TSTP Solution File: SET813+4 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET813+4 : TPTP v5.0.0. Released v3.2.0.
% 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 03:41:31 EST 2010
% Result : Theorem 0.22s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 65 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 25 ~; 22 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',singleton) ).
fof(4,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',union) ).
fof(10,axiom,
! [X1,X3] :
( member(X3,suc(X1))
<=> member(X3,union(X1,singleton(X1))) ),
file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',successor) ).
fof(11,conjecture,
! [X1] :
( member(X1,on)
=> member(X1,suc(X1)) ),
file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',thV12) ).
fof(12,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> member(X1,suc(X1)) ),
inference(assume_negation,[status(cth)],[11]) ).
fof(21,plain,
! [X3,X1] :
( ( ~ member(X3,singleton(X1))
| X3 = X1 )
& ( X3 != X1
| member(X3,singleton(X1)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(22,plain,
! [X4,X5] :
( ( ~ member(X4,singleton(X5))
| X4 = X5 )
& ( X4 != X5
| member(X4,singleton(X5)) ) ),
inference(variable_rename,[status(thm)],[21]) ).
cnf(23,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(35,plain,
! [X3,X1,X2] :
( ( ~ member(X3,union(X1,X2))
| member(X3,X1)
| member(X3,X2) )
& ( ( ~ member(X3,X1)
& ~ member(X3,X2) )
| member(X3,union(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(36,plain,
! [X4,X5,X6] :
( ( ~ member(X4,union(X5,X6))
| member(X4,X5)
| member(X4,X6) )
& ( ( ~ member(X4,X5)
& ~ member(X4,X6) )
| member(X4,union(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X4,X5,X6] :
( ( ~ member(X4,union(X5,X6))
| member(X4,X5)
| member(X4,X6) )
& ( ~ member(X4,X5)
| member(X4,union(X5,X6)) )
& ( ~ member(X4,X6)
| member(X4,union(X5,X6)) ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(38,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(100,plain,
! [X1,X3] :
( ( ~ member(X3,suc(X1))
| member(X3,union(X1,singleton(X1))) )
& ( ~ member(X3,union(X1,singleton(X1)))
| member(X3,suc(X1)) ) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(101,plain,
! [X4,X5] :
( ( ~ member(X5,suc(X4))
| member(X5,union(X4,singleton(X4))) )
& ( ~ member(X5,union(X4,singleton(X4)))
| member(X5,suc(X4)) ) ),
inference(variable_rename,[status(thm)],[100]) ).
cnf(102,plain,
( member(X1,suc(X2))
| ~ member(X1,union(X2,singleton(X2))) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(104,negated_conjecture,
? [X1] :
( member(X1,on)
& ~ member(X1,suc(X1)) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(105,negated_conjecture,
? [X2] :
( member(X2,on)
& ~ member(X2,suc(X2)) ),
inference(variable_rename,[status(thm)],[104]) ).
fof(106,negated_conjecture,
( member(esk12_0,on)
& ~ member(esk12_0,suc(esk12_0)) ),
inference(skolemize,[status(esa)],[105]) ).
cnf(107,negated_conjecture,
~ member(esk12_0,suc(esk12_0)),
inference(split_conjunct,[status(thm)],[106]) ).
cnf(110,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[23,theory(equality)]) ).
cnf(320,plain,
member(X1,union(X2,singleton(X1))),
inference(spm,[status(thm)],[38,110,theory(equality)]) ).
cnf(484,plain,
member(X1,suc(X1)),
inference(spm,[status(thm)],[102,320,theory(equality)]) ).
cnf(494,negated_conjecture,
$false,
inference(rw,[status(thm)],[107,484,theory(equality)]) ).
cnf(495,negated_conjecture,
$false,
inference(cn,[status(thm)],[494,theory(equality)]) ).
cnf(496,negated_conjecture,
$false,
495,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET813+4.p
% --creating new selector for [SET006+0.ax, SET006+4.ax]
% -running prover on /tmp/tmpcq0ZOy/sel_SET813+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET813+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET813+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET813+4.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
%
%------------------------------------------------------------------------------