TSTP Solution File: SWC029+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC029+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 10:07:04 EST 2010
% Result : Theorem 0.26s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of formulae : 87 ( 16 unt; 0 def)
% Number of atoms : 344 ( 159 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 406 ( 149 ~; 162 |; 72 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 51 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax83) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax15) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax16) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax17) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax28) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax21) ).
fof(19,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',co1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( nil != X3
& nil = X4 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(cons(X5,nil),X6) != X4
| app(X6,cons(X5,nil)) != X3 ) ) )
& neq(X4,nil) )
| ( ( nil != X2
| nil = X1 )
& ( nil != X1
| nil = X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(41,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( nil != app(X1,X2)
| ( nil = X2
& nil = X1 ) )
& ( nil != X2
| nil != X1
| nil = app(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(42,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( nil != app(X3,X4)
| ( nil = X4
& nil = X3 ) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[42]) ).
fof(44,plain,
! [X3,X4] :
( ( nil = X4
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil = X3
| nil != app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) )
& ( nil != X4
| nil != X3
| nil = app(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[43]) ).
cnf(46,plain,
( nil = X1
| ~ ssList(X1)
| ~ ssList(X2)
| nil != app(X1,X2) ),
inference(split_conjunct,[status(thm)],[44]) ).
fof(63,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ neq(X1,X2)
| X1 != X2 )
& ( X1 = X2
| neq(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(64,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) ) ) ),
inference(variable_rename,[status(thm)],[63]) ).
fof(65,plain,
! [X3,X4] :
( ~ ssList(X4)
| ( ( ~ neq(X3,X4)
| X3 != X4 )
& ( X3 = X4
| neq(X3,X4) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[64]) ).
fof(66,plain,
! [X3,X4] :
( ( ~ neq(X3,X4)
| X3 != X4
| ~ ssList(X4)
| ~ ssList(X3) )
& ( X3 = X4
| neq(X3,X4)
| ~ ssList(X4)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[65]) ).
cnf(67,plain,
( neq(X1,X2)
| X1 = X2
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[66]) ).
fof(69,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ssList(cons(X2,X1)) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(70,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3)) ) ),
inference(variable_rename,[status(thm)],[69]) ).
fof(71,plain,
! [X3,X4] :
( ~ ssItem(X4)
| ssList(cons(X4,X3))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[70]) ).
cnf(72,plain,
( ssList(cons(X2,X1))
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[71]) ).
cnf(73,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[12]) ).
fof(80,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(81,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[80]) ).
cnf(82,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[81]) ).
fof(91,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| nil != cons(X2,X1) ) ),
inference(fof_nnf,[status(thm)],[17]) ).
fof(92,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3) ) ),
inference(variable_rename,[status(thm)],[91]) ).
fof(93,plain,
! [X3,X4] :
( ~ ssItem(X4)
| nil != cons(X4,X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[92]) ).
cnf(94,plain,
( ~ ssList(X1)
| nil != cons(X2,X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[93]) ).
fof(101,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( nil = X3
| nil != X4 )
& ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& app(X6,cons(X5,nil)) = X3 ) )
| ~ neq(X4,nil) )
& ( ( nil = X2
& nil != X1 )
| ( nil = X1
& nil != X2 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(102,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( nil = X9
| nil != X10 )
& ( ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& app(cons(X11,nil),X12) = X10
& app(X12,cons(X11,nil)) = X9 ) )
| ~ neq(X10,nil) )
& ( ( nil = X8
& nil != X7 )
| ( nil = X7
& nil != X8 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[101]) ).
fof(103,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ( ( ssItem(esk9_0)
& ssList(esk10_0)
& app(cons(esk9_0,nil),esk10_0) = esk8_0
& app(esk10_0,cons(esk9_0,nil)) = esk7_0 )
| ~ neq(esk8_0,nil) )
& ( ( nil = esk6_0
& nil != esk5_0 )
| ( nil = esk5_0
& nil != esk6_0 ) ) ),
inference(skolemize,[status(esa)],[102]) ).
