TSTP Solution File: SET720+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET720+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 14:35:21 EDT 2023
% Result : Theorem 4.49s 4.62s
% Output : CNFRefutation 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 77
% Syntax : Number of formulae : 103 ( 11 unt; 73 typ; 0 def)
% Number of atoms : 155 ( 12 equ)
% Maximal formula atoms : 55 ( 5 avg)
% Number of connectives : 183 ( 58 ~; 80 |; 34 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 249 ( 69 >; 180 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-6 aty)
% Number of functors : 58 ( 58 usr; 4 con; 0-8 aty)
% Number of variables : 92 ( 0 sgn; 52 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
maps: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
compose_predicate: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_37,type,
compose_function: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_38,type,
equal_maps: ( $i * $i * $i * $i ) > $o ).
tff(decl_39,type,
identity: ( $i * $i ) > $o ).
tff(decl_40,type,
injective: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
surjective: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
one_to_one: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
inverse_predicate: ( $i * $i * $i * $i ) > $o ).
tff(decl_44,type,
inverse_function: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
image2: ( $i * $i ) > $i ).
tff(decl_46,type,
image3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
inverse_image2: ( $i * $i ) > $i ).
tff(decl_48,type,
inverse_image3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
increasing: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_50,type,
decreasing: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_51,type,
isomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_52,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk9_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk10_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk11_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk12_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk13_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
esk15_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
esk16_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk21_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
esk24_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_76,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk28_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_80,type,
esk29_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
esk30_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
esk31_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_83,type,
esk32_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_84,type,
esk33_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_85,type,
esk34_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
esk35_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
esk36_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk37_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk38_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
esk39_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk40_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
esk41_0: $i ).
tff(decl_93,type,
esk42_0: $i ).
tff(decl_94,type,
esk43_0: $i ).
fof(thII11,conjecture,
! [X6,X1,X2] :
( ( maps(X6,X1,X2)
& one_to_one(X6,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X6,X1,X2),X2,X1),X6,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII11) ).
fof(equal_maps,axiom,
! [X6,X10,X1,X2] :
( equal_maps(X6,X10,X1,X2)
<=> ! [X3,X7,X8] :
( ( member(X3,X1)
& member(X7,X2)
& member(X8,X2) )
=> ( ( apply(X6,X3,X7)
& apply(X10,X3,X8) )
=> X7 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',equal_maps) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X1)
& member(X7,X2)
& member(X8,X2) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
fof(inverse_function,axiom,
! [X6,X1,X2,X3,X5] :
( ( member(X3,X1)
& member(X5,X2) )
=> ( apply(X6,X3,X5)
<=> apply(inverse_function(X6,X1,X2),X5,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',inverse_function) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X1,X2] :
( ( maps(X6,X1,X2)
& one_to_one(X6,X1,X2) )
=> equal_maps(inverse_function(inverse_function(X6,X1,X2),X2,X1),X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thII11]) ).
fof(c_0_5,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& one_to_one(esk41_0,esk42_0,esk43_0)
& ~ equal_maps(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X99,X100,X101,X102,X103,X104,X105,X106,X107,X108,X109] :
( ( ~ equal_maps(X99,X100,X101,X102)
| ~ member(X103,X101)
| ~ member(X104,X102)
| ~ member(X105,X102)
| ~ apply(X99,X103,X104)
| ~ apply(X100,X103,X105)
| X104 = X105 )
& ( member(esk14_4(X106,X107,X108,X109),X108)
| equal_maps(X106,X107,X108,X109) )
& ( member(esk15_4(X106,X107,X108,X109),X109)
| equal_maps(X106,X107,X108,X109) )
& ( member(esk16_4(X106,X107,X108,X109),X109)
| equal_maps(X106,X107,X108,X109) )
& ( apply(X106,esk14_4(X106,X107,X108,X109),esk15_4(X106,X107,X108,X109))
| equal_maps(X106,X107,X108,X109) )
& ( apply(X107,esk14_4(X106,X107,X108,X109),esk16_4(X106,X107,X108,X109))
| equal_maps(X106,X107,X108,X109) )
& ( esk15_4(X106,X107,X108,X109) != esk16_4(X106,X107,X108,X109)
| equal_maps(X106,X107,X108,X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_maps])])])])])]) ).
