TSTP Solution File: SET507-6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET507-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 10.61s 11.11s
% Output : Proof 10.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET507-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.13 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:52:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.49 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.N0f4mEIVUx/cvc5---1.0.5_2540.p...
% 0.21/0.51 ------- get file name : TPTP file name is SET507-6
% 0.21/0.52 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2540.smt2...
% 0.21/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.51/10.76 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.61/11.11 % SZS status Unsatisfiable for SET507-6
% 10.61/11.11 % SZS output start Proof for SET507-6
% 10.61/11.12 (
% 10.61/11.12 (let ((_let_1 (tptp.subclass 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.complement tptp.element_relation))) (let ((_let_5 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))))) (let ((_let_7 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_8 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_9 (tptp.subclass tptp.element_relation _let_2))) (let ((_let_10 (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)))))) (let ((_let_11 (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))))) (let ((_let_12 (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_13 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))) (let ((_let_15 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_19 (= tptp.universal_class tptp.element_relation))) (let ((_let_20 (tptp.successor tptp.universal_class))) (let ((_let_21 (= tptp.universal_class _let_20))) (let ((_let_22 (tptp.ordered_pair tptp.universal_class tptp.universal_class))) (let ((_let_23 (tptp.ordered_pair tptp.universal_class _let_22))) (let ((_let_24 (tptp.member _let_23 tptp.null_class))) (let ((_let_25 (= _let_22 _let_20))) (let ((_let_26 (tptp.regular _let_4))) (let ((_let_27 (tptp.complement tptp.universal_class))) (let ((_let_28 (tptp.member tptp.universal_class (tptp.intersection _let_27 _let_26)))) (let ((_let_29 (= tptp.null_class (tptp.intersection _let_4 _let_26)))) (let ((_let_30 (tptp.subclass tptp.element_relation tptp.universal_class))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.subclass tptp.universal_class tptp.element_relation))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31 _let_19))) (let ((_let_35 (_let_14))) (let ((_let_36 (ASSUME :args _let_35))) (let ((_let_37 (tptp.universal_class tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_38 (_let_15))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_41 (tptp.not_subclass_element tptp.universal_class tptp.element_relation))) (let ((_let_42 (tptp.member _let_41 tptp.universal_class))) (let ((_let_43 (or _let_42 _let_32))) (let ((_let_44 (tptp.member _let_41 tptp.element_relation))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_32))) (let ((_let_47 (= tptp.element_relation tptp.null_class))) (let ((_let_48 (tptp.member _let_41 tptp.null_class))) (let ((_let_49 (not _let_42))) (let ((_let_50 (not _let_1))) (let ((_let_51 (or _let_50 _let_49 _let_48))) (let ((_let_52 (tptp.regular tptp.element_relation))) (let ((_let_53 (tptp.intersection tptp.element_relation _let_52))) (let ((_let_54 (tptp.member _let_41 _let_53))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_44))) (let ((_let_57 (= tptp.null_class _let_53))) (let ((_let_58 (or _let_47 _let_57))) (let ((_let_59 (_let_17))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (_let_16))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (ASSUME :args (_let_1)))) (let ((_let_64 (or))) (let ((_let_65 (APPLY_UF tptp.subclass))) (let ((_let_66 (ASSUME :args (_let_47)))) (let ((_let_67 (REFL :args (tptp.universal_class)))) (let ((_let_68 (ASSUME :args (_let_33)))) (let ((_let_69 (_let_18))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (_let_8))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 (forall ((X $$unsorted)) (or (= tptp.null_class X) (= tptp.null_class (tptp.intersection X (tptp.regular X))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (_let_73))) (let ((_let_76 (ASSUME :args (_let_48)))) (let ((_let_77 (APPLY_UF tptp.member))) (let ((_let_78 (ASSUME :args (_let_57)))) (let ((_let_79 (ASSUME :args (_let_55)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_31 _let_19 (not _let_34)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_76 _let_78 _let_79) :args (_let_57 _let_55 _let_48)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_79)) (CONG (REFL :args (_let_41)) (SYMM _let_78) :args _let_77) (TRUE_INTRO _let_76))) :args (_let_48 _let_57 _let_55)) :args ((not (and _let_57 _let_55 _let_48)) SB_LITERAL))) (CONG (REFL :args ((not _let_57))) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) (REFL :args ((not _let_48))) :args _let_64)) (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_47 _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_74 :args _let_40) :args _let_75))) _let_74 :args (_let_58 false _let_73)) (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_44 _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_41 tptp.element_relation _let_52 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71)) _let_72 :args (_let_56 false _let_8)) (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_49 _let_48 (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.universal_class tptp.null_class _let_41 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_69)) _let_70 :args (_let_51 false _let_18)) _let_63 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_63 _let_66 _let_68) :args (_let_1 _let_33 _let_47)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_68)) (CONG _let_67 (SYMM (SYMM _let_66)) :args _let_65) (TRUE_INTRO _let_63))) :args (_let_1 _let_47 _let_33)) :args ((not (and _let_1 _let_33 _let_47)) SB_LITERAL))) (CONG (REFL :args (_let_50)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) (REFL :args ((not _let_47))) :args _let_64)) _let_63 (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_32 _let_45 (not _let_46)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args _let_37) :args _let_61)) _let_62 :args (_let_46 false _let_16)) (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_32 _let_42 (not _let_43)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args _let_37) :args _let_59)) _let_60 :args (_let_43 false _let_17)) :args (_let_32 false _let_57 false _let_58 true _let_54 false _let_56 false _let_48 false _let_51 false _let_1 true _let_47 false _let_1 true _let_44 false _let_46 false _let_42 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args _let_40) :args _let_38)) _let_39 :args (_let_30 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args _let_37) :args _let_35)) _let_36 :args (_let_34 false _let_14)) :args (_let_19 false _let_32 false _let_30 false _let_34)))) (let ((_let_81 (tptp.member _let_22 tptp.successor_relation))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_21))) (let ((_let_84 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= Y (tptp.successor X)))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_84))) (let ((_let_87 (tptp.universal_class tptp.universal_class QUANTIFIERS_INST_ENUM))) (let ((_let_88 (tptp.regular tptp.successor_relation))) (let ((_let_89 (tptp.intersection tptp.successor_relation _let_88))) (let ((_let_90 (tptp.member _let_22 _let_89))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_81))) (let ((_let_93 (tptp.member _let_22 tptp.null_class))) (let ((_let_94 (= tptp.null_class _let_89))) (let ((_let_95 (= tptp.null_class tptp.successor_relation))) (let ((_let_96 (or _let_95 _let_94))) (let ((_let_97 (tptp.member _let_22 tptp.universal_class))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_50 _let_98 _let_93))) (let ((_let_100 (tptp.singleton tptp.universal_class))) (let ((_let_101 (tptp.unordered_pair tptp.universal_class _let_100))) (let ((_let_102 (tptp.unordered_pair _let_100 _let_101))) (let ((_let_103 (tptp.member _let_102 tptp.universal_class))) (let ((_let_104 (= tptp.universal_class _let_2))) (let ((_let_105 (= _let_22 _let_102))) (let ((_let_106 (_let_13))) (let ((_let_107 (ASSUME :args _let_106))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (_let_100 _let_101 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_106)) _let_107 :args (_let_103 false _let_13)))) (let ((_let_109 (tptp.subclass _let_2 tptp.universal_class))) (let ((_let_110 (not _let_109))) (let ((_let_111 (tptp.subclass tptp.universal_class _let_2))) (let ((_let_112 (not _let_111))) (let ((_let_113 (or _let_112 _let_110 _let_104))) (let ((_let_114 (ASSUME :args (_let_9)))) (let ((_let_115 (not _let_19))) (let ((_let_116 (and _let_9 _let_19))) (let ((_let_117 (_let_9 _let_19))) (let ((_let_118 (ASSUME :args (_let_19)))) (let ((_let_119 (SYMM _let_118))) (let ((_let_120 (SYMM _let_119))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_112 _let_110 _let_104 (not _let_113)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_116)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_114 _let_118) (SCOPE (TRUE_ELIM (TRANS (CONG _let_120 (REFL :args (_let_2)) :args _let_65) (TRUE_INTRO _let_114))) :args _let_117)) :args _let_117)) :args (true _let_116)) :args ((or (not _let_9) _let_111 _let_115))) _let_80 _let_114 :args (_let_111 false _let_19 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_38)) _let_39 :args (_let_109 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.universal_class _let_2 QUANTIFIERS_INST_ENUM)) :args _let_35)) _let_36 :args (_let_113 false _let_14)) :args (_let_104 false _let_111 false _let_109 false _let_113)))) (let ((_let_122 (_let_12))) (let ((_let_123 (ASSUME :args _let_122))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_123 :args _let_87) :args _let_122))) _let_123 :args (_let_105 false _let_12)))) (let ((_let_125 (and _let_19 _let_105 _let_104 _let_103))) (let ((_let_126 (true _let_125))) (let ((_let_127 (_let_19 _let_105 _let_104 _let_103))) (let ((_let_128 (_let_103 _let_105 _let_19 _let_104))) (let ((_let_129 (ASSUME :args (_let_103)))) (let ((_let_130 (TRUE_INTRO _let_129))) (let ((_let_131 (ASSUME :args (_let_104)))) (let ((_let_132 (SYMM (SYMM _let_131)))) (let ((_let_133 (APPLY_UF tptp.cross_product))) (let ((_let_134 (SYMM _let_120))) (let ((_let_135 (CONG _let_134 _let_134 :args _let_133))) (let ((_let_136 (TRANS _let_135 (SYMM _let_132)))) (let ((_let_137 (ASSUME :args (_let_105)))) (let ((_let_138 (CONG (SYMM (SYMM _let_137)) _let_136 :args _let_77))) (let ((_let_139 (REFL :args (_let_22)))) (let ((_let_140 (AND_INTRO _let_129 _let_137 _let_118 _let_131))) (let ((_let_141 (CNF_AND_NEG :args (_let_125)))) (let ((_let_142 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_50 _let_98 _let_93 (not _let_99)))) _let_63 (MACRO_RESOLUTION_TRUST (RESOLUTION _let_141 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_140 (SCOPE (TRUE_ELIM (TRANS (CONG _let_139 (SYMM _let_136) :args _let_77) _let_138 _let_130)) :args _let_128)) :args _let_127)) :args _let_126) _let_80 _let_124 _let_121 _let_108 :args (_let_97 false _let_19 false _let_105 false _let_104 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (tptp.universal_class tptp.null_class _let_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_69)) _let_70 :args (_let_99 false _let_18)) :args (_let_93 false _let_1 false _let_97 false _let_99)))) (let ((_let_143 (REFL :args ((not _let_93))))) (let ((_let_144 (REFL :args ((not _let_94))))) (let ((_let_145 (ASSUME :args (_let_93)))) (let ((_let_146 (TRUE_INTRO _let_145))) (let ((_let_147 (ASSUME :args (_let_94)))) (let ((_let_148 (SYMM _let_147))) (let ((_let_149 (ASSUME :args (_let_91)))) (let ((_let_150 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (tptp.successor_relation QUANTIFIERS_INST_ENUM)) :args _let_75)) _let_74 :args (_let_96 false _let_73)))) (let ((_let_151 (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_95 _let_94 (not _let_96)))))) (let ((_let_152 (not _let_95))) (let ((_let_153 (ASSUME :args (_let_82)))) (let ((_let_154 (ASSUME :args (_let_95)))) (let ((_let_155 (SYMM _let_154))) (let ((_let_156 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_82 _let_21 (not _let_83)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_145 _let_154 _let_153) :args (_let_82 _let_95 _let_93)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_146) (CONG _let_139 (SYMM _let_155) :args _let_77) (FALSE_INTRO _let_153))) :args (_let_93 _let_95 _let_82)) :args ((not (and _let_82 _let_95 _let_93)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_81))) (REFL :args (_let_152)) _let_143 :args _let_64)) _let_142 _let_151 _let_150 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_145 _let_149 _let_147) :args (_let_94 _let_91 _let_93)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_149)) (CONG _let_139 _let_148 :args _let_77) _let_146)) :args (_let_93 _let_91 _let_94)) :args ((not (and _let_94 _let_91 _let_93)) SB_LITERAL))) (CONG _let_144 (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) _let_143 :args _let_64)) _let_142 (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_81 _let_91 (not _let_92)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (_let_22 tptp.successor_relation _let_88 