%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET742+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:40:08 EDT 2023

% Result   : Theorem 26.05s 26.24s
% Output   : Proof 26.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : SET742+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 12:33:18 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 26.05/26.24  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.skDbYWajA3/cvc5---1.0.5_3519.p...
% 26.05/26.24  ------- get file name : TPTP file name is SET742+4
% 26.05/26.24  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3519.smt2...
% 26.05/26.24  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.05/26.24  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.05/26.24  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.05/26.24  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.05/26.24  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.05/26.24  % SZS status Theorem for SET742+4
% 26.05/26.24  % SZS output start Proof for SET742+4
% 26.05/26.24  (
% 26.05/26.24  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B C) (tptp.maps H C A) (tptp.one_to_one (tptp.compose_function G F A B C) A C) (tptp.one_to_one (tptp.compose_function H G B C A) B A)) (tptp.one_to_one F A B)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))))) (let ((_let_3 (forall ((F $$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))))))))) (let ((_let_4 (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_5 (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)))))))) (let ((_let_6 (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_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49))) (let ((_let_10 (not _let_7))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42)))))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15))) (let ((_let_19 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E Y))))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (= _let_21 _let_19))) (let ((_let_23 (not _let_19))) (let ((_let_24 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E A)) (not (tptp.apply F E Y))))))))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (_let_24))) (let ((_let_27 ((tptp.surjective F A B)))) (let ((_let_28 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (and _let_28 _let_21))) (let ((_let_30 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_31 (= _let_28 _let_30))) (let ((_let_32 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 A)) (not (tptp.member X2 A)) (not (tptp.member Y B)) (not (tptp.apply F X1 Y)) (not (tptp.apply F X2 Y)) (= X1 X2))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 ((tptp.injective F A B)))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_37 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_42 _let_40 _let_38 _let_36))) (let ((_let_48 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Y)))))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_42 _let_49))) (let ((_let_51 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52))) (let ((_let_56 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_59 (tptp.apply _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_60 (= _let_59 _let_57))) (let ((_let_61 (or _let_44 _let_54 _let_60))) (let ((_let_62 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.apply _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_65 (= _let_64 _let_63))) (let ((_let_66 (or _let_46 _let_54 _let_65))) (let ((_let_67 (or _let_42 _let_38 _let_52))) (let ((_let_68 (not _let_64))) (let ((_let_69 (not _let_59))) (let ((_let_70 (or _let_44 _let_46 _let_54 _let_69 _let_68 _let_36))) (let ((_let_71 (or _let_42 _let_40 _let_52))) (let ((_let_72 (or))) (let ((_let_73 (REFL :args (_let_47)))) (let ((_let_74 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y))))))))) (let ((_let_75 (and _let_74 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y2)) (= Y1 Y2)))))) (let ((_let_76 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_77 (= _let_76 _let_75))) (let ((_let_78 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 ((tptp.maps F A B)))) (let ((_let_82 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_83 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_84 (tptp.one_to_one _let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.one_to_one _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_89 (not _let_88))) (let ((_let_90 (not _let_76))) (let ((_let_91 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 _let_90 _let_89 _let_87 _let_85 _let_82))) (let ((_let_94 (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B C)) (not (tptp.maps H C A)) (not (tptp.one_to_one (tptp.compose_function G F A B C) A C)) (not (tptp.one_to_one (tptp.compose_function H G B C A) B A)) (tptp.one_to_one F A B))))) (let ((_let_95 (not _let_93))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (not _let_94))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_96) :args (_let_97))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_97) _let_94))) (REFL :args (_let_95)) :args _let_72)) _let_96 :args (_let_95 true _let_94)))) (let ((_let_99 (REFL :args (_let_93)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_75 0)) :args ((or _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_77)) :args ((or _let_90 _let_75 (not _let_77)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_93 1)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_76))) :args _let_72)) :args ((or _let_76 _let_93))) _let_98 :args (_let_76 true _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_81)) :args _let_80)) _let_79 :args (_let_77 false _let_78)) :args (_let_75 false _let_76 false _let_77)) :args (_let_74 false _let_75)))) (let ((_let_101 (_let_74))) (let ((_let_102 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) (let ((_let_103 (ASSUME :args _let_101))) (let ((_let_104 (_let_49))) (let ((_let_105 (REFL :args (_let_55)))) (let ((_let_106 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (_let_106))) (let ((_let_109 (tptp.compose_function G F A B C))) (let ((_let_110 ((not (= (tptp.member X A) false)) (not (= (tptp.member Z C) false)) _let_109))) (let ((_let_111 (_let_56))) (let ((_let_112 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_113 (not _let_60))) (let ((_let_114 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply _let_1 X1 Y)) (not (tptp.apply _let_1 X2 Y)) (= X1 X2)))))) (let ((_let_115 (tptp.injective _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_116 (= _let_115 _let_114))) (let ((_let_117 (tptp.surjective _let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_118 (and _let_115 _let_117))) (let ((_let_119 (= _let_86 _let_118))) (let ((_let_120 (_let_2))) (let ((_let_121 (ASSUME :args _let_120))) (let ((_let_122 ((tptp.one_to_one F A B)))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_119)) :args ((or _let_87 _let_118 (not _let_119)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_93 3)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_86))) :args _let_72)) :args ((or _let_86 _let_93))) _let_98 :args (_let_86 true _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (_let_58 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_122)) :args _let_120)) _let_121 :args (_let_119 false _let_2)) :args (_let_118 false _let_86 false _let_119)))) (let ((_let_124 (not _let_118))) (let ((_let_125 (_let_114))) (let ((_let_126 (not _let_65))) (let ((_let_127 (_let_62))) (let ((_let_128 (not _let_30))) (let ((_let_129 (_let_128))) (let ((_let_130 (= _let_82 _let_29))) (let ((_let_131 (not _let_29))) (let ((_let_132 (_let_23))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE 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(CNF_OR_NEG :args (_let_230 0)) (CONG _let_238 (MACRO_SR_PRED_INTRO :args ((= (not _let_226) _let_225))) :args _let_72)) :args ((or _let_225 _let_230))) _let_237 :args (_let_225 true _let_230)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_230 1)) (CONG _let_238 (MACRO_SR_PRED_INTRO :args ((= (not _let_224) _let_223))) :args _let_72)) :args ((or _let_223 _let_230))) _let_237 :args (_let_223 true _let_230)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_228) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_52 QUANTIFIERS_INST_CBQI_PROP)) :args _let_228)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_174 1)) :args ((or _let_173 _let_177))) _let_176 :args (_let_173 false _let_174)) :args (_let_227 false _let_173)) :args (_let_221 false _let_11 false _let_165 false _let_8 false _let_225 false _let_223 false _let_227)) :args (_let_217 false _let_222 false _let_221)) :args (_let_220 false _let_142 false _let_202 false _let_217)) :args (_let_197 true _let_219)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_199)) :args ((or _let_188 _let_166 _let_198 (not _let_199)))) _let_216 _let_201 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 QUANTIFIERS_INST_E_MATCHING _let_200)) :args _let_108)) _let_107 :args (_let_199 false _let_106)) :args (_let_198 false _let_187 false _let_165 false _let_199)) :args (_let_183 true _let_196 false _let_198)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_195) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_46 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply _let_83 X1 Y) false)) (not (= (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_195)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_192)) :args ((or (not _let_191) _let_190 (not _let_192)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_193 0)) :args ((or _let_191 (not _let_193)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_194)) :args ((or _let_85 _let_193 (not _let_194)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_93 4)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))) :args _let_72)) :args ((or _let_84 _let_93))) _let_98 :args (_let_84 true _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (_let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_122)) :args _let_120)) _let_121 :args (_let_194 false _let_2)) :args (_let_193 false _let_84 false _let_194)) :args (_let_191 false _let_193)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (_let_83 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_34)) _let_33 :args (_let_192 false _let_32)) :args (_let_190 false _let_191 false _let_192)) :args (_let_189 false _let_190)) :args (_let_9 false _let_16 false _let_187 false _let_185 false _let_165 false _let_183 false _let_189)) _let_182 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_12 _let_10 (not _let_13)))) _let_163 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_135) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_47 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_135)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 1)) (CONG _let_134 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_72)) :args ((or _let_14 _let_18))) _let_133 :args (_let_14 true _let_18)) :args (_let_13 false _let_14)) :args (_let_10 false _let_11 false _let_13)) :args (false false _let_9 false _let_8 true _let_7)) :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)))) (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))))) _let_6 (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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) _let_5 (forall ((F $$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 $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))) _let_4 _let_3 _let_2 (forall ((G $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.05/26.25  )
% 26.05/26.25  % SZS output end Proof for SET742+4
% 26.05/26.25  % cvc5---1.0.5 exiting
% 26.05/26.25  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------