%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET620+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 03:04:08 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   25 (  25 unt;   0 def)
%            Number of atoms       :   25 (  22 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   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   :   42 (   0 sgn  22   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
    file('/tmp/tmpiLcnQ_/sel_SET620+3.p_1',difference_distributes_over_union) ).

fof(3,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmpiLcnQ_/sel_SET620+3.p_1',commutativity_of_intersection) ).

fof(5,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/tmp/tmpiLcnQ_/sel_SET620+3.p_1',symmetric_difference_defn) ).

fof(7,conjecture,
    ! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
    file('/tmp/tmpiLcnQ_/sel_SET620+3.p_1',prove_th96) ).

fof(14,axiom,
    ! [X1,X2] : difference(X1,intersection(X1,X2)) = difference(X1,X2),
    file('/tmp/tmpiLcnQ_/sel_SET620+3.p_1',difference_into_intersection) ).

fof(15,negated_conjecture,
    ~ ! [X1,X2] : symmetric_difference(X1,X2) = difference(union(X1,X2),intersection(X1,X2)),
    inference(assume_negation,[status(cth)],[7]) ).

fof(17,plain,
    ! [X4,X5,X6] : difference(union(X4,X5),X6) = union(difference(X4,X6),difference(X5,X6)),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(18,plain,
    difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(21,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(22,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(25,plain,
    ! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(26,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(33,negated_conjecture,
    ? [X1,X2] : symmetric_difference(X1,X2) != difference(union(X1,X2),intersection(X1,X2)),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(34,negated_conjecture,
    ? [X3,X4] : symmetric_difference(X3,X4) != difference(union(X3,X4),intersection(X3,X4)),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,negated_conjecture,
    symmetric_difference(esk1_0,esk2_0) != difference(union(esk1_0,esk2_0),intersection(esk1_0,esk2_0)),
    inference(skolemize,[status(esa)],[34]) ).

cnf(36,negated_conjecture,
    symmetric_difference(esk1_0,esk2_0) != difference(union(esk1_0,esk2_0),intersection(esk1_0,esk2_0)),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(74,plain,
    ! [X3,X4] : difference(X3,intersection(X3,X4)) = difference(X3,X4),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(75,plain,
    difference(X1,intersection(X1,X2)) = difference(X1,X2),
    inference(split_conjunct,[status(thm)],[74]) ).

cnf(77,negated_conjecture,
    difference(union(esk1_0,esk2_0),intersection(esk1_0,esk2_0)) != union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0)),
    inference(rw,[status(thm)],[36,26,theory(equality)]),
    [unfolding] ).

cnf(79,plain,
    difference(X1,intersection(X2,X1)) = difference(X1,X2),
    inference(spm,[status(thm)],[75,22,theory(equality)]) ).

cnf(103,plain,
    union(difference(X1,X2),difference(X3,intersection(X1,X2))) = difference(union(X1,X3),intersection(X1,X2)),
    inference(spm,[status(thm)],[18,75,theory(equality)]) ).

cnf(194,plain,
    union(difference(X1,X2),difference(X2,X1)) = difference(union(X1,X2),intersection(X1,X2)),
    inference(spm,[status(thm)],[103,79,theory(equality)]) ).

cnf(245,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[77,194,theory(equality)]) ).

cnf(246,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[245,theory(equality)]) ).

cnf(247,negated_conjecture,
    $false,
    246,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET620+3.p
% --creating new selector for []
% -running prover on /tmp/tmpiLcnQ_/sel_SET620+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET620+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET620+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET620+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
% 
%------------------------------------------------------------------------------