TSTP Solution File: CAT032+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : CAT032+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 : Wed Aug 30 18:14:46 EDT 2023
% Result : Theorem 0.10s 0.38s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : CAT032+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.07 % Command : do_cvc5 %s %d
% 0.07/0.25 % Computer : n009.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Sun Aug 27 00:39:20 EDT 2023
% 0.07/0.25 % CPUTime :
% 0.10/0.32 %----Proving TF0_NAR, FOF, or CNF
% 0.10/0.38 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.X8OOTXMh6S/cvc5---1.0.5_11750.p...
% 0.10/0.38 ------- get file name : TPTP file name is CAT032+1
% 0.10/0.38 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11750.smt2...
% 0.10/0.38 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.10/0.38 % SZS status Theorem for CAT032+1
% 0.10/0.38 % SZS output start Proof for CAT032+1
% 0.10/0.38 (
% 0.10/0.38 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v2_cat_1 C) (tptp.l1_cat_1 C)) (tptp.v8_cat_1 (tptp.k17_isocat_2 A B C) (tptp.k12_nattra_1 A (tptp.k11_cat_2 B C)) (tptp.k11_cat_2 (tptp.k12_nattra_1 A B) (tptp.k12_nattra_1 A C))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B) (tptp.v2_cat_1 C) (tptp.l1_cat_1 C)) (tptp.m2_cat_1 (tptp.k17_isocat_2 A B C) (tptp.k12_nattra_1 A (tptp.k11_cat_2 B C)) (tptp.k11_cat_2 (tptp.k12_nattra_1 A B) (tptp.k12_nattra_1 A C))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k12_nattra_1 A B))) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (and (tptp.v1_cat_1 _let_1) (tptp.v2_cat_1 _let_1) (tptp.l1_cat_1 _let_1))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k11_cat_2 A B))) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (and (tptp.v2_cat_1 _let_1) (tptp.l1_cat_1 _let_1))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (= (tptp.r1_isocat_1 A B) (exists ((C $$unsorted)) (and (tptp.m2_cat_1 C A B) (tptp.v8_cat_1 C A B)))))))))) (let ((_let_6 (not (forall ((A $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A)) (forall ((B $$unsorted)) (=> (and (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (forall ((C $$unsorted)) (=> (and (tptp.v2_cat_1 C) (tptp.l1_cat_1 C)) (tptp.r1_isocat_1 (tptp.k12_nattra_1 A (tptp.k11_cat_2 B C)) (tptp.k11_cat_2 (tptp.k12_nattra_1 A B) (tptp.k12_nattra_1 A C)))))))))))) (let ((_let_7 (forall ((C $$unsorted)) (let ((_let_1 (tptp.k11_cat_2 (tptp.k12_nattra_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.k12_nattra_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_2 (tptp.k12_nattra_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.k11_cat_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (or (not (tptp.m2_cat_1 C _let_2 _let_1)) (not (tptp.v8_cat_1 C _let_2 _let_1)))))))) (let ((_let_8 (tptp.k12_nattra_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (tptp.k12_nattra_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.k11_cat_2 _let_9 _let_8))) (let ((_let_11 (tptp.k11_cat_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (tptp.k12_nattra_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11))) (let ((_let_13 (tptp.k17_isocat_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_14 (tptp.v8_cat_1 _let_13 _let_12 _let_10))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.m2_cat_1 _let_13 _let_12 _let_10))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15))) (let ((_let_19 (not _let_7))) (let ((_let_20 (tptp.r1_isocat_1 _let_12 _let_10))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (tptp.l1_cat_1 _let_10))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.v2_cat_1 _let_10))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.l1_cat_1 _let_12))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.v2_cat_1 _let_12))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27 _let_25 _let_23 _let_21))) (let ((_let_31 (forall ((A $$unsorted) (BOUND_VARIABLE_1242 $$unsorted)) (or (not (tptp.v2_cat_1 A)) (not (tptp.l1_cat_1 A)) (not (tptp.v2_cat_1 BOUND_VARIABLE_1242)) (not (tptp.l1_cat_1 BOUND_VARIABLE_1242)) (= (tptp.r1_isocat_1 A BOUND_VARIABLE_1242) (not (forall ((C $$unsorted)) (or (not (tptp.m2_cat_1 C A BOUND_VARIABLE_1242)) (not (tptp.v8_cat_1 C A BOUND_VARIABLE_1242)))))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (and _let_24 _let_22))) (let ((_let_34 (tptp.l1_cat_1 _let_8))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.v2_cat_1 _let_8))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.l1_cat_1 _let_9))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.v2_cat_1 _let_9))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_37 _let_35 _let_33))) (let ((_let_43 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k11_cat_2 A B))) (or (not (tptp.v2_cat_1 A)) (not (tptp.l1_cat_1 A)) (not (tptp.v2_cat_1 B)) (not (tptp.l1_cat_1 B)) (and (tptp.v2_cat_1 _let_1) (tptp.l1_cat_1 _let_1))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (_let_43))) (let ((_let_46 ((tptp.k11_cat_2 A B)))) (let ((_let_47 (and (tptp.v1_cat_1 _let_8) _let_36 _let_34))) (let ((_let_48 (tptp.l1_cat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.v2_cat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_51 (not _let_50))) (let ((_let_52 (tptp.l1_cat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.v2_cat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_51 _let_49 _let_47))) (let ((_let_57 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k12_nattra_1 A B))) (or (not (tptp.v2_cat_1 A)) (not (tptp.l1_cat_1 A)) (not (tptp.v2_cat_1 B)) (not (tptp.l1_cat_1 B)) (and (tptp.v1_cat_1 _let_1) (tptp.v2_cat_1 _let_1) (tptp.l1_cat_1 _let_1))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((tptp.k12_nattra_1 A B)))) (let ((_let_61 (tptp.l1_cat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.v2_cat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_55 _let_53 _let_64 _let_62 _let_51 _let_49 _let_20))) (let ((_let_66 (forall ((A $$unsorted) (BOUND_VARIABLE_1179 $$unsorted) (BOUND_VARIABLE_1177 $$unsorted)) (or (not (tptp.v2_cat_1 A)) (not (tptp.l1_cat_1 A)) (not (tptp.v2_cat_1 BOUND_VARIABLE_1177)) (not (tptp.l1_cat_1 BOUND_VARIABLE_1177)) (not (tptp.v2_cat_1 BOUND_VARIABLE_1179)) (not (tptp.l1_cat_1 BOUND_VARIABLE_1179)) (tptp.r1_isocat_1 (tptp.k12_nattra_1 A (tptp.k11_cat_2 BOUND_VARIABLE_1177 BOUND_VARIABLE_1179)) (tptp.k11_cat_2 (tptp.k12_nattra_1 A BOUND_VARIABLE_1177) (tptp.k12_nattra_1 A BOUND_VARIABLE_1179))))))) (let ((_let_67 (not _let_65))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (or))) (let ((_let_70 (not _let_66))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_68) :args (_let_70))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_66))) (REFL :args (_let_67)) :args _let_69)) _let_68 :args (_let_67 true _let_66)))) (let ((_let_72 (REFL :args (_let_65)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 5)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_69)) :args ((or _let_48 _let_65))) _let_71 :args (_let_48 true _let_65)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 4)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_69)) :args ((or _let_50 _let_65))) _let_71 :args (_let_50 true _let_65)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 1)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_69)) :args ((or _let_52 _let_65))) _let_71 :args (_let_52 true _let_65)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 0)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_69)) :args ((or _let_54 _let_65))) _let_71 :args (_let_54 true _let_65)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_53 _let_51 _let_49 _let_47 (not _let_56)))) _let_76 _let_75 _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_56 false _let_57)) :args (_let_47 false _let_54 false _let_52 false _let_50 false _let_48 false _let_56)))) (let ((_let_78 (not _let_47))) (let ((_let_79 (and (tptp.v1_cat_1 _let_9) _let_40 _let_38))) (let ((_let_80 (or _let_55 _let_53 _let_64 _let_62 _let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 3)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) :args _let_69)) :args ((or _let_61 _let_65))) _let_71 :args (_let_61 true _let_65)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 2)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_69)) :args ((or _let_63 _let_65))) _let_71 :args (_let_63 true _let_65)))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_55 _let_53 _let_64 _let_62 _let_79 (not _let_80)))) _let_76 _let_75 _let_82 _let_81 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_80 false _let_57)) :args (_let_79 false _let_54 false _let_52 false _let_63 false _let_61 false _let_80)))) (let ((_let_84 (not _let_79))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_39 _let_37 _let_35 _let_33 