%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET617+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 03:03:23 EST 2010
% Result : Theorem 0.17s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 20 unt; 0 def)
% Number of atoms : 38 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 15 ~; 7 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpGsLBcx/sel_SET617+3.p_1',commutativity_of_union) ).
fof(4,axiom,
! [X1] : difference(X1,empty_set) = X1,
file('/tmp/tmpGsLBcx/sel_SET617+3.p_1',no_difference_with_empty_set1) ).
fof(5,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/tmp/tmpGsLBcx/sel_SET617+3.p_1',symmetric_difference_defn) ).
fof(6,conjecture,
! [X1] :
( symmetric_difference(X1,empty_set) = X1
& symmetric_difference(empty_set,X1) = X1 ),
file('/tmp/tmpGsLBcx/sel_SET617+3.p_1',prove_th92) ).
fof(8,axiom,
! [X1] : difference(empty_set,X1) = empty_set,
file('/tmp/tmpGsLBcx/sel_SET617+3.p_1',no_difference_with_empty_set2) ).
fof(11,axiom,
! [X1] : union(X1,empty_set) = X1,
file('/tmp/tmpGsLBcx/sel_SET617+3.p_1',union_empty_set) ).
fof(14,negated_conjecture,
~ ! [X1] :
( symmetric_difference(X1,empty_set) = X1
& symmetric_difference(empty_set,X1) = X1 ),
inference(assume_negation,[status(cth)],[6]) ).
fof(19,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(20,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[19]) ).
fof(27,plain,
! [X2] : difference(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[4]) ).
cnf(28,plain,
difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[27]) ).
fof(29,plain,
! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(30,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[29]) ).
fof(31,negated_conjecture,
? [X1] :
( symmetric_difference(X1,empty_set) != X1
| symmetric_difference(empty_set,X1) != X1 ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(32,negated_conjecture,
? [X2] :
( symmetric_difference(X2,empty_set) != X2
| symmetric_difference(empty_set,X2) != X2 ),
inference(variable_rename,[status(thm)],[31]) ).
fof(33,negated_conjecture,
( symmetric_difference(esk2_0,empty_set) != esk2_0
| symmetric_difference(empty_set,esk2_0) != esk2_0 ),
inference(skolemize,[status(esa)],[32]) ).
cnf(34,negated_conjecture,
( symmetric_difference(empty_set,esk2_0) != esk2_0
| symmetric_difference(esk2_0,empty_set) != esk2_0 ),
inference(split_conjunct,[status(thm)],[33]) ).
fof(41,plain,
! [X2] : difference(empty_set,X2) = empty_set,
inference(variable_rename,[status(thm)],[8]) ).
cnf(42,plain,
difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[41]) ).
fof(60,plain,
! [X2] : union(X2,empty_set) = X2,
inference(variable_rename,[status(thm)],[11]) ).
cnf(61,plain,
union(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[60]) ).
cnf(67,negated_conjecture,
( union(difference(empty_set,esk2_0),difference(esk2_0,empty_set)) != esk2_0
| union(difference(esk2_0,empty_set),difference(empty_set,esk2_0)) != esk2_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[34,30,theory(equality)]),30,theory(equality)]),
[unfolding] ).
cnf(68,plain,
union(empty_set,X1) = X1,
inference(spm,[status(thm)],[61,20,theory(equality)]) ).
cnf(88,negated_conjecture,
( union(empty_set,esk2_0) != esk2_0
| union(difference(esk2_0,empty_set),difference(empty_set,esk2_0)) != esk2_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[67,42,theory(equality)]),28,theory(equality)]) ).
cnf(89,negated_conjecture,
( union(empty_set,esk2_0) != esk2_0
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[88,28,theory(equality)]),42,theory(equality)]),61,theory(equality)]) ).
cnf(90,negated_conjecture,
union(empty_set,esk2_0) != esk2_0,
inference(cn,[status(thm)],[89,theory(equality)]) ).
cnf(97,negated_conjecture,
$false,
inference(rw,[status(thm)],[90,68,theory(equality)]) ).
cnf(98,negated_conjecture,
$false,
inference(cn,[status(thm)],[97,theory(equality)]) ).
cnf(99,negated_conjecture,
$false,
98,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET617+3.p
% --creating new selector for []
% -running prover on /tmp/tmpGsLBcx/sel_SET617+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET617+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET617+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET617+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
%
%------------------------------------------------------------------------------