TSTP Solution File: LAT331+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT331+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:04:07 EDT 2023
% Result : Theorem 11.32s 11.52s
% Output : Proof 11.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT331+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n005.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 09:26:09 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 11.32/11.52 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Tu4gKhJF5b/cvc5---1.0.5_29963.p...
% 11.32/11.52 ------- get file name : TPTP file name is LAT331+1
% 11.32/11.52 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29963.smt2...
% 11.32/11.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.32/11.52 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.32/11.52 % SZS status Theorem for LAT331+1
% 11.32/11.52 % SZS output start Proof for LAT331+1
% 11.32/11.52 (
% 11.32/11.52 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.m2_relset_1 C A B) (tptp.m1_relset_1 C A B))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m1_filter_2 B A) (tptp.m1_filter_0 B A))))))) (let ((_let_3 (forall ((A $$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 $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))))) (let ((_let_4 (forall ((A $$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_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (tptp.l1_lattices A) (and (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.m2_relset_1 _let_3 _let_2 _let_1))))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_8 (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) (forall ((C $$unsorted)) (=> (and (not (tptp.v3_struct_0 C)) (tptp.v10_lattices C) (tptp.l3_lattices C)) (= (= C (tptp.k8_filter_0 A B)) (exists ((D $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (and (tptp.v1_funct_1 D) (tptp.v1_funct_2 D _let_1 B) (tptp.m2_relset_1 D _let_1 B) (exists ((E $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 B B))) (and (tptp.v1_funct_1 E) (tptp.v1_funct_2 E _let_1 B) (tptp.m2_relset_1 E _let_1 B) (= D (tptp.k1_realset1 (tptp.u2_lattices A) B)) (= E (tptp.k1_realset1 (tptp.u1_lattices A) B)) (= C (tptp.g3_lattices B D E))))))))))))))))) (let ((_let_9 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (and (not (tptp.v3_struct_0 B)) (tptp.v10_lattices B) (tptp.l3_lattices B)) (forall ((C $$unsorted)) (=> (tptp.m1_filter_2 C A) (forall ((D $$unsorted)) (=> (tptp.m1_filter_2 D B) (=> (and (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 B) (tptp.u2_lattices B) (tptp.u1_lattices B))) (= C D)) (= (tptp.k8_filter_0 A C) (tptp.k8_filter_0 B D)))))))))))))) (let ((_let_10 (tptp.k8_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (tptp.k8_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (= _let_11 _let_10))) (let ((_let_13 (tptp.u1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (tptp.k1_realset1 _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (tptp.u2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (tptp.k1_realset1 _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (= _let_11 (tptp.g3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_16 _let_14)))) (let ((_let_18 (tptp.u1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_19 (tptp.k1_realset1 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (tptp.u2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (tptp.k1_realset1 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (= _let_10 (tptp.g3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 _let_21 _let_19)))) (let ((_let_23 (= _let_15 _let_20))) (let ((_let_24 (= _let_13 _let_18))) (let ((_let_25 (tptp.m1_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.m1_filter_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_30 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (= (tptp.g3_lattices _let_30 _let_15 _let_13) (tptp.g3_lattices _let_29 _let_20 _let_18)))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_39 (not _let_38))) (let ((_let_40 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_43 (or _let_42 _let_41 _let_39 _let_37 _let_36 _let_34 _let_32 _let_28 _let_26 _let_12))) (let ((_let_44 (forall ((A $$unsorted) (BOUND_VARIABLE_1522 $$unsorted) (BOUND_VARIABLE_1520 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (tptp.v3_struct_0 BOUND_VARIABLE_1520) (not (tptp.v10_lattices BOUND_VARIABLE_1520)) (not (tptp.l3_lattices BOUND_VARIABLE_1520)) (not (= (tptp.g3_lattices (tptp.u1_struct_0 A) (tptp.u2_lattices A) (tptp.u1_lattices A)) (tptp.g3_lattices (tptp.u1_struct_0 BOUND_VARIABLE_1520) (tptp.u2_lattices BOUND_VARIABLE_1520) (tptp.u1_lattices