TSTP Solution File: SET729+4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET729+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n032.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 25.79s 26.00s
% Output : Proof 25.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET729+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 12:09:28 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.15/0.39 %----Proving TF0_NAR, FOF, or CNF
% 25.79/26.00 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.yu2tUtOFic/cvc5---1.0.5_31243.p...
% 25.79/26.00 ------- get file name : TPTP file name is SET729+4
% 25.79/26.00 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31243.smt2...
% 25.79/26.00 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.79/26.00 --- Run --no-e-matching --full-saturate-quant at 5...
% 25.79/26.00 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.79/26.00 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.79/26.00 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.79/26.00 % SZS status Theorem for SET729+4
% 25.79/26.00 % SZS output start Proof for SET729+4
% 25.79/26.00 (
% 25.79/26.00 (let ((_let_1 (not (forall ((F $$unsorted) (A $$unsorted)) (=> (tptp.maps F A A) (= (and (tptp.one_to_one F A A) (tptp.inverse_predicate F F A A)) (tptp.identity (tptp.compose_function F F A A A) A))))))) (let ((_let_2 (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 ((_let_3 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.one_to_one F A B) (and (tptp.injective F A B) (tptp.surjective F A B)))))) (let ((_let_4 (forall ((F $$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))))))))) (let ((_let_5 (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_6 (forall ((F $$unsorted) (A $$unsorted)) (= (tptp.identity F A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply F X X))))))) (let ((_let_7 (forall ((G $$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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) (let ((_let_8 (forall ((F $$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 $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y1 B) (tptp.member Y2 B)) (=> (and (tptp.apply F X Y1) (tptp.apply F X Y2)) (= Y1 Y2))))))))) (let ((_let_9 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57))) (let ((_let_10 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56))) (let ((_let_11 (= _let_9 _let_10))) (let ((_let_12 (not _let_9))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12))) (let ((_let_16 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56 Y)))))) (let ((_let_17 (not _let_15))) (let ((_let_18 (not _let_16))) (let ((_let_19 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18))) (let ((_let_22 (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_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y))))))))) (let ((_let_23 (forall ((X $$unsorted) (Y1 $$unsorted) (Y2 $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y1)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y2)) (= Y1 Y2))))) (let ((_let_24 (and _let_22 _let_23))) (let ((_let_25 (tptp.maps SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (forall ((F $$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 $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y1 B)) (not (tptp.member Y2 B)) (not (tptp.apply F X Y1)) (not (tptp.apply F X Y2)) (= Y1 Y2)))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (tptp.identity _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (tptp.inverse_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_32 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (and _let_32 _let_31))) (let ((_let_34 (= _let_33 _let_30))) (let ((_let_35 (not _let_25))) (let ((_let_36 (or _let_35 _let_34))) (let ((_let_37 (forall ((F $$unsorted) (A $$unsorted)) (or (not (tptp.maps F A A)) (= (and (tptp.one_to_one F A A) (tptp.inverse_predicate F F A A)) (tptp.identity (tptp.compose_function F F A A A) A)))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (or))) (let ((_let_41 (not _let_37))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_39) :args (_let_41))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) (REFL :args (_let_38)) :args _let_40)) _let_39 :args (_let_38 true _let_37)))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or _let_35 _let_24 (not _let_26)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG (REFL :args (_let_36)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_25))) :args _let_40)) :args ((or _let_25 _let_36))) _let_42 :args (_let_25 true _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.maps F A B)))) :args (_let_27))) _let_28 :args (_let_26 false _let_27)) :args (_let_24 false _let_25 false _let_26)))) (let ((_let_44 (not _let_24))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 0)) :args ((or _let_22 _let_44))) _let_43 :args (_let_22 false _let_24)))) (let ((_let_46 (_let_22))) (let ((_let_47 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) (let ((_let_48 (ASSUME :args _let_46))) (let ((_let_49 (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56)))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_20 _let_50))) (let ((_let_52 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (forall ((E $$unsorted)) (or (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 E Y))))))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (tptp.surjective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_55 (= _let_54 _let_52))) (let ((_let_56 (not _let_52))) (let ((_let_57 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.surjective F A B) (forall ((Y $$unsorted)) (or (not (tptp.member Y B)) (not (forall ((E $$unsorted)) (or (not (tptp.member E A)) (not (tptp.apply F E Y))))))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (tptp.injective SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_60 (and _let_59 _let_54))) (let ((_let_61 (forall ((X1 $$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_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X1 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X2 Y)) (= X1 X2))))) (let ((_let_62 (= _let_59 _let_61))) (let ((_let_63 (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_64 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_66 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_71 (not _let_70))) (let ((_let_72 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_73 _let_71 _let_69 _let_67 _let_65))) (let ((_let_77 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37))) (let ((_let_78 (= _let_68 _let_77))) (let ((_let_79 (or _let_75 _let_71 _let_78))) (let ((_let_80 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38))) (let ((_let_81 (= _let_66 _let_80))) (let ((_let_82 (or _let_73 _let_71 _let_81))) (let ((_let_83 (not _let_80))) (let ((_let_84 (not _let_77))) (let ((_let_85 (or _let_71 _let_75 _let_73 _let_84 _let_83 _let_65))) (let ((_let_86 (REFL :args (_let_76)))) (let ((_let_87 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X)))))) (let ((_let_88 (= _let_31 _let_87))) (let ((_let_89 (forall ((G $$unsorted) (F $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.inverse_predicate G F A B) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply G Y X)))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.inverse_predicate G F A B)))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)))) (let ((_let_92 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_93 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_94 (= _let_93 _let_92))) (let ((_let_95 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_96 (not _let_95))) (let ((_let_97 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_98 _let_96 _let_94))) (let ((_let_100 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply (tptp.compose_function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) X X))))) (let ((_let_101 (= _let_30 _let_100))) (let ((_let_102 (tptp.apply _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_103 (or _let_98 _let_102))) (let ((_let_104 (tptp.apply _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_105 (or _let_96 _let_104))) (let ((_let_106 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))))) (let ((_let_107 (not _let_106))) (let ((_let_108 (= _let_102 _let_107))) (let ((_let_109 (or _let_98 _let_98 _let_108))) (let ((_let_110 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y)))))) (let ((_let_111 (not _let_110))) (let ((_let_112 (or _let_96 _let_111))) (let ((_let_113 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))))) (let ((_let_114 (not _let_113))) (let ((_let_115 (= _let_104 _let_114))) (let ((_let_116 (or _let_96 _let_96 _let_115))) (let ((_let_117 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_118 (not _let_117))) (let ((_let_119 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_120 (not _let_119))) (let ((_let_121 (or _let_120 _let_118))) (let ((_let_122 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_123 (not _let_122))) (let ((_let_124 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_125 (not _let_124))) (let ((_let_126 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_127 (not _let_126))) (let ((_let_128 (or _let_127 _let_125 _let_123))) (let ((_let_129 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_130 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_let_202) _let_201))) :args _let_40)) :args ((or _let_201 _let_205))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_218)) :args _let_218)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_217) _let_100))) (REFL :args ((not _let_205))) :args _let_40)) (REORDERING (CNF_EQUIV_POS2 :args _let_151) :args ((or _let_30 _let_217 _let_150))) _let_149 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_186)) (CNF_EQUIV_NEG2 :args _let_145) _let_144 _let_184 _let_91 (CNF_AND_NEG :args (_let_33)) :args ((or _let_195 _let_183) false _let_198 true _let_196 false _let_197 false _let_199 false _let_216 true _let_214 false _let_206 true _let_210 false _let_212 false _let_208 false _let_209 true _let_204 false _let_201 true _let_205 true _let_100 false _let_101 false _let_203 true _let_30 true _let_34 false _let_87 false _let_88 false _let_33)) _let_182 :args (_let_195 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_194 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.one_to_one F A B)))) :args _let_193)) _let_194 :args (_let_191 false _let_3)) :args (_let_192 true _let_32 false _let_191)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_62)) :args ((or _let_59 _let_189 (not _let_62)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_190)) :args _let_190)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_189) _let_61))) (REFL :args ((not _let_76))) :args _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_75 _let_73 _let_71 _let_65 _let_84 _let_83 (not _let_85)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_172 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_171)) _let_170 :args (_let_85 false _let_23)) (REORDERING (CNF_EQUIV_POS1 :args (_let_81)) :args ((or _let_67 _let_80 (not _let_81)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_69 _let_77 (not _let_78)))) (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_73 _let_71 _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_38 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_186)) _let_185 :args (_let_82 false _let_87)) (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_75 _let_71 _let_78 (not _let_79)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_186)) _let_185 :args (_let_79 false _let_87)) (CNF_OR_NEG :args (_let_76 5)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 4)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_40)) :args ((or _let_66 _let_76))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 3)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_40)) :args ((or _let_68 _let_76))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 2)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_40)) :args ((or _let_70 _let_76))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 1)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_72))) :args _let_40)) :args ((or _let_72 _let_76))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 0)) (CONG _let_86 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_74))) :args _let_40)) :args ((or _let_74 _let_76))) :args (_let_76 false _let_85 false _let_80 false _let_77 false _let_81 false _let_82 false _let_78 false _let_79 true _let_65 false _let_66 false _let_68 false _let_70 false _let_72 false _let_74)) :args (_let_61 false _let_76)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.injective F A B)))) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_59 false _let_61 false _let_62)) :args ((not _let_54) true _let_60 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.surjective F A B)))) :args (_let_57))) _let_58 :args (_let_55 false _let_57)) :args (_let_56 true _let_54 false _let_55)) :args (_let_53 true _let_52)))) (let ((_let_225 (REFL :args (_let_51)))) (let ((_let_226 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_225 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_40)) :args ((or _let_19 _let_51))) _let_224 :args (_let_19 true _let_51)))) (let ((_let_227 (_let_18))) (let ((_let_228 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_227)) :args _let_227)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_16))) (REFL :args (_let_17)) :args _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_18 (not _let_21)))) _let_226 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_47)) :args _let_46)) _let_45 :args (_let_21 false _let_22)) :args (_let_18 false _let_19 false _let_21)) :args (_let_17 true _let_16)))) (let ((_let_229 (REFL :args (_let_15)))) (let ((_let_230 (or _let_20 _let_14 _let_11))) (let ((_let_231 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 0)) (CONG _let_229 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_40)) :args ((or _let_13 _let_15))) _let_228 :args (_let_13 true _let_15)))) (let ((_let_232 (not _let_10))) (let ((_let_233 (or _let_14 _let_232))) (let ((_let_234 (_let_49))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or _let_12 _let_10 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_233)) :args ((or _let_14 _let_232 (not _let_233)))) _let_231 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_234) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_234)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_225 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_40)) :args ((or _let_49 _let_51))) _let_224 :args (_let_49 true _let_51)) :args (_let_233 false _let_49)) :args (_let_232 false _let_13 false _let_233)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_230)) :args ((or _let_20 _let_14 _let_11 (not _let_230)))) _let_226 _let_231 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_188 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_56 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_57 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_186)) _let_185 :args (_let_230 false _let_87)) :args (_let_11 false _let_19 false _let_13 false _let_230)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_15 1)) (CONG _let_229 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_9))) :args _let_40)) :args ((or _let_9 _let_15))) _let_228 :args (_let_9 true _let_15)) :args (false true _let_10 false _let_11 false _let_9)) :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_8 (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 $$unsorted)) (and (tptp.member Y B) (tptp.apply F X Y) (tptp.apply G Y Z)))))))) _let_7 (forall ((F $$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_6 _let_5 _let_4 _let_3 _let_2 (forall ((F $$unsorted) (A $$unsorted) (B $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y B)) (= (tptp.apply F X Y) (tptp.apply (tptp.inverse_function F A B) Y X)))) (forall ((F $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.79/26.01 )
% 25.79/26.01 % SZS output end Proof for SET729+4
% 25.79/26.01 % cvc5---1.0.5 exiting
% 25.79/26.01 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------