TSTP Solution File: SEU371+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU371+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 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 16:25:12 EDT 2023
% Result : Theorem 0.19s 0.78s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 106
% Syntax : Number of formulae : 135 ( 15 unt; 97 typ; 0 def)
% Number of atoms : 200 ( 27 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 223 ( 61 ~; 60 |; 95 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 75 >; 28 *; 0 +; 0 <<)
% Number of predicates : 48 ( 46 usr; 1 prp; 0-3 aty)
% Number of functors : 51 ( 51 usr; 22 con; 0-3 aty)
% Number of variables : 38 ( 6 sgn; 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
rel_str: $i > $o ).
tff(decl_23,type,
strict_rel_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_InternalRel: $i > $i ).
tff(decl_26,type,
rel_str_of: ( $i * $i ) > $i ).
tff(decl_27,type,
latt_str: $i > $o ).
tff(decl_28,type,
strict_latt_str: $i > $o ).
tff(decl_29,type,
the_L_join: $i > $i ).
tff(decl_30,type,
the_L_meet: $i > $i ).
tff(decl_31,type,
latt_str_of: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
in: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_carrier: $i > $o ).
tff(decl_34,type,
lattice: $i > $o ).
tff(decl_35,type,
complete_latt_str: $i > $o ).
tff(decl_36,type,
join_commutative: $i > $o ).
tff(decl_37,type,
join_associative: $i > $o ).
tff(decl_38,type,
meet_commutative: $i > $o ).
tff(decl_39,type,
meet_associative: $i > $o ).
tff(decl_40,type,
meet_absorbing: $i > $o ).
tff(decl_41,type,
join_absorbing: $i > $o ).
tff(decl_42,type,
lower_bounded_semilattstr: $i > $o ).
tff(decl_43,type,
upper_bounded_semilattstr: $i > $o ).
tff(decl_44,type,
bounded_lattstr: $i > $o ).
tff(decl_45,type,
with_suprema_relstr: $i > $o ).
tff(decl_46,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_47,type,
powerset: $i > $i ).
tff(decl_48,type,
element: ( $i * $i ) > $o ).
tff(decl_49,type,
relation: $i > $o ).
tff(decl_50,type,
complete_relstr: $i > $o ).
tff(decl_51,type,
with_infima_relstr: $i > $o ).
tff(decl_52,type,
bounded_relstr: $i > $o ).
tff(decl_53,type,
lower_bounded_relstr: $i > $o ).
tff(decl_54,type,
upper_bounded_relstr: $i > $o ).
tff(decl_55,type,
boolean_lattstr: $i > $o ).
tff(decl_56,type,
distributive_lattstr: $i > $o ).
tff(decl_57,type,
complemented_lattstr: $i > $o ).
tff(decl_58,type,
modular_lattstr: $i > $o ).
tff(decl_59,type,
bottom_of_relstr: $i > $i ).
tff(decl_60,type,
empty_set: $i ).
tff(decl_61,type,
join_on_relstr: ( $i * $i ) > $i ).
tff(decl_62,type,
meet_of_latt_set: ( $i * $i ) > $i ).
tff(decl_63,type,
a_2_2_lattice3: ( $i * $i ) > $i ).
tff(decl_64,type,
join_of_latt_set: ( $i * $i ) > $i ).
tff(decl_65,type,
poset_of_lattice: $i > $i ).
tff(decl_66,type,
k2_lattice3: $i > $i ).
tff(decl_67,type,
boole_POSet: $i > $i ).
tff(decl_68,type,
boole_lattice: $i > $i ).
tff(decl_69,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_70,type,
function: $i > $o ).
tff(decl_71,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_72,type,
reflexive: $i > $o ).
tff(decl_73,type,
antisymmetric: $i > $o ).
tff(decl_74,type,
transitive: $i > $o ).
tff(decl_75,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_76,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_77,type,
meet_on_relstr: ( $i * $i ) > $i ).
tff(decl_78,type,
reflexive_relstr: $i > $o ).
tff(decl_79,type,
transitive_relstr: $i > $o ).
tff(decl_80,type,
antisymmetric_relstr: $i > $o ).
tff(decl_81,type,
meet_semilatt_str: $i > $o ).
tff(decl_82,type,
bottom_of_semilattstr: $i > $i ).
tff(decl_83,type,
relation_of_lattice: $i > $i ).
tff(decl_84,type,
one_sorted_str: $i > $o ).
tff(decl_85,type,
join_semilatt_str: $i > $o ).
tff(decl_86,type,
empty: $i > $o ).
