TSTP Solution File: LAT338+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT338+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 06:04:11 EDT 2023
% Result : Theorem 25.88s 26.44s
% Output : Proof 25.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT338+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n013.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 06:21:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 25.88/26.44 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ptfMNiyE32/cvc5---1.0.5_14420.p...
% 25.88/26.44 ------- get file name : TPTP file name is LAT338+1
% 25.88/26.44 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_14420.smt2...
% 25.88/26.44 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.88/26.44 --- Run --no-e-matching --full-saturate-quant at 5...
% 25.88/26.44 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.88/26.44 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.88/26.44 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.88/26.44 % SZS status Theorem for LAT338+1
% 25.88/26.44 % SZS output start Proof for LAT338+1
% 25.88/26.44 (
% 25.88/26.44 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (forall ((B $$unsorted)) (= (tptp.r2_hidden B (tptp.k8_conlat_1 A)) (and (tptp.v6_conlat_1 B A) (not (tptp.v7_conlat_1 B A)) (tptp.v9_conlat_1 B A) (tptp.l3_conlat_1 B A)))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))))) (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 $$unsorted) (C $$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 $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_6 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (tptp.l2_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_7 (forall ((A $$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))) (=> (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_8 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (tptp.m1_subset_1 (tptp.k16_lattice3 A B) (tptp.u1_struct_0 A)))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (tptp.m1_subset_1 (tptp.k15_lattice3 A B) (tptp.u1_struct_0 A)))))) (let ((_let_12 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_conlat_1 A))) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (= (tptp.k11_conlat_1 A) (tptp.g3_lattices (tptp.k8_conlat_1 A) (tptp.k10_conlat_1 A) (tptp.k9_conlat_1 A))))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (=> (tptp.v3_lattices A) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))))) (let ((_let_15 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k11_conlat_1 A))) (let ((_let_2 (tptp.k15_lattice3 _let_1 B))) (let ((_let_3 (tptp.k16_lattice3 _let_1 B))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 _let_1))) (and (not (tptp.v7_conlat_1 _let_3 A)) (tptp.v9_conlat_1 _let_3 A) (tptp.l3_conlat_1 _let_3 A) (not (tptp.v7_conlat_1 _let_2 A)) (tptp.v9_conlat_1 _let_2 A) (tptp.l3_conlat_1 _let_2 A)))))))))))) (let ((_let_16 (tptp.k11_conlat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (tptp.k15_lattice3 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_18 (tptp.l3_conlat_1 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_19 (tptp.v9_conlat_1 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (tptp.v7_conlat_1 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.k16_lattice3 _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (tptp.l3_conlat_1 _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (tptp.v9_conlat_1 _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (tptp.v7_conlat_1 _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_26 (not _let_25))) (let ((_let_27 (and _let_26 _let_24 _let_23 _let_21 _let_19 _let_18))) (let ((_let_28 (tptp.u1_struct_0 _let_16))) (let ((_let_29 (tptp.l2_conlat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.v3_conlat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (or _let_31 _let_30 (not (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_zfmisc_1 _let_28))) _let_27))) (let ((_let_33 (forall ((A $$unsorted) (BOUND_VARIABLE_1827 $$unsorted)) (let ((_let_1 (tptp.k11_conlat_1 A))) (let ((_let_2 (tptp.k15_lattice3 _let_1 BOUND_VARIABLE_1827))) (let ((_let_3 (tptp.k16_lattice3 _let_1 BOUND_VARIABLE_1827))) (or (tptp.v3_conlat_1 A) (not (tptp.l2_conlat_1 A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1827 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 _let_1)))) (and (not (tptp.v7_conlat_1 _let_3 A)) (tptp.v9_conlat_1 _let_3 A) (tptp.l3_conlat_1 _let_3 A) (not (tptp.v7_conlat_1 _let_2 A)) (tptp.v9_conlat_1 _let_2 A) (tptp.l3_conlat_1 _let_2 