TSTP Solution File: SEU344+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n027.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 16:31:03 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU344+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 01:12:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.63 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.BcnwU0DggM/cvc5---1.0.5_17229.p...
% 0.20/0.63 ------- get file name : TPTP file name is SEU344+1
% 0.20/0.63 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17229.smt2...
% 0.20/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.63 % SZS status Theorem for SEU344+1
% 0.20/0.63 % SZS output start Proof for SEU344+1
% 0.20/0.63 (
% 0.20/0.63 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.boole_lattice A))) (forall ((C $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (=> (tptp.element C (tptp.the_carrier _let_1)) (= (tptp.below _let_1 B C) (tptp.subset B C)))))))))) (let ((_let_3 (forall ((A $$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_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))))) (let ((_let_5 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_latt_str _let_1)))))) (let ((_let_6 (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_7 (forall ((A $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (and (tptp.strict_latt_str _let_1) (tptp.latt_str _let_1)))))) (let ((_let_8 (forall ((A $$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)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.below A B C) (= (tptp.join A B C) C)))))))))) (let ((_let_9 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_10 (tptp.boole_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_11 (tptp.join _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_12 (= _let_11 _let_9))) (let ((_let_13 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_11))) (let ((_let_15 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_9))) (let ((_let_16 (and _let_12 (= (tptp.meet _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_17 (tptp.the_carrier _let_10))) (let ((_let_18 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_17))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_17))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_21 _let_19 _let_16))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1769 $$unsorted)) (let ((_let_1 (tptp.boole_lattice A))) (let ((_let_2 (tptp.the_carrier _let_1))) (or (not (tptp.element B _let_2)) (not (tptp.element BOUND_VARIABLE_1769 _let_2)) (and (= (tptp.join _let_1 B BOUND_VARIABLE_1769) (tptp.set_union2 B BOUND_VARIABLE_1769)) (= (tptp.meet _let_1 B BOUND_VARIABLE_1769) (tptp.set_intersection2 B BOUND_VARIABLE_1769))))))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (tptp.below _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_26 (= _let_25 _let_13))) (let ((_let_27 (or _let_21 _let_19 _let_26))) (let ((_let_28 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1802 $$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_1802 _let_2)) (= (tptp.below _let_1 B BOUND_VARIABLE_1802) (tptp.subset B BOUND_VARIABLE_1802)))))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (or))) (let ((_let_32 (not _let_28))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_31)) _let_30 :args (_let_29 true _let_28)))) (let ((_let_34 (REFL :args (_let_27)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_31)) :args ((or _let_18 _let_27))) _let_33 :args (_let_18 true _let_27)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_31)) :args ((or _let_20 _let_27))) _let_33 :args (_let_20 true _let_27)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_16 0)) :args ((or _let_12 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_21 _let_19 _let_16 (not _let_22)))) _let_36 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((tptp.join (tptp.boole_lattice A) B BOUND_VARIABLE_1769)))) :args (_let_23))) _let_24 :args (_let_22 false _let_23)) :args (_let_16 false _let_20 false _let_18 false _let_22)) :args (_let_12 false _let_16)))) (let ((_let_38 (not _let_13))) (let ((_let_39 (= _let_25 _let_14))) (let ((_let_40 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_9))) (let ((_let_41 (or _let_38 _let_40))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 2)) _let_33 :args ((not _let_26) true _let_27)))) (let ((_let_43 (_let_26))) (let ((_let_44 (tptp.join_semilatt_str _let_10))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.empty_carrier _let_10))) (let ((_let_47 (or _let_46 _let_45 _let_21 _let_19 _let_39))) (let ((_let_48 (forall ((A $$unsorted) (BOUND_VARIABLE_1457 $$unsorted) (BOUND_VARIABLE_1455 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (tptp.empty_carrier A) (not (tptp.join_semilatt_str A)) (not (tptp.element BOUND_VARIABLE_1455 _let_1)) (not (tptp.element BOUND_VARIABLE_1457 _let_1)) (= (tptp.below A BOUND_VARIABLE_1455 BOUND_VARIABLE_1457) (= BOUND_VARIABLE_1457 (tptp.join A BOUND_VARIABLE_1455 BOUND_VARIABLE_1457)))))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (and (tptp.meet_semilatt_str _let_10) _let_44))) (let ((_let_51 (tptp.latt_str _let_10))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_50))) (let ((_let_54 (forall ((A $$unsorted)) (or (not (tptp.latt_str A)) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (forall ((BOUND_VARIABLE_1491 $$unsorted)) (tptp.latt_str (tptp.boole_lattice BOUND_VARIABLE_1491))))) (let ((_let_57 (_let_56))) (let ((_let_58 (forall ((BOUND_VARIABLE_1580 $$unsorted)) (not (tptp.empty_carrier (tptp.boole_lattice BOUND_VARIABLE_1580)))))) (let ((_let_59 (_let_58))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_21 _let_19 _let_46 _let_45 _let_39 (not _let_47)))) _let_36 _let_35 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_1580)))) :args _let_59)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) :args (0)) :args ((not _let_46) false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_50 1)) :args ((or _let_44 (not _let_50)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_52 _let_50 (not _let_53)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.boole_lattice BOUND_VARIABLE_1491)))) :args _let_57)) (AND_ELIM (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_51 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.latt_str A) false))))) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_50 false _let_51 false _let_53)) :args (_let_44 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.below A BOUND_VARIABLE_1455 BOUND_VARIABLE_1457)))) :args (_let_48))) _let_49 :args (_let_47 false _let_48)) :args (_let_39 false _let_20 false _let_18 true _let_46 false _let_44 false _let_47)))) (let ((_let_61 (not _let_39))) (let ((_let_62 (not _let_14))) (let ((_let_63 (_let_39))) (let ((_let_64 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= B (tptp.set_union2 A B)))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (not _let_12))) (let ((_let_67 (not _let_40))) (let ((_let_68 (REFL :args (_let_66)))) (let ((_let_69 (and _let_62 _let_12))) (let ((_let_70 (_let_62 _let_12))) (let ((_let_71 (_let_62))) (let ((_let_72 (ASSUME :args _let_71))) (let ((_let_73 (ASSUME :args (_let_12)))) (let ((_let_74 (SYMM _let_73))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_73) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)) _let_74 :args (=)) (FALSE_INTRO _let_72))) :args _let_70)) :args _let_70)) :args (true _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_14))) _let_68 (REFL :args (_let_67)) :args _let_31)) :args ((or _let_14 _let_67 _let_66))) _let_37 (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_38 _let_40 (not _let_41)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A B) false))))) :args (_let_64))) _let_65 :args (_let_41 false _let_64)) (REORDERING (CNF_EQUIV_POS2 :args _let_63) :args ((or _let_25 _let_62 _let_61))) _let_60 (REORDERING (CNF_EQUIV_NEG1 :args _let_43) :args ((or _let_25 _let_13 _let_26))) _let_42 :args (_let_25 false _let_12 false _let_40 false _let_41 true _let_14 false _let_39 false _let_13 true _let_26)))) (let ((_let_76 (_let_1))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (ASSUME :args (_let_15)))) (let ((_let_79 (ASSUME :args (_let_14)))) (let ((_let_80 (ASSUME :args (_let_38)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_78 _let_73 _let_79 _let_80) :args (_let_38 _let_14 _let_12 _let_15)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_80)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (TRANS (SYMM (SYMM _let_79)) (SYMM _let_74)) :args (APPLY_UF tptp.subset)) (TRUE_INTRO _let_78))) :args (_let_15 _let_12 _let_14 _let_38)) :args ((not (and _let_38 _let_14 _let_12 _let_15)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_13))) (REFL :args _let_71) _let_68 (REFL :args ((not _let_15))) :args _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_76)) _let_77 :args (_let_15 false _let_1)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_63) :args ((or (not _let_25) _let_14 _let_61))) _let_75 _let_60 :args (_let_14 false _let_25 false _let_39)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_43) _let_42 _let_75 :args (_let_38 true _let_26 false _let_25)) _let_37 :args (false false _let_15 false _let_14 true _let_13 false _let_12)) :args ((forall ((A $$unsorted)) (=> (tptp.latt_str A) (=> (tptp.strict_latt_str A) (= A (tptp.latt_str_of (tptp.the_carrier A) (tptp.the_L_join A) (tptp.the_L_meet A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (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 $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.apply_binary A B C) (tptp.apply A (tptp.ordered_pair B C)))))) (forall ((A $$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))))))))) (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 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.element C _let_1) (= (tptp.meet A B C) (tptp.apply_binary_as_element _let_1 _let_1 _let_1 (tptp.the_L_meet A) B C))))))))) _let_8 (forall ((A $$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_7 (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 true (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) _let_6 true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$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))))))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.cartesian_product2 _let_1 _let_1))) (let ((_let_3 (tptp.the_L_join A))) (=> (tptp.join_semilatt_str A) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) (exists ((A $$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 $$unsorted)) (tptp.relation_of2_as_subset C A B))) _let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (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)) (=> (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))) (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))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_4 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) _let_2 (forall ((A $$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)))) _let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.63 )
% 0.20/0.63 % SZS output end Proof for SEU344+1
% 0.20/0.63 % cvc5---1.0.5 exiting
% 0.20/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------