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_71)) _let_72 :args (_let_92 false _let_8)) :args (_let_81 false _let_93 false _let_95 false _let_96 true _let_94 false _let_93 true _let_90 false _let_92)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_87) :args _let_86)) _let_85 :args (_let_83 false _let_84)) :args (_let_21 false _let_81 false _let_83)))) (let ((_let_157 (tptp.member _let_23 tptp.universal_class))) (let ((_let_158 (not _let_157))) (let ((_let_159 (or _let_50 _let_158 _let_24))) (let ((_let_160 (tptp.member _let_23 _let_3))) (let ((_let_161 (tptp.member _let_22 _let_2))) (let ((_let_162 (not _let_161))) (let ((_let_163 (tptp.member tptp.universal_class tptp.universal_class))) (let ((_let_164 (not _let_163))) (let ((_let_165 (or _let_164 _let_162 _let_160))) (let ((_let_166 (_let_10))) (let ((_let_167 (ASSUME :args _let_166))) (let ((_let_168 (not _let_104))) (let ((_let_169 (CONG _let_67 _let_134 :args _let_133))) (let ((_let_170 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION _let_141 (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_140 (SCOPE (TRUE_ELIM (TRANS (CONG _let_139 (SYMM _let_169) :args _let_77) (CONG _let_139 (TRANS _let_169 (SYMM _let_135)) :args _let_77) _let_138 _let_130)) :args _let_128)) :args _let_127)) :args _let_126) :args ((or _let_161 _let_115 (not _let_105) _let_168 (not _let_103)))) _let_108 _let_121 _let_80 _let_124 :args (_let_161 false _let_103 false _let_104 false _let_19 false _let_105)))) (let ((_let_171 (or _let_162 _let_163))) (let ((_let_172 (_let_11))) (let ((_let_173 (ASSUME :args _let_172))) (let ((_let_174 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_171)) :args ((or _let_163 _let_162 (not _let_171)))) _let_170 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE 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_let_77) _let_189)) :args (_let_24 _let_19 _let_25 _let_21 _let_29 _let_195)) :args ((not (and _let_19 _let_21 _let_25 _let_24 _let_29 _let_195)) SB_LITERAL))) (CONG _let_209 _let_208 _let_207 _let_191 (REFL :args ((not _let_29))) (MACRO_SR_PRED_INTRO :args ((= (not _let_195) _let_28))) :args _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_203)) :args ((or _let_202 _let_29 (not _let_203)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_188 _let_118 _let_211 _let_213 _let_210 _let_217) :args (_let_19 _let_197 _let_21 _let_25 _let_24 _let_202)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_217)) (CONG _let_118 (REFL :args (_let_27)) :args _let_77) (CONG _let_119 (CONG _let_118 :args _let_216) :args _let_77) (CONG (TRANS _let_214 _let_212 (CONG _let_118 _let_67 :args _let_177) _let_215) (SYMM _let_210) :args _let_77) _let_189)) :args (_let_24 _let_19 _let_25 _let_21 _let_202 _let_197)) :args ((not 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_let_179 _let_156 _let_80 :args (false false _let_29 true _let_28 false _let_25 false _let_24 false _let_21 false _let_19)) :args (_let_18 _let_17 _let_16 _let_15 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))) _let_14 (forall ((U $$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_13 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) _let_12 _let_11 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) _let_10 (forall ((Z $$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))) _let_9 (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_8 (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_7 (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 $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_2) _let_6 (forall ((X $$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 $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) _let_5 (forall ((Xf $$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 $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (= (tptp.intersection _let_2 (tptp.intersection _let_2 (tptp.complement (tptp.compose _let_4 (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$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_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 $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))) (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation) (tptp.subclass tptp.application_function _let_3) (forall ((X $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.61/11.12 )
% 10.61/11.12 % SZS output end Proof for SET507-6
% 10.61/11.12 % cvc5---1.0.5 exiting
% 10.61/11.12 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------