TSTP Solution File: SWC162+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC162+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 20:23:42 EDT 2023
% Result : Theorem 44.96s 45.27s
% Output : Proof 44.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC162+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 17:51:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.49 %----Proving TF0_NAR, FOF, or CNF
% 44.96/45.27 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.amfgyzNegB/cvc5---1.0.5_2106.p...
% 44.96/45.27 ------- get file name : TPTP file name is SWC162+1
% 44.96/45.27 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2106.smt2...
% 44.96/45.27 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 44.96/45.27 --- Run --no-e-matching --full-saturate-quant at 5...
% 44.96/45.27 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 44.96/45.27 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 44.96/45.27 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 44.96/45.27 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 44.96/45.27 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 44.96/45.27 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 44.96/45.27 % SZS status Theorem for SWC162+1
% 44.96/45.27 % SZS output start Proof for SWC162+1
% 44.96/45.27 (
% 44.96/45.27 (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)) (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 $$unsorted)) (=> (tptp.ssList X3) (or (not (= (tptp.app (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) X2) (tptp.cons Z tptp.nil)) X3) U)) (not (tptp.leq Z Y)) (and (forall ((X4 $$unsorted)) (=> (tptp.ssItem X4) (or (not (tptp.memberP X2 X4)) (and (tptp.leq Y X4) (tptp.leq X4 Z))))) (tptp.leq Y Z))))))))))))) (and (not (tptp.singletonP W)) (tptp.neq X tptp.nil)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_4 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_8 (forall ((U $$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)))))))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_11 (forall ((U $$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_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.hd (tptp.cons V U)) V))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_16 (tptp.ssList tptp.nil))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_18 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_19 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))))) (let ((_let_20 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))))) (let ((_let_21 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_22 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 tptp.nil))) (let ((_let_23 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_24 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.nil))) (let ((_let_25 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_24))) (let ((_let_26 (tptp.app _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (tptp.app _let_26 _let_23))) (let ((_let_28 (tptp.app _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (= _let_28 _let_22))) (let ((_let_30 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 (tptp.hd _let_22)))) (let ((_let_31 (tptp.strictorderP _let_28))) (let ((_let_32 (tptp.hd _let_28))) (let ((_let_33 (tptp.cons _let_32 tptp.nil))) (let ((_let_34 (tptp.strictorderP _let_33))) (let ((_let_35 (not _let_29))) (let ((_let_36 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35))) (let ((_let_39 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) (tptp.app (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (not _let_39))) (let ((_let_42 (tptp.singletonP _let_28))) (let ((_let_43 (= _let_42 _let_41))) (let ((_let_44 (tptp.ssList _let_28))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43))) (let ((_let_47 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.nil))) (let ((_let_50 (not _let_42))) (let ((_let_51 (and _let_50 _let_49))) (let ((_let_52 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_28))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_59 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_66 (not _let_65))) (let ((_let_67 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_45 _let_68 _let_66 _let_64 _let_62 _let_60 (and (or (not (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (and (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) _let_58) _let_57 _let_55 _let_53 _let_51))) (let ((_let_70 (forall ((BOUND_VARIABLE_5478 $$unsorted) (BOUND_VARIABLE_5476 $$unsorted) (BOUND_VARIABLE_5474 $$unsorted) (BOUND_VARIABLE_5511 $$unsorted) (BOUND_VARIABLE_5472 $$unsorted) (BOUND_VARIABLE_5470 $$unsorted) (BOUND_VARIABLE_5468 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5470 (tptp.cons BOUND_VARIABLE_5468 tptp.nil)) BOUND_VARIABLE_5476) (tptp.cons BOUND_VARIABLE_5478 tptp.nil)) BOUND_VARIABLE_5474))) (or (not (tptp.ssList _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5468)) (not (tptp.ssItem BOUND_VARIABLE_5478)) (not (tptp.leq BOUND_VARIABLE_5478 BOUND_VARIABLE_5468)) (not (tptp.ssList BOUND_VARIABLE_5470)) (not (tptp.ssList BOUND_VARIABLE_5476)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5472)) (not (tptp.memberP BOUND_VARIABLE_5476 BOUND_VARIABLE_5472)) (and (tptp.leq BOUND_VARIABLE_5468 BOUND_VARIABLE_5472) (tptp.leq BOUND_VARIABLE_5472 BOUND_VARIABLE_5478))) (tptp.leq BOUND_VARIABLE_5468 BOUND_VARIABLE_5478)) (not (tptp.ssList BOUND_VARIABLE_5474)) (not (tptp.ssList BOUND_VARIABLE_5511)) (not (tptp.segmentP BOUND_VARIABLE_5511 _let_1)) (and (not (tptp.singletonP _let_1)) (tptp.neq BOUND_VARIABLE_5511 tptp.nil))))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (or))) (let ((_let_74 (not _let_70))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_72) :args (_let_74))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_70))) (REFL :args (_let_71)) :args _let_73)) _let_72 :args (_let_71 true _let_70)))) (let ((_let_76 (REFL :args (_let_69)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_73)) :args ((or _let_44 _let_69))) _let_75 :args (_let_44 true _let_69)))) (let ((_let_78 