TSTP Solution File: SET759+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET759+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 14:40:13 EDT 2023
% Result : Theorem 0.20s 0.70s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET759+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n013.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 09:49:47 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.55 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.PF5ic0ZucC/cvc5---1.0.5_22638.p...
% 0.20/0.70 ------- get file name : TPTP file name is SET759+4
% 0.20/0.70 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22638.smt2...
% 0.20/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.70 % SZS status Theorem for SET759+4
% 0.20/0.70 % SZS output start Proof for SET759+4
% 0.20/0.70 (
% 0.20/0.70 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted)) (=> (and (tptp.maps F A B) (tptp.injective F A B) (tptp.subset X A)) (tptp.equal_set (tptp.inverse_image3 F (tptp.image3 F X B) A) X)))))) (let ((_let_2 (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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y)))))))) (let ((_let_3 (forall ((F $$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)))))))) (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 ((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 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_8 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))))) (let ((_let_9 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_10))) (let ((_let_14 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.inverse_image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_15))) (let ((_let_17 (or _let_12 _let_16))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X (tptp.inverse_image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_15))) (let ((_let_21 (= _let_20 _let_18))) (let ((_let_22 (not _let_18))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (_let_23))) (let ((_let_26 ((tptp.subset A B)))) (let ((_let_27 (tptp.subset _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_28 (and _let_27 _let_20))) (let ((_let_29 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.inverse_image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_32 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_15))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.image3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y)))))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_38 (and _let_37 _let_36))) (let ((_let_39 (= _let_32 _let_38))) (let ((_let_40 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_14))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_41))) (let ((_let_45 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_48 (and _let_47 _let_46))) (let ((_let_49 (= _let_42 _let_48))) (let ((_let_50 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51))) (let ((_let_55 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_56 (or _let_53 _let_55))) (let ((_let_57 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_58 (not _let_47))) (let ((_let_59 (not _let_55))) (let ((_let_60 (not _let_37))) (let ((_let_61 (or _let_60 _let_59 _let_58 _let_41 _let_51 _let_57))) (let ((_let_62 (or))) (let ((_let_63 (forall ((F $$unsorted) (B $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.inverse_image3 F B A)) (and (tptp.member X A) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)))))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((tptp.member X (tptp.inverse_image3 F B A))))) (let ((_let_67 (not _let_38))) (let ((_let_68 (_let_36))) (let ((_let_69 (REFL :args (_let_44)))) (let ((_let_70 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image3 F A B)) (and (tptp.member Y B) (not (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (tptp.apply F X Y)))))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 ((tptp.member Y (tptp.image3 F A B))))) (let ((_let_74 (not _let_48))) (let ((_let_75 (_let_46))) (let ((_let_76 (REFL :args (_let_54)))) (let ((_let_77 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_78 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_79 (= _let_78 _let_77))) (let ((_let_80 (tptp.equal_set _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_81 (not _let_78))) (let ((_let_82 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_83 (not _let_82))) (let ((_let_84 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_83 _let_81 _let_80))) (let ((_let_87 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted)) (or (not (tptp.maps F A B)) (not (tptp.injective F A B)) (not (tptp.subset X A)) (tptp.equal_set (tptp.inverse_image3 F (tptp.image3 F X B) A) X))))) (let ((_let_88 (not _let_86))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (not _let_87))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_89) :args (_let_90))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_87))) (REFL :args (_let_88)) :args _let_62)) _let_89 :args (_let_88 true _let_87)))) (let ((_let_92 (REFL :args (_let_86)))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_79)) :args ((or _let_81 _let_77 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 