TSTP Solution File: SEU343+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 16:31:02 EDT 2023
% Result : Theorem 7.18s 7.40s
% Output : Proof 7.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.17/0.35 % Computer : n016.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Wed Aug 23 21:19:23 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.22/0.49 %----Proving TF0_NAR, FOF, or CNF
% 7.18/7.40 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ejnqPSvhvO/cvc5---1.0.5_27821.p...
% 7.18/7.40 ------- get file name : TPTP file name is SEU343+1
% 7.18/7.40 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27821.smt2...
% 7.18/7.40 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 7.18/7.40 % SZS status Theorem for SEU343+1
% 7.18/7.40 % SZS output start Proof for SEU343+1
% 7.18/7.40 (
% 7.18/7.40 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_lattice A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (=> (tptp.element C (tptp.the_carrier _let_1)) (and (= (tptp.join _let_1 B C) (tptp.set_union2 B C)) (= (tptp.meet _let_1 B C) (tptp.set_intersection2 B C))))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_intersection2 A B C) (tptp.set_intersection2 B C))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.set_union2 B C))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (= (tptp.apply_binary_as_element A B C D E F) (tptp.apply_binary D E F))))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (let ((_let_8 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (tptp.join_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))))) (let ((_let_9 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (=> (tptp.meet_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))))) (let ((_let_10 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))))) (let ((_let_12 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) (let ((_let_13 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.meet A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_meet A) B C))))))))))) (let ((_let_14 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.join A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_join A) B C))))))))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.strict_latt_str B) (tptp.latt_str B)) (= (= B (tptp.boole_lattice A)) (and (= (tptp.the_carrier B) (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (and (= (tptp.apply_binary (tptp.the_L_join B) C D) (tptp.subset_union2 A C D)) (= (tptp.apply_binary (tptp.the_L_meet B) C D) (tptp.subset_intersection2 A C D))))))))))))) (let ((_let_16 (tptp.boole_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_17 (tptp.the_L_meet _let_16))) (let ((_let_18 (tptp.the_carrier _let_16))) (let ((_let_19 (tptp.apply_binary_as_element _let_18 _let_18 _let_18 _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_20 (tptp.meet _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (tptp.apply_binary _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_23 (= _let_19 _let_22))) (let ((_let_24 (tptp.subset_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_25 (= _let_24 _let_22))) (let ((_let_26 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_27 (= _let_20 _let_26))) (let ((_let_28 (= _let_26 _let_24))) (let ((_let_29 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_18))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_18))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.meet_semilatt_str _let_16))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.empty_carrier _let_16))) (let ((_let_36 (or _let_35 _let_34 _let_32 _let_30 _let_21))) (let ((_let_37 (forall ((A $$unsorted) (BOUND_VARIABLE_1538 $$unsorted) (BOUND_VARIABLE_1536 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.meet_semilatt_str A)) (not (tptp.element BOUND_VARIABLE_1536 _let_1)) (not (tptp.element BOUND_VARIABLE_1538 _let_1)) (= (tptp.meet A BOUND_VARIABLE_1536 BOUND_VARIABLE_1538) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_meet A) BOUND_VARIABLE_1536 BOUND_VARIABLE_1538))))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (tptp.join_semilatt_str _let_16))) (let ((_let_40 (and _let_33 _let_39))) (let ((_let_41 (tptp.latt_str _let_16))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40))) (let ((_let_44 (forall ((A $$unsorted)) (or (not (tptp.latt_str A)) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (forall ((BOUND_VARIABLE_1571 $$unsorted)) (tptp.latt_str (tptp.boole_lattice BOUND_VARIABLE_1571))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (_let_46))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_1571)))) :args _let_48)) (AND_ELIM _let_47 :args (1)) :args (_let_41 false _let_46)))) (let ((_let_50 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_40 (not _let_43)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.latt_str