fof(104,negated_conjecture,
( ssList(esk5_0)
& ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& esk6_0 = esk8_0
& esk5_0 = esk7_0
& ( nil = esk7_0
| nil != esk8_0 )
& ( ssItem(esk9_0)
| ~ neq(esk8_0,nil) )
& ( ssList(esk10_0)
| ~ neq(esk8_0,nil) )
& ( app(cons(esk9_0,nil),esk10_0) = esk8_0
| ~ neq(esk8_0,nil) )
& ( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) )
& ( nil = esk5_0
| nil = esk6_0 )
& ( nil != esk6_0
| nil = esk6_0 )
& ( nil = esk5_0
| nil != esk5_0 )
& ( nil != esk6_0
| nil != esk5_0 ) ),
inference(distribute,[status(thm)],[103]) ).
cnf(105,negated_conjecture,
( nil != esk5_0
| nil != esk6_0 ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(108,negated_conjecture,
( nil = esk6_0
| nil = esk5_0 ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(109,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = esk7_0
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(111,negated_conjecture,
( ssList(esk10_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(112,negated_conjecture,
( ssItem(esk9_0)
| ~ neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(113,negated_conjecture,
( nil = esk7_0
| nil != esk8_0 ),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(114,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[104]) ).
cnf(115,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[104]) ).
cnf(118,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[104]) ).
cnf(122,negated_conjecture,
ssList(esk8_0),
inference(rw,[status(thm)],[118,115,theory(equality)]) ).
cnf(123,negated_conjecture,
( esk5_0 = nil
| esk8_0 = nil ),
inference(rw,[status(thm)],[108,115,theory(equality)]) ).
cnf(126,negated_conjecture,
( esk5_0 = nil
| esk8_0 != nil ),
inference(rw,[status(thm)],[113,114,theory(equality)]) ).
cnf(127,negated_conjecture,
esk5_0 = nil,
inference(csr,[status(thm)],[126,123]) ).
cnf(133,negated_conjecture,
( $false
| esk6_0 != nil ),
inference(rw,[status(thm)],[105,127,theory(equality)]) ).
cnf(134,negated_conjecture,
( $false
| esk8_0 != nil ),
inference(rw,[status(thm)],[133,115,theory(equality)]) ).
cnf(135,negated_conjecture,
esk8_0 != nil,
inference(cn,[status(thm)],[134,theory(equality)]) ).
cnf(142,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = nil
| ~ neq(esk8_0,nil) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[109,114,theory(equality)]),127,theory(equality)]) ).
cnf(151,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[112,67,theory(equality)]) ).
cnf(152,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[111,67,theory(equality)]) ).
cnf(153,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = nil
| esk8_0 = nil
| ~ ssList(nil)
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[142,67,theory(equality)]) ).
cnf(155,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[151,73,theory(equality)]) ).
cnf(156,negated_conjecture,
( ssItem(esk9_0)
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[155,theory(equality)]) ).
cnf(157,negated_conjecture,
( ssItem(esk9_0)
| ~ ssList(esk8_0) ),
inference(sr,[status(thm)],[156,135,theory(equality)]) ).
cnf(158,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[152,73,theory(equality)]) ).
cnf(159,negated_conjecture,
( ssList(esk10_0)
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[158,theory(equality)]) ).
cnf(160,negated_conjecture,
( ssList(esk10_0)
| ~ ssList(esk8_0) ),
inference(sr,[status(thm)],[159,135,theory(equality)]) ).
cnf(161,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = nil
| esk8_0 = nil
| $false
| ~ ssList(esk8_0) ),
inference(rw,[status(thm)],[153,73,theory(equality)]) ).
cnf(162,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = nil
| esk8_0 = nil
| ~ ssList(esk8_0) ),
inference(cn,[status(thm)],[161,theory(equality)]) ).
