TSTP Solution File: SWC330+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC330+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 11:30:03 EST 2010
% Result : Theorem 0.35s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 18 unt; 0 def)
% Number of atoms : 389 ( 117 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 490 ( 174 ~; 183 |; 111 &)
% ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 67 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',ax21) ).
fof(15,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( segmentP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) ) ) ),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',ax7) ).
fof(18,axiom,
equalelemsP(nil),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',ax74) ).
fof(19,axiom,
! [X1] :
( ssItem(X1)
=> equalelemsP(cons(X1,nil)) ),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',ax73) ).
fof(27,axiom,
ssList(nil),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',ax17) ).
fof(36,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',ax57) ).
fof(40,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X5,nil) != X3
| app(app(X6,X3),X7) != X4
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ),
file('/tmp/tmpjiBdYh/sel_SWC330+1.p_1',co1) ).
fof(41,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X5,nil) != X3
| app(app(X6,X3),X7) != X4
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ),
inference(assume_negation,[status(cth)],[40]) ).
fof(45,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ~ ssList(X4)
| X2 != X4
| X1 != X3
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X5,nil) != X3
| app(app(X6,X3),X7) != X4
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) )
& ( nil != X4
| nil != X3 ) )
| ( segmentP(X2,X1)
& equalelemsP(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[41,theory(equality)]) ).
fof(83,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(84,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[83]) ).
fof(85,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[84]) ).
cnf(86,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[85]) ).
fof(112,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ segmentP(X1,X2)
| ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& app(app(X3,X2),X4) = X1 ) ) )
& ( ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| app(app(X3,X2),X4) != X1 ) )
| segmentP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(113,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& app(app(X7,X6),X8) = X5 ) ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[112]) ).
fof(114,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ segmentP(X5,X6)
| ( ssList(esk7_2(X5,X6))
& ssList(esk8_2(X5,X6))
& app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) )
& ( ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| app(app(X9,X6),X10) != X5 ) )
| segmentP(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[113]) ).
fof(115,plain,
! [X5,X6,X9,X10] :
( ( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6) )
& ( ~ segmentP(X5,X6)
| ( ssList(esk7_2(X5,X6))
& ssList(esk8_2(X5,X6))
& app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) ) )
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X5,X6,X9,X10] :
( ( ~ ssList(X10)
| app(app(X9,X6),X10) != X5
| ~ ssList(X9)
| segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk7_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( ssList(esk8_2(X5,X6))
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) )
& ( app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5
| ~ segmentP(X5,X6)
| ~ ssList(X6)
| ~ ssList(X5) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(120,plain,
( segmentP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X3,X2),X4) != X1
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[116]) ).
cnf(128,plain,
equalelemsP(nil),
inference(split_conjunct,[status(thm)],[18]) ).
fof(129,plain,
! [X1] :
( ~ ssItem(X1)
| equalelemsP(cons(X1,nil)) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(130,plain,
! [X2] :
( ~ ssItem(X2)
| equalelemsP(cons(X2,nil)) ),
inference(variable_rename,[status(thm)],[129]) ).
cnf(131,plain,
( equalelemsP(cons(X1,nil))
| ~ ssItem(X1) ),
inference(split_conjunct,[status(thm)],[130]) ).
cnf(160,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[27]) ).
fof(203,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(204,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[203]) ).
cnf(205,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[204]) ).
fof(225,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& cons(X5,nil) = X3
& app(app(X6,X3),X7) = X4
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X5,X8) )
& ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ~ lt(X9,X5) ) ) ) )
| ( nil = X4
& nil = X3 ) )
& ( ~ segmentP(X2,X1)
| ~ equalelemsP(X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[45]) ).
fof(226,negated_conjecture,
? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& X11 = X13
& X10 = X12
& ( ? [X14] :
( ssItem(X14)
& ? [X15] :
( ssList(X15)
& ? [X16] :
( ssList(X16)
& cons(X14,nil) = X12
& app(app(X15,X12),X16) = X13
& ! [X17] :
( ~ ssItem(X17)
| ~ memberP(X15,X17)
| ~ lt(X14,X17) )
& ! [X18] :
( ~ ssItem(X18)
| ~ memberP(X16,X18)
| ~ lt(X18,X14) ) ) ) )
| ( nil = X13
& nil = X12 ) )
& ( ~ segmentP(X11,X10)
| ~ equalelemsP(X10) ) ) ) ) ),
inference(variable_rename,[status(thm)],[225]) ).
