%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET621+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 03:04:15 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   20 (  20 unt;   0 def)
%            Number of atoms       :   20 (  17 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    7 (   7   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  22   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] : difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
    file('/tmp/tmp3bB1Ve/sel_SET621+3.p_1',difference_distributes_over_union) ).

fof(4,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/tmp/tmp3bB1Ve/sel_SET621+3.p_1',symmetric_difference_defn) ).

fof(6,conjecture,
    ! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
    file('/tmp/tmp3bB1Ve/sel_SET621+3.p_1',prove_th97) ).

fof(10,axiom,
    ! [X1,X2,X3] : difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
    file('/tmp/tmp3bB1Ve/sel_SET621+3.p_1',difference_difference_union) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) = union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
    inference(assume_negation,[status(cth)],[6]) ).

fof(15,plain,
    ! [X4,X5,X6] : difference(union(X4,X5),X6) = union(difference(X4,X6),difference(X5,X6)),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(16,plain,
    difference(union(X1,X2),X3) = union(difference(X1,X3),difference(X2,X3)),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(21,plain,
    ! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
    inference(variable_rename,[status(thm)],[4]) ).

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

fof(29,negated_conjecture,
    ? [X1,X2,X3] : difference(symmetric_difference(X1,X2),X3) != union(difference(X1,union(X2,X3)),difference(X2,union(X1,X3))),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(30,negated_conjecture,
    ? [X4,X5,X6] : difference(symmetric_difference(X4,X5),X6) != union(difference(X4,union(X5,X6)),difference(X5,union(X4,X6))),
    inference(variable_rename,[status(thm)],[29]) ).

fof(31,negated_conjecture,
    difference(symmetric_difference(esk1_0,esk2_0),esk3_0) != union(difference(esk1_0,union(esk2_0,esk3_0)),difference(esk2_0,union(esk1_0,esk3_0))),
    inference(skolemize,[status(esa)],[30]) ).

cnf(32,negated_conjecture,
    difference(symmetric_difference(esk1_0,esk2_0),esk3_0) != union(difference(esk1_0,union(esk2_0,esk3_0)),difference(esk2_0,union(esk1_0,esk3_0))),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(56,plain,
    ! [X4,X5,X6] : difference(difference(X4,X5),X6) = difference(X4,union(X5,X6)),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(57,plain,
    difference(difference(X1,X2),X3) = difference(X1,union(X2,X3)),
    inference(split_conjunct,[status(thm)],[56]) ).

cnf(67,negated_conjecture,
    union(difference(esk1_0,union(esk2_0,esk3_0)),difference(esk2_0,union(esk1_0,esk3_0))) != difference(union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0)),esk3_0),
    inference(rw,[status(thm)],[32,22,theory(equality)]),
    [unfolding] ).

cnf(76,negated_conjecture,
    union(difference(difference(esk1_0,esk2_0),esk3_0),difference(difference(esk2_0,esk1_0),esk3_0)) != difference(union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0)),esk3_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[67,57,theory(equality)]),57,theory(equality)]) ).

cnf(117,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[76,16,theory(equality)]) ).

cnf(118,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[117,theory(equality)]) ).

cnf(119,negated_conjecture,
    $false,
    118,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET621+3.p
% --creating new selector for []
% -running prover on /tmp/tmp3bB1Ve/sel_SET621+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET621+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET621+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET621+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
% 
%------------------------------------------------------------------------------