TSTP Solution File: SET581+3 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET581+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 02:57:48 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 16 unt; 0 def)
% Number of atoms : 70 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 27 ~; 18 |; 17 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 1 sgn 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',commutativity_of_intersection) ).
fof(3,axiom,
! [X1,X2] :
( not_equal(X1,X2)
<=> X1 != X2 ),
file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',not_equal_defn) ).
fof(5,conjecture,
! [X1,X2,X3] :
( ( member(X1,X2)
& member(X1,X3) )
=> not_equal(intersection(X2,X3),empty_set) ),
file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',prove_th24) ).
fof(6,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',intersection_defn) ).
fof(7,axiom,
! [X1] : ~ member(X1,empty_set),
file('/tmp/tmp4pLK6C/sel_SET581+3.p_1',empty_set_defn) ).
fof(8,negated_conjecture,
~ ! [X1,X2,X3] :
( ( member(X1,X2)
& member(X1,X3) )
=> not_equal(intersection(X2,X3),empty_set) ),
inference(assume_negation,[status(cth)],[5]) ).
fof(10,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).
fof(11,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[1]) ).
cnf(12,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[11]) ).
fof(19,plain,
! [X1,X2] :
( ( ~ not_equal(X1,X2)
| X1 != X2 )
& ( X1 = X2
| not_equal(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(20,plain,
! [X3,X4] :
( ( ~ not_equal(X3,X4)
| X3 != X4 )
& ( X3 = X4
| not_equal(X3,X4) ) ),
inference(variable_rename,[status(thm)],[19]) ).
cnf(21,plain,
( not_equal(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[20]) ).
fof(32,negated_conjecture,
? [X1,X2,X3] :
( member(X1,X2)
& member(X1,X3)
& ~ not_equal(intersection(X2,X3),empty_set) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(33,negated_conjecture,
? [X4,X5,X6] :
( member(X4,X5)
& member(X4,X6)
& ~ not_equal(intersection(X5,X6),empty_set) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,negated_conjecture,
( member(esk3_0,esk4_0)
& member(esk3_0,esk5_0)
& ~ not_equal(intersection(esk4_0,esk5_0),empty_set) ),
inference(skolemize,[status(esa)],[33]) ).
cnf(35,negated_conjecture,
~ not_equal(intersection(esk4_0,esk5_0),empty_set),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,negated_conjecture,
member(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,negated_conjecture,
member(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[34]) ).
fof(38,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(39,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)],[38]) ).
fof(40,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)],[39]) ).
cnf(41,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X3)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[40]) ).
fof(44,plain,
! [X2] : ~ member(X2,empty_set),
inference(variable_rename,[status(thm)],[10]) ).
cnf(45,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[44]) ).
cnf(49,negated_conjecture,
intersection(esk4_0,esk5_0) = empty_set,
inference(spm,[status(thm)],[35,21,theory(equality)]) ).
cnf(69,negated_conjecture,
( member(esk3_0,intersection(X1,esk4_0))
| ~ member(esk3_0,X1) ),
inference(spm,[status(thm)],[41,37,theory(equality)]) ).
cnf(75,negated_conjecture,
member(esk3_0,intersection(esk5_0,esk4_0)),
inference(spm,[status(thm)],[69,36,theory(equality)]) ).
cnf(76,negated_conjecture,
member(esk3_0,intersection(esk4_0,esk5_0)),
inference(rw,[status(thm)],[75,12,theory(equality)]) ).
cnf(102,negated_conjecture,
member(esk3_0,empty_set),
inference(rw,[status(thm)],[76,49,theory(equality)]) ).
cnf(103,negated_conjecture,
$false,
inference(sr,[status(thm)],[102,45,theory(equality)]) ).
cnf(104,negated_conjecture,
$false,
103,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET581+3.p
% --creating new selector for []
% -running prover on /tmp/tmp4pLK6C/sel_SET581+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET581+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET581+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET581+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
%
%------------------------------------------------------------------------------