TSTP Solution File: LAT297+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT297+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 06:03:45 EDT 2023
% Result : Theorem 1.07s 1.34s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LAT297+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 06:43:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.18/0.47 %----Proving TF0_NAR, FOF, or CNF
% 1.07/1.34 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.PV48i3PYh7/cvc5---1.0.5_15038.p...
% 1.07/1.34 ------- get file name : TPTP file name is LAT297+1
% 1.07/1.34 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15038.smt2...
% 1.07/1.34 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.07/1.34 % SZS status Theorem for LAT297+1
% 1.07/1.34 % SZS output start Proof for LAT297+1
% 1.07/1.34 (
% 1.07/1.34 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (= (tptp.k4_lattices A B C) (tptp.k2_lattices A B C))))))) (let ((_let_2 (forall ((A $$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_3 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.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)))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v9_lattices A) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.u1_struct_0 A)) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (= (tptp.k2_lattices A B (tptp.k1_lattices A B C)) B)))))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (= (tptp.m2_lattice4 B A) (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (=> (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (and (tptp.r2_hidden (tptp.k4_lattices A C D) B) (tptp.r2_hidden (tptp.k3_lattices A C D) B)))))))))))))) (let ((_let_7 (forall ((A $$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_8 (not (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))) (=> (forall ((C $$unsorted)) (=> (tptp.m1_subset_1 C (tptp.u1_struct_0 A)) (forall ((D $$unsorted)) (=> (tptp.m1_subset_1 D (tptp.u1_struct_0 A)) (= (and (tptp.r2_hidden C B) (tptp.r2_hidden D B)) (tptp.r2_hidden (tptp.k4_lattices A C D) B)))))) (tptp.m2_lattice4 B A))))))))) (let ((_let_9 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.k1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_11 (tptp.k3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (tptp.k2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_10))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_13))) (let ((_let_15 (= _let_13 (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_10)))) (let ((_let_16 (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (tptp.r2_hidden _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_18 (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_19 (and _let_18 _let_17))) (let ((_let_20 (tptp.r2_hidden SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 _let_22))) (let ((_let_24 (not _let_23))) (let ((_let_25 (not _let_9))) (let ((_let_26 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 _let_22))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_24 _let_21 _let_19))) (let ((_let_29 (forall ((C $$unsorted) (BOUND_VARIABLE_1625 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1625 _let_1)) (not (tptp.r2_hidden BOUND_VARIABLE_1625 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (and (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 C BOUND_VARIABLE_1625) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.r2_hidden (tptp.k3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 C BOUND_VARIABLE_1625) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (tptp.m2_lattice4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (= _let_31 _let_29))) (let ((_let_33 (not _let_29))) (let ((_let_34 (tptp.m1_subset_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 (tptp.k1_zfmisc_1 _let_22)))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (or _let_40 _let_39 _let_37 _let_35 _let_32))) (let ((_let_42 (forall ((A $$unsorted) (BOUND_VARIABLE_1656 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1656 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (= (tptp.m2_lattice4 BOUND_VARIABLE_1656 A) (forall ((C $$unsorted) (BOUND_VARIABLE_1625 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.r2_hidden C BOUND_VARIABLE_1656)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1625 _let_1)) (not (tptp.r2_hidden BOUND_VARIABLE_1625 BOUND_VARIABLE_1656)) (and (tptp.r2_hidden (tptp.k4_lattices A C BOUND_VARIABLE_1625) BOUND_VARIABLE_1656) (tptp.r2_hidden (tptp.k3_lattices A C BOUND_VARIABLE_1625) BOUND_VARIABLE_1656)))))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (forall ((C $$unsorted) (BOUND_VARIABLE_1495 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1495 _let_1)) (= (and (tptp.r2_hidden C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.r2_hidden BOUND_VARIABLE_1495 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.r2_hidden (tptp.k4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 C BOUND_VARIABLE_1495) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_40 _let_39 _let_37 _let_35 _let_45 _let_31))) (let ((_let_47 (forall ((A $$unsorted) (BOUND_VARIABLE_1526 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1526 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))) (not (forall ((C $$unsorted) (BOUND_VARIABLE_1495 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (not (tptp.m1_subset_1 C _let_1)) (not (tptp.m1_subset_1 BOUND_VARIABLE_1495 _let_1)) (= (and (tptp.r2_hidden C BOUND_VARIABLE_1526) (tptp.r2_hidden BOUND_VARIABLE_1495 BOUND_VARIABLE_1526)) (tptp.r2_hidden (tptp.k4_lattices A C BOUND_VARIABLE_1495) BOUND_VARIABLE_1526)))))) (tptp.m2_lattice4 BOUND_VARIABLE_1526 A))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_53 (REFL :args (_let_46)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 2)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_50)) :args ((or _let_36 _let_46))) _let_52 :args (_let_36 true _let_46)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_50)) :args ((or _let_38 _let_46))) _let_52 :args (_let_38 true _let_46)))) (let ((_let_56 (not _let_40))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 0)) _let_52 :args (_let_56 true _let_46)))) (let ((_let_58 (_let_33))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_32)) :args ((or _let_31 _let_33 (not _let_32)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 5)) _let_52 :args ((not _let_31) true _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_39 _let_37 _let_35 _let_32 (not _let_41)))) _let_57 _let_55 _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 3)) (CONG _let_53 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_50)) :args ((or _let_34 _let_46))) _let_52 :args (_let_34 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.m1_subset_1 BOUND_VARIABLE_1656 (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_32 true _let_40 false _let_38 false _let_36 false _let_34 false _let_41)) :args (_let_33 true _let_31 false _let_32)) :args (_let_30 true _let_29)))) (let ((_let_60 (REFL :args (_let_28)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_9))) :args _let_50)) :args ((or _let_9 _let_28))) _let_59 :args (_let_9 true _let_28)))) (let ((_let_62 (tptp.l2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.v4_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_40 _let_65 _let_63 _let_27 _let_24 _let_12))) (let ((_let_67 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (or (tptp.v3_struct_0 A) (not (tptp.v4_lattices A)) (not (tptp.l2_lattices A)) (not (tptp.m1_subset_1 B _let_1)) (not (tptp.m1_subset_1 C _let_1)) (= (tptp.k3_lattices A B C) (tptp.k1_lattices A B C))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 2)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_50)) :args ((or _let_23 _let_28))) _let_59 :args (_let_23 true _let_28)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_50)) :args ((or _let_26 _let_28))) _let_59 :args (_let_26 true _let_28)))) (let ((_let_71 (tptp.v9_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_72 (tptp.v6_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_73 (and _let_56 _let_64 (tptp.v5_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_72 (tptp.v7_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.v8_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_71))) (let ((_let_74 (or _let_37 _let_40 _let_39 _let_73))) (let ((_let_75 (forall ((A $$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_76 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_40 _let_39 _let_37 _let_73 (not _let_74)))) _let_57 _let_55 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_75))) _let_76 :args (_let_74 false _let_75)) :args (_let_73 true _let_40 false _let_38 false _let_36 false _let_74)))) (let ((_let_78 (not _let_73))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 1)) :args ((or _let_64 _let_78))) _let_77 :args (_let_64 false _let_73)))) (let ((_let_80 (tptp.l1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_81 (and _let_80 _let_62))) (let ((_let_82 (or _let_37 _let_81))) (let ((_let_83 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_37 _let_81 (not _let_82)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_83))) _let_84 :args (_let_82 false _let_83)) :args (_let_81 false _let_36 false _let_82)))) (let ((_let_86 (not _let_81))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_81 1)) :args ((or _let_62 _let_86))) _let_85 :args (_let_62 false _let_81)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_40 _let_63 _let_65 _let_27 _let_24 _let_12 (not _let_66)))) _let_57 _let_87 _let_79 _let_70 _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k3_lattices A B C)))) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_12 true _let_40 false _let_62 false _let_64 false _let_26 false 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_let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_95) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 B BOUND_VARIABLE_1799)))) :args _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_91)) :args ((or _let_90 (not _let_71) (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 6)) :args ((or _let_71 _let_78))) _let_77 :args (_let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_40 _let_37 _let_91 (not _let_92)))) _let_57 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.v3_struct_0 A) true))))) :args (_let_93))) _let_94 :args (_let_92 false _let_93)) :args (_let_91 true _let_40 false _let_36 false _let_92)) :args (_let_90 false _let_71 false _let_91)) :args (_let_89 false _let_90)) :args (_let_14 false _let_26 false _let_23 false _let_89)) _let_88 _let_61 :args (false true _let_16 false _let_15 false _let_14 false _let_12 false _let_9)) :args (_let_8 (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_7 (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))))) _let_6 (forall ((A $$unsorted)) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.k1_binop_1 A B C) (tptp.k1_funct_1 A (tptp.k4_tarski B C)))))) (forall ((A $$unsorted)) (=> (and (not 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_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) (C $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A) (tptp.m1_subset_1 B _let_1) (tptp.m1_subset_1 C _let_1)) (tptp.m1_subset_1 (tptp.k2_lattices A B C) _let_1)))) true true _let_4 (forall ((A $$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.m1_subset_1 (tptp.k4_lattices A B C) _let_1)))) true (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_3 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_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$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))))))) 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 $$unsorted)) (tptp.l1_struct_0 A)) (exists ((A $$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 $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_lattice4 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted)) (=> (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 $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finset_1 _let_1) (tptp.v1_realset1 _let_1)))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (exists ((A $$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 $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A B))) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B)) (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 C) (tptp.m1_relset_1 D _let_1 C) (tptp.m1_subset_1 E A) (tptp.m1_subset_1 F B)) (= (tptp.k2_binop_1 A B C D E F) (tptp.k1_binop_1 D E F))))) _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (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)))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.07/1.35 )
% 1.07/1.35 % SZS output end Proof for LAT297+1
% 1.07/1.35 % cvc5---1.0.5 exiting
% 1.07/1.35 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------