TSTP Solution File: SET630+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET630+3 : TPTP v5.0.0. Released v2.2.0.
% 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 03:05:39 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 23 unt; 0 def)
% Number of atoms : 70 ( 6 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 59 ( 26 ~; 22 |; 8 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmp6MsawO/sel_SET630+3.p_1',commutativity_of_intersection) ).
fof(4,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/tmp/tmp6MsawO/sel_SET630+3.p_1',symmetric_difference_defn) ).
fof(5,conjecture,
! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
file('/tmp/tmp6MsawO/sel_SET630+3.p_1',prove_intersection_and_symmetric_difference_disjoint) ).
fof(7,axiom,
! [X1,X2] : disjoint(intersection(X1,X2),difference(X1,X2)),
file('/tmp/tmp6MsawO/sel_SET630+3.p_1',intersection_and_union_disjoint) ).
fof(10,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/tmp/tmp6MsawO/sel_SET630+3.p_1',disjoint_defn) ).
fof(12,axiom,
! [X1,X2,X3] :
( intersect(X1,union(X2,X3))
<=> ( intersect(X1,X2)
| intersect(X1,X3) ) ),
file('/tmp/tmp6MsawO/sel_SET630+3.p_1',intersect_with_union) ).
fof(13,negated_conjecture,
~ ! [X1,X2] : disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
inference(assume_negation,[status(cth)],[5]) ).
fof(14,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).
fof(17,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(18,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[17]) ).
fof(21,plain,
! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(22,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,negated_conjecture,
? [X1,X2] : ~ disjoint(intersection(X1,X2),symmetric_difference(X1,X2)),
inference(fof_nnf,[status(thm)],[13]) ).
fof(24,negated_conjecture,
? [X3,X4] : ~ disjoint(intersection(X3,X4),symmetric_difference(X3,X4)),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
~ disjoint(intersection(esk1_0,esk2_0),symmetric_difference(esk1_0,esk2_0)),
inference(skolemize,[status(esa)],[24]) ).
cnf(26,negated_conjecture,
~ disjoint(intersection(esk1_0,esk2_0),symmetric_difference(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[25]) ).
fof(35,plain,
! [X3,X4] : disjoint(intersection(X3,X4),difference(X3,X4)),
inference(variable_rename,[status(thm)],[7]) ).
cnf(36,plain,
disjoint(intersection(X1,X2),difference(X1,X2)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(49,plain,
! [X1,X2] :
( ( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) )
& ( intersect(X1,X2)
| disjoint(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(50,plain,
! [X3,X4] :
( ( ~ disjoint(X3,X4)
| ~ intersect(X3,X4) )
& ( intersect(X3,X4)
| disjoint(X3,X4) ) ),
inference(variable_rename,[status(thm)],[49]) ).
cnf(51,plain,
( disjoint(X1,X2)
| intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
cnf(52,plain,
( ~ intersect(X1,X2)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[50]) ).
fof(59,plain,
! [X1,X2,X3] :
( ( ~ intersect(X1,union(X2,X3))
| intersect(X1,X2)
| intersect(X1,X3) )
& ( ( ~ intersect(X1,X2)
& ~ intersect(X1,X3) )
| intersect(X1,union(X2,X3)) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(60,plain,
! [X4,X5,X6] :
( ( ~ intersect(X4,union(X5,X6))
| intersect(X4,X5)
| intersect(X4,X6) )
& ( ( ~ intersect(X4,X5)
& ~ intersect(X4,X6) )
| intersect(X4,union(X5,X6)) ) ),
inference(variable_rename,[status(thm)],[59]) ).
fof(61,plain,
! [X4,X5,X6] :
( ( ~ intersect(X4,union(X5,X6))
| intersect(X4,X5)
| intersect(X4,X6) )
& ( ~ intersect(X4,X5)
| intersect(X4,union(X5,X6)) )
& ( ~ intersect(X4,X6)
| intersect(X4,union(X5,X6)) ) ),
inference(distribute,[status(thm)],[60]) ).
cnf(64,plain,
( intersect(X1,X2)
| intersect(X1,X3)
| ~ intersect(X1,union(X3,X2)) ),
inference(split_conjunct,[status(thm)],[61]) ).
cnf(66,negated_conjecture,
~ disjoint(intersection(esk1_0,esk2_0),union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0))),
inference(rw,[status(thm)],[26,22,theory(equality)]),
[unfolding] ).
cnf(67,negated_conjecture,
intersect(intersection(esk1_0,esk2_0),union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0))),
inference(spm,[status(thm)],[66,51,theory(equality)]) ).
cnf(68,plain,
disjoint(intersection(X2,X1),difference(X1,X2)),
inference(spm,[status(thm)],[36,18,theory(equality)]) ).
cnf(93,negated_conjecture,
( intersect(intersection(esk1_0,esk2_0),difference(esk2_0,esk1_0))
| intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[64,67,theory(equality)]) ).
cnf(108,negated_conjecture,
( intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0))
| ~ disjoint(intersection(esk1_0,esk2_0),difference(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[52,93,theory(equality)]) ).
cnf(114,negated_conjecture,
( intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0))
| $false ),
inference(rw,[status(thm)],[108,68,theory(equality)]) ).
cnf(115,negated_conjecture,
intersect(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
inference(cn,[status(thm)],[114,theory(equality)]) ).
cnf(116,negated_conjecture,
~ disjoint(intersection(esk1_0,esk2_0),difference(esk1_0,esk2_0)),
inference(spm,[status(thm)],[52,115,theory(equality)]) ).
cnf(123,negated_conjecture,
$false,
inference(rw,[status(thm)],[116,36,theory(equality)]) ).
cnf(124,negated_conjecture,
$false,
inference(cn,[status(thm)],[123,theory(equality)]) ).
cnf(125,negated_conjecture,
$false,
124,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET630+3.p
% --creating new selector for []
% -running prover on /tmp/tmp6MsawO/sel_SET630+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET630+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET630+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET630+3.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
%
%------------------------------------------------------------------------------