%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n004.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 14:36:49 EDT 2023

% Result   : Theorem 75.28s 75.47s
% Output   : Proof 75.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET018+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.14/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n004.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 10:53:22 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 75.28/75.47  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qn0b4TriUE/cvc5---1.0.5_13760.p...
% 75.28/75.47  ------- get file name : TPTP file name is SET018+1
% 75.28/75.47  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13760.smt2...
% 75.28/75.47  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 75.28/75.47  --- Run --no-e-matching --full-saturate-quant at 5...
% 75.28/75.47  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 75.28/75.47  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 75.28/75.47  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 75.28/75.47  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 75.28/75.47  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 75.28/75.47  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 75.28/75.47  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 75.28/75.47  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 75.28/75.47  --- Run --relevant-triggers --full-saturate-quant at 5...
% 75.28/75.47  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 75.28/75.47  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 75.28/75.47  % SZS status Theorem for SET018+1
% 75.28/75.47  % SZS output start Proof for SET018+1
% 75.28/75.47  (
% 75.28/75.47  (let ((_let_1 (not (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (= (tptp.ordered_pair W X) (tptp.ordered_pair Y Z)) (tptp.member X tptp.universal_class)) (= X Z)))))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (=> (and (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class)) (and (= (tptp.first _let_1) X) (= (tptp.second _let_1) Y))))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) (and (tptp.member U X) (tptp.member V Y)))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))))))) (let ((_let_6 (forall ((X $$unsorted)) (= (tptp.singleton X) (tptp.unordered_pair X X))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_8 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.member U (tptp.unordered_pair X Y)) (and (tptp.member U tptp.universal_class) (or (= U X) (= U Y))))))) (let ((_let_9 (tptp.ordered_pair skv_7 skv_8))) (let ((_let_10 (tptp.ordered_pair skv_5 skv_6))) (let ((_let_11 (= _let_10 _let_9))) (let ((_let_12 (= skv_6 skv_8))) (let ((_let_13 (= skv_6 (tptp.second _let_10)))) (let ((_let_14 (= skv_8 (tptp.second _let_9)))) (let ((_let_15 (tptp.member skv_6 tptp.universal_class))) (let ((_let_16 (not _let_15))) (let ((_let_17 (not _let_11))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.ordered_pair W X) (tptp.ordered_pair Y Z))) (not (tptp.member X tptp.universal_class)) (= X Z)))) (not (or _let_17 _let_16 _let_12))))))))) (let ((_let_19 (NOT_NOT_ELIM (NOT_OR_ELIM _let_18 :args (0))))) (let ((_let_20 (NOT_OR_ELIM _let_18 :args (2)))) (let ((_let_21 (and (= skv_5 (tptp.first _let_10)) _let_13))) (let ((_let_22 (tptp.member skv_5 tptp.universal_class))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_16 _let_21))) (let ((_let_25 (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member X tptp.universal_class)) (not (tptp.member Y tptp.universal_class)) (and (= X (tptp.first _let_1)) (= Y (tptp.second _let_1)))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (_let_25))) (let ((_let_28 ((tptp.ordered_pair X Y)))) (let ((_let_29 (tptp.singleton skv_6))) (let ((_let_30 (tptp.unordered_pair skv_5 _let_29))) (let ((_let_31 (tptp.member skv_5 _let_30))) (let ((_let_32 (= _let_22 _let_31))) (let ((_let_33 (_let_8))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (tptp.unordered_pair skv_8 skv_8))) (let ((_let_36 (= skv_5 _let_35))) (let ((_let_37 (= _let_29 _let_35))) (let ((_let_38 (tptp.unordered_pair skv_6 skv_6))) (let ((_let_39 (= _let_29 _let_38))) (let ((_let_40 (tptp.member skv_6 _let_35))) (let ((_let_41 (tptp.member skv_6 _let_38))) (let ((_let_42 (not _let_37))) (let ((_let_43 (_let_6))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 ((tptp.singleton X)))) (let ((_let_46 (and _let_15 _let_12))) (let ((_let_47 (= _let_40 _let_46))) (let ((_let_48 (not _let_40))) (let ((_let_49 (not _let_46))) (let ((_let_50 (= _let_15 _let_41))) (let ((_let_51 (NOT_NOT_ELIM (NOT_OR_ELIM _let_18 :args (1))))) (let ((_let_52 (or))) (let ((_let_53 (ASSUME :args (_let_41)))) (let ((_let_54 (APPLY_UF tptp.member))) (let ((_let_55 (ASSUME :args (_let_39)))) (let ((_let_56 (REFL :args (skv_6)))) (let ((_let_57 (ASSUME :args (_let_37)))) (let ((_let_58 (ASSUME :args (_let_48)))) (let ((_let_59 (tptp.member _let_35 tptp.universal_class))) (let ((_let_60 (and _let_59 _let_36))) (let ((_let_61 (or _let_36 _let_37))) (let ((_let_62 (tptp.unordered_pair skv_5 skv_5))) (let ((_let_63 (tptp.member _let_35 _let_62))) (let ((_let_64 (= _let_63 _let_60))) (let ((_let_65 (and _let_59 _let_61))) (let ((_let_66 (tptp.singleton skv_5))) (let ((_let_67 (= _let_66 _let_62))) (let ((_let_68 (tptp.singleton skv_8))) (let ((_let_69 (tptp.unordered_pair skv_7 _let_68))) (let ((_let_70 (tptp.member _let_35 _let_69))) (let ((_let_71 (= _let_66 _let_69))) (let ((_let_72 (tptp.member _let_35 _let_30))) (let ((_let_73 (= _let_72 _let_65))) (let ((_let_74 (= _let_30 _let_69))) (let ((_let_75 (or _let_71 _let_74))) (let ((_let_76 (not _let_61))) (let ((_let_77 (not _let_63))) (let ((_let_78 (not _let_65))) (let ((_let_79 (= _let_68 _let_35))) (let ((_let_80 (or (= skv_7 _let_35) _let_79))) (let ((_let_81 (and _let_59 _let_80))) (let ((_let_82 (= _let_70 _let_81))) (let ((_let_83 (_let_7))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 ((tptp.unordered_pair X Y)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (skv_8 skv_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args (_let_59 false _let_7)))) (let ((_let_87 (not _let_59))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_82)) :args ((or _let_70 (not _let_81) (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_81)) :args ((or _let_87 _let_81 (not _let_80)))) _let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_80 1)) :args ((or (not _let_79) _let_80))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (skv_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_43)) _let_44 :args (_let_79 false _let_6)) :args (_let_80 false _let_79)) :args (_let_81 false _let_59 false _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_35 skv_7 _let_68 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) _let_34 :args (_let_82 false _let_8)) :args (_let_70 false _let_81 false _let_82)))) (let ((_let_89 (REFL :args ((not _let_70))))) (let ((_let_90 (ASSUME :args (_let_77)))) (let ((_let_91 (ASSUME :args (_let_67)))) (let ((_let_92 (ASSUME :args (_let_71)))) (let ((_let_93 (REFL :args (_let_35)))) (let ((_let_94 (ASSUME :args (_let_70)))) (let ((_let_95 (SYMM (TRUE_INTRO _let_94)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_35 skv_5 _let_29 QUANTIFIERS_INST_CBQI_PROP)) :args _let_33))) _let_34 :args (_let_73 false _let_8)))) (let ((_let_97 (not _let_73))) (let ((_let_98 (not _let_72))) (let ((_let_99 (_let_73))) (let ((_let_100 (tptp.member _let_69 tptp.universal_class))) (let ((_let_101 (and _let_100 _let_75))) (let ((_let_102 (tptp.unordered_pair _let_66 _let_30))) (let ((_let_103 (tptp.member _let_69 _let_102))) (let ((_let_104 (= _let_103 _let_101))) (let ((_let_105 (tptp.singleton skv_7))) (let ((_let_106 (tptp.unordered_pair _let_105 _let_69))) (let ((_let_107 (tptp.member _let_69 _let_106))) (let ((_let_108 (= _let_9 _let_106))) (let ((_let_109 (= _let_10 _let_102))) (let ((_let_110 (= _let_100 _let_107))) (let ((_let_111 (_let_5))) (let ((_let_112 (ASSUME :args _let_111))) (let ((_let_113 ((tptp.ordered_pair X Y)))) (let ((_let_114 (and _let_11 _let_109 _let_108 _let_107))) (let ((_let_115 (ASSUME :args (_let_107)))) (let ((_let_116 (ASSUME :args (_let_108)))) (let ((_let_117 (ASSUME :args (_let_11)))) (let ((_let_118 (SYMM (SYMM _let_117)))) (let ((_let_119 (ASSUME :args (_let_109)))) (let ((_let_120 (_let_98))) (let ((_let_121 (ASSUME :args _let_120))) (let ((_let_122 (ASSUME :args (_let_74)))) (let ((_let_123 (not _let_36))) (let ((_let_124 (not _let_31))) (let ((_let_125 (and _let_36 _let_124))) (let ((_let_126 (ASSUME :args (_let_124)))) (let ((_let_127 (ASSUME :args (_let_36)))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_32)) :args ((or _let_22 _let_124 (not _let_32)))) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_125)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_126 _let_127) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_127) (REFL :args (_let_30)) :args _let_54) (FALSE_INTRO _let_126))) :args (_let_124 _let_36))) :args (_let_36 _let_124))) :args (true _let_125)) (CONG (REFL :args (_let_123)) (MACRO_SR_PRED_INTRO :args ((= (not _let_124) _let_31))) (REFL :args _let_120) :args _let_52)) (REORDERING (CNF_EQUIV_POS2 :args _let_99) :args ((or _let_72 _let_78 _let_97))) _let_96 (REORDERING (CNF_AND_NEG :args (_let_65)) :args ((or _let_87 _let_65 _let_76))) _let_86 (REORDERING (CNF_OR_NEG :args (_let_61 0)) :args ((or _let_123 _let_61))) :args ((or _let_123 _let_31) false _let_72 false _let_73 false _let_65 false _let_59 false _let_61)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_121 _let_122 _let_94) :args (_let_70 _let_74 _let_98)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_95 (CONG _let_93 (SYMM _let_122) :args _let_54) (FALSE_INTRO _let_121))) :args (_let_98 _let_74 _let_70)) :args ((not (and _let_70 _let_74 _let_98)) SB_LITERAL))) (CONG _let_89 (REFL :args ((not _let_74))) (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_72))) :args _let_52)) _let_88 (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_71 _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_101 1)) :args ((or _let_75 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_104)) :args ((or _let_101 (not _let_103) (not _let_104)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_114)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_115 _let_116 _let_117 _let_119) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_69)) (TRANS (SYMM _let_119) _let_118 (SYMM (SYMM _let_116))) :args _let_54) (TRUE_INTRO _let_115))) :args (_let_107 _let_108 _let_11 _let_109))) :args (_let_11 _let_109 _let_108 _let_107))) :args (true _let_114)) _let_19 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (skv_5 skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_113)) :args _let_111)) _let_112 :args (_let_109 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (skv_7 skv_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_113)) :args _let_111)) _let_112 :args (_let_108 false _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_110)) :args ((or (not _let_100) _let_107 (not _let_110)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (skv_7 _let_68 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_83)) _let_84 :args (_let_100 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_69 _let_105 _let_69 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) _let_34 :args (_let_110 false _let_8)) :args (_let_107 false _let_100 false _let_110)) :args (_let_103 false _let_11 false _let_109 false _let_108 false _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_69 _let_66 _let_30 QUANTIFIERS_INST_CBQI_PROP)) :args _let_33))) _let_34 :args (_let_104 false _let_8)) :args (_let_101 false _let_103 false _let_104)) :args (_let_75 false _let_101)) (REORDERING (CNF_EQUIV_POS1 :args _let_99) :args ((or _let_65 _let_98 _let_97))) _let_96 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_90 _let_91 _let_92 _let_94) :args (_let_67 _let_77 _let_70 _let_71)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_95 (CONG _let_93 (TRANS (SYMM _let_92) (SYMM (SYMM _let_91))) :args _let_54) (FALSE_INTRO _let_90))) :args (_let_77 _let_67 _let_71 _let_70)) :args ((not (and _let_67 _let_77 _let_70 _let_71)) SB_LITERAL))) (CONG (REFL :args ((not _let_67))) (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_63))) _let_89 (REFL :args ((not _let_71))) :args _let_52)) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (skv_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_43)) _let_44 :args (_let_67 false _let_6)) (REORDERING (CNF_AND_POS :args (_let_65 1)) :args ((or _let_61 _let_78))) (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or _let_60 _let_77 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_35 skv_5 skv_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) _let_34 :args (_let_64 false _let_8)) (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_36 _let_37 _let_76))) (REORDERING (CNF_AND_POS :args (_let_60 1)) :args ((or _let_36 (not _let_60)))) :args (_let_61 false _let_70 false _let_74 false _let_75 true _let_72 false _let_73 true _let_71 false _let_70 false _let_67 true _let_65 true _let_63 false _let_64 true _let_61 true _let_60)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_53 _let_55 _let_57 _let_58) :args (_let_39 _let_37 _let_48 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_58)) (CONG _let_56 (SYMM _let_57) :args _let_54) (CONG _let_56 (SYMM (SYMM _let_55)) :args _let_54) (TRUE_INTRO _let_53))) :args (_let_41 _let_39 _let_37 _let_48)) :args ((not (and _let_39 _let_37 _let_48 _let_41)) SB_LITERAL))) (CONG (REFL :args ((not _let_39))) (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_40))) (REFL :args ((not _let_41))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or _let_16 _let_41 (not _let_50)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (skv_6 skv_6 skv_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) _let_34 :args (_let_50 false _let_8)) :args (_let_41 false _let_15 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or _let_46 _let_48 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_46 1)) :args ((or _let_12 _let_49))) _let_20 :args (_let_49 true _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (skv_6 skv_8 skv_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) _let_34 :args (_let_47 false _let_8)) :args (_let_48 true _let_46 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_43)) _let_44 :args (_let_39 false _let_6)) :args (_let_42 false _let_41 true _let_40 false _let_39)) :args (_let_36 true _let_37)) :args (_let_31 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (skv_5 skv_5 _let_29 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_33))) _let_34 :args (_let_32 false _let_8)) :args (_let_22 false _let_31 false _let_32)))) (let ((_let_129 (and (= skv_7 (tptp.first _let_9)) _let_14))) (let ((_let_130 (tptp.member skv_8 tptp.universal_class))) (let ((_let_131 (not _let_130))) (let ((_let_132 (tptp.member skv_7 tptp.universal_class))) (let ((_let_133 (not _let_132))) (let ((_let_134 (or _let_133 _let_131 _let_129))) (let ((_let_135 (and _let_132 _let_130))) (let ((_let_136 (tptp.member _let_9 _let_2))) (let ((_let_137 (= _let_136 _let_135))) (let ((_let_138 (_let_4))) (let ((_let_139 (ASSUME :args _let_138))) (let ((_let_140 (tptp.member _let_10 _let_2))) (let ((_let_141 (and _let_22 _let_15))) (let ((_let_142 (= _let_140 _let_141))) (let ((_let_143 (and _let_11 _let_140))) (let ((_let_144 (ASSUME :args (_let_140)))) (let ((_let_145 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_137)) :args ((or _let_135 (not _let_136) (not _let_137)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_143)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_144 _let_117) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_118) (REFL :args (_let_2)) :args _let_54) (TRUE_INTRO _let_144))) :args (_let_140 _let_11))) :args (_let_11 _let_140))) :args (true _let_143)) _let_19 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_142)) :args ((or _let_140 (not _let_141) (not _let_142)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_141)) :args ((or _let_16 _let_23 _let_141))) _let_51 _let_128 :args (_let_141 false _let_15 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_139 :args (skv_5 skv_6 tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_138)) _let_139 :args (_let_142 false _let_4)) :args (_let_140 false _let_141 false _let_142)) :args (_let_136 false _let_11 false _let_140)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_139 :args (skv_7 skv_8 tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_138)) _let_139 :args (_let_137 false _let_4)) :args (_let_135 false _let_136 false _let_137)))) (let ((_let_146 (not _let_135))) (let ((_let_147 (and _let_11 _let_13 _let_14))) (let ((_let_148 (ASSUME :args (_let_14)))) (let ((_let_149 (ASSUME :args (_let_13)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_147)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_148 _let_117 _let_149) (SCOPE (TRANS (SYMM (SYMM _let_149)) (CONG _let_118 :args (APPLY_UF tptp.second)) (SYMM _let_148)) :args (_let_14 _let_11 _let_13))) :args (_let_11 _let_13 _let_14))) :args (true _let_147)) :args ((or _let_17 _let_12 (not _let_13) (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_129 1)) :args ((or _let_14 (not _let_129)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_133 _let_131 _let_129 (not _let_134)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_135 0)) :args ((or _let_132 _let_146))) _let_145 :args (_let_132 false _let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_135 1)) :args ((or _let_130 _let_146))) _let_145 :args (_let_130 false _let_135)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (skv_7 skv_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_28)) :args _let_27)) _let_26 :args (_let_134 false _let_25)) :args (_let_129 false _let_132 false _let_130 false _let_134)) :args (_let_14 false _let_129)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_13 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_16 _let_23 _let_21 (not _let_24)))) _let_51 _let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (skv_5 skv_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_28)) :args _let_27)) _let_26 :args (_let_24 false _let_25)) :args (_let_21 false _let_15 false _let_22 false _let_24)) :args (_let_13 false _let_21)) _let_20 _let_19 :args (false false _let_14 false _let_13 true _let_12 false _let_11)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.subclass X Y) (forall ((U $$unsorted)) (=> (tptp.member