TSTP Solution File: SET725+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET725+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 4.60s 4.90s
% Output : Proof 4.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET725+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 12:21:15 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 4.60/4.90 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dnkGyEQx7A/cvc5---1.0.5_6013.p...
% 4.60/4.90 ------- get file name : TPTP file name is SET725+4
% 4.60/4.90 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_6013.smt2...
% 4.60/4.90 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.60/4.90 % SZS status Theorem for SET725+4
% 4.60/4.90 % SZS output start Proof for SET725+4
% 4.60/4.90 (
% 4.60/4.90 (let ((_let_1 (not (forall ((F $$unsorted) (G $$unsorted) (H $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.maps F A B) (tptp.maps G B A) (tptp.maps H B A) (tptp.identity (tptp.compose_function G F A B A) A) (tptp.identity (tptp.compose_function F H B A B) B)) (tptp.one_to_one F A B)))))) (let ((_let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))))) (let ((_let_3 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (=> (tptp.member Y B) (exists ((E $$unsorted)) (and (tptp.member E A) (tptp.apply F E Y))))))))) (let ((_let_4 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.injective F A B) (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X1 A) (tptp.member X2 A) (tptp.member Y B)) (=> (and (tptp.apply F X1 Y) (tptp.apply F X2 Y)) (= X1 X2)))))))) (let ((_let_5 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_6 (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_7 (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_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_9 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_10 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_11 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_12 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_13 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_125))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_91 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_125))) (let ((_let_16 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21 _let_19 _let_17 _let_8))) (let ((_let_27 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2))))) (let ((_let_28 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_29 (and _let_28 _let_27))) (let ((_let_30 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (_let_32))) (let ((_let_35 ((tptp.maps F A B)))) (let ((_let_36 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_37 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_38 (tptp.identity _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (tptp.identity _let_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_46 (not _let_45))) (let ((_let_47 (not _let_30))) (let ((_let_48 (or _let_47 _let_46 _let_44 _let_42 _let_39 _let_36))) (let ((_let_49 (forall ((F $$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.one_to_one F A B))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_31)) :args ((or _let_47 _let_29 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_30))) :args _let_52)) :args ((or _let_30 _let_48))) _let_54 :args (_let_30 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_34)) _let_33 :args (_let_31 false _let_32)) :args (_let_29 false _let_30 false _let_31)))) (let ((_let_57 (not _let_29))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_27 _let_57))) _let_56 :args (_let_27 false _let_29)))) (let ((_let_59 (_let_27))) (let ((_let_60 (not (= (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false)))) (let ((_let_61 (_let_60 (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2) false))))) (let ((_let_62 (ASSUME :args _let_59))) (let ((_let_63 (or _let_21 _let_17))) (let ((_let_64 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y)))))) (let ((_let_65 (not _let_63))) (let ((_let_66 (not _let_64))) (let ((_let_67 (or _let_25 _let_66))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_28 _let_57))) _let_56 :args (_let_28 false _let_29)))) (let ((_let_69 (_let_28))) (let ((_let_70 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) (let ((_let_71 (ASSUME :args _let_69))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_73 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_25 _let_76 _let_23 _let_19 _let_74 _let_72))) (let ((_let_78 (forall ((X1 $$unsorted) (X2 $$unsorted) (Y $$unsorted)) (or (not (tptp.member X1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member X2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_81 (= _let_80 _let_78))) (let ((_let_82 (not _let_78))) (let ((_let_83 (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_84 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_86 (and _let_80 _let_85))) (let ((_let_87 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E Y))))))))) (let ((_let_88 (= _let_85 _let_87))) (let ((_let_89 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E