fof(c_0_7,plain,
! [X54,X55,X56,X57,X59,X60,X61,X62,X63,X64,X66] :
( ( member(esk4_4(X54,X55,X56,X57),X56)
| ~ member(X57,X55)
| ~ maps(X54,X55,X56) )
& ( apply(X54,X57,esk4_4(X54,X55,X56,X57))
| ~ member(X57,X55)
| ~ maps(X54,X55,X56) )
& ( ~ member(X59,X55)
| ~ member(X60,X56)
| ~ member(X61,X56)
| ~ apply(X54,X59,X60)
| ~ apply(X54,X59,X61)
| X60 = X61
| ~ maps(X54,X55,X56) )
& ( member(esk6_3(X62,X63,X64),X63)
| member(esk5_3(X62,X63,X64),X63)
| maps(X62,X63,X64) )
& ( member(esk7_3(X62,X63,X64),X64)
| member(esk5_3(X62,X63,X64),X63)
| maps(X62,X63,X64) )
& ( member(esk8_3(X62,X63,X64),X64)
| member(esk5_3(X62,X63,X64),X63)
| maps(X62,X63,X64) )
& ( apply(X62,esk6_3(X62,X63,X64),esk7_3(X62,X63,X64))
| member(esk5_3(X62,X63,X64),X63)
| maps(X62,X63,X64) )
& ( apply(X62,esk6_3(X62,X63,X64),esk8_3(X62,X63,X64))
| member(esk5_3(X62,X63,X64),X63)
| maps(X62,X63,X64) )
& ( esk7_3(X62,X63,X64) != esk8_3(X62,X63,X64)
| member(esk5_3(X62,X63,X64),X63)
| maps(X62,X63,X64) )
& ( member(esk6_3(X62,X63,X64),X63)
| ~ member(X66,X64)
| ~ apply(X62,esk5_3(X62,X63,X64),X66)
| maps(X62,X63,X64) )
& ( member(esk7_3(X62,X63,X64),X64)
| ~ member(X66,X64)
| ~ apply(X62,esk5_3(X62,X63,X64),X66)
| maps(X62,X63,X64) )
& ( member(esk8_3(X62,X63,X64),X64)
| ~ member(X66,X64)
| ~ apply(X62,esk5_3(X62,X63,X64),X66)
| maps(X62,X63,X64) )
& ( apply(X62,esk6_3(X62,X63,X64),esk7_3(X62,X63,X64))
| ~ member(X66,X64)
| ~ apply(X62,esk5_3(X62,X63,X64),X66)
| maps(X62,X63,X64) )
& ( apply(X62,esk6_3(X62,X63,X64),esk8_3(X62,X63,X64))
| ~ member(X66,X64)
| ~ apply(X62,esk5_3(X62,X63,X64),X66)
| maps(X62,X63,X64) )
& ( esk7_3(X62,X63,X64) != esk8_3(X62,X63,X64)
| ~ member(X66,X64)
| ~ apply(X62,esk5_3(X62,X63,X64),X66)
| maps(X62,X63,X64) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[maps])])])])])]) ).
fof(c_0_8,plain,
! [X156,X157,X158,X159,X160] :
( ( ~ apply(X156,X159,X160)
| apply(inverse_function(X156,X157,X158),X160,X159)
| ~ member(X159,X157)
| ~ member(X160,X158) )
& ( ~ apply(inverse_function(X156,X157,X158),X160,X159)
| apply(X156,X159,X160)
| ~ member(X159,X157)
| ~ member(X160,X158) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inverse_function])])]) ).
cnf(c_0_9,negated_conjecture,
~ equal_maps(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( apply(X1,esk14_4(X1,X2,X3,X4),esk15_4(X1,X2,X3,X4))
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(esk15_4(X1,X2,X3,X4),X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(esk14_4(X1,X2,X3,X4),X3)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( X3 = X5
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ member(X5,X4)
| ~ apply(X6,X1,X3)
| ~ apply(X6,X1,X5)
| ~ maps(X6,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
maps(esk41_0,esk42_0,esk43_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( apply(X1,esk14_4(X2,X1,X3,X4),esk16_4(X2,X1,X3,X4))
| equal_maps(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,plain,
( member(esk16_4(X1,X2,X3,X4),X4)
| equal_maps(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( apply(X1,X5,X4)
| ~ apply(inverse_function(X1,X2,X3),X4,X5)
| ~ member(X5,X2)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
apply(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_19,negated_conjecture,
member(esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk43_0),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_20,negated_conjecture,
member(esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk42_0),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( X1 = X2
| ~ apply(esk41_0,X3,X2)
| ~ apply(esk41_0,X3,X1)
| ~ member(X2,esk43_0)
| ~ member(X1,esk43_0)
| ~ member(X3,esk42_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
member(esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk43_0),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
apply(inverse_function(esk41_0,esk42_0,esk43_0),esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_25,plain,
( equal_maps(X1,X2,X3,X4)
| esk15_4(X1,X2,X3,X4) != esk16_4(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
( esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0) = X1
| ~ apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),X1)
| ~ member(X1,esk43_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
apply(esk41_0,esk14_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_24]),c_0_20]),c_0_19])]) ).
cnf(c_0_28,negated_conjecture,
esk16_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0) != esk15_4(inverse_function(inverse_function(esk41_0,esk42_0,esk43_0),esk43_0,esk42_0),esk41_0,esk42_0,esk43_0),
inference(spm,[status(thm)],[c_0_9,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET720+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:05:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 4.49/4.62 % Version : CSE_E---1.5
% 4.49/4.62 % Problem : theBenchmark.p
% 4.49/4.62 % Proof found
% 4.49/4.62 % SZS status Theorem for theBenchmark.p
% 4.49/4.62 % SZS output start Proof
% See solution above
% 4.49/4.62 % Total time : 4.037000 s
% 4.49/4.62 % SZS output end Proof
% 4.49/4.62 % Total time : 4.041000 s
%------------------------------------------------------------------------------