BOUND_VARIABLE_1520)))) (not (tptp.m1_filter_2 BOUND_VARIABLE_1522 A)) (not (tptp.m1_filter_2 BOUND_VARIABLE_1522 BOUND_VARIABLE_1520)) (= (tptp.k8_filter_0 A BOUND_VARIABLE_1522) (tptp.k8_filter_0 BOUND_VARIABLE_1520 BOUND_VARIABLE_1522)))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (or))) (let ((_let_48 (not _let_44))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_46) :args (_let_48))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_44))) (REFL :args (_let_45)) :args _let_47)) _let_46 :args (_let_45 true _let_44)))) (let ((_let_50 (tptp.k2_zfmisc_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_51 (and (tptp.v1_funct_1 _let_14) (tptp.v1_funct_2 _let_14 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.m2_relset_1 _let_14 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.v1_funct_1 _let_16) (tptp.v1_funct_2 _let_16 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.m2_relset_1 _let_16 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_17))) (let ((_let_52 (tptp.l3_lattices _let_11))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.v10_lattices _let_11))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.v3_struct_0 _let_11))) (let ((_let_57 (tptp.m1_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_42 _let_41 _let_39 _let_58 _let_56 _let_55 _let_53 _let_51))) (let ((_let_60 (forall ((A $$unsorted) (BOUND_VARIABLE_1706 $$unsorted) (BOUND_VARIABLE_1704 $$unsorted)) (let ((_let_1 (tptp.k1_realset1 (tptp.u1_lattices A) BOUND_VARIABLE_1704))) (let ((_let_2 (tptp.k1_realset1 (tptp.u2_lattices A) BOUND_VARIABLE_1704))) (let ((_let_3 (tptp.k2_zfmisc_1 BOUND_VARIABLE_1704 BOUND_VARIABLE_1704))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_filter_0 BOUND_VARIABLE_1704 A)) (tptp.v3_struct_0 BOUND_VARIABLE_1706) (not (tptp.v10_lattices BOUND_VARIABLE_1706)) (not (tptp.l3_lattices BOUND_VARIABLE_1706)) (= (= BOUND_VARIABLE_1706 (tptp.k8_filter_0 A BOUND_VARIABLE_1704)) (and (tptp.v1_funct_1 _let_1) (tptp.v1_funct_2 _let_1 _let_3 BOUND_VARIABLE_1704) (tptp.m2_relset_1 _let_1 _let_3 BOUND_VARIABLE_1704) (tptp.v1_funct_1 _let_2) (tptp.v1_funct_2 _let_2 _let_3 BOUND_VARIABLE_1704) (tptp.m2_relset_1 _let_2 _let_3 BOUND_VARIABLE_1704) (= BOUND_VARIABLE_1706 (tptp.g3_lattices BOUND_VARIABLE_1704 _let_2 _let_1))))))))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 (not _let_56))) (let ((_let_64 (and _let_63 _let_54 _let_52))) (let ((_let_65 (or _let_42 _let_41 _let_39 _let_58 _let_64))) (let ((_let_66 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A B))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.m1_filter_0 B A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (_let_66))) (let ((_let_69 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_ENUM))) (let ((_let_70 (= _let_27 _let_57))) (let ((_let_71 (or _let_42 _let_41 _let_39 _let_70))) (let ((_let_72 (forall ((A $$unsorted) (BOUND_VARIABLE_2192 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.m1_filter_2 BOUND_VARIABLE_2192 A) (tptp.m1_filter_0 BOUND_VARIABLE_2192 A)))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (_let_72))) (let ((_let_75 (REFL :args (_let_43)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 2)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_47)) :args ((or _let_38 _let_43))) _let_49 :args (_let_38 true _let_43)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 1)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_47)) :args ((or _let_40 _let_43))) _let_49 :args (_let_40 true _let_43)))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 0)) _let_49 :args ((not _let_42) true _let_43)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_70)) :args ((or _let_28 _let_57 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 7)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_47)) :args ((or _let_27 _let_43))) _let_49 :args (_let_27 true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_42 _let_41 _let_39 _let_70 (not _let_71)))) _let_78 _let_77 _let_76 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args _let_69) :args _let_74)) _let_73 :args (_let_71 false _let_72)) :args (_let_70 true _let_42 false _let_40 false _let_38 false _let_71)) :args (_let_57 false _let_27 false _let_70)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_42 _let_41 _let_39 _let_58 _let_64 (not _let_65)))) _let_78 _let_77 _let_76 _let_79 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args _let_69) :args _let_68)) _let_67 :args (_let_65 false _let_66)) :args (_let_64 true _let_42 false _let_40 false _let_38 false _let_57 false _let_65)))) (let ((_let_81 (not _let_64))) (let ((_let_82 (and (tptp.v1_funct_1 _let_19) (tptp.v1_funct_2 _let_19 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.m2_relset_1 _let_19 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.v1_funct_1 _let_21) (tptp.v1_funct_2 _let_21 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.m2_relset_1 _let_21 _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_22))) (let ((_let_83 (tptp.l3_lattices _let_10))) (let ((_let_84 (not _let_83))) (let ((_let_85 (tptp.v10_lattices _let_10))) (let ((_let_86 (not _let_85))) (let ((_let_87 (tptp.v3_struct_0 _let_10))) (let ((_let_88 (tptp.m1_filter_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or _let_37 _let_36 _let_34 _let_89 _let_87 _let_86 _let_84 _let_82))) (let ((_let_91 (not _let_87))) (let ((_let_92 (and _let_91 _let_85 _let_83))) (let ((_let_93 (or _let_37 _let_36 _let_34 _let_89 _let_92))) (let ((_let_94 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_ENUM))) (let ((_let_95 (= _let_25 _let_88))) (let ((_let_96 (or _let_37 _let_36 _let_34 _let_95))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 5)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_47)) :args ((or _let_33 _let_43))) _let_49 :args (_let_33 true _let_43)))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 4)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_47)) :args ((or _let_35 _let_43))) _let_49 :args (_let_35 true _let_43)))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 3)) _let_49 :args ((not _let_37) true _let_43)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_95)) :args ((or _let_26 _let_88 (not _let_95)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 8)) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_47)) :args ((or _let_25 _let_43))) _let_49 :args (_let_25 true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_37 _let_36 _let_34 _let_95 (not _let_96)))) 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(MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_62))) _let_61 :args (_let_59 false _let_60)) :args (_let_51 true _let_42 false _let_40 false _let_38 false _let_57 true _let_56 false _let_54 false _let_52 false _let_59)) :args (_let_17 false _let_51)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 9)) _let_49 :args ((not _let_12) true _let_43)) :args (false false _let_24 false _let_23 false _let_22 false _let_17 true _let_12)) :args (_let_9 (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 $$unsorted)) (=> (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$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 $$unsorted) (B $$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 $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A)) (and _let_1 (tptp.v10_lattices A)))))) _let_8 (forall ((A $$unsorted)) (=> (tptp.v1_relat_1 A) (forall ((B $$unsorted)) (= (tptp.k1_realset1 A B) (tptp.k7_relat_1 A (tptp.k2_zfmisc_1 B B)))))) (forall ((A $$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)))))) true true true true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k7_relat_1 A B)))) _let_7 (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_6 (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_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) _let_5 true _let_4 (exists ((A $$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_lattice4 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.v1_relat_1 A) (tptp.v1_relat_1 (tptp.k1_realset1 A B)))) (forall ((A $$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) (B $$unsorted)) (let ((_let_1 (tptp.k8_filter_0 A B))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A) (tptp.m1_filter_0 B A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.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 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k1_realset1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$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 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.k7_relat_1 A B))) (=> (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A)) (and (tptp.v1_relat_1 _let_1) (tptp.v1_funct_1 _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_xboole_0 B))) (not (tptp.v1_xboole_0 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.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_3 (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (tptp.m2_lattice4 B A) (not (tptp.v1_xboole_0 B)))))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A))) _let_2 _let_1 (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.32/11.52 )
% 11.32/11.52 % SZS output end Proof for LAT331+1
% 11.32/11.52 % cvc5---1.0.5 exiting
% 11.32/11.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------