%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET619+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 03:03:59 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 2 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',commutativity_of_intersection) ).
fof(3,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',commutativity_of_union) ).
fof(4,axiom,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',associativity_of_union) ).
fof(5,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',symmetric_difference_defn) ).
fof(7,axiom,
! [X1,X2] : union(X1,intersection(X1,X2)) = X1,
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',union_intersection) ).
fof(13,axiom,
! [X1,X2] : union(intersection(X1,X2),difference(X1,X2)) = X1,
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',union_intersection_difference) ).
fof(14,conjecture,
! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
file('/tmp/tmphZlqmz/sel_SET619+3.p_1',prove_th95) ).
fof(15,negated_conjecture,
~ ! [X1,X2] : union(X1,X2) = union(symmetric_difference(X1,X2),intersection(X1,X2)),
inference(assume_negation,[status(cth)],[14]) ).
fof(18,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[2]) ).
cnf(19,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[18]) ).
fof(20,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[3]) ).
cnf(21,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[20]) ).
fof(22,plain,
! [X4,X5,X6] : union(union(X4,X5),X6) = union(X4,union(X5,X6)),
inference(variable_rename,[status(thm)],[4]) ).
cnf(23,plain,
union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(split_conjunct,[status(thm)],[22]) ).
fof(24,plain,
! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
inference(variable_rename,[status(thm)],[5]) ).
cnf(25,plain,
symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
inference(split_conjunct,[status(thm)],[24]) ).
fof(32,plain,
! [X3,X4] : union(X3,intersection(X3,X4)) = X3,
inference(variable_rename,[status(thm)],[7]) ).
cnf(33,plain,
union(X1,intersection(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[32]) ).
fof(65,plain,
! [X3,X4] : union(intersection(X3,X4),difference(X3,X4)) = X3,
inference(variable_rename,[status(thm)],[13]) ).
cnf(66,plain,
union(intersection(X1,X2),difference(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[65]) ).
fof(67,negated_conjecture,
? [X1,X2] : union(X1,X2) != union(symmetric_difference(X1,X2),intersection(X1,X2)),
inference(fof_nnf,[status(thm)],[15]) ).
fof(68,negated_conjecture,
? [X3,X4] : union(X3,X4) != union(symmetric_difference(X3,X4),intersection(X3,X4)),
inference(variable_rename,[status(thm)],[67]) ).
fof(69,negated_conjecture,
union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(skolemize,[status(esa)],[68]) ).
cnf(70,negated_conjecture,
union(esk3_0,esk4_0) != union(symmetric_difference(esk3_0,esk4_0),intersection(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[69]) ).
cnf(72,negated_conjecture,
union(union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0)),intersection(esk3_0,esk4_0)) != union(esk3_0,esk4_0),
inference(rw,[status(thm)],[70,25,theory(equality)]),
[unfolding] ).
cnf(75,negated_conjecture,
union(intersection(esk3_0,esk4_0),union(difference(esk3_0,esk4_0),difference(esk4_0,esk3_0))) != union(esk3_0,esk4_0),
inference(rw,[status(thm)],[72,21,theory(equality)]) ).
cnf(80,plain,
union(intersection(X2,X1),difference(X1,X2)) = X1,
inference(spm,[status(thm)],[66,19,theory(equality)]) ).
cnf(83,plain,
union(X1,X3) = union(X1,union(intersection(X1,X2),X3)),
inference(spm,[status(thm)],[23,33,theory(equality)]) ).
cnf(84,plain,
union(X1,X3) = union(intersection(X1,X2),union(difference(X1,X2),X3)),
inference(spm,[status(thm)],[23,66,theory(equality)]) ).
cnf(210,plain,
union(X1,X2) = union(X1,difference(X2,X1)),
inference(spm,[status(thm)],[83,80,theory(equality)]) ).
cnf(600,negated_conjecture,
$false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[75,84,theory(equality)]),210,theory(equality)]) ).
cnf(601,negated_conjecture,
$false,
inference(cn,[status(thm)],[600,theory(equality)]) ).
cnf(602,negated_conjecture,
$false,
601,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET619+3.p
% --creating new selector for []
% -running prover on /tmp/tmphZlqmz/sel_SET619+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET619+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET619+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET619+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
%
%------------------------------------------------------------------------------