%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU134+1 : TPTP v5.0.0. Released v3.3.0.
% 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 04:45:50 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   19 (   6 unt;   0 def)
%            Number of atoms       :   42 (  19 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   41 (  18   ~;  15   |;   5   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (   0 sgn  10   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(8,conjecture,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/tmp/tmpPirpxs/sel_SEU134+1.p_1',t37_xboole_1) ).

fof(10,axiom,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/tmp/tmpPirpxs/sel_SEU134+1.p_1',l32_xboole_1) ).

fof(15,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(X1,X2) = empty_set
      <=> subset(X1,X2) ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(33,negated_conjecture,
    ? [X1,X2] :
      ( ( set_difference(X1,X2) != empty_set
        | ~ subset(X1,X2) )
      & ( set_difference(X1,X2) = empty_set
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(34,negated_conjecture,
    ? [X3,X4] :
      ( ( set_difference(X3,X4) != empty_set
        | ~ subset(X3,X4) )
      & ( set_difference(X3,X4) = empty_set
        | subset(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,negated_conjecture,
    ( ( set_difference(esk2_0,esk3_0) != empty_set
      | ~ subset(esk2_0,esk3_0) )
    & ( set_difference(esk2_0,esk3_0) = empty_set
      | subset(esk2_0,esk3_0) ) ),
    inference(skolemize,[status(esa)],[34]) ).

cnf(36,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    | set_difference(esk2_0,esk3_0) = empty_set ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(37,negated_conjecture,
    ( ~ subset(esk2_0,esk3_0)
    | set_difference(esk2_0,esk3_0) != empty_set ),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(41,plain,
    ! [X1,X2] :
      ( ( set_difference(X1,X2) != empty_set
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | set_difference(X1,X2) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(42,plain,
    ! [X3,X4] :
      ( ( set_difference(X3,X4) != empty_set
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | set_difference(X3,X4) = empty_set ) ),
    inference(variable_rename,[status(thm)],[41]) ).

cnf(43,plain,
    ( set_difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[42]) ).

cnf(44,plain,
    ( subset(X1,X2)
    | set_difference(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[42]) ).

cnf(59,negated_conjecture,
    set_difference(esk2_0,esk3_0) = empty_set,
    inference(spm,[status(thm)],[43,36,theory(equality)]) ).

cnf(64,negated_conjecture,
    ( $false
    | ~ subset(esk2_0,esk3_0) ),
    inference(rw,[status(thm)],[37,59,theory(equality)]) ).

cnf(65,negated_conjecture,
    ~ subset(esk2_0,esk3_0),
    inference(cn,[status(thm)],[64,theory(equality)]) ).

cnf(67,negated_conjecture,
    set_difference(esk2_0,esk3_0) != empty_set,
    inference(spm,[status(thm)],[65,44,theory(equality)]) ).

cnf(68,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[67,59,theory(equality)]) ).

cnf(69,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[68,theory(equality)]) ).

cnf(70,negated_conjecture,
    $false,
    69,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU134+1.p
% --creating new selector for []
% -running prover on /tmp/tmpPirpxs/sel_SEU134+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU134+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU134+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU134+1.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
% 
%------------------------------------------------------------------------------