%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET018-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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 14:36:50 EDT 2023

% Result   : Unsatisfiable 25.65s 25.98s
% Output   : Proof 25.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET018-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n020.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 14:28:44 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.50  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.EDxgltQ5Bg/cvc5---1.0.5_25469.p...
% 0.22/0.52  ------- get file name : TPTP file name is SET018-6
% 0.22/0.52  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25469.smt2...
% 0.22/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.47/10.68  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.53/15.72  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.55/20.77  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.57/25.81  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.65/25.98  % SZS status Unsatisfiable for SET018-6
% 25.65/25.98  % SZS output start Proof for SET018-6
% 25.65/25.99  (
% 25.65/25.99  (let ((_let_1 (= tptp.x tptp.z))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.member tptp.x tptp.universal_class))) (let ((_let_4 (tptp.ordered_pair tptp.y tptp.z))) (let ((_let_5 (tptp.ordered_pair tptp.w tptp.x))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_8 (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_9 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_11 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))) (let ((_let_13 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_14 (tptp.unordered_pair tptp.y tptp.y))) (let ((_let_15 (tptp.singleton tptp.y))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (tptp.singleton tptp.z))) (let ((_let_18 (tptp.member _let_17 _let_14))) (let ((_let_19 (= tptp.w _let_17))) (let ((_let_20 (tptp.singleton tptp.x))) (let ((_let_21 (tptp.unordered_pair tptp.w _let_20))) (let ((_let_22 (tptp.member tptp.w _let_21))) (let ((_let_23 (= _let_21 _let_15))) (let ((_let_24 (_let_9))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 ((tptp.singleton X)))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24))) _let_25 :args (_let_16 false _let_9)))) (let ((_let_28 (= tptp.y _let_17))) (let ((_let_29 (not _let_18))) (let ((_let_30 (or _let_29 _let_28 _let_28))) (let ((_let_31 (_let_13))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (= tptp.y _let_20))) (let ((_let_34 (= _let_20 _let_17))) (let ((_let_35 (not _let_28))) (let ((_let_36 (tptp.member _let_20 _let_14))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_33 _let_33))) (let ((_let_39 (tptp.unordered_pair tptp.y _let_17))) (let ((_let_40 (tptp.member _let_20 _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_33 _let_34))) (let ((_let_43 (tptp.member _let_20 _let_21))) (let ((_let_44 (= _let_21 _let_39))) (let ((_let_45 (tptp.unordered_pair _let_15 _let_39))) (let ((_let_46 (tptp.member _let_21 _let_45))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_23 _let_44))) (let ((_let_49 (tptp.unordered_pair tptp.z tptp.z))) (let ((_let_50 (tptp.member tptp.x _let_49))) (let ((_let_51 (tptp.unordered_pair tptp.x tptp.x))) (let ((_let_52 (tptp.member tptp.x _let_51))) (let ((_let_53 (= _let_17 _let_49))) (let ((_let_54 (= _let_20 _let_51))) (let ((_let_55 (not _let_34))) (let ((_let_56 (not _let_50))) (let ((_let_57 (or _let_56 _let_1 _let_1))) (let ((_let_58 (not _let_3))) (let ((_let_59 (or _let_58 _let_52))) (let ((_let_60 (_let_12))) (let ((_let_61 (ASSUME :args _let_60))) (let ((_let_62 ((tptp.unordered_pair X Y)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.z QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24))) _let_25 :args (_let_53 false _let_9)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24))) _let_25 :args (_let_54 false _let_9)))) (let ((_let_65 (or))) (let ((_let_66 (_let_55))) (let ((_let_67 (not _let_53))) (let ((_let_68 (REFL :args (_let_67)))) (let ((_let_69 (not _let_54))) (let ((_let_70 (REFL :args (_let_69)))) (let ((_let_71 (ASSUME :args (_let_52)))) (let ((_let_72 (APPLY_UF tptp.member))) (let ((_let_73 (ASSUME :args (_let_54)))) (let ((_let_74 (SYMM (SYMM _let_73)))) (let ((_let_75 (ASSUME :args (_let_34)))) (let ((_let_76 (ASSUME :args (_let_53)))) (let ((_let_77 (SYMM _let_76))) (let ((_let_78 (ASSUME :args (_let_56)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_71 _let_73 _let_75 _let_76 _let_78) :args (_let_54 _let_53 _let_34 _let_52 _let_56)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_78)) (CONG (REFL :args (tptp.x)) (TRANS _let_77 (SYMM _let_75) _let_74) :args _let_72) (TRUE_INTRO _let_71))) :args (_let_52 _let_54 _let_34 _let_53 _let_56)) :args ((not (and _let_54 _let_53 _let_34 _let_52 _let_56)) SB_LITERAL))) (CONG _let_70 _let_68 (REFL :args _let_66) (REFL :args ((not _let_52))) (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_50))) :args _let_65)) _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_52 (not _let_59)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.x tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_60)) _let_61 :args (_let_59 false _let_12)) :args (_let_52 false _let_3 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_57))) :args ((or _let_1 _let_56 (not _let_57)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.x tptp.z tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_31)) _let_32 :args (_let_57 false _let_13)) :args (_let_56 true _let_1 false _let_57)) :args (_let_55 false _let_54 false _let_53 false _let_52 true _let_50)))) (let ((_let_80 (tptp.member _let_20 tptp.universal_class))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_81 _let_43))) (let ((_let_83 (_let_11))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 ((tptp.unordered_pair X Y)))) (let ((_let_86 (tptp.member _let_51 tptp.universal_class))) (let ((_let_87 (_let_10))) (let ((_let_88 (ASSUME :args _let_87))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.x tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_87)) _let_88 :args (_let_86 false _let_10)))) (let ((_let_90 (not _let_86))) (let ((_let_91 (and _let_54 _let_86))) (let ((_let_92 (ASSUME :args (_let_86)))) (let ((_let_93 (TRUE_INTRO _let_92))) (let ((_let_94 (REFL :args (tptp.universal_class)))) (let ((_let_95 (CONG _let_74 _let_94 :args _let_72))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_81 _let_43 (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_91)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_92 _let_73) (SCOPE (TRUE_ELIM (TRANS _let_95 _let_93)) :args (_let_86 _let_54))) :args (_let_54 _let_86))) :args (true _let_91)) :args ((or _let_80 _let_69 _let_90))) _let_64 _let_89 :args (_let_80 false _let_54 false _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_20 tptp.w QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args (_let_82 false _let_11)) :args (_let_43 false _let_80 false _let_82)))) (let ((_let_97 (REFL :args ((not _let_44))))) (let ((_let_98 (REFL :args ((not _let_43))))) (let ((_let_99 (ASSUME :args (_let_43)))) (let ((_let_100 (TRUE_INTRO _let_99))) (let ((_let_101 (ASSUME :args (_let_44)))) (let ((_let_102 (SYMM _let_101))) (let ((_let_103 (REFL :args (_let_20)))) (let ((_let_104 (tptp.singleton tptp.w))) (let ((_let_105 (tptp.unordered_pair _let_104 _let_21))) (let ((_let_106 (tptp.member _let_21 _let_105))) (let ((_let_107 (= _let_4 _let_45))) (let ((_let_108 (= _let_5 _let_105))) (let ((_let_109 (tptp.member _let_21 tptp.universal_class))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_110 _let_106))) (let ((_let_112 ((tptp.unordered_pair X Y)))) (let ((_let_113 (_let_8))) (let ((_let_114 (ASSUME :args _let_113))) (let ((_let_115 ((tptp.ordered_pair X Y)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.y tptp.z QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113))) _let_114 :args (_let_107 false _let_8)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.w tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113))) _let_114 :args (_let_108 false _let_8)))) (let ((_let_118 (ASSUME :args (_let_6)))) (let ((_let_119 (and _let_6 _let_108 _let_107 _let_106))) (let ((_let_120 (ASSUME :args (_let_106)))) (let ((_let_121 (ASSUME :args (_let_108)))) (let ((_let_122 (SYMM _let_121))) (let ((_let_123 (SYMM (SYMM _let_118)))) (let ((_let_124 (ASSUME :args (_let_107)))) (let ((_let_125 (SYMM (SYMM _let_124)))) (let ((_let_126 (REFL :args (_let_21)))) (let ((_let_127 (not _let_23))) (let ((_let_128 (REFL :args (_let_127)))) (let ((_let_129 (not _let_16))) (let ((_let_130 (REFL :args (_let_129)))) (let ((_let_131 (ASSUME :args (_let_37)))) (let ((_let_132 (ASSUME :args (_let_16)))) (let ((_let_133 (SYMM _let_132))) (let ((_let_134 (SYMM _let_133))) (let ((_let_135 (ASSUME :args (_let_23)))) (let ((_let_136 (TRANS (SYMM (SYMM _let_135)) _let_134))) (let ((_let_137 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_131 _let_132 _let_135 _let_99) :args (_let_43 _let_16 _let_23 _let_37)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM _let_100) (CONG _let_103 _let_136 :args _let_72) (FALSE_INTRO _let_131))) :args (_let_37 _let_16 _let_23 _let_43)) :args ((not (and _let_43 _let_16 _let_23 _let_37)) SB_LITERAL))) (CONG _let_98 _let_130 _let_128 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_65)) _let_96 _let_27 (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_47 _let_23 _let_44 (not _let_48)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_21 _let_15 _let_39 QUANTIFIERS_INST_CBQI_PROP)) :args _let_31)) _let_32 :args (_let_48 false _let_13)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_119)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_120 _let_121 _let_118 _let_124) (SCOPE (TRUE_ELIM (TRANS (CONG _let_126 (TRANS (SYMM _let_125) (SYMM _let_123) (SYMM _let_122)) :args _let_72) (TRUE_INTRO _let_120))) :args (_let_106 _let_108 _let_6 _let_107))) :args (_let_6 _let_108 _let_107 _let_106))) :args (true _let_119)) _let_118 _let_117 _let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_110 _let_106 (not _let_111)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.w _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_87)) _let_88 :args (_let_109 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (_let_21 _let_104 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args (_let_111 false _let_11)) :args (_let_106 false _let_109 false _let_111)) :args (_let_46 false _let_6 false _let_108 false _let_107 false _let_106)) (EQ_RESOLVE (NOT_AND (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO (ASSUME :args (_let_41)))) (CONG _let_103 _let_102 :args _let_72) _let_100)) :args (_let_43 _let_44 _let_41))) (CONG _let_98 _let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_65)) _let_96 (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_33 _let_41 _let_34 (not _let_42)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_20 tptp.y _let_17 QUANTIFIERS_INST_CBQI_PROP)) :args _let_31))) _let_32 :args (_let_42 false _let_13)) _let_79 (REORDERING (FACTORING (CNF_OR_POS :args (_let_38))) :args ((or _let_37 _let_33 (not _let_38)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_20 tptp.y tptp.y QUANTIFIERS_INST_CBQI_PROP)) :args _let_31))) _let_32 :args (_let_38 false _let_13)) :args (_let_33 false _let_43 false _let_16 false _let_23 false _let_48 false _let_46 true _let_44 false _let_43 true _let_40 false _let_42 true _let_34 true _let_36 false _let_38)))) (let ((_let_138 (not _let_33))) (let ((_let_139 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_34))))) (let ((_let_140 (REFL :args (_let_138)))) (let ((_let_141 (and _let_33 _let_55))) (let ((_let_142 (ASSUME :args _let_66))) (let ((_let_143 (FALSE_INTRO _let_142))) (let ((_let_144 (REFL :args (_let_17)))) (let ((_let_145 (ASSUME :args (_let_33)))) (let ((_let_146 (SYMM (SYMM _let_145)))) (let ((_let_147 (tptp.unordered_pair tptp.w tptp.w))) (let ((_let_148 (tptp.member _let_17 _let_147))) (let ((_let_149 (not _let_148))) (let ((_let_150 (or _let_149 _let_19 _let_19))) (let ((_let_151 (tptp.member _let_17 _let_21))) (let ((_let_152 (not _let_151))) (let ((_let_153 (or _let_152 _let_19 _let_34))) (let ((_let_154 (tptp.member _let_17 _let_39))) (let ((_let_155 (tptp.member _let_39 _let_105))) (let ((_let_156 (= _let_104 _let_39))) (let ((_let_157 (not _let_155))) (let ((_let_158 (or _let_157 _let_156 _let_44))) (let ((_let_159 (= _let_104 _let_147))) (let ((_let_160 (tptp.member _let_17 tptp.universal_class))) (let ((_let_161 (not _let_160))) (let ((_let_162 (or _let_161 _let_154))) (let ((_let_163 (tptp.member _let_49 tptp.universal_class))) (let ((_let_164 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (tptp.z tptp.z QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_87)) _let_88 :args (_let_163 false _let_10)))) (let ((_let_165 (not _let_163))) (let ((_let_166 (and _let_53 _let_163))) (let ((_let_167 (ASSUME :args (_let_163)))) (let ((_let_168 (TRUE_INTRO _let_167))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_162)) :args ((or _let_161 _let_154 (not _let_162)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_166)) 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(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_7) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (= (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))) (forall ((Xf $$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 $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (= (tptp.intersection _let_7 (tptp.intersection _let_7 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$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_6 _let_3 _let_2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.65/25.99  )
% 25.65/25.99  % SZS output end Proof for SET018-6
% 25.65/26.00  % cvc5---1.0.5 exiting
% 25.65/26.00  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------