TSTP Solution File: SWC254+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SWC254+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 11:05:56 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 201 ( 51 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 239 ( 75 ~; 77 |; 67 &)
% ( 1 <=>; 19 =>; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 29 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1] :
( ssList(X1)
=> ( singletonP(X1)
<=> ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) ) ),
file('/tmp/tmpuc8spJ/sel_SWC254+1.p_1',ax4) ).
fof(21,conjecture,
! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X3
| app(X6,cons(X5,nil)) != X4 ) ) )
| singletonP(X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
file('/tmp/tmpuc8spJ/sel_SWC254+1.p_1',co1) ).
fof(22,negated_conjecture,
~ ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( X2 != X4
| X1 != X3
| ( ( ~ neq(X2,nil)
| ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X3
| app(X6,cons(X5,nil)) != X4 ) ) )
| singletonP(X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[21]) ).
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)
=> ! [X6] :
( ssList(X6)
=> ( cons(X5,nil) != X3
| app(X6,cons(X5,nil)) != X4 ) ) )
| singletonP(X1) )
& ( ~ neq(X2,nil)
| neq(X4,nil) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).
fof(34,plain,
! [X1] :
( ~ ssList(X1)
| ( ( ~ singletonP(X1)
| ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X1 ) )
& ( ! [X2] :
( ~ ssItem(X2)
| cons(X2,nil) != X1 )
| singletonP(X1) ) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(35,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ? [X4] :
( ssItem(X4)
& cons(X4,nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(variable_rename,[status(thm)],[34]) ).
fof(36,plain,
! [X3] :
( ~ ssList(X3)
| ( ( ~ singletonP(X3)
| ( ssItem(esk3_1(X3))
& cons(esk3_1(X3),nil) = X3 ) )
& ( ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X3 )
| singletonP(X3) ) ) ),
inference(skolemize,[status(esa)],[35]) ).
fof(37,plain,
! [X3,X5] :
( ( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3) )
& ( ~ singletonP(X3)
| ( ssItem(esk3_1(X3))
& cons(esk3_1(X3),nil) = X3 ) ) )
| ~ ssList(X3) ),
inference(shift_quantors,[status(thm)],[36]) ).
fof(38,plain,
! [X3,X5] :
( ( ~ ssItem(X5)
| cons(X5,nil) != X3
| singletonP(X3)
| ~ ssList(X3) )
& ( ssItem(esk3_1(X3))
| ~ singletonP(X3)
| ~ ssList(X3) )
& ( cons(esk3_1(X3),nil) = X3
| ~ singletonP(X3)
| ~ ssList(X3) ) ),
inference(distribute,[status(thm)],[37]) ).
cnf(41,plain,
( singletonP(X1)
| ~ ssList(X1)
| cons(X2,nil) != X1
| ~ ssItem(X2) ),
inference(split_conjunct,[status(thm)],[38]) ).
fof(114,negated_conjecture,
? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ssList(X4)
& X2 = X4
& X1 = X3
& ( ( neq(X2,nil)
& ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& cons(X5,nil) = X3
& app(X6,cons(X5,nil)) = X4 ) )
& ~ singletonP(X1) )
| ( neq(X2,nil)
& ~ neq(X4,nil) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(115,negated_conjecture,
? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X8 = X10
& X7 = X9
& ( ( neq(X8,nil)
& ? [X11] :
( ssItem(X11)
& ? [X12] :
( ssList(X12)
& cons(X11,nil) = X9
& app(X12,cons(X11,nil)) = X10 ) )
& ~ singletonP(X7) )
| ( neq(X8,nil)
& ~ neq(X10,nil) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[114]) ).
fof(116,negated_conjecture,
( ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& esk7_0 = esk9_0
& esk6_0 = esk8_0
& ( ( neq(esk7_0,nil)
& ssItem(esk10_0)
& ssList(esk11_0)
& cons(esk10_0,nil) = esk8_0
& app(esk11_0,cons(esk10_0,nil)) = esk9_0
& ~ singletonP(esk6_0) )
| ( neq(esk7_0,nil)
& ~ neq(esk9_0,nil) ) ) ),
inference(skolemize,[status(esa)],[115]) ).
