TSTP Solution File: SEU372+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU372+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 16:31:14 EDT 2023
% Result : Theorem 27.14s 27.33s
% Output : Proof 27.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU372+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : do_cvc5 %s %d
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Wed Aug 23 15:05:26 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.16/0.41 %----Proving TF0_NAR, FOF, or CNF
% 27.14/27.33 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.NceFbCR5Ex/cvc5---1.0.5_8902.p...
% 27.14/27.33 ------- get file name : TPTP file name is SEU372+1
% 27.14/27.33 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8902.smt2...
% 27.14/27.33 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 27.14/27.33 --- Run --no-e-matching --full-saturate-quant at 5...
% 27.14/27.33 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 27.14/27.33 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 27.14/27.33 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 27.14/27.33 % SZS status Theorem for SEU372+1
% 27.14/27.33 % SZS output start Proof for SEU372+1
% 27.14/27.33 (
% 27.14/27.33 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.in C (tptp.topstr_closure A B)) (forall ((D $$unsorted)) (=> (tptp.point_neighbourhood D A C) (not (tptp.disjoint D B)))))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (=> (and (tptp.open_subset B A) (tptp.in C B)) (tptp.point_neighbourhood B A C)))))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset (tptp.interior A B) A))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.subset (tptp.interior A B) B))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))))) (let ((_let_8 (tptp.relation tptp.empty_set))) (let ((_let_9 (tptp.empty tptp.empty_set))) (let ((_let_10 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (forall ((C $$unsorted)) (=> (tptp.point_neighbourhood C A B) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (=> (and (tptp.top_str A) (tptp.element B _let_1)) (tptp.element (tptp.topstr_closure A B) _let_1)))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (=> (and (tptp.top_str A) (tptp.element B _let_1)) (tptp.element (tptp.interior A B) _let_1)))))) (let ((_let_15 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (= (tptp.point_neighbourhood C A B) (tptp.in B (tptp.interior A C))))))))))) (let ((_let_16 (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 $$unsorted)) (=> (tptp.element E (tptp.powerset (tptp.the_carrier A))) (not (and (tptp.open_subset E A) (tptp.in D E) (tptp.disjoint B E))))))))))))))))) (let ((_let_17 (forall ((A $$unsorted) (BOUND_VARIABLE_1523 $$unsorted) (BOUND_VARIABLE_1521 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1521 (tptp.powerset _let_1))) (not (tptp.open_subset BOUND_VARIABLE_1521 A)) (not (tptp.element BOUND_VARIABLE_1523 _let_1)) (not (tptp.in BOUND_VARIABLE_1523 BOUND_VARIABLE_1521)) (tptp.point_neighbourhood BOUND_VARIABLE_1521 A BOUND_VARIABLE_1523)))))) (let ((_let_18 (tptp.point_neighbourhood SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_19 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_22 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_21))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.open_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.powerset _let_21))) (let ((_let_27 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 _let_26))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.topological_space SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_34 (or _let_33 _let_32 _let_30 _let_28 _let_25 _let_23 _let_20 _let_18))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_18))) (let ((_let_40 (or _let_39 _let_38))) (let ((_let_41 (forall ((D $$unsorted)) (or (not (tptp.point_neighbourhood D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)) (not (tptp.disjoint D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))))) (let ((_let_42 (tptp.topstr_closure SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_43 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_42))) (let ((_let_44 (= _let_43 _let_41))) (let ((_let_45 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_26))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_33 _let_32 _let_30 _let_46 _let_23 _let_44))) (let ((_let_48 (forall ((A $$unsorted) (BOUND_VARIABLE_1601 $$unsorted) (BOUND_VARIABLE_1599 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1599 (tptp.powerset _let_1))) (not (tptp.element BOUND_VARIABLE_1601 _let_1)) (= (tptp.in BOUND_VARIABLE_1601 (tptp.topstr_closure A BOUND_VARIABLE_1599)) (forall ((D $$unsorted)) (or (not (tptp.point_neighbourhood D A BOUND_VARIABLE_1601)) (not (tptp.disjoint D BOUND_VARIABLE_1599)))))))))) (let ((_let_49 (not _let_47))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (or))) (let ((_let_52 (not _let_48))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_50) :args (_let_52))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_48))) (REFL :args (_let_49)) :args _let_51)) _let_50 :args (_let_49 true _let_48)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 5)) _let_53 :args ((not _let_44) true _let_47)))) (let ((_let_55 (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (not (tptp.open_subset E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (not (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 E)) (not (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 E)))))) (let ((_let_56 (= _let_43 _let_55))) (let ((_let_57 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.point_neighbourhood SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58))) (let ((_let_62 (tptp.interior SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_63 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_62))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_62))) (let ((_let_66 (not _let_65))) (let ((_let_67 (tptp.open_subset _let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.element _let_62 _let_26))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_68 _let_66 _let_64))) (let ((_let_72 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_26))) (let ((_let_73 (or _let_33 _let_32 _let_30 _let_23 _let_60 _let_72))) (let ((_let_74 (= _let_59 _let_65))) (let ((_let_75 (not _let_72))) (let ((_let_76 (or _let_33 _let_32 _let_30 _let_23 _let_75 _let_74))) (let ((_let_77 (or _let_30 _let_75 _let_69))) (let ((_let_78 (tptp.subset _let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_79 (or _let_30 _let_75 _let_78))) (let ((_let_80 (or _let_32 _let_30 _let_75 _let_67))) (let ((_let_81 (tptp.disjoint _let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_82 (not _let_78))) (let ((_let_83 (or _let_82 _let_58 _let_81))) (let ((_let_84 (not _let_81))) (let ((_let_85 (or _let_84 _let_63))) (let ((_let_86 (not _let_43))) (let ((_let_87 (_let_44))) (let ((_let_88 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_21))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_89 _let_56))) (let ((_let_91 (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (= (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (not (tptp.open_subset E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (not (tptp.in D E)) (not (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 E)))) (tptp.in D (tptp.topstr_closure SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))))) (let ((_let_92 (tptp.element _let_42 _let_26))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_30 _let_46 _let_93 _let_91))) (let ((_let_95 (forall ((A $$unsorted) (BOUND_VARIABLE_1146 $$unsorted) (BOUND_VARIABLE_1144 $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1144 _let_1)) (not (tptp.element BOUND_VARIABLE_1146 _let_1)) (= (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.the_carrier A))) (= (forall ((E $$unsorted)) (or (not (tptp.element E (tptp.powerset (tptp.the_carrier A)))) (not (tptp.open_subset E A)) (not (tptp.in D E)) (not (tptp.disjoint BOUND_VARIABLE_1144 E)))) (tptp.in D BOUND_VARIABLE_1146)))) (= BOUND_VARIABLE_1146 (tptp.topstr_closure A BOUND_VARIABLE_1144)))))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (or _let_30 _let_46 _let_92))) (let ((_let_98 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (or (not (tptp.top_str A)) (not (tptp.element B _let_1)) (tptp.element (tptp.topstr_closure A B) _let_1)))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (REFL :args (_let_47)))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 3)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_51)) :args ((or _let_45 _let_47))) _let_53 :args (_let_45 true _let_47)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 2)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_51)) :args ((or _let_29 _let_47))) _let_53 :args (_let_29 true _let_47)))) (let ((_let_103 (_let_91))) (let ((_let_104 (tptp.empty _let_21))) (let ((_let_105 (or _let_23 _let_104 _let_88))) (let ((_let_106 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element A B)) (tptp.empty B) (tptp.in A B))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (not _let_104))) (let ((_let_109 (tptp.one_sorted_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_33 _let_110 _let_108))) (let ((_let_112 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (or _let_30 _let_109))) (let ((_let_115 (forall ((A $$unsorted)) (or (not (tptp.top_str A)) (tptp.one_sorted_str A))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 0)) _let_53 :args ((not _let_33) true _let_47)))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 4)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_51)) :args ((or _let_22 _let_47))) _let_53 :args (_let_22 true _let_47)))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_89 _let_56 (not _let_90)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_23 _let_104 _let_88 (not _let_105)))) _let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_33 _let_110 _let_108 (not _let_111)))) _let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_30 _let_109 (not _let_114)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.top_str A) false))))) :args (_let_115))) _let_116 :args (_let_114 false _let_115)) :args (_let_109 false _let_29 false _let_114)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.empty_carrier A) true))))) :args (_let_112))) _let_113 :args (_let_111 false _let_112)) :args (_let_108 true _let_33 false _let_109 false _let_111)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.element A B) false))))) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_88 false _let_22 true _let_104 false _let_105)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_103) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_CBQI_PROP)) :args _let_103))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_30 _let_46 _let_93 _let_91 (not _let_94)))) _let_102 _let_101 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_30 _let_46 _let_92 (not _let_97)))) _let_102 _let_101 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.topstr_closure A B)))) :args (_let_98))) _let_99 :args (_let_97 false _let_98)) :args (_let_92 false _let_29 false _let_45 false _let_97)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_95)))) _let_96 :args (_let_94 false _let_95)) :args (_let_91 false _let_29 false _let_45 false _let_92 false _let_94)) :args (_let_90 false _let_91)) :args (_let_56 false _let_88 false _let_90)))) (let ((_let_120 (not _let_56))) (let ((_let_121 (_let_56))) (let ((_let_122 (not _let_41))) (let ((_let_123 (_let_122))) (let ((_let_124 (_let_55))) (let ((_let_125 (REFL :args (_let_61)))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 1)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_51)) :args ((or _let_31 _let_47))) _let_53 :args (_let_31 true _let_47)))) (let ((_let_127 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1253 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element B _let_1)) (not (tptp.point_neighbourhood BOUND_VARIABLE_1253 A B)) (tptp.element BOUND_VARIABLE_1253 (tptp.powerset _let_1))))))) (let ((_let_128 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_129 (forall ((A $$unsorted) (BOUND_VARIABLE_1206 $$unsorted) (BOUND_VARIABLE_1204 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1204 _let_1)) (not (tptp.element BOUND_VARIABLE_1206 (tptp.powerset _let_1))) (= (tptp.point_neighbourhood BOUND_VARIABLE_1206 A BOUND_VARIABLE_1204) (tptp.in BOUND_VARIABLE_1204 (tptp.interior A BOUND_VARIABLE_1206)))))))) (let ((_let_130 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_131 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (or (not (tptp.top_str A)) (not (tptp.element B _let_1)) (tptp.element (tptp.interior A B) _let_1)))))) (let ((_let_132 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_133 (forall ((A $$unsorted) (BOUND_VARIABLE_1440 $$unsorted)) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1440 (tptp.powerset (tptp.the_carrier A)))) (tptp.subset (tptp.interior A BOUND_VARIABLE_1440) BOUND_VARIABLE_1440))))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (forall ((A $$unsorted) (BOUND_VARIABLE_1471 $$unsorted)) (or (not (tptp.topological_space A)) (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1471 (tptp.powerset (tptp.the_carrier A)))) (tptp.open_subset (tptp.interior A BOUND_VARIABLE_1471) A))))) (let ((_let_136 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_137 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.disjoint B C)) (tptp.disjoint A C))))) (let ((_let_138 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_139 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.disjoint A B)) (tptp.disjoint B A))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (_let_139))) (let ((_let_142 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_63 _let_84 (not _let_85)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_140 :args (_let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.disjoint B A) true))))) :args _let_141)) _let_140 :args (_let_85 false _let_139)) (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_58 _let_82 _let_81 (not _let_83)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_138 :args (_let_62 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subset A B) false)) (not (= (tptp.disjoint B C) false))))) :args (_let_137))) _let_138 :args (_let_83 false _let_137)) (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_66 _let_70 _let_68 _let_64 (not _let_71)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_74)) :args ((or _let_60 _let_65 (not _let_74)))) (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_32 _let_30 _let_75 _let_67 (not _let_80)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_136 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1471 (tptp.powerset (tptp.the_carrier A))) false))))) :args (_let_135))) _let_136 :args (_let_80 false _let_135)) _let_102 _let_126 (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_30 _let_75 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1440 (tptp.powerset (tptp.the_carrier A))) false))))) :args (_let_133))) _let_134 :args (_let_79 false _let_133)) _let_102 (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_30 _let_75 _let_69 (not _let_77)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_132 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.interior A B)))) :args (_let_131))) _let_132 :args (_let_77 false _let_131)) _let_102 (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_33 _let_32 _let_30 _let_23 _let_75 _let_74 (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.point_neighbourhood BOUND_VARIABLE_1206 A BOUND_VARIABLE_1204)))) :args (_let_129))) _let_130 :args (_let_76 