%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET745+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n020.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 14:40:09 EDT 2023

% Result   : Theorem 0.22s 0.66s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET745+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat Aug 26 13:00:29 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.66  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.o3XTVnzxqg/cvc5---1.0.5_24417.p...
% 0.22/0.66  ------- get file name : TPTP file name is SET745+4
% 0.22/0.66  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24417.smt2...
% 0.22/0.66  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.66  % SZS status Theorem for SET745+4
% 0.22/0.66  % SZS output start Proof for SET745+4
% 0.22/0.66  (
% 0.22/0.66  (let ((_let_1 (not (forall ((F1 $$unsorted) (F2 $$unsorted) (F $$unsorted) (A1 $$unsorted) (A2 $$unsorted) (B $$unsorted)) (=> (and (tptp.maps F1 A1 B) (tptp.maps F2 A2 B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X (tptp.union A1 A2)) (tptp.member Y B)) (= (tptp.apply F X Y) (or (and (tptp.member X A1) (tptp.apply F1 X Y)) (and (tptp.member X A2) (tptp.apply F2 X Y))))))) (= (tptp.maps F (tptp.union A1 A2) B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A1) (tptp.member X A2) (tptp.member Y1 B) (tptp.member Y2 B) (tptp.apply F1 X Y1) (tptp.apply F2 X Y2)) (= Y1 Y2))))))))) (let ((_let_2 (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_5 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_6 (and _let_5 _let_4))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (and _let_8 _let_7))) (let ((_let_10 (or _let_9 _let_6))) (let ((_let_11 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_15))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_14 _let_12))) (let ((_let_19 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y) (or (and (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (and (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)))))))) (let ((_let_20 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y2)) (= Y1 Y2))))) (let ((_let_21 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (not _let_19))) (let ((_let_24 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_22))) (let ((_let_29 (forall ((F1 $$unsorted) (F2 $$unsorted) (F $$unsorted) (A1 $$unsorted) (A2 $$unsorted) (B $$unsorted)) (or (not (tptp.maps F1 A1 B)) (not (tptp.maps F2 A2 B)) (not (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X (tptp.union A1 A2))) (not (tptp.member Y B)) (= (tptp.apply F X Y) (or (and (tptp.member X A1) (tptp.apply F1 X Y)) (and (tptp.member X A2) (tptp.apply F2 X Y))))))) (= (tptp.maps F (tptp.union A1 A2) B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X A1)) (not (tptp.member X A2)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F1 X Y1)) (not (tptp.apply F2 X Y2)) (= Y1 Y2)))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_31) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST _let_34 _let_31 :args (_let_30 true _let_29)))) (let ((_let_36 (REFL :args (_let_28)))) (let ((_let_37 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_19))) :args _let_32)) :args ((or _let_19 _let_28))))) (let ((_let_38 (MACRO_RESOLUTION_TRUST _let_37 _let_35 :args (_let_19 true _let_28)))) (let ((_let_39 (_let_19))) (let ((_let_40 ((tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y)))) (let ((_let_41 (ASSUME :args _let_39))) (let ((_let_42 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)))) (let ((_let_43 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_44 (not _let_11))) (let ((_let_45 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_17 _let_48 _let_14 _let_46 _let_44 _let_43))) (let ((_let_50 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y2)) (= Y1 Y2))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y))))))))) (let ((_let_53 (and _let_52 _let_50))) (let ((_let_54 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_55 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 _let_15))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_62 _let_60 _let_58 _let_56 _let_54))) (let ((_let_66 (= _let_21 _let_53))) (let ((_let_67 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_70 (not _let_69))) (let ((_let_71 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_72 (not _let_71))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 _let_72 _let_62 _let_60 _let_70 _let_68 _let_54))) (let ((_let_76 (or _let_73 _let_71))) (let ((_let_77 (and _let_73 _let_69))) (let ((_let_78 (and _let_71 _let_67))) (let ((_let_79 (= _let_63 _let_76))) (let ((_let_80 (or _let_77 (and _let_71 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))))) (let ((_let_81 (or (and _let_73 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22)) _let_78))) (let ((_let_82 (= _let_57 _let_80))) (let ((_let_83 (or _let_64 _let_62 _let_82))) (let ((_let_84 (= _let_55 _let_81))) (let ((_let_85 (or _let_64 _let_60 _let_84))) (let ((_let_86 (not _let_50))) (let ((_let_87 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Y)))))) (let ((_let_88 (not _let_87))) (let ((_let_89 