%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC115+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 20:23:22 EDT 2023

% Result   : Theorem 40.39s 40.69s
% Output   : Proof 40.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWC115+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon Aug 28 15:55:23 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 40.39/40.69  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.3M8rbEw8Cf/cvc5---1.0.5_23914.p...
% 40.39/40.69  ------- get file name : TPTP file name is SWC115+1
% 40.39/40.69  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23914.smt2...
% 40.39/40.69  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 40.39/40.69  --- Run --no-e-matching --full-saturate-quant at 5...
% 40.39/40.69  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 40.39/40.69  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 40.39/40.69  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 40.39/40.69  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 40.39/40.69  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.39/40.69  % SZS status Theorem for SWC115+1
% 40.39/40.69  % SZS output start Proof for SWC115+1
% 40.39/40.69  (
% 40.39/40.69  (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)) (and (= tptp.nil V) (= tptp.nil U)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (or (not (= (tptp.cons Y tptp.nil) W)) (not (tptp.memberP X Y)) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (not (= Y Z)) (tptp.memberP X Z) (tptp.leq Z Y)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (tptp.neq U tptp.nil) (tptp.segmentP V U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_12 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (not _let_12))) (let ((_let_16 (not _let_13))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_19 (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Z)) (not (tptp.leq Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))))) (let ((_let_26 (and _let_25 _let_17))) (let ((_let_27 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_29 (and _let_28 _let_27))) (let ((_let_30 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_14 _let_29 _let_26))) (let ((_let_35 (forall ((U $$unsorted) (BOUND_VARIABLE_5420 $$unsorted) (BOUND_VARIABLE_5418 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (let ((_let_2 (= tptp.nil BOUND_VARIABLE_5418))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5418)) (and _let_2 _let_1) (and (tptp.neq U tptp.nil) (tptp.segmentP BOUND_VARIABLE_5418 U)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5420)) (not (= U (tptp.cons BOUND_VARIABLE_5420 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5418 BOUND_VARIABLE_5420)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z BOUND_VARIABLE_5420) (not (tptp.memberP BOUND_VARIABLE_5418 Z)) (not (tptp.leq Z BOUND_VARIABLE_5420)))))) (or (not _let_2) (not _let_1))))))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (= tptp.nil _let_20))) (let ((_let_42 (not _let_41))) (let ((_let_43 (not _let_8))) (let ((_let_44 (or _let_43 _let_24 _let_42))) (let ((_let_45 (forall ((W $$unsorted) (BOUND_VARIABLE_2149 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2149)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2149)))))))) (let ((_let_46 (not _let_45))) (let ((_let_47 (= _let_18 _let_46))) (let ((_let_48 (or _let_31 _let_24 _let_47))) (let ((_let_49 (= _let_28 _let_15))) (let ((_let_50 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_51 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_50))) (let ((_let_52 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_51))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55 _let_53))) (let ((_let_59 (= _let_50 (tptp.app _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)))) (let ((_let_60 (or _let_55 _let_24 _let_59))) (let ((_let_61 (tptp.ssList _let_50))) (let ((_let_62 (or _let_55 _let_24 _let_61))) (let ((_let_63 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_64 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_65 (tptp.segmentP (tptp.app _let_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_66 (not _let_63))) (let ((_let_67 (or _let_33 _let_33 _let_66 _let_43 _let_55 _let_65))) (let ((_let_68 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_69 (tptp.segmentP (tptp.app _let_51 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_70 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_64))) (let ((_let_71 (tptp.segmentP _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_72 (not _let_71))) (let ((_let_73 (not _let_61))) (let ((_let_74 (or _let_73 _let_33 _let_72 _let_57 _let_43 _let_69))) (let ((_let_75 (REFL :args (_let_25)))) (let ((_let_76 (ASSUME :args (_let_8)))) (let ((_let_77 (forall ((U $$unsorted) (BOUND_VARIABLE_3332 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3332)) (not (= U (tptp.cons BOUND_VARIABLE_3332 U))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (REFL :args (_let_34)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 1)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_38)) :args ((or _let_30 _let_34))) _let_40 :args (_let_30 true _let_34)))) (let ((_let_81 (forall ((U $$unsorted) (BOUND_VARIABLE_2175 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2175)) (= (tptp.memberP U BOUND_VARIABLE_2175) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2149 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2149)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2175 BOUND_VARIABLE_2149)))))))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (and _let_21 _let_42))) (let ((_let_84 (ASSUME :args (_let_42)))) (let ((_let_85 (ASSUME :args (_let_21)))) (let ((_let_86 (SYMM _let_85))) (let ((_let_87 (REFL :args (tptp.nil)))) (let ((_let_88 (or _let_33 _let_43 _let_49))) (let ((_let_89 (forall ((U $$unsorted) (BOUND_VARIABLE_3284 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3284)) (= (tptp.neq U BOUND_VARIABLE_3284) (not (= U BOUND_VARIABLE_3284))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_38)) :args ((or _let_32 _let_34))) _let_40 :args (_let_32 true _let_34)))) (let ((_let_92 (not _let_49))) (let ((_let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_12))))) (let ((_let_94 (_let_46))) (let ((_let_95 (REFL :args (_let_58)))) (let ((_let_96 (forall ((U $$unsorted) (BOUND_VARIABLE_4795 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4795)) (= (tptp.cons BOUND_VARIABLE_4795 U) (tptp.app (tptp.cons BOUND_VARIABLE_4795 tptp.nil) U)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (forall ((U $$unsorted) (BOUND_VARIABLE_3307 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3307)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3307 U)))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (or _let_33 _let_63))) (let ((_let_101 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (forall ((U $$unsorted) (BOUND_VARIABLE_4458 $$unsorted) (BOUND_VARIABLE_4456 $$unsorted) (BOUND_VARIABLE_4454 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4454)) (not (tptp.segmentP U BOUND_VARIABLE_4454)) (not (tptp.ssList BOUND_VARIABLE_4458)) (not (tptp.ssList BOUND_VARIABLE_4456)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4458 U) BOUND_VARIABLE_4456) BOUND_VARIABLE_4454))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (_let_103))) (let ((_let_106 (or _let_31 _let_68))) (let ((_let_107 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (not _let_27))) (let ((_let_110 (and _let_109 _let_68 _let_52))) (let ((_let_111 (_let_109 _let_68 _let_52))) (let ((_let_112 (ASSUME :args (_let_109)))) (let ((_let_113 (APPLY_UF tptp.segmentP))) (let ((_let_114 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_115 (ASSUME :args (_let_68)))) (let ((_let_116 (APPLY_UF tptp.app))) (let ((_let_117 (ASSUME :args (_let_52)))) (let ((_let_118 (or _let_33 _let_70))) (let ((_let_119 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (and _let_21 _let_70 _let_59 _let_65))) (let ((_let_122 (ASSUME :args (_let_65)))) (let ((_let_123 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)))) (let ((_let_124 (ASSUME :args (_let_70)))) (let ((_let_125 (ASSUME :args (_let_59)))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_26)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 4)) _let_40 :args ((not _let_26) true _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_43 _let_33 _let_57 _let_73 _let_72 _let_69 (not _let_74)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4458 U) BOUND_VARIABLE_4456) BOUND_VARIABLE_4454) true))))) :args _let_105)) _let_104 :args (_let_74 false _let_103)) _let_91 _let_76 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_122 _let_124 _let_85 _let_125) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_125)) (CONG _let_86 _let_123 :args _let_116) (CONG (SYMM (SYMM _let_124)) _let_123 :args _let_116)) _let_114 :args _let_113) (TRUE_INTRO _let_122))) :args (_let_65 _let_70 _let_21 _let_59))) :args (_let_21 _let_70 _let_59 _let_65))) :args (true _let_121)) :args ((or _let_22 (not _let_70) _let_71 (not _let_59) (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_33 _let_70 (not _let_118)))) _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_119))) _let_120 :args (_let_118 false _let_119)) :args (_let_70 false _let_32 false _let_118)) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_110)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_112 _let_115 _let_117) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (SYMM _let_117) _let_87 :args _let_116) (SYMM _let_115)) _let_114 :args _let_113) (FALSE_INTRO _let_112))) :args _let_111)) :args _let_111)) :args (true _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_27))) (REFL :args ((not _let_68))) (REFL :args (_let_53)) (REFL :args ((not _let_69))) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_31 _let_68 (not _let_106)))) _let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_68 false _let_30 false _let_106)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_67))) :args ((or _let_43 _let_33 _let_66 _let_55 _let_65 (not _let_67)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_105)) _let_104 :args (_let_67 false _let_103)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_33 _let_63 (not _let_100)))) _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_101))) _let_102 :args (_let_100 false _let_101)) :args (_let_63 false 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(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 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$$unsorted)) (=> (tptp.ssList U) (forall ((V $$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 $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$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_6 (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 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$$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (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)))))))) _let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) _let_2 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 40.50/40.70  )
% 40.50/40.70  % SZS output end Proof for SWC115+1
% 40.50/40.70  % cvc5---1.0.5 exiting
% 40.50/40.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------