%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 14:39:21 EDT 2023

% Result   : Theorem 0.46s 0.79s
% Output   : Proof 0.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n014.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 14:07:17 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.46/0.79  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.y76szf9DjQ/cvc5---1.0.5_5228.p...
% 0.46/0.79  ------- get file name : TPTP file name is SET601+3
% 0.46/0.79  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_5228.smt2...
% 0.46/0.79  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.46/0.79  % SZS status Theorem for SET601+3
% 0.46/0.79  % SZS output start Proof for SET601+3
% 0.46/0.79  (
% 0.46/0.79  (let ((_let_1 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.union (tptp.union (tptp.intersection B C) (tptp.intersection C D)) (tptp.intersection D B)) (tptp.intersection (tptp.intersection (tptp.union B C) (tptp.union C D)) (tptp.union D B)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersection B C) (tptp.intersection C B))))) (let ((_let_4 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.union B C) (tptp.union C B))))) (let ((_let_5 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.union B (tptp.intersection C D)) (tptp.intersection (tptp.union B C) (tptp.union B D)))))) (let ((_let_6 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.union B (tptp.intersection B C)) B)))) (let ((_let_7 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.intersection (tptp.intersection B C) D) (tptp.intersection B (tptp.intersection C D)))))) (let ((_let_8 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.union (tptp.union B C) D) (tptp.union B (tptp.union C D)))))) (let ((_let_9 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_11 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (tptp.intersection _let_11 _let_10))) (let ((_let_13 (tptp.intersection _let_12 _let_9))) (let ((_let_14 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (tptp.union _let_16 _let_15))) (let ((_let_18 (tptp.union _let_17 _let_14))) (let ((_let_19 (= _let_18 _let_13))) (let ((_let_20 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_15))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20))) (let ((_let_22 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) (let ((_let_24 (tptp.union _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (tptp.union _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (tptp.intersection _let_25 _let_24))) (let ((_let_27 (= _let_17 _let_26))) (let ((_let_28 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (= _let_11 _let_28))) (let ((_let_30 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (= _let_10 _let_30))) (let ((_let_32 (= _let_18 (tptp.union _let_14 _let_17)))) (let ((_let_33 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_34 (= _let_16 _let_33))) (let ((_let_35 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (= _let_15 _let_35))) (let ((_let_37 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (= _let_14 _let_37))) (let ((_let_39 (tptp.intersection _let_10 _let_11))) (let ((_let_40 (= _let_12 _let_39))) (let ((_let_41 (tptp.intersection _let_9 _let_12))) (let ((_let_42 (= _let_13 _let_41))) (let ((_let_43 (= (tptp.union _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.union _let_16 (tptp.union _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_44 (tptp.union _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_45 (= (tptp.union _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_44)))) (let ((_let_46 (tptp.union _let_30 _let_15))) (let ((_let_47 (= _let_46 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20)))) (let ((_let_48 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_33)))) (let ((_let_49 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_35))) (let ((_let_50 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_49))) (let ((_let_51 (tptp.union _let_10 _let_39))) (let ((_let_52 (= _let_10 _let_51))) (let ((_let_53 (tptp.intersection _let_10 _let_9))) (let ((_let_54 (= _let_10 (tptp.union _let_10 _let_53)))) (let ((_let_55 (= _let_9 (tptp.union _let_9 _let_41)))) (let ((_let_56 (tptp.union _let_25 _let_26))) (let ((_let_57 (= _let_25 _let_56))) (let ((_let_58 (= (tptp.union _let_16 _let_35) (tptp.intersection _let_24 _let_25)))) (let ((_let_59 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_60 (tptp.intersection _let_59 _let_10))) (let ((_let_61 (= _let_20 _let_60))) (let ((_let_62 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_63 (tptp.intersection _let_62 _let_9))) (let ((_let_64 (= _let_22 _let_63))) (let ((_let_65 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_37))) (let ((_let_66 (= _let_65 (tptp.intersection _let_28 _let_10)))) (let ((_let_67 (= (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_33) (tptp.intersection _let_30 _let_9)))) (let ((_let_68 (= _let_20 (tptp.union _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_69 (tptp.union _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_70 (= _let_22 _let_69))) (let ((_let_71 (= _let_25 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16)))) (let ((_let_72 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16))) (let ((_let_73 (= _let_24 _let_72))) (let ((_let_74 (tptp.intersection _let_9 _let_10))) (let ((_let_75 (= _let_53 _let_74))) (let ((_let_76 (tptp.union _let_14 _let_9))) (let ((_let_77 (= (tptp.union _let_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_76))) (let ((_let_78 (= (tptp.union _let_56 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.union _let_25 (tptp.union _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_79 (= _let_51 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_39))))) (let ((_let_80 (tptp.union _let_10 _let_16))) (let ((_let_81 (= (tptp.union _let_80 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.union _let_10 _let_24)))) (let ((_let_82 (tptp.intersection _let_10 _let_25))) (let ((_let_83 (= (tptp.intersection _let_74 _let_25) (tptp.intersection _let_9 _let_82)))) (let ((_let_84 (= (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_35) (tptp.intersection _let_10 _let_59)))) (let ((_let_85 (= (tptp.union _let_15 _let_63) (tptp.intersection (tptp.union _let_15 _let_62) (tptp.union _let_15 _let_9))))) (let ((_let_86 (= _let_46 (tptp.intersection (tptp.union _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.union _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_87 (= (tptp.union _let_9 _let_13) (tptp.intersection (tptp.union _let_9 _let_12) (tptp.union _let_9 _let_9))))) (let ((_let_88 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_10))) (let ((_let_89 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_59))) (let ((_let_90 (tptp.intersection _let_89 _let_88))) (let ((_let_91 (= (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_60) _let_90))) (let ((_let_92 (= _let_65 (tptp.union _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_93 (= _let_49 (tptp.union _let_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_94 (= _let_80 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_72)))) (let ((_let_95 (= (tptp.union _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_30)))) (let ((_let_96 (= (tptp.intersection _let_90 _let_10) (tptp.intersection _let_89 (tptp.intersection _let_88 _let_10))))) (let ((_let_97 (= (tptp.union _let_14 (tptp.intersection _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.intersection _let_76 _let_44)))) (let ((_let_98 (not _let_19))) (let ((_let_99 (_let_2))) (let ((_let_100 (ASSUME :args _let_99))) (let ((_let_101 (or))) (let ((_let_102 (_let_98))) (let ((_let_103 (forall ((B $$unsorted) (C $$unsorted)) (= B (tptp.union B (tptp.intersection B C)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (_let_103))) (let ((_let_106 ((tptp.intersection B C)))) (let ((_let_107 (_let_5))) (let ((_let_108 (ASSUME :args _let_107))) (let ((_let_109 ((tptp.union B (tptp.intersection C D))))) (let ((_let_110 (_let_4))) (let ((_let_111 (ASSUME :args _let_110))) (let ((_let_112 ((tptp.union B C)))) (let ((_let_113 (_let_3))) (let ((_let_114 (ASSUME :args _let_113))) (let ((_let_115 ((tptp.intersection B C)))) (let ((_let_116 (_let_8))) (let ((_let_117 (ASSUME :args _let_116))) (let ((_let_118 ((tptp.union (tptp.union B C) D)))) (let ((_let_119 ((tptp.union B (tptp.union C D))))) (let ((_let_120 ((tptp.intersection (tptp.union B C) (tptp.union B D))))) (let ((_let_121 (_let_7))) (let ((_let_122 (ASSUME :args _let_121))) (let ((_let_123 ((tptp.intersection (tptp.intersection B C) D)))) (let ((_let_124 (and _let_98 _let_21 _let_23 _let_27 _let_29 _let_31 _let_32 _let_34 _let_36 _let_38 _let_40 _let_42 _let_43 _let_45 _let_47 _let_48 _let_50 _let_52 _let_54 _let_55 _let_57 _let_58 _let_61 _let_64 _let_66 _let_67 _let_68 _let_70 _let_71 _let_73 _let_75 _let_77 _let_78 _let_79 _let_81 _let_83 _let_84 _let_85 _let_86 _let_87 _let_91 _let_92 _let_93 _let_94 _let_95 _let_96))) (let ((_let_125 (ASSUME :args _let_102))) (let ((_let_126 (ASSUME :args (_let_42)))) (let ((_let_127 (SYMM _let_126))) (let ((_let_128 (APPLY_UF tptp.intersection))) (let ((_let_129 (REFL :args (_let_10)))) (let ((_let_130 (ASSUME :args (_let_29)))) (let ((_let_131 (CONG (SYMM (SYMM _let_130)) _let_129 :args _let_128))) (let ((_let_132 (ASSUME :args (_let_66)))) (let ((_let_133 (ASSUME :args (_let_92)))) (let ((_let_134 (SYMM _let_133))) (let ((_let_135 (APPLY_UF tptp.union))) (let ((_let_136 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_137 (ASSUME :args (_let_38)))) (let ((_let_138 (CONG (SYMM _let_137) _let_136 :args _let_135))) (let ((_let_139 (ASSUME :args (_let_23)))) (let ((_let_140 (SYMM _let_139))) (let ((_let_141 (ASSUME :args (_let_70)))) (let ((_let_142 (TRANS (SYMM _let_141) _let_140))) (let ((_let_143 (ASSUME :args (_let_77)))) (let ((_let_144 (ASSUME :args (_let_32)))) (let ((_let_145 (ASSUME :args (_let_36)))) (let ((_let_146 (REFL :args (_let_16)))) (let ((_let_147 (ASSUME :args (_let_58)))) (let ((_let_148 (ASSUME :args (_let_73)))) (let ((_let_149 (ASSUME :args (_let_34)))) (let ((_let_150 (SYMM _let_149))) (let ((_let_151 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_152 (ASSUME :args (_let_67)))) (let ((_let_153 (REFL :args (_let_9)))) (let ((_let_154 (ASSUME :args (_let_31)))) (let ((_let_155 (SYMM _let_154))) (let ((_let_156 (SYMM _let_155))) (let ((_let_157 (TRANS (CONG _let_156 _let_153 :args _let_128) (SYMM _let_152) (CONG _let_151 _let_150 :args _let_135) (SYMM _let_148)))) (let ((_let_158 (ASSUME :args (_let_75)))) (let ((_let_159 (ASSUME :args (_let_83)))) (let ((_let_160 (ASSUME :args (_let_55)))) (let ((_let_161 (ASSUME :args (_let_87)))) (let ((_let_162 (TRANS (SYMM _let_161) (CONG _let_153 (SYMM _let_127) :args _let_135) (SYMM _let_160)))) (let ((_let_163 (ASSUME :args (_let_71)))) (let ((_let_164 (SYMM _let_163))) (let ((_let_165 (CONG _let_136 _let_150 :args _let_135))) (let ((_let_166 (ASSUME :args (_let_48)))) (let ((_let_167 (SYMM _let_166))) (let ((_let_168 (SYMM _let_167))) (let ((_let_169 (ASSUME :args (_let_21)))) (let ((_let_170 (SYMM _let_169))) (let ((_let_171 (ASSUME :args (_let_61)))) (let ((_let_172 (SYMM _let_171))) (let ((_let_173 (ASSUME :args (_let_91)))) (let ((_let_174 (TRANS (SYMM _let_173) (CONG _let_136 (TRANS _let_172 _let_170) :args _let_135)))) (let ((_let_175 (ASSUME :args (_let_96)))) (let ((_let_176 (ASSUME :args (_let_54)))) (let ((_let_177 (ASSUME :args (_let_81)))) (let ((_let_178 (ASSUME :args (_let_50)))) (let ((_let_179 (SYMM _let_178))) (let ((_let_180 (ASSUME :args (_let_93)))) (let ((_let_181 (SYMM _let_180))) (let ((_let_182 (CONG _let_145 _let_151 :args _let_135))) (let ((_let_183 (ASSUME :args (_let_64)))) (let ((_let_184 (ASSUME :args (_let_85)))) (let ((_let_185 (TRANS (SYMM _let_184) (CONG (REFL :args (_let_15)) (TRANS (SYMM _let_183) _let_140) :args _let_135) _let_182 _let_181 _let_179))) (let ((_let_186 (TRANS _let_163 (SYMM _let_165) _let_167))) (let ((_let_187 (CONG _let_151 _let_186 :args _let_135))) (let ((_let_188 (CONG (TRANS _let_187 _let_155) _let_146 :args _let_135))) (let ((_let_189 (ASSUME :args (_let_94)))) (let ((_let_190 (ASSUME :args (_let_43)))) (let ((_let_191 (ASSUME :args (_let_27)))) (let ((_let_192 (ASSUME :args (_let_78)))) (let ((_let_193 (ASSUME :args (_let_57)))) (let ((_let_194 (ASSUME :args (_let_45)))) (let ((_let_195 (ASSUME :args (_let_40)))) (let ((_let_196 (CONG _let_136 (TRANS (CONG (SYMM _let_142) (TRANS (SYMM _let_195) _let_131 (SYMM _let_132) (SYMM _let_134) _let_138) :args _let_135) (CONG _let_142 (REFL :args (_let_44)) :args _let_135) (SYMM _let_194) (CONG _let_140 _let_136 :args _let_135) _let_155) :args _let_135))) (let ((_let_197 (ASSUME :args (_let_79)))) (let ((_let_198 (SYMM _let_197))) (let ((_let_199 (ASSUME :args (_let_52)))) (let ((_let_200 (SYMM _let_199))) (let ((_let_201 (SYMM _let_196))) (let ((_let_202 (ASSUME :args (_let_95)))) (let ((_let_203 (ASSUME :args (_let_68)))) (let ((_let_204 (CONG _let_187 (TRANS (SYMM _let_203) _let_170) :args _let_135))) (let ((_let_205 (ASSUME :args (_let_86)))) (let ((_let_206 (ASSUME :args (_let_47)))) (let ((_let_207 (ASSUME :args (_let_84)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_124)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_125 _let_144 _let_145 _let_147 _let_148 _let_149 _let_152 _let_154 _let_158 _let_159 _let_160 _let_126 _let_161 _let_163 _let_166 _let_169 _let_171 _let_173 _let_175 _let_139 _let_194 _let_141 _let_137 _let_133 _let_132 _let_130 _let_195 _let_197 _let_199 _let_202 _let_203 _let_176 _let_177 _let_178 _let_180 _let_183 _let_184 _let_189 _let_190 _let_191 _let_192 _let_193 _let_205 _let_206 _let_207 _let_143) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (REFL :args (_let_14)) (TRANS (CONG (SYMM _let_162) (TRANS _let_169 (CONG _let_136 _let_145 :args _let_135) (SYMM (SYMM _let_207)) (CONG _let_129 (SYMM _let_174) :args _let_128) (CONG _let_129 (TRANS (CONG (REFL :args (_let_89)) (TRANS _let_201 _let_198 _let_200 _let_156 (CONG _let_151 _let_169 :args _let_135) (SYMM _let_206) (SYMM (SYMM _let_205)) (CONG (TRANS (SYMM _let_204) (TRANS _let_204 (CONG _let_155 _let_136 :args _let_135) (SYMM (SYMM _let_202)) (CONG _let_136 _let_155 :args _let_135) _let_201 _let_198 _let_200) (TRANS (SYMM _let_200) (SYMM _let_198) _let_196)) (TRANS (CONG _let_155 _let_151 :args _let_135) (CONG (TRANS (TRANS (CONG (TRANS _let_168 _let_165 _let_164 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(REFL :args ((not _let_23))) (REFL :args ((not _let_27))) (REFL :args ((not _let_29))) (REFL :args ((not _let_31))) (REFL :args ((not _let_32))) (REFL :args ((not _let_34))) (REFL :args ((not _let_36))) (REFL :args ((not _let_38))) (REFL :args ((not _let_40))) (REFL :args ((not _let_42))) (REFL :args ((not _let_43))) (REFL :args ((not _let_45))) (REFL :args ((not _let_47))) (REFL :args ((not _let_48))) (REFL :args ((not _let_50))) (REFL :args ((not _let_52))) (REFL :args ((not _let_54))) (REFL :args ((not _let_55))) (REFL :args ((not _let_57))) (REFL :args ((not _let_58))) (REFL :args ((not _let_61))) (REFL :args ((not _let_64))) (REFL :args ((not _let_66))) (REFL :args ((not _let_67))) (REFL :args ((not _let_68))) (REFL :args ((not _let_70))) (REFL :args ((not _let_71))) (REFL :args ((not _let_73))) (REFL :args ((not _let_75))) (REFL :args ((not _let_77))) (REFL :args ((not _let_78))) (REFL :args ((not _let_79))) (REFL :args ((not _let_81))) (REFL :args ((not _let_83))) (REFL :args ((not _let_84))) (REFL :args ((not _let_85))) (REFL :args ((not _let_86))) (REFL :args ((not _let_87))) (REFL :args ((not _let_91))) (REFL :args ((not _let_92))) (REFL :args ((not _let_93))) (REFL :args ((not _let_94))) (REFL :args ((not _let_95))) (REFL :args ((not _let_96))) (REFL :args ((not _let_97))) :args _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_14 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_120)) :args _let_107)) _let_108 :args (_let_97 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_122 :args (_let_89 _let_88 _let_10 QUANTIFIERS_INST_E_MATCHING _let_123)) :args _let_121)) _let_122 :args (_let_96 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_95 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_94 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_93 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_37 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_92 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_59 _let_10 QUANTIFIERS_INST_E_MATCHING _let_109)) :args _let_107)) _let_108 :args (_let_91 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_9 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false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (_let_10 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_119)) :args _let_116)) _let_117 :args (_let_81 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_39 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_79 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (_let_25 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_78 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_77 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE 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(_let_68 