TSTP Solution File: SEU170+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU170+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 16:29:47 EDT 2023
% Result : Theorem 1.73s 1.95s
% Output : Proof 1.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU170+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 13:09:05 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 1.73/1.95 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.GtkafLE5V8/cvc5---1.0.5_15472.p...
% 1.73/1.95 ------- get file name : TPTP file name is SEU170+2
% 1.73/1.95 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15472.smt2...
% 1.73/1.95 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.73/1.95 % SZS status Theorem for SEU170+2
% 1.73/1.95 % SZS output start Proof for SEU170+2
% 1.73/1.95 (
% 1.73/1.95 (let ((_let_1 (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))))) (let ((_let_6 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C)))))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))) (let ((_let_15 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_18 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))))) (let ((_let_19 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_20 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_21 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_25 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24))) (let ((_let_26 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_27 (= _let_26 _let_25))) (let ((_let_28 (tptp.set_intersection2 _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (= _let_24 _let_28))) (let ((_let_30 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_26))) (let ((_let_31 (tptp.set_union2 _let_26 _let_30))) (let ((_let_32 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_31))) (let ((_let_33 (= _let_31 (tptp.set_union2 _let_30 _let_26)))) (let ((_let_34 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24))) (let ((_let_35 (= _let_28 _let_34))) (let ((_let_36 (= _let_34 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_25)))) (let ((_let_37 (tptp.set_difference _let_30 _let_30))) (let ((_let_38 (= tptp.empty_set _let_37))) (let ((_let_39 (tptp.subset _let_24 _let_21))) (let ((_let_40 (= _let_30 (tptp.set_union2 _let_30 _let_37)))) (let ((_let_41 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_22))) (let ((_let_42 (= tptp.empty_set _let_26))) (let ((_let_43 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_44 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_43))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_23))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_50 (= _let_49 _let_41))) (let ((_let_51 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_45 _let_50))) (let ((_let_54 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_2013 $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element BOUND_VARIABLE_2013 _let_1)) (= (tptp.disjoint B BOUND_VARIABLE_2013) (tptp.subset B (tptp.subset_complement A BOUND_VARIABLE_2013)))))))) (let ((_let_55 (not _let_53))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or))) (let ((_let_58 (not _let_54))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_56) :args (_let_58))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_54))) (REFL :args (_let_55)) :args _let_57)) _let_56 :args (_let_55 true _let_54)))) (let ((_let_60 (REFL :args (_let_53)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_57)) :args ((or _let_44 _let_53))) _let_59 :args (_let_44 true _let_53)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_23 (not _let_46)))) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset A)) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_23 false _let_44 false _let_46)))) (let ((_let_63 (_let_4))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_63))) _let_64 :args (_let_27 false _let_4)))) (let ((_let_66 (tptp.subset _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_29))) (let ((_let_69 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= A (tptp.set_intersection2 A B)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 ((not (= (tptp.subset A B) false))))) (let ((_let_73 (_let_8))) (let ((_let_74 (ASSUME :args _let_73))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_67 _let_29 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A B)))) :args _let_73)) _let_74 :args (_let_66 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_71)) _let_70 :args (_let_68 false _let_69)) :args (_let_29 false _let_66 false _let_68)))) (let ((_let_76 (tptp.subset _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_32))) (let ((_let_79 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= B (tptp.set_union2 A (tptp.set_difference B A))))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 ((not (= (tptp.subset A B) false))))) (let ((_let_83 (_let_11))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 ((tptp.set_intersection2 A B)))) (let ((_let_86 (_let_20))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 (_let_19))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 ((tptp.set_intersection2 A B)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_90)) :args _let_88)) _let_89 :args (_let_35 false _let_19)))) (let ((_let_92 ((tptp.set_difference A (tptp.set_difference A B))))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_24 QUANTIFIERS_INST_E_MATCHING _let_92)) :args _let_63))) _let_64 :args (_let_36 false _let_4)))) (let ((_let_94 (tptp.subset _let_30 _let_30))) (let ((_let_95 (= _let_94 _let_38))) (let ((_let_96 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (= tptp.empty_set (tptp.set_difference A B)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (tptp.subset _let_28 _let_24))) (let ((_let_99 (not _let_36))) (let ((_let_100 (not _let_35))) (let ((_let_101 (not _let_29))) (let ((_let_102 (not _let_27))) (let ((_let_103 (and _let_27 _let_29 _let_35 _let_98 _let_36))) (let ((_let_104 (ASSUME :args (_let_98)))) (let ((_let_105 (APPLY_UF tptp.subset))) (let ((_let_106 (REFL :args (_let_24)))) (let ((_let_107 (ASSUME :args (_let_29)))) (let ((_let_108 (SYMM _let_107))) (let ((_let_109 (SYMM _let_108))) (let ((_let_110 (ASSUME :args (_let_35)))) (let ((_let_111 (SYMM (SYMM _let_110)))) (let ((_let_112 (ASSUME :args (_let_36)))) (let ((_let_113 (SYMM (SYMM _let_112)))) (let ((_let_114 (APPLY_UF tptp.set_difference))) (let ((_let_115 (ASSUME :args (_let_27)))) (let ((_let_116 (SYMM _let_115))) (let ((_let_117 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_118 (TRANS (CONG _let_117 (SYMM _let_116) :args _let_114) (SYMM _let_113) (SYMM _let_111) _let_108))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_103)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_104 _let_107 _let_110 _let_112 _let_115) (SCOPE (TRUE_ELIM (TRANS (CONG _let_118 _let_118 :args _let_105) (CONG _let_109 _let_106 :args _let_105) (TRUE_INTRO _let_104))) :args (_let_98 _let_29 _let_35 _let_36 _let_27))) :args (_let_27 _let_29 _let_35 _let_98 _let_36))) :args (true _let_103)) :args ((or _let_102 _let_101 _let_94 _let_100 (not _let_98) _let_99))) _let_65 _let_75 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args (_let_98 false _let_11)) _let_93 :args (_let_94 false _let_27 false _let_29 false _let_35 false _let_98 false _let_36)))) (let ((_let_120 (not _let_94))) (let ((_let_121 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_122 (not _let_121))) (let ((_let_123 (or _let_122 _let_39))) (let ((_let_124 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (tptp.union _let_43))) (let ((_let_127 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_126))) (let ((_let_128 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_126))) (let ((_let_129 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_43))) (let ((_let_130 (not _let_129))) (let ((_let_131 (or _let_130 _let_127))) (let ((_let_132 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.subset A (tptp.union B)))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (_let_132))) (let ((_let_135 ((not (= (tptp.in A B) false))))) (let ((_let_136 (= _let_51 _let_129))) (let ((_let_137 (tptp.empty _let_43))) (let ((_let_138 (or _let_137 _let_136))) (let ((_let_139 (forall ((BOUND_VARIABLE_1624 $$unsorted) (BOUND_VARIABLE_1626 $$unsorted)) (or (tptp.empty BOUND_VARIABLE_1624) (= (tptp.element BOUND_VARIABLE_1626 BOUND_VARIABLE_1624) (tptp.in BOUND_VARIABLE_1626 BOUND_VARIABLE_1624)))))) (let ((_let_140 (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))) :args (0)))) (let ((_let_141 (_let_139))) (let ((_let_142 ((tptp.element BOUND_VARIABLE_1626 BOUND_VARIABLE_1624)))) (let ((_let_143 (ASSUME :args _let_141))) (let ((_let_144 (_let_15))) (let ((_let_145 (ASSUME :args _let_144))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_145 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.powerset A)))) :args _let_144)) _let_145 :args ((not _let_137) false _let_15)))) (let ((_let_147 (forall ((A $$unsorted)) (= A (tptp.union (tptp.powerset A)))))) (let ((_let_148 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_148 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.powerset A)))) :args (_let_147))) _let_148 :args (_let_128 false _let_147)))) (let 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SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_168 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21))) (let ((_let_169 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_168))) (let ((_let_170 (= _let_163 _let_169))) (let ((_let_171 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= A (tptp.set_difference A B)))))) (let ((_let_172 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_173 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21))) (let ((_let_174 (= (tptp.set_difference _let_173 _let_21) _let_168))) (let ((_let_175 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_176 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_175))) (let ((_let_177 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_178 (= _let_177 _let_175))) (let ((_let_179 (= (tptp.set_difference 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$$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) _let_18 (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 $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) _let_17 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_16 (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true true true true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) _let_15 (tptp.empty tptp.empty_set) (forall ((A $$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 $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) (forall ((A $$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))) _let_14 (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))))) _let_13 (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 $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$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)) _let_12 (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 $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) _let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$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 $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) _let_10 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (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)) _let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))) _let_8 (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 $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (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))))) (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) _let_7 _let_6 _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) _let_4 (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (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 $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) _let_3 (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))) _let_2 (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)))) _let_1 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.73/1.96 )
% 1.73/1.96 % SZS output end Proof for SEU170+2
% 1.73/1.96 % cvc5---1.0.5 exiting
% 1.73/1.96 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------