%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 14:38:01 EDT 2023

% Result   : Theorem 1.62s 1.81s
% Output   : Proof 1.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 10:31:48 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 1.62/1.81  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qmyxTCWFCd/cvc5---1.0.5_16312.p...
% 1.62/1.81  ------- get file name : TPTP file name is SET169+3
% 1.62/1.81  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_16312.smt2...
% 1.62/1.81  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.62/1.81  % SZS status Theorem for SET169+3
% 1.62/1.81  % SZS output start Proof for SET169+3
% 1.62/1.81  (
% 1.62/1.81  (let ((_let_1 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.intersection B (tptp.union C D)) (tptp.union (tptp.intersection B C) (tptp.intersection B D)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C))))))) (let ((_let_4 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.union B C) (tptp.union C B))))) (let ((_let_5 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.intersection B C)) (and (tptp.member D B) (tptp.member D C)))))) (let ((_let_6 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.union B C)) (or (tptp.member D B) (tptp.member D C)))))) (let ((_let_7 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 _let_7))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (= _let_8 _let_11))) (let ((_let_13 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 _let_13))) (let ((_let_15 (or _let_14 _let_8))) (let ((_let_16 (not _let_8))) (let ((_let_17 (tptp.union _let_13 _let_7))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 _let_17))) (let ((_let_19 (= _let_18 _let_15))) (let ((_let_20 (not _let_15))) (let ((_let_21 (_let_6))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 ((tptp.member D (tptp.union B C))))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (_let_13 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_22 :args (_let_19 false _let_6)))) (let ((_let_25 (tptp.union _let_7 _let_13))) (let ((_let_26 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 _let_25))) (let ((_let_27 (= _let_25 _let_17))) (let ((_let_28 (not _let_18))) (let ((_let_29 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 _let_30))) (let ((_let_32 (= _let_26 _let_31))) (let ((_let_33 (not _let_26))) (let ((_let_34 (or _let_16 _let_31))) (let ((_let_35 (forall ((D $$unsorted)) (or (not (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_36 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 _let_30))) (let ((_let_37 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 _let_7))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36))) (let ((_let_40 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (or _let_38 _let_40))) (let ((_let_42 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 _let_29))) (let ((_let_43 (or _let_38 _let_42))) (let ((_let_44 (and _let_40 _let_42))) (let ((_let_45 (= _let_36 _let_44))) (let ((_let_46 (or))) (let ((_let_47 (forall ((D $$unsorted)) (or (not (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 _let_7))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48))) (let ((_let_52 (and _let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_53 (= _let_49 _let_52))) (let ((_let_54 (_let_5))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 ((tptp.member D (tptp.intersection B C))))) (let ((_let_57 (not _let_47))) (let ((_let_58 (_let_57))) (let ((_let_59 (_let_47))) (let ((_let_60 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member D _let_7) false)))))) (let ((_let_61 (forall ((D $$unsorted)) (or (not (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member D (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 _let_29))) (let ((_let_63 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 _let_7))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_62))) (let ((_let_66 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_67 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_66))) (let ((_let_68 (= _let_63 _let_67))) (let ((_let_69 (not _let_66))) (let ((_let_70 (or _let_69 _let_62))) (let ((_let_71 (forall ((D $$unsorted)) (or (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member D (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_72 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 _let_29))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 _let_72))) (let ((_let_76 (or _let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_77 (= _let_72 _let_76))) (let ((_let_78 (not _let_71))) (let ((_let_79 (_let_78))) (let ((_let_80 (_let_71))) (let ((_let_81 ((not (= (tptp.member D _let_29) true))))) (let ((_let_82 (not _let_61))) (let ((_let_83 (_let_82))) (let ((_let_84 (_let_61))) (let ((_let_85 (not _let_35))) (let ((_let_86 (_let_85))) (let ((_let_87 (_let_35))) (let ((_let_88 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member D _let_30) true)))))) (let ((_let_89 (not _let_14))) (let ((_let_90 (or _let_89 _let_31))) (let ((_let_91 (forall ((D $$unsorted)) (= (tptp.member D (tptp.union (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_92 (not _let_32))) (let ((_let_93 (= _let_30 _let_25))) (let ((_let_94 (= _let_93 _let_91))) (let ((_let_95 (not _let_91))) (let ((_let_96 (_let_3))) (let ((_let_97 (ASSUME :args _let_96))) (let ((_let_98 (not _let_93))) (let ((_let_99 (_let_2))) (let ((_let_100 (ASSUME :args _let_99))) (let ((_let_101 (_let_95))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_101)) :args _let_101)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_91))) (REFL :args (_let_92)) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_94)) :args ((or _let_93 _let_95 (not _let_94)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_100) :args _let_99)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_98)) :args _let_46)) _let_100 :args (_let_98 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_25 _let_30 QUANTIFIERS_INST_ENUM)) :args _let_96))) _let_97 :args (_let_94 false _let_3)) :args (_let_95 true _let_93 false _let_94)) :args (_let_92 true _let_91)))) (let ((_let_103 (_let_32))) (let ((_let_104 (forall ((D $$unsorted)) (or (not (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_105 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 _let_30))) (let ((_let_106 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 _let_13))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_105))) (let ((_let_109 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 _let_29))) (let ((_let_110 (or _let_107 _let_109))) (let ((_let_111 (forall ((D $$unsorted)) (or (not (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_112 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 _let_29))) (let ((_let_113 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 _let_13))) (let ((_let_114 (not _let_113))) (let ((_let_115 (or _let_114 _let_112))) (let ((_let_116 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_117 (or _let_114 _let_116))) (let ((_let_118 (not _let_116))) (let ((_let_119 (or _let_118 _let_112))) (let ((_let_120 (forall ((D $$unsorted)) (or (not (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_121 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_122 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 _let_13))) (let ((_let_123 (not _let_122))) (let ((_let_124 (or _let_123 _let_121))) (let ((_let_125 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_121))) (let ((_let_126 (= _let_122 _let_125))) (let ((_let_127 (not _let_120))) (let ((_let_128 (_let_127))) (let ((_let_129 (_let_120))) (let ((_let_130 ((not (= (tptp.member D _let_13) false))))) (let ((_let_131 (forall ((D $$unsorted)) (or (not (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member D (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_132 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 _let_29))) (let ((_let_133 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_134 (not _let_133))) (let ((_let_135 (or _let_134 _let_132))) (let ((_let_136 (or (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_133))) (let ((_let_137 (= _let_132 _let_136))) (let ((_let_138 (not _let_131))) (let ((_let_139 (_let_138))) (let ((_let_140 (_let_131))) (let ((_let_141 (not _let_111))) (let ((_let_142 (_let_141))) (let ((_let_143 (_let_111))) (let ((_let_144 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_145 (and _let_144 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_146 (= _let_106 _let_145))) (let ((_let_147 (and _let_144 _let_109))) (let ((_let_148 (= _let_105 _let_147))) (let ((_let_149 (not _let_110))) (let ((_let_150 (not _let_104))) (let ((_let_151 (_let_150))) (let ((_let_152 (_let_104))) (let ((_let_153 (not _let_19))) (let ((_let_154 (_let_19))) (let ((_let_155 (_let_4))) (let ((_let_156 (ASSUME :args _let_155))) (let ((_let_157 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_156 :args (_let_7 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union B C)))) :args _let_155)) _let_156 :args (_let_27 false _let_4)))) (let ((_let_158 (and _let_27 _let_26))) (let ((_let_159 (ASSUME :args (_let_26)))) (let ((_let_160 (ASSUME :args (_let_27)))) (let ((_let_161 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101)) (SYMM _let_160) :args (APPLY_UF tptp.member)))) (let ((_let_162 (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_158)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_159 _let_160) (SCOPE (TRUE_ELIM (TRANS _let_161 (TRUE_INTRO _let_159))) :args (_let_26 _let_27))) :args (_let_27 _let_26))) :args (true _let_158)) _let_157 (REORDERING (CNF_EQUIV_POS1 :args _let_154) :args ((or _let_15 _let_28 _let_153))) _let_24 (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_14 _let_8 _let_20))) (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_31 _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_152) :args _let_88) :args _let_152)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_151)) :args _let_151)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_150) _let_104))) (REFL :args ((not _let_108))) :args _let_46)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_147)) (REORDERING (CNF_AND_POS :args (_let_145 0)) :args ((or _let_144 (not _let_145)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_148)) :args ((or _let_105 (not _let_147) (not _let_148)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_148 false _let_5)) (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_107 _let_109 _let_149))) (REORDERING (CNF_EQUIV_POS1 :args (_let_146)) :args ((or _let_107 _let_145 (not _let_146)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_146 false _let_5)) (CNF_OR_NEG :args (_let_108 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_108 0)) (CONG (REFL :args (_let_108)) (MACRO_SR_PRED_INTRO :args ((= (not _let_107) _let_106))) :args _let_46)) :args ((or _let_106 _let_108))) :args ((or _let_108 _let_149) false _let_144 true _let_147 false _let_148 false _let_109 false _let_145 false _let_146 true _let_105 false _let_106)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_143) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_130)) :args _let_143)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_142)) :args _let_142)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_141) _let_111))) (REFL :args ((not _let_115))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_112 _let_118 (not _let_119)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_140) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_140)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_139)) :args _let_139)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_138) _let_131))) (REFL :args ((not _let_135))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_137)) :args ((or _let_132 (not _let_136) (not _let_137)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_22 :args (_let_137 false _let_6)) (REORDERING (CNF_OR_NEG :args (_let_136 1)) :args ((or _let_134 _let_136))) (CNF_OR_NEG :args (_let_135 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_135 0)) (CONG (REFL :args (_let_135)) (MACRO_SR_PRED_INTRO :args ((= (not _let_134) _let_133))) :args _let_46)) :args ((or _let_133 _let_135))) :args (_let_135 false _let_137 false _let_136 true _let_132 false _let_133)) :args (_let_131 false _let_135)) :args (_let_119 false _let_131)) (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_114 _let_116 (not _let_117)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_129) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_90 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_130)) :args _let_129)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_128)) :args _let_128)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_120))) (REFL :args ((not _let_124))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_125 1)) :args ((or _let_121 (not _let_125)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_126)) :args ((or _let_123 _let_125 (not _let_126)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_126 false _let_5)) (CNF_OR_NEG :args (_let_124 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_124 0)) (CONG (REFL :args (_let_124)) (MACRO_SR_PRED_INTRO :args ((= (not _let_123) _let_122))) :args _let_46)) :args ((or _let_122 _let_124))) :args (_let_124 false _let_125 false _let_126 true _let_121 false _let_122)) :args (_let_120 false _let_124)) :args (_let_117 false _let_120)) (CNF_OR_NEG :args (_let_115 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_115 0)) (CONG (REFL :args (_let_115)) (MACRO_SR_PRED_INTRO :args ((= (not _let_114) _let_113))) :args _let_46)) :args ((or _let_113 _let_115))) :args (_let_115 false _let_119 false _let_116 false _let_117 true _let_112 false _let_113)) :args (_let_111 false _let_115)) :args (_let_110 false _let_111)) :args (_let_108 false _let_110)) :args (_let_104 false _let_108)) :args (_let_90 false _let_104)) (REORDERING (CNF_EQUIV_NEG1 :args _let_103) :args ((or _let_26 _let_31 _let_32))) _let_102 :args ((or _let_31 _let_8) false _let_27 true _let_18 false _let_19 true _let_15 true _let_14 false _let_90 false _let_26 true _let_32)) (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_31 _let_16 (not _let_34)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_87) :args _let_88) :args _let_87)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_86)) :args _let_86)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_35))) (REFL :args ((not _let_39))) :args _let_46)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_44)) (REORDERING (CNF_EQUIV_POS2 :args (_let_45)) :args ((or _let_36 (not _let_44) (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_70 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_45 false _let_5)) (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_38 _let_42 (not _let_43)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args _let_60) :args _let_84)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_61))) (REFL :args ((not _let_65))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_66 (not _let_67)))) (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_62 _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_80)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_71))) (REFL :args ((not _let_75))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_77)) :args ((or _let_72 (not _let_76) (not _let_77)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_22 :args (_let_77 false _let_6)) (REORDERING (CNF_OR_NEG :args (_let_76 0)) :args ((or _let_74 _let_76))) (CNF_OR_NEG :args (_let_75 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_75 0)) (CONG (REFL :args (_let_75)) (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) :args _let_46)) :args ((or _let_73 _let_75))) :args (_let_75 false _let_77 false _let_76 true _let_72 false _let_73)) :args (_let_71 false _let_75)) :args (_let_70 false _let_71)) (REORDERING (CNF_EQUIV_POS1 :args (_let_68)) :args ((or _let_64 _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_65 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_68 false _let_5)) (CNF_OR_NEG :args (_let_65 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 