TSTP Solution File: LAT324+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT324+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 06:04:03 EDT 2023
% Result : Theorem 40.98s 41.25s
% Output : Proof 40.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LAT324+1 : TPTP v8.1.2. Released v3.4.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.16/0.36 % Computer : n023.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu Aug 24 06:35:12 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 40.98/41.25 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.hGqB8EObwO/cvc5---1.0.5_23965.p...
% 40.98/41.25 ------- get file name : TPTP file name is LAT324+1
% 40.98/41.25 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23965.smt2...
% 40.98/41.25 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 40.98/41.25 --- Run --no-e-matching --full-saturate-quant at 5...
% 40.98/41.25 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 40.98/41.25 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 40.98/41.25 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 40.98/41.25 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 40.98/41.25 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.98/41.25 % SZS status Theorem for LAT324+1
% 40.98/41.25 % SZS output start Proof for LAT324+1
% 40.98/41.25 (
% 40.98/41.25 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (not (and (not (= B C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden C D))) (let ((_let_2 (tptp.r2_hidden B D))) (=> (tptp.m1_filter_0 D A) (not (and (tptp.v1_filter_0 D A) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))))))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (= (tptp.r2_filter_2 A B) (tptp.v1_filter_0 (tptp.k15_filter_2 A B) (tptp.k1_lattice2 A))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (= (tptp.k15_filter_2 A B) (tptp.k7_filter_2 A B)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B (tptp.k1_lattice2 A))) (= (tptp.k14_filter_2 A B) (tptp.k8_filter_2 A B)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m1_relset_1 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))))) (let ((_let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.v11_lattices _let_1) (tptp.v12_lattices _let_1) (tptp.v13_lattices _let_1) (tptp.v14_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v16_lattices _let_1) (tptp.v17_lattices _let_1))))))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (tptp.l2_lattices 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))))))))) (let ((_let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (tptp.l1_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_13 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.l3_lattices A) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B (tptp.k1_lattice2 A))) (tptp.m2_filter_2 (tptp.k14_filter_2 A B) A))))) (let ((_let_15 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A)))) (= (tptp.k8_filter_2 A B) B))))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (= (tptp.k7_filter_2 A B) B))))))) (let ((_let_17 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (= (tptp.k1_lattice2 A) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A))))))) (let ((_let_18 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (=> (tptp.v3_lattices A) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))))) (let ((_let_19 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (not (and (not (= B C)) (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden C D))) (let ((_let_2 (tptp.r2_hidden B D))) (=> (tptp.m2_filter_2 D A) (not (and (tptp.r2_filter_2 A D) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1))))))))))))))))))) (let ((_let_20 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (tptp.v1_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 _let_20))) (let ((_let_22 (tptp.k15_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214))) (let ((_let_23 (tptp.k7_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214))) (let ((_let_24 (= _let_23 _let_22))) (let ((_let_25 (tptp.v1_filter_0 _let_22 _let_20))) (let ((_let_26 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 _let_23))) (let ((_let_27 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214))) (let ((_let_28 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214))) (let ((_let_29 (and (or (not _let_28) _let_27) (or _let_28 (not _let_27))))) (let ((_let_30 (not _let_21))) (let ((_let_31 (tptp.m1_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_214 _let_20))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30 _let_29))) (let ((_let_34 (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 D))) (let ((_let_2 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 D))) (let ((_let_3 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.m1_filter_0 D _let_3)) (not (tptp.v1_filter_0 D _let_3)) (and (or (not _let_2) _let_1) (or _let_2 (not _let_1)))))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (not _let_34))) (let ((_let_37 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (tptp.u1_struct_0 _let_20))) (let ((_let_39 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_38))) (let ((_let_40 (not _let_39))) (let ((_let_41 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_38))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.l3_lattices _let_20))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.v17_lattices _let_20))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.v10_lattices _let_20))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.v3_struct_0 _let_20))) (let ((_let_50 (or _let_49 _let_48 _let_46 _let_44 _let_42 _let_40 _let_37 _let_36))) (let ((_let_51 (forall ((A $$unsorted) (BOUND_VARIABLE_2838 $$unsorted) (BOUND_VARIABLE_2836 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2836 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2838 _let_1)) (= BOUND_VARIABLE_2836 BOUND_VARIABLE_2838) (not (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden BOUND_VARIABLE_2838 D))) (let ((_let_2 (tptp.r2_hidden BOUND_VARIABLE_2836 D))) (or (not (tptp.m1_filter_0 D A)) (not (tptp.v1_filter_0 D A)) (and (or (not _let_2) _let_1) (or _let_2 (not _let_1))))))))))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (tptp.u1_struct_0 A))) (let ((_let_54 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_55 (= _let_54 _let_38))) (let ((_let_56 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_54))) (let ((_let_57 (tptp.u1_lattices _let_20))) (let ((_let_58 (tptp.u2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_59 (tptp.u2_lattices _let_20))) (let ((_let_60 (tptp.u1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_61 (and _let_55 (= _let_60 _let_59) (= _let_58 _let_57)))) (let ((_let_62 (tptp.g3_lattices _let_38 _let_59 _let_57))) (let ((_let_63 (tptp.g3_lattices _let_54 _let_60 _let_58))) (let ((_let_64 (= _let_63 _let_62))) (let ((_let_65 (not _let_64))) (let ((_let_66 (tptp.k2_zfmisc_1 _let_54 _let_54))) (let ((_let_67 (tptp.m1_relset_1 _let_58 _let_66 _let_54))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.v1_funct_2 _let_58 _let_66 _let_54))) (let ((_let_70 (not _let_69))) (let ((_let_71 (tptp.v1_funct_1 _let_58))) (let ((_let_72 (not _let_71))) (let ((_let_73 (tptp.m1_relset_1 _let_60 _let_66 _let_54))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.v1_funct_2 _let_60 _let_66 _let_54))) (let ((_let_76 (not _let_75))) (let ((_let_77 (tptp.v1_funct_1 _let_60))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_78 _let_76 _let_74 _let_72 _let_70 _let_68 _let_65 _let_61))) (let ((_let_80 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2474 $$unsorted) (BOUND_VARIABLE_2472 $$unsorted) (BOUND_VARIABLE_2470 $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (or (not (tptp.v1_funct_1 B)) (not (tptp.v1_funct_2 B _let_1 A)) (not (tptp.m1_relset_1 B _let_1 A)) (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C _let_1 A)) (not (tptp.m1_relset_1 C _let_1 A)) (not (= (tptp.g3_lattices A B C) (tptp.g3_lattices BOUND_VARIABLE_2470 BOUND_VARIABLE_2472 BOUND_VARIABLE_2474))) (and (= A BOUND_VARIABLE_2470) (= B BOUND_VARIABLE_2472) (= C BOUND_VARIABLE_2474))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (= _let_20 _let_62))) (let ((_let_83 (= _let_20 _let_63))) (let ((_let_84 (tptp.v3_lattices _let_20))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_44 _let_85 _let_82))) (let ((_let_87 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (not (tptp.v3_lattices A)) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (and _let_84 _let_43))) (let ((_let_90 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_89))) (let ((_let_93 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (not (tptp.l3_lattices A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 D))) (let ((_let_2 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 D))) (or (not (tptp.m2_filter_2 D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.r2_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 D)) (and (or (not _let_2) _let_1) (or _let_2 (not _let_1))))))))) (let ((_let_96 (not _let_95))) (let ((_let_97 (not _let_56))) (let ((_let_98 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_54))) (let ((_let_99 (not _let_98))) (let ((_let_100 (tptp.v17_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_101 (not _let_100))) (let ((_let_102 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_105 (or _let_104 _let_103 _let_101 _let_91 _let_99 _let_97 _let_37 _let_96))) (let ((_let_106 (forall ((A $$unsorted) (BOUND_VARIABLE_1908 $$unsorted) (BOUND_VARIABLE_1906 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1906 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1908 _let_1)) (= BOUND_VARIABLE_1906 BOUND_VARIABLE_1908) (not (forall ((D $$unsorted)) (let ((_let_1 (tptp.r2_hidden BOUND_VARIABLE_1908 D))) (let ((_let_2 (tptp.r2_hidden BOUND_VARIABLE_1906 D))) (or (not (tptp.m2_filter_2 D A)) (not (tptp.r2_filter_2 A D)) (and (or (not _let_2) _let_1) (or _let_2 (not _let_1))))))))))))) (let ((_let_107 (not _let_105))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (or))) (let ((_let_110 (not _let_106))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_108) :args (_let_110)) (REWRITE :args ((=> _let_110 (not (or _let_104 _let_103 _let_101 _let_91 _let_99 _let_97 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_96))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_110) _let_106))) (REFL :args (_let_107)) :args _let_109)) _let_108 :args (_let_107 true _let_106)))) (let ((_let_112 (REFL :args (_let_105)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_105 3)) (CONG _let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) :args _let_109)) :args ((or _let_90 _let_105))) _let_111 :args 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A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v11_lattices A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v12_lattices A))))))) _let_17 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k5_filter_2 A B) B))))) _let_16 _let_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_14 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (tptp.m1_filter_2 (tptp.k15_filter_2 A B) (tptp.k1_lattice2 A)))) _let_13 true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m1_subset_1 (tptp.k5_filter_2 A B) (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (tptp.m1_subset_1 (tptp.k7_filter_2 A B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (tptp.m1_subset_1 (tptp.k8_filter_2 A B) (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))) (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _let_12 _let_11 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) _let_10 true _let_9 (exists ((A $$unsorted)) (tptp.l1_lattices A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (exists ((A $$unsorted)) (tptp.l2_lattices A)) (exists ((A $$unsorted)) (tptp.l3_lattices A)) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_0 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_2 B A)))) (forall ((A $$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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_filter_2 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_lattice4 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v1_xboole_0 (tptp.k7_filter_2 A B))))) _let_8 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))) (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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 (tptp.k1_lattice2 A))))) (not (tptp.v1_xboole_0 (tptp.k8_filter_2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) _let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$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)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))) _let_6 (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v12_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v17_lattices A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (tptp.m2_lattice4 B A) (not (tptp.v1_xboole_0 B)))))) (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 $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_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 $$unsorted)) (not (tptp.v1_xboole_0 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A))) _let_5 _let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m1_filter_2 B A) (tptp.m1_filter_0 B A))))) _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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 40.98/41.27 )
% 40.98/41.27 % SZS output end Proof for LAT324+1
% 40.98/41.27 % cvc5---1.0.5 exiting
% 40.98/41.27 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------