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_120)) :args _let_107)) _let_108 :args (_let_67 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_120)) :args _let_107)) _let_108 :args (_let_66 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_109)) :args _let_107)) _let_108 :args (_let_64 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_109)) :args _let_107)) _let_108 :args (_let_61 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_109)) :args _let_107)) _let_108 :args (_let_58 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_25 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_57 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_9 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_55 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_10 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_54 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (_let_10 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_52 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_50 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_48 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_15 QUANTIFIERS_INST_E_MATCHING _let_119)) :args _let_116)) _let_117 :args (_let_47 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_45 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_117 :args (_let_16 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_118)) :args _let_116)) _let_117 :args (_let_43 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_12 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113)) _let_114 :args (_let_42 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (_let_11 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113)) _let_114 :args (_let_40 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113)) _let_114 :args (_let_38 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113)) _let_114 :args (_let_36 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_115)) :args _let_113)) _let_114 :args (_let_34 false _let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_17 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_32 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_31 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_112)) :args _let_110)) _let_111 :args (_let_29 false _let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (_let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_109)) :args _let_107)) _let_108 :args (_let_27 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_23 false _let_103)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_106)) :args _let_105)) _let_104 :args (_let_21 false _let_103)) (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_102) :args _let_101)) _let_100 :args (_let_98 true _let_1)) :args (false false _let_97 false _let_96 false _let_95 false _let_94 false _let_93 false _let_92 false _let_91 false _let_87 false _let_86 false _let_85 false _let_84 false _let_83 false _let_81 false _let_79 false _let_78 false _let_77 false _let_75 false _let_73 false _let_71 false _let_70 false _let_68 false _let_67 false _let_66 false _let_64 false _let_61 false _let_58 false _let_57 false _let_55 false _let_54 false _let_52 false _let_50 false _let_48 false _let_47 false _let_45 false _let_43 false _let_42 false _let_40 false _let_38 false _let_36 false _let_34 false _let_32 false _let_31 false _let_29 false _let_27 false _let_23 false _let_21 true _let_19)) :args (_let_8 (forall ((B $$unsorted)) (= (tptp.intersection B B) B)) _let_7 _let_6 _let_5 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.union B C)) (or (tptp.member D B) (tptp.member D C)))) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.intersection B C)) (and (tptp.member D B) (tptp.member D C)))) (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (and (tptp.subset B C) (tptp.subset C B)))) _let_4 _let_3 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.member D B) (tptp.member D C))))) (forall ((B $$unsorted)) (tptp.subset B B)) (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C))))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.46/0.79  )
% 0.46/0.79  % SZS output end Proof for SET601+3
% 0.46/0.79  % cvc5---1.0.5 exiting
% 0.46/0.80  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------