A))))))))) (let ((_let_34 (not _let_32))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (or))) (let ((_let_37 (not _let_33))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_35) :args (_let_37))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_33))) (REFL :args (_let_34)) :args _let_36)) _let_35 :args (_let_34 true _let_33)))) (let ((_let_39 (and (tptp.v6_conlat_1 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_21 _let_19 _let_18))) (let ((_let_40 (tptp.k8_conlat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (tptp.r2_hidden _let_17 _let_40))) (let ((_let_42 (= _let_41 _let_39))) (let ((_let_43 (or _let_31 _let_30 _let_42))) (let ((_let_44 (forall ((A $$unsorted) (BOUND_VARIABLE_2657 $$unsorted)) (or (tptp.v3_conlat_1 A) (not (tptp.l2_conlat_1 A)) (= (tptp.r2_hidden BOUND_VARIABLE_2657 (tptp.k8_conlat_1 A)) (and (tptp.v6_conlat_1 BOUND_VARIABLE_2657 A) (not (tptp.v7_conlat_1 BOUND_VARIABLE_2657 A)) (tptp.v9_conlat_1 BOUND_VARIABLE_2657 A) (tptp.l3_conlat_1 BOUND_VARIABLE_2657 A))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (_let_44))) (let ((_let_47 ((tptp.v7_conlat_1 BOUND_VARIABLE_2657 A)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 1)) (CONG (REFL :args (_let_32)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_36)) :args ((or _let_29 _let_32))) _let_38 :args (_let_29 true _let_32)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_32 0)) _let_38 :args ((not _let_31) true _let_32)))) (let ((_let_50 (tptp.r2_hidden _let_17 _let_28))) (let ((_let_51 (= _let_28 _let_40))) (let ((_let_52 (tptp.v1_xboole_0 _let_28))) (let ((_let_53 (tptp.m1_subset_1 _let_17 _let_28))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52 _let_50))) (let ((_let_56 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.m1_subset_1 A B)) (tptp.v1_xboole_0 B) (tptp.r2_hidden A B))))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (_let_56))) (let ((_let_59 ((not (= (tptp.m1_subset_1 A B) false))))) (let ((_let_60 (tptp.l3_lattices _let_16))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.v3_struct_0 _let_16))) (let ((_let_63 (or _let_62 _let_61 _let_53))) (let ((_let_64 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l3_lattices A)) (tptp.m1_subset_1 (tptp.k15_lattice3 A B) (tptp.u1_struct_0 A)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (tptp.v3_lattices _let_16))) (let ((_let_67 (not _let_62))) (let ((_let_68 (and _let_67 _let_66 _let_60))) (let ((_let_69 (or _let_31 _let_30 _let_68))) (let ((_let_70 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_conlat_1 A))) (or (tptp.v3_conlat_1 A) (not (tptp.l2_conlat_1 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_31 _let_30 _let_68 (not _let_69)))) _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_conlat_1 A) true))))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_68 true _let_31 false _let_29 false _let_69)))) (let ((_let_73 (not _let_68))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 0)) :args ((or _let_67 _let_73))) _let_72 :args (_let_67 false _let_68)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 2)) :args ((or _let_60 _let_73))) _let_72 :args (_let_60 false _let_68)))) (let ((_let_76 (not _let_52))) (let ((_let_77 (tptp.l1_struct_0 _let_16))) (let ((_let_78 (not _let_77))) (let ((_let_79 (or _let_62 _let_78 _let_76))) (let ((_let_80 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (tptp.l1_lattices _let_16))) (let ((_let_83 (not _let_82))) (let ((_let_84 (or _let_83 _let_77))) (let ((_let_85 (forall ((A $$unsorted)) (or (not (tptp.l1_lattices A)) (tptp.l1_struct_0 A))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_16 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_88 (tptp.l2_lattices _let_16))) (let ((_let_89 (and _let_82 _let_88))) (let ((_let_90 (or _let_61 _let_89))) (let ((_let_91 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_61 _let_89 (not _let_90)))) _let_75 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args _let_87) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_89 false _let_60 false _let_90)))) (let ((_let_94 (not _let_89))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_89 0)) :args ((or _let_82 _let_94))) _let_93 :args (_let_82 false _let_89)))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_62 _let_78 _let_76 (not _let_79)))) _let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_83 _let_77 (not _let_84)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args _let_87) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_77 false _let_82 