TSTP Solution File: SET506-6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET506-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:38:58 EDT 2023
% Result : Unsatisfiable 11.00s 11.19s
% Output : Proof 11.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET506-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 11:12:26 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.rMQNKpAsd0/cvc5---1.0.5_30936.p...
% 0.21/0.51 ------- get file name : TPTP file name is SET506-6
% 0.21/0.52 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30936.smt2...
% 0.21/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.53/10.73 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.00/11.19 % SZS status Unsatisfiable for SET506-6
% 11.00/11.19 % SZS output start Proof for SET506-6
% 11.00/11.20 (
% 11.00/11.20 (let ((_let_1 (= tptp.universal_class tptp.null_class))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (tptp.cross_product tptp.universal_class _let_2))) (let ((_let_4 (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation))) (let ((_let_5 (= _let_4 tptp.singleton_relation))) (let ((_let_6 (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation))) (let ((_let_7 (= _let_6 tptp.identity_relation))) (let ((_let_8 (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation)))) (let ((_let_9 (tptp.complement _let_8))) (let ((_let_10 (= (tptp.intersection _let_2 (tptp.intersection _let_2 _let_9)) tptp.subset_relation))) (let ((_let_11 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))) (let ((_let_12 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_13 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))))) (let ((_let_19 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))) (let ((_let_20 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_21 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_22 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_23 (tptp.member _let_8 _let_9))) (let ((_let_24 (tptp.member _let_8 tptp.null_class))) (let ((_let_25 (= tptp.null_class _let_9))) (let ((_let_26 (tptp.member _let_8 _let_8))) (let ((_let_27 (not _let_26))) (let ((_let_28 (not _let_23))) (let ((_let_29 (or _let_28 _let_27))) (let ((_let_30 (_let_12))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (_let_8 _let_8 QUANTIFIERS_INST_ENUM))) (let ((_let_33 (tptp.ordered_pair _let_8 _let_8))) (let ((_let_34 (tptp.member _let_33 tptp.element_relation))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_26))) (let ((_let_37 (_let_14))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (tptp.singleton _let_8))) (let ((_let_40 (tptp.unordered_pair _let_8 _let_39))) (let ((_let_41 (tptp.unordered_pair _let_39 _let_40))) (let ((_let_42 (tptp.member _let_41 tptp.null_class))) (let ((_let_43 (= _let_33 _let_41))) (let ((_let_44 (= tptp.element_relation tptp.null_class))) (let ((_let_45 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.null_class)))) (let ((_let_46 (SYMM (ASSUME :args (_let_10))))) (let ((_let_47 (EQ_RESOLVE (SYMM (ASSUME :args (_let_7))) (MACRO_SR_EQ_INTRO _let_46 :args ((= tptp.identity_relation _let_6) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (AND_INTRO (ASSUME :args (_let_1)) (EQ_RESOLVE (SYMM (ASSUME :args (_let_5))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_47 _let_46) :args ((= tptp.singleton_relation _let_4) SB_DEFAULT SBA_FIXPOINT))) _let_47 _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO _let_48 :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (_let_15))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (tptp.subclass tptp.null_class tptp.element_relation))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.subclass tptp.element_relation tptp.null_class))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_44))) (let ((_let_57 (_let_17))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (tptp.subclass tptp.element_relation tptp.element_relation))) (let ((_let_60 (tptp.not_subclass_element tptp.null_class tptp.element_relation))) (let ((_let_61 (tptp.member _let_60 tptp.null_class))) (let ((_let_62 (or _let_61 _let_52))) (let ((_let_63 (tptp.member _let_60 tptp.element_relation))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_52))) (let ((_let_66 (tptp.regular tptp.element_relation))) (let ((_let_67 (tptp.intersection tptp.element_relation _let_66))) (let ((_let_68 (= tptp.null_class _let_67))) (let ((_let_69 (or _let_44 _let_68))) (let ((_let_70 (tptp.member _let_60 _let_67))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_63))) (let ((_let_73 (forall ((Y $$unsorted)) (tptp.subclass Y Y)))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_76 (or))) (let ((_let_77 (not _let_44))) (let ((_let_78 (ASSUME :args (_let_59)))) (let ((_let_79 (ASSUME :args (_let_44)))) (let ((_let_80 (SYMM _let_79))) (let ((_let_81 (ASSUME :args (_let_53)))) (let ((_let_82 (_let_21))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (tptp.null_class tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_85 (_let_20))) (let ((_let_86 (ASSUME :args _let_85))) (let ((_let_87 (forall ((X $$unsorted)) (or (= tptp.null_class X) (= tptp.null_class (tptp.intersection X (tptp.regular