%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET633+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 03:06:02 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (   9 unt;   0 def)
%            Number of atoms       :   42 (   3 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   36 (  15   ~;   9   |;   9   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   30 (   0 sgn  19   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    file('/tmp/tmpGCkjy_/sel_SET633+3.p_1',symmetric_difference_defn) ).

fof(4,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(difference(X1,X2),X3)
        & subset(difference(X2,X1),X3) )
     => subset(symmetric_difference(X1,X2),X3) ),
    file('/tmp/tmpGCkjy_/sel_SET633+3.p_1',prove_th115) ).

fof(5,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(union(X1,X3),X2) ),
    file('/tmp/tmpGCkjy_/sel_SET633+3.p_1',union_subset) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(difference(X1,X2),X3)
          & subset(difference(X2,X1),X3) )
       => subset(symmetric_difference(X1,X2),X3) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(16,plain,
    ! [X3,X4] : symmetric_difference(X3,X4) = union(difference(X3,X4),difference(X4,X3)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(17,plain,
    symmetric_difference(X1,X2) = union(difference(X1,X2),difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(difference(X1,X2),X3)
      & subset(difference(X2,X1),X3)
      & ~ subset(symmetric_difference(X1,X2),X3) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(19,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(difference(X4,X5),X6)
      & subset(difference(X5,X4),X6)
      & ~ subset(symmetric_difference(X4,X5),X6) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,negated_conjecture,
    ( subset(difference(esk1_0,esk2_0),esk3_0)
    & subset(difference(esk2_0,esk1_0),esk3_0)
    & ~ subset(symmetric_difference(esk1_0,esk2_0),esk3_0) ),
    inference(skolemize,[status(esa)],[19]) ).

cnf(21,negated_conjecture,
    ~ subset(symmetric_difference(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,negated_conjecture,
    subset(difference(esk2_0,esk1_0),esk3_0),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,negated_conjecture,
    subset(difference(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(24,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X3,X2)
      | subset(union(X1,X3),X2) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(25,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X6,X5)
      | subset(union(X4,X6),X5) ),
    inference(variable_rename,[status(thm)],[24]) ).

cnf(26,plain,
    ( subset(union(X1,X2),X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(53,negated_conjecture,
    ~ subset(union(difference(esk1_0,esk2_0),difference(esk2_0,esk1_0)),esk3_0),
    inference(rw,[status(thm)],[21,17,theory(equality)]),
    [unfolding] ).

cnf(63,negated_conjecture,
    ( ~ subset(difference(esk2_0,esk1_0),esk3_0)
    | ~ subset(difference(esk1_0,esk2_0),esk3_0) ),
    inference(spm,[status(thm)],[53,26,theory(equality)]) ).

cnf(65,negated_conjecture,
    ( $false
    | ~ subset(difference(esk1_0,esk2_0),esk3_0) ),
    inference(rw,[status(thm)],[63,22,theory(equality)]) ).

cnf(66,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[65,23,theory(equality)]) ).

cnf(67,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[66,theory(equality)]) ).

cnf(68,negated_conjecture,
    $false,
    67,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET633+3.p
% --creating new selector for []
% -running prover on /tmp/tmpGCkjy_/sel_SET633+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET633+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET633+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET633+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
% 
%------------------------------------------------------------------------------