%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET626+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 03:05:04 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 102 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 109 ( 44 ~; 39 |; 21 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 3 sgn 45 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmp923gaT/sel_SET626+3.p_1',commutativity_of_intersection) ).
fof(2,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmp923gaT/sel_SET626+3.p_1',intersect_defn) ).
fof(3,axiom,
! [X1,X2] :
( intersect(X1,X2)
=> intersect(X2,X1) ),
file('/tmp/tmp923gaT/sel_SET626+3.p_1',symmetry_of_intersect) ).
fof(5,conjecture,
! [X1,X2,X3] :
( intersect(X1,intersection(X2,X3))
=> intersect(X1,X2) ),
file('/tmp/tmp923gaT/sel_SET626+3.p_1',prove_th102) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmp923gaT/sel_SET626+3.p_1',intersection_defn) ).
fof(7,negated_conjecture,
~ ! [X1,X2,X3] :
( intersect(X1,intersection(X2,X3))
=> intersect(X1,X2) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(8,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(9,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[8]) ).
fof(10,plain,
! [X1,X2] :
( ( ~ intersect(X1,X2)
| ? [X3] :
( member(X3,X1)
& member(X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X2) )
| intersect(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(11,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ? [X6] :
( member(X6,X4)
& member(X6,X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(variable_rename,[status(thm)],[10]) ).
fof(12,plain,
! [X4,X5] :
( ( ~ intersect(X4,X5)
| ( member(esk1_2(X4,X5),X4)
& member(esk1_2(X4,X5),X5) ) )
& ( ! [X7] :
( ~ member(X7,X4)
| ~ member(X7,X5) )
| intersect(X4,X5) ) ),
inference(skolemize,[status(esa)],[11]) ).
fof(13,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( ~ intersect(X4,X5)
| ( member(esk1_2(X4,X5),X4)
& member(esk1_2(X4,X5),X5) ) ) ),
inference(shift_quantors,[status(thm)],[12]) ).
fof(14,plain,
! [X4,X5,X7] :
( ( ~ member(X7,X4)
| ~ member(X7,X5)
| intersect(X4,X5) )
& ( member(esk1_2(X4,X5),X4)
| ~ intersect(X4,X5) )
& ( member(esk1_2(X4,X5),X5)
| ~ intersect(X4,X5) ) ),
inference(distribute,[status(thm)],[13]) ).
cnf(15,plain,
( member(esk1_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(16,plain,
( member(esk1_2(X1,X2),X1)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[14]) ).
cnf(17,plain,
( intersect(X1,X2)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[14]) ).
fof(18,plain,
! [X1,X2] :
( ~ intersect(X1,X2)
| intersect(X2,X1) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(19,plain,
! [X3,X4] :
( ~ intersect(X3,X4)
| intersect(X4,X3) ),
inference(variable_rename,[status(thm)],[18]) ).
cnf(20,plain,
( intersect(X1,X2)
| ~ intersect(X2,X1) ),
inference(split_conjunct,[status(thm)],[19]) ).
fof(30,negated_conjecture,
? [X1,X2,X3] :
( intersect(X1,intersection(X2,X3))
& ~ intersect(X1,X2) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(31,negated_conjecture,
? [X4,X5,X6] :
( intersect(X4,intersection(X5,X6))
& ~ intersect(X4,X5) ),
inference(variable_rename,[status(thm)],[30]) ).
fof(32,negated_conjecture,
( intersect(esk3_0,intersection(esk4_0,esk5_0))
& ~ intersect(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[31]) ).
cnf(33,negated_conjecture,
~ intersect(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[32]) ).
cnf(34,negated_conjecture,
intersect(esk3_0,intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[32]) ).
fof(35,plain,
! [X1,X2,X3] :
( ( ~ 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)],[6]) ).
fof(36,plain,
! [X4,X5,X6] :
( ( ~ member(X6,intersection(X4,X5))
| ( member(X6,X4)
& member(X6,X5) ) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[36]) ).
cnf(39,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(41,negated_conjecture,
intersect(intersection(esk4_0,esk5_0),esk3_0),
inference(spm,[status(thm)],[20,34,theory(equality)]) ).
cnf(45,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| ~ intersect(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[39,16,theory(equality)]) ).
cnf(50,plain,
( intersect(X1,X2)
| ~ member(esk1_2(X3,X2),X1)
| ~ intersect(X3,X2) ),
inference(spm,[status(thm)],[17,15,theory(equality)]) ).
cnf(106,plain,
( intersect(X1,X2)
| ~ intersect(intersection(X3,X1),X2) ),
inference(spm,[status(thm)],[50,45,theory(equality)]) ).
cnf(114,plain,
( intersect(X1,X2)
| ~ intersect(intersection(X1,X3),X2) ),
inference(spm,[status(thm)],[106,9,theory(equality)]) ).
cnf(125,negated_conjecture,
intersect(esk4_0,esk3_0),
inference(spm,[status(thm)],[114,41,theory(equality)]) ).
cnf(130,negated_conjecture,
intersect(esk3_0,esk4_0),
inference(spm,[status(thm)],[20,125,theory(equality)]) ).
cnf(132,negated_conjecture,
$false,
inference(sr,[status(thm)],[130,33,theory(equality)]) ).
cnf(133,negated_conjecture,
$false,
132,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET626+3.p
% --creating new selector for []
% -running prover on /tmp/tmp923gaT/sel_SET626+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET626+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET626+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET626+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
%
%------------------------------------------------------------------------------