%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET723+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 14:40:04 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : SET723+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.33  % Computer : n007.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Sat Aug 26 13:28:56 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.20/0.47  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.59  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.5dmOoV3DOy/cvc5---1.0.5_8805.p...
% 0.20/0.59  ------- get file name : TPTP file name is SET723+4
% 0.20/0.59  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8805.smt2...
% 0.20/0.59  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.59  % SZS status Theorem for SET723+4
% 0.20/0.59  % SZS output start Proof for SET723+4
% 0.20/0.59  (
% 0.20/0.59  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.maps F B C) (tptp.maps G A B) (tptp.maps H A B) (tptp.injective F B C) (tptp.equal_maps (tptp.compose_function F G A B C) (tptp.compose_function F H A B C) A C)) (tptp.equal_maps G H A B)))))) (let ((_let_2 (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_3 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply G X Y2)) (= Y1 Y2)))))))) (let ((_let_4 (forall ((G $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (let ((_let_5 (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_10 (not _let_6))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)))))) (let ((_let_15 (not _let_13))) (let ((_let_16 (not _let_14))) (let ((_let_17 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16))) (let ((_let_20 (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_2 X Y))))))))) (let ((_let_21 (and _let_20 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2)))))) (let ((_let_22 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_25 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (tptp.equal_maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_27 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_28 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_29 (tptp.equal_maps _let_28 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_32 (not _let_31))) (let ((_let_33 (not _let_22))) (let ((_let_34 (or _let_33 (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) _let_32 _let_30 _let_26))) (let ((_let_35 (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.maps F B C)) (not (tptp.maps G A B)) (not (tptp.maps H A B)) (not (tptp.injective F B C)) (not (tptp.equal_maps (tptp.compose_function F G A B C) (tptp.compose_function F H A B C) A C)) (tptp.equal_maps G H A B))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (or))) (let ((_let_39 (not _let_35))) (let ((_let_40 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_37) :args (_let_39))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_35))) (REFL :args (_let_36)) :args _let_38)) _let_37 :args (_let_36 true _let_35)))) (let ((_let_41 (REFL :args (_let_34)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_20 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or _let_33 _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_22))) :args _let_38)) :args ((or _let_22 _let_34))) _let_40 :args (_let_22 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.maps F A B)))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_21 false _let_22 false _let_23)) :args (_let_20 false _let_21)))) (let ((_let_43 (_let_20))) (let ((_let_44 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) (let ((_let_45 (ASSUME :args _let_43))) (let ((_let_46 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_47 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_18 _let_52 _let_50 _let_48 _let_46))) (let ((_let_56 (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_6)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y2)) (= Y1 Y2))))) (let ((_let_57 (not _let_55))) (let ((_let_58 (= _let_26 _let_56))) (let ((_let_59 (not _let_56))) (let ((_let_60 (forall ((F $$unsorted) (G $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.equal_maps F G A B) (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 G X Y2)) (= Y1 Y2))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((tptp.equal_maps F G A B)))) (let ((_let_64 (_let_59))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_56))) (REFL :args (_let_57)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_58)) :args ((or _let_26 _let_59 (not _let_58)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 5)) _let_40 :args ((not _let_26) true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_58 false _let_60)) :args (_let_59 true _let_26 false _let_58)) :args (_let_57 true _let_56)))) (let ((_let_66 (REFL :args (_let_55)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 1)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_38)) :args ((or _let_17 _let_55))) _let_65 :args (_let_17 true _let_55)))) (let ((_let_68 (_let_16))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_68)) :args _let_68)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_14))) (REFL :args (_let_15)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_18 _let_16 (not _let_19)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_19 false _let_20)) :args (_let_16 false _let_17 false _let_19)) :args (_let_15 true _let_14)))) (let ((_let_70 (REFL :args (_let_13)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 1)) (CONG _let_70 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_6))) :args _let_38)) :args ((or _let_6 _let_13))) _let_69 :args (_let_6 true _let_13)))) (let ((_let_72 (not _let_7))) (let ((_let_73 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_52 _let_18 _let_76 _let_74 _let_72 _let_46))) (let ((_let_78 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_79 (= _let_31 _let_78))) (let ((_let_80 (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_81 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_79)) :args ((or _let_32 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 3)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_38)) :args ((or _let_31 _let_34))) _let_40 :args (_let_31 true _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.injective F A B)))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_78 false _let_31 false _let_79)))) (let ((_let_83 (_let_78))) (let ((_let_84 (not (= (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false)))) (let ((_let_85 (ASSUME :args _let_83))) (let ((_let_86 (or _let_76 _let_74))) (let ((_let_87 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Y)))))) (let ((_let_88 (not _let_86))) (let ((_let_89 (not _let_87))) (let ((_let_90 (or _let_52 _let_89))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 2)) (CONG _let_66 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_38)) :args ((or _let_51 _let_55))) _let_65 :args (_let_51 true _let_55)))) (let ((_let_92 (_let_89))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_92)) :args _let_92)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_87))) (REFL :args (_let_88)) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_52 _let_89 (not _let_90)))) _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_90 false _let_20)) :args (_let_89 false _let_51 false _let_90)) :args (_let_88 true _let_87)))) (let ((_let_94 (REFL :args (_let_86)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 1)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) :args _let_38)) :args ((or _let_73 _let_86))) _let_93 :args (_let_73 true _let_86)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 0)) (CONG _let_94 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_38)) :args ((or _let_75 _let_86))) _let_93 :args (_let_75 true 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$$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.59  )
% 0.20/0.59  % SZS output end Proof for SET723+4
% 0.20/0.59  % cvc5---1.0.5 exiting
% 0.20/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------