%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET605+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 03:00:41 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (  13 unt;   0 def)
%            Number of atoms       :   25 (  12 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (  11   ~;   5   |;   2   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   22 (   1 sgn  14   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2] : difference(X1,union(X1,X2)) = empty_set,
    file('/tmp/tmpqfigIc/sel_SET605+3.p_1',prove_th76) ).

fof(9,axiom,
    ! [X1,X2] :
      ( difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/tmp/tmpqfigIc/sel_SET605+3.p_1',difference_empty_set) ).

fof(11,axiom,
    ! [X1,X2] : subset(X1,union(X1,X2)),
    file('/tmp/tmpqfigIc/sel_SET605+3.p_1',subset_of_union) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2] : difference(X1,union(X1,X2)) = empty_set,
    inference(assume_negation,[status(cth)],[2]) ).

fof(19,negated_conjecture,
    ? [X1,X2] : difference(X1,union(X1,X2)) != empty_set,
    inference(fof_nnf,[status(thm)],[13]) ).

fof(20,negated_conjecture,
    ? [X3,X4] : difference(X3,union(X3,X4)) != empty_set,
    inference(variable_rename,[status(thm)],[19]) ).

fof(21,negated_conjecture,
    difference(esk1_0,union(esk1_0,esk2_0)) != empty_set,
    inference(skolemize,[status(esa)],[20]) ).

cnf(22,negated_conjecture,
    difference(esk1_0,union(esk1_0,esk2_0)) != empty_set,
    inference(split_conjunct,[status(thm)],[21]) ).

fof(60,plain,
    ! [X1,X2] :
      ( ( difference(X1,X2) != empty_set
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | difference(X1,X2) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(61,plain,
    ! [X3,X4] :
      ( ( difference(X3,X4) != empty_set
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | difference(X3,X4) = empty_set ) ),
    inference(variable_rename,[status(thm)],[60]) ).

cnf(62,plain,
    ( difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[61]) ).

fof(70,plain,
    ! [X3,X4] : subset(X3,union(X3,X4)),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(71,plain,
    subset(X1,union(X1,X2)),
    inference(split_conjunct,[status(thm)],[70]) ).

cnf(82,negated_conjecture,
    ~ subset(esk1_0,union(esk1_0,esk2_0)),
    inference(spm,[status(thm)],[22,62,theory(equality)]) ).

cnf(83,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[82,71,theory(equality)]) ).

cnf(84,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[83,theory(equality)]) ).

cnf(85,negated_conjecture,
    $false,
    84,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET605+3.p
% --creating new selector for []
% -running prover on /tmp/tmpqfigIc/sel_SET605+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET605+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET605+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET605+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
% 
%------------------------------------------------------------------------------