%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 06:03:41 EDT 2023

% Result   : Theorem 0.67s 0.89s
% Output   : Proof 0.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Thu Aug 24 07:19:34 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.67/0.89  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YZ3bva0uLE/cvc5---1.0.5_28706.p...
% 0.67/0.89  ------- get file name : TPTP file name is LAT292+1
% 0.67/0.89  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28706.smt2...
% 0.67/0.89  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.67/0.89  % SZS status Theorem for LAT292+1
% 0.67/0.89  % SZS output start Proof for LAT292+1
% 0.67/0.89  (
% 0.67/0.89  (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (tptp.r1_filter_1 A (tptp.k12_lopclset A)))))) (let ((_let_2 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v1_pre_topc _let_1) (tptp.v2_pre_topc _let_1))))))) (let ((_let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (and (tptp.v1_pre_topc _let_1) (tptp.v2_pre_topc _let_1) (tptp.l1_pre_topc _let_1))))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (= (tptp.k12_lopclset A) (tptp.k6_lopclset (tptp.k11_lopclset A))))))) (let ((_let_5 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (not (tptp.v3_struct_0 B)) (tptp.v2_pre_topc B) (tptp.l1_pre_topc B) (tptp.r1_filter_1 A (tptp.k6_lopclset B))))))))) (let ((_let_6 (tptp.k11_lopclset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_7 (tptp.k6_lopclset _let_6))) (let ((_let_8 (tptp.k12_lopclset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_9 (= _let_8 _let_7))) (let ((_let_10 (tptp.r1_filter_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_11 (tptp.r1_filter_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_7))) (let ((_let_12 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.v3_realset2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.v17_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (or _let_19 _let_18 _let_16 _let_14 _let_13 _let_9))) (let ((_let_21 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (= (tptp.k12_lopclset A) (tptp.k6_lopclset (tptp.k11_lopclset A))))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (forall ((B $$unsorted)) (or (tptp.v3_struct_0 B) (not (tptp.v2_pre_topc B)) (not (tptp.l1_pre_topc B)) (not (tptp.r1_filter_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.k6_lopclset B))))))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_19 _let_18 _let_16 _let_14 _let_13 _let_24))) (let ((_let_26 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (not (forall ((B $$unsorted)) (or (tptp.v3_struct_0 B) (not (tptp.v2_pre_topc B)) (not (tptp.l1_pre_topc B)) (not (tptp.r1_filter_1 A (tptp.k6_lopclset B)))))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 4)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_29)) :args ((or _let_12 _let_25))) _let_31 :args (_let_12 true _let_25)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 3)) _let_31 :args ((not _let_14) true _let_25)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_29)) :args ((or _let_15 _let_25))) _let_31 :args (_let_15 true _let_25)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_29)) :args ((or _let_17 _let_25))) _let_31 :args (_let_17 true _let_25)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 0)) _let_31 :args ((not _let_19) true _let_25)))) (let ((_let_38 (or _let_19 _let_18 _let_16 _let_14 _let_13 _let_10))) (let ((_let_39 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (tptp.r1_filter_1 A (tptp.k12_lopclset A)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not _let_11))) (let ((_let_42 (tptp.l1_pre_topc _let_6))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.v2_pre_topc _let_6))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.v3_struct_0 _let_6))) (let ((_let_47 (or _let_46 _let_45 _let_43 _let_41))) (let ((_let_48 (_let_23))) (let ((_let_49 (tptp.v1_pre_topc _let_6))) (let ((_let_50 (and _let_49 _let_44 _let_42))) (let ((_let_51 (or _let_19 _let_18 _let_16 _let_14 _let_13 _let_50))) (let ((_let_52 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_lopclset A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (and (tptp.v1_pre_topc _let_1) (tptp.v2_pre_topc _let_1) (tptp.l1_pre_topc _let_1))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_13 _let_50 (not _let_51)))) _let_37 _let_36 _let_35 _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_50 true _let_19 false _let_17 false _let_15 true _let_14 false _let_12 false _let_51)))) (let ((_let_55 (not _let_50))) (let ((_let_56 (not _let_46))) (let ((_let_57 (and _let_56 _let_49 _let_44))) (let ((_let_58 (or _let_19 _let_18 _let_16 _let_14 _let_13 _let_57))) (let ((_let_59 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k11_lopclset A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v17_lattices A)) (tptp.v3_realset2 A) (not (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v1_pre_topc _let_1) (tptp.v2_pre_topc _let_1))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (ASSUME :args (_let_41)))) (let ((_let_62 (ASSUME :args (_let_9)))) (let ((_let_63 (ASSUME :args (_let_10)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_61 _let_62 _let_63) :args (_let_9 _let_10 _let_41)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_63)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (SYMM (SYMM _let_62)) :args (APPLY_UF tptp.r1_filter_1)) (FALSE_INTRO _let_61))) :args (_let_41 _let_9 _let_10)) :args ((not (and _let_9 _let_10 _let_41)) SB_LITERAL))) (CONG (REFL :args ((not _let_9))) (REFL :args ((not _let_10))) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_11))) :args _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_45 _let_43 _let_41 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_57 0)) :args ((or _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_13 _let_57 (not _let_58)))) _let_37 _let_36 _let_35 _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v10_lattices A) false))))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_57 true _let_19 false _let_17 false _let_15 true _let_14 false _let_12 false _let_58)) :args (_let_56 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 1)) :args ((or _let_44 _let_55))) _let_54 :args (_let_44 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 2)) :args ((or _let_42 _let_55))) _let_54 :args (_let_42 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args (_let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 B) true))))) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 5)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_29)) :args ((or _let_23 _let_25))) _let_31 :args (_let_23 true _let_25)) :args (_let_47 false _let_23)) :args (_let_41 true _let_46 false _let_44 false _let_42 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_13 _let_10 (not _let_38)))) _let_37 _let_36 _let_35 _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_10 true _let_19 false _let_17 false _let_15 true _let_14 false _let_12 false _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_13 _let_9 (not _let_20)))) _let_37 _let_36 _let_35 _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_21))) _let_22 :args (_let_20 false _let_21)) :args (_let_9 true _let_19 false _let_17 false _let_15 true _let_14 false _let_12 false _let_20)) :args (false true _let_11 false _let_10 false _let_9)) :args (_let_5 (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (=> (tptp.v1_pre_topc A) (= A (tptp.g1_pre_topc (tptp.u1_struct_0 A) (tptp.u1_pre_topc A)))))) (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (=> (tptp.v3_lattices A) (= A (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (not (tptp.r2_hidden B A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (tptp.v1_xcmplx_0 B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B A) (and (tptp.v1_xcmplx_0 B) (tptp.v4_ordinal2 B) (tptp.v1_xreal_0 B) (tptp.v1_int_1 B) (tptp.v1_rat_1 B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (and (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A)))) (forall ((A $$unsorted)) (=> (tptp.v1_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_membered B))))) (forall ((A $$unsorted)) (=> (tptp.v2_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v3_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v4_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_finset_1 A))) (forall ((A $$unsorted)) (=> (tptp.v4_finsub_1 A) (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.v1_funct_1 C))) (=> (tptp.m1_relset_1 C A B) (=> (and _let_1 (tptp.v1_partfun1 C A B)) (and _let_1 (tptp.v1_funct_2 C A B)))))) (forall ((A $$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)))))) (forall ((A $$unsorted)) (=> (tptp.v5_membered A) (tptp.v4_membered A))) (forall ((A $$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 $$unsorted)) (=> (tptp.v5_membered A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (and (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B)))))) (forall ((A $$unsorted)) (=> (tptp.v1_finset_1 A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_finset_1 B))))) (forall ((A $$unsorted)) (=> (and (tptp.v1_finsub_1 A) (tptp.v3_finsub_1 A)) (tptp.v4_finsub_1 A))) (forall ((A $$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 $$unsorted)) (=> (tptp.v4_membered A) (tptp.v3_membered A))) (forall ((A $$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 $$unsorted)) (=> (tptp.v3_membered A) (tptp.v2_membered A))) (forall ((A $$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 $$unsorted)) (=> (tptp.v2_membered A) (tptp.v1_membered A))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v17_lattices A)) (and _let_1 (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)))))) (forall ((A $$unsorted) (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 $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v11_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)) (and _let_1 (tptp.v17_lattices A)))))) (forall ((A $$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))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_pre_topc A)) (= (tptp.k1_lopclset A) (tptp.a_1_0_lopclset