TSTP Solution File: SWC083+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC083+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 20:23:06 EDT 2023
% Result : Theorem 26.70s 26.96s
% Output : Proof 26.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC083+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 17:19:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 26.70/26.96 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.9B2YXfy16y/cvc5---1.0.5_24046.p...
% 26.70/26.96 ------- get file name : TPTP file name is SWC083+1
% 26.70/26.96 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24046.smt2...
% 26.70/26.96 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.70/26.96 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.70/26.96 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.70/26.96 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.70/26.96 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.70/26.96 % SZS status Theorem for SWC083+1
% 26.70/26.96 % SZS output start Proof for SWC083+1
% 26.70/26.96 (
% 26.70/26.96 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (or (not (tptp.ssList X2)) (not (= (tptp.app (tptp.app Z X1) X2) W)) (not (= (tptp.app Z X2) X))))))))))))))))))) (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 $$unsorted)) (=> (tptp.ssList V) (forall ((W $$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.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.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_10 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_12 (tptp.app _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.segmentP _let_12 _let_10))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_15 (tptp.app tptp.nil _let_10))) (let ((_let_16 (= _let_10 _let_15))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil)))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_19 (= _let_12 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_20 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (tptp.segmentP (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_10))) (let ((_let_22 (not _let_13))) (let ((_let_23 (tptp.segmentP _let_10 _let_10))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.neq _let_10 tptp.nil))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.ssList _let_10))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_24 _let_22))) (let ((_let_30 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) Y)) (not (tptp.segmentP (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) Y)))))) (let ((_let_31 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_36 (not _let_35))) (let ((_let_37 (not _let_30))) (let ((_let_38 (tptp.ssList _let_12))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_28 _let_26 _let_37 _let_36 _let_34 _let_32))) (let ((_let_41 (forall ((BOUND_VARIABLE_5433 $$unsorted) (BOUND_VARIABLE_5431 $$unsorted) (BOUND_VARIABLE_5429 $$unsorted)) (let ((_let_1 (tptp.app BOUND_VARIABLE_5433 BOUND_VARIABLE_5431))) (or (not (tptp.ssList (tptp.app (tptp.app BOUND_VARIABLE_5433 BOUND_VARIABLE_5429) BOUND_VARIABLE_5431))) (not (tptp.ssList _let_1)) (not (tptp.neq _let_1 tptp.nil)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP (tptp.app BOUND_VARIABLE_5433 BOUND_VARIABLE_5431) Y)) (not (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_5433 BOUND_VARIABLE_5429) BOUND_VARIABLE_5431) Y))))) (not (tptp.ssList BOUND_VARIABLE_5433)) (not (tptp.ssList BOUND_VARIABLE_5431)) (not (tptp.ssList BOUND_VARIABLE_5429))))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (REFL :args (_let_40)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 3)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_30))) :args _let_44)) :args ((or _let_30 _let_40))) _let_46 :args (_let_30 true _let_40)))) (let ((_let_49 (_let_30))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (or _let_28 _let_23))) (let ((_let_52 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_44)) :args ((or _let_27 _let_40))) _let_46 :args (_let_27 true _let_40)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_28 _let_23 (not _let_51)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (_let_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_54)) _let_53 :args (_let_51 false _let_52)) :args (_let_23 false _let_27 false _let_51)))) (let ((_let_57 (or _let_36 _let_14))) (let ((_let_58 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (_let_58))) (let ((_let_61 ((not (= (tptp.ssList U) false))))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 4)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_44)) :args ((or _let_35 _let_40))) _let_46 :args (_let_35 true _let_40)))) (let ((_let_63 (or _let_28 _let_16))) (let ((_let_64 (or _let_36 _let_17))) (let ((_let_65 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 ((not (= (tptp.ssList U) false))))) (let ((_let_69 (or _let_32 _let_18))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 6)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_44)) :args ((or _let_31 _let_40))) _let_46 :args (_let_31 true _let_40)))) (let ((_let_71 (or _let_36 _let_32 _let_34 _let_19))) (let ((_let_72 (forall ((U $$unsorted) (BOUND_VARIABLE_4840 $$unsorted) (BOUND_VARIABLE_4838 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4838)) (not (tptp.ssList BOUND_VARIABLE_4840)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4838) BOUND_VARIABLE_4840) (tptp.app U (tptp.app