TSTP Solution File: SWC380+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC380+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 11:40:43 EST 2010
% Result : Theorem 0.20s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 10 unt; 0 def)
% Number of atoms : 287 ( 75 equ)
% Maximal formula atoms : 34 ( 5 avg)
% Number of connectives : 354 ( 122 ~; 126 |; 82 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 46 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,X1) = app(cons(X2,nil),X1) ) ),
file('/tmp/tmpaBMvUT/sel_SWC380+1.p_1',ax81) ).
fof(19,axiom,
! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ( memberP(cons(X2,X3),X1)
<=> ( X1 = X2
| memberP(X3,X1) ) ) ) ) ),
file('/tmp/tmpaBMvUT/sel_SWC380+1.p_1',ax37) ).
fof(23,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& memberP(X2,X5) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X6,nil) != X3
| app(cons(X6,nil),X7) != X4 ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpaBMvUT/sel_SWC380+1.p_1',co1) ).
fof(24,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& memberP(X2,X5) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X6,nil) != X3
| app(cons(X6,nil),X7) != X4 ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(26,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X1
& memberP(X2,X5) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X6,nil) != X3
| app(cons(X6,nil),X7) != X4 ) ) ) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).
fof(41,plain,
! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,X1) = app(cons(X2,nil),X1) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(42,plain,
! [X3] :
( ~ ssList(X3)
| ! [X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3) ) ),
inference(variable_rename,[status(thm)],[41]) ).
fof(43,plain,
! [X3,X4] :
( ~ ssItem(X4)
| cons(X4,X3) = app(cons(X4,nil),X3)
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[42]) ).
cnf(44,plain,
( cons(X2,X1) = app(cons(X2,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[43]) ).
fof(113,plain,
! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssList(X3)
| ( ( ~ memberP(cons(X2,X3),X1)
| X1 = X2
| memberP(X3,X1) )
& ( ( X1 != X2
& ~ memberP(X3,X1) )
| memberP(cons(X2,X3),X1) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(114,plain,
! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| ( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4) )
& ( ( X4 != X5
& ~ memberP(X6,X4) )
| memberP(cons(X5,X6),X4) ) ) ) ) ),
inference(variable_rename,[status(thm)],[113]) ).
fof(115,plain,
! [X4,X5,X6] :
( ~ ssList(X6)
| ( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4) )
& ( ( X4 != X5
& ~ memberP(X6,X4) )
| memberP(cons(X5,X6),X4) ) )
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(shift_quantors,[status(thm)],[114]) ).
fof(116,plain,
! [X4,X5,X6] :
( ( ~ memberP(cons(X5,X6),X4)
| X4 = X5
| memberP(X6,X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) )
& ( X4 != X5
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) )
& ( ~ memberP(X6,X4)
| memberP(cons(X5,X6),X4)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ) ),
inference(distribute,[status(thm)],[115]) ).
cnf(118,plain,
( memberP(cons(X2,X3),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[116]) ).
fof(133,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X1
| ~ memberP(X2,X5) )
& ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& cons(X6,nil) = X3
& app(cons(X6,nil),X7) = X4 ) ) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(134,negated_conjecture,
? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& ? [X11] :
( ssList(X11)
& X9 = X11
& X8 = X10
& ( ( neq(X9,nil)
& ! [X12] :
( ~ ssItem(X12)
| cons(X12,nil) != X8
| ~ memberP(X9,X12) )
& ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& cons(X13,nil) = X10
& app(cons(X13,nil),X14) = X11 ) ) )
| ( neq(X9,nil)
& ~ neq(X11,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[133]) ).
fof(135,negated_conjecture,
( ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& ssList(esk10_0)
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ( ( neq(esk8_0,nil)
& ! [X12] :
( ~ ssItem(X12)
| cons(X12,nil) != esk7_0
| ~ memberP(esk8_0,X12) )
& ssItem(esk11_0)
& ssList(esk12_0)
& cons(esk11_0,nil) = esk9_0
& app(cons(esk11_0,nil),esk12_0) = esk10_0 )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) ) ),
inference(skolemize,[status(esa)],[134]) ).
fof(136,negated_conjecture,
! [X12] :
( ( ( ( ~ ssItem(X12)
| cons(X12,nil) != esk7_0
| ~ memberP(esk8_0,X12) )
& neq(esk8_0,nil)
& ssItem(esk11_0)
& ssList(esk12_0)
& cons(esk11_0,nil) = esk9_0
& app(cons(esk11_0,nil),esk12_0) = esk10_0 )
| ( neq(esk8_0,nil)
& ~ neq(esk10_0,nil) ) )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(shift_quantors,[status(thm)],[135]) ).
fof(137,negated_conjecture,
! [X12] :
( ( neq(esk8_0,nil)
| ~ ssItem(X12)
| cons(X12,nil) != esk7_0
| ~ memberP(esk8_0,X12) )
& ( ~ neq(esk10_0,nil)
| ~ ssItem(X12)
| cons(X12,nil) != esk7_0
| ~ memberP(esk8_0,X12) )
& ( neq(esk8_0,nil)
| neq(esk8_0,nil) )
& ( ~ neq(esk10_0,nil)
| neq(esk8_0,nil) )
& ( neq(esk8_0,nil)
| ssItem(esk11_0) )
& ( ~ neq(esk10_0,nil)
| ssItem(esk11_0) )
& ( neq(esk8_0,nil)
| ssList(esk12_0) )
& ( ~ neq(esk10_0,nil)
| ssList(esk12_0) )
& ( neq(esk8_0,nil)
| cons(esk11_0,nil) = esk9_0 )
& ( ~ neq(esk10_0,nil)
| cons(esk11_0,nil) = esk9_0 )
& ( neq(esk8_0,nil)
| app(cons(esk11_0,nil),esk12_0) = esk10_0 )
& ( ~ neq(esk10_0,nil)
| app(cons(esk11_0,nil),esk12_0) = esk10_0 )
& esk8_0 = esk10_0
& esk7_0 = esk9_0
& ssList(esk10_0)
& ssList(esk9_0)
& ssList(esk8_0)
& ssList(esk7_0) ),
inference(distribute,[status(thm)],[136]) ).