2)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_78))) :args _let_62)) :args ((or _let_78 _let_86))) _let_91 :args (_let_78 true _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_79 false _let_23)) :args (_let_77 false _let_78 false _let_79)))) (let ((_let_94 (_let_77))) (let ((_let_95 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) (let ((_let_96 (ASSUME :args _let_94))) (let ((_let_97 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_98 (= _let_82 _let_97))) (let ((_let_99 (forall ((F $$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_100 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_97))) (let ((_let_102 (not _let_31))) (let ((_let_103 (ASSUME :args (_let_52)))) (let ((_let_104 (ASSUME :args (_let_57)))) (let ((_let_105 (ASSUME :args (_let_102)))) (let ((_let_106 (not _let_29))) (let ((_let_107 (_let_106))) (let ((_let_108 (= _let_80 _let_28))) (let ((_let_109 (not _let_28))) (let ((_let_110 (_let_6))) (let ((_let_111 (ASSUME :args _let_110))) (let ((_let_112 (_let_22))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_112)) :args _let_112)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_18))) (REFL :args (_let_19)) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_21)) :args ((or _let_20 _let_22 (not _let_21)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_108)) :args ((or _let_80 _let_109 (not _let_108)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_86 3)) _let_91 :args ((not _let_80) true _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_110)) _let_111 :args (_let_108 false _let_6)) :args (_let_109 true _let_80 false _let_108)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_30)) :args ((or _let_27 _let_106 (not _let_30)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_107)) :args _let_107)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_106) _let_29))) (REFL :args ((not _let_34))) :args _let_62)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_103 _let_104 _let_105) :args (_let_102 _let_52 _let_57)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_105)) (CONG (SYMM (SYMM _let_104)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_103))) :args (_let_52 _let_57 _let_102)) :args ((not (and _let_102 _let_52 _let_57)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_102) _let_31))) (REFL :args (_let_53)) (REFL :args ((not _let_57))) :args _let_62)) (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_60 _let_41 _let_58 _let_51 _let_59 _let_57 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_101) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y) false))))) :args _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_98)) :args ((or _let_83 _let_97 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 1)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_82))) :args _let_62)) :args ((or _let_82 _let_86))) _let_91 :args (_let_82 true _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.injective F A B)))) :args (_let_99))) _let_100 :args (_let_98 false _let_99)) :args (_let_97 false _let_82 false _let_98)) :args (_let_61 false _let_97)) (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_53 _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_95)) :args _let_94)) _let_93 :args (_let_56 false _let_77)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 1)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_62)) :args ((or _let_50 _let_54))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 0)) (CONG _let_76 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_62)) :args ((or _let_52 _let_54))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_75)) :args _let_75)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) (REFL :args ((not _let_54))) :args _let_62)) (REORDERING (CNF_AND_POS :args (_let_48 1)) :args ((or _let_46 _let_74))) (REORDERING (CNF_AND_POS :args (_let_48 0)) :args ((or _let_47 _let_74))) (REORDERING (CNF_EQUIV_POS1 :args (_let_49)) :args ((or _let_43 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING _let_66)) :args _let_65)) _let_64 :args (_let_39 false _let_63)) (CNF_OR_NEG :args (_let_34 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG (REFL :args (_let_34)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_62)) :args ((or _let_32 _let_34))) :args (_let_34 false _let_57 false _let_61 false _let_55 false _let_56 false _let_50 false _let_52 true _let_54 true _let_45 false _let_47 false _let_48 false _let_49 false _let_40 false _let_42 true _let_44 true _let_35 false _let_37 false _let_38 false _let_39 true _let_31 false _let_32)) :args (_let_29 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_25)) _let_24 :args (_let_30 false _let_23)) :args (_let_27 false _let_29 false 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(tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y)))))) (let ((_let_121 (not _let_120))) (let ((_let_122 (not _let_114))) (let ((_let_123 (or _let_122 _let_121))) (let ((_let_124 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_14))) (let ((_let_125 (not _let_124))) (let ((_let_126 (or _let_125 _let_10))) (let ((_let_127 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_128 (not _let_127))) (let ((_let_129 (or _let_128 _let_10))) (let ((_let_130 (not _let_8))) (let ((_let_131 (and _let_127 _let_130))) (let ((_let_132 (= _let_124 _let_131))) (let ((_let_133 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_62)) :args ((or _let_11 _let_17))))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_95)) :args _let_94)) _let_93 :args (_let_115 false _let_77)))) (let ((_let_135 (REORDERING (CNF_OR_POS :args (_let_115)) :args ((or _let_12 _let_114 (not _let_115)))))) (let ((_let_136 (_let_118))) (let ((_let_137 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_138 (and _let_137 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2)))))) (let ((_let_139 (= _let_84 _let_138))) (let ((_let_140 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.maps F A B) (and 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(REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_86 0)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_85) _let_84))) :args _let_62)) :args ((or _let_84 _let_86))) _let_91 :args (_let_84 true _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_141 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.maps F A B)))) :args (_let_140))) _let_141 :args (_let_139 false _let_140)) :args (_let_138 false _let_84 false _let_139)) :args (_let_137 false _let_138)) :args (_let_123 false _let_137)))) (let ((_let_144 (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_122 _let_121 (not _let_123)))))) (let ((_let_145 (_let_116))) (let ((_let_146 (not _let_129))) (let ((_let_147 (_let_121))) (let ((_let_148 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_147)) :args _let_147)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_121) _let_120))) (REFL :args (_let_146)) :args _let_62)))) (let ((_let_149 (REFL :args (_let_129)))) (let ((_let_150 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_129 1)) (CONG _let_149 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_62)) :args ((or _let_9 _let_129))))) (let ((_let_151 (_let_131))) (let ((_let_152 (not _let_13))) (let ((_let_153 (MACRO_RESOLUTION_TRUST _let_133 _let_113 :args (_let_11 true _let_17)))) (let ((_let_154 (_let_8))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_154) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_154)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_13)) :args ((or _let_12 _let_10 _let_152))) _let_153 (MACRO_RESOLUTION_TRUST _let_150 (MACRO_RESOLUTION_TRUST _let_148 (MACRO_RESOLUTION_TRUST _let_144 (MACRO_RESOLUTION_TRUST _let_135 _let_153 _let_134 :args (_let_114 false _let_11 false _let_115)) _let_143 :args (_let_121 false _let_114 false _let_123)) :args (_let_146 true _let_120)) :args (_let_9 true _let_129)) :args (_let_152 false _let_11 false _let_9)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_132)) :args ((or _let_124 (not _let_131) (not _let_132)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING _let_73)) :args _let_72)) _let_71 :args (_let_132 false _let_70)) (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_10 _let_125 (not _let_126)))) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_151) (CONG (REFL :args _let_151) (REFL :args (_let_128)) (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_8))) :args _let_62)) :args ((or _let_128 _let_8 _let_131))) _let_150 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_129 0)) (CONG _let_149 (MACRO_SR_PRED_INTRO :args ((= (not _let_128) _let_127))) :args _let_62)) :args ((or _let_127 _let_129))) _let_148 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_145) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Y) false))))) :args _let_145)) _let_144 _let_143 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_136) (CONG (REFL :args _let_136) (REFL :args (_let_122)) (MACRO_SR_PRED_INTRO :args ((= (not _let_117) _let_116))) :args _let_62)) :args ((or _let_116 _let_118 _let_122))) (REORDERING (CNF_EQUIV_POS2 :args (_let_119)) :args ((or _let_16 (not _let_118) (not _let_119)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING _let_66)) :args _let_65)) _let_64 :args (_let_119 false _let_63)) _let_135 _let_134 (CNF_OR_NEG :args (_let_17 1)) _let_133 :args ((or _let_17 _let_8) false _let_132 true _let_124 false _let_131 false _let_9 false _let_127 true _let_129 false _let_126 true _let_120 false _let_123 false _let_116 true _let_118 false _let_119 false _let_114 false _let_115 true _let_16 false _let_11)) _let_113 :args (_let_8 true _let_17)) :args (false true _let_13 false _let_8)) :args (_let_7 _let_6 (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_5 (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 $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))) _let_4 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))) (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))) (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) (forall ((F $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.image2 F A)) (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.apply F X Y))))) _let_3 (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))))) _let_2 (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 SET759+4
% 0.20/0.70 % cvc5---1.0.5 exiting
% 0.20/0.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------