TSTP Solution File: LAT319+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT319+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 06:03:59 EDT 2023
% Result : Theorem 0.45s 0.65s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : LAT319+1 : TPTP v8.1.2. Released v3.4.0.
% 0.10/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n023.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 08:44:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.45/0.65 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.EK0LjLUYDt/cvc5---1.0.5_31576.p...
% 0.45/0.65 ------- get file name : TPTP file name is LAT319+1
% 0.45/0.65 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31576.smt2...
% 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.45/0.65 % SZS status Theorem for LAT319+1
% 0.45/0.65 % SZS output start Proof for LAT319+1
% 0.45/0.65 (
% 0.45/0.65 (let ((_let_1 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (and _let_4 _let_3 _let_2) (= (and _let_4 _let_3 (tptp.v11_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v11_lattices _let_1) (tptp.l3_lattices _let_1))))))))))) (let ((_let_2 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (and _let_4 _let_3 _let_2) (= (and _let_4 _let_3 (tptp.v15_lattices A) (tptp.v16_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v16_lattices _let_1) (tptp.l3_lattices _let_1))))))))))) (let ((_let_3 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))))) (let ((_let_4 (forall ((A $$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_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.l3_lattices A) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (= (tptp.v17_lattices A) (and (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v11_lattices A))))))) (let ((_let_7 (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v11_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A)) (and _let_1 (tptp.v17_lattices A)))))))) (let ((_let_8 (forall ((A $$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)))))))) (let ((_let_9 (not (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (not (tptp.v3_struct_0 A)))) (=> (and _let_4 _let_3 _let_2) (= (and _let_4 _let_3 (tptp.v17_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v17_lattices _let_1) (tptp.l3_lattices _let_1)))))))))))) (let ((_let_10 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (tptp.v11_lattices _let_10))) (let ((_let_12 (tptp.v16_lattices _let_10))) (let ((_let_13 (tptp.v15_lattices _let_10))) (let ((_let_14 (and _let_13 _let_12 _let_11))) (let ((_let_15 (tptp.l3_lattices _let_10))) (let ((_let_16 (tptp.v10_lattices _let_10))) (let ((_let_17 (tptp.v3_struct_0 _let_10))) (let ((_let_18 (not _let_17))) (let ((_let_19 (and _let_18 _let_16 _let_11 _let_15))) (let ((_let_20 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (tptp.v11_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_22 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (not _let_23))) (let ((_let_25 (and _let_24 _let_22 _let_21 _let_20))) (let ((_let_26 (= _let_25 _let_19))) (let ((_let_27 (not _let_20))) (let ((_let_28 (not _let_22))) (let ((_let_29 (or _let_23 _let_28 _let_27 _let_26))) (let ((_let_30 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (tptp.v3_struct_0 A))) (or _let_4 (not _let_3) (not _let_2) (= (and (not _let_4) _let_3 (tptp.v11_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v11_lattices _let_1) (tptp.l3_lattices _let_1))))))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (tptp.v17_lattices _let_10))) (let ((_let_33 (and _let_18 _let_16 _let_32 _let_15))) (let ((_let_34 (tptp.v17_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (and _let_24 _let_22 _let_34 _let_20))) (let ((_let_36 (= _let_35 _let_33))) (let ((_let_37 (or _let_23 _let_28 _let_27 _let_36))) (let ((_let_38 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (tptp.v3_struct_0 A))) (or _let_4 (not _let_3) (not _let_2) (= (and (not _let_4) _let_3 (tptp.v17_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v17_lattices _let_1) (tptp.l3_lattices _let_1))))))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)))) (let ((_let_44 (REFL :args (_let_37)))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 2)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_20))) :args _let_41)) :args ((or _let_20 _let_37))) _let_43 :args (_let_20 true _let_37)))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 1)) (CONG _let_44 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_22))) :args _let_41)) :args ((or _let_22 _let_37))) _let_43 :args (_let_22 true _let_37)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_37 0)) :args ((or _let_24 _let_37))) _let_43 :args (_let_24 true _let_37)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_23 _let_28 _let_27 _let_26 (not _let_29)))) _let_47 _let_46 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_lattice2 A)))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_26 true _let_23 false _let_22 false _let_20 false _let_29)))) (let ((_let_49 (tptp.v16_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_50 (tptp.v15_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_51 (and _let_50 _let_49 _let_21))) (let ((_let_52 (= _let_34 _let_51))) (let ((_let_53 (or _let_23 _let_27 _let_52))) (let ((_let_54 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l3_lattices A)) (= (tptp.v17_lattices A) (and (tptp.v15_lattices A) (tptp.v16_lattices A) (tptp.v11_lattices A))))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (_let_54))) (let ((_let_57 ((not (= (tptp.v3_struct_0 A) true))))) (let ((_let_58 (and _let_24 _let_34))) (let ((_let_59 (and _let_18 _let_11 (tptp.v13_lattices _let_10) (tptp.v14_lattices _let_10) _let_13 _let_12))) (let ((_let_60 (not _let_32))) (let ((_let_61 (not _let_15))) (let ((_let_62 (or _let_61 _let_17 _let_60 _let_59))) (let ((_let_63 (and _let_18 _let_16 _let_13 _let_12 _let_15))) (let ((_let_64 (and _let_24 _let_22 _let_50 _let_49 _let_20))) (let ((_let_65 (= _let_64 _let_63))) (let ((_let_66 (not _let_49))) (let ((_let_67 (not _let_50))) (let ((_let_68 (not _let_21))) (let ((_let_69 (or _let_27 _let_23 _let_68 _let_67 _let_66 _let_58))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 3)) _let_43 :args ((not _let_36) true _let_37)))) (let ((_let_71 (_let_36))) (let ((_let_72 (not _let_33))) (let ((_let_73 (tptp.v3_lattices _let_10))) (let ((_let_74 (and _let_18 _let_73))) (let ((_let_75 (or _let_23 _let_27 _let_74))) (let ((_let_76 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (tptp.v3_struct_0 A) (not (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_74 0)) :args ((or _let_18 (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_23 _let_27 _let_74 (not _let_75)))) _let_47 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_76))) _let_77 :args (_let_75 false _let_76)) :args (_let_74 true _let_23 false _let_20 false _let_75)) :args (_let_18 false _let_74)))) (let ((_let_79 (and _let_73 _let_15))) (let ((_let_80 (or _let_27 _let_79))) (let ((_let_81 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (not (tptp.l3_lattices A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_79 1)) :args ((or _let_15 (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_27 _let_79 (not _let_80)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_lattice2 A)))) :args (_let_81))) _let_82 :args (_let_80 false _let_81)) :args (_let_79 false _let_20 false _let_80)) :args (_let_15 false _let_79)))) (let ((_let_84 (forall ((A $$unsorted)) (let ((_let_1 (tptp.v3_struct_0 A))) (or (not (tptp.l3_lattices A)) _let_1 (not (tptp.v17_lattices A)) (and (not _let_1) (tptp.v11_lattices A) (tptp.v13_lattices A) (tptp.v14_lattices A) (tptp.v15_lattices A) (tptp.v16_lattices A))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (not _let_59))) (let ((_let_87 (and _let_18 _let_73 (tptp.v4_lattices _let_10) (tptp.v5_lattices _let_10) (tptp.v6_lattices _let_10) (tptp.v7_lattices _let_10) (tptp.v8_lattices _let_10) (tptp.v9_lattices _let_10) _let_16))) (let ((_let_88 (or _let_23 _let_28 _let_27 _let_87))) (let ((_let_89 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1) (tptp.v4_lattices _let_1) (tptp.v5_lattices _let_1) (tptp.v6_lattices _let_1) (tptp.v7_lattices _let_1) (tptp.v8_lattices _let_1) (tptp.v9_lattices _let_1) (tptp.v10_lattices _let_1))))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_87 8)) :args ((or _let_16 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_23 _let_28 _let_27 _let_87 (not _let_88)))) _let_47 _let_46 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_89))) _let_90 :args (_let_88 false _let_89)) :args (_let_87 true _let_23 false _let_22 false _let_20 false _let_88)) :args (_let_16 false _let_87)))) (let ((_let_92 (not _let_11))) (let ((_let_93 (not _let_16))) (let ((_let_94 (REFL :args (_let_61)))) (let ((_let_95 (REFL :args (_let_93)))) (let ((_let_96 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))))) (let ((_let_97 (_let_19))) (let ((_let_98 (not _let_12))) (let ((_let_99 (not _let_13))) (let ((_let_100 (_let_63))) (let ((_let_101 (not _let_26))) (let ((_let_102 (not _let_19))) (let ((_let_103 (_let_26))) (let ((_let_104 (or _let_23 _let_28 _let_27 _let_65))) (let ((_let_105 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (let ((_let_2 (tptp.l3_lattices A))) (let ((_let_3 (tptp.v10_lattices A))) (let ((_let_4 (tptp.v3_struct_0 A))) (or _let_4 (not _let_3) (not _let_2) (= (and (not _let_4) _let_3 (tptp.v15_lattices A) (tptp.v16_lattices A) _let_2) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v10_lattices _let_1) (tptp.v15_lattices _let_1) (tptp.v16_lattices _let_1) (tptp.l3_lattices _let_1))))))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_23 _let_28 _let_27 _let_65 (not _let_104)))) _let_47 _let_46 _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_lattice2 A)))) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_65 true _let_23 false _let_22 false _let_20 false _let_104)))) (let ((_let_108 (not _let_65))) (let ((_let_109 (not _let_63))) (let ((_let_110 (_let_65))) (let ((_let_111 (not _let_25))) (let ((_let_112 (not _let_64))) (let ((_let_113 (forall ((A $$unsorted)) (let ((_let_1 (tptp.v3_struct_0 A))) (or (not (tptp.l3_lattices A)) _let_1 (not (tptp.v11_lattices A)) (not (tptp.v15_lattices A)) (not (tptp.v16_lattices A)) (and (not _let_1) (tptp.v17_lattices A))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_23 _let_27 _let_67 _let_68 _let_66 _let_58 (not _let_69)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_113))) _let_114 :args (_let_69 false _let_113)) _let_45 _let_47 (REORDERING (CNF_AND_POS :args (_let_64 3)) :args ((or _let_49 _let_112))) (REORDERING (CNF_AND_POS :args (_let_64 2)) :args ((or _let_50 _let_112))) (REORDERING (CNF_AND_POS :args (_let_25 2)) :args ((or _let_21 _let_111))) (REORDERING (CNF_EQUIV_POS2 :args _let_110) :args ((or _let_64 _let_109 _let_108))) _let_107 (REORDERING (CNF_EQUIV_POS2 :args _let_103) :args ((or _let_25 _let_102 _let_101))) _let_48 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_100) (CONG (REFL :args _let_100) _let_96 _let_95 (REFL :args (_let_99)) (REFL :args (_let_98)) _let_94 :args _let_41)) :args ((or _let_17 _let_93 _let_61 _let_99 _let_63 _let_98))) _let_83 _let_91 _let_78 (REORDERING (EQ_RESOLVE 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false _let_15 false _let_125)) :args (_let_124 true _let_32 false _let_123)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 2)) :args ((or _let_11 _let_102))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_103) :args ((or _let_19 _let_111 _let_101))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_122) (CONG (REFL :args _let_122) _let_121 _let_120 (REFL :args (_let_68)) _let_119 :args _let_41)) :args ((or _let_23 _let_28 _let_27 _let_68 _let_25))) _let_47 _let_46 _let_45 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_51 2)) :args ((or _let_21 _let_118))) _let_117 :args (_let_21 false _let_51)) :args (_let_25 true _let_23 false _let_22 false _let_20 false _let_21)) _let_48 :args (_let_19 false _let_25 false _let_26)) :args (_let_11 false _let_19)) :args (false false _let_12 false _let_13 true _let_14 false _let_11)) :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)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)) (and _let_1 (tptp.v15_lattices A)))))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v15_lattices A)) (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)))))) _let_8 _let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.v10_lattices A))) (let ((_let_2 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_2 _let_1 (tptp.v11_lattices A)) (and _let_2 (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) _let_1 (tptp.v12_lattices A))))))) _let_6 (forall ((A $$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))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_5 true true true (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))) true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) (forall ((A $$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))))))) 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 $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) _let_4 (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v6_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$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 (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 $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$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 $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (forall ((A $$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)) (= (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 $$unsorted)) (=> (and (tptp.r2_hidden A B) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 C))) (tptp.m1_subset_1 A C))) _let_2 (forall ((A $$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)))) _let_1 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.45/0.65 )
% 0.45/0.65 % SZS output end Proof for LAT319+1
% 0.45/0.65 % cvc5---1.0.5 exiting
% 0.45/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------