fof(227,negated_conjecture,
( ssList(esk13_0)
& ssList(esk14_0)
& ssList(esk15_0)
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& ( ( ssItem(esk17_0)
& ssList(esk18_0)
& ssList(esk19_0)
& cons(esk17_0,nil) = esk15_0
& app(app(esk18_0,esk15_0),esk19_0) = esk16_0
& ! [X17] :
( ~ ssItem(X17)
| ~ memberP(esk18_0,X17)
| ~ lt(esk17_0,X17) )
& ! [X18] :
( ~ ssItem(X18)
| ~ memberP(esk19_0,X18)
| ~ lt(X18,esk17_0) ) )
| ( nil = esk16_0
& nil = esk15_0 ) )
& ( ~ segmentP(esk14_0,esk13_0)
| ~ equalelemsP(esk13_0) ) ),
inference(skolemize,[status(esa)],[226]) ).
fof(228,negated_conjecture,
! [X17,X18] :
( ( ( ( ~ ssItem(X18)
| ~ memberP(esk19_0,X18)
| ~ lt(X18,esk17_0) )
& ( ~ ssItem(X17)
| ~ memberP(esk18_0,X17)
| ~ lt(esk17_0,X17) )
& ssList(esk19_0)
& cons(esk17_0,nil) = esk15_0
& app(app(esk18_0,esk15_0),esk19_0) = esk16_0
& ssList(esk18_0)
& ssItem(esk17_0) )
| ( nil = esk16_0
& nil = esk15_0 ) )
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& ( ~ segmentP(esk14_0,esk13_0)
| ~ equalelemsP(esk13_0) )
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(shift_quantors,[status(thm)],[227]) ).
fof(229,negated_conjecture,
! [X17,X18] :
( ( nil = esk16_0
| ~ ssItem(X18)
| ~ memberP(esk19_0,X18)
| ~ lt(X18,esk17_0) )
& ( nil = esk15_0
| ~ ssItem(X18)
| ~ memberP(esk19_0,X18)
| ~ lt(X18,esk17_0) )
& ( nil = esk16_0
| ~ ssItem(X17)
| ~ memberP(esk18_0,X17)
| ~ lt(esk17_0,X17) )
& ( nil = esk15_0
| ~ ssItem(X17)
| ~ memberP(esk18_0,X17)
| ~ lt(esk17_0,X17) )
& ( nil = esk16_0
| ssList(esk19_0) )
& ( nil = esk15_0
| ssList(esk19_0) )
& ( nil = esk16_0
| cons(esk17_0,nil) = esk15_0 )
& ( nil = esk15_0
| cons(esk17_0,nil) = esk15_0 )
& ( nil = esk16_0
| app(app(esk18_0,esk15_0),esk19_0) = esk16_0 )
& ( nil = esk15_0
| app(app(esk18_0,esk15_0),esk19_0) = esk16_0 )
& ( nil = esk16_0
| ssList(esk18_0) )
& ( nil = esk15_0
| ssList(esk18_0) )
& ( nil = esk16_0
| ssItem(esk17_0) )
& ( nil = esk15_0
| ssItem(esk17_0) )
& ssList(esk16_0)
& esk14_0 = esk16_0
& esk13_0 = esk15_0
& ( ~ segmentP(esk14_0,esk13_0)
| ~ equalelemsP(esk13_0) )
& ssList(esk15_0)
& ssList(esk14_0)
& ssList(esk13_0) ),
inference(distribute,[status(thm)],[228]) ).
cnf(230,negated_conjecture,
ssList(esk13_0),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(231,negated_conjecture,
ssList(esk14_0),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(233,negated_conjecture,
( ~ equalelemsP(esk13_0)
| ~ segmentP(esk14_0,esk13_0) ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(234,negated_conjecture,
esk13_0 = esk15_0,
inference(split_conjunct,[status(thm)],[229]) ).
cnf(235,negated_conjecture,
esk14_0 = esk16_0,
inference(split_conjunct,[status(thm)],[229]) ).
cnf(237,negated_conjecture,
( ssItem(esk17_0)
| nil = esk15_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(238,negated_conjecture,
( ssItem(esk17_0)
| nil = esk16_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(239,negated_conjecture,
( ssList(esk18_0)
| nil = esk15_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(241,negated_conjecture,
( app(app(esk18_0,esk15_0),esk19_0) = esk16_0
| nil = esk15_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(243,negated_conjecture,
( cons(esk17_0,nil) = esk15_0
| nil = esk15_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(244,negated_conjecture,
( cons(esk17_0,nil) = esk15_0
| nil = esk16_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(245,negated_conjecture,
( ssList(esk19_0)
| nil = esk15_0 ),
inference(split_conjunct,[status(thm)],[229]) ).
cnf(251,negated_conjecture,
ssList(esk15_0),
inference(rw,[status(thm)],[230,234,theory(equality)]) ).
cnf(252,negated_conjecture,
ssList(esk16_0),
inference(rw,[status(thm)],[231,235,theory(equality)]) ).
cnf(253,negated_conjecture,
( ~ equalelemsP(esk15_0)
| ~ segmentP(esk14_0,esk13_0) ),
inference(rw,[status(thm)],[233,234,theory(equality)]) ).
