TSTP Solution File: SEU336+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU336+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 16:31:00 EDT 2023
% Result : Theorem 0.66s 0.88s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU336+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 20:19:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.66/0.88 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.cOLRcCQmq0/cvc5---1.0.5_22918.p...
% 0.66/0.88 ------- get file name : TPTP file name is SEU336+1
% 0.66/0.88 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22918.smt2...
% 0.66/0.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.66/0.88 % SZS status Theorem for SEU336+1
% 0.66/0.88 % SZS output start Proof for SEU336+1
% 0.66/0.88 (
% 0.66/0.88 (let ((_let_1 (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.open_subset B A) (tptp.closed_subset (tptp.subset_complement _let_1 B) A))))))))) (let ((_let_2 (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_complement _let_1 B) A))))))))) (let ((_let_3 (not (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element B (tptp.powerset (tptp.powerset _let_1))) (= (tptp.closed_subsets B A) (tptp.open_subsets (tptp.complements_of_subsets _let_1 B) A)))))))))) (let ((_let_4 (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_5 (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_6 (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_7 (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_8 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.closed_subsets B A) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (=> (tptp.in C B) (tptp.closed_subset C A))))))))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (= (tptp.open_subsets B A) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.the_carrier A))) (=> (tptp.in C B) (tptp.open_subset C A))))))))))) (let ((_let_10 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.subset_complement _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_12 (tptp.closed_subset _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.in _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.powerset _let_10))) (let ((_let_16 (tptp.element _let_11 _let_15))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_14 _let_12))) (let ((_let_19 (tptp.open_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (= _let_19 _let_12))) (let ((_let_21 (not _let_12))) (let ((_let_22 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 _let_15))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.top_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_20))) (let ((_let_27 (forall ((A $$unsorted) (BOUND_VARIABLE_1587 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1587 (tptp.powerset _let_1))) (= (tptp.open_subset BOUND_VARIABLE_1587 A) (tptp.closed_subset (tptp.subset_complement _let_1 BOUND_VARIABLE_1587) A))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (tptp.complements_of_subsets _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_30 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_23 _let_31 _let_19))) (let ((_let_33 (forall ((C $$unsorted)) (let ((_let_1 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.element C (tptp.powerset _let_1))) (not (tptp.in C (tptp.complements_of_subsets _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (tptp.open_subset C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (tptp.open_subsets _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (= _let_35 _let_33))) (let ((_let_37 (not _let_33))) (let ((_let_38 (tptp.powerset _let_15))) (let ((_let_39 (tptp.element _let_29 _let_38))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_25 _let_40 _let_36))) (let ((_let_42 (forall ((A $$unsorted) (BOUND_VARIABLE_1361 $$unsorted)) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1361 (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (= (tptp.open_subsets BOUND_VARIABLE_1361 A) (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.the_carrier A)))) (not (tptp.in C BOUND_VARIABLE_1361)) (tptp.open_subset C A)))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_38))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_39))) (let ((_let_47 (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_48 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (tptp.closed_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_50 (= _let_49 _let_35))) (let ((_let_51 (or _let_25 _let_45 _let_50))) (let ((_let_52 (forall ((A $$unsorted) (BOUND_VARIABLE_1532 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1532 (tptp.powerset (tptp.powerset _let_1)))) (= (tptp.closed_subsets BOUND_VARIABLE_1532 A) (tptp.open_subsets (tptp.complements_of_subsets _let_1 BOUND_VARIABLE_1532) A))))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (or))) (let ((_let_56 (not _let_52))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_54) :args (_let_56))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_52))) (REFL :args (_let_53)) :args _let_55)) _let_54 :args (_let_53 true _let_52)))) (let ((_let_58 (REFL :args (_let_51)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_55)) :args ((or _let_44 _let_51))) _let_57 :args (_let_44 true _let_51)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_39 (not _let_46)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complements_of_subsets A B)))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_39 false _let_44 false _let_46)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_55)) :args ((or _let_24 _let_51))) _let_57 :args (_let_24 true _let_51)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_25 _let_40 _let_36 (not _let_41)))) _let_61 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.open_subsets BOUND_VARIABLE_1361 A)))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_36 