tff(decl_87,type,
latt_set_smaller: ( $i * $i * $i ) > $o ).
tff(decl_88,type,
subset: ( $i * $i ) > $o ).
tff(decl_89,type,
esk1_0: $i ).
tff(decl_90,type,
esk2_0: $i ).
tff(decl_91,type,
esk3_0: $i ).
tff(decl_92,type,
esk4_0: $i ).
tff(decl_93,type,
esk5_0: $i ).
tff(decl_94,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_95,type,
esk7_1: $i > $i ).
tff(decl_96,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_97,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
esk10_0: $i ).
tff(decl_99,type,
esk11_0: $i ).
tff(decl_100,type,
esk12_0: $i ).
tff(decl_101,type,
esk13_0: $i ).
tff(decl_102,type,
esk14_0: $i ).
tff(decl_103,type,
esk15_0: $i ).
tff(decl_104,type,
esk16_1: $i > $i ).
tff(decl_105,type,
esk17_0: $i ).
tff(decl_106,type,
esk18_0: $i ).
tff(decl_107,type,
esk19_0: $i ).
tff(decl_108,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk21_1: $i > $i ).
tff(decl_110,type,
esk22_0: $i ).
tff(decl_111,type,
esk23_0: $i ).
tff(decl_112,type,
esk24_0: $i ).
tff(decl_113,type,
esk25_0: $i ).
tff(decl_114,type,
esk26_1: $i > $i ).
tff(decl_115,type,
esk27_0: $i ).
tff(decl_116,type,
esk28_0: $i ).
tff(decl_117,type,
esk29_0: $i ).
tff(decl_118,type,
esk30_2: ( $i * $i ) > $i ).
fof(t18_yellow_1,conjecture,
! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(t29_yellow_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
& meet_of_latt_set(X1,X2) = meet_on_relstr(poset_of_lattice(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_yellow_0) ).
fof(dt_k3_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(t50_lattice3,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
fof(fc1_knaster,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_knaster) ).
fof(d2_yellow_1,axiom,
! [X1] : boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(d11_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(t3_lattice3,axiom,
! [X1] :
( lower_bounded_semilattstr(boole_lattice(X1))
& bottom_of_semilattstr(boole_lattice(X1)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] : bottom_of_relstr(boole_POSet(X1)) = empty_set,
inference(assume_negation,[status(cth)],[t18_yellow_1]) ).
fof(c_0_10,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ! [X2] :
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
& meet_of_latt_set(X1,X2) = meet_on_relstr(poset_of_lattice(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[t29_yellow_0]) ).
fof(c_0_11,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ( strict_rel_str(poset_of_lattice(X1))
& reflexive_relstr(poset_of_lattice(X1))
& transitive_relstr(poset_of_lattice(X1))
& antisymmetric_relstr(poset_of_lattice(X1))
& rel_str(poset_of_lattice(X1)) ) ),
inference(fof_simplification,[status(thm)],[dt_k3_lattice3]) ).
fof(c_0_12,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& complete_latt_str(X1)
& latt_str(X1) )
=> ( ~ empty_carrier(X1)
& lattice(X1)
& lower_bounded_semilattstr(X1)
& latt_str(X1)
& bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set) ) ),
inference(fof_simplification,[status(thm)],[t50_lattice3]) ).
fof(c_0_13,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1))
& join_commutative(boole_lattice(X1))
& join_associative(boole_lattice(X1))
& meet_commutative(boole_lattice(X1))
& meet_associative(boole_lattice(X1))
& meet_absorbing(boole_lattice(X1))
& join_absorbing(boole_lattice(X1))
& lattice(boole_lattice(X1))
& distributive_lattstr(boole_lattice(X1))
& modular_lattstr(boole_lattice(X1))
& lower_bounded_semilattstr(boole_lattice(X1))
& upper_bounded_semilattstr(boole_lattice(X1))
& bounded_lattstr(boole_lattice(X1))
& complemented_lattstr(boole_lattice(X1))
& boolean_lattstr(boole_lattice(X1))
& complete_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_knaster]) ).
fof(c_0_14,negated_conjecture,
bottom_of_relstr(boole_POSet(esk29_0)) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_15,plain,
! [X32] : boole_POSet(X32) = poset_of_lattice(boole_lattice(X32)),
inference(variable_rename,[status(thm)],[d2_yellow_1]) ).
fof(c_0_16,plain,
! [X28] :
( ~ rel_str(X28)
| bottom_of_relstr(X28) = join_on_relstr(X28,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])]) ).
