TSTP Solution File: LAT308+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT308+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:03:52 EDT 2023
% Result : Theorem 28.74s 28.91s
% Output : Proof 28.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT308+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 09:12:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 28.74/28.91 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DyNkGw1DYm/cvc5---1.0.5_11378.p...
% 28.74/28.91 ------- get file name : TPTP file name is LAT308+1
% 28.74/28.91 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11378.smt2...
% 28.74/28.91 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 28.74/28.91 --- Run --no-e-matching --full-saturate-quant at 5...
% 28.74/28.91 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 28.74/28.91 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 28.74/28.91 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 28.74/28.91 % SZS status Theorem for LAT308+1
% 28.74/28.91 % SZS output start Proof for LAT308+1
% 28.74/28.91 (
% 28.74/28.91 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.k5_filter_2 A B))) (let ((_let_2 (tptp.k1_lattice2 A))) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (and (= (tptp.k18_filter_2 A B) (tptp.k2_filter_2 _let_2 _let_1)) (= (tptp.k18_filter_2 _let_2 _let_1) (tptp.k2_filter_2 A B))))))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (not (and (not (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k4_lattices A B C) B)))) (= (tptp.k2_filter_0 A B) _let_1)))))))))) (let ((_let_3 (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k2_lattices A B C))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k1_lattices A B C))))))) (let ((_let_6 (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.k2_filter_2 A B) (tptp.k2_filter_0 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 $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))))) (let ((_let_9 (forall ((A $$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_10 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (tptp.l2_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_11 (forall ((A $$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_12 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m1_subset_1 (tptp.k5_filter_2 A B) (tptp.u1_struct_0 (tptp.k1_lattice2 A))))))) (let ((_let_14 (forall ((A $$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_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))))) (let ((_let_16 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k5_filter_2 A B) B))))))) (let ((_let_17 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k2_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u1_lattices A) B C))))))))))) (let ((_let_18 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (= (tptp.k1_lattice2 A) (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u1_lattices A) (tptp.u2_lattices A))))))) (let ((_let_19 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 C _let_1) (= (tptp.k1_lattices A B C) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u2_lattices A) B C))))))))))) (let ((_let_20 (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v10_lattices A)) (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)))))))) (let ((_let_21 (forall ((A $$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_22 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (tptp.m1_subset_1 B _let_1) (not (and (not (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k3_lattices A B C) B)))) (= (tptp.k18_filter_2 A B) _let_1))))))))))) (let ((_let_23 (tptp.k3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_24 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_23))) (let ((_let_25 (tptp.k1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (= _let_23 _let_25))) (let ((_let_27 (tptp.u2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (= _let_25 (tptp.k2_binop_1 _let_28 _let_28 _let_28 _let_27 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_30 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (tptp.u1_struct_0 _let_30))) (let ((_let_32 (= _let_28 _let_31))) (let ((_let_33 (tptp.u1_lattices _let_30))) (let ((_let_34 (= _let_27 _let_33))) (let ((_let_35 (tptp.k2_lattices _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_36 (= _let_35 (tptp.k2_binop_1 _let_31 _let_31 _let_31 _let_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_37 (tptp.k4_lattices _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_38 (= _let_35 _let_37))) (let ((_let_39 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_37))) (let ((_let_40 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_28))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.k18_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (= _let_28 _let_42))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_28))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_50 (not _let_49))) (let ((_let_51 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_52 (or _let_51 _let_50 _let_48 _let_46 _let_44 _let_41 _let_24))) (let ((_let_53 (not _let_24))) (let ((_let_54 (forall ((A $$unsorted) (BOUND_VARIABLE_2014 $$unsorted) (BOUND_VARIABLE_2012 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2012 _let_1)) (not (= _let_1 (tptp.k18_filter_2 A BOUND_VARIABLE_2012))) (not (tptp.m1_subset_1 BOUND_VARIABLE_2014 _let_1)) (= BOUND_VARIABLE_2012 (tptp.k3_lattices A BOUND_VARIABLE_2012 BOUND_VARIABLE_2014))))))) (let ((_let_55 (not _let_52))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (or))) (let ((_let_58 (not _let_54))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_56) :args (_let_58))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_54))) (REFL :args (_let_55)) :args _let_57)) _let_56 :args (_let_55 true _let_54)))) (let ((_let_60 (tptp.l2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.v4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_51 _let_63 _let_61 _let_46 _let_41 _let_26))) (let ((_let_65 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v4_lattices A)) (not (tptp.l2_lattices A)) (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k1_lattices A B