TSTP Solution File: SWC200+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 20:23:58 EDT 2023
% Result : Theorem 33.72s 33.90s
% Output : Proof 33.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.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 17:54:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 33.72/33.90 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.vk9lbaJc2o/cvc5---1.0.5_9701.p...
% 33.72/33.90 ------- get file name : TPTP file name is SWC200+1
% 33.72/33.90 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9701.smt2...
% 33.72/33.90 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 33.72/33.90 --- Run --no-e-matching --full-saturate-quant at 5...
% 33.72/33.90 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 33.72/33.90 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 33.72/33.90 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 33.72/33.90 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 33.72/33.90 % SZS status Theorem for SWC200+1
% 33.72/33.90 % SZS output start Proof for SWC200+1
% 33.72/33.90 (
% 33.72/33.90 (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.singletonP W)) (exists ((Y $$unsorted)) (and (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (or (not (tptp.memberP U Z)) (= Y Z)))))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_3 (tptp.singletonP tptp.nil))) (let ((_let_4 (not _let_3))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_11 (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))))) (let ((_let_12 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (= _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_14 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (tptp.memberP _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_16 (or _let_13 _let_15))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_18 (= _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_19 (not _let_13))) (let ((_let_20 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_17))) (let ((_let_25 (not _let_17))) (let ((_let_26 (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Z)) (= Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_27 (not _let_24))) (let ((_let_28 (not _let_26))) (let ((_let_29 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28))) (let ((_let_32 (forall ((Y $$unsorted)) (or (not (tptp.ssItem Y)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Z)) (= Y Z)))))))) (let ((_let_33 (tptp.singletonP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_34 (not _let_33))) (let ((_let_35 (not _let_32))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_34))) (let ((_let_39 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssItem Y)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.memberP U Z)) (= Y Z))))))) (not (tptp.singletonP U)))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (or))) (let ((_let_42 (not _let_39))) (let ((_let_43 (_let_42))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_43)) :args _let_43)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_39))) (REFL :args (_let_40)) :args _let_41)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_40 true _let_39)))) (let ((_let_45 (REFL :args (_let_38)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_32))) :args _let_41)) :args ((or _let_32 _let_38))) _let_44 :args (_let_32 true _let_38)))) (let ((_let_47 (_let_32))) (let ((_let_48 ((not (= (tptp.ssItem Y) false))))) (let ((_let_49 (ASSUME :args _let_47))) (let ((_let_50 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_30 _let_51 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_53 (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Z)) (= Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (not _let_53))) (let ((_let_56 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55))) (let ((_let_59 (or _let_57 (not (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_60 (forall ((U $$unsorted) (BOUND_VARIABLE_2101 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_2101)) (= U BOUND_VARIABLE_2101))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (not _let_60))) (let ((_let_64 (_let_55))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64) (REWRITE :args ((=> _let_55 (not (or _let_30 _let_51 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_53))) (REFL :args (_let_54)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_55 (not _let_58)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_41)) :args ((or _let_56 _let_59))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_63))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_60))) (REFL :args (_let_61)) :args _let_41)) _let_62 :args (_let_61 true _let_60)) :args (_let_56 true _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47))) _let_46 :args (_let_58 false _let_32)) :args (_let_55 false _let_56 false _let_58)) :args (_let_54 true _let_53)))) (let ((_let_66 (REFL :args (_let_52)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_41)) :args ((or _let_29 _let_52))) _let_65 :args (_let_29 true _let_52)))) (let ((_let_68 (_let_28))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_68)) :args _let_68) (REWRITE :args ((=> _let_28 (not (or _let_23 _let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_26))) (REFL :args (_let_27)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 (not _let_31)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47))) _let_46 :args (_let_31 false _let_32)) :args (_let_28 false _let_29 false _let_31)) :args (_let_27 true _let_26)))) (let ((_let_70 (tptp.memberP _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_71 (or _let_18 _let_70))) (let ((_let_72 (tptp.cons _let_12 _let_14))) (let ((_let_73 (tptp.memberP _let_72 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_74 (= _let_73 _let_71))) (let ((_let_75 (tptp.ssList _let_14))) (let ((_let_76 (not _let_75))) (let ((_let_77 (tptp.ssItem _let_12))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_30 _let_78 _let_76 _let_74))) (let ((_let_80 (forall ((U $$unsorted) (BOUND_VARIABLE_3905 $$unsorted) (BOUND_VARIABLE_3903 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_3903)) (not (tptp.ssList BOUND_VARIABLE_3905)) (= (tptp.memberP (tptp.cons BOUND_VARIABLE_3903 BOUND_VARIABLE_3905) U) (or (= U BOUND_VARIABLE_3903) (tptp.memberP BOUND_VARIABLE_3905 U))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.memberP (tptp.cons BOUND_VARIABLE_3903 BOUND_VARIABLE_3905) U)))) (let ((_let_84 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.nil))) (let ((_let_85 (= tptp.nil (tptp.tl _let_84)))) (let ((_let_86 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_84))) (let ((_let_87 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_88 (not _let_87))) (let ((_let_89 (not _let_9))) (let ((_let_90 (or _let_89 _let_88 _let_85))) (let ((_let_91 (forall ((U $$unsorted) (BOUND_VARIABLE_3527 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3527)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3527 U))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (not _let_86))) (let ((_let_94 (or _let_88 _let_93))) (let ((_let_95 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_96 (not _let_94))) (let ((_let_97 (not _let_95))) (let ((_let_98 (= _let_33 _let_97))) (let ((_let_99 (or _let_37 _let_98))) (let ((_let_100 (forall ((U $$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_101 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_41)) :args ((or _let_36 _let_38))) _let_44 :args (_let_36 true _let_38)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_41)) :args ((or _let_33 _let_38))) _let_44 :args (_let_33 true _let_38)))) (let ((_let_104 (_let_97))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_104)) :args _let_104) (REWRITE :args ((=> _let_97 (not (or _let_88 (not (= _let_84 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_97) _let_95))) (REFL :args (_let_96)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_98)) :args ((or _let_34 _let_97 (not _let_98)))) _let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_37 _let_98 (not _let_99)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_100)))) _let_101 :args (_let_99 false _let_100)) :args (_let_98 false _let_36 false _let_99)) :args (_let_97 false _let_33 false _let_98)) :args (_let_96 true _let_95)))) (let ((_let_106 (REFL :args (_let_94)))) (let ((_let_107 (ASSUME :args (_let_9)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_89 _let_88 _let_85 (not _let_90)))) _let_107 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_94 0)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_87))) :args _let_41)) :args ((or _let_87 _let_94))) _let_105 :args (_let_87 true _let_94)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_85 false _let_9 false _let_87 false _let_90)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_94 1)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_86))) :args _let_41)) :args ((or _let_86 _let_94))) _let_105 :args (_let_86 true _let_94)))) (let ((_let_110 (and _let_9 _let_86 _let_85))) (let ((_let_111 (ASSUME :args (_let_85)))) (let ((_let_112 (ASSUME :args (_let_86)))) (let ((_let_113 (TRANS (CONG (SYMM (SYMM _let_112)) :args (APPLY_UF tptp.tl)) (SYMM _let_111)))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_110)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_107 _let_111 _let_112) (SCOPE (TRUE_ELIM (TRANS (CONG _let_113 :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_107))) :args (_let_9 _let_85 _let_86))) :args (_let_9 _let_86 _let_85))) :args (true _let_110)) _let_107 _let_109 _let_108 :args (_let_75 false _let_9 false _let_86 false _let_85)))) (let ((_let_115 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_116 (or _let_37 _let_115 _let_77))) (let ((_let_117 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (not _let_115))) (let ((_let_120 (ASSUME :args (_let_4)))) (let ((_let_121 (ASSUME :args (_let_33)))) (let ((_let_122 (ASSUME :args (_let_115)))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_121 _let_122 _let_120) :args (_let_4 _let_33 _let_115)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_120)) (CONG (SYMM (SYMM _let_122)) :args (APPLY_UF tptp.singletonP)) (TRUE_INTRO _let_121))) :args (_let_33 _let_115 _let_4)) :args ((not (and _let_4 _let_33 _let_115)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_4) _let_3))) (REFL :args (_let_34)) (REFL :args (_let_119)) :args _let_41)) _let_103 _let_120 :args (_let_119 false _let_33 true _let_3)))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_116)) :args ((or _let_37 _let_115 _let_77 (not _let_116)))) _let_102 _let_123 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_117))) _let_118 :args (_let_116 false _let_117)) :args (_let_77 false _let_36 true _let_115 false _let_116)))) (let ((_let_125 (= 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U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) 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U) (tptp.lt V W))))))))))))))) (forall ((U $$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))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))) _let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (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 $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_8 (forall ((U $$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))))) _let_7 (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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) _let_6 _let_5 _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$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))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 33.72/33.90 )
% 33.72/33.90 % SZS output end Proof for SWC200+1
% 33.72/33.90 % cvc5---1.0.5 exiting
% 33.72/33.91 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------