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_15))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_90 _let_88))) (let ((_let_92 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_93 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_94 (or _let_93 _let_92))) (let ((_let_95 (= _let_89 _let_94))) (let ((_let_96 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_97 (not _let_96))) (let ((_let_98 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_99 (not _let_98))) (let ((_let_100 (or _let_99 _let_97))) (let ((_let_101 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_102 (not _let_101))) (let ((_let_103 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_104 (not _let_103))) (let ((_let_105 (or _let_104 _let_102))) (let ((_let_106 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Y)))))) (let ((_let_107 (not _let_106))) (let ((_let_108 (not _let_92))) (let ((_let_109 (or _let_108 _let_107))) (let ((_let_110 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_111 (not _let_110))) (let ((_let_112 (or _let_99 _let_111))) (let ((_let_113 (and _let_92 _let_110))) (let ((_let_114 (or (and _let_93 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) _let_113))) (let ((_let_115 (= _let_96 _let_114))) (let ((_let_116 (or _let_90 _let_99 _let_115))) (let ((_let_117 (REFL :args (_let_91)))) (let ((_let_118 (_let_3))) (let ((_let_119 (ASSUME :args _let_118))) (let ((_let_120 ((tptp.member X (tptp.union A B))))) (let ((_let_121 (_let_87))) (let ((_let_122 ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false))))) (let ((_let_123 (ASSUME :args _let_121))) (let ((_let_124 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 Y)))))) (let ((_let_125 (not _let_124))) (let ((_let_126 (not _let_93))) (let ((_let_127 (or _let_126 _let_125))) (let ((_let_128 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_129 (not _let_128))) (let ((_let_130 (or _let_104 _let_129))) (let ((_let_131 (and _let_93 _let_128))) (let ((_let_132 (or _let_131 (and _let_92 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))))) (let ((_let_133 (= _let_101 _let_132))) (let ((_let_134 (or _let_90 _let_104 _let_133))) (let ((_let_135 (not _let_105))) (let ((_let_136 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_137 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2))))) (let ((_let_138 (and _let_136 _let_137))) (let ((_let_139 (= _let_26 _let_138))) (let ((_let_140 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.maps F A B) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y))))))) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_141 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_142 (_let_140))) (let ((_let_143 ((tptp.maps F A B)))) (let ((_let_144 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_139)) :args ((or _let_27 _let_138 (not _let_139)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_32)) :args ((or _let_26 _let_28))) _let_35 :args (_let_26 true _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_141 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_143)) :args _let_142)) _let_141 :args (_let_139 false _let_140)) :args (_let_138 false _let_26 false _let_139)))) (let ((_let_145 (not _let_138))) (let ((_let_146 (_let_136))) (let ((_let_147 (_let_125))) (let ((_let_148 (REFL :args (_let_130)))) (let ((_let_149 ((tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)))) (let ((_let_150 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((Y $$unsorted)) (or 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false _let_138)) :args (_let_188 false _let_137)))) (let ((_let_192 (and _let_8 _let_184))) (let ((_let_193 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_194 (and _let_5 _let_193))) (let ((_let_195 (or _let_192 _let_194))) (let ((_let_196 (= _let_45 _let_195))) (let ((_let_197 (or _let_17 _let_48 _let_196))) (let ((_let_198 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_32)) :args ((or _let_47 _let_49))) _let_175 :args (_let_47 true _let_49)))) (let ((_let_199 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_196)) :args ((or _let_46 _let_195 (not _let_196)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 3)) (CONG _let_176 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_32)) :args ((or _let_45 _let_49))) _let_175 :args 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true _let_49)))) (let ((_let_208 (not _let_21))) (let ((_let_209 (REORDERING (CNF_AND_POS :args (_let_53 1)) :args ((or _let_50 _let_165))))) (let ((_let_210 (REORDERING (CNF_EQUIV_POS1 :args _let_166) :args ((or _let_208 _let_53 _let_164))))) (let ((_let_211 (REORDERING (CNF_EQUIV_NEG1 :args _let_168) :args ((or _let_21 _let_20 _let_22))))) (let ((_let_212 (_let_20))) (let ((_let_213 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)) (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false)) (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false))))) (let ((_let_214 (ASSUME :args _let_212))) (let ((_let_215 (not _let_202))) (let ((_let_216 (not _let_195))) (let ((_let_217 (REORDERING (CNF_AND_POS :args (_let_9 1)) :args ((or _let_7 _let_183))))) (let ((_let_218 (REORDERING (CNF_OR_POS :args (_let_188)) :args ((or _let_48 _let_14 _let_43 _let_187 _let_185 _let_186 (not _let_188)))))) (let ((_let_219 (not _let_192))) (let ((_let_220 (REORDERING (CNF_AND_POS :args (_let_192 1)) :args ((or _let_184 _let_219))))) (let ((_let_221 (REORDERING (CNF_OR_POS :args (_let_195)) :args ((or _let_192 _let_194 _let_216))))) (let ((_let_222 (_let_151))) (let ((_let_223 (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_6 (not _let_10)))))) (let ((_let_224 (not _let_6))) (let ((_let_225 (REORDERING (CNF_AND_POS :args (_let_6 1)) :args ((or _let_4 _let_224))))) (let ((_let_226 (MACRO_RESOLUTION_TRUST _let_221 (MACRO_RESOLUTION_TRUST _let_225 _let_223 _let_182 (REORDERING (CNF_OR_POS :args (_let_204)) :args ((or _let_48 _let_14 _let_43 _let_201 _let_200 _let_203 (not _let_204)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_222) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1) false)) _let_190))) :args _let_222))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_152 1)) :args ((or _let_151 _let_155))) _let_154 :args (_let_151 false _let_152)) :args (_let_204 false _let_151)) _let_207 _let_177 _let_198 (MACRO_RESOLUTION_TRUST _let_221 _let_206 _let_220 (REORDERING (CNF_OR_POS :args (_let_202)) :args ((or _let_48 _let_14 _let_43 _let_187 _let_201 _let_200 _let_186 _let_215))) _let_218 _let_191 _let_217 (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_8 _let_183))) :args ((or _let_48 _let_14 _let_43 _let_201 _let_216 _let_183 _let_215) true _let_194 true _let_192 true _let_193 true _let_184 false _let_188 false _let_7 false _let_8)) _let_199 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_214 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING _let_213)) :args _let_212))) (MACRO_RESOLUTION_TRUST _let_211 (MACRO_RESOLUTION_TRUST _let_210 (MACRO_RESOLUTION_TRUST _let_209 _let_172 :args (_let_165 true _let_50)) _let_163 :args (_let_208 true _let_53 false _let_66)) _let_167 :args (_let_20 true _let_21 true _let_22)) :args (_let_202 false _let_20)) _let_207 _let_198 _let_177 _let_206 (REORDERING (CNF_AND_POS :args (_let_194 0)) :args ((or _let_5 _let_205))) :args (_let_205 false _let_6 false _let_10 true _let_4 false _let_204 true _let_43 false _let_13 false _let_47 true _let_9 false _let_195 false _let_202 true _let_43 false _let_47 false _let_13 false _let_193 false _let_5)) _let_199 :args (_let_192 true _let_194 false _let_195)))) (let ((_let_227 (MACRO_RESOLUTION_TRUST _let_220 _let_226 :args (_let_184 false _let_192)))) (let ((_let_228 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_192 0)) :args ((or _let_8 _let_219))) _let_226 :args (_let_8 false _let_192)))) (let ((_let_229 (MACRO_RESOLUTION_TRUST _let_217 (MACRO_RESOLUTION_TRUST _let_218 _let_198 _let_177 _let_207 _let_228 _let_227 _let_191 :args (_let_186 false _let_47 false _let_13 true _let_43 false _let_8 false _let_184 false _let_188)) :args (_let_183 true _let_7)))) (let ((_let_230 (or _let_8 _let_5))) (let ((_let_231 (= _let_16 _let_230))) (let ((_let_232 (or _let_187 _let_201 _let_48 _let_14 _let_185 _let_203 _let_43))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_6 0)) :args ((or _let_5 _let_224))) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST _let_225 (REORDERING (CNF_OR_POS :args (_let_232)) :args ((or _let_48 _let_14 _let_43 _let_187 _let_201 _let_185 _let_203 (not _let_232)))) _let_223 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_214 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING _let_213)) :args _let_212)) _let_181 _let_211 _let_167 _let_180 _let_210 _let_163 _let_174 _let_209 _let_179 (REORDERING (CNF_EQUIV_POS2 :args (_let_231)) :args ((or _let_16 (not _let_230) (not _let_231)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_119 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_120)) :args _let_118)) _let_119 (CNF_OR_NEG :args (_let_230 0)) _let_42 _let_37 _let_34 _let_31 :args ((or _let_50 _let_48 _let_14 _let_43 _let_9 _let_187 _let_201 _let_185) true _let_4 false _let_6 false _let_232 false _let_10 false _let_20 true _let_22 false _let_11 true _let_21 false _let_66 true _let_49 true _let_53 false _let_12 false _let_16 false _let_231 false _let_3 false _let_230 false _let_18 false _let_19 true _let_28 true _let_29)) _let_172 _let_198 _let_177 _let_207 _let_229 _let_228 _let_227 :args (_let_201 true _let_50 false _let_47 false _let_13 true _let_43 true _let_9 false _let_8 false _let_184)) (MACRO_RESOLUTION_TRUST _let_223 _let_229 _let_182 :args (_let_6 true _let_9 false _let_10)) :args (false true _let_5 false _let_6)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) _let_3 (forall ((X $$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))))) _let_2 (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 $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))) (forall ((F $$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))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y)))))) (forall ((F $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.66  )
% 0.22/0.66  % SZS output end Proof for SET745+4
% 0.22/0.66  % cvc5---1.0.5 exiting
% 0.22/0.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------