TSTP Solution File: SWC302+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC302+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 20:24:36 EDT 2023
% Result : Theorem 42.76s 43.13s
% Output : Proof 42.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC302+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n015.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
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 15:12:40 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 42.76/43.13 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qY9dwP38EX/cvc5---1.0.5_16320.p...
% 42.76/43.13 ------- get file name : TPTP file name is SWC302+1
% 42.76/43.13 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16320.smt2...
% 42.76/43.13 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 42.76/43.13 --- Run --no-e-matching --full-saturate-quant at 5...
% 42.76/43.13 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 42.76/43.13 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 42.76/43.13 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 42.76/43.13 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 42.76/43.13 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 42.76/43.13 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 42.76/43.13 % SZS status Theorem for SWC302+1
% 42.76/43.13 % SZS output start Proof for SWC302+1
% 42.76/43.13 (
% 42.76/43.13 (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.segmentP X W)) (not (tptp.totalorderedP 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) (forall ((X3 $$unsorted)) (=> (tptp.ssList X3) (or (not (= (tptp.app (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) X2) (tptp.cons Z tptp.nil)) X3) U)) (not (tptp.lt Z Y))))))))))))))))))))))))) (let ((_let_2 (forall ((U $$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)))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))))) (let ((_let_4 (forall ((U $$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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_6 (forall ((U $$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_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.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_10 (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))))))))))))))))) (let ((_let_11 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11))) (let ((_let_13 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_13))) (let ((_let_15 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_16 (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_15))) (let ((_let_18 (tptp.app _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (= _let_18 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_16)))) (let ((_let_20 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_21 (tptp.app _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_22 (tptp.app (tptp.app _let_18 _let_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (= _let_22 (tptp.app _let_18 _let_21)))) (let ((_let_24 (= _let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_11)))) (let ((_let_25 (= _let_21 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13)))) (let ((_let_26 (= _let_22 (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_27 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_12))) (let ((_let_30 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_30))) (let ((_let_33 ((not (= (tptp.ssList U) false))))) (let ((_let_34 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.totalorderedP _let_22))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.ssList _let_22))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_43 _let_41 _let_39 _let_37 _let_28 _let_35 (not (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))))) (let ((_let_49 (forall ((BOUND_VARIABLE_5432 $$unsorted) (BOUND_VARIABLE_5409 $$unsorted) (BOUND_VARIABLE_5407 $$unsorted) (BOUND_VARIABLE_5405 $$unsorted) (BOUND_VARIABLE_5403 $$unsorted) (BOUND_VARIABLE_5401 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5403 (tptp.cons BOUND_VARIABLE_5401 tptp.nil)) BOUND_VARIABLE_5407) (tptp.cons BOUND_VARIABLE_5409 tptp.nil)) BOUND_VARIABLE_5405))) (or (not (tptp.ssList _let_1)) (not (tptp.totalorderedP _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5401)) (not (tptp.ssItem BOUND_VARIABLE_5409)) (not (tptp.lt BOUND_VARIABLE_5409 BOUND_VARIABLE_5401)) (not (tptp.ssList BOUND_VARIABLE_5403)) (not (tptp.ssList BOUND_VARIABLE_5407)) (not (tptp.ssList BOUND_VARIABLE_5405)) (not (tptp.ssList BOUND_VARIABLE_5432)) (not (tptp.segmentP BOUND_VARIABLE_5432 _let_1))))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 6)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_52)) :args ((or _let_27 _let_48))) _let_54 :args (_let_27 true _let_48)))) (let ((_let_57 (or _let_35 _let_14))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 7)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_52)) :args ((or _let_34 _let_48))) _let_54 :args (_let_34 true _let_48)))) (let ((_let_59 (tptp.ssList _let_15))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_37 _let_60 _let_28 _let_19))) (let ((_let_62 (forall ((U $$unsorted) (BOUND_VARIABLE_4847 $$unsorted) (BOUND_VARIABLE_4845 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4845)) (not (tptp.ssList BOUND_VARIABLE_4847)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4845) BOUND_VARIABLE_4847) (tptp.app U (tptp.app BOUND_VARIABLE_4845 BOUND_VARIABLE_4847))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (_let_62))) (let ((_let_65 ((tptp.app (tptp.app U BOUND_VARIABLE_4845) BOUND_VARIABLE_4847)))) (let ((_let_66 (not _let_8))) (let ((_let_67 (or _let_66 _let_43 _let_59))) (let ((_let_68 (forall ((U $$unsorted) (BOUND_VARIABLE_3315 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3315)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3315 U)))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (_let_68))) (let ((_let_71 ((tptp.cons BOUND_VARIABLE_3315 U)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_52)) :args ((or _let_42 _let_48))) _let_54 :args (_let_42 