%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET752+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n004.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 14:40:11 EDT 2023

% Result   : Theorem 0.18s 0.57s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET752+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.11/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.32  % Computer : n004.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Sat Aug 26 12:37:53 EDT 2023
% 0.13/0.32  % CPUTime    : 
% 0.18/0.46  %----Proving TF0_NAR, FOF, or CNF
% 0.18/0.57  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.B6jb6C4Jpf/cvc5---1.0.5_31865.p...
% 0.18/0.57  ------- get file name : TPTP file name is SET752+4
% 0.18/0.57  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31865.smt2...
% 0.18/0.57  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.18/0.57  % SZS status Theorem for SET752+4
% 0.18/0.57  % SZS output start Proof for SET752+4
% 0.18/0.57  (
% 0.18/0.57  (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.maps F A B) (tptp.subset X A) (tptp.subset Y A)) (tptp.equal_set (tptp.image2 F (tptp.union X Y)) (tptp.union (tptp.image2 F X) (tptp.image2 F Y)))))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_7 (or _let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_8 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_8))) (let ((_let_10 (= _let_9 _let_7))) (let ((_let_11 (_let_3))) (let ((_let_12 (ASSUME :args _let_11))) (let ((_let_13 ((tptp.member X (tptp.union A B))))) (let ((_let_14 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_15 (not _let_14))) (let ((_let_16 (not _let_6))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (not _let_18))) (let ((_let_21 (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_21))) (let ((_let_23 (= _let_22 _let_20))) (let ((_let_24 (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (tptp.apply F X Y))))))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (_let_24))) (let ((_let_27 ((tptp.member Y (tptp.image2 F A))))) (let ((_let_28 (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_28))) (let ((_let_30 (or _let_22 _let_29))) (let ((_let_31 (tptp.union _let_21 _let_28))) (let ((_let_32 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_31))) (let ((_let_33 (= _let_32 _let_30))) (let ((_let_34 (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_34))) (let ((_let_36 (not _let_32))) (let ((_let_37 (or _let_36 _let_35))) (let ((_let_38 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (tptp.member X (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (tptp.subset _let_31 _let_34))) (let ((_let_41 (= _let_40 _let_38))) (let ((_let_42 (not _let_38))) (let ((_let_43 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (_let_43))) (let ((_let_46 ((tptp.subset A B)))) (let ((_let_47 (tptp.subset _let_34 _let_31))) (let ((_let_48 (and _let_47 _let_40))) (let ((_let_49 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (tptp.member X (tptp.union (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (tptp.image2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))))) (let ((_let_50 (= _let_47 _let_49))) (let ((_let_51 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_31))) (let ((_let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_34))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51))) (let ((_let_55 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union 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_56 (not _let_55))) (let ((_let_57 (= _let_52 _let_56))) (let ((_let_58 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_28))) (let ((_let_59 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_21))) (let ((_let_60 (or _let_59 _let_58))) (let ((_let_61 (= _let_51 _let_60))) (let ((_let_62 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_8))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63))) (let ((_let_67 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (= _let_59 _let_68))) (let ((_let_70 (forall ((X $$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_71 (not _let_70))) (let ((_let_72 (= _let_58 _let_71))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_74 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_75 (or _let_74 _let_73))) (let ((_let_76 (= _let_64 _let_75))) (let ((_let_77 (not _let_74))) (let ((_let_78 (or _let_77 _let_63))) (let ((_let_79 (not _let_73))) (let ((_let_80 (or _let_79 _let_63))) (let ((_let_81 (or))) (let ((_let_82 (_let_56))) (let ((_let_83 (REFL :args (_let_66)))) (let ((_let_84 (not _let_69))) (let ((_let_85 (not _let_72))) (let ((_let_86 (_let_67))) (let ((_let_87 (_let_70))) (let ((_let_88 (not _let_49))) (let ((_let_89 (_let_88))) (let ((_let_90 (tptp.equal_set _let_34 _let_31))) (let ((_let_91 (= _let_90 _let_48))) (let ((_let_92 (not _let_48))) (let ((_let_93 (_let_4))) (let ((_let_94 (ASSUME :args _let_93))) (let ((_let_95 (or (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_90))) (let ((_let_96 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.subset X A)) (not (tptp.subset Y A)) (tptp.equal_set (tptp.image2 F (tptp.union X Y)) (tptp.union (tptp.image2 F X) (tptp.image2 F Y))))))) (let ((_let_97 (not _let_95))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (not _let_96))) (let ((_let_100 (_let_42))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_100)) :args _let_100)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_41)) :args ((or _let_40 _let_42 (not _let_41)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_91)) :args ((or _let_90 _let_92 (not _let_91)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_95 3)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_98) :args (_let_99))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_96))) (REFL :args (_let_97)) :args _let_81)) _let_98 :args (_let_97 true _let_96)) :args ((not _let_90) true _let_95)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_34 _let_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_93)) _let_94 :args (_let_91 false _let_4)) :args (_let_92 true _let_90 false _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_50)) :args ((or _let_47 _let_88 (not _let_50)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_89)) :args _let_89)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_49))) (REFL :args ((not _let_54))) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_74 _let_73 (not _let_75)))) (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_63 _let_79 (not _let_80)))) (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_63 _let_77 (not _let_78)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_87) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_87)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_86) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_86)) (REORDERING (CNF_EQUIV_POS1 :args (_let_76)) :args ((or _let_65 _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_76 false _let_3)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_72)) (CONG (REFL :args (_let_85)) (REFL :args (_let_58)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_81)) :args ((or _let_58 _let_70 _let_85))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_26)) _let_25 :args (_let_72 false _let_24)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_69)) (CONG (REFL :args (_let_84)) (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_81)) :args ((or _let_59 _let_67 _let_84))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_26)) _let_25 :args (_let_69 false _let_24)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_81)) :args ((or _let_62 _let_66))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_66 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_81)) :args ((or _let_64 _let_66))) (CNF_OR_NEG :args (_let_60 1)) (CNF_OR_NEG :args (_let_60 0)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) (REFL :args ((not _let_66))) :args _let_81)) (REORDERING (CNF_EQUIV_POS2 :args (_let_61)) :args ((or _let_51 (not _let_60) (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_21 _let_28 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_61 false _let_3)) (REORDERING (CNF_EQUIV_POS1 :args (_let_57)) :args ((or _let_53 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_26)) _let_25 :args (_let_57 false _let_24)) (CNF_OR_NEG :args (_let_54 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 0)) (CONG (REFL :args (_let_54)) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_81)) :args ((or _let_52 _let_54))) :args (_let_54 true _let_73 true _let_74 false _let_80 false _let_78 false _let_75 false _let_76 false _let_70 false _let_72 false _let_67 false _let_69 false _let_62 false _let_64 true _let_58 true _let_59 true _let_66 true _let_60 false _let_61 true _let_55 false _let_57 true _let_51 false _let_52)) :args (_let_49 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_34 _let_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_50 false _let_43)) :args (_let_47 false _let_49 false _let_50)) :args ((not _let_40) true _let_48 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_31 _let_34 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_41 false _let_43)) :args (_let_42 true _let_40 false _let_41)) :args (_let_39 true _let_38)))) (let ((_let_102 (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_12)))))) (let ((_let_103 (not _let_102))) (let ((_let_104 (= _let_29 _let_103))) (let ((_let_105 (not _let_29))) (let ((_let_106 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_107 (not _let_106))) (let ((_let_108 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_109 (not _let_108))) (let ((_let_110 (or _let_109 _let_107))) (let ((_let_111 (or (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_108))) (let ((_let_112 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 _let_8))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_113 _let_107))) (let ((_let_115 (= _let_112 _let_111))) (let ((_let_116 (REFL :args (_let_110)))) (let ((_let_117 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_118 (not _let_117))) (let ((_let_119 (= _let_35 _let_118))) (let ((_let_120 (not _let_119))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_119)) (CONG (REFL :args (_let_120)) (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_118) _let_117))) :args _let_81)) :args ((or _let_35 _let_117 _let_120))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 1)) _let_101 :args ((not _let_35) true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_26)) _let_25 :args (_let_119 false _let_24)) :args (_let_117 true _let_35 false _let_119)))) (let ((_let_122 (_let_117))) (let ((_let_123 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) false))))) (let ((_let_124 (ASSUME :args _let_122))) (let ((_let_125 (_let_103))) (let ((_let_126 (_let_20))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_126)) :args _let_126)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_18))) (REFL :args (_let_19)) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or (not _let_22) _let_20 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_22 _let_29 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_104)) :args ((or _let_105 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_125)) :args _let_125)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_102))) (REFL :args ((not _let_110))) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_115)) :args ((or _let_112 (not _let_111) (not _let_115)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_115 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_107 _let_113 (not _let_114)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_124 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_123)) :args _let_122)) _let_121 :args (_let_114 false _let_117)) (REORDERING (CNF_OR_NEG :args (_let_111 1)) :args ((or _let_109 _let_111))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_110 1)) (CONG _let_116 (MACRO_SR_PRED_INTRO :args ((= (not _let_107) _let_106))) :args _let_81)) :args ((or _let_106 _let_110))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_110 0)) (CONG _let_116 (MACRO_SR_PRED_INTRO :args ((= (not _let_109) _let_108))) :args _let_81)) :args ((or _let_108 _let_110))) :args (_let_110 false _let_115 true _let_112 false _let_114 false _let_111 false _let_106 false _let_108)) :args (_let_102 false _let_110)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_26)) _let_25 :args (_let_104 false _let_24)) :args (_let_105 false _let_102 false _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or _let_36 _let_30 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) :args _let_81)) :args ((or _let_32 _let_37))) _let_101 :args (_let_32 true _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_21 _let_28 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_33 false _let_3)) :args (_let_30 false _let_32 false _let_33)) :args (_let_22 true _let_29 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_26)) _let_25 :args (_let_23 false _let_24)) :args (_let_20 false _let_22 false _let_23)) :args (_let_19 true _let_18)))) (let ((_let_128 (REFL :args (_let_17)))) (let ((_let_129 (not _let_9))) (let ((_let_130 (or _let_129 _let_15))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_10)) :args ((or _let_9 (not _let_7) (not _let_10)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_130)) :args ((or _let_15 _let_129 (not _let_130)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 1)) (CONG _let_128 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_81)) :args ((or _let_14 _let_17))) _let_127 :args (_let_14 true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_124 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_123)) :args _let_122)) _let_121 :args (_let_130 false _let_117)) :args (_let_129 false _let_14 false _let_130)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_7 0)) :args ((or _let_16 _let_7))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG _let_128 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_6))) :args _let_81)) :args ((or _let_6 _let_17))) _let_127 :args (_let_6 true _let_17)) :args (_let_7 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_10 false _let_3)) :args (false true _let_9 false _let_7 false _let_10)) :args (_let_5 _let_4 (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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((F $$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))))) (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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) _let_2 (forall ((F $$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)))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.59  )
% 0.18/0.59  % SZS output end Proof for SET752+4
% 0.18/0.59  % cvc5---1.0.5 exiting
% 0.18/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------