TSTP Solution File: SWC188+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC188+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 20:23:53 EDT 2023
% Result : Theorem 28.41s 28.71s
% Output : Proof 28.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC188+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 18:47:26 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 %----Proving TF0_NAR, FOF, or CNF
% 28.41/28.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ig6214gGJ3/cvc5---1.0.5_27533.p...
% 28.41/28.71 ------- get file name : TPTP file name is SWC188+1
% 28.41/28.71 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27533.smt2...
% 28.41/28.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.41/28.71 --- Run --no-e-matching --full-saturate-quant at 5...
% 28.41/28.71 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.41/28.71 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.41/28.71 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.41/28.71 % SZS status Theorem for SWC188+1
% 28.41/28.71 % SZS output start Proof for SWC188+1
% 28.41/28.71 (
% 28.41/28.71 (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)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (or (not (= (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) (tptp.cons Z tptp.nil)) X2) U)) (= Y Z)))))))))) (and (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (or (not (= (tptp.cons X3 tptp.nil) W)) (not (tptp.memberP X X3)) (exists ((X4 $$unsorted)) (and (tptp.ssItem X4) (not (= X3 X4)) (tptp.memberP X X4) (tptp.leq X4 X3)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))))))))))))))) (let ((_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))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_5 (forall ((U $$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)))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_9 (forall ((U $$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))))))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_17 (tptp.ssList tptp.nil))) (let ((_let_18 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_19 (forall ((U $$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))))))))))))))) (let ((_let_20 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$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 (= V W)))))))))))))))))) (let ((_let_21 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_22 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_23 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_22))) (let ((_let_24 (tptp.app _let_23 _let_21))) (let ((_let_25 (tptp.app _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_26 (tptp.app tptp.nil _let_25))) (let ((_let_27 (= _let_25 _let_26))) (let ((_let_28 (= _let_21 (tptp.app _let_21 tptp.nil)))) (let ((_let_29 (tptp.app _let_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_30 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (= _let_25 (tptp.app _let_23 _let_29)))) (let ((_let_33 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_34 (= _let_25 _let_33))) (let ((_let_35 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.hd _let_33)))) (let ((_let_36 (= tptp.nil (tptp.tl _let_33)))) (let ((_let_37 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_38 (= _let_25 _let_37))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 (tptp.tl _let_37)))) (let ((_let_40 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 (tptp.hd _let_37)))) (let ((_let_41 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_42 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_43 (= _let_26 (tptp.app _let_23 _let_25)))) (let ((_let_44 (tptp.ssList _let_25))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_27))) (let ((_let_47 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (= tptp.nil _let_25))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or (not (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) _let_50))) (let ((_let_52 (not _let_34))) (let ((_let_53 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52 (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (= X4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 X4)) (not (tptp.leq X4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))))) (let ((_let_56 (and _let_55 _let_51))) (let ((_let_57 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_58 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_59 (not _let_58))) (let ((_let_60 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_45 _let_65 _let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_61 _let_59 _let_57 _let_56))) (let ((_let_67 (forall ((BOUND_VARIABLE_5558 $$unsorted) (BOUND_VARIABLE_5556 $$unsorted) (BOUND_VARIABLE_5537 $$unsorted) (BOUND_VARIABLE_5535 $$unsorted) (BOUND_VARIABLE_5533 $$unsorted) (BOUND_VARIABLE_5531 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5533 (tptp.cons BOUND_VARIABLE_5531 tptp.nil)) (tptp.cons BOUND_VARIABLE_5537 tptp.nil)) BOUND_VARIABLE_5535))) (or (not (tptp.ssList _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5531)) (not (tptp.ssItem BOUND_VARIABLE_5537)) (= BOUND_VARIABLE_5531 BOUND_VARIABLE_5537) (not (tptp.ssList BOUND_VARIABLE_5533)) (not (tptp.ssList BOUND_VARIABLE_5535)) (not (tptp.ssList BOUND_VARIABLE_5556)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5558)) (not (= _let_1 (tptp.cons BOUND_VARIABLE_5558 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5556 BOUND_VARIABLE_5558)) (not (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (= X4 BOUND_VARIABLE_5558) (not (tptp.memberP BOUND_VARIABLE_5556 X4)) (not (tptp.leq X4 BOUND_VARIABLE_5558)))))) (or (not (= tptp.nil BOUND_VARIABLE_5556)) (not (= tptp.nil _let_1))))))))) (let ((_let_68 (not _let_66))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (or))) (let ((_let_71 (not _let_67))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_69) :args (_let_71)) (REWRITE :args ((=> _let_71 (not (or _let_45 _let_65 _let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_61 _let_59 _let_57 _let_56))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_67))) (REFL :args (_let_68)) :args _let_70)) _let_69 :args (_let_68 true _let_67)))) (let ((_let_73 (REFL :args (_let_66)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 0)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_70)) :args ((or _let_44 _let_66))) _let_72 :args (_let_44 true _let_66)))) (let ((_let_75 (not _let_17))) (let ((_let_76 (or _let_75 _let_63 _let_28))) (let ((_let_77 (forall ((U $$unsorted) (BOUND_VARIABLE_4818 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4818)) (= (tptp.cons BOUND_VARIABLE_4818 U) (tptp.app (tptp.cons BOUND_VARIABLE_4818 