%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC357+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 11:38:11 EST 2010
% Result : Theorem 0.32s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 16 unt; 0 def)
% Number of atoms : 274 ( 66 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 326 ( 117 ~; 131 |; 55 &)
% ( 1 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 54 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(7,axiom,
! [X1] :
( ssList(X1)
=> app(nil,X1) = X1 ),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',ax28) ).
fof(19,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X1,X2)
<=> ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) ) ) ),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',ax5) ).
fof(27,axiom,
ssList(nil),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',ax17) ).
fof(30,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,X1) ),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',ax55) ).
fof(31,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( segmentP(X1,X2)
=> segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',ax56) ).
fof(32,axiom,
! [X1] :
( ssList(X1)
=> segmentP(X1,nil) ),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',ax57) ).
fof(34,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
file('/tmp/tmp2waik2/sel_SWC357+1.p_1',co1) ).
fof(35,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[34]) ).
fof(36,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ~ neq(X2,nil)
| segmentP(X2,X1)
| ( ( nil != X4
| nil != X3 )
& ( ~ neq(X3,nil)
| ~ frontsegP(X4,X3) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[35,theory(equality)]) ).
fof(64,plain,
! [X1] :
( ~ ssList(X1)
| app(nil,X1) = X1 ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(65,plain,
! [X2] :
( ~ ssList(X2)
| app(nil,X2) = X2 ),
inference(variable_rename,[status(thm)],[64]) ).
cnf(66,plain,
( app(nil,X1) = X1
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[65]) ).
fof(121,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ frontsegP(X1,X2)
| ? [X3] :
( ssList(X3)
& app(X2,X3) = X1 ) )
& ( ! [X3] :
( ~ ssList(X3)
| app(X2,X3) != X1 )
| frontsegP(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(122,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ? [X6] :
( ssList(X6)
& app(X5,X6) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(variable_rename,[status(thm)],[121]) ).
fof(123,plain,
! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ( ( ~ frontsegP(X4,X5)
| ( ssList(esk7_2(X4,X5))
& app(X5,esk7_2(X4,X5)) = X4 ) )
& ( ! [X7] :
( ~ ssList(X7)
| app(X5,X7) != X4 )
| frontsegP(X4,X5) ) ) ) ),
inference(skolemize,[status(esa)],[122]) ).
fof(124,plain,
! [X4,X5,X7] :
( ( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5) )
& ( ~ frontsegP(X4,X5)
| ( ssList(esk7_2(X4,X5))
& app(X5,esk7_2(X4,X5)) = X4 ) ) )
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(shift_quantors,[status(thm)],[123]) ).
fof(125,plain,
! [X4,X5,X7] :
( ( ~ ssList(X7)
| app(X5,X7) != X4
| frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( ssList(esk7_2(X4,X5))
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) )
& ( app(X5,esk7_2(X4,X5)) = X4
| ~ frontsegP(X4,X5)
| ~ ssList(X5)
| ~ ssList(X4) ) ),
inference(distribute,[status(thm)],[124]) ).
cnf(126,plain,
( app(X2,esk7_2(X1,X2)) = X1
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[125]) ).
cnf(127,plain,
( ssList(esk7_2(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2) ),
inference(split_conjunct,[status(thm)],[125]) ).
cnf(162,plain,
ssList(nil),
inference(split_conjunct,[status(thm)],[27]) ).
fof(171,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,X1) ),
inference(fof_nnf,[status(thm)],[30]) ).
fof(172,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,X2) ),
inference(variable_rename,[status(thm)],[171]) ).
cnf(173,plain,
( segmentP(X1,X1)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[172]) ).
fof(174,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssList(X4)
| ~ segmentP(X1,X2)
| segmentP(app(app(X3,X1),X4),X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[31]) ).
fof(175,plain,
! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6) ) ) ) ),
inference(variable_rename,[status(thm)],[174]) ).
fof(176,plain,
! [X5,X6,X7,X8] :
( ~ ssList(X8)
| ~ segmentP(X5,X6)
| segmentP(app(app(X7,X5),X8),X6)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssList(X5) ),
inference(shift_quantors,[status(thm)],[175]) ).
cnf(177,plain,
( segmentP(app(app(X3,X1),X4),X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X1,X2)
| ~ ssList(X4) ),
inference(split_conjunct,[status(thm)],[176]) ).
fof(178,plain,
! [X1] :
( ~ ssList(X1)
| segmentP(X1,nil) ),
inference(fof_nnf,[status(thm)],[32]) ).
fof(179,plain,
! [X2] :
( ~ ssList(X2)
| segmentP(X2,nil) ),
inference(variable_rename,[status(thm)],[178]) ).
cnf(180,plain,
( segmentP(X1,nil)
| ~ ssList(X1) ),
inference(split_conjunct,[status(thm)],[179]) ).
fof(187,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& neq(X2,nil)
& ~ segmentP(X2,X1)
& ( ( nil = X4
& nil = X3 )
| ( neq(X3,nil)
& frontsegP(X4,X3) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[36]) ).
fof(188,negated_conjecture,
? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& X6 = X8
& X5 = X7
& neq(X6,nil)
& ~ segmentP(X6,X5)
& ( ( nil = X8
& nil = X7 )
| ( neq(X7,nil)
& frontsegP(X8,X7) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[187]) ).
fof(189,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& neq(esk9_0,nil)
& ~ segmentP(esk9_0,esk8_0)
& ( ( nil = esk11_0
& nil = esk10_0 )
| ( neq(esk10_0,nil)
& frontsegP(esk11_0,esk10_0) ) ) ),
inference(skolemize,[status(esa)],[188]) ).
