TSTP Solution File: LAT302+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT302+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 06:03:49 EDT 2023
% Result : Theorem 0.84s 1.08s
% Output : Proof 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT302+1 : TPTP v8.1.2. Released v3.4.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 05:19:20 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.84/1.08 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZhSfpqS5MO/cvc5---1.0.5_31902.p...
% 0.84/1.08 ------- get file name : TPTP file name is LAT302+1
% 0.84/1.08 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31902.smt2...
% 0.84/1.08 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.84/1.08 % SZS status Theorem for LAT302+1
% 0.84/1.08 % SZS output start Proof for LAT302+1
% 0.84/1.08 (
% 0.84/1.08 (let ((_let_1 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.v13_lattices A) (tptp.l3_lattices A)) (= (tptp.k5_lattices A) (tptp.k6_lattices (tptp.k1_lattice2 A))))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (= (tptp.v13_lattices A) (tptp.v14_lattices (tptp.k1_lattice2 A))))))) (let ((_let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m2_filter_2 B A) (tptp.m1_filter_2 B (tptp.k1_lattice2 A)))))))) (let ((_let_4 (forall ((A $$unsorted)) (let ((_let_1 (tptp.l3_lattices A))) (let ((_let_2 (tptp.v10_lattices A))) (let ((_let_3 (not (tptp.v3_struct_0 A)))) (=> (and _let_3 _let_2 _let_1) (=> (and _let_3 _let_2 (tptp.v14_lattices A) _let_1) (tptp.m1_filter_0 (tptp.k6_domain_1 (tptp.u1_struct_0 A) (tptp.k6_lattices A)) A))))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (= (tptp.m1_filter_2 B A) (tptp.m1_filter_0 B A))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (= (tptp.k6_domain_1 A B) (tptp.k1_tarski B)))))) (let ((_let_7 (forall ((A $$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_8 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_10 (forall ((A $$unsorted)) (=> (tptp.l3_lattices A) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.l1_lattices A) (tptp.l1_struct_0 A))))) (let ((_let_12 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l2_lattices A)) (tptp.m1_subset_1 (tptp.k6_lattices A) (tptp.u1_struct_0 A)))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_lattices A)) (tptp.m1_subset_1 (tptp.k5_lattices A) (tptp.u1_struct_0 A)))))) (let ((_let_14 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (=> (tptp.l3_lattices A) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_15 (not (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (=> (tptp.v13_lattices A) (tptp.m2_filter_2 (tptp.k6_domain_1 (tptp.u1_struct_0 A) (tptp.k5_lattices A)) A))))))) (let ((_let_16 (tptp.k5_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (tptp.u1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (tptp.k6_domain_1 _let_17 _let_16))) (let ((_let_19 (tptp.m2_filter_2 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (tptp.k1_lattice2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_21 (tptp.k6_lattices _let_20))) (let ((_let_22 (= _let_16 _let_21))) (let ((_let_23 (= _let_18 (tptp.k1_tarski _let_16)))) (let ((_let_24 (tptp.u1_struct_0 _let_20))) (let ((_let_25 (tptp.k6_domain_1 _let_24 _let_21))) (let ((_let_26 (tptp.m2_filter_2 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_27 (= _let_25 (tptp.k1_tarski _let_21)))) (let ((_let_28 (tptp.v13_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.l3_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (not _let_30))) (let ((_let_32 (tptp.v10_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (tptp.v3_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (or _let_34 _let_33 _let_31 _let_29 _let_19))) (let ((_let_36 (not _let_19))) (let ((_let_37 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.v13_lattices A)) (tptp.m2_filter_2 (tptp.k6_domain_1 (tptp.u1_struct_0 A) (tptp.k5_lattices A)) A))))) (let ((_let_38 (not _let_35))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (or))) (let ((_let_41 (not _let_37))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_39) :args (_let_41))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) (REFL :args (_let_38)) :args _let_40)) _let_39 :args (_let_38 true _let_37)))) (let ((_let_43 (or _let_34 _let_33 _let_29 _let_31 _let_22))) (let ((_let_44 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.v13_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.k5_lattices A) (tptp.k6_lattices (tptp.k1_lattice2 A))))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (REFL :args (_let_35)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 3)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_40)) :args ((or _let_28 _let_35))) _let_42 :args (_let_28 true _let_35)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_40)) :args ((or _let_30 _let_35))) _let_42 :args (_let_30 true _let_35)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_40)) :args ((or _let_32 _let_35))) _let_42 :args (_let_32 true _let_35)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 0)) _let_42 :args ((not _let_34) true _let_35)))) (let ((_let_51 (tptp.m1_subset_1 _let_16 _let_17))) (let ((_let_52 (not _let_51))) (let ((_let_53 (tptp.v1_xboole_0 _let_17))) (let ((_let_54 (or _let_53 _let_52 _let_23))) (let ((_let_55 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.v1_xboole_0 A) (not (tptp.m1_subset_1 B A)) (= (tptp.k6_domain_1 A B) (tptp.k1_tarski B)))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (_let_55))) (let ((_let_58 (tptp.l1_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_34 _let_59 _let_51))) (let ((_let_61 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l1_lattices A)) (tptp.m1_subset_1 (tptp.k5_lattices A) (tptp.u1_struct_0 A)))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (and _let_58 (tptp.l2_lattices SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_64 (or _let_31 _let_63))) (let ((_let_65 (forall ((A $$unsorted)) (or (not (tptp.l3_lattices A)) (and (tptp.l1_lattices A) (tptp.l2_lattices A)))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_63 0)) :args ((or _let_58 (not _let_63)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_31 _let_63 (not _let_64)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args _let_67)) _let_66 :args (_let_64 false _let_65)) :args (_let_63 false _let_30 false _let_64)) :args (_let_58 false _let_63)))) (let ((_let_69 (not _let_53))) (let ((_let_70 (tptp.l1_struct_0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_34 _let_71 _let_69))) (let ((_let_73 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l1_struct_0 A)) (not (tptp.v1_xboole_0 (tptp.u1_struct_0 A))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (_let_73))) (let ((_let_76 ((not (= (tptp.v3_struct_0 A) true))))) (let ((_let_77 (or _let_59 _let_70))) (let ((_let_78 (forall ((A $$unsorted)) (or (not (tptp.l1_lattices A)) (tptp.l1_struct_0 A))))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (_let_78))) (let ((_let_81 ((not (= (tptp.l1_lattices A) false))))) (let ((_let_82 (tptp.m1_filter_2 _let_25 _let_20))) (let ((_let_83 (= _let_82 _let_26))) (let ((_let_84 (or _let_34 _let_33 _let_31 _let_83))) (let ((_let_85 (forall ((A $$unsorted) (BOUND_VARIABLE_2217 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.m2_filter_2 BOUND_VARIABLE_2217 A) (tptp.m1_filter_2 BOUND_VARIABLE_2217 (tptp.k1_lattice2 A))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (tptp.m1_filter_0 _let_25 _let_20))) (let ((_let_88 (= _let_87 _let_82))) (let ((_let_89 (tptp.l3_lattices _let_20))) (let ((_let_90 (not _let_89))) (let ((_let_91 (tptp.v10_lattices _let_20))) (let ((_let_92 (not _let_91))) (let ((_let_93 (tptp.v3_struct_0 _let_20))) (let ((_let_94 (or _let_93 _let_92 _let_90 _let_88))) (let ((_let_95 (forall ((A $$unsorted) (BOUND_VARIABLE_2184 $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.m1_filter_2 BOUND_VARIABLE_2184 A) (tptp.m1_filter_0 BOUND_VARIABLE_2184 A)))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (tptp.v3_lattices _let_20))) (let ((_let_98 (and _let_97 _let_89))) (let ((_let_99 (or _let_31 _let_98))) (let ((_let_100 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (not (tptp.l3_lattices A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1))))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_98 1)) :args ((or _let_89 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_31 _let_98 (not _let_99)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.k1_lattice2 A)))) :args (_let_100))) _let_101 :args (_let_99 false _let_100)) :args (_let_98 false _let_30 false _let_99)) :args (_let_89 false _let_98)))) (let ((_let_103 (not _let_93))) (let ((_let_104 (and _let_103 _let_97 (tptp.v4_lattices _let_20) (tptp.v5_lattices _let_20) (tptp.v6_lattices _let_20) (tptp.v7_lattices _let_20) (tptp.v8_lattices _let_20) (tptp.v9_lattices _let_20) _let_91))) (let ((_let_105 (or _let_34 _let_33 _let_31 _let_104))) (let ((_let_106 (forall ((A $$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_107 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_104 8)) :args ((or _let_91 (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_34 _let_33 _let_31 _let_104 (not _let_105)))) _let_50 _let_49 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_104 true _let_34 false _let_32 false _let_30 false _let_105)) :args (_let_91 false _let_104)))) (let ((_let_109 (and _let_103 _let_97))) (let ((_let_110 (or _let_34 _let_31 _let_109))) (let ((_let_111 (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_lattice2 A))) (or (tptp.v3_struct_0 A) (not (tptp.l3_lattices A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_109 0)) :args ((or _let_103 (not _let_109)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_34 _let_31 _let_109 (not _let_110)))) _let_50 _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.l3_lattices A) false))))) :args (_let_111))) _let_112 :args (_let_110 false _let_111)) :args (_let_109 true _let_34 false _let_30 false _let_110)) :args (_let_103 false _let_109)))) (let ((_let_114 (tptp.v14_lattices _let_20))) (let ((_let_115 (not _let_114))) (let ((_let_116 (or _let_93 _let_92 _let_90 _let_115 _let_87))) (let ((_let_117 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (not (tptp.v14_lattices A)) (tptp.m1_filter_0 (tptp.k6_domain_1 (tptp.u1_struct_0 A) (tptp.k6_lattices A)) A))))) (let ((_let_118 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_119 (= _let_28 _let_114))) (let ((_let_120 (or _let_34 _let_33 _let_31 _let_119))) (let ((_let_121 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.v10_lattices A)) (not (tptp.l3_lattices A)) (= (tptp.v13_lattices A) (tptp.v14_lattices (tptp.k1_lattice2 A))))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (tptp.m1_subset_1 _let_21 _let_24))) (let ((_let_124 (not _let_123))) (let ((_let_125 (tptp.v1_xboole_0 _let_24))) (let ((_let_126 (or _let_125 _let_124 _let_27))) (let ((_let_127 (tptp.l2_lattices _let_20))) (let ((_let_128 (not _let_127))) (let ((_let_129 (or _let_93 _let_128 _let_123))) (let ((_let_130 (forall ((A $$unsorted)) (or (tptp.v3_struct_0 A) (not (tptp.l2_lattices A)) (tptp.m1_subset_1 (tptp.k6_lattices A) (tptp.u1_struct_0 A)))))) (let ((_let_131 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT 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(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)) (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 $$unsorted)) (let ((_let_1 (not (tptp.v3_struct_0 A)))) (=> (tptp.l3_lattices A) (=> (and _let_1 (tptp.v15_lattices A)) (and _let_1 (tptp.v13_lattices A) (tptp.v14_lattices A)))))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (tptp.v3_lattices _let_1) (tptp.l3_lattices _let_1)))))) _let_14 true true true true _let_13 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.m1_subset_1 B A)) (tptp.m1_subset_1 (tptp.k6_domain_1 A B) (tptp.k1_zfmisc_1 A)))) _let_12 _let_11 true (forall ((A $$unsorted)) (=> (tptp.l2_lattices A) (tptp.l1_struct_0 A))) _let_10 (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_0 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A)))))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m1_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) true true (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_filter_2 B A) (and (not (tptp.v1_xboole_0 B)) (tptp.m2_lattice4 B A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (forall ((B $$unsorted)) (=> (tptp.m2_lattice4 B A) (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.m2_relset_1 C A B) (tptp.m1_subset_1 C (tptp.k1_zfmisc_1 (tptp.k2_zfmisc_1 A B))))) (forall ((A $$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)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_0 