%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET727+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 14:40:05 EDT 2023

% Result   : Theorem 0.20s 0.69s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET727+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 14:55:50 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.69  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8AMcif8v47/cvc5---1.0.5_15007.p...
% 0.20/0.69  ------- get file name : TPTP file name is SET727+4
% 0.20/0.69  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15007.smt2...
% 0.20/0.69  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.69  % SZS status Theorem for SET727+4
% 0.20/0.69  % SZS output start Proof for SET727+4
% 0.20/0.69  (
% 0.20/0.69  (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B A) (tptp.maps H B A) (tptp.identity (tptp.compose_function G F A B A) A) (tptp.identity (tptp.compose_function F H B A B) B)) (tptp.equal_maps (tptp.inverse_function F A B) H B A)))))) (let ((_let_2 (forall ((F $$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 ((_let_3 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_4 (forall ((F $$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_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 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_11 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_12 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_14 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_19 _let_17 _let_15 _let_7))) (let ((_let_25 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2))))) (let ((_let_26 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_27 (and _let_26 _let_25))) (let ((_let_28 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_29 (= _let_28 _let_27))) (let ((_let_30 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_30))) (let ((_let_33 ((tptp.maps F A B)))) (let ((_let_34 (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_35 (tptp.equal_maps _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_37 (tptp.identity _let_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (tptp.identity _let_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_45 (not _let_44))) (let ((_let_46 (not _let_28))) (let ((_let_47 (or _let_46 _let_45 _let_43 _let_41 _let_38 _let_35))) (let ((_let_48 (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.maps G B A)) (not (tptp.maps H B A)) (not (tptp.identity (tptp.compose_function G F A B A) A)) (not (tptp.identity (tptp.compose_function F H B A B) B)) (tptp.equal_maps (tptp.inverse_function F A B) H B A))))) (let ((_let_49 (not _let_47))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (or))) (let ((_let_52 (not _let_48))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_50) :args (_let_52))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_48))) (REFL :args (_let_49)) :args _let_51)) _let_50 :args (_let_49 true _let_48)))) (let ((_let_54 (REFL :args (_let_47)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_29)) :args ((or _let_46 _let_27 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_28))) :args _let_51)) :args ((or _let_28 _let_47))) _let_53 :args (_let_28 true _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_29 false _let_30)) :args (_let_27 false _let_28 false _let_29)))) (let ((_let_56 (not _let_27))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_27 1)) :args ((or _let_25 _let_56))) _let_55 :args (_let_25 false _let_27)))) (let ((_let_58 (_let_25))) (let ((_let_59 (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false)))) (let ((_let_60 (ASSUME :args _let_58))) (let ((_let_61 (or _let_19 _let_15))) (let ((_let_62 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Y)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (not _let_62))) (let ((_let_65 (or _let_23 _let_64))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_27 0)) :args ((or _let_26 _let_56))) _let_55 :args (_let_26 false _let_27)))) (let ((_let_67 (_let_26))) (let ((_let_68 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) (let ((_let_69 (ASSUME :args _let_67))) (let ((_let_70 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_71 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_72 (not _let_71))) (let ((_let_73 (tptp.apply _let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_21 _let_23 _let_76 _let_74 _let_72 _let_70))) (let ((_let_78 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply (tptp.inverse_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y2)) (= Y1 Y2))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (= _let_35 _let_78))) (let ((_let_81 (not _let_78))) (let ((_let_82 (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_83 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (_let_81))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_78))) (REFL :args (_let_79)) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_80)) :args ((or _let_35 _let_81 (not _let_80)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_47 5)) _let_53 :args ((not _let_35) true _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (_let_34 