TSTP Solution File: SEU450+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU450+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 16:31:52 EDT 2023
% Result : Theorem 3.35s 3.59s
% Output : Proof 3.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SEU450+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Wed Aug 23 17:53:37 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.42 %----Proving TF0_NAR, FOF, or CNF
% 3.35/3.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.62xRICfdxf/cvc5---1.0.5_32130.p...
% 3.35/3.59 ------- get file name : TPTP file name is SEU450+1
% 3.35/3.59 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32130.smt2...
% 3.35/3.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.35/3.59 % SZS status Theorem for SEU450+1
% 3.35/3.59 % SZS output start Proof for SEU450+1
% 3.35/3.59 (
% 3.35/3.59 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 B)) (forall ((E $$unsorted)) (=> (tptp.m2_relset_1 E A B) (= (tptp.r1_tarski C (tptp.k8_relset_2 B A D (tptp.k6_relset_1 A B E))) (tptp.r1_tarski D (tptp.k8_relset_2 A B C E))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 A)) (forall ((E $$unsorted)) (=> (tptp.m1_subset_1 E (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (=> (tptp.r1_tarski C D) (tptp.r1_tarski (tptp.k8_relset_2 A B D E) (tptp.k8_relset_2 A B C E))))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_4 (tptp.v1_relat_1 tptp.k1_xboole_0))) (let ((_let_5 (tptp.v1_xboole_0 tptp.k1_xboole_0))) (let ((_let_6 (forall ((A $$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))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B)))) (tptp.m1_subset_1 (tptp.k8_relset_2 A B C D) (tptp.k1_zfmisc_1 B)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (tptp.m2_relset_1 (tptp.k6_relset_1 A B C) B A))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.r1_tarski A B) (tptp.r1_tarski B A)))))) (let ((_let_10 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 B)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.k6_relset_1 A B E))) (let ((_let_2 (tptp.k8_relset_2 B A D _let_1))) (let ((_let_3 (tptp.k8_relset_2 A B C E))) (=> (tptp.m2_relset_1 E A B) (and (= _let_3 (tptp.k8_relset_2 A B (tptp.k8_relset_2 B A _let_3 _let_1) E)) (= _let_2 (tptp.k8_relset_2 B A (tptp.k8_relset_2 A B _let_2 E) _let_1))))))))))))))) (let ((_let_11 (tptp.k6_relset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_12 (tptp.k8_relset_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.k8_relset_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 _let_11))) (let ((_let_14 (tptp.k8_relset_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (= _let_12 _let_14))) (let ((_let_16 (tptp.r1_tarski _let_12 _let_14))) (let ((_let_17 (tptp.r1_tarski _let_14 _let_12))) (let ((_let_18 (and _let_17 _let_16))) (let ((_let_19 (= _let_15 _let_18))) (let ((_let_20 (tptp.k8_relset_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11))) (let ((_let_21 (tptp.k8_relset_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (tptp.k8_relset_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_21 _let_11))) (let ((_let_23 (= _let_20 _let_22))) (let ((_let_24 (and _let_15 _let_23))) (let ((_let_25 (tptp.r1_tarski _let_22 _let_20))) (let ((_let_26 (tptp.r1_tarski _let_20 _let_22))) (let ((_let_27 (and _let_26 _let_25))) (let ((_let_28 (= _let_23 _let_27))) (let ((_let_29 (_let_9))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 ((tptp.r1_tarski A B)))) (let ((_let_32 (tptp.r1_tarski _let_21 _let_21))) (let ((_let_33 (= _let_32 _let_26))) (let ((_let_34 (tptp.m2_relset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.k1_zfmisc_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_37 (tptp.m1_subset_1 _let_21 _let_36))) (let ((_let_38 (not _let_37))) (let ((_let_39 (tptp.k1_zfmisc_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_40 (tptp.m1_subset_1 _let_20 _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_38 _let_35 _let_33))) (let ((_let_43 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1481 $$unsorted) (BOUND_VARIABLE_1479 $$unsorted)) (or (not (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A))) (not (tptp.m1_subset_1 BOUND_VARIABLE_1479 (tptp.k1_zfmisc_1 B))) (not (tptp.m2_relset_1 BOUND_VARIABLE_1481 A B)) (= (tptp.r1_tarski C (tptp.k8_relset_2 B A BOUND_VARIABLE_1479 (tptp.k6_relset_1 A B BOUND_VARIABLE_1481))) (tptp.r1_tarski BOUND_VARIABLE_1479 (tptp.k8_relset_2 A B C BOUND_VARIABLE_1481))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (_let_43))) (let ((_let_46 (tptp.k8_relset_2 B A BOUND_VARIABLE_1479 (tptp.k6_relset_1 A B BOUND_VARIABLE_1481)))) (let ((_let_47 (_let_46 (not (= (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) false))))) (let ((_let_48 