TSTP Solution File: SET815+4 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET815+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 14:40:26 EDT 2023
% Result : Theorem 27.43s 27.75s
% Output : Proof 27.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SET815+4 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.11 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 15:21:23 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.43 %----Proving TF0_NAR, FOF, or CNF
% 27.43/27.75 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.r9hfeO2Wli/cvc5---1.0.5_15472.p...
% 27.43/27.75 ------- get file name : TPTP file name is SET815+4
% 27.43/27.75 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15472.smt2...
% 27.43/27.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.43/27.75 --- Run --no-e-matching --full-saturate-quant at 5...
% 27.43/27.75 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.43/27.75 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.43/27.75 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.43/27.75 % SZS status Theorem for SET815+4
% 27.43/27.75 % SZS output start Proof for SET815+4
% 27.43/27.75 (
% 27.43/27.75 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.member A tptp.on) (tptp.equal_set (tptp.sum (tptp.suc A)) A)))))) (let ((_let_2 (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.suc A)) (tptp.member X (tptp.union A (tptp.singleton A))))))) (let ((_let_3 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))))) (let ((_let_5 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))))) (let ((_let_6 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_9 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_11 (_let_5))) (let ((_let_12 (ASSUME :args _let_11))) (let ((_let_13 (or (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_10))) (let ((_let_14 (not _let_10))) (let ((_let_15 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15))) (let ((_let_17 (= _let_16 _let_13))) (let ((_let_18 (not _let_13))) (let ((_let_19 (_let_6))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (tptp.suc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_21))) (let ((_let_23 (= _let_22 _let_16))) (let ((_let_24 (not _let_16))) (let ((_let_25 (_let_2))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 ((tptp.member X (tptp.suc A))))) (let ((_let_28 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_22))) (let ((_let_31 (or _let_30 _let_29))) (let ((_let_32 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.suc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 Y)))))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.sum _let_21))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_34))) (let ((_let_36 (= _let_35 _let_33))) (let ((_let_37 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y A)) (not (tptp.member X Y))))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 ((tptp.member X (tptp.sum A))))) (let ((_let_41 (or _let_29 _let_35))) (let ((_let_42 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.sum (tptp.suc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_34))) (let ((_let_45 (= _let_44 _let_42))) (let ((_let_46 (not _let_42))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (_let_47))) (let ((_let_50 ((tptp.subset A B)))) (let ((_let_51 (tptp.subset _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (and _let_51 _let_44))) (let ((_let_53 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.sum (tptp.suc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_54 (= _let_51 _let_53))) (let ((_let_55 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_56 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_34))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55))) (let ((_let_59 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.suc SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (= _let_56 _let_60))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63))) (let ((_let_67 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_15))) (let ((_let_68 (= _let_64 _let_67))) (let ((_let_69 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_9))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (or _let_70 _let_69))) (let ((_let_72 (= _let_67 _let_71))) (let ((_let_73 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_74 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_75 (= _let_73 _let_74))) (let ((_let_76 (or _let_63 _let_55))) (let ((_let_77 (or))) (let ((_let_78 (_let_60))) (let ((_let_79 (REFL :args (_let_66)))) (let ((_let_80 (not _let_70))) (let ((_let_81 (or _let_80 _let_73))) (let ((_let_82 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_83 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_84 (not _let_83))) (let ((_let_85 (or _let_84 _let_82))) (let ((_let_86 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_87 (= _let_69 _let_86))) (let ((_let_88 (not _let_71))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_75 false _let_47)))) (let ((_let_90 (not _let_75))) (let ((_let_91 (not _let_74))) (let ((_let_92 (_let_75))) (let ((_let_93 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_94 (and (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_93))) (let ((_let_95 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_96 (= _let_95 _let_94))) (let ((_let_97 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.subset X A)))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (tptp.equal_set _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_100 (not _let_95))) (let ((_let_101 (or _let_100 _let_99))) (let ((_let_102 (forall ((A $$unsorted)) (or (not (tptp.member A tptp.on)) (tptp.equal_set (tptp.sum (tptp.suc A)) A))))) (let ((_let_103 (not _let_101))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (not _let_102))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_104) :args (_let_105))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_105) _let_102))) (REFL :args (_let_103)) :args _let_77)) _let_104 :args (_let_103 true _let_102)))) (let ((_let_107 (_let_93))) (let ((_let_108 (_let_91))) (let ((_let_109 (not _let_82))) (let ((_let_110 (ASSUME :args (_let_109)))) (let ((_let_111 (ASSUME :args (_let_86)))) (let ((_let_112 (ASSUME :args (_let_83)))) (let ((_let_113 (_let_74))) (let ((_let_114 (not _let_53))) (let ((_let_115 (_let_114))) (let ((_let_116 (= _let_99 _let_52))) (let ((_let_117 (not _let_52))) (let ((_let_118 (_let_7))) (let ((_let_119 (ASSUME :args _let_118))) (let ((_let_120 (_let_46))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_120)) :args _let_120)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_42))) (REFL :args (_let_43)) :args _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_45)) :args ((or _let_44 _let_46 (not _let_45)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_116)) :args ((or _let_99 _let_117 (not _let_116)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_101 1)) _let_106 :args ((not _let_99) true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (_let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_118)) _let_119 :args (_let_116 false _let_7)) :args (_let_117 true _let_99 false _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_54)) :args ((or _let_51 _let_114 (not _let_54)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_115)) :args _let_115)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_114) _let_53))) (REFL :args ((not _let_58))) :args _let_77)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_113) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_113)) (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_55 _let_63 (not _let_76)))) (REORDERING (CNF_EQUIV_POS1 :args _let_92) :args ((or (not _let_73) _let_74 _let_90))) _let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_110 _let_111 _let_112) :args (_let_83 _let_109 _let_86)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_112)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) (SYMM _let_111) :args (APPLY_UF tptp.member)) (FALSE_INTRO _let_110))) :args (_let_109 _let_86 _let_83)) :args ((not (and _let_83 _let_109 _let_86)) SB_LITERAL))) (CONG (REFL :args (_let_84)) (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_82))) (REFL :args ((not _let_86))) :args _let_77)) (REORDERING (CNF_EQUIV_POS1 :args (_let_87)) :args ((or (not _let_69) _let_86 (not _let_87)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_PROP)) :args _let_11))) _let_12 :args (_let_87 false _let_5)) (CNF_OR_NEG :args (_let_85 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_85 0)) (CONG (REFL :args (_let_85)) (MACRO_SR_PRED_INTRO :args ((= (not _let_84) _let_83))) :args _let_77)) :args ((or _let_83 _let_85))) (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_70 _let_69 _let_88))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_108)) :args _let_108)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_74))) (REFL :args ((not _let_85))) :args _let_77)) (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_73 _let_80 (not _let_81)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_107) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) true))))) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_94 2)) :args ((or _let_93 (not _let_94)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_96)) :args ((or _let_100 _let_94 (not _let_96)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_101 0)) (CONG (REFL :args (_let_101)) (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_95))) :args _let_77)) :args ((or _let_95 _let_101))) _let_106 :args (_let_95 true _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member A tptp.on)))) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_94 false _let_95 false _let_96)) :args (_let_93 false _let_94)) :args (_let_81 false _let_93)) (REORDERING (CNF_EQUIV_POS2 :args _let_92) :args ((or _let_73 _let_91 _let_90))) _let_89 :args ((or _let_73 _let_88) false _let_86 false _let_87 true _let_82 false _let_83 false _let_69 true _let_85 true _let_70 false _let_81 true _let_74 false _let_75)) (REORDERING (CNF_EQUIV_POS1 :args (_let_72)) :args ((or (not _let_67) _let_71 (not _let_72)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING ((tptp.member X (tptp.union A B))))) :args _let_19)) _let_20 :args (_let_72 false _let_6)) (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_65 _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_68 false _let_2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 1)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_77)) :args ((or _let_62 _let_66))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_77)) :args ((or _let_64 _let_66))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_78)) :args _let_78)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) (REFL :args ((not _let_66))) :args _let_77)) (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_57 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21 QUANTIFIERS_INST_E_MATCHING _let_40)) :args _let_39)) _let_38 :args (_let_61 false _let_37)) (CNF_OR_NEG :args (_let_58 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG (REFL :args (_let_58)) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_77)) :args ((or _let_56 _let_58))) :args (_let_58 true _let_76 false _let_74 false _let_75 false _let_73 false _let_71 false _let_72 false _let_67 false _let_68 false _let_62 false _let_64 true _let_66 true _let_59 false _let_61 true _let_55 false _let_56)) :args (_let_53 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_54 false _let_47)) :args (_let_51 false _let_53 false _let_54)) :args ((not _let_44) true _let_52 false _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_45 false _let_47)) :args (_let_46 true _let_44 false _let_45)) :args (_let_43 true _let_42)))) (let ((_let_122 (not _let_36))) (let ((_let_123 (_let_32))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_11))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_13 1)) :args ((or _let_14 _let_13))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_17)) :args ((or _let_16 _let_18 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_23)) :args ((or _let_22 _let_24 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_29 _let_30 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_77)) :args ((or _let_28 _let_41))) _let_121 :args (_let_28 true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_123) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_123)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_36)) (CONG (REFL :args (_let_122)) (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_77)) :args ((or _let_35 _let_32 _let_122))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_41 1)) _let_121 :args ((not _let_35) true _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_21 QUANTIFIERS_INST_E_MATCHING _let_40)) :args _let_39)) _let_38 :args (_let_36 false _let_37)) :args (_let_32 true _let_35 false _let_36)) :args (_let_31 false _let_32)) :args (_let_30 false _let_28 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_23 false _let_2)) :args (_let_24 true _let_22 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_19)) _let_20 :args (_let_17 false _let_6)) :args (_let_18 true _let_16 false _let_17)) :args (_let_14 true _let_13)) _let_12 :args (false true _let_10 false _let_5)) :args (_let_8 _let_7 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) _let_6 (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) _let_5 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) _let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_3 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted)) (=> (and (tptp.subset A E) (exists ((X $$unsorted)) (tptp.member X A))) (exists ((Y $$unsorted)) (tptp.least Y R A))))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (not (and (tptp.apply R X Y) (tptp.apply R Y X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) (forall ((X $$unsorted)) (=> (tptp.set X) (forall ((Y $$unsorted)) (=> (tptp.member Y X) (tptp.set Y))))) (forall ((X $$unsorted) (R $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.initial_segment X R A)) (and (tptp.member Y A) (tptp.apply R Y X)))) _let_2 (forall ((A $$unsorted) (X $$unsorted)) (=> (tptp.member X A) (tptp.subset (tptp.singleton X) A))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.43/27.76 )
% 27.43/27.76 % SZS output end Proof for SET815+4
% 27.43/27.76 % cvc5---1.0.5 exiting
% 27.43/27.76 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------