%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU167+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 05:00:51 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 13 |; 13 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 29 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('/tmp/tmpvHs1-X/sel_SEU167+1.p_1',t118_zfmisc_1) ).
fof(3,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/tmp/tmpvHs1-X/sel_SEU167+1.p_1',t1_xboole_1) ).
fof(4,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/tmp/tmpvHs1-X/sel_SEU167+1.p_1',t119_zfmisc_1) ).
fof(6,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(7,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(8,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ( subset(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
& subset(cartesian_product2(X6,X4),cartesian_product2(X6,X5)) ) ),
inference(variable_rename,[status(thm)],[7]) ).
fof(9,plain,
! [X4,X5,X6] :
( ( subset(cartesian_product2(X4,X6),cartesian_product2(X5,X6))
| ~ subset(X4,X5) )
& ( subset(cartesian_product2(X6,X4),cartesian_product2(X6,X5))
| ~ subset(X4,X5) ) ),
inference(distribute,[status(thm)],[8]) ).
cnf(10,plain,
( subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[9]) ).
cnf(11,plain,
( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[9]) ).
fof(13,plain,
! [X1,X2,X3] :
( ~ subset(X1,X2)
| ~ subset(X2,X3)
| subset(X1,X3) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(14,plain,
! [X4,X5,X6] :
( ~ subset(X4,X5)
| ~ subset(X5,X6)
| subset(X4,X6) ),
inference(variable_rename,[status(thm)],[13]) ).
cnf(15,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(16,negated_conjecture,
? [X1,X2,X3,X4] :
( subset(X1,X2)
& subset(X3,X4)
& ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(17,negated_conjecture,
? [X5,X6,X7,X8] :
( subset(X5,X6)
& subset(X7,X8)
& ~ subset(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
inference(variable_rename,[status(thm)],[16]) ).
fof(18,negated_conjecture,
( subset(esk1_0,esk2_0)
& subset(esk3_0,esk4_0)
& ~ subset(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[17]) ).
cnf(19,negated_conjecture,
~ subset(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,negated_conjecture,
subset(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(28,negated_conjecture,
subset(cartesian_product2(X1,esk3_0),cartesian_product2(X1,esk4_0)),
inference(spm,[status(thm)],[10,20,theory(equality)]) ).
cnf(31,negated_conjecture,
subset(cartesian_product2(esk1_0,X1),cartesian_product2(esk2_0,X1)),
inference(spm,[status(thm)],[11,21,theory(equality)]) ).
cnf(44,negated_conjecture,
( subset(X1,cartesian_product2(X2,esk4_0))
| ~ subset(X1,cartesian_product2(X2,esk3_0)) ),
inference(spm,[status(thm)],[15,28,theory(equality)]) ).
cnf(53,negated_conjecture,
subset(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)),
inference(spm,[status(thm)],[44,31,theory(equality)]) ).
cnf(54,negated_conjecture,
$false,
inference(sr,[status(thm)],[53,19,theory(equality)]) ).
cnf(55,negated_conjecture,
$false,
54,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU167+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvHs1-X/sel_SEU167+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU167+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU167+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU167+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
%
%------------------------------------------------------------------------------