U X) (tptp.member U Y))))) (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (= (= X Y) (and (tptp.subclass X Y) (tptp.subclass Y X)))) _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (tptp.member Z (tptp.cross_product X Y)) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair X Y) tptp.element_relation) (and (tptp.member Y tptp.universal_class) (tptp.member X Y)))) (tptp.subclass tptp.element_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.intersection X Y)) (and (tptp.member Z X) (tptp.member Z Y)))) (forall ((X $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.complement X)) (and (tptp.member Z tptp.universal_class) (not (tptp.member Z X))))) (forall ((X $$unsorted) (XR $$unsorted) (Y $$unsorted)) (= (tptp.restrict XR X Y) (tptp.intersection XR (tptp.cross_product X Y)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.null_class))) (forall ((X $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.domain_of X)) (and (tptp.member Z tptp.universal_class) (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class))))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (= (tptp.member _let_1 (tptp.rotate X)) (and (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) 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 $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (= (tptp.member _let_1 (tptp.flip X)) (and (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class)) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.member Z (tptp.union X Y)) (or (tptp.member Z X) (tptp.member Z Y)))) (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton X)))) (tptp.subclass tptp.successor_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation) (and (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class) (= (tptp.successor X) Y)))) (forall ((Y $$unsorted)) (= (tptp.inverse Y) (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))))) (forall ((Z $$unsorted)) (= (tptp.range_of Z) (tptp.domain_of (tptp.inverse Z)))) (forall ((X $$unsorted) (XR $$unsorted)) (= (tptp.image XR X) (tptp.range_of (tptp.restrict XR X tptp.universal_class)))) (forall ((X $$unsorted)) (= (tptp.inductive X) (and (tptp.member tptp.null_class X) (tptp.subclass (tptp.image tptp.successor_relation X) X)))) (exists ((X $$unsorted)) (and (tptp.member X tptp.universal_class) (tptp.inductive X) (forall ((Y $$unsorted)) (=> (tptp.inductive Y) (tptp.subclass X Y))))) (forall ((U $$unsorted) (X $$unsorted)) (= (tptp.member U (tptp.sum_class X)) (exists ((Y $$unsorted)) (and (tptp.member U Y) (tptp.member Y X))))) (forall ((X $$unsorted)) (=> (tptp.member X tptp.universal_class) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((U $$unsorted) (X $$unsorted)) (= (tptp.member U (tptp.power_class X)) (and (tptp.member U tptp.universal_class) (tptp.subclass U X)))) (forall ((U $$unsorted)) (=> (tptp.member U tptp.universal_class) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((XR $$unsorted) (YR $$unsorted)) (tptp.subclass (tptp.compose YR XR) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((XR $$unsorted) (YR $$unsorted) (U $$unsorted) (V $$unsorted)) (= (tptp.member (tptp.ordered_pair U V) (tptp.compose YR XR)) (and (tptp.member U tptp.universal_class) (tptp.member V (tptp.image YR (tptp.image XR (tptp.singleton U))))))) (forall ((Z $$unsorted)) (= (tptp.member Z tptp.identity_relation) (exists ((X $$unsorted)) (and (tptp.member X tptp.universal_class) (= Z (tptp.ordered_pair X X)))))) (forall ((XF $$unsorted)) (= (tptp.function XF) (and (tptp.subclass XF (tptp.cross_product tptp.universal_class tptp.universal_class)) (tptp.subclass (tptp.compose XF (tptp.inverse XF)) tptp.identity_relation)))) (forall ((X $$unsorted) (XF $$unsorted)) (=> (and (tptp.member X tptp.universal_class) (tptp.function XF)) (tptp.member (tptp.image XF X) tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.disjoint X Y) (forall ((U $$unsorted)) (not (and (tptp.member U X) (tptp.member U Y)))))) (forall ((X $$unsorted)) (=> (not (= X tptp.null_class)) (exists ((U $$unsorted)) (and (tptp.member U tptp.universal_class) (tptp.member U X) (tptp.disjoint U X))))) (forall ((XF $$unsorted) (Y $$unsorted)) (= (tptp.apply XF Y) (tptp.sum_class (tptp.image XF (tptp.singleton Y))))) (exists ((XF $$unsorted)) (and (tptp.function XF) (forall ((Y $$unsorted)) (=> (tptp.member Y tptp.universal_class) (or (= Y tptp.null_class) (tptp.member (tptp.apply XF Y) Y)))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 75.28/75.48  )
% 75.28/75.48  % SZS output end Proof for SET018+1
% 75.28/75.48  % cvc5---1.0.5 exiting
% 75.28/75.49  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------