%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LAT322+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 06:04:01 EDT 2023

% Result   : Theorem 26.84s 27.18s
% Output   : Proof 26.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT322+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 04:30:17 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  %----Proving TF0_NAR, FOF, or CNF
% 26.84/27.18  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ArwdefYA23/cvc5---1.0.5_7688.p...
% 26.84/27.18  ------- get file name : TPTP file name is LAT322+1
% 26.84/27.18  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7688.smt2...
% 26.84/27.18  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.84/27.18  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.84/27.18  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.84/27.18  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.84/27.18  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.84/27.18  % SZS status Theorem for LAT322+1
% 26.84/27.18  % SZS output start Proof for LAT322+1
% 26.84/27.18  (
% 26.84/27.18  (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_filter_0 B A) (= (and (not (= B (tptp.k1_filter_0 A))) (tptp.v2_filter_0 B A)) (tptp.v1_filter_0 B A)))))))) (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.v1_filter_2 B A) (tptp.v2_filter_0 (tptp.k15_filter_2 A B) (tptp.k1_lattice2 A))))))))) (let ((_let_3 (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_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m1_filter_2 B A) (tptp.m1_filter_0 B A))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (= (tptp.k15_filter_2 A B) (tptp.k7_filter_2 A B)))))) (let ((_let_7 (forall ((A $$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 $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))))) (let ((_let_8 (forall ((A $$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))))))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1) (tptp.v11_lattices _let_1) (tptp.v12_lattices _let_1) (tptp.v13_lattices _let_1) (tptp.v14_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v16_lattices _let_1) (tptp.v17_lattices _let_1))))))) (let ((_let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.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))))))))) (let ((_let_11 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_12 (forall ((A $$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_13 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (tptp.l1_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))))) (let ((_let_15 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_17 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.l3_lattices A) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_18 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m2_filter_2 B A)) (tptp.m1_filter_2 (tptp.k15_filter_2 A B) (tptp.k1_lattice2 A)))))) (let ((_let_19 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k17_filter_2 A) (tptp.u1_struct_0 A)))))) (let ((_let_20 (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_21 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (= (tptp.k1_lattice2 A) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A))))))) (let ((_let_22 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_filter_0 A) (tptp.u1_struct_0 A)))))) (let ((_let_23 (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v10_lattices A)) (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)))))))) (let ((_let_24 (forall ((A $$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_25 (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.m2_filter_2 B A) (= (and (not (= B (tptp.k17_filter_2 A))) (tptp.v1_filter_2 B A)) (tptp.r2_filter_2 A B))))))))) (let ((_let_26 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (tptp.k17_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (tptp.k7_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_30 (tptp.k15_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_31 (= _let_30 _let_29))) (let ((_let_32 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_29))) (let ((_let_33 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_34 (tptp.k1_filter_0 _let_33))) (let ((_let_35 (tptp.u1_struct_0 _let_33))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (= _let_26 _let_35))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_27))) (let ((_let_39 (= _let_30 _let_34))) (let ((_let_40 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_45 (or _let_44 _let_43 _let_41 _let_28))) (let ((_let_46 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.k17_filter_2 A) (tptp.u1_struct_0 A)))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (tptp.v1_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (not _let_38))) (let ((_let_50 (and _let_49 _let_48))) (let ((_let_51 (tptp.r2_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_52 (= _let_51 _let_50))) (let ((_let_53 (tptp.m2_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.v17_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_44 _let_43 _let_56 _let_41 _let_54 _let_52))) (let ((_let_58 (forall ((A $$unsorted) (BOUND_VARIABLE_1801 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_filter_2 BOUND_VARIABLE_1801 A)) (= (tptp.r2_filter_2 A BOUND_VARIABLE_1801) (and (not (= (tptp.k17_filter_2 A) BOUND_VARIABLE_1801)) (tptp.v1_filter_2 BOUND_VARIABLE_1801 A))))))) (let ((_let_59 (not _let_57))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (or))) (let ((_let_62 (not _let_58))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_60) :args (_let_62)) (REWRITE :args ((=> _let_62 (not (or _let_44 _let_43 _let_56 _let_41 _let_54 (= _let_51 (and (not (= _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_48))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_58))) (REFL :args (_let_59)) :args _let_61)) _let_60 :args (_let_59 true _let_58)))) (let ((_let_64 (REFL :args (_let_57)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 3)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_61)) :args ((or _let_40 _let_57))) _let_63 :args (_let_40 true _let_57)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 1)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_61)) :args ((or _let_42 _let_57))) _let_63 :args (_let_42 true _let_57)))) (let ((_let_67 (not _let_44))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 0)) _let_63 :args (_let_67 true _let_57)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_43 _let_41 _let_28 (not _let_45)))) _let_68 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_28 true _let_44 false _let_42 false _let_40 false _let_45)))) (let ((_let_70 (or _let_44 _let_43 _let_41 _let_54 _let_31))) (let ((_let_71 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_filter_2 B A)) (= (tptp.k15_filter_2 A B) (tptp.k7_filter_2 A B)))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 4)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_61)) :args ((or _let_53 _let_57))) _let_63 :args (_let_53 true _let_57)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_44 _let_43 _let_41 _let_54 _let_31 (not _let_70)))) _let_68 _let_66 _let_65 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_filter_2 B A) false))))) :args (_let_71))) _let_72 :args (_let_70 false _let_71)) :args (_let_31 true _let_44 false _let_42 false _let_40 false _let_53 false _let_70)))) (let ((_let_75 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_zfmisc_1 _let_26)))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_44 _let_43 _let_41 _let_76 _let_32))) (let ((_let_78 (forall ((A $$unsorted) (BOUND_VARIABLE_1941 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1941 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= BOUND_VARIABLE_1941 (tptp.k7_filter_2 A BOUND_VARIABLE_1941)))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (tptp.m2_lattice4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_81 (not _let_80))) (let ((_let_82 (or _let_44 _let_43 _let_41 _let_81 _let_75))) (let ((_let_83 (forall ((A $$unsorted) (BOUND_VARIABLE_2114 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_lattice4 BOUND_VARIABLE_2114 A)) (tptp.m1_subset_1 BOUND_VARIABLE_2114 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (and (not (tptp.v1_xboole_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_80))) (let ((_let_86 (or _let_44 _let_43 _let_41 _let_54 _let_85))) (let ((_let_87 (forall ((A $$unsorted) (BOUND_VARIABLE_2088 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m2_filter_2 BOUND_VARIABLE_2088 A)) (and (not (tptp.v1_xboole_0 BOUND_VARIABLE_2088)) (tptp.m2_lattice4 BOUND_VARIABLE_2088 A)))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_44 _let_43 _let_41 _let_76 _let_32 (not _let_77)))) _let_68 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_44 _let_43 _let_41 _let_81 _let_75 (not _let_82)))) _let_68 _let_66 _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_85 1)) :args ((or _let_80 (not _let_85)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_44 _let_43 _let_41 _let_54 _let_85 (not _let_86)))) _let_68 _let_66 _let_65 _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_filter_2 BOUND_VARIABLE_2088 A) false))))) :args (_let_87))) _let_88 :args (_let_86 false _let_87)) :args (_let_85 true _let_44 false _let_42 false _let_40 false _let_53 false _let_86)) :args (_let_80 false _let_85)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.m2_lattice4 BOUND_VARIABLE_2114 A) false))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_75 true _let_44 false _let_42 false _let_40 false _let_80 false _let_82)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_79 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k7_filter_2 A