A)) (not (tptp.apply F E Y))))))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_92 (not _let_91))) (let ((_let_93 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_92))) (let ((_let_96 (tptp.apply _let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_97 (or _let_94 _let_96))) (let ((_let_98 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))))) (let ((_let_99 (not _let_98))) (let ((_let_100 (= _let_96 _let_99))) (let ((_let_101 (or _let_94 _let_94 _let_100))) (let ((_let_102 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_105 (not _let_104))) (let ((_let_106 (or _let_105 _let_103))) (let ((_let_107 (or _let_105 (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)) _let_103))) (let ((_let_108 (REFL :args (_let_95)))) (let ((_let_109 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.apply (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) X X))))) (let ((_let_110 (= _let_38 _let_109))) (let ((_let_111 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply F X X))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (_let_111))) (let ((_let_114 ((tptp.identity F A)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_110)) :args ((or _let_39 _let_109 (not _let_110)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 4)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_52)) :args ((or _let_38 _let_48))) _let_54 :args (_let_38 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (_let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113)) _let_112 :args (_let_110 false _let_111)) :args (_let_109 false _let_38 false _let_110)))) (let ((_let_116 (_let_109))) (let ((_let_117 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) (let ((_let_118 (ASSUME :args _let_116))) (let ((_let_119 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted) (C $$unsorted) (X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Z C)) (= (tptp.apply (tptp.compose_function G F A B C) X Z) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (tptp.apply F X Y)) (not (tptp.apply G Y Z)))))))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (_let_119))) (let ((_let_122 ((tptp.apply (tptp.compose_function G F A B C) X Z)))) (let ((_let_123 (_let_91))) (let ((_let_124 (_let_99))) (let ((_let_125 (REFL :args (_let_107)))) (let ((_let_126 (not _let_87))) (let ((_let_127 (_let_126))) (let ((_let_128 (= _let_36 _let_86))) (let ((_let_129 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Y))))))))) (let ((_let_191 (forall ((X $$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 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y2)) (= Y1 Y2))))) (let ((_let_192 (and _let_190 _let_191))) (let ((_let_193 (= _let_43 _let_192))) (let ((_let_194 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_193)) :args ((or _let_44 _let_192 (not _let_193)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_52)) :args ((or _let_43 _let_48))) _let_54 :args (_let_43 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 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_let_236))) (let ((_let_239 (not _let_237))) (let ((_let_240 (or _let_76 _let_239))) (let ((_let_241 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG _let_134 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_52)) :args ((or _let_75 _let_77))) _let_133 :args (_let_75 true _let_77)))) (let ((_let_242 (_let_239))) (let ((_let_243 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_242)) :args _let_242)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_239) _let_237))) (REFL :args (_let_238)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_240)) :args ((or _let_76 _let_239 (not _let_240)))) _let_241 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_70)) :args _let_69)) _let_68 :args (_let_240 false _let_28)) :args (_let_239 false _let_75 false _let_240)) :args (_let_238 true 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(SCOPE (TRUE_ELIM (TRANS (CONG _let_259 _let_258 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)) :args _let_256) _let_255)) :args (_let_223 _let_224))) :args (_let_224 _let_223))) :args (true _let_253)) _let_252 _let_249 :args (_let_214 false _let_224 false _let_223)))) (let ((_let_261 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_226 0)) (CONG _let_248 (MACRO_SR_PRED_INTRO :args ((= (not _let_217) _let_216))) :args _let_52)) :args ((or _let_216 _let_226))) _let_247 :args (_let_216 true _let_226)))) (let ((_let_262 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_185 1)) (CONG _let_203 (MACRO_SR_PRED_INTRO :args ((= (not _let_184) _let_183))) :args _let_52)) :args ((or _let_183 _let_185))) _let_202 :args (_let_183 true _let_185)))) (let ((_let_263 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_218)) :args ((or _let_23 _let_172 _let_184 _let_217 _let_215 _let_211 (not _let_218)))) _let_141 _let_204 _let_262 _let_261 _let_260 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_222 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_E_MATCHING _let_221)) :args _let_220)) _let_219 :args (_let_218 false _let_191)) :args (_let_211 false _let_22 false _let_171 false _let_183 false _let_216 false _let_214 false _let_218)))) (let ((_let_264 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_265 (not _let_264))) (let ((_let_266 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_267 (not _let_266))) (let ((_let_268 (or _let_23 _let_217 _let_267 _let_215 _let_265 _let_212))) (let ((_let_269 (not _let_213))) (let ((_let_270 (or _let_267 _let_265 _let_269))) (let ((_let_271 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_301 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_173)) :args ((or _let_172 _let_21 _let_166 _let_170 _let_168 _let_10 (not _let_173)))) _let_204 _let_139 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_287)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_288 _let_294 _let_297 _let_290) (SCOPE (TRUE_ELIM (TRANS (CONG _let_300 (TRANS _let_299 _let_296) _let_293 :args _let_256) _let_289)) :args (_let_213 _let_212 _let_211 _let_8))) :args (_let_213 _let_8 _let_212 _let_211))) :args (true _let_287)) :args ((or _let_269 _let_165 _let_286 _let_285 _let_284))) _let_283 _let_142 _let_282 _let_263 :args (_let_165 false _let_213 false _let_8 false _let_212 false _let_211)) _let_210 _let_209 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_59))) _let_58 :args (_let_173 false _let_27)) :args (_let_10 false _let_171 false _let_20 false _let_165 false _let_169 false _let_167 false _let_173)))) (let ((_let_302 (not _let_11))) (let ((_let_303 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_304 (not _let_303))) (let ((_let_305 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_306 (not _let_305))) (let ((_let_307 (or _let_306 _let_76 _let_25 _let_304 _let_302 _let_72))) (let ((_let_308 (forall ((X $$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 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y2)) (= Y1 Y2))))) (let ((_let_309 (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_5)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y))))))))) (let ((_let_310 (and _let_309 _let_308))) (let ((_let_311 (= _let_45 _let_310))) (let ((_let_312 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_311)) :args ((or _let_46 _let_310 (not _let_311)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 1)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_52)) :args ((or _let_45 _let_48))) _let_54 :args (_let_45 true _let_48)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_34)) _let_33 :args (_let_311 false _let_32)) :args (_let_310 false _let_45 false _let_311)))) (let ((_let_313 (not _let_310))) (let ((_let_314 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_310 1)) :args ((or _let_308 _let_313))) _let_312 :args (_let_308 false _let_310)))) (let ((_let_315 (_let_308))) (let ((_let_316 (not (= (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false)))) (let ((_let_317 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y1) false)) _let_316))) (let ((_let_318 (ASSUME :args _let_315))) (let ((_let_319 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_320 (not _let_319))) (let ((_let_321 (or _let_306 _let_320 _let_304))) (let ((_let_322 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))))) (let ((_let_323 (not _let_321))) (let ((_let_324 (not _let_322))) (let ((_let_325 (tptp.apply _let_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_326 (= _let_325 _let_324))) (let ((_let_327 (or _let_76 _let_76 _let_326))) (let ((_let_328 (or _let_76 _let_325))) (let ((_let_329 (_let_324))) (let ((_let_330 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_329)) :args _let_329)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_324) _let_322))) (REFL :args (_let_323)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_326)) :args ((or (not _let_325) _let_324 (not _let_326)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_328)) :args ((or _let_76 _let_325 (not _let_328)))) _let_241 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_161 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_160)) :args _let_159)) _let_158 :args (_let_328 false _let_156)) :args (_let_325 false _let_75 false _let_328)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_327))) :args ((or _let_76 _let_326 (not _let_327)))) _let_241 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (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 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_122)) :args _let_121)) _let_120 :args (_let_327 false _let_119)) :args (_let_326 false _let_75 false _let_327)) :args (_let_324 false _let_325 false _let_326)) :args (_let_323 true _let_322)))) (let ((_let_331 (REFL :args (_let_321)))) (let ((_let_332 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_321 2)) (CONG _let_331 (MACRO_SR_PRED_INTRO :args ((= (not _let_304) _let_303))) :args _let_52)) :args ((or _let_303 _let_321))) _let_330 :args (_let_303 true _let_321)))) (let ((_let_333 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_321 0)) (CONG _let_331 (MACRO_SR_PRED_INTRO :args ((= (not _let_306) _let_305))) :args _let_52)) :args ((or _let_305 _let_321))) _let_330 :args (_let_305 true _let_321)))) (let ((_let_334 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_335 (not _let_334))) (let ((_let_336 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_337 (not _let_336))) (let ((_let_338 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_339 (not _let_338))) (let ((_let_340 (or _let_217 _let_23 _let_339 _let_337 _let_335 _let_12))) (let ((_let_341 (and _let_213 _let_212))) (let ((_let_342 (_let_213 _let_212))) (let ((_let_343 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_344 (not _let_343))) (let ((_let_345 (or _let_339 _let_344))) (let ((_let_346 (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_17 Y)))))) (let ((_let_347 (not _let_345))) (let ((_let_348 (not _let_346))) (let ((_let_349 (or _let_172 _let_348))) (let ((_let_350 (_let_348))) (let ((_let_351 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_350)) :args _let_350)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_348) _let_346))) (REFL :args (_let_347)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_349)) :args ((or _let_172 _let_348 (not _let_349)))) _let_204 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_70)) :args _let_69)) _let_68 :args (_let_349 false _let_28)) :args (_let_348 false _let_171 false _let_349)) :args (_let_347 true _let_346)))) (let ((_let_352 (REFL :args (_let_345)))) (let ((_let_353 (and _let_343 _let_211))) (let ((_let_354 (_let_343 _let_211))) (let ((_let_355 (ASSUME :args (_let_343)))) (let ((_let_356 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_345 0)) (CONG _let_352 (MACRO_SR_PRED_INTRO :args ((= (not _let_339) _let_338))) :args _let_52)) :args ((or _let_338 _let_345))) _let_351 :args (_let_338 true _let_345)))) (let ((_let_357 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_340)) :args ((or _let_23 _let_217 _let_339 _let_12 _let_335 _let_337 (not _let_340)))) _let_141 _let_261 _let_356 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_353)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_355 _let_297) (SCOPE (TRUE_ELIM (TRANS (CONG _let_300 _let_298 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)) :args _let_256) (TRUE_INTRO _let_355))) :args _let_354)) :args _let_354)) :args (true _let_353)) :args ((or _let_344 _let_334 _let_284))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_345 1)) (CONG _let_352 (MACRO_SR_PRED_INTRO :args ((= (not _let_344) _let_343))) :args _let_52)) :args ((or _let_343 _let_345))) _let_351 :args (_let_343 true _let_345)) _let_263 :args (_let_334 false _let_343 false _let_211)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_341)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_288 _let_294) (SCOPE (TRUE_ELIM (TRANS (CONG _let_300 _let_296 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) :args _let_256) _let_289)) :args _let_342)) :args _let_342)) :args (true _let_341)) _let_283 _let_282 :args (_let_336 false _let_213 false _let_212)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_59)) _let_58 :args (_let_340 false _let_27)) :args (_let_12 false _let_22 false _let_216 false _let_338 false _let_334 false _let_336 false _let_340)))) (let ((_let_358 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_359 (not _let_358))) (let ((_let_360 (or _let_76 _let_170 _let_306 _let_359 _let_320 _let_13))) (let ((_let_361 (not _let_10))) (let ((_let_362 (and _let_73 _let_8 _let_10))) (let ((_let_363 (_let_73 _let_8 _let_10))) (let ((_let_364 (ASSUME :args (_let_73)))) (let ((_let_365 (TRUE_INTRO _let_364))) (let ((_let_366 (ASSUME :args (_let_10)))) (let ((_let_367 (SYMM _let_366))) (let ((_let_368 (SYMM _let_367))) (let ((_let_369 (SYMM _let_368))) (let ((_let_370 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_371 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_360)) :args ((or _let_76 _let_306 _let_320 _let_170 _let_359 _let_13 (not _let_360)))) _let_241 _let_333 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_321 1)) (CONG _let_331 (MACRO_SR_PRED_INTRO :args ((= (not _let_320) _let_319))) :args _let_52)) :args ((or _let_319 _let_321))) _let_330 :args (_let_319 true _let_321)) _let_210 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_362)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_364 _let_290 _let_366) (SCOPE (TRUE_ELIM (TRANS (CONG _let_300 _let_370 (TRANS _let_369 _let_293) :args _let_256) _let_365)) :args _let_363)) :args _let_363)) :args (true _let_362)) :args ((or _let_74 _let_286 _let_358 _let_361))) _let_251 _let_142 _let_301 :args (_let_358 false _let_73 false _let_8 false _let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_59))) _let_58 :args (_let_360 false _let_27)) :args (_let_13 false _let_75 false _let_305 false _let_319 false _let_169 false _let_358 false _let_360)))) (let ((_let_372 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_373 (not _let_372))) (let ((_let_374 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_125))) (let ((_let_375 (not _let_374))) (let ((_let_376 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_125 