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m1_filter_2 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m1_relset_1 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.m1_subset_1 B A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_filter_2 B A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (tptp.m2_lattice4 B A)))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.m2_relset_1 C A B))) _let_9 _let_8 (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_zfmisc_1 A)))) (tptp.v1_xboole_0 tptp.k1_xboole_0) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v4_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v1_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted)) (not (tptp.v1_xboole_0 (tptp.k1_tarski A)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u2_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v5_lattices A) (tptp.l2_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.g3_lattices A B C))) (let ((_let_2 (tptp.k2_zfmisc_1 A A))) (=> (and (not (tptp.v1_xboole_0 A)) (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_2 A) (tptp.m1_relset_1 B _let_2 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_2 A) (tptp.m1_relset_1 C _let_2 A)) (and (not (tptp.v3_struct_0 _let_1)) (tptp.v3_lattices _let_1)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.k1_tarski A))) (and (not (tptp.v1_xboole_0 _let_1)) (tptp.v1_finset_1 _let_1) (tptp.v1_realset1 _let_1)))) (forall ((A $$unsorted)) (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 $$unsorted)) (let ((_let_1 (tptp.u1_struct_0 A))) (let ((_let_2 (tptp.k2_zfmisc_1 _let_1 _let_1))) (let ((_let_3 (tptp.u1_lattices A))) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v7_lattices A) (tptp.l1_lattices A)) (and (tptp.v1_relat_1 _let_3) (tptp.v1_funct_1 _let_3) (tptp.v1_funct_2 _let_3 _let_2 _let_1) (tptp.v2_binop_1 _let_3 _let_1) (tptp.v1_partfun1 _let_3 _let_2 _let_1))))))) _let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.k2_zfmisc_1 A A))) (=> (and (tptp.v1_funct_1 B) (tptp.v1_funct_2 B _let_1 A) (tptp.m1_relset_1 B _let_1 A) (tptp.v1_funct_1 C) (tptp.v1_funct_2 C _let_1 A) (tptp.m1_relset_1 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.g3_lattices A B C) (tptp.g3_lattices D E F)) (and (= A D) (= B E) (= C F))))))) (exists ((A $$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 $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.v10_lattices A) (tptp.l3_lattices A)) (exists ((B $$unsorted)) (and (tptp.m2_lattice4 B A) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (tptp.v1_realset1 A))) (forall ((A $$unsorted)) (=> (not (tptp.v1_xboole_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (tptp.v1_xboole_0 A)) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_xboole_0 A) (tptp.v1_funct_1 A))) (exists ((A $$unsorted)) (and (not (tptp.v1_xboole_0 A)) (not (tptp.v1_realset1 A)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 A)) (tptp.v1_xboole_0 B)))) (exists ((A $$unsorted)) (not (tptp.v1_xboole_0 A))) (exists ((A $$unsorted)) (and (tptp.v1_relat_1 A) (tptp.v1_funct_1 A) (tptp.v2_funct_1 A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l1_struct_0 A) (not (tptp.v3_struct_0 A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.v3_struct_0 A)) (tptp.l1_struct_0 A)) (exists ((B $$unsorted)) (and (tptp.m1_subset_1 B (tptp.k1_zfmisc_1 (tptp.u1_struct_0 A))) (not (tptp.v1_xboole_0 B)))))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A))) (exists ((A $$unsorted)) (and (tptp.l3_lattices A) (not (tptp.v3_struct_0 A)) (tptp.v3_lattices A) (tptp.v4_lattices A) (tptp.v5_lattices A) (tptp.v6_lattices A) (tptp.v7_lattices A) (tptp.v8_lattices A) (tptp.v9_lattices A) (tptp.v10_lattices A))) _let_6 _let_5 (forall ((A $$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)) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.r2_hidden A B) (tptp.m1_subset_1 A B))) _let_3 (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)))) _let_2 (forall ((A $$unsorted)) (=> (tptp.v1_xboole_0 A) (= A tptp.k1_xboole_0))) _let_1 (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.84/1.09 )
% 0.84/1.09 % SZS output end Proof for LAT302+1
% 0.84/1.09 % cvc5---1.0.5 exiting
% 0.84/1.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------