TSTP Solution File: SET978+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET978+1 : 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 03:57:36 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 53 ( 14 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 26 ~; 17 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 8 sgn 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
file('/tmp/tmpCOK0C4/sel_SET978+1.p_1',t17_zfmisc_1) ).
fof(4,conjecture,
! [X1,X2,X3,X4] :
( X1 != X2
=> ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
& disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
file('/tmp/tmpCOK0C4/sel_SET978+1.p_1',t131_zfmisc_1) ).
fof(6,axiom,
! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/tmp/tmpCOK0C4/sel_SET978+1.p_1',t127_zfmisc_1) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( X1 != X2
=> ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
& disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(15,plain,
! [X1,X2] :
( X1 = X2
| disjoint(singleton(X1),singleton(X2)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(16,plain,
! [X3,X4] :
( X3 = X4
| disjoint(singleton(X3),singleton(X4)) ),
inference(variable_rename,[status(thm)],[15]) ).
cnf(17,plain,
( disjoint(singleton(X1),singleton(X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[16]) ).
fof(18,negated_conjecture,
? [X1,X2,X3,X4] :
( X1 != X2
& ( ~ disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
| ~ disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(19,negated_conjecture,
? [X5,X6,X7,X8] :
( X5 != X6
& ( ~ disjoint(cartesian_product2(singleton(X5),X7),cartesian_product2(singleton(X6),X8))
| ~ disjoint(cartesian_product2(X7,singleton(X5)),cartesian_product2(X8,singleton(X6))) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,negated_conjecture,
( esk2_0 != esk3_0
& ( ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0))
| ~ disjoint(cartesian_product2(esk4_0,singleton(esk2_0)),cartesian_product2(esk5_0,singleton(esk3_0))) ) ),
inference(skolemize,[status(esa)],[19]) ).
cnf(21,negated_conjecture,
( ~ disjoint(cartesian_product2(esk4_0,singleton(esk2_0)),cartesian_product2(esk5_0,singleton(esk3_0)))
| ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0)) ),
inference(split_conjunct,[status(thm)],[20]) ).
cnf(22,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[20]) ).
fof(26,plain,
! [X1,X2,X3,X4] :
( ( ~ disjoint(X1,X2)
& ~ disjoint(X3,X4) )
| disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(27,plain,
! [X5,X6,X7,X8] :
( ( ~ disjoint(X5,X6)
& ~ disjoint(X7,X8) )
| disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[26]) ).
fof(28,plain,
! [X5,X6,X7,X8] :
( ( ~ disjoint(X5,X6)
| disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) )
& ( ~ disjoint(X7,X8)
| disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ) ),
inference(distribute,[status(thm)],[27]) ).
cnf(29,plain,
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ disjoint(X2,X4) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(30,plain,
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ disjoint(X1,X3) ),
inference(split_conjunct,[status(thm)],[28]) ).
cnf(31,plain,
( disjoint(cartesian_product2(X1,singleton(X2)),cartesian_product2(X3,singleton(X4)))
| X2 = X4 ),
inference(spm,[status(thm)],[29,17,theory(equality)]) ).
cnf(32,plain,
( disjoint(cartesian_product2(singleton(X1),X2),cartesian_product2(singleton(X3),X4))
| X1 = X3 ),
inference(spm,[status(thm)],[30,17,theory(equality)]) ).
cnf(34,negated_conjecture,
( esk2_0 = esk3_0
| ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0)) ),
inference(spm,[status(thm)],[21,31,theory(equality)]) ).
cnf(38,negated_conjecture,
~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0)),
inference(sr,[status(thm)],[34,22,theory(equality)]) ).
cnf(54,negated_conjecture,
esk2_0 = esk3_0,
inference(spm,[status(thm)],[38,32,theory(equality)]) ).
cnf(55,negated_conjecture,
$false,
inference(sr,[status(thm)],[54,22,theory(equality)]) ).
cnf(56,negated_conjecture,
$false,
55,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET978+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCOK0C4/sel_SET978+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET978+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET978+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET978+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
%
%------------------------------------------------------------------------------