fof(117,negated_conjecture,
( ssList(esk6_0)
& ssList(esk7_0)
& ssList(esk8_0)
& ssList(esk9_0)
& esk7_0 = esk9_0
& esk6_0 = esk8_0
& ( neq(esk7_0,nil)
| neq(esk7_0,nil) )
& ( ~ neq(esk9_0,nil)
| neq(esk7_0,nil) )
& ( neq(esk7_0,nil)
| ssItem(esk10_0) )
& ( ~ neq(esk9_0,nil)
| ssItem(esk10_0) )
& ( neq(esk7_0,nil)
| ssList(esk11_0) )
& ( ~ neq(esk9_0,nil)
| ssList(esk11_0) )
& ( neq(esk7_0,nil)
| cons(esk10_0,nil) = esk8_0 )
& ( ~ neq(esk9_0,nil)
| cons(esk10_0,nil) = esk8_0 )
& ( neq(esk7_0,nil)
| app(esk11_0,cons(esk10_0,nil)) = esk9_0 )
& ( ~ neq(esk9_0,nil)
| app(esk11_0,cons(esk10_0,nil)) = esk9_0 )
& ( neq(esk7_0,nil)
| ~ singletonP(esk6_0) )
& ( ~ neq(esk9_0,nil)
| ~ singletonP(esk6_0) ) ),
inference(distribute,[status(thm)],[116]) ).
cnf(118,negated_conjecture,
( ~ singletonP(esk6_0)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(122,negated_conjecture,
( cons(esk10_0,nil) = esk8_0
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(126,negated_conjecture,
( ssItem(esk10_0)
| ~ neq(esk9_0,nil) ),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(129,negated_conjecture,
( neq(esk7_0,nil)
| neq(esk7_0,nil) ),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(130,negated_conjecture,
esk6_0 = esk8_0,
inference(split_conjunct,[status(thm)],[117]) ).
cnf(131,negated_conjecture,
esk7_0 = esk9_0,
inference(split_conjunct,[status(thm)],[117]) ).
cnf(135,negated_conjecture,
ssList(esk6_0),
inference(split_conjunct,[status(thm)],[117]) ).
cnf(139,negated_conjecture,
neq(esk9_0,nil),
inference(rw,[status(thm)],[129,131,theory(equality)]) ).
cnf(143,negated_conjecture,
( ssItem(esk10_0)
| $false ),
inference(rw,[status(thm)],[126,139,theory(equality)]) ).
cnf(144,negated_conjecture,
ssItem(esk10_0),
inference(cn,[status(thm)],[143,theory(equality)]) ).
cnf(147,negated_conjecture,
( ~ singletonP(esk6_0)
| $false ),
inference(rw,[status(thm)],[118,139,theory(equality)]) ).
cnf(148,negated_conjecture,
~ singletonP(esk6_0),
inference(cn,[status(thm)],[147,theory(equality)]) ).
cnf(154,negated_conjecture,
( cons(esk10_0,nil) = esk6_0
| ~ neq(esk9_0,nil) ),
inference(rw,[status(thm)],[122,130,theory(equality)]) ).
cnf(155,negated_conjecture,
( cons(esk10_0,nil) = esk6_0
| $false ),
inference(rw,[status(thm)],[154,139,theory(equality)]) ).
cnf(156,negated_conjecture,
cons(esk10_0,nil) = esk6_0,
inference(cn,[status(thm)],[155,theory(equality)]) ).
cnf(201,negated_conjecture,
( singletonP(X1)
| esk6_0 != X1
| ~ ssList(X1)
| ~ ssItem(esk10_0) ),
inference(spm,[status(thm)],[41,156,theory(equality)]) ).
cnf(203,negated_conjecture,
( singletonP(X1)
| esk6_0 != X1
| ~ ssList(X1)
| $false ),
inference(rw,[status(thm)],[201,144,theory(equality)]) ).
cnf(204,negated_conjecture,
( singletonP(X1)
| esk6_0 != X1
| ~ ssList(X1) ),
inference(cn,[status(thm)],[203,theory(equality)]) ).
cnf(361,negated_conjecture,
( singletonP(esk6_0)
| ~ ssList(esk6_0) ),
inference(er,[status(thm)],[204,theory(equality)]) ).
cnf(362,negated_conjecture,
( singletonP(esk6_0)
| $false ),
inference(rw,[status(thm)],[361,135,theory(equality)]) ).
cnf(363,negated_conjecture,
singletonP(esk6_0),
inference(cn,[status(thm)],[362,theory(equality)]) ).
cnf(364,negated_conjecture,
$false,
inference(sr,[status(thm)],[363,148,theory(equality)]) ).
cnf(365,negated_conjecture,
$false,
364,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC254+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpuc8spJ/sel_SWC254+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC254+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC254+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC254+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
%
%------------------------------------------------------------------------------