A) false))))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_40 false _let_41 false _let_43)))) (let ((_let_51 (not _let_40))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_40 0)) :args ((or _let_33 _let_51))) _let_50 :args (_let_33 false _let_40)))) (let ((_let_53 (forall ((BOUND_VARIABLE_1674 $$unsorted)) (not (tptp.empty_carrier (tptp.boole_lattice BOUND_VARIABLE_1674)))))) (let ((_let_54 (0))) (let ((_let_55 (_let_53))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_1674)))) :args _let_55)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args _let_54) :args ((not _let_35) false _let_53)))) (let ((_let_57 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_58 (tptp.join _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_59 (= _let_58 _let_57))) (let ((_let_60 (and _let_59 _let_27))) (let ((_let_61 (or _let_32 _let_30 _let_60))) (let ((_let_62 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1890 $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (let ((_let_2 (tptp.the_carrier _let_1))) (or (not (tptp.element B _let_2)) (not (tptp.element BOUND_VARIABLE_1890 _let_2)) (and (= (tptp.join _let_1 B BOUND_VARIABLE_1890) (tptp.set_union2 B BOUND_VARIABLE_1890)) (= (tptp.meet _let_1 B BOUND_VARIABLE_1890) (tptp.set_intersection2 B BOUND_VARIABLE_1890))))))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (or))) (let ((_let_66 (not _let_62))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_64) :args (_let_66))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_62))) (REFL :args (_let_63)) :args _let_65)) _let_64 :args (_let_63 true _let_62)))) (let ((_let_68 (REFL :args (_let_61)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_65)) :args ((or _let_29 _let_61))) _let_67 :args (_let_29 true _let_61)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_65)) :args ((or _let_31 _let_61))) _let_67 :args (_let_31 true _let_61)))) (let ((_let_71 (tptp.cartesian_product2 _let_18 _let_18))) (let ((_let_72 (tptp.relation_of2 _let_17 _let_71 _let_18))) (let ((_let_73 (not _let_72))) (let ((_let_74 (tptp.quasi_total _let_17 _let_71 _let_18))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.function _let_17))) (let ((_let_77 (not _let_76))) (let ((_let_78 (tptp.empty _let_18))) (let ((_let_79 (or _let_78 _let_78 _let_77 _let_75 _let_73 _let_32 _let_30 _let_23))) (let ((_let_80 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (or (tptp.empty A) (tptp.empty B) (not (tptp.function D)) (not (tptp.quasi_total D _let_1 C)) (not (tptp.relation_of2 D _let_1 C)) (not (tptp.element E A)) (not (tptp.element F B)) (= (tptp.apply_binary_as_element A B C D E F) (tptp.apply_binary D E F))))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((tptp.apply_binary_as_element A B C D E F)))) (let ((_let_84 (tptp.relation_of2_as_subset _let_17 _let_71 _let_18))) (let ((_let_85 (= _let_84 _let_72))) (let ((_let_86 (_let_2))) (let ((_let_87 (ASSUME :args _let_86))) (let ((_let_88 ((tptp.relation_of2_as_subset C A B)))) (let ((_let_89 (and _let_76 _let_74 _let_84))) (let ((_let_90 (or _let_34 _let_89))) (let ((_let_91 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_meet A))) (or (not (tptp.meet_semilatt_str A)) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_34 _let_89 (not _let_90)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.the_carrier A)))) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_89 false _let_33 false _let_90)))) (let ((_let_94 (not _let_89))) (let ((_let_95 (not _let_78))) (let ((_let_96 (tptp.one_sorted_str _let_16))) (let ((_let_97 (not _let_96))) (let ((_let_98 (or _let_35 _let_97 _let_95))) (let ((_let_99 (forall ((A $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (or _let_34 _let_96))) (let ((_let_102 (forall ((A $$unsorted)) (or (not (tptp.meet_semilatt_str A)) (tptp.one_sorted_str A))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_35 _let_97 _let_95 (not _let_98)))) _let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_34 _let_96 (not _let_101)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.meet_semilatt_str A) false))))) :args (_let_102))) _let_103 :args (_let_101 false _let_102)) :args (_let_96 false _let_33 false _let_101)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_100 :args (_let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.the_carrier A)))) :args (_let_99))) _let_100 :args (_let_98 false _let_99)) :args (_let_95 true _let_35 false _let_96 false _let_98)))) (let ((_let_105 (tptp.the_L_join _let_16))) (let ((_let_106 (tptp.apply_binary _let_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_107 (tptp.subset_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_108 (= _let_107 _let_106))) (let ((_let_109 (and _let_108 _let_25))) (let ((_let_110 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_111 