real\<close>\<close>, "*") #>
-  SMT_Builtin.add_builtin_fun' Z3_Interface.smtlib_z3C
-    (\<^Const>\<open>divide \<^Type>\<open>real\<close>\<close>, "/")
+    (Term.dest_Const \<^Const>\<open>times \<^Type>\<open>real\<close>\<close>, times)
 
 end
 
@@ -52,12 +70,12 @@
 (* Z3 constructors *)
 
 local
-  fun z3_mk_builtin_typ (Z3_Interface.Sym ("Real", _)) = SOME \<^typ>\<open>real\<close>
-    | z3_mk_builtin_typ (Z3_Interface.Sym ("real", _)) = SOME \<^typ>\<open>real\<close>
+  fun smt_mk_builtin_typ (Z3_Interface.Sym ("Real", _)) = SOME \<^typ>\<open>real\<close>
+    | smt_mk_builtin_typ (Z3_Interface.Sym ("real", _)) = SOME \<^typ>\<open>real\<close>
         (*FIXME: delete*)
-    | z3_mk_builtin_typ _ = NONE
+    | smt_mk_builtin_typ _ = NONE
 
-  fun z3_mk_builtin_num _ i T =
+  fun smt_mk_builtin_num _ i T =
     if T = \<^typ>\<open>real\<close> then SOME (Numeral.mk_cnumber \<^ctyp>\<open>real\<close> i)
     else NONE
 
@@ -73,24 +91,24 @@
   val mk_lt = Thm.mk_binop \<^cterm>\<open>(<) :: real \<Rightarrow> _\<close>
   val mk_le = Thm.mk_binop \<^cterm>\<open>(\<le>) :: real \<Rightarrow> _\<close>
 
-  fun z3_mk_builtin_fun (Z3_Interface.Sym ("-", _)) [ct] = SOME (mk_uminus ct)
-    | z3_mk_builtin_fun (Z3_Interface.Sym ("+", _)) cts = SOME (mk_nary add real0 cts)
-    | z3_mk_builtin_fun (Z3_Interface.Sym ("-", _)) [ct, cu] = SOME (mk_sub ct cu)
-    | z3_mk_builtin_fun (Z3_Interface.Sym ("*", _)) [ct, cu] = SOME (mk_mul ct cu)
-    | z3_mk_builtin_fun (Z3_Interface.Sym ("/", _)) [ct, cu] = SOME (mk_div ct cu)
-    | z3_mk_builtin_fun (Z3_Interface.Sym ("<", _)) [ct, cu] = SOME (mk_lt ct cu)
-    | z3_mk_builtin_fun (Z3_Interface.Sym ("<=", _)) [ct, cu] = SOME (mk_le ct cu)
-    | z3_mk_builtin_fun (Z3_Interface.Sym (">", _)) [ct, cu] = SOME (mk_lt cu ct)
-    | z3_mk_builtin_fun (Z3_Interface.Sym (">=", _)) [ct, cu] = SOME (mk_le cu ct)
-    | z3_mk_builtin_fun _ _ = NONE
+  fun smt_mk_builtin_fun (Z3_Interface.Sym ("-", _)) [ct] = SOME (mk_uminus ct)
+    | smt_mk_builtin_fun (Z3_Interface.Sym ("+", _)) cts = SOME (mk_nary add real0 cts)
+    | smt_mk_builtin_fun (Z3_Interface.Sym ("-", _)) [ct, cu] = SOME (mk_sub ct cu)
+    | smt_mk_builtin_fun (Z3_Interface.Sym ("*", _)) [ct, cu] = SOME (mk_mul ct cu)
+    | smt_mk_builtin_fun (Z3_Interface.Sym ("/", _)) [ct, cu] = SOME (mk_div ct cu)
+    | smt_mk_builtin_fun (Z3_Interface.Sym ("<", _)) [ct, cu] = SOME (mk_lt ct cu)
+    | smt_mk_builtin_fun (Z3_Interface.Sym ("<=", _)) [ct, cu] = SOME (mk_le ct cu)
+    | smt_mk_builtin_fun (Z3_Interface.Sym (">", _)) [ct, cu] = SOME (mk_lt cu ct)
+    | smt_mk_builtin_fun (Z3_Interface.Sym (">=", _)) [ct, cu] = SOME (mk_le cu ct)
+    | smt_mk_builtin_fun _ _ = NONE
 in
 
