TSTP Solution File: SEU313+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU313+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 16:30:50 EDT 2023
% Result : Theorem 28.26s 28.62s
% Output : Proof 28.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU313+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 23 19:36:44 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 28.26/28.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3DlEirvlKP/cvc5---1.0.5_15518.p...
% 28.26/28.62 ------- get file name : TPTP file name is SEU313+1
% 28.26/28.62 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15518.smt2...
% 28.26/28.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.26/28.62 --- Run --no-e-matching --full-saturate-quant at 5...
% 28.26/28.62 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.26/28.62 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.26/28.62 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.26/28.62 % SZS status Theorem for SEU313+1
% 28.26/28.62 % SZS output start Proof for SEU313+1
% 28.26/28.62 (
% 28.26/28.62 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.in C (tptp.the_carrier A)) (= (tptp.in C (tptp.topstr_closure A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset (tptp.the_carrier A))) (=> (and (tptp.closed_subset D A) (tptp.subset B D)) (tptp.in C D)))))))))))))) (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)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (let ((_let_1 (tptp.cast_as_carrier_subset A))) (let ((_let_2 (tptp.the_carrier A))) (=> (tptp.element B (tptp.powerset _let_2)) (= (tptp.subset_difference _let_2 _let_1 (tptp.subset_difference _let_2 _let_1 B)) B))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element B (tptp.powerset _let_1)) (= (tptp.subset_complement _let_1 B) (tptp.subset_difference _let_1 (tptp.cast_as_carrier_subset A) B))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))))) (let ((_let_7 (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (=> (and (tptp.top_str A) (tptp.element B _let_1)) (tptp.element (tptp.topstr_closure A B) _let_1)))))) (let ((_let_10 (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)))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (tptp.element (tptp.cast_as_carrier_subset A) (tptp.powerset (tptp.the_carrier A))))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element B (tptp.powerset _let_1)) (= (tptp.closed_subset B A) (tptp.open_subset (tptp.subset_difference _let_1 (tptp.cast_as_carrier_subset A) B) A))))))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (= (tptp.cast_as_carrier_subset A) (tptp.the_carrier A)))))) (let ((_let_15 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (= (= C (tptp.topstr_closure A B)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.the_carrier A)) (= (tptp.in D C) (forall ((E $$unsorted)) (=> (tptp.element E (tptp.powerset (tptp.the_carrier A))) (not (and (tptp.open_subset E A) (tptp.in D E) (tptp.disjoint B E))))))))))))))))) (let ((_let_16 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_17 (tptp.cast_as_carrier_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.subset_difference _let_18 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_20 (tptp.subset_difference _let_18 _let_17 _let_19))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_20))) (let ((_let_22 (tptp.set_difference _let_17 _let_19))) (let ((_let_23 (= _let_20 _let_22))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_22))) (let ((_let_25 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_26 (not _let_25))) (let ((_let_27 (not _let_16))) (let ((_let_28 (tptp.open_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.powerset _let_18))) (let ((_let_31 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 _let_30))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_29 _let_27 _let_26))) (let ((_let_34 (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (not (tptp.open_subset E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 E)) (not (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 E)))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (tptp.topstr_closure SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_37 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_36))) (let ((_let_38 (= _let_37 _let_34))) (let ((_let_39 (not _let_34))) (let ((_let_40 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_18))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_38))) (let ((_let_43 (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (= (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (not (tptp.open_subset E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.in D E)) (not (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 E)))) (tptp.in D (tptp.topstr_closure SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_44 (tptp.element _let_36 _let_30))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_30))) (let ((_let_47 (not _let_46))) (let ((_let_48 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_47 _let_45 _let_43))) (let ((_let_51 (forall ((A $$unsorted) (BOUND_VARIABLE_1534 $$unsorted) (BOUND_VARIABLE_1532 $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1532 _let_1)) (not (tptp.element BOUND_VARIABLE_1534 _let_1)) (= (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.the_carrier A))) (= (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.the_carrier A)))) (not (tptp.open_subset E A)) (not (tptp.in D E)) (not (tptp.disjoint BOUND_VARIABLE_1532 E)))) (tptp.in D BOUND_VARIABLE_1534)))) (= BOUND_VARIABLE_1534 (tptp.topstr_closure A BOUND_VARIABLE_1532)))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or _let_49 _let_47 _let_44))) (let ((_let_54 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (or (not (tptp.top_str A)) (not (tptp.element B _let_1)) (tptp.element (tptp.topstr_closure A B) _let_1)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (not (tptp.closed_subset D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 D)) (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 D))))) (let ((_let_57 (= _let_37 _let_56))) (let ((_let_58 (or _let_49 _let_47 _let_41 _let_57))) (let ((_let_59 (forall ((A $$unsorted) (BOUND_VARIABLE_1825 $$unsorted) (BOUND_VARIABLE_1823 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1823 (tptp.powerset _let_1))) (not (tptp.in BOUND_VARIABLE_1825 _let_1)) (= (tptp.in BOUND_VARIABLE_1825 (tptp.topstr_closure A BOUND_VARIABLE_1823)) (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.powerset (tptp.the_carrier A)))) (not (tptp.closed_subset D A)) (not (tptp.subset BOUND_VARIABLE_1823 D)) (tptp.in BOUND_VARIABLE_1825 D))))))))) (let ((_let_60 (not _let_58))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (or))) (let ((_let_63 (not _let_59))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_61) :args (_let_63))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_59))) (REFL :args (_let_60)) :args _let_62)) _let_61 :args (_let_60 true _let_59)))) (let ((_let_65 (REFL :args (_let_58)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_62)) :args ((or _let_46 _let_58))) _let_64 :args (_let_46 true _let_58)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_62)) :args ((or _let_48 _let_58))) _let_64 :args (_let_48 true _let_58)))) (let ((_let_68 (_let_43))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 2)) (CONG _let_65 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_62)) :args ((or _let_40 _let_58))) _let_64 :args (_let_40 true _let_58)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_38 (not _let_42)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_68) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP)) :args _let_68))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_47 _let_45 _let_43 (not _let_50)))) _let_67 _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_49 _let_47 _let_44 (not _let_53)))) _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.topstr_closure A B)))) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_44 false _let_48 false _let_46 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_51)))) _let_52 :args (_let_50 false _let_51)) :args (_let_43 false _let_48 false _let_46 false _let_44 false _let_50)) :args (_let_42 false _let_43)) :args (_let_38 false _let_40 false _let_42)))) (let ((_let_71 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_72 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.closed_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_30))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_75 _let_73 _let_71))) (let ((_let_79 (tptp.subset_difference _let_18 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_80 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_79))) (let ((_let_81 (not _let_80))) (let ((_let_82 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_79))) (let ((_let_83 (not _let_82))) (let ((_let_84 (tptp.open_subset _let_79 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.element _let_79 _let_30))) (let ((_let_87 (not _let_86))) (let ((_let_88 (or _let_87 _let_85 _let_83 _let_81))) (let ((_let_89 (= _let_74 _let_84))) (let ((_let_90 (or _let_49 _let_77 _let_89))) (let ((_let_91 (tptp.subset_complement _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_92 (tptp.subset_complement _let_18 _let_91))) (let ((_let_93 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_92))) (let ((_let_94 (or _let_77 _let_93))) (let ((_let_95 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_96 (= _let_79 _let_91))) (let ((_let_97 (not _let_95))) (let ((_let_98 (or _let_97 _let_77 _let_96))) (let ((_let_99 (tptp.subset_difference _let_18 _let_17 _let_79))) (let ((_let_100 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_99))) (let ((_let_101 (or _let_97 _let_77 _let_100))) (let ((_let_102 (tptp.element _let_91 _let_30))) (let ((_let_103 (or _let_77 _let_102))) (let ((_let_104 (tptp.element _let_17 _let_30))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_77 _let_86))) (let ((_let_107 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_92))) (let ((_let_108 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_91))) (let ((_let_109 (= _let_108 _let_107))) (let ((_let_110 (not _let_102))) (let ((_let_111 (or _let_47 _let_110 _let_109))) (let ((_let_112 (tptp.set_difference _let_17 _let_79))) (let ((_let_113 (= _let_99 _let_112))) (let ((_let_114 (or _let_105 _let_87 _let_113))) (let ((_let_115 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_112))) (let ((_let_116 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17))) (let ((_let_117 (and _let_116 _let_83))) (let ((_let_118 (= _let_115 _let_117))) (let ((_let_119 (not _let_37))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_58 3)) _let_64 :args ((not _let_57) true _let_58)))) (let ((_let_121 (_let_57))) (let ((_let_122 (not _let_38))) (let ((_let_123 (_let_38))) (let ((_let_124 (not _let_56))) (let ((_let_125 (_let_124))) (let ((_let_126 (_let_34))) (let ((_let_127 (REFL :args (_let_78)))) (let ((_let_128 (forall ((A $$unsorted) (BOUND_VARIABLE_1574 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1574 (tptp.powerset _let_1))) (= (tptp.closed_subset BOUND_VARIABLE_1574 A) (tptp.open_subset (tptp.subset_difference _let_1 (tptp.cast_as_carrier_subset A) BOUND_VARIABLE_1574) A))))))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (_let_128))) (let ((_let_131 (tptp.the_carrier A))) (let ((_let_132 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (= B (tptp.subset_complement A (tptp.subset_complement A B))))))) (let ((_let_133 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_134 (or _let_49 _let_95))) (let ((_let_135 (forall ((A $$unsorted)) (or 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((_let_216 (not _let_211))) (let ((_let_217 (tptp.subset_complement _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_218 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_217))) (let ((_let_219 (= _let_19 _let_217))) (let ((_let_220 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_217))) (let ((_let_221 (not _let_220))) (let ((_let_222 (tptp.closed_subset _let_217 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_223 (not _let_222))) (let ((_let_224 (tptp.element _let_217 _let_30))) (let ((_let_225 (not _let_224))) (let ((_let_226 (or _let_225 _let_223 _let_221 _let_218))) (let ((_let_227 (_let_56))) (let ((_let_228 (tptp.closed_subset _let_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_229 (tptp.open_subset _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_230 (= _let_228 _let_229))) (let ((_let_231 (or _let_49 _let_205 _let_230))) (let ((_let_232 (and _let_28 _let_21))) (let ((_let_233 (_let_28 _let_21))) (let ((_let_234 (ASSUME :args (_let_28)))) (let ((_let_235 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_236 (ASSUME :args (_let_21)))) (let ((_let_237 (SYMM (SYMM _let_236)))) (let ((_let_238 (or _let_97 _let_32 _let_219))) (let ((_let_239 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_238)) :args ((or _let_97 _let_32 _let_219 (not _let_238)))) _let_137 _let_202 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_139 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING _let_141)) :args _let_140))) _let_139 :args (_let_238 false _let_138)) :args (_let_219 false _let_95 false _let_31 false _let_238)))) (let ((_let_240 (and _let_219 _let_228))) (let ((_let_241 (ASSUME :args (_let_228)))) (let ((_let_242 (ASSUME :args (_let_219)))) (let ((_let_243 (SYMM (SYMM _let_242)))) (let ((_let_244 (or _let_32 _let_224))) (let ((_let_245 (= _let_25 _let_220))) (let ((_let_246 (or _let_47 _let_32 _let_245))) (let ((_let_247 (and _let_219 _let_218))) (let ((_let_248 (ASSUME :args (_let_218)))) (let ((_let_249 (ASSUME :args (_let_213)))) (let ((_let_250 (ASSUME :args (_let_23)))) (let ((_let_251 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_249 _let_250 _let_236 _let_251) :args (_let_16 _let_21 _let_23 _let_213)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_251)) (CONG _let_178 (TRANS _let_237 (SYMM (SYMM _let_250))) :args _let_175) (FALSE_INTRO _let_249))) :args (_let_213 _let_23 _let_21 _let_16)) :args ((not (and _let_16 _let_21 _let_23 _let_213)) SB_LITERAL))) (CONG (REFL :args (_let_27)) (REFL :args ((not _let_21))) (REFL :args ((not _let_23))) (MACRO_SR_PRED_INTRO :args ((= (not _let_213) _let_24))) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_212)) :args ((or _let_211 _let_213 (not _let_212)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_211 1)) :args ((or _let_210 _let_216))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_247)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_248 _let_242) (SCOPE (TRUE_ELIM (TRANS (CONG _let_178 _let_243 :args _let_175) (TRUE_INTRO _let_248))) :args (_let_218 _let_219))) :args (_let_219 _let_218))) :args (true _let_247)) :args ((or (not _let_219) _let_209 (not _let_218)))) _let_239 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_226)) :args ((or _let_221 _let_225 _let_223 _let_218 (not _let_226)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_245)) :args ((or _let_26 _let_220 (not _let_245)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 3)) (CONG _let_200 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_62)) :args ((or _let_25 _let_33))) _let_199 :args (_let_25 true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_246)) :args ((or _let_47 _let_32 _let_245 (not _let_246)))) _let_66 _let_202 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_159 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING (_let_161 (tptp.disjoint B BOUND_VARIABLE_1769)))) :args _let_160)) _let_159 :args (_let_246 false _let_158)) :args (_let_245 false _let_46 false _let_31 false _let_246)) :args (_let_220 false _let_25 false _let_245)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_244)) :args ((or _let_32 _let_224 (not _let_244)))) _let_202 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_147 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_149)) :args _let_148)) _let_147 :args (_let_244 false _let_146)) :args (_let_224 false _let_31 false _let_244)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_240)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_241 _let_242) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_243) _let_235 :args (APPLY_UF tptp.closed_subset)) (TRUE_INTRO _let_241))) :args (_let_228 _let_219))) :args (_let_219 _let_228))) :args (true _let_240)) _let_239 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_230)) :args ((or _let_228 (not _let_229) (not _let_230)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_232)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_234 _let_236) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_237) _let_235 :args (APPLY_UF tptp.open_subset)) (TRUE_INTRO _let_234))) :args _let_233)) :args _let_233)) :args (true _let_232)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG _let_200 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_62)) :args ((or _let_28 _let_33))) _let_199 :args (_let_28 true _let_33)) _let_203 :args (_let_229 false _let_28 false _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_231)) :args ((or _let_49 _let_205 _let_230 (not _let_231)))) _let_67 _let_208 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_129 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_19 QUANTIFIERS_INST_E_MATCHING ((tptp.subset_difference _let_131 (tptp.cast_as_carrier_subset A) BOUND_VARIABLE_1574)))) :args _let_130)) _let_129 :args (_let_231 false _let_128)) :args (_let_230 false _let_48 false _let_204 false _let_231)) :args (_let_228 false _let_229 false _let_230)) :args (_let_222 false _let_219 false _let_228)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_227) :args (_let_217 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_227)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_121) :args ((or _let_37 _let_56 _let_57))) _let_197 _let_120 :args (_let_56 true _let_37 true _let_57)) :args (_let_226 false _let_56)) :args (_let_218 false _let_220 false _let_224 false _let_222 false _let_226)) :args (_let_209 false _let_219 false _let_218)) :args (_let_216 false _let_209)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_215) :args _let_183) :args _let_215)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_181 :args (_let_17 _let_19 _let_22 QUANTIFIERS_INST_CBQI_PROP)) :args _let_180))) _let_181 :args (_let_214 false _let_13)) :args (_let_212 false _let_214)) :args (_let_213 true _let_211 false _let_212)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_206)) :args ((or _let_105 _let_205 _let_23 (not _let_206)))) _let_153 _let_208 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_163 :args (_let_18 _let_17 _let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_165)) :args _let_164)) _let_163 :args (_let_206 false _let_162)) :args (_let_23 false _let_104 false _let_204 false _let_206)) _let_203 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 2)) (CONG _let_200 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_16))) :args _let_62)) :args ((or _let_16 _let_33))) _let_199 :args (_let_16 true _let_33)) :args (false true _let_24 false _let_23 false _let_21 false _let_16)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (tptp.v1_xcmplx_0 B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B A) (and (tptp.v1_xcmplx_0 B) (tptp.natural B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.v1_membered B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) _let_15 _let_14 _let_13 _let_12 true true _let_11 _let_10 true _let_9 _let_8 _let_7 true true true (exists ((A $$unsorted)) (tptp.top_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_membered A) (tptp.v1_membered (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v2_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v3_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v4_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.set_difference A B))) (=> (tptp.v5_membered A) (and (tptp.v1_membered _let_1) (tptp.v2_membered _let_1) (tptp.v3_membered _let_1) (tptp.v4_membered _let_1) (tptp.v5_membered _let_1))))) (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set)) _let_6 (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_2 _let_1 (forall ((A $$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 $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.26/28.63 )
% 28.26/28.63 % SZS output end Proof for SEU313+1
% 28.26/28.63 % cvc5---1.0.5 exiting
% 28.26/28.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------