TSTP Solution File: SET983+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET983+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 04:02:50 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 119 ( 19 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 147 ( 53 ~; 56 |; 34 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 70 ( 0 sgn 42 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
file('/tmp/tmpW9eT86/sel_SET983+1.p_1',t137_zfmisc_1) ).
fof(5,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/tmp/tmpW9eT86/sel_SET983+1.p_1',t123_zfmisc_1) ).
fof(7,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/tmp/tmpW9eT86/sel_SET983+1.p_1',d3_xboole_0) ).
fof(9,negated_conjecture,
~ ! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(14,negated_conjecture,
? [X1,X2,X3,X4,X5] :
( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5))
& ~ in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(15,negated_conjecture,
? [X6,X7,X8,X9,X10] :
( in(X6,cartesian_product2(X7,X8))
& in(X6,cartesian_product2(X9,X10))
& ~ in(X6,cartesian_product2(set_intersection2(X7,X9),set_intersection2(X8,X10))) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,negated_conjecture,
( in(esk1_0,cartesian_product2(esk2_0,esk3_0))
& in(esk1_0,cartesian_product2(esk4_0,esk5_0))
& ~ in(esk1_0,cartesian_product2(set_intersection2(esk2_0,esk4_0),set_intersection2(esk3_0,esk5_0))) ),
inference(skolemize,[status(esa)],[15]) ).
cnf(17,negated_conjecture,
~ in(esk1_0,cartesian_product2(set_intersection2(esk2_0,esk4_0),set_intersection2(esk3_0,esk5_0))),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(18,negated_conjecture,
in(esk1_0,cartesian_product2(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[16]) ).
cnf(19,negated_conjecture,
in(esk1_0,cartesian_product2(esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[16]) ).
fof(25,plain,
! [X5,X6,X7,X8] : cartesian_product2(set_intersection2(X5,X6),set_intersection2(X7,X8)) = set_intersection2(cartesian_product2(X5,X7),cartesian_product2(X6,X8)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(26,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[25]) ).
fof(30,plain,
! [X1,X2,X3] :
( ( X3 != set_intersection2(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| ~ in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& in(X4,X2) ) ) )
| X3 = set_intersection2(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(31,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| ~ in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& in(X9,X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,plain,
! [X5,X6,X7] :
( ( X7 != set_intersection2(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| ( in(esk8_3(X5,X6,X7),X5)
& in(esk8_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(skolemize,[status(esa)],[31]) ).
fof(33,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& in(X8,X6) ) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7) ) )
| X7 != set_intersection2(X5,X6) )
& ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
| ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X6) )
& ( in(esk8_3(X5,X6,X7),X7)
| ( in(esk8_3(X5,X6,X7),X5)
& in(esk8_3(X5,X6,X7),X6) ) ) )
| X7 = set_intersection2(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[32]) ).
fof(34,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( in(X8,X6)
| ~ in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(X8,X5)
| ~ in(X8,X6)
| in(X8,X7)
| X7 != set_intersection2(X5,X6) )
& ( ~ in(esk8_3(X5,X6,X7),X7)
| ~ in(esk8_3(X5,X6,X7),X5)
| ~ in(esk8_3(X5,X6,X7),X6)
| X7 = set_intersection2(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X5)
| in(esk8_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) )
& ( in(esk8_3(X5,X6,X7),X6)
| in(esk8_3(X5,X6,X7),X7)
| X7 = set_intersection2(X5,X6) ) ),
inference(distribute,[status(thm)],[33]) ).
cnf(38,plain,
( in(X4,X1)
| X1 != set_intersection2(X2,X3)
| ~ in(X4,X3)
| ~ in(X4,X2) ),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(60,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[38,theory(equality)]) ).
cnf(103,plain,
( in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5)))
| ~ in(X1,cartesian_product2(X4,X5))
| ~ in(X1,cartesian_product2(X2,X3)) ),
inference(spm,[status(thm)],[60,26,theory(equality)]) ).
cnf(691,negated_conjecture,
( ~ in(esk1_0,cartesian_product2(esk4_0,esk5_0))
| ~ in(esk1_0,cartesian_product2(esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[17,103,theory(equality)]) ).
cnf(715,negated_conjecture,
( $false
| ~ in(esk1_0,cartesian_product2(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[691,18,theory(equality)]) ).
cnf(716,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[715,19,theory(equality)]) ).
cnf(717,negated_conjecture,
$false,
inference(cn,[status(thm)],[716,theory(equality)]) ).
cnf(718,negated_conjecture,
$false,
717,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET983+1.p
% --creating new selector for []
% -running prover on /tmp/tmpW9eT86/sel_SET983+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET983+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET983+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET983+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
%
%------------------------------------------------------------------------------