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_41 _let_49 _let_37))) (let ((_let_51 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A))) (not (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B)))) (tptp.m1_subset_1 (tptp.k8_relset_2 A B C D) (tptp.k1_zfmisc_1 B)))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (_let_51))) (let ((_let_54 ((tptp.k8_relset_2 A B C D)))) (let ((_let_55 (tptp.m1_subset_1 _let_11 (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_36))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_40))) (let ((_let_60 (tptp.m2_relset_1 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_55))) (let ((_let_63 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.m2_relset_1 C A B)) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 ((not (= (tptp.m2_relset_1 C A B) false))))) (let ((_let_67 (tptp.m1_relset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_60))) (let ((_let_70 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.m1_relset_1 C A B)) (tptp.m2_relset_1 (tptp.k6_relset_1 A B C) B A))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (= _let_34 _let_67))) (let ((_let_73 (_let_3))) (let ((_let_74 (ASSUME :args _let_73))) (let ((_let_75 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_39))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_58 _let_35 _let_24))) (let ((_let_78 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1155 $$unsorted) (BOUND_VARIABLE_1153 $$unsorted)) (let ((_let_1 (tptp.k6_relset_1 A B BOUND_VARIABLE_1155))) (let ((_let_2 (tptp.k8_relset_2 B A BOUND_VARIABLE_1153 _let_1))) (let ((_let_3 (tptp.k8_relset_2 A B C BOUND_VARIABLE_1155))) (or (not (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A))) (not (tptp.m1_subset_1 BOUND_VARIABLE_1153 (tptp.k1_zfmisc_1 B))) (not (tptp.m2_relset_1 BOUND_VARIABLE_1155 A B)) (and (= _let_3 (tptp.k8_relset_2 A B (tptp.k8_relset_2 B A _let_3 _let_1) BOUND_VARIABLE_1155)) (= _let_2 (tptp.k8_relset_2 B A (tptp.k8_relset_2 A B _let_2 BOUND_VARIABLE_1155) _let_1)))))))))) (let ((_let_79 (not _let_77))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (or))) (let ((_let_82 (not _let_78))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_80) :args (_let_82))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_78))) (REFL :args (_let_79)) :args _let_81)) _let_80 :args (_let_79 true _let_78)))) (let ((_let_84 (REFL :args (_let_77)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 2)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_81)) :args ((or _let_34 _let_77))) _let_83 :args (_let_34 true _let_77)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_55 _let_61 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_60 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_72)) :args ((or _let_35 _let_67 (not _let_72)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.m2_relset_1 C A B)))) :args _let_73)) _let_74 :args (_let_72 false _let_3)) :args (_let_67 false _let_34 false _let_72)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k6_relset_1 A B C)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_60 false _let_67 false _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_62 false _let_63)) :args (_let_55 false _let_60 false _let_62)))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 1)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_81)) :args ((or _let_57 _let_77))) _let_83 :args (_let_57 true _let_77)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_58 _let_40 _let_56 (not _let_59)))) _let_87 _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53)) _let_52 :args (_let_59 false _let_51)) :args (_let_40 false _let_57 false _let_55 false _let_59)))) (let ((_let_89 (or _let_35 _let_48))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_35 _let_48 (not _let_89)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_65)) _let_64 :args (_let_89 false _let_63)) :args (_let_48 false _let_34 false _let_89)))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_49 _let_41 _let_37 (not _let_50)))) _let_90 _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53)) _let_52 :args (_let_50 false _let_51)) :args (_let_37 false _let_48 false _let_40 false _let_50)))) (let ((_let_92 (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_58 _let_38 _let_93 _let_56 _let_25))) (let ((_let_95 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1419 $$unsorted) (BOUND_VARIABLE_1417 $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1417 _let_1)) (not (tptp.r1_tarski C BOUND_VARIABLE_1417)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1419 (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B)))) (tptp.r1_tarski (tptp.k8_relset_2 A B BOUND_VARIABLE_1417 BOUND_VARIABLE_1419) (tptp.k8_relset_2 A B C