TSTP Solution File: SET622+3 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET622+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 03:04:19 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,conjecture,
! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
file('/tmp/tmpmHM3v1/sel_SET622+3.p_1',prove_th98) ).
fof(4,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/tmp/tmpmHM3v1/sel_SET622+3.p_1',commutativity_of_union) ).
fof(6,axiom,
! [X1,X2,X3] : difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
file('/tmp/tmpmHM3v1/sel_SET622+3.p_1',difference_difference_union2) ).
fof(8,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/tmp/tmpmHM3v1/sel_SET622+3.p_1',commutativity_of_intersection) ).
fof(10,axiom,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/tmp/tmpmHM3v1/sel_SET622+3.p_1',associativity_of_intersection) ).
fof(13,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
file('/tmp/tmpmHM3v1/sel_SET622+3.p_1',symmetric_difference_and_difference) ).
fof(16,negated_conjecture,
~ ! [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) = union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
inference(assume_negation,[status(cth)],[2]) ).
fof(20,negated_conjecture,
? [X1,X2,X3] : difference(X1,symmetric_difference(X2,X3)) != union(difference(X1,union(X2,X3)),intersection(intersection(X1,X2),X3)),
inference(fof_nnf,[status(thm)],[16]) ).
fof(21,negated_conjecture,
? [X4,X5,X6] : difference(X4,symmetric_difference(X5,X6)) != union(difference(X4,union(X5,X6)),intersection(intersection(X4,X5),X6)),
inference(variable_rename,[status(thm)],[20]) ).
fof(22,negated_conjecture,
difference(esk1_0,symmetric_difference(esk2_0,esk3_0)) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(skolemize,[status(esa)],[21]) ).
cnf(23,negated_conjecture,
difference(esk1_0,symmetric_difference(esk2_0,esk3_0)) != union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)),
inference(split_conjunct,[status(thm)],[22]) ).
fof(30,plain,
! [X3,X4] : union(X3,X4) = union(X4,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(31,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[30]) ).
fof(34,plain,
! [X4,X5,X6] : difference(X4,difference(X5,X6)) = union(difference(X4,X5),intersection(X4,X6)),
inference(variable_rename,[status(thm)],[6]) ).
cnf(35,plain,
difference(X1,difference(X2,X3)) = union(difference(X1,X2),intersection(X1,X3)),
inference(split_conjunct,[status(thm)],[34]) ).
fof(42,plain,
! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
inference(variable_rename,[status(thm)],[8]) ).
cnf(43,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[42]) ).
fof(46,plain,
! [X4,X5,X6] : intersection(intersection(X4,X5),X6) = intersection(X4,intersection(X5,X6)),
inference(variable_rename,[status(thm)],[10]) ).
cnf(47,plain,
intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(split_conjunct,[status(thm)],[46]) ).
fof(65,plain,
! [X3,X4] : symmetric_difference(X3,X4) = difference(union(X3,X4),intersection(X3,X4)),
inference(variable_rename,[status(thm)],[13]) ).
cnf(66,plain,
symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
inference(split_conjunct,[status(thm)],[65]) ).
cnf(81,negated_conjecture,
union(difference(esk1_0,union(esk2_0,esk3_0)),intersection(intersection(esk1_0,esk2_0),esk3_0)) != difference(esk1_0,difference(union(esk2_0,esk3_0),intersection(esk2_0,esk3_0))),
inference(rw,[status(thm)],[23,66,theory(equality)]),
[unfolding] ).
cnf(82,negated_conjecture,
union(intersection(intersection(esk1_0,esk2_0),esk3_0),difference(esk1_0,union(esk2_0,esk3_0))) != difference(esk1_0,difference(union(esk2_0,esk3_0),intersection(esk2_0,esk3_0))),
inference(rw,[status(thm)],[81,31,theory(equality)]) ).
cnf(116,plain,
difference(X1,difference(X2,X3)) = union(intersection(X1,X3),difference(X1,X2)),
inference(spm,[status(thm)],[31,35,theory(equality)]) ).
cnf(148,negated_conjecture,
union(intersection(esk2_0,intersection(esk3_0,esk1_0)),difference(esk1_0,union(esk2_0,esk3_0))) != difference(esk1_0,difference(union(esk2_0,esk3_0),intersection(esk2_0,esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[82,43,theory(equality)]),47,theory(equality)]),43,theory(equality)]) ).
cnf(203,plain,
union(intersection(X2,X1),difference(X1,X3)) = difference(X1,difference(X3,X2)),
inference(spm,[status(thm)],[116,43,theory(equality)]) ).
cnf(229,plain,
union(intersection(X1,intersection(X2,X3)),difference(X3,X4)) = difference(X3,difference(X4,intersection(X1,X2))),
inference(spm,[status(thm)],[203,47,theory(equality)]) ).
cnf(520,negated_conjecture,
$false,
inference(rw,[status(thm)],[148,229,theory(equality)]) ).
cnf(521,negated_conjecture,
$false,
inference(cn,[status(thm)],[520,theory(equality)]) ).
cnf(522,negated_conjecture,
$false,
521,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET622+3.p
% --creating new selector for []
% -running prover on /tmp/tmpmHM3v1/sel_SET622+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET622+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET622+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET622+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
%
%------------------------------------------------------------------------------