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_40 _let_84))) _let_83 :args (_let_40 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 2)) :args ((or _let_38 _let_84))) _let_83 :args (_let_38 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 1)) :args ((or _let_36 _let_78))) _let_77 :args (_let_36 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 2)) :args ((or _let_34 _let_78))) _let_77 :args (_let_34 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_9 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_42 false _let_43)) :args (_let_33 false _let_40 false _let_38 false _let_36 false _let_34 false _let_42)))) (let ((_let_86 (not _let_33))) (let ((_let_87 (and (tptp.v1_cat_1 _let_12) _let_28 _let_26))) (let ((_let_88 (tptp.l1_cat_1 _let_11))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.v2_cat_1 _let_11))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_55 _let_53 _let_91 _let_89 _let_87))) (let ((_let_93 (and _let_90 _let_88))) (let ((_let_94 (or _let_64 _let_62 _let_51 _let_49 _let_93))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_64 _let_62 _let_51 _let_49 _let_93 (not _let_94)))) _let_82 _let_81 _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_46)) :args _let_45)) _let_44 :args (_let_94 false _let_43)) :args (_let_93 false _let_63 false _let_61 false _let_50 false _let_48 false _let_94)))) (let ((_let_96 (not _let_93))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_55 _let_53 _let_91 _let_89 _let_87 (not _let_92)))) _let_76 _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 0)) :args ((or _let_90 _let_96))) _let_95 :args (_let_90 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_93 1)) :args ((or _let_88 _let_96))) _let_95 :args (_let_88 false _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_92 false _let_57)) :args (_let_87 false _let_54 false _let_52 false _let_90 false _let_88 false _let_92)))) (let ((_let_98 (not _let_87))) (let ((_let_99 (not _let_21))) (let ((_let_100 (not _let_18))) (let ((_let_101 (or _let_55 _let_53 _let_64 _let_62 _let_51 _let_49 _let_14))) (let ((_let_102 (forall ((A $$unsorted) (BOUND_VARIABLE_1561 $$unsorted) (BOUND_VARIABLE_1559 $$unsorted)) (or (not (tptp.v2_cat_1 A)) (not (tptp.l1_cat_1 A)) (not (tptp.v2_cat_1 BOUND_VARIABLE_1559)) (not (tptp.l1_cat_1 BOUND_VARIABLE_1559)) (not (tptp.v2_cat_1 BOUND_VARIABLE_1561)) (not (tptp.l1_cat_1 BOUND_VARIABLE_1561)) (tptp.v8_cat_1 (tptp.k17_isocat_2 A BOUND_VARIABLE_1559 BOUND_VARIABLE_1561) (tptp.k12_nattra_1 A (tptp.k11_cat_2 BOUND_VARIABLE_1559 BOUND_VARIABLE_1561)) (tptp.k11_cat_2 (tptp.k12_nattra_1 A BOUND_VARIABLE_1559) (tptp.k12_nattra_1 A BOUND_VARIABLE_1561))))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (or _let_55 _let_53 _let_64 _let_62 _let_51 _let_49 _let_16))) (let ((_let_105 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.v2_cat_1 A)) (not (tptp.l1_cat_1 A)) (not (tptp.v2_cat_1 B)) (not (tptp.l1_cat_1 B)) (not (tptp.v2_cat_1 C)) (not (tptp.l1_cat_1 C)) (tptp.m2_cat_1 (tptp.k17_isocat_2 A B C) (tptp.k12_nattra_1 A (tptp.k11_cat_2 B C)) (tptp.k11_cat_2 (tptp.k12_nattra_1 A B) (tptp.k12_nattra_1 A C))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (_let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_107) :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_cat_1 C _let_12 _let_10) false))))) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_15 _let_100))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_55 _let_53 _let_64 _let_62 _let_51 _let_49 _let_16 (not _let_104)))) _let_76 _let_75 _let_82 _let_81 _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((tptp.k12_nattra_1 A (tptp.k11_cat_2 B C))))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_16 false _let_54 false _let_52 false _let_63 false _let_61 false _let_50 false _let_48 false _let_104)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_55 _let_53 _let_64 _let_62 _let_51 _let_49 _let_14 (not _let_101)))) _let_76 _let_75 _let_82 _let_81 _let_74 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.k12_nattra_1 A (tptp.k11_cat_2 BOUND_VARIABLE_1559 BOUND_VARIABLE_1561))))) :args (_let_102))) _let_103 :args (_let_101 false _let_102)) :args (_let_14 false _let_54 false _let_52 false _let_63 false _let_61 false _let_50 false _let_48 false _let_101)) :args (_let_100 false _let_16 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_21)) (CONG (REFL :args (_let_99)) (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_7))) :args _let_69)) :args ((or _let_20 _let_7 _let_99))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_65 6)) _let_71 :args ((not _let_20) true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_27 _let_25 _let_23 _let_21 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 1)) :args ((or _let_28 _let_98))) _let_97 :args (_let_28 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 2)) :args ((or _let_26 _let_98))) _let_97 :args (_let_26 false _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_33 0)) :args ((or _let_24 _let_86))) _let_85 :args (_let_24 false _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_33 1)) :args ((or _let_22 _let_86))) _let_85 :args (_let_22 false _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_12 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.r1_isocat_1 A BOUND_VARIABLE_1242)))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_21 false _let_28 false _let_26 false _let_24 false _let_22 false _let_30)) :args (_let_7 true _let_20 false _let_21)) :args (false true _let_18 false _let_7)) :args (_let_6 (forall ((A $$unsorted)) (=> (tptp.l1_cat_1 A) (=> (tptp.v1_cat_1 A) (= A (tptp.g1_cat_1 (tptp.u1_cat_1 A) (tptp.u2_cat_1 A) (tptp.u3_cat_1 A) (tptp.u4_cat_1 A) (tptp.u5_cat_1 A) (tptp.u6_cat_1 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.g1_cat_1 A B C D E F))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C B A) (tptp.m1_relset_1 C B A) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m1_relset_1 D B A) (tptp.v1_funct_1 E) (tptp.m1_relset_1 E (tptp.k2_zfmisc_1 B B) B) (tptp.v1_funct_1 F) (tptp.v1_funct_2 F A B) (tptp.m1_relset_1 F A B)) (and (tptp.v1_cat_1 _let_1) (tptp.l1_cat_1 _let_1))))) _let_4 _let_3 _let_2 true true true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u2_cat_1 B))) (let ((_let_2 (tptp.u2_cat_1 A))) (=> (tptp.m2_cat_1 C A B) (and (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 _let_1) (tptp.m2_relset_1 C _let_2 _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted)) (=> (tptp.l1_cat_1 A) (not (tptp.v1_xboole_0 (tptp.u1_cat_1 A))))) (forall ((A $$unsorted)) (=> (tptp.l1_cat_1 A) (not (tptp.v1_xboole_0 (tptp.u2_cat_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_cat_1 A))) (let ((_let_2 (tptp.u2_cat_1 A))) (let ((_let_3 (tptp.u3_cat_1 A))) (=> (tptp.l1_cat_1 A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_cat_1 A))) (let ((_let_2 (tptp.u2_cat_1 A))) (let ((_let_3 (tptp.u4_cat_1 A))) (=> (tptp.l1_cat_1 A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u2_cat_1 A))) (let ((_let_2 (tptp.u5_cat_1 A))) (=> (tptp.l1_cat_1 A) (and (tptp.v1_funct_1 _let_2) (tptp.m2_relset_1 _let_2 (tptp.k2_zfmisc_1 _let_1 _let_1) _let_1)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u2_cat_1 A))) (let ((_let_2 (tptp.u1_cat_1 A))) (let ((_let_3 (tptp.u6_cat_1 A))) (=> (tptp.l1_cat_1 A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (exists ((A $$unsorted)) (tptp.l1_cat_1 A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (exists ((C $$unsorted)) (tptp.m2_cat_1 C A B)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C B A) (tptp.m1_relset_1 C B A) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D B A) (tptp.m1_relset_1 D B A) (tptp.v1_funct_1 E) (tptp.m1_relset_1 E (tptp.k2_zfmisc_1 B B) B) (tptp.v1_funct_1 F) (tptp.v1_funct_2 F A B) (tptp.m1_relset_1 F A B)) (forall ((G $$unsorted) (H $$unsorted) (I $$unsorted) (J $$unsorted) (K $$unsorted) (L $$unsorted)) (=> (= (tptp.g1_cat_1 A B C D E F) (tptp.g1_cat_1 G H I J K L)) (and (= A G) (= B H) (= C I) (= D J) (= E K) (= F L)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (tptp.r1_isocat_1 A A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.v2_cat_1 A) (tptp.l1_cat_1 A) (tptp.v2_cat_1 B) (tptp.l1_cat_1 B)) (=> (tptp.r1_isocat_1 A B) (tptp.r1_isocat_1 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C)) (tptp.v1_xboole_0 C)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.r2_hidden A B) (tptp.v1_xboole_0 B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.v1_xboole_0 A) (not (= A B)) (tptp.v1_xboole_0 B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.10/0.38 )
% 0.10/0.38 % SZS output end Proof for CAT032+1
% 0.10/0.38 % cvc5---1.0.5 exiting
% 0.10/0.38 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------