tptp.nil) U)))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (_let_77))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 2)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_70)) :args ((or _let_62 _let_66))) _let_72 :args (_let_62 true _let_66)))) (let ((_let_81 (ASSUME :args (_let_17)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_63 _let_28 (not _let_76)))) _let_81 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4818 U)))) :args _let_79)) _let_78 :args (_let_76 false _let_77)) :args (_let_28 false _let_17 false _let_62 false _let_76)))) (let ((_let_83 (or _let_59 _let_63 _let_31))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 5)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_58))) :args _let_70)) :args ((or _let_58 _let_66))) _let_72 :args (_let_58 true _let_66)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_63 _let_59 _let_31 (not _let_83)))) _let_80 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.ssList U) false)) (not (= (tptp.ssItem BOUND_VARIABLE_4818) false))))) :args _let_79)) _let_78 :args (_let_83 false _let_77)) :args (_let_31 false _let_62 false _let_58 false _let_83)))) (let ((_let_86 (tptp.ssList _let_21))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.ssList _let_23))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 _let_87 _let_59 _let_32))) (let ((_let_91 (forall ((U $$unsorted) (BOUND_VARIABLE_4862 $$unsorted) (BOUND_VARIABLE_4860 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4860)) (not (tptp.ssList BOUND_VARIABLE_4862)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4860) BOUND_VARIABLE_4862) (tptp.app U (tptp.app BOUND_VARIABLE_4860 BOUND_VARIABLE_4862))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (or _let_75 _let_63 _let_86))) (let ((_let_94 (forall ((U $$unsorted) (BOUND_VARIABLE_3330 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3330)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3330 U)))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (_let_94))) (let ((_let_97 ((tptp.cons BOUND_VARIABLE_3330 U)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_75 _let_63 _let_86 (not _let_93)))) _let_81 _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_93 false _let_94)) :args (_let_86 false _let_17 false _let_62 false _let_93)))) (let ((_let_99 (tptp.ssList _let_22))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_61 _let_100 _let_88))) (let ((_let_102 (forall ((U $$unsorted) (BOUND_VARIABLE_3588 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3588)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3588)))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (_let_102))) (let ((_let_105 ((tptp.app U BOUND_VARIABLE_3588)))) (let ((_let_106 (or _let_75 _let_65 _let_99))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 1)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_70)) :args ((or _let_64 _let_66))) _let_72 :args (_let_64 true _let_66)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_75 _let_65 _let_99 (not _let_106)))) _let_81 _let_107 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_106 false _let_94)) :args (_let_99 false _let_17 false _let_64 false _let_106)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 4)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_70)) :args ((or _let_60 _let_66))) _let_72 :args (_let_60 true _let_66)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_61 _let_100 _let_88 (not _let_101)))) _let_109 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_105)) :args _let_104)) _let_103 :args (_let_101 false _let_102)) :args (_let_88 false _let_60 false _let_99 false _let_101)))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_59 _let_89 _let_87 _let_32 (not _let_90)))) _let_84 _let_110 _let_98 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 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_let_164 :args (_let_38 true _let_154)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_145)) :args ((or _let_75 _let_54 _let_36 (not _let_145)))) _let_81 _let_144 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_147 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3566 U)))) :args _let_148)) _let_147 :args (_let_145 false _let_146)) :args (_let_36 false _let_17 false _let_53 false _let_145)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_140)) :args ((or _let_75 _let_54 _let_35 (not _let_140)))) _let_81 _let_144 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_142 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3536 U)))) :args _let_143)) _let_142 :args (_let_140 false _let_141)) :args (_let_35 false _let_17 false _let_53 false _let_140)) _let_139 _let_111 _let_85 _let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_27 (not _let_46)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_27 false _let_44 false _let_46)) :args (false true _let_43 false _let_42 false _let_41 false _let_40 false _let_39 false _let_38 false _let_36 false _let_35 false _let_34 false _let_32 false _let_31 false _let_28 false _let_27)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (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))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$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) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$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) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$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) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP U) (forall ((V $$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) (tptp.lt V W))))))))))))))) _let_20 _let_19 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_18 _let_17 _let_16 (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))))))))))) _let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) _let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_13 _let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_11 (forall ((U $$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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$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)))))) _let_10 _let_9 _let_8 (not (tptp.singletonP tptp.nil)) (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)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) _let_7 (tptp.duplicatefreeP tptp.nil) _let_6 (tptp.equalelemsP tptp.nil) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) _let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_4 _let_3 _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.41/28.72 )
% 28.41/28.72 % SZS output end Proof for SWC188+1
% 28.41/28.72 % cvc5---1.0.5 exiting
% 28.55/28.72 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------