-val z3_mk_builtins = {
-  mk_builtin_typ = z3_mk_builtin_typ,
-  mk_builtin_num = z3_mk_builtin_num,
+val smt_mk_builtins = {
+  mk_builtin_typ = smt_mk_builtin_typ,
+  mk_builtin_num = smt_mk_builtin_num,
   mk_builtin_fun = (fn _ => fn sym => fn cts =>
     (case try (Thm.typ_of_cterm o hd) cts of
-      SOME \<^typ>\<open>real\<close> => z3_mk_builtin_fun sym cts
+      SOME \<^typ>\<open>real\<close> => smt_mk_builtin_fun sym cts
     | _ => NONE)) }
 
 end
@@ -109,7 +127,7 @@
 val _ = Theory.setup (Context.theory_map (
   SMTLIB_Interface.add_logic (10, smtlib_logic) #>
   setup_builtins #>
-  Z3_Interface.add_mk_builtins z3_mk_builtins #>
+  Z3_Interface.add_mk_builtins smt_mk_builtins #>
   SMT_Replay.add_simproc real_linarith_proc))
 
 end;

--- a/src/HOL/Tools/SMT/smt_replay_methods.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/smt_replay_methods.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -103,7 +103,7 @@
 
 fun replay_error ctxt msg rule thms t = error (Pretty.string_of (pretty_goal ctxt msg rule thms t))
 
-fun replay_rule_error name ctxt = replay_error ctxt ("Failed to replay" ^ name ^ " proof step")
+fun replay_rule_error name ctxt = replay_error ctxt ("Failed to replay " ^ name ^ " proof step")
 
 fun trace_goal ctxt rule thms t =
   trace ctxt (fn () => Pretty.string_of (pretty_goal ctxt "Goal" rule thms t))

--- a/src/HOL/Tools/SMT/smt_systems.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/smt_systems.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -121,7 +121,7 @@
   avail = make_avail "CVC5",
   command = make_command "CVC5",
   options = cvc5_options,
-  smt_options = [(":produce-unsat-cores", "true")],
+  smt_options = [(":produce-proofs", "true")],
   good_slices =
     (* FUDGE *)
     [((2, false, false, 512, meshN), ["--full-saturate-quant", "--inst-when=full-last-call", "--inst-no-entail", "--term-db-mode=relevant", "--multi-trigger-linear"]),
@@ -133,7 +133,7 @@
      ((2, false, false, 256, meshN), ["--finite-model-find", "--fmf-inst-engine"])],
   outcome = on_first_line (outcome_of "unsat" "sat" "unknown" "timeout"),
   parse_proof = SOME (K CVC_Proof_Parse.parse_proof),
-  replay = NONE }
+  replay = SOME CVC5_Replay.replay }
 
 end
 

--- a/src/HOL/Tools/SMT/smtlib_interface.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/smtlib_interface.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -10,6 +10,7 @@
   val smtlibC: SMT_Util.class
   val hosmtlibC: SMT_Util.class
   val bvsmlibC: SMT_Util.class
+  val realsmlibC: SMT_Util.class
   val add_logic: int * (string -> term list -> string option) -> Context.generic -> Context.generic
   val del_logic: int * (string -> term list -> string option) -> Context.generic -> Context.generic
   val translate_config: SMT_Util.order -> Proof.context -> SMT_Translate.config
@@ -25,6 +26,7 @@
 val smtlibC = ["smtlib"]   (* SMT-LIB 2 *)
 val hosmtlibC = smtlibC @ hoC   (* possibly SMT-LIB 3 *)
 val bvsmlibC = smtlibC @ ["BV"] (* if BV are supported *)
+val realsmlibC = ["Real"]
 
 (* builtins *)
 
@@ -138,7 +140,7 @@
 
 val conjecture_prefix = "conjecture" (* FUDGE *)
 val hypothesis_prefix = "hypothesis" (* FUDGE *)
-val axiom_prefix = "axiom" (* FUDGE *)
+val axiom_prefix = "a" (* matching Alethe's convention *)
 
 fun assert_prefix_of_role SMT_Util.Conjecture = conjecture_prefix
   | assert_prefix_of_role SMT_Util.Hypothesis = hypothesis_prefix