false _let_24 false _let_39 false _let_41)))) (let ((_let_63 (not _let_35))) (let ((_let_64 (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.closed_subset C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_65 (= _let_49 _let_64))) (let ((_let_66 (tptp.closed_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_67 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_15))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_68 _let_66))) (let ((_let_72 (tptp.subset_complement _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_73 (tptp.open_subset _let_72 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_74 (tptp.in _let_72 _let_29))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.element _let_72 _let_15))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_75 _let_73))) (let ((_let_79 (= _let_66 _let_73))) (let ((_let_80 (or _let_25 _let_70 _let_79))) (let ((_let_81 (or _let_70 _let_76))) (let ((_let_82 (= _let_67 _let_74))) (let ((_let_83 (or _let_70 _let_82))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 2)) _let_57 :args ((not _let_50) true _let_51)))) (let ((_let_85 (_let_50))) (let ((_let_86 (or _let_25 _let_45 _let_65))) (let ((_let_87 (forall ((A $$unsorted) (BOUND_VARIABLE_1394 $$unsorted)) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1394 (tptp.powerset (tptp.powerset (tptp.the_carrier A))))) (= (tptp.closed_subsets BOUND_VARIABLE_1394 A) (forall ((C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.the_carrier A)))) (not (tptp.in C BOUND_VARIABLE_1394)) (tptp.closed_subset C A)))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_25 _let_45 _let_65 (not _let_86)))) _let_61 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1394 (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) false))))) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_65 false _let_24 false _let_44 false _let_86)))) (let ((_let_90 (not _let_65))) (let ((_let_91 (not _let_64))) (let ((_let_92 (_let_65))) (let ((_let_93 (not _let_36))) (let ((_let_94 (_let_36))) (let ((_let_95 (_let_91))) (let ((_let_96 (_let_33))) (let ((_let_97 (REFL :args (_let_71)))) (let ((_let_98 (forall ((A $$unsorted) (BOUND_VARIABLE_1560 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.top_str A)) (not (tptp.element BOUND_VARIABLE_1560 (tptp.powerset _let_1))) (= (tptp.closed_subset BOUND_VARIABLE_1560 A) (tptp.open_subset (tptp.subset_complement _let_1 BOUND_VARIABLE_1560) A))))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (tptp.element (tptp.subset_complement A B) _let_1)))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (_let_100))) (let ((_let_103 ((tptp.subset_complement A B)))) (let ((_let_104 (forall ((D $$unsorted)) (let ((_let_1 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.element D (tptp.powerset _let_1))) (= (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in (tptp.subset_complement _let_1 D) (tptp.complements_of_subsets _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))))) (let ((_let_105 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.complements_of_subsets _let_10 _let_29)))) (let ((_let_106 (= _let_105 _let_104))) (let ((_let_107 (or _let_40 _let_45 _let_106))) (let ((_let_108 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1425 $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (or (not (tptp.element B _let_1)) (not (tptp.element BOUND_VARIABLE_1425 _let_1)) (= (= (tptp.complements_of_subsets A B) BOUND_VARIABLE_1425) (forall ((D $$unsorted)) (or (not (tptp.element D (tptp.powerset A))) (= (tptp.in (tptp.subset_complement A D) B) (tptp.in D BOUND_VARIABLE_1425)))))))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (_let_108))) (let ((_let_111 (tptp.powerset (tptp.powerset A)))) (let ((_let_112 ((not (= (tptp.element B _let_111) false)) (not (= (tptp.element BOUND_VARIABLE_1425 _let_111) false))))) (let ((_let_113 (or _let_45 _let_105))) (let ((_let_114 (forall ((A $$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_115 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (_let_104))) (let ((_let_117 ((not (= (tptp.element D _let_15) false))))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_82)) :args ((or _let_68 _let_74 (not _let_82)))) (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_73 _let_77 _let_75 (not _let_78)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_79)) :args ((or _let_66 (not _let_73) (not _let_79)))) (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_70 _let_82 (not _let_83)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_116) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_117)) :args _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_106)) :args ((or (not _let_105) _let_104 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_45 _let_105 (not _let_113)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_114))) _let_115 :args (_let_113 false _let_114)) :args (_let_105 false _let_44 false _let_113)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_45 _let_40 _let_106 (not _let_107)))) _let_59 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_109 :args (_let_10 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_112)) :args _let_110))) _let_109 :args (_let_107 false _let_108)) :args (_let_106 false _let_44 false _let_39 false _let_107)) :args (_let_104 false _let_105 false _let_106)) :args (_let_83 false _let_104)) (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_70 _let_76 (not _let_81)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_103)) :args _let_102)) _let_101 :args (_let_81 false _let_100)) (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_25 _let_70 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_99 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1560 (tptp.powerset (tptp.the_carrier