TSTP Solution File: SET761+4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET761+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 14:40:14 EDT 2023
% Result : Theorem 0.15s 0.51s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET761+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sat Aug 26 08:32:58 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.15/0.40 %----Proving TF0_NAR, FOF, or CNF
% 0.15/0.51 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Z9egjUM5Jd/cvc5---1.0.5_18289.p...
% 0.15/0.51 ------- get file name : TPTP file name is SET761+4
% 0.15/0.51 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18289.smt2...
% 0.15/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.15/0.51 % SZS status Theorem for SET761+4
% 0.15/0.51 % SZS output start Proof for SET761+4
% 0.15/0.51 (
% 0.15/0.51 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.maps F A B) (tptp.injective F A B) (tptp.subset X A) (tptp.subset Y A)) (tptp.equal_set (tptp.image3 F (tptp.intersection X Y) B) (tptp.intersection (tptp.image3 F X B) (tptp.image3 F Y B)))))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y)))))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (not _let_7))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (and _let_14 _let_13))) (let ((_let_16 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_16))) (let ((_let_18 (= _let_17 _let_15))) (let ((_let_19 (not _let_15))) (let ((_let_20 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (tptp.apply F X Y)))))))))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (_let_20))) (let ((_let_23 ((tptp.member Y (tptp.image3 F A B))))) (let ((_let_24 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_24))) (let ((_let_26 (and _let_17 _let_25))) (let ((_let_27 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (and _let_14 _let_28))) (let ((_let_30 (= _let_25 _let_29))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_9))) (let ((_let_34 (not _let_33))) (let ((_let_35 (and _let_10 _let_31))) (let ((_let_36 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_37 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_36))) (let ((_let_38 (= _let_37 _let_35))) (let ((_let_39 (_let_4))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 ((tptp.member X (tptp.intersection A B))))) (let ((_let_42 (not _let_37))) (let ((_let_43 (or _let_42 _let_9))) (let ((_let_44 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (not _let_44))) (let ((_let_47 (and _let_14 _let_46))) (let ((_let_48 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_48))) (let ((_let_50 (= _let_49 _let_47))) (let ((_let_51 (tptp.intersection _let_16 _let_24))) (let ((_let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_51))) (let ((_let_53 (not _let_49))) (let ((_let_54 (or _let_53 _let_52))) (let ((_let_55 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member X (tptp.intersection (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_56 (not _let_54))) (let ((_let_57 (tptp.subset _let_48 _let_51))) (let ((_let_58 (= _let_57 _let_55))) (let ((_let_59 (not _let_55))) (let ((_let_60 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((tptp.subset A B)))) (let ((_let_64 (tptp.subset _let_51 _let_48))) (let ((_let_65 (and _let_57 _let_64))) (let ((_let_66 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (tptp.member X (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_67 (= _let_64 _let_66))) (let ((_let_68 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_48))) (let ((_let_69 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_51))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_70 _let_68))) (let ((_let_72 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_24))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_16))) (let ((_let_74 (and _let_73 _let_72))) (let ((_let_75 (= _let_69 _let_74))) (let ((_let_76 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_79 (and _let_78 _let_77))) (let ((_let_80 (= _let_68 _let_79))) (let ((_let_81 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_82 (not _let_81))) (let ((_let_83 (and _let_78 _let_82))) (let ((_let_84 (= _let_73 _let_83))) (let ((_let_85 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_86 (not _let_85))) (let ((_let_87 (and _let_78 _let_86))) (let ((_let_88 (= _let_72 _let_87))) (let ((_let_89 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_90 (not _let_89))) (let ((_let_91 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 _let_90))) (let ((_let_94 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_95 (not _let_94))) (let ((_let_96 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_97 _let_95))) (let ((_let_99 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 _let_36))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_100 _let_90))) (let ((_let_102 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_103 (or _let_92 _let_102))) (let ((_let_104 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_105 (or _let_97 _let_104))) (let ((_let_106 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_107 (and _let_91 _let_106))) (let ((_let_108 (= _let_99 _let_107))) (let ((_let_109 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_110 (not _let_78))) (let ((_let_111 (not _let_104))) (let ((_let_112 (not _let_102))) (let ((_let_113 (or _let_112 _let_111 _let_110 _let_90 _let_95 _let_109))) (let ((_let_114 (or))) (let ((_let_115 (not _let_74))) (let ((_let_116 (not _let_83))) (let ((_let_117 (_let_79))) (let ((_let_118 (_let_82))) (let ((_let_119 (_let_86))) (let ((_let_120 (_let_76))) (let ((_let_121 (REFL :args (_let_93)))) (let ((_let_122 (REFL :args (_let_98)))) (let ((_let_123 