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_maps F G A B)))) :args (_let_82))) _let_83 :args (_let_80 false _let_82)) :args (_let_81 true _let_35 false _let_80)) :args (_let_79 true _let_78)))) (let ((_let_86 (REFL :args (_let_77)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_51)) :args ((or _let_22 _let_77))) _let_85 :args (_let_22 true _let_77)))) (let ((_let_88 (_let_64))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_88)) :args _let_88)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_62))) (REFL :args (_let_63)) :args _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_23 _let_64 (not _let_65)))) _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_67)) _let_66 :args (_let_65 false _let_26)) :args (_let_64 false _let_22 false _let_65)) :args (_let_63 true _let_62)))) (let ((_let_90 (REFL :args (_let_61)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_51)) :args ((or _let_18 _let_61))) _let_89 :args (_let_18 true _let_61)))) (let ((_let_92 (= _let_73 _let_16))) (let ((_let_93 (or _let_23 _let_21 _let_92))) (let ((_let_94 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_51)) :args ((or _let_20 _let_77))) _let_85 :args (_let_20 true _let_77)))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_92)) :args ((or _let_74 _let_16 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 3)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) :args _let_51)) :args ((or _let_73 _let_77))) _let_85 :args (_let_73 true _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_21 _let_23 _let_92 (not _let_93)))) _let_96 _let_87 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((tptp.apply (tptp.inverse_function F A B) Y X)))) :args (_let_94)))) _let_95 :args (_let_93 false _let_94)) :args (_let_92 false _let_20 false _let_22 false _let_93)) :args (_let_16 false _let_73 false _let_92)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_21 _let_23 _let_17 _let_19 _let_15 _let_7 (not _let_24)))) _let_96 _let_87 _let_97 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_51)) :args ((or _let_14 _let_61))) _let_89 :args (_let_14 true _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)) _let_59 (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) :args _let_58)) _let_57 :args (_let_24 false _let_25)) :args (_let_7 false _let_20 false _let_22 false _let_16 false _let_18 false _let_14 false 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_let_270 _let_266 _let_13 _let_268 (not _let_271)))) _let_96 _let_231 _let_290 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_276 2)) (CONG _let_289 (MACRO_SR_PRED_INTRO :args ((= (not _let_266) _let_265))) :args _let_51)) :args ((or _let_265 _let_276))) _let_288 :args (_let_265 true _let_276)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_292)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_221 _let_199 _let_295 _let_293) (SCOPE (TRUE_ELIM (TRANS (CONG _let_201 (TRANS (SYMM _let_295) _let_200) (SYMM _let_294) :args _let_165) _let_222)) :args (_let_170 _let_180 _let_272 _let_11))) :args (_let_170 _let_180 _let_11 _let_272))) :args (true _let_292)) :args ((or _let_171 (not _let_180) _let_291 _let_267 (not _let_272)))) _let_210 _let_194 _let_232 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_275)) :args ((or _let_21 _let_76 _let_72 _let_270 _let_274 _let_272 (not _let_275)))) _let_96 _let_115 _let_160 _let_290 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_276 1)) (CONG _let_289 (MACRO_SR_PRED_INTRO :args ((= (not _let_274) _let_273))) :args _let_51)) :args ((or _let_273 _let_276))) _let_288 :args (_let_273 true _let_276)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_147 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING _let_146)) :args _let_144))) _let_143 :args (_let_275 false _let_137)) :args (_let_272 false _let_20 false _let_75 false _let_71 false _let_269 false _let_273 false _let_275)) :args (_let_267 false _let_170 false _let_180 false _let_11 false _let_272)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING _let_179)) :args _let_58))) _let_57 :args (_let_271 false _let_25)) :args (_let_13 false _let_20 false _let_216 false _let_269 false _let_265 false _let_267 false _let_271)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_236)) :args ((or _let_23 _let_76 _let_70 _let_19 _let_235 _let_233 (not _let_236)))) _let_87 _let_115 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_77 5)) _let_85 :args ((not _let_70) true _let_77)) _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_260)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_261 _let_263 _let_167) (SCOPE (TRUE_ELIM (TRANS (CONG _let_264 _let_169 _let_262 :args _let_165) (CONG _let_264 (SYMM (SYMM _let_263)) _let_262 :args _let_165) (TRUE_INTRO _let_261))) :args (_let_242 _let_241 _let_7))) :args (_let_7 _let_242 _let_241))) :args (true _let_260)) :args ((or _let_234 _let_161 _let_248 (not _let_241)))) _let_98 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_249 2)) (CONG _let_259 (MACRO_SR_PRED_INTRO :args ((= (not _let_248) _let_242))) :args _let_51)) :args ((or _let_242 _let_249))) _let_258 :args (_let_242 true _let_249)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_247)) :args ((or _let_21 _let_23 _let_17 _let_246 _let_244 _let_241 (not _let_247)))) _let_96 _let_87 _let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_249 0)) (CONG _let_259 (MACRO_SR_PRED_INTRO :args ((= (not _let_246) _let_245))) :args _let_51)) :args ((or _let_245 _let_249))) _let_258 :args (_let_245 true _let_249)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_249 1)) (CONG _let_259 (MACRO_SR_PRED_INTRO :args ((= (not _let_244) _let_243))) :args _let_51)) :args ((or _let_243 _let_249))) _let_258 :args (_let_243 true _let_249)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING _let_179)) :args _let_58)) _let_57 :args (_let_247 false _let_25)) :args (_let_241 false _let_20 false _let_22 false _let_16 false _let_245 false _let_243 false _let_247)) :args (_let_234 false _let_7 false _let_242 false _let_241)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_240) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING _let_184)) :args _let_240)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_238 1)) :args ((or _let_237 (not _let_238)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_239)) :args ((or _let_45 _let_238 (not _let_239)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 1)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_51)) :args ((or _let_44 _let_47))) _let_53 :args (_let_44 true _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_239 false _let_30)) :args (_let_238 false _let_44 false _let_239)) :args (_let_237 false _let_238)) :args (_let_236 false _let_237)) :args (_let_233 false _let_22 false _let_75 true _let_70 false _let_18 false _let_234 false _let_236)) _let_232 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_178)) :args ((or _let_177 _let_175 _let_171 _let_103 _let_173 _let_10 (not _let_178)))) _let_193 _let_211 _let_210 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_104 0)) (CONG _let_129 (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_102))) :args _let_51)) :args ((or _let_102 _let_104))) _let_128 :args (_let_102 true _let_104)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_195)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_197 _let_199) (SCOPE (TRUE_ELIM (TRANS (CONG _let_201 (SYMM _let_200) _let_198 :args _let_165) (TRUE_INTRO _let_197))) :args _let_196)) :args _let_196)) :args (true _let_195)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_104 1)) (CONG _let_129 (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_100))) :args _let_51)) :args ((or _let_100 _let_104))) _let_128 :args (_let_100 true _let_104)) _let_194 :args (_let_172 false _let_100 false _let_180)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING _let_179)) :args _let_58))) _let_57 :args (_let_178 false _let_25)) :args (_let_10 false _let_176 false _let_174 false _let_170 false _let_102 false _let_172 false _let_178)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_136)) :args ((or _let_76 _let_19 _let_133 _let_135 _let_131 _let_9 (not _let_136)))) _let_115 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_162)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_164 _let_167) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_169 _let_166 :args _let_165) (TRUE_INTRO _let_164))) :args _let_163)) :args _let_163)) :args (true _let_162)) :args ((or _let_72 _let_132 _let_161))) _let_160 _let_98 :args (_let_132 false _let_71 false _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_148 0)) (CONG _let_159 (MACRO_SR_PRED_INTRO :args ((= (not _let_135) _let_134))) :args _let_51)) :args ((or _let_134 _let_148))) _let_158 :args (_let_134 true _let_148)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_148 1)) (CONG _let_159 (MACRO_SR_PRED_INTRO :args ((= (not _let_131) _let_130))) :args _let_51)) :args ((or _let_130 _let_148))) _let_158 :args (_let_130 true _let_148)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_147 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 QUANTIFIERS_INST_E_MATCHING _let_146)) :args _let_144)) _let_143 :args (_let_136 false _let_137)) :args (_let_9 false _let_75 false _let_18 false _let_132 false _let_134 false _let_130 false _let_136)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_104 2)) (CONG _let_129 (MACRO_SR_PRED_INTRO :args ((= (not _let_99) _let_8))) :args _let_51)) :args ((or _let_8 _let_104))) _let_128 :args (_let_8 true _let_104)) _let_98 :args (false false _let_13 true _let_12 false _let_11 false _let_10 false _let_9 false _let_8 false _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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) _let_5 _let_4 _let_3 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))) (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) _let_2 (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) (forall ((F $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.70  )
% 0.20/0.70  % SZS output end Proof for SET727+4
% 0.20/0.70  % cvc5---1.0.5 exiting
% 0.20/0.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------