C))))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (tptp.l1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_68 (and _let_67 _let_60))) (let ((_let_69 (or _let_48 _let_68))) (let ((_let_70 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 (REFL :args (_let_52)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 2)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_57)) :args ((or _let_47 _let_52))) _let_59 :args (_let_47 true _let_52)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_48 _let_68 (not _let_69)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args _let_72)) _let_71 :args (_let_69 false _let_70)) :args (_let_68 false _let_47 false _let_69)))) (let ((_let_76 (not _let_68))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 1)) :args ((or _let_60 _let_76))) _let_75 :args (_let_60 false _let_68)))) (let ((_let_78 (not _let_51))) (let ((_let_79 (and _let_78 _let_62 (tptp.v5_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v6_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v7_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v8_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v9_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_80 (or _let_48 _let_51 _let_50 _let_79))) (let ((_let_81 (forall ((A $$unsorted)) (let ((_let_1 (tptp.v3_struct_0 A))) (or (not (tptp.l3_lattices A)) _let_1 (not (tptp.v10_lattices A)) (and (not _let_1) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_57)) :args ((or _let_49 _let_52))) _let_59 :args (_let_49 true _let_52)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 0)) _let_59 :args (_let_78 true _let_52)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 5)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_57)) :args ((or _let_40 _let_52))) _let_59 :args (_let_40 true _let_52)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 3)) (CONG _let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_57)) :args ((or _let_45 _let_52))) _let_59 :args (_let_45 true _let_52)))) (let ((_let_87 (or _let_51 _let_61 _let_46 _let_41 _let_29))) (let ((_let_88 (forall ((A $$unsorted) (BOUND_VARIABLE_2149 $$unsorted) (BOUND_VARIABLE_2147 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.l2_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2147 _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_2149 _let_1)) (= (tptp.k1_lattices A BOUND_VARIABLE_2147 BOUND_VARIABLE_2149) (tptp.k2_binop_1 _let_1 _let_1 _let_1 (tptp.u2_lattices A) BOUND_VARIABLE_2147 BOUND_VARIABLE_2149))))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (tptp.u2_lattices _let_30))) (let ((_let_91 (tptp.u1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_92 (and _let_32 (= _let_91 _let_90) _let_34))) (let ((_let_93 (tptp.g3_lattices _let_31 _let_90 _let_33))) (let ((_let_94 (tptp.g3_lattices _let_28 _let_91 _let_27))) (let ((_let_95 (= _let_94 _let_93))) (let ((_let_96 (not _let_95))) (let ((_let_97 (tptp.k2_zfmisc_1 _let_28 _let_28))) (let ((_let_98 (tptp.m1_relset_1 _let_27 _let_97 _let_28))) (let ((_let_99 (not _let_98))) (let ((_let_100 (tptp.v1_funct_2 _let_27 _let_97 _let_28))) (let ((_let_101 (not _let_100))) (let ((_let_102 (tptp.v1_funct_1 _let_27))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.m1_relset_1 _let_91 _let_97 _let_28))) (let ((_let_105 (not _let_104))) (let ((_let_106 (tptp.v1_funct_2 _let_91 _let_97 _let_28))) (let ((_let_107 (not _let_106))) (let ((_let_108 (tptp.v1_funct_1 _let_91))) (let ((_let_109 (not _let_108))) (let ((_let_110 (or _let_109 _let_107 _let_105 _let_103 _let_101 _let_99 _let_96 _let_92))) (let ((_let_111 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_2752 $$unsorted) (BOUND_VARIABLE_2750 $$unsorted) (BOUND_VARIABLE_2748 $$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_2748 BOUND_VARIABLE_2750 BOUND_VARIABLE_2752))) (and (= A BOUND_VARIABLE_2748) (= B BOUND_VARIABLE_2750) (= C BOUND_VARIABLE_2752))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (= _let_30 _let_93))) (let ((_let_114 (= _let_30 _let_94))) (let ((_let_115 (tptp.v3_lattices _let_30))) (let ((_let_116 (not _let_115))) (let ((_let_117 (tptp.l3_lattices _let_30))) (let ((_let_118 (not _let_117))) (let ((_let_119 (or _let_118 _let_116 _let_113))) (let ((_let_120 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (not (tptp.v3_lattices A)) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) 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false _let_47 false _let_130)))) (let ((_let_134 (not _let_129))) (let ((_let_135 (or _let_48 _let_114))) (let ((_let_136 (forall ((A $$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_137 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_48 _let_114 (not _let_135)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_137 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_136))) _let_137 :args (_let_135 false _let_136)) :args (_let_114 false _let_47 false _let_135)))) (let ((_let_139 (and _let_114 _let_113))) (let ((_let_140 (ASSUME :args (_let_113)))) (let ((_let_141 (ASSUME :args (_let_114)))) (let ((_let_142 (SYMM _let_141))) (let ((_let_143 (tptp.m2_relset_1 _let_91 _let_97 _let_28))) (let ((_let_144 (= _let_143 _let_104))) (let ((_let_145 (_let_3))) (let ((_let_146 (ASSUME :args _let_145))) (let ((_let_147 ((tptp.m2_relset_1 C A B)))) (let ((_let_148 (and _let_108 _let_106 _let_143))) (let ((_let_149 (not _let_67))) (let ((_let_150 (or _let_149 _let_148))) (let ((_let_151 (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_152 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_153 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_150)) :args ((or _let_149 _let_148 (not _let_150)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 0)) :args ((or _let_67 _let_76))) 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(REORDERING (CNF_EQUIV_POS1 :args (_let_157)) :args ((or (not _let_156) _let_98 (not _let_157)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_158 2)) :args ((or _let_156 _let_163))) _let_162 :args (_let_156 false _let_158)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_146 :args (_let_97 _let_28 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_147)) :args _let_145)) _let_146 :args (_let_157 false _let_3)) :args (_let_98 false _let_156 false _let_157)))) (let ((_let_165 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_158 1)) :args ((or _let_100 _let_163))) _let_162 :args (_let_100 false _let_158)))) (let ((_let_166 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_158 0)) :args ((or _let_102 _let_163))) _let_162 :args (_let_102 false _let_158)))) (let ((_let_167 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_148 1)) :args ((or _let_106 _let_154))) _let_153 :args (_let_106 false _let_148)))) (let ((_let_168 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_148 0)) :args ((or _let_108 _let_154))) _let_153 :args (_let_108 false _let_148)))) (let ((_let_169 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_109 _let_107 _let_103 _let_101 _let_99 _let_105 _let_96 _let_92 (not _let_110)))) _let_168 _let_167 _let_166 _let_165 _let_164 _let_155 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_139)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_140 _let_141) (SCOPE (TRANS _let_142 (SYMM (SYMM _let_140))) :args (_let_113 _let_114))) :args (_let_114 _let_113))) :args (true _let_139)) _let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_116 _let_118 _let_113 (not _let_119)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_129 1)) :args ((or _let_115 _let_134))) _let_133 :args (_let_115 false _let_129)) _let_126 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args 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(_let_79 1)) :args ((or _let_62 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_51 _let_50 _let_48 _let_79 (not _let_80)))) _let_84 _let_83 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_79 true _let_51 false _let_49 false _let_47 false _let_80)) :args (_let_62 false _let_79)) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k3_lattices A B C)))) :args (_let_65))) _let_66 :args (_let_64 false _let_65)) :args (_let_26 true _let_51 false _let_45 false _let_40 false _let_62 false _let_60 false _let_64)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 6)) _let_59 :args (_let_53 true _let_52)) :args (false false _let_39 false _let_38 false _let_36 false _let_34 false _let_32 false _let_29 false _let_26 true _let_24)) :args (_let_22 _let_21 (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_20 (forall ((A $$unsorted)) (=> (not (tptp.v1_realset1 A)) (not (tptp.v1_xboole_0 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))) (tptp.v1_relat_1 C))) (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 $$unsorted) (B $$unsorted)) (= (tptp.k2_tarski A B) (tptp.k2_tarski B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k3_lattices A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k4_lattices A C B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k1_binop_1 A B C) (tptp.k1_funct_1 A (tptp.k4_tarski B C)))))) _let_19 _let_18 _let_17 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k2_filter_0 A B) (tptp.a_2_0_filter_0 A B)))))) _let_16 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.k4_tarski A B) (tptp.k2_tarski (tptp.k2_tarski A B) (tptp.k1_tarski A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (= (tptp.k18_filter_2 A B) (tptp.a_2_0_filter_2 A B)))))) _let_15 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B (tptp.u1_struct_0 A))) (tptp.m2_filter_2 (tptp.k18_filter_2 A B) A))) true true _let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k1_lattices A B C) _let_1)))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (tptp.m1_subset_1 (tptp.k2_binop_1 A B C D E F) C)))) (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_filter_0 (tptp.k2_filter_0 A B) 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.u1_struct_0 A))) (tptp.m1_filter_2 (tptp.k2_filter_2 A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k2_lattices A B C) _let_1)))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k3_lattices A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k4_lattices A B C) _let_1)))) true _let_13 (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _let_12 (forall ((A $$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 $$unsorted)) (=> (tptp.m1_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) true true (forall ((A $$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_11 true _let_10 (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))) _let_9 (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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_tarski 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 $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finset_1 _let_1) (tptp.v1_realset1 _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k2_tarski A B)))) (forall ((A $$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.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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (tptp.m1_subset_1 C (tptp.u1_struct_0 B))) (= (tptp.r2_hidden A (tptp.a_2_0_filter_0 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (= A D) (tptp.r3_lattices B C D)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B) (tptp.m1_subset_1 C (tptp.u1_struct_0 B))) (= (tptp.r2_hidden A (tptp.a_2_0_filter_2 B C)) (exists ((D $$unsorted)) (and (tptp.m1_subset_1 D (tptp.u1_struct_0 B)) (= A D) (tptp.r3_lattices B D C)))))) _let_7 (exists ((A $$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)))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_realset1 A))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_realset1 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))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (= (tptp.k2_binop_1 A B C D E F) (tptp.k1_binop_1 D E F))))) _let_6 _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) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.r3_lattices A B C) (tptp.r1_lattices A B C))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.l3_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.r3_lattices A B B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 A B) (or (tptp.v1_xboole_0 B) (tptp.r2_hidden A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 28.74/28.92 )
% 28.74/28.92 % SZS output end Proof for LAT308+1
% 28.74/28.93 % cvc5---1.0.5 exiting
% 28.74/28.93 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------