%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC218+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 10:52:54 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 9
% Syntax : Number of formulae : 99 ( 27 unt; 0 def)
% Number of atoms : 315 ( 119 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 351 ( 135 ~; 142 |; 46 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 64 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ssList(app(X1,X2)) ) ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax26) ).
fof(5,axiom,
! [X1] :
( ssList(X1)
=> app(X1,nil) = X1 ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax84) ).
fof(6,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( nil = app(X1,X2)
<=> ( nil = X2
& nil = X1 ) ) ) ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax83) ).
fof(10,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(X1,X2)
<=> X1 != X2 ) ) ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax15) ).
fof(11,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ssList(cons(X2,X1)) ) ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax16) ).
fof(12,axiom,
ssList(nil),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax17) ).
fof(14,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax28) ).
fof(17,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> nil != cons(X2,X1) ) ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',ax21) ).
fof(19,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X5,X6) != X4
| ! [X7] :
( ssItem(X7)
=> app(app(X5,cons(X7,nil)),X6) != X3 ) ) ) )
| neq(X1,nil) ) ) ) ) ),
file('/tmp/tmpj0_4nc/sel_SWC218+1.p_1',co1) ).
fof(20,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X5,X6) != X4
| ! [X7] :
( ssItem(X7)
=> app(app(X5,cons(X7,nil)),X6) != X3 ) ) ) )
| neq(X1,nil) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(26,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ssList(app(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(27,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ssList(app(X3,X4)) ) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X3,X4] :
( ~ ssList(X4)
| ssList(app(X3,X4))
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[27]) ).
cnf(29,plain,
( ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(split_conjunct,[status(thm)],[28]) ).
fof(38,plain,
! [X1] :
( ~ ssList(X1)
| app(X1,nil) = X1 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(39,plain,
! [X2] :
( ~ ssList(X2)
| app(X2,nil) = X2 ),
inference(variable_rename,[status(thm)],[38]) ).
cnf(40,plain,
( app(X1,nil) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[39]) ).
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]) ).
cnf(47,plain,
( nil = X2
| ~ 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
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(X5,X6) = X4
& ? [X7] :
( ssItem(X7)
& app(app(X5,cons(X7,nil)),X6) = X3 ) ) )
& ~ neq(X1,nil) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(102,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ? [X12] :
( ssList(X12)
& ? [X13] :
( ssList(X13)
& app(X12,X13) = X11
& ? [X14] :
( ssItem(X14)
& app(app(X12,cons(X14,nil)),X13) = X10 ) ) )
& ~ neq(X8,nil) ) ) ) ),
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
& ssList(esk9_0)
& ssList(esk10_0)
& app(esk9_0,esk10_0) = esk8_0
& ssItem(esk11_0)
& app(app(esk9_0,cons(esk11_0,nil)),esk10_0) = esk7_0
& ~ neq(esk5_0,nil) ),
inference(skolemize,[status(esa)],[102]) ).
cnf(104,negated_conjecture,
~ neq(esk5_0,nil),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(105,negated_conjecture,
app(app(esk9_0,cons(esk11_0,nil)),esk10_0) = esk7_0,
inference(split_conjunct,[status(thm)],[103]) ).
cnf(106,negated_conjecture,
ssItem(esk11_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(107,negated_conjecture,
app(esk9_0,esk10_0) = esk8_0,
inference(split_conjunct,[status(thm)],[103]) ).
cnf(108,negated_conjecture,
ssList(esk10_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(109,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(110,negated_conjecture,
esk5_0 = esk7_0,
inference(split_conjunct,[status(thm)],[103]) ).
cnf(111,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[103]) ).
cnf(114,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(115,negated_conjecture,
ssList(esk5_0),
inference(split_conjunct,[status(thm)],[103]) ).
cnf(118,negated_conjecture,
ssList(esk8_0),
inference(rw,[status(thm)],[114,111,theory(equality)]) ).
cnf(119,negated_conjecture,
app(app(esk9_0,cons(esk11_0,nil)),esk10_0) = esk5_0,
inference(rw,[status(thm)],[105,110,theory(equality)]) ).
cnf(130,negated_conjecture,
( esk5_0 = nil
| ~ ssList(nil)
| ~ ssList(esk5_0) ),
inference(spm,[status(thm)],[104,67,theory(equality)]) ).
cnf(131,negated_conjecture,
( esk5_0 = nil
| $false
| ~ ssList(esk5_0) ),
inference(rw,[status(thm)],[130,73,theory(equality)]) ).
cnf(132,negated_conjecture,
( esk5_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[131,115,theory(equality)]) ).
cnf(133,negated_conjecture,
esk5_0 = nil,
inference(cn,[status(thm)],[132,theory(equality)]) ).
cnf(238,negated_conjecture,
app(app(esk9_0,cons(esk11_0,nil)),esk10_0) = nil,
inference(rw,[status(thm)],[119,133,theory(equality)]) ).
cnf(251,negated_conjecture,
( nil = esk10_0
| ~ ssList(esk10_0)
| ~ ssList(app(esk9_0,cons(esk11_0,nil))) ),
inference(spm,[status(thm)],[47,238,theory(equality)]) ).
cnf(265,negated_conjecture,
( esk10_0 = nil
| ~ ssList(app(esk9_0,cons(esk11_0,nil))) ),
inference(spm,[status(thm)],[251,108,theory(equality)]) ).
cnf(266,negated_conjecture,
( esk10_0 = nil
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[265,29,theory(equality)]) ).
cnf(267,negated_conjecture,
( esk10_0 = nil
| ~ ssList(cons(esk11_0,nil)) ),
inference(spm,[status(thm)],[266,109,theory(equality)]) ).
