%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET061-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 14:37:15 EDT 2023

% Result   : Unsatisfiable 13.75s 13.95s
% Output   : Proof 13.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SET061-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat Aug 26 15:22:19 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.55  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.KEYNZ2KS4E/cvc5---1.0.5_20625.p...
% 0.22/0.57  ------- get file name : TPTP file name is SET061-6
% 0.22/0.58  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20625.smt2...
% 0.22/0.58  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.49/10.79  --- Run --no-e-matching --full-saturate-quant at 5...
% 13.75/13.95  % SZS status Unsatisfiable for SET061-6
% 13.75/13.95  % SZS output start Proof for SET061-6
% 13.75/13.96  (
% 13.75/13.96  (let ((_let_1 (tptp.member tptp.z tptp.null_class))) (let ((_let_2 (tptp.complement tptp.element_relation))) (let ((_let_3 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_4 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))) (let ((_let_5 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))))) (let ((_let_6 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_7 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_8 (tptp.subclass tptp.element_relation _let_3))) (let ((_let_9 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))) (let ((_let_11 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_15 (tptp.member tptp.universal_class tptp.universal_class))) (let ((_let_16 (= tptp.universal_class tptp.z))) (let ((_let_17 (= tptp.universal_class tptp.null_class))) (let ((_let_18 (= tptp.universal_class tptp.element_relation))) (let ((_let_19 (= tptp.element_relation _let_3))) (let ((_let_20 (tptp.regular _let_2))) (let ((_let_21 (tptp.intersection _let_2 _let_20))) (let ((_let_22 (tptp.member tptp.universal_class _let_21))) (let ((_let_23 (= tptp.null_class _let_21))) (let ((_let_24 (tptp.unordered_pair tptp.universal_class tptp.universal_class))) (let ((_let_25 (tptp.member tptp.universal_class _let_24))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.subclass _let_24 tptp.universal_class))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_15))) (let ((_let_30 (_let_14))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (_let_11))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 (_let_24 QUANTIFIERS_INST_ENUM))) (let ((_let_35 (tptp.regular _let_24))) (let ((_let_36 (tptp.member _let_35 _let_24))) (let ((_let_37 (= tptp.null_class _let_24))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (tptp.member tptp.z _let_24))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_16 _let_16))) (let ((_let_42 (= tptp.universal_class _let_35))) (let ((_let_43 (not _let_36))) (let ((_let_44 (or _let_43 _let_42 _let_42))) (let ((_let_45 (_let_9))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (or))) (let ((_let_48 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))))) (let ((_let_49 (ASSUME :args (_let_26)))) (let ((_let_50 (FALSE_INTRO _let_49))) (let ((_let_51 (APPLY_UF tptp.member))) (let ((_let_52 (REFL :args (_let_24)))) (let ((_let_53 (ASSUME :args (_let_42)))) (let ((_let_54 (ASSUME :args (_let_36)))) (let ((_let_55 (forall ((X $$unsorted)) (or (= tptp.null_class X) (tptp.member (tptp.regular X) X))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (ASSUME :args (_let_1)))) (let ((_let_58 (and _let_1 _let_37))) (let ((_let_59 (_let_1 _let_37))) (let ((_let_60 (TRUE_INTRO _let_57))) (let ((_let_61 (ASSUME :args (_let_37)))) (let ((_let_62 (SYMM (SYMM _let_61)))) (let ((_let_63 (REFL :args (tptp.z)))) (let ((_let_64 (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_57 _let_61) (SCOPE (TRUE_ELIM (TRANS (CONG _let_63 (SYMM _let_62) :args _let_51) _let_60)) :args _let_59)) :args _let_59)) :args (true _let_58)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.z tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_PROP)) :args _let_45))) _let_46 :args (_let_41 false _let_9)))) (let ((_let_66 (REORDERING (FACTORING (CNF_OR_POS :args (_let_41))) :args ((or _let_40 _let_16 (not _let_41)))))) (let ((_let_67 (not _let_16))) (let ((_let_68 (REFL :args (_let_67)))) (let ((_let_69 (REFL :args ((not _let_1))))) (let ((_let_70 (ASSUME :args (_let_16)))) (let ((_let_71 (SYMM _let_70))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_15 _let_26 _let_28 (not _let_29)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_49 _let_70 _let_61 _let_57) :args (_let_1 _let_26 _let_37 _let_16)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_60) (CONG _let_63 _let_62 :args _let_51) (CONG _let_71 _let_52 :args _let_51) _let_50)) :args (_let_26 _let_16 _let_37 _let_1)) :args ((not (and _let_1 _let_26 _let_37 _let_16)) SB_LITERAL))) (CONG _let_69 _let_48 (REFL :args ((not _let_37))) _let_68 :args _let_47)) _let_57 _let_66 _let_65 _let_64 _let_57 (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_36 (not _let_38)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args _let_34) :args (_let_55))) _let_56 :args (_let_38 false _let_55)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_49 _let_53 _let_54) :args (_let_26 _let_36 _let_42)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_54)) (CONG (SYMM _let_53) _let_52 :args _let_51) _let_50)) :args (_let_26 _let_42 _let_36)) :args ((not (and _let_26 _let_36 _let_42)) SB_LITERAL))) (CONG _let_48 (REFL :args (_let_43)) (REFL :args ((not _let_42))) :args _let_47)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_44))) :args ((or _let_43 _let_42 (not _let_44)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_35 tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_PROP)) :args _let_45))) _let_46 :args (_let_44 false _let_9)) :args ((or _let_25 _let_43) false _let_42 false _let_44)) :args (_let_25 false _let_1 false _let_16 false _let_41 false _let_39 false _let_1 false _let_37 false _let_38 true _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args _let_34) :args _let_32)) _let_33 :args (_let_27 false _let_11)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_24 tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_30)) _let_31 :args (_let_29 false _let_14)) :args (_let_15 false _let_25 false _let_27 false _let_29)))) (let ((_let_73 (tptp.intersection _let_24 _let_35))) (let ((_let_74 (tptp.member tptp.z _let_73))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_39))) (let ((_let_77 (= tptp.null_class _let_73))) (let ((_let_78 (or _let_37 _let_77))) (let ((_let_79 (_let_7))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (forall ((X $$unsorted)) (or (= tptp.null_class X) (= tptp.null_class (tptp.intersection X (tptp.regular X))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (_let_81))) (let ((_let_84 (MACRO_RESOLUTION_TRUST _let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_75)))) (CONG _let_63 (SYMM (ASSUME :args (_let_77))) :args _let_51) _let_60)) :args (_let_1 _let_77 _let_75))) (CONG _let_69 (REFL :args ((not _let_77))) (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_74))) :args _let_47)) _let_57 (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_37 _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args _let_34) :args _let_83)) _let_82 :args (_let_78 false _let_81)) (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_39 _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.z _let_24 _let_35 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79)) _let_80 :args (_let_76 false _let_7)) _let_64 _let_57 :args (_let_39 false _let_1 false _let_77 false _let_78 true _let_74 false _let_76 true _let_37 false _let_1)) _let_65 :args (_let_16 false _let_39 false _let_41)))) (let ((_let_85 (= tptp.null_class (tptp.intersection tptp.universal_class (tptp.regular tptp.universal_class))))) (let ((_let_86 (or _let_17 _let_85))) (let ((_let_87 (tptp.member tptp.universal_class _let_2))) (let ((_let_88 (tptp.member tptp.universal_class tptp.element_relation))) (let ((_let_89 (not _let_88))) (let ((_let_90 (not _let_87))) (let ((_let_91 (or _let_90 _let_89))) (let ((_let_92 (tptp.regular tptp.element_relation))) (let ((_let_93 (tptp.intersection tptp.element_relation _let_92))) (let ((_let_94 (tptp.member tptp.universal_class _let_93))) (let ((_let_95 (not _let_94))) (let ((_let_96 (or _let_95 _let_88))) (let ((_let_97 (= tptp.null_class _let_93))) (let ((_let_98 (= tptp.element_relation tptp.null_class))) (let ((_let_99 (or _let_98 _let_97))) (let ((_let_100 (not _let_85))) (let ((_let_101 (not _let_22))) (let ((_let_102 (or _let_101 _let_87))) (let ((_let_103 (= tptp.null_class _let_2))) (let ((_let_104 (or _let_103 _let_23))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.universal_class _let_2 _let_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79)) _let_80 :args (_let_102 false _let_7)))) (let ((_let_106 (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_87 _let_101 (not _let_102)))))) (let ((_let_107 (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_22))))) (let ((_let_108 (REFL :args ((not _let_23))))) (let ((_let_109 (REFL :args (_let_100)))) (let ((_let_110 (SYMM _let_71))) (let ((_let_111 (CONG _let_110 (REFL :args (tptp.null_class)) :args _let_51))) (let ((_let_112 (ASSUME :args (_let_85)))) (let ((_let_113 (CONG _let_71 (SYMM _let_112) :args _let_51))) (let ((_let_114 (ASSUME :args (_let_23)))) (let ((_let_115 (SYMM _let_114))) (let ((_let_116 (ASSUME :args (_let_101)))) (let ((_let_117 (SYMM (FALSE_INTRO _let_116)))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (_let_2 QUANTIFIERS_INST_ENUM)) :args _let_83)) _let_82 :args (_let_104 false _let_81)))) (let ((_let_119 (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_103 _let_23 (not _let_104)))))) (let ((_let_120 (not _let_103))) (let ((_let_121 (REFL :args (_let_120)))) (let ((_let_122 (ASSUME :args (_let_103)))) (let ((_let_123 (SYMM _let_122))) (let ((_let_124 (_let_90))) (let ((_let_125 (ASSUME :args _let_124))) (let ((_let_126 (_let_6))) (let ((_let_127 (ASSUME :args _let_126))) (let ((_let_128 (tptp.universal_class tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_129 (REFL :args ((not _let_97))))) (let ((_let_130 (ASSUME :args (_let_97)))) (let ((_let_131 (SYMM _let_130))) (let ((_let_132 (ASSUME :args (_let_95)))) (let ((_let_133 (tptp.element_relation QUANTIFIERS_INST_ENUM))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_82 :args _let_133) :args _let_83))) _let_82 :args (_let_99 false _let_81)))) (let ((_let_135 (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_98 _let_97 (not _let_99)))))) (let ((_let_136 (not _let_98))) (let ((_let_137 (REFL :args (_let_136)))) (let ((_let_138 (ASSUME :args (_let_98)))) (let ((_let_139 (SYMM (SYMM _let_138)))) (let ((_let_140 (ASSUME :args (_let_89)))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_17 _let_85 (not _let_86)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_57 _let_70 _let_112 _let_138 _let_140) :args (_let_1 _let_85 _let_89 _let_98 _let_16)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_140)) (CONG _let_110 (TRANS _let_139 _let_112) :args _let_51) _let_113 _let_111 _let_60)) :args (_let_1 _let_16 _let_85 _let_98 _let_89)) :args ((not (and _let_1 _let_85 _let_89 _let_98 _let_16)) SB_LITERAL))) (CONG _let_69 _let_109 (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_88))) _let_137 _let_68 :args _let_47)) _let_84 _let_57 _let_135 _let_134 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_57 _let_70 _let_112 _let_130 _let_132) :args (_let_1 _let_85 _let_97 _let_16 _let_95)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_132)) (CONG _let_110 (TRANS _let_131 _let_112) :args _let_51) _let_113 _let_111 _let_60)) :args (_let_1 _let_16 _let_85 _let_97 _let_95)) :args ((not (and _let_1 _let_85 _let_97 _let_16 _let_95)) SB_LITERAL))) (CONG _let_69 _let_109 _let_129 _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_94))) :args _let_47)) _let_84 _let_57 (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_88 _let_95 (not _let_96)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (tptp.universal_class tptp.element_relation _let_92 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79)) _let_80 :args (_let_96 false _let_7)) (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_89 _let_90 (not _let_91)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args _let_128) :args _let_126)) _let_127 :args (_let_91 false _let_6)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_57 _let_70 _let_112 _let_122 _let_125) :args (_let_1 _let_85 _let_90 _let_103 _let_16)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_125)) (CONG _let_110 (TRANS _let_123 _let_112) :args _let_51) _let_113 _let_111 _let_60)) :args (_let_1 _let_16 _let_85 _let_103 _let_90)) :args ((not (and _let_1 _let_85 _let_90 _let_103 _let_16)) SB_LITERAL))) (CONG _let_69 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(IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_82 :args (tptp.universal_class QUANTIFIERS_INST_ENUM)) :args _let_83))) _let_82 :args (_let_86 false _let_81)) :args (_let_17 true _let_85 false _let_86)))) (let ((_let_142 (tptp.subclass tptp.element_relation tptp.universal_class))) (let ((_let_143 (not _let_142))) (let ((_let_144 (tptp.subclass tptp.universal_class tptp.element_relation))) (let ((_let_145 (not _let_144))) (let ((_let_146 (or _let_145 _let_143 _let_18))) (let ((_let_147 (_let_10))) (let ((_let_148 (ASSUME :args _let_147))) (let ((_let_149 (tptp.not_subclass_element tptp.universal_class tptp.element_relation))) (let ((_let_150 (tptp.member _let_149 tptp.universal_class))) (let ((_let_151 (or _let_150 _let_144))) (let ((_let_152 (tptp.member _let_149 tptp.element_relation))) (let ((_let_153 (not _let_152))) (let ((_let_154 (or _let_153 _let_144))) (let ((_let_155 (_let_13))) (let ((_let_156 (ASSUME :args _let_155))) (let ((_let_157 (_let_12))) (let ((_let_158 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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 $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) _let_5 _let_4 (forall ((Xf $$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 $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (= (tptp.intersection _let_3 (tptp.intersection _let_3 (tptp.complement (tptp.compose _let_2 (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$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))))) _let_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 13.75/13.96  )
% 13.75/13.97  % SZS output end Proof for SET061-6
% 13.75/13.97  % cvc5---1.0.5 exiting
% 13.75/13.97  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------