0)) (CONG (REFL :args (_let_65)) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_46)) :args ((or _let_63 _let_65))) :args (_let_65 true _let_66 false _let_70 false _let_67 false _let_68 true _let_62 false _let_63)) :args (_let_61 false _let_65)) :args (_let_43 false _let_61)) (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_38 _let_40 (not _let_41)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args _let_60) :args _let_59)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_47))) (REFL :args ((not _let_51))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_52 0)) :args ((or _let_48 (not _let_52)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_53)) :args ((or _let_50 _let_52 (not _let_53)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_53 false _let_5)) (CNF_OR_NEG :args (_let_51 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG (REFL :args (_let_51)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_46)) :args ((or _let_49 _let_51))) :args (_let_51 false _let_52 false _let_53 true _let_48 false _let_49)) :args (_let_47 false _let_51)) :args (_let_41 false _let_47)) (CNF_OR_NEG :args (_let_39 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_46)) :args ((or _let_37 _let_39))) :args (_let_39 true _let_44 false _let_45 false _let_42 false _let_43 false _let_40 false _let_41 true _let_36 false _let_37)) :args (_let_35 false _let_39)) :args (_let_34 false _let_35)) :args (_let_31 true _let_8 false _let_34)))) (let ((_let_163 (and _let_27 _let_33))) (let ((_let_164 (ASSUME :args (_let_33)))) (let ((_let_165 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_154) :args ((or _let_18 _let_20 _let_153))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_163)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_164 _let_160) (SCOPE (FALSE_ELIM (TRANS _let_161 (FALSE_INTRO _let_164))) :args (_let_33 _let_27))) :args (_let_27 _let_33))) :args (true _let_163)) (CONG (REFL :args ((not _let_27))) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_26))) (REFL :args (_let_28)) :args _let_46)) _let_157 (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_103) _let_102 _let_162 :args (_let_33 true _let_32 false _let_31)) :args (_let_28 false _let_27 true _let_26)) _let_24 :args (_let_20 true _let_18 false _let_19)))) (let ((_let_166 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 _let_29))) (let ((_let_167 (and _let_10 _let_166))) (let ((_let_168 (= _let_31 _let_167))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_168)) :args ((or (not _let_31) _let_167 (not _let_168)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_168 false _let_5)) :args (_let_167 false _let_31 false _let_168)))) (let ((_let_170 (not _let_167))) (let ((_let_171 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_167 0)) :args ((or _let_10 _let_170))) _let_169 :args (_let_10 false _let_167)))) (let ((_let_172 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_173 (or _let_9 _let_172))) (let ((_let_174 (= _let_166 _let_173))) (let ((_let_175 (and _let_10 _let_172))) (let ((_let_176 (not _let_172))) (let ((_let_177 (= _let_14 _let_175))) (let ((_let_178 (not _let_175))) (let ((_let_179 (not _let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_12)) :args ((or _let_8 (not _let_11) (not _let_12)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_12 false _let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_11)) :args ((or (not _let_9) _let_179 _let_11))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_173)) :args ((or _let_9 _let_172 (not _let_173)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_175)) :args ((or _let_179 _let_175 _let_176))) _let_171 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_177)) :args ((or _let_14 _let_178 (not _let_177)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 0)) _let_165 :args (_let_89 true _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 QUANTIFIERS_INST_E_MATCHING _let_56)) :args _let_54)) _let_55 :args (_let_177 false _let_5)) :args (_let_178 true _let_14 false _let_177)) :args (_let_176 false _let_10 true _let_175)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_174)) :args ((or (not _let_166) _let_173 (not _let_174)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_167 1)) :args ((or _let_166 _let_170))) _let_169 :args (_let_166 false _let_167)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_101 QUANTIFIERS_INST_E_MATCHING _let_23)) :args _let_21)) _let_22 :args (_let_174 false _let_6)) :args (_let_173 false _let_166 false _let_174)) :args (_let_9 true _let_172 false _let_173)) _let_171 :args (_let_11 false _let_9 false _let_10)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_15 1)) _let_165 :args (_let_16 true _let_15)) :args (false false _let_12 false _let_11 true _let_8)) :args (_let_6 _let_5 (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (and (tptp.subset B C) (tptp.subset C B)))) _let_4 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersection B C) (tptp.intersection C B))) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.member D B) (tptp.member D C))))) (forall ((B $$unsorted)) (tptp.subset B B)) _let_3 _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.62/1.82  )
% 1.62/1.82  % SZS output end Proof for SET169+3
% 1.62/1.82  % cvc5---1.0.5 exiting
% 1.62/1.82  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------