BOUND_VARIABLE_1941)))) :args (_let_78))) _let_79 :args (_let_77 false _let_78)) :args (_let_32 true _let_44 false _let_42 false _let_40 false _let_75 false _let_77)))) (let ((_let_90 (tptp.l3_lattices _let_33))) (let ((_let_91 (not _let_90))) (let ((_let_92 (tptp.v10_lattices _let_33))) (let ((_let_93 (not _let_92))) (let ((_let_94 (tptp.v3_struct_0 _let_33))) (let ((_let_95 (or _let_94 _let_93 _let_91 _let_36))) (let ((_let_96 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.k1_filter_0 A) (tptp.u1_struct_0 A)))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (tptp.v3_lattices _let_33))) (let ((_let_99 (and _let_98 _let_90))) (let ((_let_100 (or _let_41 _let_99))) (let ((_let_101 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (not (tptp.l3_lattices A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_99 1)) :args ((or _let_90 (not _let_99)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_41 _let_99 (not _let_100)))) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_lattice2 A)))) :args (_let_101))) _let_102 :args (_let_100 false _let_101)) :args (_let_99 false _let_40 false _let_100)) :args (_let_90 false _let_99)))) (let ((_let_104 (tptp.v17_lattices _let_33))) (let ((_let_105 (not _let_94))) (let ((_let_106 (and _let_105 _let_98 (tptp.v4_lattices _let_33) (tptp.v5_lattices _let_33) (tptp.v6_lattices _let_33) (tptp.v7_lattices _let_33) (tptp.v8_lattices _let_33) (tptp.v9_lattices _let_33) _let_92 (tptp.v11_lattices _let_33) (tptp.v12_lattices _let_33) (tptp.v13_lattices _let_33) (tptp.v14_lattices _let_33) (tptp.v15_lattices _let_33) (tptp.v16_lattices _let_33) _let_104))) (let ((_let_107 (or _let_44 _let_43 _let_56 _let_41 _let_106))) (let ((_let_108 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (not (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_109 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_44 _let_43 _let_56 _let_41 _let_106 (not _let_107)))) _let_68 _let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 2)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_61)) :args ((or _let_55 _let_57))) _let_63 :args (_let_55 true _let_57)) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_109 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_108))) _let_109 :args (_let_107 false _let_108)) :args (_let_106 true _let_44 false _let_42 false _let_55 false _let_40 false _let_107)))) (let ((_let_111 (not _let_106))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_106 8)) :args ((or _let_92 _let_111))) _let_110 :args (_let_92 false _let_106)))) (let ((_let_113 (and _let_105 _let_98))) (let ((_let_114 (or _let_44 _let_41 _let_113))) (let ((_let_115 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (tptp.v3_struct_0 A) (not (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_44 _let_41 _let_113 (not _let_114)))) _let_68 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_115))) _let_116 :args (_let_114 false _let_115)) :args (_let_113 true _let_44 false _let_40 false _let_114)))) (let ((_let_118 (not _let_113))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_113 0)) :args ((or _let_105 _let_118))) _let_117 :args (_let_105 false _let_113)))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_94 _let_93 _let_91 _let_36 (not _let_95)))) _let_119 _let_112 _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_96)))) _let_97 :args (_let_95 false _let_96)) :args (_let_36 true _let_94 false _let_92 false _let_90 false _let_95)))) (let ((_let_121 (tptp.u1_lattices _let_33))) (let ((_let_122 (tptp.u2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_123 (tptp.u2_lattices _let_33))) (let ((_let_124 (tptp.u1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_125 (and _let_37 (= _let_124 _let_123) (= _let_122 _let_121)))) (let ((_let_126 (tptp.g3_lattices _let_35 _let_123 _let_121))) (let ((_let_127 (tptp.g3_lattices _let_26 _let_124 _let_122))) (let ((_let_128 (= _let_127 _let_126))) (let ((_let_129 (not _let_128))) (let ((_let_130 (tptp.k2_zfmisc_1 _let_26 _let_26))) (let ((_let_131 (tptp.m1_relset_1 _let_122 _let_130 _let_26))) (let ((_let_132 (not _let_131))) (let ((_let_133 (tptp.v1_funct_2 _let_122 _let_130 _let_26))) (let ((_let_134 (not _let_133))) (let ((_let_135 (tptp.v1_funct_1 _let_122))) (let ((_let_136 (not _let_135))) (let ((_let_137 (tptp.m1_relset_1 _let_124 _let_130 _let_26))) (let ((_let_138 (not _let_137))) (let ((_let_139 (tptp.v1_funct_2 _let_124 _let_130 _let_26))) (let ((_let_140 (not _let_139))) (let ((_let_141 (tptp.v1_funct_1 _let_124))) (let ((_let_142 (not _let_141))) (let ((_let_143 (or _let_142 _let_140 _let_138 _let_136 _let_134 _let_132 _let_129 _let_125))) (let ((_let_144 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2315 $$unsorted) (BOUND_VARIABLE_2313 $$unsorted) (BOUND_VARIABLE_2311 $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (or (not (tptp.v1_funct_1 B)) (not (tptp.v1_funct_2 B _let_1 A)) (not (tptp.m1_relset_1 B _let_1 A)) (not (tptp.v1_funct_1 C)) (not (tptp.v1_funct_2 C _let_1 A)) (not (tptp.m1_relset_1 C _let_1 A)) (not (= (tptp.g3_lattices A B C) (tptp.g3_lattices BOUND_VARIABLE_2311 BOUND_VARIABLE_2313 BOUND_VARIABLE_2315))) (and (= A BOUND_VARIABLE_2311) (= B BOUND_VARIABLE_2313) (= C BOUND_VARIABLE_2315))))))) (let ((_let_145 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_146 (= _let_33 _let_126))) (let ((_let_147 (= _let_33 _let_127))) (let ((_let_148 (not _let_98))) (let ((_let_149 (or _let_91 _let_148 _let_146))) (let ((_let_150 (forall ((A $$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_151 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_152 (or _let_41 _let_147))) (let ((_let_153 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (= (tptp.k1_lattice2 A) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A))))))) (let ((_let_154 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_155 (and _let_147 _let_146))) (let ((_let_156 (ASSUME :args (_let_146)))) (let ((_let_157 (ASSUME :args (_let_147)))) (let ((_let_158 (tptp.m2_relset_1 _let_124 _let_130 _let_26))) (let ((_let_159 (= _let_137 _let_158))) (let ((_let_160 (_let_4))) (let ((_let_161 (ASSUME :args _let_160))) (let ((_let_162 (and _let_141 _let_139 _let_158))) (let ((_let_163 (tptp.l1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_164 (not _let_163))) (let ((_let_165 (or _let_164 _let_162))) (let ((_let_166 (forall ((A $$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))) (or (not (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_167 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_168 (tptp.l2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_169 (and _let_163 _let_168))) (let ((_let_170 (or _let_41 _let_169))) (let ((_let_171 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_172 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_173 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_170)) :args ((or _let_41 _let_169 (not _let_170)))) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_172 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_171))) _let_172 :args (_let_170 false _let_171)) :args (_let_169 false _let_40 false _let_170)))) (let ((_let_174 (not _let_169))) (let ((_let_175 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_169 0)) :args ((or _let_163 _let_174))) _let_173 :args (_let_163 false _let_169)))) (let ((_let_176 (tptp.m2_relset_1 _let_122 _let_130 _let_26))) (let ((_let_177 (= _let_131 _let_176))) (let ((_let_178 (and _let_135 _let_133 _let_176))) (let ((_let_179 (not _let_168))) (let ((_let_180 (or _let_179 _let_178))) (let ((_let_181 (forall ((A $$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))) (or (not (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_182 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_183 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_169 1)) :args ((or _let_168 _let_174))) _let_173 :args (_let_168 false _let_169)))) (let ((_let_184 (and (tptp.v1_relat_1 _let_124) _let_141 _let_139 (tptp.v1_binop_1 _let_124 _let_26) (tptp.v1_partfun1 _let_124 _let_130 _let_26)))) (let ((_let_185 (tptp.v6_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_186 (not _let_185))) (let ((_let_187 (or _let_44 _let_186 _let_164 _let_184))) (let ((_let_188 (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))) (or (tptp.v3_struct_0 A) (not (tptp.v6_lattices A)) (not (tptp.l1_lattices A)) (and 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(FALSE_ELIM (TRANS (CONG (TRANS (SYMM _let_277) _let_275) (TRANS (SYMM _let_273) (SYMM _let_271) (SYMM _let_269)) :args _let_267) (FALSE_INTRO _let_266))) :args (_let_211 _let_31 _let_32 _let_36 _let_37 _let_28))) :args (_let_28 _let_31 _let_36 _let_32 _let_211 _let_37))) :args (true _let_264)) (CONG _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 (REFL :args _let_257) :args _let_61)) :args ((or _let_49 _let_256 _let_255 _let_39 _let_254 _let_253 _let_252))) _let_206 _let_120 _let_89 _let_74 _let_69 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_251) (CONG (REFL :args _let_251) _let_250 (REFL :args (_let_249)) :args _let_61)) :args ((or _let_38 _let_50 _let_249))) (REORDERING (CNF_EQUIV_POS2 :args _let_248) :args ((or _let_48 _let_247 _let_246))) _let_245 (REORDERING (CNF_AND_POS :args (_let_212 1)) :args ((or _let_210 _let_241))) (REORDERING (CNF_AND_POS :args (_let_212 0)) :args ((or _let_211 _let_241))) (REORDERING (CNF_EQUIV_POS1 :args _let_240) :args ((or _let_239 _let_212 _let_238))) _let_237 (REORDERING (CNF_EQUIV_POS1 :args _let_222) :args ((or _let_215 _let_208 _let_221))) _let_220 (CNF_EQUIV_NEG2 :args _let_216) _let_207 :args (_let_215 false _let_37 false _let_36 false _let_32 false _let_31 false _let_28 false _let_38 