A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (= (tptp.k6_lopclset A) (tptp.g3_lattices (tptp.k1_lopclset A) (tptp.k4_lopclset A) (tptp.k5_lopclset A))))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.g1_pre_topc A B))) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 A))) (and (tptp.v1_pre_topc _let_1) (tptp.l1_pre_topc _let_1))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k12_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_pre_topc A)) (tptp.m1_subset_1 (tptp.k1_lopclset A) (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))) true true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lopclset A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k4_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc 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))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lopclset A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.k5_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k6_lopclset A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))) (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$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))))))) (forall ((A $$unsorted)) (=> (tptp.l1_pre_topc A) (tptp.m1_subset_1 (tptp.u1_pre_topc A) (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))) true (forall ((A $$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))))))) (exists ((A $$unsorted)) (tptp.l1_lattices A)) (exists ((A $$unsorted)) (tptp.l1_pre_topc 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) (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) (B $$unsorted)) (=> (and (tptp.v1_finset_1 A) (tptp.v1_finset_1 B)) (tptp.v1_finset_1 (tptp.k2_zfmisc_1 A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_zfmisc_1 A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finsub_1 _let_1) (tptp.v3_finsub_1 _let_1) (tptp.v4_finsub_1 _let_1)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (not (tptp.v1_xboole_0 (tptp.k1_lopclset A))))) (forall ((A $$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 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) _let_2 (and (tptp.v1_xboole_0 tptp.k1_xboole_0) (tptp.v1_membered tptp.k1_xboole_0) (tptp.v2_membered tptp.k1_xboole_0) (tptp.v3_membered tptp.k1_xboole_0) (tptp.v4_membered tptp.k1_xboole_0) (tptp.v5_membered tptp.k1_xboole_0)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.l1_pre_topc B)) (= (tptp.r2_hidden A (tptp.a_1_0_lopclset B)) (exists ((C $$unsorted)) (and (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.u1_struct_0 B))) (= A C) (tptp.v3_pre_topc C B) (tptp.v4_pre_topc C B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.k1_zfmisc_1 A))) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.g1_pre_topc A B) (tptp.g1_pre_topc C D)) (and (= A C) (= B D)))))) (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))))))) (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 $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_finset_1 A))) (forall ((A $$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)))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A) (tptp.v11_lattices A) (tptp.v12_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v17_lattices A) (not (tptp.v3_realset2 A)))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_membered A) (tptp.v2_membered A) (tptp.v3_membered A) (tptp.v4_membered A) (tptp.v5_membered A))) (exists ((A $$unsorted)) (and (tptp.l1_pre_topc A) (tptp.v1_pre_topc A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.m1_relset_1 C A B) (tptp.v1_relat_1 C) (tptp.v1_funct_1 C)))) (exists ((A $$unsorted)) (and (tptp.l1_pre_topc A) (not (tptp.v3_struct_0 A)) (tptp.v1_pre_topc A) (tptp.v2_pre_topc A))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (exists ((A $$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)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_finset_1 B))))) (forall ((A $$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 $$unsorted)) (=> (and (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (tptp.v4_pre_topc B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v2_pre_topc A) (tptp.l1_pre_topc A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)) (tptp.v4_pre_topc B A))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_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.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (tptp.r1_filter_1 A A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.r1_tarski A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (=> (tptp.r1_filter_1 A B) (tptp.r1_filter_1 B 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)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.r2_hidden C A) (tptp.r2_hidden C B))) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.m1_subset_1 A (tptp.k1_zfmisc_1 B)) (tptp.r1_tarski A B))) _let_1 (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.67/0.89  )
% 0.67/0.89  % SZS output end Proof for LAT292+1
% 0.67/0.89  % cvc5---1.0.5 exiting
% 0.67/0.90  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------