BOUND_VARIABLE_1419))))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (_let_95))) (let ((_let_98 ((not (= (tptp.r1_tarski (tptp.k8_relset_2 A B BOUND_VARIABLE_1417 BOUND_VARIABLE_1419) (tptp.k8_relset_2 A B C BOUND_VARIABLE_1419)) true))))) (let ((_let_99 (tptp.r1_tarski _let_20 _let_20))) (let ((_let_100 (= _let_99 _let_92))) (let ((_let_101 (or _let_41 _let_58 _let_35 _let_100))) (let ((_let_102 ((tptp.r1_tarski C _let_46)))) (let ((_let_103 (tptp.r1_tarski _let_13 _let_13))) (let ((_let_104 (= _let_103 _let_16))) (let ((_let_105 (tptp.m1_subset_1 _let_12 _let_36))) (let ((_let_106 (not _let_105))) (let ((_let_107 (tptp.m1_subset_1 _let_13 _let_39))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_108 _let_106 _let_35 _let_104))) (let ((_let_110 (or _let_76 _let_49 _let_105))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 0)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_81)) :args ((or _let_75 _let_77))) _let_83 :args (_let_75 true _let_77)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_76 _let_49 _let_105 (not _let_110)))) _let_111 _let_90 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53)) _let_52 :args (_let_110 false _let_51)) :args (_let_105 false _let_75 false _let_48 false _let_110)))) (let ((_let_113 (or _let_106 _let_56 _let_107))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_107 _let_56 _let_106 (not _let_113)))) _let_86 _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_54)) :args _let_53)) _let_52 :args (_let_113 false _let_51)) :args (_let_107 false _let_55 false _let_105 false _let_113)))) (let ((_let_115 (tptp.r1_tarski SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13))) (let ((_let_116 (not _let_115))) (let ((_let_117 (or _let_76 _let_108 _let_116 _let_49 _let_17))) (let ((_let_118 (tptp.r1_tarski _let_12 _let_12))) (let ((_let_119 (= _let_118 _let_115))) (let ((_let_120 (or _let_76 _let_106 _let_35 _let_119))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_19)) :args ((or _let_15 (not _let_18) (not _let_19)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_14 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29))) _let_30 :args (_let_19 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_18)) :args ((or (not _let_17) (not _let_16) _let_18))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_76 _let_49 _let_108 _let_116 _let_17 (not _let_117)))) _let_111 _let_90 _let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_119)) :args ((or (not _let_118) _let_115 (not _let_119)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_12 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29))) _let_30 :args (_let_118 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_76 _let_35 _let_106 _let_119 (not _let_120)))) _let_111 _let_85 _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12 QUANTIFIERS_INST_E_MATCHING _let_47)) :args _let_45))) _let_44 :args (_let_120 false _let_43)) :args (_let_119 false _let_75 false _let_34 false _let_105 false _let_120)) :args (_let_115 false _let_118 false _let_119)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_13 QUANTIFIERS_INST_E_MATCHING _let_98)) :args _let_97)) _let_96 :args (_let_117 false _let_95)) :args (_let_17 false _let_75 false _let_48 false _let_107 false _let_115 false _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_104)) :args ((or (not _let_103) _let_16 (not _let_104)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_13 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29))) _let_30 :args (_let_103 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_35 _let_108 _let_106 _let_104 (not _let_109)))) _let_85 _let_114 _let_112 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_12 QUANTIFIERS_INST_E_MATCHING _let_102)) :args _let_45)) _let_44 :args (_let_109 false _let_43)) :args (_let_104 false _let_34 false _let_107 false _let_105 false _let_109)) :args (_let_16 false _let_103 false _let_104)) :args (_let_18 false _let_17 false _let_16)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_24)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_77 3)) _let_83 :args ((not _let_24) true _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_28)) :args ((or _let_23 (not _let_27) (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_27)) :args ((or (not _let_25) (not _let_26) _let_27))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_58 _let_56 _let_38 _let_25 _let_93 (not _let_94)))) _let_87 _let_86 _let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_100)) :args ((or (not _let_99) _let_92 (not _let_100)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_20 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29))) _let_30 :args (_let_99 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_58 _let_35 _let_41 _let_100 (not _let_101)))) _let_87 _let_85 _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING _let_102)) :args _let_45)) _let_44 :args (_let_101 false _let_43)) :args (_let_100 false _let_57 false _let_34 false _let_40 false _let_101)) :args (_let_92 false _let_99 false _let_100)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_11 _let_21 QUANTIFIERS_INST_E_MATCHING _let_98)) :args _let_97)) _let_96 :args (_let_94 false _let_95)) :args (_let_25 false _let_57 false _let_55 false _let_37 false _let_92 false _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or (not _let_32) _let_26 (not _let_33)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_21 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29))) _let_30 :args (_let_32 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_35 _let_41 _let_38 _let_33 (not _let_42)))) _let_85 _let_88 _let_91 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_44 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_21 QUANTIFIERS_INST_E_MATCHING _let_47)) :args _let_45))) _let_44 :args (_let_42 false _let_43)) :args (_let_33 false _let_34 false _let_40 false _let_37 false _let_42)) :args (_let_26 false _let_32 false _let_33)) :args (_let_27 false _let_25 false _let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_20 _let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_31)) :args _let_29)) _let_30 :args (_let_28 false _let_9)) :args (_let_23 false _let_27 false _let_28)) :args ((not _let_15) true _let_24 false _let_23)) :args (false false _let_19 false _let_18 true _let_15)) :args (_let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_relat_1 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) _let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (= (tptp.k7_relset_2 A B C D) (tptp.k8_setfam_1 B (tptp.k4_relset_2 (tptp.k1_zfmisc_1 A) B (tptp.k6_relset_2 B A D) (tptp.k3_pua2mss1 C)))))))) true true true (forall ((A $$unsorted)) (tptp.m1_eqrel_1 (tptp.k3_pua2mss1 A) A)) (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k4_relat_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 B))) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A _let_1))) (tptp.m1_subset_1 (tptp.k4_relset_2 A B C D) (tptp.k1_zfmisc_1 _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k5_relset_2 A B))) (=> (tptp.v1_relat_1 B) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (let ((_let_2 (tptp.k1_zfmisc_1 B))) (let ((_let_3 (tptp.k6_relset_2 A B C))) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 B 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))))))) true _let_7 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 _let_1)) (tptp.m1_subset_1 (tptp.k8_setfam_1 A B) _let_1)))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_eqrel_1 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 A))))) true true _let_6 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_eqrel_1 B 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 $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k4_relat_1 A))) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_xboole_0 _let_1) (tptp.v1_relat_1 _let_1))))) (and _let_5 _let_4 (tptp.v3_relat_1 tptp.k1_xboole_0)) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.v1_relat_1 (tptp.k2_zfmisc_1 A B))) (and _let_5 _let_4) (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 $$unsorted)) (=> (tptp.v1_relat_1 A) (= (tptp.k4_relat_1 (tptp.k4_relat_1 A)) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k6_relset_1 A B (tptp.k6_relset_1 A B C)) C))) (exists ((A $$unsorted)) (and (tptp.v1_xboole_0 A) (tptp.v1_relat_1 A))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_relat_1 A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v3_relat_1 A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A (tptp.k1_zfmisc_1 B)))) (= (tptp.k4_relset_2 A B C D) (tptp.k9_relat_1 C D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_relset_1 C A B) (= (tptp.k6_relset_1 A B C) (tptp.k4_relat_1 C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 B A))) (= (tptp.k6_relset_2 A B C) (tptp.k5_relset_2 B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 A)) (tptp.m1_subset_1 D (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B)))) (= (tptp.k8_relset_2 A B C D) (tptp.k7_relset_2 A B C D)))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A 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)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) (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)))) _let_1 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.35/3.60 )
% 3.35/3.60 % SZS output end Proof for SEU450+1
% 3.35/3.60 % cvc5---1.0.5 exiting
% 3.35/3.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------