fof(190,negated_conjecture,
( ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& ssList(esk11_0)
& esk9_0 = esk11_0
& esk8_0 = esk10_0
& neq(esk9_0,nil)
& ~ segmentP(esk9_0,esk8_0)
& ( neq(esk10_0,nil)
| nil = esk11_0 )
& ( frontsegP(esk11_0,esk10_0)
| nil = esk11_0 )
& ( neq(esk10_0,nil)
| nil = esk10_0 )
& ( frontsegP(esk11_0,esk10_0)
| nil = esk10_0 ) ),
inference(distribute,[status(thm)],[189]) ).
cnf(191,negated_conjecture,
( nil = esk10_0
| frontsegP(esk11_0,esk10_0) ),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(195,negated_conjecture,
~ segmentP(esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(197,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[190]) ).
cnf(198,negated_conjecture,
esk9_0 = esk11_0,
inference(split_conjunct,[status(thm)],[190]) ).
cnf(201,negated_conjecture,
ssList(esk9_0),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(202,negated_conjecture,
ssList(esk8_0),
inference(split_conjunct,[status(thm)],[190]) ).
cnf(203,negated_conjecture,
ssList(esk10_0),
inference(rw,[status(thm)],[202,197,theory(equality)]) ).
cnf(204,negated_conjecture,
ssList(esk11_0),
inference(rw,[status(thm)],[201,198,theory(equality)]) ).
cnf(206,negated_conjecture,
~ segmentP(esk11_0,esk10_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[195,198,theory(equality)]),197,theory(equality)]) ).
cnf(243,negated_conjecture,
( ssList(esk7_2(esk11_0,esk10_0))
| esk10_0 = nil
| ~ ssList(esk10_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[127,191,theory(equality)]) ).
cnf(281,negated_conjecture,
( app(esk10_0,esk7_2(esk11_0,esk10_0)) = esk11_0
| esk10_0 = nil
| ~ ssList(esk10_0)
| ~ ssList(esk11_0) ),
inference(spm,[status(thm)],[126,191,theory(equality)]) ).
cnf(335,plain,
( segmentP(app(app(X1,X2),X3),X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X2) ),
inference(spm,[status(thm)],[177,173,theory(equality)]) ).
cnf(585,negated_conjecture,
( ssList(esk7_2(esk11_0,esk10_0))
| esk10_0 = nil
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[243,203,theory(equality)]) ).
cnf(586,negated_conjecture,
( ssList(esk7_2(esk11_0,esk10_0))
| esk10_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[585,204,theory(equality)]) ).
cnf(587,negated_conjecture,
( ssList(esk7_2(esk11_0,esk10_0))
| esk10_0 = nil ),
inference(cn,[status(thm)],[586,theory(equality)]) ).
cnf(927,negated_conjecture,
( app(esk10_0,esk7_2(esk11_0,esk10_0)) = esk11_0
| esk10_0 = nil
| $false
| ~ ssList(esk11_0) ),
inference(rw,[status(thm)],[281,203,theory(equality)]) ).
cnf(928,negated_conjecture,
( app(esk10_0,esk7_2(esk11_0,esk10_0)) = esk11_0
| esk10_0 = nil
| $false
| $false ),
inference(rw,[status(thm)],[927,204,theory(equality)]) ).
cnf(929,negated_conjecture,
( app(esk10_0,esk7_2(esk11_0,esk10_0)) = esk11_0
| esk10_0 = nil ),
inference(cn,[status(thm)],[928,theory(equality)]) ).
cnf(2756,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[335,66,theory(equality)]) ).
cnf(2782,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[2756,162,theory(equality)]) ).
cnf(2783,plain,
( segmentP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[2782,theory(equality)]) ).
cnf(3920,negated_conjecture,
( segmentP(esk11_0,esk10_0)
| esk10_0 = nil
| ~ ssList(esk7_2(esk11_0,esk10_0))
| ~ ssList(esk10_0) ),
inference(spm,[status(thm)],[2783,929,theory(equality)]) ).
cnf(3939,negated_conjecture,
( segmentP(esk11_0,esk10_0)
| esk10_0 = nil
| ~ ssList(esk7_2(esk11_0,esk10_0))
| $false ),
inference(rw,[status(thm)],[3920,203,theory(equality)]) ).
cnf(3940,negated_conjecture,
( segmentP(esk11_0,esk10_0)
| esk10_0 = nil
| ~ ssList(esk7_2(esk11_0,esk10_0)) ),
inference(cn,[status(thm)],[3939,theory(equality)]) ).
cnf(3941,negated_conjecture,
( esk10_0 = nil
| ~ ssList(esk7_2(esk11_0,esk10_0)) ),
inference(sr,[status(thm)],[3940,206,theory(equality)]) ).
cnf(3962,negated_conjecture,
esk10_0 = nil,
inference(csr,[status(thm)],[3941,587]) ).
cnf(3967,negated_conjecture,
~ segmentP(esk11_0,nil),
inference(rw,[status(thm)],[206,3962,theory(equality)]) ).
cnf(4023,negated_conjecture,
~ ssList(esk11_0),
inference(spm,[status(thm)],[3967,180,theory(equality)]) ).
cnf(4025,negated_conjecture,
$false,
inference(rw,[status(thm)],[4023,204,theory(equality)]) ).
cnf(4026,negated_conjecture,
$false,
inference(cn,[status(thm)],[4025,theory(equality)]) ).
cnf(4027,negated_conjecture,
$false,
4026,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC357+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp2waik2/sel_SWC357+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC357+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC357+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC357+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
%
%------------------------------------------------------------------------------