TSTP Solution File: SET510-6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET510-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 14:38:59 EDT 2023
% Result : Unsatisfiable 14.63s 14.89s
% Output : Proof 14.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET510-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 13:46:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.GtxPxxuPaf/cvc5---1.0.5_30897.p...
% 0.20/0.51 ------- get file name : TPTP file name is SET510-6
% 0.20/0.52 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_30897.smt2...
% 0.20/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.54/10.71 --- Run --no-e-matching --full-saturate-quant at 5...
% 14.63/14.89 % SZS status Unsatisfiable for SET510-6
% 14.63/14.89 % SZS output start Proof for SET510-6
% 14.63/14.89 (
% 14.63/14.89 (let ((_let_1 (tptp.singleton tptp.universal_class))) (let ((_let_2 (not (= _let_1 tptp.null_class)))) (let ((_let_3 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_4 (tptp.cross_product tptp.universal_class _let_3))) (let ((_let_5 (tptp.complement tptp.element_relation))) (let ((_let_6 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))) (let ((_let_7 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))) (let ((_let_8 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_9 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_12 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_13 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_17 (tptp.unordered_pair tptp.universal_class tptp.universal_class))) (let ((_let_18 (tptp.regular _let_17))) (let ((_let_19 (= tptp.null_class (tptp.intersection _let_17 _let_18)))) (let ((_let_20 (= tptp.universal_class _let_18))) (let ((_let_21 (tptp.member tptp.universal_class (tptp.intersection _let_17 tptp.universal_class)))) (let ((_let_22 (tptp.member tptp.universal_class _let_5))) (let ((_let_23 (= tptp.null_class _let_5))) (let ((_let_24 (= tptp.null_class _let_17))) (let ((_let_25 (or _let_24 _let_19))) (let ((_let_26 (forall ((X $$unsorted)) (or (= tptp.null_class X) (= tptp.null_class (tptp.intersection X (tptp.regular X))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 (_let_17 QUANTIFIERS_INST_ENUM))) (let ((_let_30 (= _let_1 _let_17))) (let ((_let_31 (= tptp.null_class _let_1))) (let ((_let_32 (not _let_24))) (let ((_let_33 (_let_11))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (SYMM (ASSUME :args (_let_2))))) (let ((_let_36 (or))) (let ((_let_37 (not _let_31))) (let ((_let_38 (and _let_37 _let_30))) (let ((_let_39 (_let_37 _let_30))) (let ((_let_40 (ASSUME :args (_let_30)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_38)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_35 _let_40) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (tptp.null_class)) (SYMM _let_40) :args (=)) (FALSE_INTRO _let_35))) :args _let_39)) :args _let_39)) :args (true _let_38)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_31))) (REFL :args ((not _let_30))) (REFL :args (_let_32)) :args _let_36)) _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.universal_class QUANTIFIERS_INST_ENUM)) :args _let_33))) _let_34 :args (_let_30 false _let_11)) :args (_let_32 true _let_31 false _let_30)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_19 (not _let_25)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args _let_29) :args _let_28)) _let_27 :args (_let_25 false _let_26)) :args (_let_19 true _let_24 false _let_25)))) (let ((_let_43 (tptp.member _let_18 _let_17))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_20 _let_20))) (let ((_let_46 (_let_12))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 (or _let_24 _let_43))) (let ((_let_49 (forall ((X $$unsorted)) (or (= tptp.null_class X) (tptp.member (tptp.regular X) X))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_24 _let_43 (not _let_48)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args _let_29) :args (_let_49))) _let_50 :args (_let_48 false _let_49)) :args (_let_43 true _let_24 false _let_48)))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_45))) :args ((or _let_44 _let_20 (not _let_45)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_47 :args (_let_18 tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_PROP)) :args _let_46))) _let_47 :args (_let_45 false _let_12)) :args (_let_20 false _let_43 false _let_45)))) (let ((_let_53 (tptp.member tptp.universal_class tptp.universal_class))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.member tptp.universal_class _let_17))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54 _let_21))) (let ((_let_58 (_let_9))) (let ((_let_59 (ASSUME :args _let_58))) (let ((_let_60 (not _let_20))) (let ((_let_61 (and _let_43 _let_20))) (let ((_let_62 (_let_43 _let_20))) (let ((_let_63 (ASSUME :args (_let_43)))) (let ((_let_64 (APPLY_UF tptp.member))) (let ((_let_65 (REFL :args (_let_17)))) (let ((_let_66 (ASSUME :args (_let_20)))) (let ((_let_67 (SYMM _let_66))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_61)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_63 _let_66) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_67) _let_65 :args _let_64) (TRUE_INTRO _let_63))) :args _let_62)) :args _let_62)) :args (true _let_61)) :args ((or _let_55 _let_44 _let_60))) _let_51 _let_52 :args (_let_55 false _let_43 false _let_20)))) (let ((_let_69 (tptp.subclass _let_17 tptp.universal_class))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_56 _let_53))) (let ((_let_72 (_let_16))) (let ((_let_73 (ASSUME :args _let_72))) (let ((_let_74 (_let_13))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_54 _let_56 _let_21 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_53 _let_56 _let_70 (not _let_71)))) _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args _let_29) :args _let_74)) _let_75 :args (_let_69 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (_let_17 tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_72)) _let_73 :args (_let_71 false _let_16)) :args (_let_53 false _let_55 false _let_69 false _let_71)) _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.universal_class _let_17 tptp.universal_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_58)) _let_59 :args (_let_57 false _let_9)) :args (_let_21 false _let_53 false _let_55 false _let_57)))) (let ((_let_77 (tptp.member tptp.universal_class tptp.element_relation))) (let ((_let_78 (not _let_77))) (let ((_let_79 (not _let_22))) (let ((_let_80 (or _let_79 _let_78))) (let ((_let_81 (_let_8))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (tptp.member tptp.universal_class tptp.null_class))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.subclass tptp.null_class tptp.element_relation))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_84 _let_77))) (let ((_let_88 (not _let_21))) (let ((_let_89 (not _let_19))) (let ((_let_90 (and _let_19 _let_20 _let_21))) (let ((_let_91 (ASSUME :args (_let_21)))) (let ((_let_92 (TRUE_INTRO _let_91))) (let ((_let_93 (ASSUME :args (_let_19)))) (let ((_let_94 (REFL :args (tptp.universal_class)))) (let ((_let_95 (CONG _let_94 (TRANS (SYMM (SYMM _let_93)) (CONG _let_65 _let_67 :args (APPLY_UF tptp.intersection))) :args _let_64))) (let ((_let_96 (tptp.not_subclass_element tptp.null_class tptp.element_relation))) (let ((_let_97 (tptp.member _let_96 tptp.null_class))) (let ((_let_98 (or _let_97 _let_85))) (let ((_let_99 (tptp.member _let_96 tptp.element_relation))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_100 _let_85))) (let ((_let_102 (tptp.regular tptp.element_relation))) (let ((_let_103 (tptp.intersection tptp.element_relation _let_102))) (let ((_let_104 (= tptp.null_class _let_103))) (let ((_let_105 (= tptp.element_relation tptp.null_class))) (let ((_let_106 (or _let_105 _let_104))) (let ((_let_107 (_let_15))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 (tptp.null_class tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args _let_109) :args _let_107)) _let_108 :args (_let_98 false _let_15)))) (let ((_let_111 (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_85 _let_97 (not _let_98)))))) (let ((_let_112 (_let_14))) (let ((_let_113 (ASSUME :args _let_112))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args _let_109) :args _let_112)) _let_113 :args (_let_101 false _let_14)))) (let ((_let_115 (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_85 _let_100 (not _let_101)))))) (let ((_let_116 (tptp.member _let_96 _let_103))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_117 _let_99))) (let ((_let_119 (_let_10))) (let ((_let_120 (ASSUME :args _let_119))) (let ((_let_121 (and _let_104 _let_97))) (let ((_let_122 (ASSUME :args (_let_97)))) (let ((_let_123 (TRUE_INTRO _let_122))) (let ((_let_124 (ASSUME :args (_let_104)))) (let ((_let_125 (REFL :args (_let_96)))) (let ((_let_126 (not _let_97))) (let ((_let_127 (not _let_105))) (let ((_let_128 (ASSUME :args (_let_105)))) (let ((_let_129 (ASSUME :args (_let_100)))) (let ((_let_130 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_78 _let_79 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_77 _let_86 _let_84 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_122 _let_128 _let_129) :args (_let_105 _let_97 _let_100)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_129)) (CONG _let_125 (SYMM (SYMM _let_128)) :args _let_64) _let_123)) :args (_let_97 _let_105 _let_100)) :args ((not (and _let_105 _let_97 _let_100)) SB_LITERAL))) (CONG (REFL :args (_let_127)) (REFL :args (_let_126)) (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_99))) :args _let_36)) :args ((or _let_127 _let_99 _let_126))) (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_105 _let_104 (not _let_106)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.element_relation QUANTIFIERS_INST_ENUM)) :args _let_28))) _let_27 :args (_let_106 false _let_26)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_121)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_122 _let_124) (SCOPE (TRUE_ELIM (TRANS (CONG _let_125 (SYMM _let_124) :args _let_64) _let_123)) :args (_let_97 _let_104))) :args (_let_104 _let_97))) :args (true _let_121)) (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_99 _let_117 (not _let_118)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (_let_96 tptp.element_relation _let_102 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_119)) _let_120 :args (_let_118 false _let_10)) _let_115 _let_114 _let_111 _let_110 :args ((or (not _let_104) _let_85) true _let_116 false _let_118 true _let_99 false _let_101 false _let_97 false _let_98)) _let_115 _let_114 _let_111 _let_110 :args (_let_85 false _let_105 false _let_106 true _let_104 true _let_99 false _let_101 false _let_97 false _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_90)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_91 _let_66 _let_93) (SCOPE (TRUE_ELIM (TRANS _let_95 _let_92)) :args (_let_21 _let_20 _let_19))) :args (_let_19 _let_20 _let_21))) :args (true _let_90)) :args ((or _let_83 _let_89 _let_60 _let_88))) _let_42 _let_52 _let_76 :args (_let_83 false _let_19 false _let_20 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (tptp.null_class tptp.element_relation tptp.universal_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_72)) _let_73 :args (_let_87 false _let_16)) :args (_let_77 false _let_85 false _let_83 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (tptp.universal_class tptp.element_relation QUANTIFIERS_INST_ENUM)) :args _let_81)) _let_82 :args (_let_80 false _let_8)) :args (_let_79 false _let_77 false _let_80)))) (let ((_let_131 (tptp.regular _let_5))) (let ((_let_132 (tptp.intersection _let_5 _let_131))) (let ((_let_133 (= tptp.null_class _let_132))) (let ((_let_134 (or _let_23 _let_133))) (let ((_let_135 (tptp.member tptp.universal_class _let_132))) (let ((_let_136 (not _let_133))) (let ((_let_137 (not _let_135))) (let ((_let_138 (or _let_137 _let_22))) (let ((_let_139 (REFL :args (_let_88)))) (let ((_let_140 (REFL :args (_let_60)))) (let ((_let_141 (REFL :args (_let_89)))) (let ((_let_142 (ASSUME :args (_let_133)))) (let ((_let_143 (ASSUME :args (_let_137)))) (let ((_let_144 (ASSUME :args (_let_23)))) (let ((_let_145 (ASSUME :args (_let_79)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_91 _let_66 _let_93 _let_144 _let_145) :args (_let_79 _let_23 _let_19 _let_20 _let_21)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_145)) (CONG _let_94 (SYMM _let_144) :args _let_64) _let_95 _let_92)) :args (_let_21 _let_20 _let_19 _let_23 _let_79)) :args ((not (and _let_79 _let_23 _let_19 _let_20 _let_21)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_22))) (REFL :args ((not _let_23))) _let_141 _let_140 _let_139 :args _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_23 _let_133 (not _let_134)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_91 _let_66 _let_93 _let_142 _let_143) :args (_let_133 _let_19 _let_20 _let_21 _let_137)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_143)) (CONG _let_94 (SYMM _let_142) :args _let_64) _let_95 _let_92)) :args (_let_21 _let_20 _let_19 _let_133 _let_137)) :args ((not (and _let_133 _let_19 _let_20 _let_21 _let_137)) SB_LITERAL))) (CONG (REFL :args (_let_136)) _let_141 _let_140 _let_139 (MACRO_SR_PRED_INTRO :args ((= (not _let_137) _let_135))) :args _let_36)) _let_42 _let_52 _let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_138)) :args ((or _let_22 _let_137 (not _let_138)))) _let_130 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (tptp.universal_class _let_5 _let_131 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_119)) _let_120 :args (_let_138 false _let_10)) :args (_let_137 true _let_22 false _let_138)) :args (_let_136 false _let_19 false _let_20 false _let_21 true _let_135)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_5 QUANTIFIERS_INST_ENUM)) :args _let_28)) _let_27 :args (_let_134 false _let_26)) :args (_let_23 true _let_133 false _let_134)) _let_130 _let_76 _let_52 _let_42 :args (false false _let_23 true _let_22 false _let_21 false _let_20 false _let_19)) :args (_let_16 _let_15 _let_14 _let_13 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))) _let_12 (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)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) _let_11 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (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 $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_3) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) _let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) _let_9 _let_8 (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 $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_3) (forall ((X $$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))) _let_7 _let_6 (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))) (= (tptp.intersection _let_3 (tptp.intersection _let_3 (tptp.complement (tptp.compose _let_5 (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (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 $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_4) (forall ((X $$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_3) (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))) (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation) (tptp.subclass tptp.application_function _let_4) (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_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 14.63/14.89 )
% 14.63/14.90 % SZS output end Proof for SET510-6
% 14.73/14.90 % cvc5---1.0.5 exiting
% 14.73/14.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------