false _let_48 false _let_214 false _let_210 true _let_39 false _let_212 false _let_213 false _let_208 false _let_209 true _let_50 true _let_52)))) (let ((_let_279 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_216) :args ((or _let_51 _let_50 _let_52))) _let_278 _let_207 :args (_let_50 true _let_51 true _let_52)))) (let ((_let_280 (not _let_50))) (let ((_let_281 (_let_212))) (let ((_let_282 (and _let_49 _let_28 _let_31 _let_36 _let_32 _let_37))) (let ((_let_283 (ASSUME :args _let_257))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_282)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_283 _let_276 _let_274 _let_272 _let_270 _let_268) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (SYMM _let_275) _let_277) (TRANS _let_269 _let_271 _let_273) :args _let_267) (FALSE_INTRO _let_283))) :args (_let_49 _let_32 _let_31 _let_28 _let_37 _let_36))) :args (_let_49 _let_28 _let_31 _let_36 _let_32 _let_37))) :args (true _let_282)) (CONG _let_250 _let_263 _let_262 _let_261 _let_260 _let_258 (REFL :args _let_265) :args _let_61)) :args ((or _let_38 _let_256 _let_255 _let_211 _let_254 _let_253 _let_252))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_281) (CONG (REFL :args _let_281) _let_259 (REFL :args (_let_247)) :args _let_61)) :args ((or _let_247 _let_39 _let_212))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_248) :args ((or _let_249 _let_210 _let_246))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 1)) :args ((or _let_48 _let_280))) _let_279 :args (_let_48 false _let_50)) _let_245 :args (_let_210 false _let_48 false _let_214)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_240) :args ((or _let_208 _let_241 _let_238))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_222) :args ((or _let_51 _let_239 _let_221))) _let_278 _let_220 :args (_let_239 true _let_51 false _let_209)) _let_237 :args (_let_241 true _let_208 false _let_213)) :args (_let_39 false _let_210 true _let_212)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 0)) :args ((or _let_49 _let_280))) _let_279 :args (_let_49 false _let_50)) _let_206 _let_120 _let_89 _let_74 _let_69 :args (false false _let_39 true _let_38 false _let_37 false _let_36 false _let_32 false _let_31 false _let_28)) :args (_let_25 _let_24 (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_funct_1 A))) _let_23 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 A))) (let ((_let_2 (tptp.v1_relat_1 A))) (=> (and _let_2 (tptp.v1_xboole_0 A) _let_1) (and _let_2 _let_1 (tptp.v2_funct_1 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)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v17_lattices A)) (and _let_1 (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v11_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)) (and _let_1 (tptp.v17_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices 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_22 _let_21 _let_20 _let_19 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_18 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m2_filter_2 (tptp.k17_filter_2 A) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m1_filter_0 (tptp.k1_filter_0 A) A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (tptp.m1_filter_2 (tptp.k1_filter_2 A) A))) _let_17 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.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 $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _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_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)))))))) (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 _let_15 _let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) _let_13 true _let_12 (exists ((A $$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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (tptp.v1_xboole_0 (tptp.k7_filter_2 A B))))) _let_11 (forall ((A $$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 $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) _let_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.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 $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) _let_9 _let_8 (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))) _let_7 (exists ((A $$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_6 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.k1_filter_2 A) (tptp.k1_filter_0 A)))) _let_5 _let_4 (forall ((A $$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 $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) _let_2 (forall ((A $$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))) _let_1 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.84/27.19  )
% 26.84/27.19  % SZS output end Proof for LAT322+1
% 26.84/27.19  % cvc5---1.0.5 exiting
% 26.84/27.19  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------