false _let_129)) _let_118 _let_102 _let_126 _let_117 (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_33 _let_32 _let_30 _let_23 _let_60 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_128 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.point_neighbourhood BOUND_VARIABLE_1253 A B) false))))) :args (_let_127))) _let_128 :args (_let_73 false _let_127)) _let_118 _let_102 _let_126 _let_117 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_125 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_51)) :args ((or _let_57 _let_61))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_125 (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_51)) :args ((or _let_59 _let_61))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_124) :args (_let_62 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 E) false))))) :args _let_124)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_123)) :args _let_123)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_122) _let_41))) (REFL :args ((not _let_61))) :args _let_51)) (REORDERING (CNF_EQUIV_POS1 :args _let_121) :args ((or _let_86 _let_55 _let_120))) _let_119 (CNF_EQUIV_NEG2 :args _let_87) _let_54 :args (_let_86 false _let_85 false _let_81 false _let_83 true _let_63 false _let_65 false _let_67 false _let_80 false _let_29 false _let_31 false _let_78 false _let_79 false _let_29 false _let_69 false _let_77 false _let_29 false _let_74 false _let_76 false _let_22 false _let_29 false _let_31 true _let_33 false _let_72 false _let_73 false _let_22 false _let_29 false _let_31 true _let_33 false _let_57 false _let_59 false _let_71 true _let_61 false _let_55 false _let_56 true _let_41 true _let_44)))) (let ((_let_143 (_let_41))) (let ((_let_144 (tptp.disjoint SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43))) (let ((_let_145 (not _let_144))) (let ((_let_146 (or _let_145 _let_37))) (let ((_let_147 (or _let_28 _let_25 _let_20 _let_145))) (let ((_let_148 (not _let_147))) (let ((_let_149 (not _let_55))) (let ((_let_150 (_let_149))) (let ((_let_151 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_150)) :args _let_150)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_149) _let_55))) (REFL :args (_let_148)) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_121) :args ((or _let_43 _let_149 _let_120))) _let_142 _let_119 :args (_let_149 true _let_43 false _let_56)) :args (_let_148 true _let_55)))) (let ((_let_152 (REFL :args (_let_147)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_32 _let_30 _let_23 _let_28 _let_25 _let_20 _let_18 _let_36))) _let_117 _let_126 _let_102 _let_118 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_147 0)) (CONG _let_152 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_51)) :args ((or _let_27 _let_147))) _let_151 :args (_let_27 true _let_147)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_147 1)) (CONG _let_152 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_51)) :args ((or _let_24 _let_147))) _let_151 :args (_let_24 true _let_147)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_147 2)) (CONG _let_152 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_51)) :args ((or _let_19 _let_147))) _let_151 :args (_let_19 true _let_147)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_38 _let_39 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_146)) :args ((or _let_145 _let_37 (not _let_146)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_147 3)) (CONG _let_152 (MACRO_SR_PRED_INTRO :args ((= (not _let_145) _let_144))) :args _let_51)) :args ((or _let_144 _let_147))) _let_151 :args (_let_144 true _let_147)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_140 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.disjoint A B) false))))) :args _let_141)) _let_140 :args (_let_146 false _let_139)) :args (_let_37 false _let_144 false _let_146)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_143) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.disjoint D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) false))))) :args _let_143)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_87) :args ((or _let_43 _let_41 _let_44))) _let_142 _let_54 :args (_let_41 true _let_43 true _let_44)) :args (_let_40 false _let_41)) :args (_let_39 false _let_37 false _let_40)) :args (_let_36 true _let_33 false _let_31 false _let_29 false _let_22 false _let_27 false _let_24 false _let_19 true _let_18)) _let_35 :args (false true _let_34 false _let_17)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) _let_16 _let_15 _let_14 true true _let_13 _let_12 true _let_11 true true (exists ((A $$unsorted)) (tptp.top_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.the_carrier A))) (exists ((C $$unsorted)) (tptp.point_neighbourhood C A B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (and _let_9 _let_8 (tptp.relation_empty_yielding tptp.empty_set)) _let_10 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (and _let_9 _let_8) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) _let_2 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 27.14/27.33 )
% 27.14/27.33 % SZS output end Proof for SEU372+1
% 27.14/27.33 % cvc5---1.0.5 exiting
% 27.14/27.34 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------