TSTP Solution File: NUM397+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM397+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 10:43:41 EDT 2023
% Result : Theorem 26.62s 26.93s
% Output : Proof 26.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM397+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.33 % Computer : n005.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Aug 25 09:18:23 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.18/0.47 %----Proving TF0_NAR, FOF, or CNF
% 26.62/26.93 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.1Ij8ZCbZz1/cvc5---1.0.5_478.p...
% 26.62/26.93 ------- get file name : TPTP file name is NUM397+1
% 26.62/26.93 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_478.smt2...
% 26.62/26.93 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.62/26.93 --- Run --no-e-matching --full-saturate-quant at 5...
% 26.62/26.93 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.62/26.93 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.62/26.93 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.62/26.93 % SZS status Theorem for NUM397+1
% 26.62/26.93 % SZS output start Proof for NUM397+1
% 26.62/26.93 (
% 26.62/26.93 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))))) (let ((_let_5 (not (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.ordinal (tptp.union A))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))) (let ((_let_7 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.in A B)) (not (= A B)) (not (tptp.in B A)))))))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in A B) (tptp.ordinal A)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))) (let ((_let_10 (tptp.relation tptp.empty_set))) (let ((_let_11 (tptp.empty tptp.empty_set))) (let ((_let_12 (tptp.ordinal tptp.empty_set))) (let ((_let_13 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_14 (and _let_10 _let_13 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_11 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) _let_12))) (let ((_let_15 (and _let_11 _let_10 _let_13))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))))) (let ((_let_17 (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B A) (tptp.in C A) (not (tptp.in B C)) (not (= B C)) (not (tptp.in C B))))))))) (let ((_let_18 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))))) (let ((_let_19 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (or (tptp.ordinal_subset A B) (tptp.ordinal_subset B A)))))) (let ((_let_20 (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))))) (let ((_let_21 (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))) (let ((_let_22 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_25 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26 _let_22 _let_23 _let_24))) (let ((_let_30 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_31 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 _let_30))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_30))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_22 _let_23 _let_24))) (let ((_let_36 (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (or (not (tptp.in B _let_1)) (not (tptp.in C _let_1)) (tptp.in B C) (= B C) (tptp.in C B)))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (tptp.epsilon_connected _let_30))) (let ((_let_39 (= _let_38 _let_36))) (let ((_let_40 (not _let_36))) (let ((_let_41 (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B A)) (not (tptp.in C A)) (tptp.in B C) (= B C) (tptp.in C B))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (tptp.ordinal _let_30))) (let ((_let_44 (not _let_38))) (let ((_let_45 (tptp.epsilon_transitive _let_30))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_43))) (let ((_let_48 (forall ((A $$unsorted)) (or (not (tptp.epsilon_transitive A)) (not (tptp.epsilon_connected A)) (tptp.ordinal A))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (forall ((B $$unsorted)) (let ((_let_1 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (or (not (tptp.in B _let_1)) (tptp.subset B _let_1)))))) (let ((_let_51 (= _let_45 _let_50))) (let ((_let_52 (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (or (not (tptp.in B A)) (tptp.subset B A))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (_let_52))) (let ((_let_55 ((tptp.epsilon_transitive A)))) (let ((_let_56 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_30))) (let ((_let_57 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_30))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56))) (let ((_let_60 (forall ((D $$unsorted)) (or (not (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 D)) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))))) (let ((_let_61 (not _let_60))) (let ((_let_62 (= _let_57 _let_61))) (let ((_let_63 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_56))) (let ((_let_66 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 _let_67))) (let ((_let_71 (not _let_11))) (let ((_let_72 (tptp.powerset tptp.empty_set))) (let ((_let_73 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_72))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_69 _let_74 _let_71))) (let ((_let_76 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_77 (tptp.ordinal SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_78 (not _let_76))) (let ((_let_79 (or _let_78 _let_67 _let_77))) (let ((_let_80 