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_110))) (let ((_let_112 (not _let_111))) (let ((_let_113 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_110))) (let ((_let_114 (not _let_113))) (let ((_let_115 (or _let_114 _let_112 _let_109))) (let ((_let_116 (forall ((C $$unsorted) (BOUND_VARIABLE_1434 $$unsorted)) (let ((_let_1 (tptp.boole_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_2 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (or (not (tptp.element C _let_2)) (not (tptp.element BOUND_VARIABLE_1434 _let_2)) (and (= (tptp.subset_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 C BOUND_VARIABLE_1434) (tptp.apply_binary (tptp.the_L_join _let_1) C BOUND_VARIABLE_1434)) (= (tptp.subset_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 C BOUND_VARIABLE_1434) (tptp.apply_binary (tptp.the_L_meet _let_1) C BOUND_VARIABLE_1434))))))))) (let ((_let_117 (= _let_18 _let_110))) (let ((_let_118 (and _let_117 _let_116))) (let ((_let_119 (tptp.strict_latt_str _let_16))) (let ((_let_120 (not _let_119))) (let ((_let_121 (or _let_120 _let_42 _let_118))) (let ((_let_122 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.strict_latt_str B)) (not (tptp.latt_str B)) (= (= B (tptp.boole_lattice A)) (and (= (tptp.the_carrier B) (tptp.powerset A)) (forall ((C $$unsorted) (BOUND_VARIABLE_1434 $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element C _let_1)) (not (tptp.element BOUND_VARIABLE_1434 _let_1)) (and (= (tptp.apply_binary (tptp.the_L_join B) C BOUND_VARIABLE_1434) (tptp.subset_union2 A C BOUND_VARIABLE_1434)) (= (tptp.apply_binary (tptp.the_L_meet B) C BOUND_VARIABLE_1434) (tptp.subset_intersection2 A C BOUND_VARIABLE_1434)))))))))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (forall ((BOUND_VARIABLE_1565 $$unsorted)) 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(tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.subset_union2 A C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_intersection2 A B C) (tptp.subset_intersection2 A C B))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.apply_binary A B C) (tptp.apply A (tptp.ordered_pair B C)))))) _let_15 _let_14 _let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) true true _let_12 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.join_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.join A B C) _let_1)))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (E $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A B))) (=> (and (not (tptp.empty A)) (not (tptp.empty B)) (tptp.function D) (tptp.quasi_total D _let_1 C) (tptp.relation_of2 D _let_1 C) (tptp.element E A) (tptp.element F B)) (tptp.element (tptp.apply_binary_as_element A B C D E F) C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (not (tptp.empty_carrier A)) (tptp.meet_semilatt_str A) (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.meet A B C) _let_1)))) true true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_union2 A B C) _let_1)))) true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_intersection2 A B C) _let_1)))) _let_11 true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) _let_10 true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) _let_9 true _let_8 (exists ((A $$unsorted)) (tptp.meet_semilatt_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (exists ((A $$unsorted)) (tptp.join_semilatt_str A)) (exists ((A $$unsorted)) (tptp.latt_str A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) _let_7 _let_6 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.latt_str_of A B C))) (let ((_let_2 (tptp.cartesian_product2 A A))) (=> (and (not (tptp.empty A)) (tptp.function B) (tptp.quasi_total B _let_2 A) (tptp.relation_of2 B _let_2 A) (tptp.function C) (tptp.quasi_total C _let_2 A) (tptp.relation_of2 C _let_2 A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.cartesian_product2 A A))) (=> (and (tptp.function B) (tptp.quasi_total B _let_1 A) (tptp.relation_of2 B _let_1 A) (tptp.function C) (tptp.quasi_total C _let_1 A) (tptp.relation_of2 C _let_1 A)) (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (= (tptp.latt_str_of A B C) (tptp.latt_str_of D E F)) (and (= A D) (= B E) (= C F))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B B) B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_intersection2 A B B) B)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (tptp.strict_latt_str A))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (and (tptp.latt_str A) (not (tptp.empty_carrier A)) (tptp.strict_latt_str A))) _let_5 _let_4 _let_3 _let_2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 7.18/7.42 )
% 7.18/7.42 % SZS output end Proof for SEU343+1
% 7.18/7.42 % cvc5---1.0.5 exiting
% 7.18/7.42 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------