BOUND_VARIABLE_4838 BOUND_VARIABLE_4840))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 5)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_44)) :args ((or _let_33 _let_40))) _let_46 :args (_let_33 true _let_40)))) (let ((_let_75 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_76 (not _let_20))) (let ((_let_77 (= _let_76 _let_75))) (let ((_let_78 (not _let_8))) (let ((_let_79 (or _let_34 _let_78 _let_77))) (let ((_let_80 (forall ((U $$unsorted) (BOUND_VARIABLE_3285 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3285)) (= (tptp.neq U BOUND_VARIABLE_3285) (not (= U BOUND_VARIABLE_3285))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (ASSUME :args (_let_8)))) (let ((_let_83 (tptp.segmentP _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.segmentP _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_86 (not _let_85))) (let ((_let_87 (not _let_75))) (let ((_let_88 (or _let_34 _let_87 _let_86 _let_84))) (let ((_let_89 (tptp.app _let_12 tptp.nil))) (let ((_let_90 (tptp.segmentP _let_89 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_91 (= _let_12 _let_89))) (let ((_let_92 (tptp.ssList _let_11))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_34 _let_34 _let_95 _let_93 _let_78 _let_90))) (let ((_let_97 (forall ((U $$unsorted) (BOUND_VARIABLE_4459 $$unsorted) (BOUND_VARIABLE_4457 $$unsorted) (BOUND_VARIABLE_4455 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4455)) (not (tptp.segmentP U BOUND_VARIABLE_4455)) (not (tptp.ssList BOUND_VARIABLE_4459)) (not (tptp.ssList BOUND_VARIABLE_4457)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4459 U) BOUND_VARIABLE_4457) BOUND_VARIABLE_4455))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (_let_97))) (let ((_let_100 (or _let_34 _let_94))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_34 _let_94 (not _let_100)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args _let_54)) _let_53 :args (_let_100 false _let_52)) :args (_let_94 false _let_33 false _let_100)))) (let ((_let_102 (or _let_36 _let_32 _let_92))) (let ((_let_103 (forall ((U $$unsorted) (BOUND_VARIABLE_3566 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3566)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3566)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (or _let_39 _let_91))) (let ((_let_106 (and _let_91 _let_90))) (let ((_let_107 (ASSUME :args (_let_90)))) (let ((_let_108 (APPLY_UF tptp.segmentP))) (let ((_let_109 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_110 (ASSUME :args (_let_91)))) (let ((_let_111 (tptp.app _let_10 tptp.nil))) (let ((_let_112 (tptp.segmentP _let_111 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_113 (= _let_10 _let_111))) (let ((_let_114 (or _let_34 _let_34 _let_95 _let_36 _let_78 _let_112))) (let ((_let_115 (or _let_28 _let_113))) (let ((_let_116 (and _let_113 _let_112))) (let ((_let_117 (ASSUME :args (_let_112)))) (let ((_let_118 (ASSUME :args (_let_113)))) (let ((_let_119 (not _let_77))) (let ((_let_120 (or _let_28 _let_28 _let_24 _let_78 _let_32 _let_21))) (let ((_let_121 (ASSUME :args (_let_21)))) (let ((_let_122 (APPLY_UF tptp.app))) (let ((_let_123 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_124 (ASSUME :args (_let_16)))) (let ((_let_125 (ASSUME :args (_let_14)))) (let ((_let_126 (ASSUME :args (_let_20)))) (let ((_let_127 (SYMM _let_126))) (let ((_let_128 (ASSUME :args (_let_17)))) (let ((_let_129 (ASSUME :args (_let_18)))) (let ((_let_130 (ASSUME :args (_let_19)))) (let ((_let_131 (ASSUME :args (_let_22)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_121 _let_124 _let_125 _let_126 _let_128 _let_129 _let_130 _let_131) :args (_let_20 _let_22 _let_14 _let_16 _let_17 _let_18 _let_19 _let_21)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_131)) (CONG (TRANS (SYMM (SYMM _let_130)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (TRANS (CONG _let_123 _let_127 :args _let_122) (SYMM _let_129)) :args _let_122) (CONG (TRANS (TRANS (SYMM (SYMM _let_128)) (CONG _let_125 (SYMM _let_127) :args _let_122) (CONG (SYMM _let_125) _let_109 :args _let_122)) (SYMM (SYMM _let_124))) _let_123 :args _let_122)) (REFL :args (_let_10)) 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(REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_77)) (CONG (REFL :args (_let_119)) (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_20))) (REFL :args (_let_75)) :args _let_44)) :args ((or _let_20 _let_75 _let_119))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_34 _let_86 _let_87 _let_84 (not _let_88)))) _let_74 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_116)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_117 _let_118) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_118)) _let_109 :args _let_108) (TRUE_INTRO _let_117))) :args (_let_112 _let_113))) :args (_let_113 _let_112))) :args (true _let_116)) :args ((or _let_85 (not _let_113) (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_28 _let_113 (not _let_115)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_67)) 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(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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) _let_3 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.70/26.96 )
% 26.70/26.96 % SZS output end Proof for SWC083+1
% 26.70/26.96 % cvc5---1.0.5 exiting
% 26.70/26.97 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------