cnf(254,negated_conjecture,
( ~ equalelemsP(esk15_0)
| ~ segmentP(esk16_0,esk15_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[253,235,theory(equality)]),234,theory(equality)]) ).
cnf(255,negated_conjecture,
( equalelemsP(esk15_0)
| esk15_0 = nil
| ~ ssItem(esk17_0) ),
inference(spm,[status(thm)],[131,243,theory(equality)]) ).
cnf(285,negated_conjecture,
( esk16_0 = nil
| esk15_0 != nil
| ~ ssItem(esk17_0)
| ~ ssList(nil) ),
inference(spm,[status(thm)],[86,244,theory(equality)]) ).
cnf(288,negated_conjecture,
( esk16_0 = nil
| esk15_0 != nil
| ~ ssItem(esk17_0)
| $false ),
inference(rw,[status(thm)],[285,160,theory(equality)]) ).
cnf(289,negated_conjecture,
( esk16_0 = nil
| esk15_0 != nil
| ~ ssItem(esk17_0) ),
inference(cn,[status(thm)],[288,theory(equality)]) ).
cnf(522,negated_conjecture,
( segmentP(X1,esk15_0)
| esk15_0 = nil
| esk16_0 != X1
| ~ ssList(esk19_0)
| ~ ssList(esk18_0)
| ~ ssList(esk15_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[120,241,theory(equality)]) ).
cnf(635,negated_conjecture,
( esk15_0 = nil
| equalelemsP(esk15_0) ),
inference(csr,[status(thm)],[255,237]) ).
cnf(636,negated_conjecture,
( esk15_0 = nil
| ~ segmentP(esk16_0,esk15_0) ),
inference(spm,[status(thm)],[254,635,theory(equality)]) ).
cnf(637,negated_conjecture,
( esk16_0 = nil
| esk15_0 != nil ),
inference(csr,[status(thm)],[289,238]) ).
cnf(3909,negated_conjecture,
( segmentP(X1,esk15_0)
| esk15_0 = nil
| esk16_0 != X1
| ~ ssList(esk19_0)
| ~ ssList(esk18_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[522,251,theory(equality)]) ).
cnf(3910,negated_conjecture,
( segmentP(X1,esk15_0)
| esk15_0 = nil
| esk16_0 != X1
| ~ ssList(esk19_0)
| ~ ssList(esk18_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[3909,theory(equality)]) ).
cnf(3911,negated_conjecture,
( esk15_0 = nil
| segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(esk19_0)
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3910,239]) ).
cnf(3912,negated_conjecture,
( esk15_0 = nil
| segmentP(X1,esk15_0)
| esk16_0 != X1
| ~ ssList(X1) ),
inference(csr,[status(thm)],[3911,245]) ).
cnf(3916,negated_conjecture,
( esk15_0 = nil
| ~ ssList(esk16_0) ),
inference(spm,[status(thm)],[636,3912,theory(equality)]) ).
cnf(3926,negated_conjecture,
( esk15_0 = nil
| $false ),
inference(rw,[status(thm)],[3916,252,theory(equality)]) ).
cnf(3927,negated_conjecture,
esk15_0 = nil,
inference(cn,[status(thm)],[3926,theory(equality)]) ).
cnf(4108,negated_conjecture,
( esk16_0 = nil
| $false ),
inference(rw,[status(thm)],[637,3927,theory(equality)]) ).
cnf(4109,negated_conjecture,
esk16_0 = nil,
inference(cn,[status(thm)],[4108,theory(equality)]) ).
cnf(4121,negated_conjecture,
( $false
| ~ segmentP(esk16_0,esk15_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[254,3927,theory(equality)]),128,theory(equality)]) ).
cnf(4122,negated_conjecture,
( $false
| ~ segmentP(esk16_0,nil) ),
inference(rw,[status(thm)],[4121,3927,theory(equality)]) ).
cnf(4123,negated_conjecture,
~ segmentP(esk16_0,nil),
inference(cn,[status(thm)],[4122,theory(equality)]) ).
cnf(4153,negated_conjecture,
~ segmentP(nil,nil),
inference(rw,[status(thm)],[4123,4109,theory(equality)]) ).
cnf(4154,negated_conjecture,
~ ssList(nil),
inference(spm,[status(thm)],[4153,205,theory(equality)]) ).
cnf(4158,negated_conjecture,
$false,
inference(rw,[status(thm)],[4154,160,theory(equality)]) ).
cnf(4159,negated_conjecture,
$false,
inference(cn,[status(thm)],[4158,theory(equality)]) ).
cnf(4160,negated_conjecture,
$false,
4159,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC330+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpjiBdYh/sel_SWC330+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC330+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC330+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC330+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------