%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% 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 16:31:06 EDT 2023

% Result   : Theorem 0.22s 0.66s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15  % Problem    : SEU350+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.16  % Command    : do_cvc5 %s %d
% 0.15/0.37  % Computer : n023.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Wed Aug 23 16:40:13 EDT 2023
% 0.15/0.37  % CPUTime    : 
% 0.22/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.66  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.qLnsdHxowA/cvc5---1.0.5_19146.p...
% 0.22/0.66  ------- get file name : TPTP file name is SEU350+1
% 0.22/0.66  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19146.smt2...
% 0.22/0.66  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.66  % SZS status Theorem for SEU350+1
% 0.22/0.66  % SZS output start Proof for SEU350+1
% 0.22/0.66  (
% 0.22/0.66  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice B))) (=> (tptp.element C (tptp.the_carrier _let_1)) (= (tptp.relstr_set_smaller _let_1 A C) (tptp.latt_element_smaller B (tptp.cast_to_el_of_lattice B C) A)))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier B)) (tptp.lattice B) (tptp.latt_str B)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier B)) (= (tptp.latt_element_smaller B C A) (tptp.relstr_set_smaller (tptp.poset_of_lattice B) A (tptp.cast_to_el_of_LattPOSet B C))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A)))) (tptp.element (tptp.cast_to_el_of_lattice A B) (tptp.the_carrier A)))))) (let ((_let_4 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A))) (= (tptp.cast_to_el_of_lattice A B) B))))))) (let ((_let_5 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (= (tptp.cast_to_el_of_LattPOSet A B) B))))))) (let ((_let_6 (tptp.cast_to_el_of_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 _let_6))) (let ((_let_8 (tptp.cast_to_el_of_LattPOSet SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_6))) (let ((_let_9 (= _let_6 _let_8))) (let ((_let_10 (tptp.poset_of_lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_11 (tptp.relstr_set_smaller _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_12 (tptp.relstr_set_smaller _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_8))) (let ((_let_13 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 (tptp.the_carrier _let_10)))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.latt_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.lattice SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.empty_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_20 (or _let_19 _let_18 _let_16 _let_14 _let_7))) (let ((_let_21 (forall ((A $$unsorted) (BOUND_VARIABLE_1312 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_1312 (tptp.the_carrier (tptp.poset_of_lattice A)))) (= BOUND_VARIABLE_1312 (tptp.cast_to_el_of_lattice A BOUND_VARIABLE_1312)))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (tptp.latt_element_smaller SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_24 (= _let_11 _let_23))) (let ((_let_25 (or _let_19 _let_18 _let_16 _let_14 _let_24))) (let ((_let_26 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1621 $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice B))) (or (tptp.empty_carrier B) (not (tptp.lattice B)) (not (tptp.latt_str B)) (not (tptp.element BOUND_VARIABLE_1621 (tptp.the_carrier _let_1))) (= (tptp.relstr_set_smaller _let_1 A BOUND_VARIABLE_1621) (tptp.latt_element_smaller B (tptp.cast_to_el_of_lattice B BOUND_VARIABLE_1621) A))))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 3)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_29)) :args ((or _let_13 _let_25))) _let_31 :args (_let_13 true _let_25)))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_29)) :args ((or _let_15 _let_25))) _let_31 :args (_let_15 true _let_25)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_29)) :args ((or _let_17 _let_25))) _let_31 :args (_let_17 true _let_25)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 0)) _let_31 :args ((not _let_19) true _let_25)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_7 (not _let_20)))) _let_36 _let_35 _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1312 (tptp.the_carrier (tptp.poset_of_lattice A))) false))))) :args (_let_21))) _let_22 :args (_let_20 false _let_21)) :args (_let_7 true _let_19 false _let_17 false _let_15 false _let_13 false _let_20)))) (let ((_let_38 (tptp.element _let_6 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13)))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_19 _let_18 _let_16 _let_39 _let_9))) (let ((_let_41 (forall ((A $$unsorted) (BOUND_VARIABLE_1285 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element BOUND_VARIABLE_1285 (tptp.the_carrier A))) (= BOUND_VARIABLE_1285 (tptp.cast_to_el_of_LattPOSet A BOUND_VARIABLE_1285)))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or _let_19 _let_18 _let_16 _let_14 _let_38))) (let ((_let_44 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.lattice A)) (not (tptp.latt_str A)) (not (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A)))) (tptp.element (tptp.cast_to_el_of_lattice A B) (tptp.the_carrier A)))))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_19 _let_18 _let_16 _let_14 _let_38 (not _let_43)))) _let_36 _let_35 _let_34 _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.the_carrier (tptp.poset_of_lattice A))) false))))) :args (_let_44))) _let_45 :args (_let_43 false _let_44)) :args (_let_38 true _let_19 false _let_17 false _let_15 false _let_13 false _let_43)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_19 _let_18 _let_16 _let_39 _let_9 (not _let_40)))) _let_36 _let_35 _let_34 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element BOUND_VARIABLE_1285 (tptp.the_carrier A)) false))))) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_9 true _let_19 false _let_17 false _let_15 false _let_38 false _let_40)))) (let ((_let_48 (= _let_23 _let_12))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 4)) _let_31 :args ((not _let_24) true _let_25)))) (let ((_let_50 (_let_24))) (let ((_let_51 (or _let_19 _let_18 _let_16 _let_39 _let_48))) (let ((_let_52 (forall ((A $$unsorted) (B $$unsorted) (BOUND_VARIABLE_1595 $$unsorted)) (or (tptp.empty_carrier B) (not (tptp.lattice B)) (not (tptp.latt_str B)) (not (tptp.element BOUND_VARIABLE_1595 (tptp.the_carrier B))) (= (tptp.latt_element_smaller B BOUND_VARIABLE_1595 A) (tptp.relstr_set_smaller (tptp.poset_of_lattice B) A (tptp.cast_to_el_of_LattPOSet B BOUND_VARIABLE_1595))))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_19 _let_18 _let_16 _let_39 _let_48 (not _let_51)))) _let_36 _let_35 _let_34 _let_46 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.latt_element_smaller B BOUND_VARIABLE_1595 A)))) :args (_let_52))) _let_53 :args (_let_51 false _let_52)) :args (_let_48 true _let_19 false _let_17 false _let_15 false _let_38 false _let_51)))) (let ((_let_55 (not _let_48))) (let ((_let_56 (not _let_23))) (let ((_let_57 (_let_48))) (let ((_let_58 (not _let_9))) (let ((_let_59 (not _let_12))) (let ((_let_60 (not _let_7))) (let ((_let_61 (not _let_11))) (let ((_let_62 (and _let_61 _let_7 _let_9))) (let ((_let_63 (_let_61 _let_7 _let_9))) (let ((_let_64 (ASSUME :args (_let_61)))) (let ((_let_65 (ASSUME :args (_let_7)))) (let ((_let_66 (ASSUME :args (_let_9)))) (let ((_let_67 (CONG (REFL :args (_let_10)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)) (TRANS (SYMM _let_66) (SYMM _let_65)) :args (APPLY_UF tptp.relstr_set_smaller)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_62)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_64 _let_65 _let_66) (SCOPE (FALSE_ELIM (TRANS _let_67 (FALSE_INTRO _let_64))) :args _let_63)) :args _let_63)) :args (true _let_62)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_11))) (REFL :args (_let_60)) (REFL :args (_let_58)) (REFL :args (_let_59)) :args _let_29)) :args ((or _let_11 _let_60 _let_59 _let_58))) _let_47 _let_37 (REORDERING (CNF_EQUIV_POS1 :args _let_57) :args ((or _let_56 _let_12 _let_55))) _let_54 (REORDERING (CNF_EQUIV_NEG1 :args _let_50) :args ((or _let_11 _let_23 _let_24))) _let_49 :args (_let_11 false _let_9 false _let_7 false _let_12 false _let_48 false _let_23 true _let_24)))) (let ((_let_69 (and _let_11 _let_7 _let_9))) (let ((_let_70 (_let_11 _let_7 _let_9))) (let ((_let_71 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_69)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_71 _let_65 _let_66) (SCOPE (TRUE_ELIM (TRANS _let_67 (TRUE_INTRO _let_71))) :args _let_70)) :args _let_70)) :args (true _let_69)) :args ((or _let_61 _let_12 _let_60 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_57) :args ((or _let_23 _let_59 _let_55))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_50) _let_49 _let_68 :args (_let_56 true _let_24 false _let_11)) _let_54 :args (_let_59 true _let_23 false _let_48)) _let_68 _let_47 _let_37 :args (false true _let_12 false _let_11 false _let_9 false _let_7)) :args ((forall ((A $$unsorted)) (=> (tptp.rel_str A) (=> (tptp.strict_rel_str A) (= A (tptp.rel_str_of (tptp.the_carrier A) (tptp.the_InternalRel A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.lattice A)) (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (let ((_let_1 (not (tptp.empty_carrier A)))) (=> (tptp.latt_str A) (=> (and _let_1 (tptp.join_commutative A) (tptp.join_associative A) (tptp.meet_commutative A) (tptp.meet_associative A) (tptp.meet_absorbing A) (tptp.join_absorbing A)) (and _let_1 (tptp.lattice A)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.poset_of_lattice A) (tptp.rel_str_of (tptp.the_carrier A) (tptp.k2_lattice3 A))))) _let_5 _let_4 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (tptp.relation_of2 B A A) (and (tptp.strict_rel_str _let_1) (tptp.rel_str _let_1))))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.k2_lattice3 A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.reflexive _let_2) (tptp.antisymmetric _let_2) (tptp.transitive _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1) (tptp.relation_of2_as_subset _let_2 _let_1 _let_1)))))) true (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1) (tptp.rel_str _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A) (tptp.element B (tptp.the_carrier A))) (tptp.element (tptp.cast_to_el_of_LattPOSet A B) (tptp.the_carrier (tptp.poset_of_lattice A))))) _let_3 (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (tptp.relation (tptp.relation_of_lattice A)))) (forall ((A $$unsorted)) (=> (tptp.meet_semilatt_str A) (tptp.one_sorted_str A))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true (forall ((A $$unsorted)) (=> (tptp.join_semilatt_str A) (tptp.one_sorted_str A))) (forall ((A $$unsorted)) (=> (tptp.latt_str A) (and (tptp.meet_semilatt_str A) (tptp.join_semilatt_str A)))) 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))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) true (exists ((A $$unsorted)) (tptp.meet_semilatt_str A)) (exists ((A $$unsorted)) (tptp.rel_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 $$unsorted)) (tptp.relation_of2_as_subset C A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (not (tptp.empty A)) (tptp.relation_of2 B A A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1))))) (forall ((A $$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)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_InternalRel A))) (=> (and (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr A) (tptp.rel_str A)) (and (tptp.relation _let_2) (tptp.reflexive _let_2) (tptp.antisymmetric _let_2) (tptp.transitive _let_2) (tptp.v1_partfun1 _let_2 _let_1 _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.rel_str_of A B))) (=> (and (tptp.reflexive B) (tptp.antisymmetric B) (tptp.transitive B) (tptp.v1_partfun1 B A A) (tptp.relation_of2 B A A)) (and (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.poset_of_lattice A))) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_rel_str _let_1) (tptp.reflexive_relstr _let_1) (tptp.transitive_relstr _let_1) (tptp.antisymmetric_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation_of2 B A A) (forall ((C $$unsorted) (D $$unsorted)) (=> (= (tptp.rel_str_of A B) (tptp.rel_str_of C D)) (and (= A C) (= B D)))))) (exists ((A $$unsorted)) (and (tptp.rel_str A) (tptp.strict_rel_str A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.rel_str A) (not (tptp.empty_carrier A)) (tptp.strict_rel_str A) (tptp.reflexive_relstr A) (tptp.transitive_relstr A) (tptp.antisymmetric_relstr 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.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)))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.lattice A) (tptp.latt_str A)) (= (tptp.k2_lattice3 A) (tptp.relation_of_lattice A)))) (forall ((A $$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)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) _let_2 _let_1 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.66  )
% 0.22/0.66  % SZS output end Proof for SEU350+1
% 0.22/0.66  % cvc5---1.0.5 exiting
% 0.22/0.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------