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_124 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_125 (= _let_124 _let_123))) (let ((_let_126 (tptp.equal_set _let_48 _let_51))) (let ((_let_127 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_128 (not _let_127))) (let ((_let_129 (not _let_124))) (let ((_let_130 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_131 (not _let_130))) (let ((_let_132 (or (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_131 _let_129 _let_128 _let_126))) (let ((_let_133 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.injective F A B)) (not (tptp.subset X A)) (not (tptp.subset Y A)) (tptp.equal_set (tptp.image3 F (tptp.intersection X Y) B) (tptp.intersection (tptp.image3 F X B) (tptp.image3 F Y B))))))) (let ((_let_134 (not _let_132))) (let ((_let_135 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (not _let_133))) (let ((_let_137 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_135) :args (_let_136))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_136) _let_133))) (REFL :args (_let_134)) :args _let_114)) _let_135 :args (_let_134 true _let_133)))) (let ((_let_138 (REFL :args (_let_132)))) (let ((_let_139 (_let_123))) (let ((_let_140 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_141 (= _let_127 _let_140))) (let ((_let_142 (_let_140))) (let ((_let_143 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_144 (= _let_130 _let_143))) (let ((_let_145 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member X2 A)) (not (tptp.member Y B)) (not (tptp.apply F X1 Y)) (not (tptp.apply F X2 Y)) (= X1 X2))))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_147 (_let_143))) (let ((_let_148 (and _let_96 _let_109))) (let ((_let_149 (_let_96 _let_109))) (let ((_let_150 (ASSUME :args (_let_96)))) (let ((_let_151 (ASSUME :args (_let_109)))) (let ((_let_152 (not _let_66))) (let ((_let_153 (_let_152))) (let ((_let_154 (= _let_126 _let_65))) (let ((_let_155 (not _let_65))) (let ((_let_156 (_let_5))) (let ((_let_157 (ASSUME :args _let_156))) (let ((_let_158 (_let_59))) (let ((_let_159 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_158)) :args _let_158)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_55))) (REFL :args (_let_56)) :args _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_58)) :args ((or _let_57 _let_59 (not _let_58)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_154)) :args ((or _let_126 _let_155 (not _let_154)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_132 4)) _let_137 :args ((not _let_126) true _let_132)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_157 :args (_let_48 _let_51 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_156)) _let_157 :args (_let_154 false _let_5)) :args (_let_155 true _let_126 false _let_154)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_67)) :args ((or _let_64 _let_152 (not _let_67)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_153)) :args _let_153)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_152) _let_66))) (REFL :args ((not _let_71))) :args _let_114)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_148)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_150 _let_151) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_151)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_150))) :args _let_149)) :args _let_149)) :args (true _let_148)) :args ((or _let_97 _let_106 (not _let_109)))) (REORDERING (CNF_AND_NEG :args (_let_107)) :args ((or _let_92 _let_107 (not _let_106)))) (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_110 _let_90 _let_95 _let_112 _let_111 _let_109 (not _let_113)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_147) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 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_let_14 true _let_15)) :args (false true _let_12 false _let_7)) :args (_let_6 _let_5 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) _let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.maps F A B) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))) (forall ((H $$unsorted) (G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.compose_predicate H G F A B C) (forall ((X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply H X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))) (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))) (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))) _let_3 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))) (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) _let_2 (forall ((F $$unsorted) (B $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image2 F B)) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y))))) (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image3 F B A)) (and (tptp.member X A) (exists ((Y $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.increasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y1 Y2))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.decreasing F A R B S) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply R X1 X2) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (tptp.apply S Y2 Y1))))) (forall ((F $$unsorted) (A $$unsorted) (R $$unsorted) (B $$unsorted) (S $$unsorted)) (= (tptp.isomorphism F A R B S) (and (tptp.maps F A B) (tptp.one_to_one F A B) (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member Y1 B) (tptp.member X2 A) (tptp.member Y2 B) (tptp.apply F X1 Y1) (tptp.apply F X2 Y2)) (= (tptp.apply R X1 X2) (tptp.apply S Y1 Y2))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.15/0.51 )
% 0.15/0.51 % SZS output end Proof for SET761+4
% 0.15/0.51 % cvc5---1.0.5 exiting
% 0.15/0.51 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------