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_79 (not _let_78))) (let ((_let_80 (= _let_49 _let_79))) (let ((_let_81 (not _let_16))) (let ((_let_82 (or _let_55 _let_81 _let_80))) (let ((_let_83 (forall ((U $$unsorted) (BOUND_VARIABLE_3307 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3307)) (= (tptp.neq U BOUND_VARIABLE_3307) (not (= U BOUND_VARIABLE_3307))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 8)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_73)) :args ((or _let_54 _let_69))) _let_75 :args (_let_54 true _let_69)))) (let ((_let_86 (ASSUME :args (_let_16)))) (let ((_let_87 (tptp.segmentP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_88 (= _let_78 _let_87))) (let ((_let_89 (or _let_55 _let_88))) (let ((_let_90 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_90))) (let ((_let_93 ((not (= (tptp.ssList U) false))))) (let ((_let_94 (tptp.segmentP tptp.nil _let_28))) (let ((_let_95 (not _let_87))) (let ((_let_96 (or _let_81 _let_55 _let_95 _let_45 _let_53 _let_94))) (let ((_let_97 (forall ((U $$unsorted) (BOUND_VARIABLE_4370 $$unsorted) (BOUND_VARIABLE_4368 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4368)) (not (tptp.segmentP U BOUND_VARIABLE_4368)) (not (tptp.ssList BOUND_VARIABLE_4370)) (not (tptp.segmentP BOUND_VARIABLE_4368 BOUND_VARIABLE_4370)) (tptp.segmentP U BOUND_VARIABLE_4370))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (= tptp.nil _let_28))) (let ((_let_100 (= _let_99 _let_94))) (let ((_let_101 (not _let_94))) (let ((_let_102 (or _let_45 _let_100))) (let ((_let_103 (= tptp.nil _let_27))) (let ((_let_104 (and (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_103))) (let ((_let_105 (= _let_99 _let_104))) (let ((_let_106 (not _let_99))) (let ((_let_107 (tptp.ssList _let_27))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_108 _let_57 _let_105))) (let ((_let_110 (forall ((U $$unsorted) (BOUND_VARIABLE_4888 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4888)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4888)) (and (= tptp.nil BOUND_VARIABLE_4888) (= tptp.nil U))))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (_let_110))) (let ((_let_113 ((tptp.app U BOUND_VARIABLE_4888)))) (let ((_let_114 (tptp.ssList _let_23))) (let ((_let_115 (not _let_114))) (let ((_let_116 (tptp.ssList _let_26))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_117 _let_115 _let_107))) (let ((_let_119 (forall ((U $$unsorted) (BOUND_VARIABLE_3588 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3588)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3588)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (_let_119))) (let ((_let_122 ((tptp.app U BOUND_VARIABLE_3588)))) (let ((_let_123 (or _let_81 _let_66 _let_114))) (let ((_let_124 (forall ((U $$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_125 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (_let_124))) (let ((_let_127 ((tptp.cons BOUND_VARIABLE_3330 U)))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 2)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_73)) :args ((or _let_65 _let_69))) _let_75 :args (_let_65 true _let_69)))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_81 _let_66 _let_114 (not _let_123)))) _let_86 _let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_127)) :args _let_126)) _let_125 :args (_let_123 false _let_124)) :args (_let_114 false _let_16 false _let_65 false _let_123)))) (let ((_let_130 (tptp.ssList _let_25))) (let ((_let_131 (not _let_130))) (let ((_let_132 (or _let_131 _let_60 _let_116))) (let ((_let_133 (tptp.ssList _let_24))) (let ((_let_134 (not _let_133))) (let ((_let_135 (or _let_62 _let_134 _let_130))) (let ((_let_136 (or _let_81 _let_68 _let_133))) (let ((_let_137 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_73)) :args ((or _let_67 _let_69))) _let_75 :args (_let_67 true _let_69)))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_81 _let_68 _let_133 (not _let_136)))) _let_86 _let_137 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_127)) :args _let_126)) _let_125 :args (_let_136 false _let_124)) 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(_let_173 false _let_188 false _let_187 false _let_186 false _let_185 false _let_184 false _let_183 false _let_180)) :args (_let_177 false _let_67 false _let_61 false _let_59 false _let_56 true _let_175 false _let_173)) :args ((not _let_166) true _let_176)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_169)) :args ((or _let_45 _let_167 (not _let_169)))) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_171 :args (_let_28 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_170)))) _let_171 :args (_let_169 false _let_170)) :args (_let_167 false _let_44 false _let_169)) :args (_let_168 true _let_166 false _let_167)) _let_165 _let_161 :args (false false _let_34 true _let_31 false _let_30 false _let_29)) :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 $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))) _let_21 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) _let_20 _let_19 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))) (forall ((U $$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_18 _let_17 _let_16 _let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_14 _let_13 (forall ((U $$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))))) _let_12 _let_11 _let_10 _let_9 (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (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)))) _let_8 (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))) _let_7 (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) _let_6 (tptp.strictorderP tptp.nil) _let_5 (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 _let_3 (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) _let_2 (forall ((U $$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)))))))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 44.96/45.27 )
% 44.96/45.27 % SZS output end Proof for SWC162+1
% 44.96/45.27 % cvc5---1.0.5 exiting
% 44.96/45.27 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------