cnf(268,negated_conjecture,
( esk10_0 = nil
| ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[267,72,theory(equality)]) ).
cnf(269,negated_conjecture,
( esk10_0 = nil
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[268,73,theory(equality)]) ).
cnf(270,negated_conjecture,
( esk10_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[269,106,theory(equality)]) ).
cnf(271,negated_conjecture,
esk10_0 = nil,
inference(cn,[status(thm)],[270,theory(equality)]) ).
cnf(275,negated_conjecture,
app(app(esk9_0,cons(esk11_0,nil)),nil) = nil,
inference(rw,[status(thm)],[238,271,theory(equality)]) ).
cnf(276,negated_conjecture,
app(esk9_0,nil) = esk8_0,
inference(rw,[status(thm)],[107,271,theory(equality)]) ).
cnf(286,negated_conjecture,
( esk8_0 = esk9_0
| ~ ssList(esk9_0) ),
inference(spm,[status(thm)],[40,276,theory(equality)]) ).
cnf(312,negated_conjecture,
esk9_0 = esk8_0,
inference(spm,[status(thm)],[286,109,theory(equality)]) ).
cnf(377,negated_conjecture,
app(app(esk8_0,cons(esk11_0,nil)),nil) = nil,
inference(rw,[status(thm)],[275,312,theory(equality)]) ).
cnf(378,negated_conjecture,
( nil = app(esk8_0,cons(esk11_0,nil))
| ~ ssList(app(esk8_0,cons(esk11_0,nil))) ),
inference(spm,[status(thm)],[40,377,theory(equality)]) ).
cnf(487,negated_conjecture,
( app(esk8_0,cons(esk11_0,nil)) = nil
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[378,29,theory(equality)]) ).
cnf(489,negated_conjecture,
( app(esk8_0,cons(esk11_0,nil)) = nil
| ~ ssList(cons(esk11_0,nil))
| $false ),
inference(rw,[status(thm)],[487,118,theory(equality)]) ).
cnf(490,negated_conjecture,
( app(esk8_0,cons(esk11_0,nil)) = nil
| ~ ssList(cons(esk11_0,nil)) ),
inference(cn,[status(thm)],[489,theory(equality)]) ).
cnf(491,negated_conjecture,
( app(esk8_0,cons(esk11_0,nil)) = nil
| ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[490,72,theory(equality)]) ).
cnf(492,negated_conjecture,
( app(esk8_0,cons(esk11_0,nil)) = nil
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[491,73,theory(equality)]) ).
cnf(493,negated_conjecture,
( app(esk8_0,cons(esk11_0,nil)) = nil
| $false
| $false ),
inference(rw,[status(thm)],[492,106,theory(equality)]) ).
cnf(494,negated_conjecture,
app(esk8_0,cons(esk11_0,nil)) = nil,
inference(cn,[status(thm)],[493,theory(equality)]) ).
cnf(497,negated_conjecture,
( nil = esk8_0
| ~ ssList(cons(esk11_0,nil))
| ~ ssList(esk8_0) ),
inference(spm,[status(thm)],[46,494,theory(equality)]) ).
cnf(516,negated_conjecture,
( nil = esk8_0
| ~ ssList(cons(esk11_0,nil))
| $false ),
inference(rw,[status(thm)],[497,118,theory(equality)]) ).
cnf(517,negated_conjecture,
( nil = esk8_0
| ~ ssList(cons(esk11_0,nil)) ),
inference(cn,[status(thm)],[516,theory(equality)]) ).
cnf(558,negated_conjecture,
( esk8_0 = nil
| ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[517,72,theory(equality)]) ).
cnf(559,negated_conjecture,
( esk8_0 = nil
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[558,73,theory(equality)]) ).
cnf(560,negated_conjecture,
( esk8_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[559,106,theory(equality)]) ).
cnf(561,negated_conjecture,
esk8_0 = nil,
inference(cn,[status(thm)],[560,theory(equality)]) ).
cnf(562,negated_conjecture,
app(nil,cons(esk11_0,nil)) = nil,
inference(rw,[status(thm)],[494,561,theory(equality)]) ).
cnf(589,negated_conjecture,
( nil = cons(esk11_0,nil)
| ~ ssList(cons(esk11_0,nil)) ),
inference(spm,[status(thm)],[82,562,theory(equality)]) ).
cnf(618,negated_conjecture,
( cons(esk11_0,nil) = nil
| ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[589,72,theory(equality)]) ).
cnf(619,negated_conjecture,
( cons(esk11_0,nil) = nil
| $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[618,73,theory(equality)]) ).
cnf(620,negated_conjecture,
( cons(esk11_0,nil) = nil
| $false
| $false ),
inference(rw,[status(thm)],[619,106,theory(equality)]) ).
cnf(621,negated_conjecture,
cons(esk11_0,nil) = nil,
inference(cn,[status(thm)],[620,theory(equality)]) ).
cnf(623,negated_conjecture,
( ~ ssList(nil)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[94,621,theory(equality)]) ).
cnf(639,negated_conjecture,
( $false
| ~ ssItem(esk11_0) ),
inference(rw,[status(thm)],[623,73,theory(equality)]) ).
cnf(640,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[639,106,theory(equality)]) ).
cnf(641,negated_conjecture,
$false,
inference(cn,[status(thm)],[640,theory(equality)]) ).
cnf(642,negated_conjecture,
$false,
641,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC218+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpj0_4nc/sel_SWC218+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC218+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC218+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC218+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
%
%------------------------------------------------------------------------------