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.u1_struct_0 A)))) :args (_let_80))) _let_81 :args (_let_79 false _let_80)) :args (_let_76 true _let_62 false _let_77 false _let_79)))) (let ((_let_97 (tptp.k9_conlat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_98 (tptp.u1_lattices _let_16))) (let ((_let_99 (tptp.k10_conlat_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_100 (tptp.u2_lattices _let_16))) (let ((_let_101 (and _let_51 (= _let_100 _let_99) (= _let_98 _let_97)))) (let ((_let_102 (tptp.g3_lattices _let_40 _let_99 _let_97))) (let ((_let_103 (tptp.g3_lattices _let_28 _let_100 _let_98))) (let ((_let_104 (= _let_103 _let_102))) (let ((_let_105 (not _let_104))) (let ((_let_106 (tptp.k2_zfmisc_1 _let_28 _let_28))) (let ((_let_107 (tptp.m1_relset_1 _let_98 _let_106 _let_28))) (let ((_let_108 (not _let_107))) (let ((_let_109 (tptp.v1_funct_2 _let_98 _let_106 _let_28))) (let ((_let_110 (not _let_109))) (let ((_let_111 (tptp.v1_funct_1 _let_98))) (let ((_let_112 (not _let_111))) (let ((_let_113 (tptp.m1_relset_1 _let_100 _let_106 _let_28))) (let ((_let_114 (not _let_113))) (let ((_let_115 (tptp.v1_funct_2 _let_100 _let_106 _let_28))) (let ((_let_116 (not _let_115))) (let ((_let_117 (tptp.v1_funct_1 _let_100))) (let ((_let_118 (not _let_117))) (let ((_let_119 (or _let_118 _let_116 _let_114 _let_112 _let_110 _let_108 _let_105 _let_101))) (let ((_let_120 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2377 $$unsorted) (BOUND_VARIABLE_2375 $$unsorted) (BOUND_VARIABLE_2373 $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (or (not (tptp.v1_funct_1 B)) (not (tptp.v1_funct_2 B _let_1 A)) (not (tptp.m1_relset_1 B _let_1 A)) (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C _let_1 A)) (not (tptp.m1_relset_1 C _let_1 A)) (not (= (tptp.g3_lattices A B C) (tptp.g3_lattices BOUND_VARIABLE_2373 BOUND_VARIABLE_2375 BOUND_VARIABLE_2377))) (and (= A BOUND_VARIABLE_2373) (= B BOUND_VARIABLE_2375) (= C BOUND_VARIABLE_2377))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (= _let_16 _let_102))) (let ((_let_123 (= _let_16 _let_103))) (let ((_let_124 (or _let_31 _let_30 _let_122))) (let ((_let_125 (forall ((A $$unsorted)) (or (tptp.v3_conlat_1 A) (not (tptp.l2_conlat_1 A)) (= (tptp.k11_conlat_1 A) (tptp.g3_lattices (tptp.k8_conlat_1 A) (tptp.k10_conlat_1 A) (tptp.k9_conlat_1 A))))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT 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$$unsorted)) (=> (tptp.l3_conlat_1 B A) (tptp.v8_conlat_1 B A))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)) (and _let_1 (tptp.v10_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)) (and _let_1 (tptp.v15_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v15_lattices A)) (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.v1_xboole_0 B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.v1_funct_2 C A B))) (let ((_let_2 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_2 _let_1) (and _let_2 (not (tptp.v1_xboole_0 C)) (tptp.v1_partfun1 C A B) _let_1)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.k16_lattice3 A B) (tptp.k15_lattice3 A (tptp.a_2_1_lattice3 A B)))))) _let_13 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_conlat_1 A B C))) (=> (and (tptp.l1_conlat_1 A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_conlat_1 A))) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u2_conlat_1 A)))) (and (tptp.v6_conlat_1 _let_1 A) (tptp.l3_conlat_1 _let_1 A))))) (forall ((A $$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)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k8_conlat_1 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k10_conlat_1 A))) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) _let_12 _let_11 _let_10 true true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (not (tptp.v1_xboole_0 (tptp.k7_conlat_1 A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (tptp.m1_conlat_1 (tptp.k8_conlat_1 A) A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k8_conlat_1 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k9_conlat_1 A))) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_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))))))) true _let_9 true (forall ((A $$unsorted)) (=> (tptp.l2_conlat_1 A) (tptp.l1_conlat_1 A))) (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) true _let_8 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (forall ((B $$unsorted)) (=> (tptp.m1_conlat_1 B A) (not (tptp.v1_xboole_0 B)))))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) true _let_7 true true _let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.l1_conlat_1 A) (tptp.l3_conlat_1 B A)) (tptp.m1_subset_1 (tptp.u4_conlat_1 A B) (tptp.k1_zfmisc_1 (tptp.u1_conlat_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.l1_conlat_1 A) (tptp.l3_conlat_1 B A)) (tptp.m1_subset_1 (tptp.u5_conlat_1 A B) (tptp.k1_zfmisc_1 (tptp.u2_conlat_1 A))))) (exists ((A $$unsorted)) (tptp.l1_conlat_1 A)) (exists ((A $$unsorted)) (tptp.l1_lattices A)) (exists ((A $$unsorted)) (tptp.l1_struct_0 A)) (exists ((A $$unsorted)) (tptp.l2_conlat_1 A)) (exists ((A $$unsorted)) (tptp.l2_lattices A)) (forall ((A $$unsorted)) (=> (tptp.l1_conlat_1 A) (exists ((B $$unsorted)) (tptp.l3_conlat_1 B A)))) (exists ((A $$unsorted)) (tptp.l3_lattices A)) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (exists ((B $$unsorted)) (tptp.m1_conlat_1 B A)))) (forall ((A $$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)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l1_conlat_1 A)) (not (tptp.v1_xboole_0 (tptp.u2_conlat_1 A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_conlat_1 A))) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.v13_lattices _let_1) (tptp.v14_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v4_lattice3 _let_1))))) _let_5 (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l1_conlat_1 A)) (not (tptp.v1_xboole_0 (tptp.u1_conlat_1 A))))) (forall ((A $$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 $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (not (tptp.v1_xboole_0 (tptp.k7_conlat_1 A))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_conlat_1 A))) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 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))))) (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.k11_conlat_1 A))) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 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.v4_lattice3 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.l3_lattices B)) (= (tptp.r2_hidden A (tptp.a_2_1_lattice3 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (= A D) (tptp.r3_lattice3 B D C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.l1_conlat_1 A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_conlat_1 A))) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u2_conlat_1 A)))) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.g3_conlat_1 A B C) (tptp.g3_conlat_1 D E F)) (and (= A D) (= B E) (= C F)))))) _let_4 (forall ((A $$unsorted)) (=> (tptp.l1_conlat_1 A) (exists ((B $$unsorted)) (and (tptp.l3_conlat_1 B A) (tptp.v6_conlat_1 B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l1_conlat_1 A)) (exists ((B $$unsorted)) (and (tptp.l3_conlat_1 B A) (tptp.v6_conlat_1 B A) (not (tptp.v7_conlat_1 B A)))))) (exists ((A $$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))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l1_conlat_1 A)) (exists ((B $$unsorted)) (and (tptp.l3_conlat_1 B A) (tptp.v6_conlat_1 B A) (tptp.v8_conlat_1 B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (exists ((B $$unsorted)) (and (tptp.l3_conlat_1 B A) (not (tptp.v7_conlat_1 B A)) (tptp.v9_conlat_1 B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (exists ((B $$unsorted)) (and (tptp.l3_conlat_1 B A) (tptp.v6_conlat_1 B A) (not (tptp.v7_conlat_1 B A)) (tptp.v9_conlat_1 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C A B)))) (forall ((A $$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)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (forall ((A $$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 $$unsorted)) (and (tptp.l3_lattices A) (tptp.v3_lattices A))) (exists ((A $$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 $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l1_conlat_1 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_conlat_1 A))) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l1_conlat_1 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u2_conlat_1 A))) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (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))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_conlat_1 A)) (tptp.l2_conlat_1 A)) (= (tptp.k8_conlat_1 A) (tptp.k7_conlat_1 A)))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.r2_hidden C B))) (= A B))) _let_1 (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)))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.88/26.44 )
% 25.88/26.44 % SZS output end Proof for LAT338+1
% 25.88/26.44 % cvc5---1.0.5 exiting
% 25.88/26.44 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------