true _let_48)))) (let ((_let_73 (ASSUME :args (_let_8)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_43 _let_59 (not _let_67)))) _let_73 _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) _let_69 :args (_let_67 false _let_68)) :args (_let_59 false _let_8 false _let_42 false _let_67)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 5)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_52)) :args ((or _let_36 _let_48))) _let_54 :args (_let_36 true _let_48)))) (let ((_let_76 (tptp.ssList _let_20))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.ssList _let_18))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77 _let_35 _let_23))) (let ((_let_81 (or _let_66 _let_41 _let_76))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 3)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_52)) :args ((or _let_40 _let_48))) _let_54 :args (_let_40 true _let_48)))) (let ((_let_83 (tptp.ssList _let_17))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_28 _let_78))) (let ((_let_86 (forall ((U $$unsorted) (BOUND_VARIABLE_3573 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3573)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3573)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (_let_86))) (let ((_let_89 ((tptp.app U BOUND_VARIABLE_3573)))) (let ((_let_90 (or _let_37 _let_60 _let_83))) (let ((_let_91 (or _let_28 _let_66 _let_43 _let_24))) (let ((_let_92 (forall ((U $$unsorted) (BOUND_VARIABLE_3615 $$unsorted) (BOUND_VARIABLE_3613 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3613)) (not (tptp.ssItem BOUND_VARIABLE_3615)) (= (tptp.cons BOUND_VARIABLE_3615 (tptp.app BOUND_VARIABLE_3613 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3615 BOUND_VARIABLE_3613) U)))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_92))) (let ((_let_95 (or _let_35 _let_66 _let_41 _let_25))) (let ((_let_96 (not _let_26))) (let ((_let_97 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_98 (or _let_43 _let_41 _let_97 _let_37 _let_28 _let_35 _let_96))) (let ((_let_99 (forall ((V $$unsorted) (BOUND_VARIABLE_2881 $$unsorted) (BOUND_VARIABLE_2879 $$unsorted) (BOUND_VARIABLE_2877 $$unsorted) (BOUND_VARIABLE_2875 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2875)) (tptp.leq V BOUND_VARIABLE_2875) (not (tptp.ssList BOUND_VARIABLE_2881)) (not (tptp.ssList BOUND_VARIABLE_2877)) (not (tptp.ssList BOUND_VARIABLE_2879)) (not (= (tptp.app (tptp.app BOUND_VARIABLE_2881 (tptp.cons V BOUND_VARIABLE_2877)) (tptp.cons BOUND_VARIABLE_2875 BOUND_VARIABLE_2879)) (tptp.app (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_100 (= _let_44 _let_99))) (let ((_let_101 (or _let_47 _let_100))) (let ((_let_102 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.totalorderedP U) (forall ((V $$unsorted) (BOUND_VARIABLE_2881 $$unsorted) (BOUND_VARIABLE_2879 $$unsorted) (BOUND_VARIABLE_2877 $$unsorted) (BOUND_VARIABLE_2875 $$unsorted)) (or (not (tptp.ssItem V)) (not (tptp.ssItem BOUND_VARIABLE_2875)) (tptp.leq V BOUND_VARIABLE_2875) (not (tptp.ssList BOUND_VARIABLE_2881)) (not (tptp.ssList BOUND_VARIABLE_2877)) (not (tptp.ssList BOUND_VARIABLE_2879)) (not (= U (tptp.app (tptp.app BOUND_VARIABLE_2881 (tptp.cons V BOUND_VARIABLE_2877)) (tptp.cons BOUND_VARIABLE_2875 BOUND_VARIABLE_2879))))))))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (_let_99))) (let ((_let_105 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_106 (not _let_97))) (let ((_let_107 (or _let_43 _let_41 _let_106 _let_43 _let_39 _let_105))) (let ((_let_108 (forall ((U $$unsorted) (BOUND_VARIABLE_5078 $$unsorted) (BOUND_VARIABLE_5076 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_5076)) (not (tptp.leq U BOUND_VARIABLE_5076)) (not (tptp.ssItem BOUND_VARIABLE_5078)) (not (tptp.lt BOUND_VARIABLE_5076 BOUND_VARIABLE_5078)) (tptp.lt U BOUND_VARIABLE_5078))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (not _let_105))) (let ((_let_111 (or _let_43 _let_110))) (let ((_let_112 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.lt U U)))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (ASSUME :args (_let_96)))) (let ((_let_115 (APPLY_UF tptp.app))) (let ((_let_116 (APPLY_UF tptp.cons))) (let ((_let_117 (ASSUME :args (_let_14)))) (let ((_let_118 (ASSUME :args (_let_25)))) (let ((_let_119 (ASSUME :args (_let_12)))) (let ((_let_120 (ASSUME :args (_let_24)))) (let ((_let_121 (ASSUME :args (_let_19)))) (let ((_let_122 (ASSUME :args (_let_23)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_114 (MODUS_PONENS (AND_INTRO _let_119 _let_120 _let_121 _let_117 _let_118 _let_122) (SCOPE (TRANS (SYMM (SYMM _let_122)) (CONG (TRANS (SYMM (SYMM _let_121)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (TRANS (SYMM (SYMM _let_120)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)) (SYMM _let_119) :args _let_116)) :args _let_115)) (TRANS (SYMM (SYMM _let_118)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (SYMM _let_117) :args _let_116)) :args _let_115)) :args (_let_12 _let_24 _let_19 _let_14 _let_25 _let_23)))) :args (_let_12 _let_14 _let_19 _let_23 _let_24 _let_25 _let_96)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_26)))))) (FALSE_INTRO _let_114))) :args (_let_96 _let_26)) :args ((not (and _let_12 _let_14 _let_19 _let_23 _let_24 _let_25 _let_96)) SB_LITERAL))) (CONG (REFL :args ((not _let_12))) (REFL :args ((not _let_14))) (REFL :args ((not _let_19))) (REFL :args ((not _let_23))) (REFL :args ((not _let_24))) (REFL :args ((not _let_25))) (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_26))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or 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(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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$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_4 (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) _let_3 _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 42.76/43.14 )
% 42.76/43.14 % SZS output end Proof for SWC302+1
% 42.76/43.14 % cvc5---1.0.5 exiting
% 42.76/43.14 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------