TSTP Solution File: SEU174+2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 16:29:48 EDT 2023
% Result : Theorem 1.92s 2.20s
% Output : Proof 1.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU174+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 19:12:23 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 1.92/2.20 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZxClPJjjIt/cvc5---1.0.5_19250.p...
% 1.92/2.20 ------- get file name : TPTP file name is SEU174+2
% 1.92/2.20 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19250.smt2...
% 1.92/2.20 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.92/2.20 % SZS status Theorem for SEU174+2
% 1.92/2.20 % SZS output start Proof for SEU174+2
% 1.92/2.20 (
% 1.92/2.20 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) _let_1))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_5 (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (=> (tptp.element B _let_1) (tptp.element (tptp.complements_of_subsets A B) _let_1)))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset A))) (= (= C (tptp.complements_of_subsets A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (= (tptp.in D C) (tptp.in (tptp.subset_complement A D) B))))))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_14 (forall ((BOUND_VARIABLE_2188 $$unsorted) (BOUND_VARIABLE_2190 $$unsorted) (BOUND_VARIABLE_2204 $$unsorted)) (or (not (tptp.disjoint BOUND_VARIABLE_2188 BOUND_VARIABLE_2190)) (not (tptp.in BOUND_VARIABLE_2204 BOUND_VARIABLE_2188)) (not (tptp.in BOUND_VARIABLE_2204 BOUND_VARIABLE_2190)))))) (let ((_let_15 (tptp.complements_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_16 (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_17 (tptp.in _let_16 _let_15))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.disjoint _let_15 _let_15))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_18))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (not _let_21))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (= _let_24 _let_17))) (let ((_let_26 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_26))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_25))) (let ((_let_30 (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (= (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.in (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 D) (tptp.complements_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_31 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.complements_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15)))) (let ((_let_32 (= _let_31 _let_30))) (let ((_let_33 (tptp.powerset _let_26))) (let ((_let_34 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_33))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.element _let_15 _let_33))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_32))) (let ((_let_39 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1867 $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (or (not (tptp.element B _let_1)) (not (tptp.element BOUND_VARIABLE_1867 _let_1)) (= (= (tptp.complements_of_subsets A B) BOUND_VARIABLE_1867) (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.powerset A))) (= (tptp.in (tptp.subset_complement A D) B) (tptp.in D BOUND_VARIABLE_1867)))))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (tptp.powerset (tptp.powerset A)))) (let ((_let_42 (or _let_35 _let_36))) (let ((_let_43 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (or (not (tptp.element B _let_1)) (tptp.element (tptp.complements_of_subsets A B) _let_1)))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (= tptp.empty_set _let_15))) (let ((_let_46 (not _let_45))) (let ((_let_47 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_48 (or _let_35 _let_47 _let_46))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= tptp.empty_set B) (not (= tptp.empty_set (tptp.complements_of_subsets A B))))))) (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 0)) (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_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_35 _let_36 (not _let_42)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complements_of_subsets A B)))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_36 false _let_34 false _let_42)))) (let ((_let_58 (or _let_35 _let_31))) (let ((_let_59 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= B (tptp.complements_of_subsets A (tptp.complements_of_subsets A B))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_30))) (let ((_let_62 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_26))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_27))) (let ((_let_65 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (not _let_24))) (let ((_let_68 (or _let_63 _let_67))) (let ((_let_69 (forall ((C $$unsorted)) (or (not (tptp.in C (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_70 (not _let_68))) (let ((_let_71 (not _let_69))) (let ((_let_72 (tptp.disjoint _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_73 (or _let_72 _let_71))) (let ((_let_74 (forall ((BOUND_VARIABLE_2173 $$unsorted) (BOUND_VARIABLE_2175 $$unsorted)) (or (tptp.disjoint BOUND_VARIABLE_2173 BOUND_VARIABLE_2175) (not (forall ((C $$unsorted)) (or (not (tptp.in C BOUND_VARIABLE_2173)) (not (tptp.in C BOUND_VARIABLE_2175))))))))) (let ((_let_75 (_let_74))) (let ((_let_76 (tptp.set_intersection2 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_77 (= tptp.empty_set _let_76))) (let ((_let_78 (= _let_72 _let_77))) (let ((_let_79 (not _let_72))) (let ((_let_80 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= tptp.empty_set (tptp.set_intersection2 A B)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26))) (let ((_let_83 (= _let_82 _let_76))) (let ((_let_84 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_82))) (let ((_let_85 (not _let_77))) (let ((_let_86 (_let_13))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 _let_84))) (let ((_let_91 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= A (tptp.set_intersection2 A B)))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (= _let_34 _let_88))) (let ((_let_94 (_let_4))) (let ((_let_95 (ASSUME :args _let_94))) (let ((_let_96 ((tptp.element A (tptp.powerset B))))) (let ((_let_97 (not _let_47))) (let ((_let_98 (and _let_97 _let_84 _let_83))) (let ((_let_99 (_let_97 _let_84 _let_83))) (let ((_let_100 (ASSUME :args (_let_97)))) (let ((_let_101 (ASSUME :args (_let_84)))) (let ((_let_102 (ASSUME :args (_let_83)))) (let ((_let_103 (_let_71))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_103)) :args _let_103)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_69))) (REFL :args (_let_70)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_72 _let_71 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_79 _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_98)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_100 _let_101 _let_102) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.empty_set)) (TRANS (SYMM _let_102) (SYMM _let_101)) :args (=)) (FALSE_INTRO _let_100))) :args _let_99)) :args _let_99)) :args (true _let_98)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_97) _let_47))) (REFL :args ((not _let_84))) (REFL :args ((not _let_83))) (REFL :args (_let_85)) :args _let_52)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_48 1)) _let_54 :args (_let_97 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_89 _let_84 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or _let_35 _let_88 (not _let_93)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26 QUANTIFIERS_INST_E_MATCHING _let_96)) :args _let_94)) _let_95 :args (_let_93 false _let_4)) :args (_let_88 false _let_34 false _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A B) false))))) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_84 false _let_88 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_86)) _let_87 :args (_let_83 false _let_13)) :args (_let_85 true _let_47 false _let_84 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.disjoint A B)))) :args (_let_80))) _let_81 :args (_let_78 false _let_80)) :args (_let_79 true _let_77 false _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_75) :args (_let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.disjoint BOUND_VARIABLE_2173 BOUND_VARIABLE_2175) true))))) :args _let_75)) (AND_ELIM _let_22 :args (0)) :args (_let_73 false _let_74)) :args (_let_71 true _let_72 false _let_73)) :args (_let_70 true _let_69)))) (let ((_let_105 (REFL :args (_let_68)))) (let ((_let_106 (tptp.subset_complement _let_26 _let_15))) (let ((_let_107 (tptp.subset _let_15 _let_106))) (let ((_let_108 (= _let_19 _let_107))) (let ((_let_109 (or _let_37 _let_37 _let_108))) (let ((_let_110 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_2233 $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element BOUND_VARIABLE_2233 _let_1)) (= (tptp.disjoint B BOUND_VARIABLE_2233) (tptp.subset B (tptp.subset_complement A BOUND_VARIABLE_2233)))))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (= _let_26 (tptp.set_difference _let_26 tptp.empty_set)))) (let ((_let_113 (tptp.subset _let_15 _let_26))) (let ((_let_114 (= _let_106 (tptp.set_difference _let_26 _let_15)))) (let ((_let_115 (forall ((A $$unsorted)) (= A (tptp.set_difference A tptp.empty_set))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (= _let_36 _let_113))) (let ((_let_118 (or _let_37 _let_114))) (let ((_let_119 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (and _let_45 _let_114 _let_113 _let_112))) (let ((_let_122 (ASSUME :args (_let_113)))) (let ((_let_123 (ASSUME :args (_let_112)))) (let ((_let_124 (ASSUME :args (_let_45)))) (let ((_let_125 (ASSUME :args (_let_114)))) (let ((_let_126 (_let_14))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_126) :args (_let_15 _let_15 _let_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in BOUND_VARIABLE_2204 BOUND_VARIABLE_2190) false)) (not (= (tptp.disjoint BOUND_VARIABLE_2188 BOUND_VARIABLE_2190) false))))) :args _let_126)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_21))) :args ((or _let_20 _let_18 _let_23))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_108)) :args ((or _let_19 (not _let_107) (not _let_108)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_122 _let_123 _let_124 _let_125) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_15)) (TRANS (SYMM (SYMM _let_125)) (CONG (REFL :args (_let_26)) (SYMM _let_124) :args (APPLY_UF tptp.set_difference)) (SYMM _let_123)) :args (APPLY_UF tptp.subset)) (TRUE_INTRO _let_122))) :args (_let_113 _let_112 _let_45 _let_114))) :args (_let_45 _let_114 _let_113 _let_112))) :args (true _let_121)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_52)) :args ((or _let_45 _let_48))) _let_54 :args (_let_45 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_37 _let_114 (not _let_118)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (_let_26 _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset A)) false))))) :args (_let_119))) _let_120 :args (_let_118 false _let_119)) :args (_let_114 false _let_36 false _let_118)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_117)) :args ((or _let_37 _let_113 (not _let_117)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_15 _let_26 QUANTIFIERS_INST_E_MATCHING _let_96)) :args _let_94)) _let_95 :args (_let_117 false _let_4)) :args (_let_113 false _let_36 false _let_117)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (_let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A tptp.empty_set)))) :args (_let_115))) _let_116 :args (_let_112 false _let_115)) :args (_let_107 false _let_45 false _let_114 false _let_113 false _let_112)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_109))) :args ((or _let_37 _let_108 (not _let_109)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_26 _let_15 _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.subset B (tptp.subset_complement A BOUND_VARIABLE_2233))))) :args (_let_110))) _let_111 :args (_let_109 false _let_110)) :args (_let_108 false _let_36 false _let_109)) :args (_let_19 false _let_107 false _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_25)) :args ((or _let_67 _let_17 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_24))) :args _let_52)) :args ((or _let_24 _let_68))) _let_104 :args (_let_24 true _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_25 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_63 _let_27 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_52)) :args ((or _let_62 _let_68))) _let_104 :args (_let_62 true _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A B) false))))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_27 false _let_62 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) :args _let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_32)) :args ((or (not _let_31) _let_30 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_35 _let_31 (not _let_58)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_31 false _let_34 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_35 _let_37 _let_32 (not _let_38)))) _let_56 _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B _let_41) false)) (not (= (tptp.element BOUND_VARIABLE_1867 _let_41) false))))) :args (_let_39)))) _let_40 :args (_let_38 false _let_39)) :args (_let_32 false _let_34 false _let_36 false _let_38)) :args (_let_30 false _let_31 false _let_32)) :args (_let_29 false _let_30)) :args (_let_25 false _let_27 false _let_29)) :args (_let_17 false _let_24 false _let_25)) :args (_let_23 false _let_19 false _let_17)) (AND_ELIM _let_22 :args (1)) :args (false true _let_21 false _let_14)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) _let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) _let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_11 _let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true true true _let_9 true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.powerset C) B))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) _let_6 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) _let_5 _let_4 _let_3 (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (=> (tptp.subset E C) (tptp.in E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.92/2.22 )
% 1.92/2.22 % SZS output end Proof for SEU174+2
% 1.92/2.22 % cvc5---1.0.5 exiting
% 1.92/2.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------