TSTP Solution File: SWC174+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC174+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:23:47 EDT 2023
% Result : Theorem 34.95s 35.18s
% Output : Proof 34.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC174+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 17:42:37 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 34.95/35.18 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.cw9faYZxbv/cvc5---1.0.5_25023.p...
% 34.95/35.18 ------- get file name : TPTP file name is SWC174+1
% 34.95/35.18 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_25023.smt2...
% 34.95/35.18 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 34.95/35.18 --- Run --no-e-matching --full-saturate-quant at 5...
% 34.95/35.18 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 34.95/35.18 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 34.95/35.18 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 34.95/35.18 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 34.95/35.18 % SZS status Theorem for SWC174+1
% 34.95/35.18 % SZS output start Proof for SWC174+1
% 34.95/35.18 (
% 34.95/35.18 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.singletonP W)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (or (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (not (= (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) (tptp.cons Z tptp.nil)) X2) U)))))) (tptp.neq Y Z)))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))))) (let ((_let_5 (tptp.singletonP tptp.nil))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_13 (tptp.ssList tptp.nil))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_18 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.nil))) (let ((_let_19 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_20 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil))) (let ((_let_21 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_20))) (let ((_let_22 (tptp.app (tptp.app _let_21 _let_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (= _let_22 _let_18))) (let ((_let_24 (tptp.hd _let_22))) (let ((_let_25 (= _let_22 (tptp.cons _let_24 (tptp.tl _let_22))))) (let ((_let_26 (= tptp.nil (tptp.tl _let_18)))) (let ((_let_27 (tptp.cyclefreeP _let_22))) (let ((_let_28 (tptp.cyclefreeP (tptp.cons _let_24 tptp.nil)))) (let ((_let_29 (not _let_23))) (let ((_let_30 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29))) (let ((_let_33 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (not _let_33))) (let ((_let_36 (tptp.singletonP _let_22))) (let ((_let_37 (= _let_36 _let_35))) (let ((_let_38 (tptp.ssList _let_22))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_48 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_51 (not _let_50))) (let ((_let_52 (not _let_36))) (let ((_let_53 (or _let_39 _let_52 _let_51 _let_49 _let_47 _let_46 _let_44))) (let ((_let_54 (forall ((BOUND_VARIABLE_5348 $$unsorted) (BOUND_VARIABLE_5346 $$unsorted) (BOUND_VARIABLE_5344 $$unsorted) (BOUND_VARIABLE_5342 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5344 (tptp.cons BOUND_VARIABLE_5342 tptp.nil)) (tptp.cons BOUND_VARIABLE_5348 tptp.nil)) BOUND_VARIABLE_5346))) (or (not (tptp.ssList _let_1)) (not (tptp.singletonP _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5342)) (not (tptp.ssItem BOUND_VARIABLE_5348)) (tptp.neq BOUND_VARIABLE_5342 BOUND_VARIABLE_5348) (not (tptp.ssList BOUND_VARIABLE_5344)) (not (tptp.ssList BOUND_VARIABLE_5346))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (or))) (let ((_let_57 (not _let_54))) (let ((_let_58 (_let_57))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_54))) (REFL :args (_let_55)) :args _let_56)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_55 true _let_54)))) (let ((_let_60 (REFL :args (_let_53)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_56)) :args ((or _let_38 _let_53))) _let_59 :args (_let_38 true _let_53)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_36))) :args _let_56)) :args ((or _let_36 _let_53))) _let_59 :args (_let_36 true _let_53)))) (let ((_let_63 (_let_35))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63) (REWRITE :args ((=> _let_35 (not (or _let_31 (not (= _let_18 _let_22))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_33))) (REFL :args (_let_34)) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_52 _let_35 (not _let_37)))) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 (not _let_40)))) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_41)))) _let_42 :args (_let_40 false _let_41)) :args (_let_37 false _let_38 false _let_40)) :args (_let_35 false _let_36 false _let_37)) :args (_let_34 true _let_33)))) (let ((_let_65 (REFL :args (_let_32)))) (let ((_let_66 (= tptp.nil _let_22))) (let ((_let_67 (or _let_39 _let_66 _let_25))) (let ((_let_68 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (not _let_66))) (let ((_let_71 (ASSUME :args (_let_6)))) (let ((_let_72 (ASSUME :args (_let_36)))) (let ((_let_73 (ASSUME :args (_let_66)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_72 _let_73 _let_71) :args (_let_6 _let_36 _let_66)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_71)) (CONG (SYMM (SYMM _let_73)) :args (APPLY_UF tptp.singletonP)) (TRUE_INTRO _let_72))) :args (_let_36 _let_66 _let_6)) :args ((not (and _let_6 _let_36 _let_66)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) (REFL :args (_let_52)) (REFL :args (_let_70)) :args _let_56)) _let_62 _let_71 :args (_let_70 false _let_36 true _let_5)))) (let ((_let_75 (not _let_13))) (let ((_let_76 (or _let_75 _let_31 _let_26))) (let ((_let_77 (forall ((U $$unsorted) (BOUND_VARIABLE_3542 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3542)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3542 U))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (ASSUME :args (_let_13)))) (let ((_let_80 (forall ((V $$unsorted) (BOUND_VARIABLE_2465 $$unsorted) (BOUND_VARIABLE_2463 $$unsorted) (BOUND_VARIABLE_2461 $$unsorted) (BOUND_VARIABLE_2459 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2459)) (not (tptp.leq V BOUND_VARIABLE_2459)) (not (tptp.leq BOUND_VARIABLE_2459 V)) (not (tptp.ssList BOUND_VARIABLE_2465)) (not (tptp.ssList BOUND_VARIABLE_2461)) (not (tptp.ssList BOUND_VARIABLE_2463)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_2465 (tptp.cons V BOUND_VARIABLE_2461)) (tptp.cons BOUND_VARIABLE_2459 BOUND_VARIABLE_2463)) (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_81 (= _let_27 _let_80))) (let ((_let_82 (not _let_27))) (let ((_let_83 (or _let_39 _let_81))) (let ((_let_84 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.cyclefreeP U) (forall ((V $$unsorted) (BOUND_VARIABLE_2465 $$unsorted) (BOUND_VARIABLE_2463 $$unsorted) (BOUND_VARIABLE_2461 $$unsorted) (BOUND_VARIABLE_2459 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2459)) (not (tptp.leq V BOUND_VARIABLE_2459)) (not (tptp.leq BOUND_VARIABLE_2459 V)) (not (tptp.ssList BOUND_VARIABLE_2465)) (not (tptp.ssList BOUND_VARIABLE_2461)) (not (tptp.ssList BOUND_VARIABLE_2463)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_2465 (tptp.cons V BOUND_VARIABLE_2461)) (tptp.cons BOUND_VARIABLE_2459 BOUND_VARIABLE_2463))))))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (= _let_22 (tptp.app _let_21 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_51 _let_51 _let_89 _let_89 _let_46 _let_75 _let_44 _let_87))) (let ((_let_91 (not _let_90))) (let ((_let_92 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_93 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_94 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_93))) (let ((_let_95 (tptp.app _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_96 (= _let_22 (tptp.app _let_21 _let_95)))) (let ((_let_97 (= _let_95 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_93)))) (let ((_let_98 (not _let_92))) (let ((_let_99 (= _let_47 _let_98))) (let ((_let_100 (or _let_51 _let_49 _let_99))) (let ((_let_101 (forall ((U $$unsorted) (BOUND_VARIABLE_2086 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_2086)) (= (tptp.neq U BOUND_VARIABLE_2086) (not (= U BOUND_VARIABLE_2086))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 3)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_56)) :args ((or _let_48 _let_53))) _let_59 :args (_let_48 true _let_53)))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 2)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_56)) :args ((or _let_50 _let_53))) _let_59 :args (_let_50 true _let_53)))) (let ((_let_105 (not _let_99))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_99)) (CONG (REFL :args (_let_105)) (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_92))) :args _let_56)) :args ((or _let_47 _let_92 _let_105))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 4)) _let_59 :args ((not _let_47) true _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_51 _let_49 _let_99 (not _let_100)))) _let_104 _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_101)))) _let_102 :args (_let_100 false _let_101)) :args (_let_99 false _let_50 false _let_48 false _let_100)) :args (_let_92 true _let_47 false _let_99)))) (let ((_let_107 (or _let_44 _let_94))) (let ((_let_108 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 6)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_56)) :args ((or _let_43 _let_53))) _let_59 :args (_let_43 true _let_53)))) (let ((_let_111 (tptp.ssList _let_19))) (let ((_let_112 (not _let_111))) (let ((_let_113 (tptp.ssList _let_21))) (let ((_let_114 (not _let_113))) (let ((_let_115 (or _let_114 _let_112 _let_44 _let_96))) (let ((_let_116 (forall ((U $$unsorted) (BOUND_VARIABLE_4838 $$unsorted) (BOUND_VARIABLE_4836 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4836)) (not (tptp.ssList BOUND_VARIABLE_4838)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4836) BOUND_VARIABLE_4838) (tptp.app U (tptp.app BOUND_VARIABLE_4836 BOUND_VARIABLE_4838))))))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (tptp.ssList _let_20))) (let ((_let_119 (not _let_118))) (let ((_let_120 (or _let_46 _let_119 _let_113))) (let ((_let_121 (forall ((U $$unsorted) 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(tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_14 _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_11 _let_10 _let_9 _let_8 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) _let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) _let_4 (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) _let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 34.95/35.19 )
% 34.95/35.19 % SZS output end Proof for SWC174+1
% 34.95/35.19 % cvc5---1.0.5 exiting
% 34.95/35.19 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------