%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET702+4 : TPTP v5.0.0. Released v2.2.0.
% 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 03:13:16 EST 2010
% Result : Theorem 2.17s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 140 ( 52 ~; 56 |; 27 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 4 sgn 52 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/tmp/tmpL5N2Cd/sel_SET702+4.p_1',subset) ).
fof(2,axiom,
! [X3,X1] :
( member(X3,product(X1))
<=> ! [X4] :
( member(X4,X1)
=> member(X3,X4) ) ),
file('/tmp/tmpL5N2Cd/sel_SET702+4.p_1',product) ).
fof(3,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmpL5N2Cd/sel_SET702+4.p_1',intersection) ).
fof(4,conjecture,
! [X1,X2] : subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
file('/tmp/tmpL5N2Cd/sel_SET702+4.p_1',thI36) ).
fof(5,negated_conjecture,
~ ! [X1,X2] : subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
inference(assume_negation,[status(cth)],[4]) ).
fof(6,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ member(X3,X1)
| member(X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ member(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[1]) ).
fof(7,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ? [X7] :
( member(X7,X4)
& ~ member(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[6]) ).
fof(8,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ member(X6,X4)
| member(X6,X5) ) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[7]) ).
fof(9,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( ( member(esk1_2(X4,X5),X4)
& ~ member(esk1_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[8]) ).
fof(10,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ subset(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ member(esk1_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[9]) ).
cnf(11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[10]) ).
cnf(12,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[10]) ).
fof(14,plain,
! [X3,X1] :
( ( ~ member(X3,product(X1))
| ! [X4] :
( ~ member(X4,X1)
| member(X3,X4) ) )
& ( ? [X4] :
( member(X4,X1)
& ~ member(X3,X4) )
| member(X3,product(X1)) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(15,plain,
! [X5,X6] :
( ( ~ member(X5,product(X6))
| ! [X7] :
( ~ member(X7,X6)
| member(X5,X7) ) )
& ( ? [X8] :
( member(X8,X6)
& ~ member(X5,X8) )
| member(X5,product(X6)) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X5,X6] :
( ( ~ member(X5,product(X6))
| ! [X7] :
( ~ member(X7,X6)
| member(X5,X7) ) )
& ( ( member(esk2_2(X5,X6),X6)
& ~ member(X5,esk2_2(X5,X6)) )
| member(X5,product(X6)) ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,plain,
! [X5,X6,X7] :
( ( ~ member(X7,X6)
| member(X5,X7)
| ~ member(X5,product(X6)) )
& ( ( member(esk2_2(X5,X6),X6)
& ~ member(X5,esk2_2(X5,X6)) )
| member(X5,product(X6)) ) ),
inference(shift_quantors,[status(thm)],[16]) ).
fof(18,plain,
! [X5,X6,X7] :
( ( ~ member(X7,X6)
| member(X5,X7)
| ~ member(X5,product(X6)) )
& ( member(esk2_2(X5,X6),X6)
| member(X5,product(X6)) )
& ( ~ member(X5,esk2_2(X5,X6))
| member(X5,product(X6)) ) ),
inference(distribute,[status(thm)],[17]) ).
cnf(19,plain,
( member(X1,product(X2))
| ~ member(X1,esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(20,plain,
( member(X1,product(X2))
| member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[18]) ).
cnf(21,plain,
( member(X1,X3)
| ~ member(X1,product(X2))
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(22,plain,
! [X3,X1,X2] :
( ( ~ member(X3,intersection(X1,X2))
| ( member(X3,X1)
& member(X3,X2) ) )
& ( ~ member(X3,X1)
| ~ member(X3,X2)
| member(X3,intersection(X1,X2)) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(23,plain,
! [X4,X5,X6] :
( ( ~ member(X4,intersection(X5,X6))
| ( member(X4,X5)
& member(X4,X6) ) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[22]) ).
fof(24,plain,
! [X4,X5,X6] :
( ( member(X4,X5)
| ~ member(X4,intersection(X5,X6)) )
& ( member(X4,X6)
| ~ member(X4,intersection(X5,X6)) )
& ( ~ member(X4,X5)
| ~ member(X4,X6)
| member(X4,intersection(X5,X6)) ) ),
inference(distribute,[status(thm)],[23]) ).
cnf(26,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(28,negated_conjecture,
? [X1,X2] : ~ subset(intersection(product(X1),product(X2)),product(intersection(X1,X2))),
inference(fof_nnf,[status(thm)],[5]) ).
fof(29,negated_conjecture,
? [X3,X4] : ~ subset(intersection(product(X3),product(X4)),product(intersection(X3,X4))),
inference(variable_rename,[status(thm)],[28]) ).
fof(30,negated_conjecture,
~ subset(intersection(product(esk3_0),product(esk4_0)),product(intersection(esk3_0,esk4_0))),
inference(skolemize,[status(esa)],[29]) ).
cnf(31,negated_conjecture,
~ subset(intersection(product(esk3_0),product(esk4_0)),product(intersection(esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[30]) ).
cnf(33,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[26,12,theory(equality)]) ).
cnf(35,plain,
( member(esk2_2(X1,intersection(X2,X3)),X3)
| member(X1,product(intersection(X2,X3))) ),
inference(spm,[status(thm)],[26,20,theory(equality)]) ).
cnf(46,plain,
( member(esk1_2(intersection(X1,product(X2)),X3),X4)
| subset(intersection(X1,product(X2)),X3)
| ~ member(X4,X2) ),
inference(spm,[status(thm)],[21,33,theory(equality)]) ).
cnf(200,plain,
( member(esk1_2(intersection(X1,product(X2)),X3),product(X4))
| subset(intersection(X1,product(X2)),X3)
| ~ member(esk2_2(esk1_2(intersection(X1,product(X2)),X3),X4),X2) ),
inference(spm,[status(thm)],[19,46,theory(equality)]) ).
cnf(5936,plain,
( member(esk1_2(intersection(X1,product(X2)),X3),product(intersection(X4,X2)))
| subset(intersection(X1,product(X2)),X3) ),
inference(spm,[status(thm)],[200,35,theory(equality)]) ).
cnf(20383,plain,
subset(intersection(X1,product(X2)),product(intersection(X3,X2))),
inference(spm,[status(thm)],[11,5936,theory(equality)]) ).
cnf(20409,negated_conjecture,
$false,
inference(rw,[status(thm)],[31,20383,theory(equality)]) ).
cnf(20410,negated_conjecture,
$false,
inference(cn,[status(thm)],[20409,theory(equality)]) ).
cnf(20411,negated_conjecture,
$false,
20410,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET702+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpL5N2Cd/sel_SET702+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET702+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET702+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET702+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
%
%------------------------------------------------------------------------------