A))) false))))) :args (_let_98))) _let_99 :args (_let_80 false _let_98)) _let_61 (CNF_OR_NEG :args (_let_71 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 1)) (CONG _let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_55)) :args ((or _let_67 _let_71))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 0)) (CONG _let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_69))) :args _let_55)) :args ((or _let_69 _let_71))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_96) :args (_let_72 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.open_subset C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) true))))) :args _let_96)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_95)) :args _let_95)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_64))) (REFL :args ((not _let_71))) :args _let_55)) (REORDERING (CNF_EQUIV_POS1 :args _let_94) :args ((or _let_63 _let_33 _let_93))) _let_62 (REORDERING (CNF_EQUIV_POS2 :args _let_92) :args ((or _let_49 _let_91 _let_90))) _let_89 (REORDERING (CNF_EQUIV_NEG1 :args _let_85) :args ((or _let_49 _let_35 _let_50))) _let_84 :args (_let_49 true _let_74 true _let_73 false _let_82 false _let_83 false _let_76 false _let_81 false _let_79 false _let_80 false _let_24 true _let_66 false _let_67 false _let_69 false _let_78 true _let_71 false _let_33 false _let_36 true _let_64 false _let_65 false _let_35 true _let_50)))) (let ((_let_119 (_let_37))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_119)) :args _let_119)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_33))) (REFL :args (_let_34)) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_94) :args ((or _let_35 _let_37 _let_93))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_85) _let_84 _let_118 :args (_let_63 true _let_50 false _let_49)) _let_62 :args (_let_37 true _let_35 false _let_36)) :args (_let_34 true _let_33)))) (let ((_let_121 (REFL :args (_let_32)))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 0)) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_55)) :args ((or _let_22 _let_32))) _let_120 :args (_let_22 true _let_32)))) (let ((_let_123 (= _let_30 _let_13))) (let ((_let_124 (or _let_23 _let_123))) (let ((_let_125 (forall ((D $$unsorted)) (let ((_let_1 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (or (not (tptp.element D (tptp.powerset _let_1))) (= (tptp.in (tptp.subset_complement _let_1 D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.in D (tptp.complements_of_subsets _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))))))) (let ((_let_126 (or _let_45 _let_40 _let_125))) (let ((_let_127 (_let_125))) (let ((_let_128 (_let_64))) (let ((_let_129 (or _let_23 _let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_12 _let_14 _let_17 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_129)) :args ((or _let_23 _let_16 (not _let_129)))) _let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_103)) :args _let_102)) _let_101 :args (_let_129 false _let_100)) :args (_let_16 false _let_22 false _let_129)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_128) :args (_let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_128)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_92) :args ((or (not _let_49) _let_64 _let_90))) _let_118 _let_89 :args (_let_64 false _let_49 false _let_65)) :args (_let_18 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_123)) :args ((or _let_31 _let_13 (not _let_123)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 1)) (CONG _let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_55)) :args ((or _let_30 _let_32))) _let_120 :args (_let_30 true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_23 _let_123 (not _let_124)))) _let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_127) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_117)) :args _let_127))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_45 _let_40 _let_125 (not _let_126)))) _let_59 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_109 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_29 QUANTIFIERS_INST_E_MATCHING _let_112)) :args _let_110))) _let_109 :args (_let_126 false _let_108)) :args (_let_125 false _let_44 false _let_39 false _let_126)) :args (_let_124 false _let_125)) :args (_let_123 false _let_22 false _let_124)) :args (_let_13 false _let_30 false _let_123)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_20)) :args ((or _let_19 _let_21 (not _let_20)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_32 2)) _let_120 :args ((not _let_19) true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 _let_20 (not _let_26)))) _let_61 _let_122 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1587 (tptp.powerset (tptp.the_carrier A))) false))))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_20 false _let_24 false _let_22 false _let_26)) :args (_let_21 true _let_19 false _let_20)) :args (false false _let_16 false _let_18 false _let_13 true _let_12)) :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 $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) _let_9 _let_8 _let_7 true true _let_6 _let_5 (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))) 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 $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (and (tptp.empty tptp.empty_set) (tptp.v1_membered tptp.empty_set) (tptp.v2_membered tptp.empty_set) (tptp.v3_membered tptp.empty_set) (tptp.v4_membered tptp.empty_set) (tptp.v5_membered tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) _let_4 (exists ((A $$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)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.66/0.88 )
% 0.66/0.88 % SZS output end Proof for SEU336+1
% 0.66/0.88 % cvc5---1.0.5 exiting
% 0.66/0.89 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------