fof(c_0_17,plain,
! [X147,X148] :
( ( join_of_latt_set(X147,X148) = join_on_relstr(poset_of_lattice(X147),X148)
| empty_carrier(X147)
| ~ lattice(X147)
| ~ complete_latt_str(X147)
| ~ latt_str(X147) )
& ( meet_of_latt_set(X147,X148) = meet_on_relstr(poset_of_lattice(X147),X148)
| empty_carrier(X147)
| ~ lattice(X147)
| ~ complete_latt_str(X147)
| ~ latt_str(X147) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_18,plain,
! [X48] :
( ( strict_rel_str(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( reflexive_relstr(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( transitive_relstr(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( antisymmetric_relstr(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) )
& ( rel_str(poset_of_lattice(X48))
| empty_carrier(X48)
| ~ lattice(X48)
| ~ latt_str(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_19,plain,
! [X154] :
( lower_bounded_semilattstr(boole_lattice(X154))
& bottom_of_semilattstr(boole_lattice(X154)) = empty_set ),
inference(variable_rename,[status(thm)],[t3_lattice3]) ).
fof(c_0_20,plain,
! [X160] :
( ( ~ empty_carrier(X160)
| empty_carrier(X160)
| ~ lattice(X160)
| ~ complete_latt_str(X160)
| ~ latt_str(X160) )
& ( lattice(X160)
| empty_carrier(X160)
| ~ lattice(X160)
| ~ complete_latt_str(X160)
| ~ latt_str(X160) )
& ( lower_bounded_semilattstr(X160)
| empty_carrier(X160)
| ~ lattice(X160)
| ~ complete_latt_str(X160)
| ~ latt_str(X160) )
& ( latt_str(X160)
| empty_carrier(X160)
| ~ lattice(X160)
| ~ complete_latt_str(X160)
| ~ latt_str(X160) )
& ( bottom_of_semilattstr(X160) = join_of_latt_set(X160,empty_set)
| empty_carrier(X160)
| ~ lattice(X160)
| ~ complete_latt_str(X160)
| ~ latt_str(X160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_21,plain,
! [X76] :
( ~ empty_carrier(boole_lattice(X76))
& strict_latt_str(boole_lattice(X76))
& join_commutative(boole_lattice(X76))
& join_associative(boole_lattice(X76))
& meet_commutative(boole_lattice(X76))
& meet_associative(boole_lattice(X76))
& meet_absorbing(boole_lattice(X76))
& join_absorbing(boole_lattice(X76))
& lattice(boole_lattice(X76))
& distributive_lattstr(boole_lattice(X76))
& modular_lattstr(boole_lattice(X76))
& lower_bounded_semilattstr(boole_lattice(X76))
& upper_bounded_semilattstr(boole_lattice(X76))
& bounded_lattstr(boole_lattice(X76))
& complemented_lattstr(boole_lattice(X76))
& boolean_lattstr(boole_lattice(X76))
& complete_latt_str(boole_lattice(X76)) ),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_22,plain,
! [X42] :
( strict_latt_str(boole_lattice(X42))
& latt_str(boole_lattice(X42)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
cnf(c_0_23,negated_conjecture,
bottom_of_relstr(boole_POSet(esk29_0)) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
boole_POSet(X1) = poset_of_lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( bottom_of_relstr(X1) = join_on_relstr(X1,empty_set)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
( join_of_latt_set(X1,X2) = join_on_relstr(poset_of_lattice(X1),X2)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( rel_str(poset_of_lattice(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
bottom_of_semilattstr(boole_lattice(X1)) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( bottom_of_semilattstr(X1) = join_of_latt_set(X1,empty_set)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ complete_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
complete_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
lattice(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,negated_conjecture,
bottom_of_relstr(poset_of_lattice(boole_lattice(esk29_0))) != empty_set,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
( bottom_of_relstr(poset_of_lattice(X1)) = join_of_latt_set(X1,empty_set)
| empty_carrier(X1)
| ~ complete_latt_str(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_36,plain,
join_of_latt_set(boole_lattice(X1),empty_set) = empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_30]),c_0_31]),c_0_32])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU371+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Wed Aug 23 15:05:16 EDT 2023
% 0.16/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.78 % Version : CSE_E---1.5
% 0.19/0.78 % Problem : theBenchmark.p
% 0.19/0.78 % Proof found
% 0.19/0.78 % SZS status Theorem for theBenchmark.p
% 0.19/0.78 % SZS output start Proof
% See solution above
% 0.19/0.79 % Total time : 0.224000 s
% 0.19/0.79 % SZS output end Proof
% 0.19/0.79 % Total time : 0.229000 s
%------------------------------------------------------------------------------