cnf(163,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = nil
| ~ ssList(esk8_0) ),
inference(sr,[status(thm)],[162,135,theory(equality)]) ).
cnf(255,negated_conjecture,
( ssItem(esk9_0)
| $false ),
inference(rw,[status(thm)],[157,122,theory(equality)]) ).
cnf(256,negated_conjecture,
ssItem(esk9_0),
inference(cn,[status(thm)],[255,theory(equality)]) ).
cnf(258,negated_conjecture,
( ssList(esk10_0)
| $false ),
inference(rw,[status(thm)],[160,122,theory(equality)]) ).
cnf(259,negated_conjecture,
ssList(esk10_0),
inference(cn,[status(thm)],[258,theory(equality)]) ).
cnf(265,negated_conjecture,
( app(esk10_0,cons(esk9_0,nil)) = nil
| $false ),
inference(rw,[status(thm)],[163,122,theory(equality)]) ).
cnf(266,negated_conjecture,
app(esk10_0,cons(esk9_0,nil)) = nil,
inference(cn,[status(thm)],[265,theory(equality)]) ).
cnf(269,negated_conjecture,
( nil = esk10_0
| ~ ssList(cons(esk9_0,nil))
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[46,266,theory(equality)]) ).
cnf(283,negated_conjecture,
( nil = esk10_0
| ~ ssList(cons(esk9_0,nil))
| $false ),
inference(rw,[status(thm)],[269,259,theory(equality)]) ).
cnf(284,negated_conjecture,
( nil = esk10_0
| ~ ssList(cons(esk9_0,nil)) ),
inference(cn,[status(thm)],[283,theory(equality)]) ).
cnf(297,negated_conjecture,
( esk10_0 = nil
| ~ ssList(nil)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[284,72,theory(equality)]) ).
cnf(298,negated_conjecture,
( esk10_0 = nil
| $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[297,73,theory(equality)]) ).
cnf(299,negated_conjecture,
( esk10_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[298,256,theory(equality)]) ).
cnf(300,negated_conjecture,
esk10_0 = nil,
inference(cn,[status(thm)],[299,theory(equality)]) ).
cnf(301,negated_conjecture,
app(nil,cons(esk9_0,nil)) = nil,
inference(rw,[status(thm)],[266,300,theory(equality)]) ).
cnf(306,negated_conjecture,
( nil = cons(esk9_0,nil)
| ~ ssList(cons(esk9_0,nil)) ),
inference(spm,[status(thm)],[82,301,theory(equality)]) ).
cnf(332,negated_conjecture,
( cons(esk9_0,nil) = nil
| ~ ssList(nil)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[306,72,theory(equality)]) ).
cnf(333,negated_conjecture,
( cons(esk9_0,nil) = nil
| $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[332,73,theory(equality)]) ).
cnf(334,negated_conjecture,
( cons(esk9_0,nil) = nil
| $false
| $false ),
inference(rw,[status(thm)],[333,256,theory(equality)]) ).
cnf(335,negated_conjecture,
cons(esk9_0,nil) = nil,
inference(cn,[status(thm)],[334,theory(equality)]) ).
cnf(337,negated_conjecture,
( ~ ssList(nil)
| ~ ssItem(esk9_0) ),
inference(spm,[status(thm)],[94,335,theory(equality)]) ).
cnf(352,negated_conjecture,
( $false
| ~ ssItem(esk9_0) ),
inference(rw,[status(thm)],[337,73,theory(equality)]) ).
cnf(353,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[352,256,theory(equality)]) ).
cnf(354,negated_conjecture,
$false,
inference(cn,[status(thm)],[353,theory(equality)]) ).
cnf(355,negated_conjecture,
$false,
354,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC029+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpe4roiI/sel_SWC029+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC029+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC029+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC029+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
%
%------------------------------------------------------------------------------