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_377 (not _let_376))) (let ((_let_378 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_379 (not _let_378))) (let ((_let_380 (or _let_379 _let_377 _let_339 _let_375 _let_373 _let_14))) (let ((_let_381 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_382 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_92))) (let ((_let_383 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77))) (let ((_let_384 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_125))) (let ((_let_385 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_67))) (let ((_let_386 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_387 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_29))) (let ((_let_388 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_389 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75))) (let ((_let_390 (not _let_389))) (let ((_let_391 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_392 (not _let_391))) (let ((_let_393 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_75 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_394 (not _let_393))) (let ((_let_395 (or _let_23 _let_76 _let_394 _let_392 _let_390 _let_381))) (let ((_let_396 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X Y1) false)) _let_316))) (let ((_let_397 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40))) (let ((_let_398 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_77))) (let ((_let_399 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_400 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35))) (let ((_let_401 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26))) (let ((_let_402 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_416 (not _let_415))) (let ((_let_417 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_418 (not _let_417))) (let ((_let_419 (or _let_418 _let_408 _let_416 _let_414 _let_412 _let_397))) (let ((_let_420 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_421 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_422 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_40))) (let ((_let_423 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_424 (not _let_423))) (let ((_let_425 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_426 (not _let_425))) (let 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true _let_574)))) (let ((_let_584 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_573)) :args ((or _let_428 _let_572 _let_570 _let_547 _let_543 _let_400 (not _let_573)))) _let_463 _let_583 _let_582 _let_567 _let_566 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_26 QUANTIFIERS_INST_E_MATCHING _let_61)) :args _let_59))) _let_58 :args (_let_573 false _let_27)) :args (_let_400 false _let_427 false _let_571 false _let_569 false _let_546 false _let_542 false _let_573)))) (let ((_let_585 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_586 (not _let_585))) (let ((_let_587 (or _let_428 _let_306 _let_572 _let_586 _let_570 _let_401))) (let ((_let_588 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))) (let ((_let_589 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))) (let ((_let_590 (not _let_589))) (let ((_let_591 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_592 (not _let_591))) (let ((_let_593 (or _let_172 _let_592 _let_170 _let_590 _let_168 _let_588))) (let ((_let_594 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))) (let ((_let_595 (not _let_594))) (let ((_let_596 (or _let_592 _let_595))) (let ((_let_597 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 Y)))))) (let ((_let_598 (not _let_596))) (let ((_let_599 (not _let_597))) (let ((_let_600 (or _let_217 _let_599))) (let ((_let_601 (_let_599))) (let ((_let_602 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE 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(MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_42 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_70)) :args _let_69)) _let_68 :args (_let_801 false _let_28)) :args (_let_800 false _let_754 false _let_801)) :args (_let_799 true _let_798)))) (let ((_let_804 (REFL :args (_let_797)))) (let ((_let_805 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_797 1)) (CONG _let_804 (MACRO_SR_PRED_INTRO :args ((= (not _let_749) _let_748))) :args _let_52)) :args ((or _let_748 _let_797))) _let_803 :args (_let_748 true _let_797)))) (let ((_let_806 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_797 0)) (CONG _let_804 (MACRO_SR_PRED_INTRO :args ((= (not _let_753) _let_752))) :args _let_52)) :args ((or _let_752 _let_797))) _let_803 :args (_let_752 true _let_797)))) (let ((_let_807 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_41))) (let 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B)) (and (tptp.member Y B) (exists ((X $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.60/4.92 )
% 4.60/4.92 % SZS output end Proof for SET725+4
% 4.60/4.92 % cvc5---1.0.5 exiting
% 4.60/4.92 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------