X))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_87))) (let ((_let_90 (_let_13))) (let ((_let_91 (ASSUME :args _let_90))) (let ((_let_92 (and _let_68 _let_61))) (let ((_let_93 (ASSUME :args (_let_61)))) (let ((_let_94 (APPLY_UF tptp.member))) (let ((_let_95 (ASSUME :args (_let_68)))) (let ((_let_96 (forall ((X $$unsorted)) (tptp.subclass X tptp.null_class)))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO _let_48 :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (_let_96))) (let ((_let_99 (and _let_44 _let_43 _let_42))) (let ((_let_100 (ASSUME :args (_let_42)))) (let ((_let_101 (ASSUME :args (_let_43)))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_26 _let_35 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_99)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_100 _let_101 _let_79) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_101)) (SYMM _let_80) :args _let_94) (TRUE_INTRO _let_100))) :args (_let_42 _let_43 _let_44))) :args (_let_44 _let_43 _let_42))) :args (true _let_99)) :args ((or _let_77 _let_34 (not _let_43) (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_53 _let_44 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args _let_75) :args _let_98)) _let_97 :args (_let_54 false _let_96)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_92)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_93 _let_95) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_60)) (SYMM _let_95) :args _let_94) (TRUE_INTRO _let_93))) :args (_let_61 _let_68))) :args (_let_68 _let_61))) :args (true _let_92)) (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_63 _let_71 (not _let_72)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_60 tptp.element_relation _let_66 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_90)) _let_91 :args (_let_72 false _let_13)) (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_44 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_88 :args _let_75) :args _let_89))) _let_88 :args (_let_69 false _let_87)) (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_52 _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args _let_84) :args _let_85)) _let_86 :args (_let_65 false _let_20)) (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_52 _let_61 (not _let_62)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args _let_84) :args _let_82)) _let_83 :args (_let_62 false _let_21)) (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_78 _let_79 _let_81) :args (_let_59 _let_53 _let_44)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_81)) (CONG _let_80 (REFL :args (tptp.element_relation)) :args (APPLY_UF tptp.subclass)) (TRUE_INTRO _let_78))) :args (_let_59 _let_44 _let_53)) :args ((not (and _let_59 _let_53 _let_44)) SB_LITERAL))) (CONG (REFL :args ((not _let_59))) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) (REFL :args (_let_77)) :args _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args _let_75) :args (_let_73))) _let_74 :args (_let_59 false _let_73)) :args (_let_52 true _let_70 false _let_72 false _let_68 false _let_69 true _let_63 false _let_65 false _let_61 false _let_62 true _let_44 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.element_relation tptp.null_class QUANTIFIERS_INST_ENUM)) :args _let_57)) _let_58 :args (_let_56 false _let_17)) :args (_let_44 false _let_54 false _let_52 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args _let_32) :args _let_50))) _let_51 :args (_let_43 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_39 _let_40 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_45))) _let_49 :args (_let_42 false _let_45)) :args (_let_34 false _let_44 false _let_43 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args _let_32) :args _let_37)) _let_38 :args (_let_36 false _let_14)) :args (_let_26 false _let_34 false _let_36)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_27 _let_28 (not _let_29)))) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args _let_32) :args _let_30)) _let_31 :args (_let_29 false _let_12)) :args (_let_28 false _let_26 false _let_29)))) (let ((_let_104 (tptp.subclass _let_8 tptp.null_class))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_27 _let_24))) (let ((_let_107 (_let_22))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_24 _let_105 _let_27 (not _let_106)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_8 QUANTIFIERS_INST_ENUM)) :args _let_98)) _let_97 :args (_let_104 false _let_96)) _let_102 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_8 tptp.null_class _let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_107)) _let_108 :args (_let_106 false _let_22)) :args (_let_24 false _let_104 false _let_26 false _let_106)))) (let ((_let_110 (tptp.regular _let_9))) (let ((_let_111 (tptp.intersection _let_9 _let_110))) (let ((_let_112 (= tptp.null_class _let_111))) (let ((_let_113 (or _let_25 _let_112))) (let ((_let_114 (tptp.member _let_8 _let_111))) (let ((_let_115 (not _let_112))) (let ((_let_116 (not _let_114))) (let ((_let_117 (or _let_116 _let_23))) (let ((_let_118 (REFL :args ((not _let_24))))) (let ((_let_119 (ASSUME :args (_let_24)))) (let ((_let_120 (TRUE_INTRO _let_119))) (let ((_let_121 (REFL :args (_let_8)))) (let ((_let_122 (ASSUME :args (_let_25)))) (let ((_let_123 (ASSUME :args (_let_28)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_119 _let_122 _let_123) :args (_let_24 _let_28 _let_25)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_123)) (CONG _let_121 (SYMM _let_122) :args _let_94) _let_120)) :args (_let_24 _let_25 _let_28)) :args ((not (and _let_24 _let_28 _let_25)) SB_LITERAL))) (CONG _let_118 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_23))) (REFL :args ((not _let_25))) :args _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_25 _let_112 (not _let_113)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_116)))) (CONG _let_121 (SYMM (ASSUME :args (_let_112))) :args _let_94) _let_120)) :args (_let_24 _let_112 _let_116))) (CONG _let_118 (REFL :args (_let_115)) (MACRO_SR_PRED_INTRO :args ((= (not _let_116) _let_114))) :args _let_76)) _let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_23 _let_116 (not _let_117)))) _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_8 _let_9 _let_110 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_90)) _let_91 :args (_let_117 false _let_13)) :args (_let_116 true _let_23 false _let_117)) :args (_let_115 false _let_24 true _let_114)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_9 QUANTIFIERS_INST_ENUM)) :args _let_89)) _let_88 :args (_let_113 false _let_87)) :args (_let_25 true _let_112 false _let_113)) _let_109 _let_103 :args (false false _let_25 false _let_24 true _let_23)) :args (_let_22 _let_21 _let_20 _let_19 _let_18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))) _let_17 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) _let_16 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) _let_15 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_2) _let_14 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) _let_13 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) _let_12 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))) (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))) (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.rotate X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.flip X))))) (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))) (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))) (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (= (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) _let_11 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (tptp.function tptp.choice) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))) (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) _let_10 _let_7 (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))) (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (= (tptp.cross_product _let_2 _let_2) _let_1))))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.function Xf)) (not (= (tptp.cross_product _let_2 _let_2) _let_1)) (not (tptp.subclass (tptp.range_of Xf) _let_2)) (tptp.operation Xf))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member _let_1 (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 _let_1)))))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (let ((_let_1 (tptp.not_homomorphism2 Xh Xf1 Xf2))) (let ((_let_2 (tptp.not_homomorphism1 Xh Xf1 Xf2))) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh _let_2) (tptp.apply Xh _let_1))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair _let_2 _let_1))))) (tptp.homomorphism Xh Xf1 Xf2))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.compose_class X) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X))) (= (tptp.compose X Y) Z))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_3) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.composition_function)) (= (tptp.compose X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.compose X Y))) tptp.composition_function))) (tptp.subclass tptp.domain_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.domain_relation)) (= (tptp.domain_of X) Y))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.domain_of X)) tptp.domain_relation))) (forall ((X $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued1 X))) (forall ((X $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued2 X))) (forall ((X $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))) _let_5 (tptp.subclass tptp.application_function _let_3) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (tptp.member Y (tptp.domain_of X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (= (tptp.apply X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class)))) (not (tptp.member Y (tptp.domain_of X))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.apply X Y))) tptp.application_function))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subclass (tptp.range_of Xf) Y))) (forall ((Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.subclass (tptp.range_of Xf) Y)) (tptp.maps Xf (tptp.domain_of Xf) Y))) _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.00/11.20 )
% 11.00/11.20 % SZS output end Proof for SET506-6
% 11.00/11.20 % cvc5---1.0.5 exiting
% 11.06/11.40 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------