--- a/src/HOL/Tools/SMT/verit_replay_methods.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/verit_replay_methods.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -120,7 +120,7 @@
   | choose Bind = ignore_insts bind
   | choose Bool_Simplify = ignore_args rewrite_bool_simplify
   | choose Comp_Simplify = ignore_args rewrite_comp_simplify
-  | choose Cong = ignore_args cong
+  | choose Cong = ignore_args (cong "verit")
   | choose Connective_Def = ignore_args rewrite_connective_def
   | choose Duplicate_Literals = ignore_args duplicate_literals
   | choose Eq_Congruent = ignore_args eq_congruent
@@ -156,7 +156,7 @@
   | choose LA_Tautology = ignore_args SMT_Replay_Methods.arith_th_lemma_wo_shallow
   | choose LA_Totality = ignore_args SMT_Replay_Methods.arith_th_lemma_wo_shallow
   | choose LIA_Generic = ignore_args lia_generic
-  | choose Local_Input = ignore_args refl
+  | choose Local_Input = ignore_args (refl "verit")
   | choose Minus_Simplify = ignore_args rewrite_minus_simplify
   | choose NLA_Generic = ignore_args SMT_Replay_Methods.arith_th_lemma_wo_shallow
   | choose Normalized_Input = ignore_args normalized_input
@@ -180,7 +180,7 @@
   | choose Qnt_Rm_Unused = ignore_args qnt_rm_unused
   | choose Onepoint = ignore_args onepoint
   | choose Qnt_Simplify = ignore_args qnt_simplify
-  | choose Refl = ignore_args refl
+  | choose Refl = ignore_args (refl "verit")
   | choose Resolution = ignore_args unit_res
   | choose Skolem_Ex = ignore_args skolem_ex
   | choose Skolem_Forall = ignore_args skolem_forall

--- a/src/HOL/Tools/SMT/z3_real.ML	Sat Jun 17 17:41:02 2023 +0200
+++ b/src/HOL/Tools/SMT/z3_real.ML	Mon Jun 19 22:28:09 2023 +0200
@@ -1,32 +1,20 @@
 (*  Title:      HOL/Tools/SMT/z3_real.ML
     Author:     Sascha Boehme, TU Muenchen
 
-Z3 setup for reals.
+Z3 setup for reals  based on a relaxed version of SMT-LIB (outside of LIRA).
 *)
 
 structure Z3_Real: sig end =
 struct
 
-fun real_type_parser (SMTLIB.Sym "Real", []) = SOME \<^typ>\<open>Real.real\<close>
-  | real_type_parser _ = NONE
-
-fun real_term_parser (SMTLIB.Dec (i, 0), []) = SOME (HOLogic.mk_number \<^typ>\<open>Real.real\<close> i)
-  | real_term_parser (SMTLIB.Sym "/", [t1, t2]) =
-      SOME (\<^term>\<open>Rings.divide :: real => _\<close> $ t1 $ t2)
-  | real_term_parser (SMTLIB.Sym "to_real", [t]) = SOME (\<^term>\<open>Int.of_int :: int => _\<close> $ t)
-  | real_term_parser _ = NONE
+val setup_builtins =
+  SMT_Builtin.add_builtin_fun' Z3_Interface.smtlib_z3C
+    (\<^Const>\<open>times \<^Type>\<open>real\<close>\<close>, "*") #>
+  SMT_Builtin.add_builtin_fun' Z3_Interface.smtlib_z3C
+    (\<^Const>\<open>divide \<^Type>\<open>real\<close>\<close>, "/")
 
-fun abstract abs t =
-  (case t of
-    (c as \<^term>\<open>Rings.divide :: real => _\<close>) $ t1 $ t2 =>
-      abs t1 ##>> abs t2 #>> (fn (u1, u2) => SOME (c $ u1 $ u2))
-  | (c as \<^term>\<open>Int.of_int :: int => _\<close>) $ t =>
-      abs t #>> (fn u => SOME (c $ u))
-  | _ => pair NONE)
 
-val _ = Theory.setup (Context.theory_map (
-  SMTLIB_Proof.add_type_parser real_type_parser #>
-  SMTLIB_Proof.add_term_parser real_term_parser #>
-  SMT_Replay_Methods.add_arith_abstracter abstract))
+val _ = Theory.setup (Context.theory_map
+  setup_builtins)
 
 end;