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_81 (or _let_67 _let_80))) (let ((_let_82 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.empty_set))) (let ((_let_83 (= _let_73 _let_82))) (let ((_let_84 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_85 (= _let_80 _let_84))) (let ((_let_86 (not _let_77))) (let ((_let_87 (or _let_86 _let_78 _let_85))) (let ((_let_88 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.empty_set))) (let ((_let_89 (= _let_82 _let_88))) (let ((_let_90 (not _let_12))) (let ((_let_91 (or _let_86 _let_90 _let_89))) (let ((_let_92 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_93 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_92))) (let ((_let_94 (= _let_80 _let_93))) (let ((_let_95 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_96 (not _let_93))) (let ((_let_97 (or _let_69 _let_96 _let_95))) (let ((_let_98 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_99 (tptp.empty SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_100 (not _let_95))) (let ((_let_101 (or _let_100 _let_99 _let_63))) (let ((_let_102 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 tptp.empty_set))) (let ((_let_103 (tptp.in tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_104 (or _let_90 _let_78 _let_103 _let_98 _let_102))) (let ((_let_105 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_92))) (let ((_let_106 (not _let_99))) (let ((_let_107 (not _let_105))) (let ((_let_108 (not _let_103))) (let ((_let_109 (or _let_108 _let_107 _let_106))) (let ((_let_110 (or))) (let ((_let_111 (forall ((C $$unsorted)) (= (tptp.in C (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (not (forall ((D $$unsorted)) (or (not (tptp.in C D)) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))))))) (let ((_let_112 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (not (forall ((D $$unsorted)) (or (not (tptp.in C D)) (not (tptp.in D A))))))))))) (let ((_let_113 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_30 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_112)))) _let_113 :args (_let_111 false _let_112)))) (let ((_let_115 (_let_111))) (let ((_let_116 ((tptp.in C _let_30)))) (let ((_let_117 (ASSUME :args _let_115))) (let ((_let_118 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.subset A (tptp.union B)))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (_let_61))) (let ((_let_121 (REFL :args (_let_70)))) (let ((_let_122 (AND_ELIM (ASSUME :args (_let_15)) :args (0)))) (let ((_let_123 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.in A B)) (not (tptp.element B (tptp.powerset C))) (not (tptp.empty C)))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (_let_123))) (let ((_let_126 (or _let_78 _let_43))) (let ((_let_127 (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (tptp.ordinal (tptp.union A)))))) (let ((_let_128 (not _let_126))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (not _let_127))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_129) :args (_let_130))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_127))) (REFL :args (_let_128)) :args _let_110)) _let_129 :args (_let_128 true _let_127)))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_126 0)) (CONG (REFL :args (_let_126)) (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_76))) :args _let_110)) :args ((or _let_76 _let_126))) _let_131 :args (_let_76 true _let_126)))) (let ((_let_133 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal B)) (not (tptp.in A B)) (tptp.ordinal A))))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (_let_133))) (let ((_let_136 ((not (= (tptp.in A B) false))))) (let ((_let_137 (forall ((B $$unsorted)) (or (not (tptp.in B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)) (tptp.subset B SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_138 (tptp.epsilon_transitive SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_139 (= _let_138 _let_137))) (let ((_let_140 (and _let_138 (tptp.epsilon_connected SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_141 (or _let_78 _let_140))) (let ((_let_142 (forall ((A $$unsorted)) (or (not (tptp.ordinal A)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))))) (let ((_let_143 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_144 (_let_137))) (let ((_let_145 (_let_4))) (let ((_let_146 (ASSUME :args _let_145))) (let ((_let_147 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))))) (let ((_let_148 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (_let_147))) (let ((_let_150 (AND_ELIM (ASSUME :args (_let_14)) :args (7)))) (let ((_let_151 ((not (= (tptp.ordinal A) false)) (not (= (tptp.ordinal B) false))))) (let ((_let_152 ((tptp.subset A B)))) (let ((_let_153 (not _let_80))) (let ((_let_154 (not _let_88))) (let ((_let_155 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.in A B)) (not (tptp.element B (tptp.powerset C))) (tptp.element A C))))) (let ((_let_156 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_157 (not _let_84))) (let ((_let_158 (not _let_98))) (let ((_let_159 (ASSUME :args (_let_154)))) (let ((_let_160 (ASSUME :args (_let_98)))) (let ((_let_161 (ASSUME :args (_let_84)))) (let ((_let_162 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element A B)) (tptp.empty B) (tptp.in A B))))) (let ((_let_163 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_164 (forall ((A $$unsorted) (BOUND_VARIABLE_1171 $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal BOUND_VARIABLE_1171)) (tptp.in A BOUND_VARIABLE_1171) (= A BOUND_VARIABLE_1171) (tptp.in BOUND_VARIABLE_1171 A))))) (let ((_let_165 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_166 (_let_164))) (let ((_let_167 (tptp.element tptp.empty_set _let_72))) (let ((_let_168 (not _let_167))) (let ((_let_169 (not _let_102))) (let ((_let_170 (or _let_169 _let_168 _let_71))) (let ((_let_171 (tptp.subset tptp.empty_set tptp.empty_set))) (let ((_let_172 (= _let_171 _let_167))) (let ((_let_173 (tptp.ordinal_subset tptp.empty_set tptp.empty_set))) (let ((_let_174 (= _let_173 _let_171))) (let ((_let_175 (or _let_90 _let_90 _let_174))) (let ((_let_176 (or _let_90 _let_90 _let_173 _let_173))) (let ((_let_177 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.ordinal A)) (not (tptp.ordinal B)) (tptp.ordinal_subset A B) (tptp.ordinal_subset B A))))) (let ((_let_178 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_179 (_let_177))) (let ((_let_180 ((not (= (tptp.ordinal A) false)) (not (= (tptp.ordinal B) false))))) (let ((_let_181 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_182 (= _let_181 _let_105))) (let ((_let_183 (tptp.ordinal_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_184 (= _let_183 _let_181))) (let ((_let_185 (or _let_78 _let_78 _let_184))) (let ((_let_186 (or _let_78 _let_78 _let_183 _let_183))) (let ((_let_187 (not _let_50))) (let ((_let_188 (_let_187))) (let ((_let_189 (_let_40))) (let ((_let_190 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_189)) :args _let_189)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_36))) (REFL :args (_let_37)) :args 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_let_31 false _let_220)) :args (_let_218 true _let_217)))) (let ((_let_223 (REFL :args (_let_216)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_22 _let_23 _let_24 _let_28 _let_26 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_212)) :args ((or _let_25 _let_209 _let_211 (not _let_212)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_216 0)) (CONG _let_223 (MACRO_SR_PRED_INTRO :args ((= (not _let_209) _let_208))) :args _let_110)) :args ((or _let_208 _let_216))) _let_222 :args (_let_208 true _let_216)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_215)) :args ((or _let_78 _let_214 _let_210 (not _let_215)))) _let_132 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_216 1)) (CONG _let_223 (MACRO_SR_PRED_INTRO :args ((= (not _let_214) _let_213))) :args _let_110)) :args ((or _let_213 _let_216))) _let_222 :args (_let_213 true _let_216)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_136)) :args _let_135)) _let_134 :args (_let_215 false _let_133)) :args (_let_210 false _let_76 false _let_213 false _let_215)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_136)) :args _let_135)) _let_134 :args (_let_212 false _let_133)) :args (_let_25 false _let_208 false _let_210 false _let_212)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_195)) :args ((or _let_27 _let_192 _let_194 (not _let_195)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_199 0)) (CONG _let_207 (MACRO_SR_PRED_INTRO :args ((= (not _let_192) _let_191))) :args _let_110)) :args ((or _let_191 _let_199))) _let_206 :args (_let_191 true _let_199)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_198)) :args ((or _let_78 _let_197 _let_193 (not _let_198)))) _let_132 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_199 1)) (CONG _let_207 (MACRO_SR_PRED_INTRO :args ((= (not _let_197) _let_196))) :args _let_110)) :args ((or _let_196 _let_199))) _let_206 :args (_let_196 true _let_199)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_136)) :args _let_135)) _let_134 :args (_let_198 false _let_133)) :args (_let_193 false _let_76 false _let_196 false _let_198)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_136)) :args _let_135)) _let_134 :args (_let_195 false _let_133)) :args (_let_27 false _let_191 false _let_193 false _let_195)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_165 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in A BOUND_VARIABLE_1171) true))))) :args _let_166)) _let_165 :args (_let_29 false _let_164)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 4)) _let_190 :args ((not _let_24) true _let_35)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 3)) _let_190 :args ((not _let_23) true _let_35)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 2)) _let_190 :args ((not _let_22) true _let_35)) :args (false false _let_25 false _let_27 false _let_29 true _let_24 true _let_23 true _let_22)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) _let_21 (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) _let_20 (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) _let_19 _let_18 _let_17 (forall ((A $$unsorted)) (= (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) _let_16 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) _let_15 _let_11 _let_14 (and _let_11 _let_10) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_non_empty A) (tptp.function A))) _let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (tptp.ordinal_subset A A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.62/26.93 )
% 26.62/26.93 % SZS output end Proof for NUM397+1
% 26.62/26.94 % cvc5---1.0.5 exiting
% 26.62/26.94 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------