cnf(142,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(143,negated_conjecture,
esk8_0 = esk10_0,
inference(split_conjunct,[status(thm)],[137]) ).
cnf(144,negated_conjecture,
( app(cons(esk11_0,nil),esk12_0) = esk10_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(146,negated_conjecture,
( cons(esk11_0,nil) = esk9_0
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(148,negated_conjecture,
( ssList(esk12_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(150,negated_conjecture,
( ssItem(esk11_0)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(153,negated_conjecture,
( neq(esk8_0,nil)
| neq(esk8_0,nil) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(154,negated_conjecture,
( ~ memberP(esk8_0,X1)
| cons(X1,nil) != esk7_0
| ~ ssItem(X1)
| ~ neq(esk10_0,nil) ),
inference(split_conjunct,[status(thm)],[137]) ).
cnf(162,negated_conjecture,
( ssList(esk12_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[148,143,theory(equality)]),153,theory(equality)]) ).
cnf(163,negated_conjecture,
ssList(esk12_0),
inference(cn,[status(thm)],[162,theory(equality)]) ).
cnf(164,negated_conjecture,
( ssItem(esk11_0)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[150,143,theory(equality)]),153,theory(equality)]) ).
cnf(165,negated_conjecture,
ssItem(esk11_0),
inference(cn,[status(thm)],[164,theory(equality)]) ).
cnf(177,negated_conjecture,
( cons(esk11_0,nil) = esk7_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[146,142,theory(equality)]) ).
cnf(178,negated_conjecture,
( cons(esk11_0,nil) = esk7_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[177,143,theory(equality)]),153,theory(equality)]) ).
cnf(179,negated_conjecture,
cons(esk11_0,nil) = esk7_0,
inference(cn,[status(thm)],[178,theory(equality)]) ).
cnf(197,negated_conjecture,
( app(esk7_0,esk12_0) = esk10_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[144,179,theory(equality)]) ).
cnf(198,negated_conjecture,
( app(esk7_0,esk12_0) = esk8_0
| ~ neq(esk10_0,nil) ),
inference(rw,[status(thm)],[197,143,theory(equality)]) ).
cnf(199,negated_conjecture,
( app(esk7_0,esk12_0) = esk8_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[198,143,theory(equality)]),153,theory(equality)]) ).
cnf(200,negated_conjecture,
app(esk7_0,esk12_0) = esk8_0,
inference(cn,[status(thm)],[199,theory(equality)]) ).
cnf(225,negated_conjecture,
( cons(X1,nil) != esk7_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1)
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[154,143,theory(equality)]),153,theory(equality)]) ).
cnf(226,negated_conjecture,
( cons(X1,nil) != esk7_0
| ~ ssItem(X1)
| ~ memberP(esk8_0,X1) ),
inference(cn,[status(thm)],[225,theory(equality)]) ).
cnf(227,negated_conjecture,
( ~ memberP(esk8_0,esk11_0)
| ~ ssItem(esk11_0) ),
inference(spm,[status(thm)],[226,179,theory(equality)]) ).
cnf(228,negated_conjecture,
( ~ memberP(esk8_0,esk11_0)
| $false ),
inference(rw,[status(thm)],[227,165,theory(equality)]) ).
cnf(229,negated_conjecture,
~ memberP(esk8_0,esk11_0),
inference(cn,[status(thm)],[228,theory(equality)]) ).
cnf(230,negated_conjecture,
( app(esk7_0,X1) = cons(esk11_0,X1)
| ~ ssItem(esk11_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[44,179,theory(equality)]) ).
cnf(234,negated_conjecture,
( app(esk7_0,X1) = cons(esk11_0,X1)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[230,165,theory(equality)]) ).
cnf(235,negated_conjecture,
( app(esk7_0,X1) = cons(esk11_0,X1)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(236,plain,
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(er,[status(thm)],[118,theory(equality)]) ).
cnf(597,negated_conjecture,
( memberP(app(esk7_0,X1),esk11_0)
| ~ ssItem(esk11_0)
| ~ ssList(X1) ),
inference(spm,[status(thm)],[236,235,theory(equality)]) ).
cnf(601,negated_conjecture,
( memberP(app(esk7_0,X1),esk11_0)
| $false
| ~ ssList(X1) ),
inference(rw,[status(thm)],[597,165,theory(equality)]) ).
cnf(602,negated_conjecture,
( memberP(app(esk7_0,X1),esk11_0)
| ~ ssList(X1) ),
inference(cn,[status(thm)],[601,theory(equality)]) ).
cnf(670,negated_conjecture,
( memberP(esk8_0,esk11_0)
| ~ ssList(esk12_0) ),
inference(spm,[status(thm)],[602,200,theory(equality)]) ).
cnf(680,negated_conjecture,
( memberP(esk8_0,esk11_0)
| $false ),
inference(rw,[status(thm)],[670,163,theory(equality)]) ).
cnf(681,negated_conjecture,
memberP(esk8_0,esk11_0),
inference(cn,[status(thm)],[680,theory(equality)]) ).
cnf(682,negated_conjecture,
$false,
inference(sr,[status(thm)],[681,229,theory(equality)]) ).
cnf(683,negated_conjecture,
$false,
682,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC380+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpaBMvUT/sel_SWC380+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC380+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC380+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC380+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
%
%------------------------------------------------------------------------------