%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET574+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 02:56:57 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   19 (   6 unt;   0 def)
%            Number of atoms       :   60 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   65 (  24   ~;  19   |;  19   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  23   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2,X3] :
      ( ( member(X1,X2)
        & member(X1,X3) )
     => intersect(X2,X3) ),
    file('/tmp/tmp4lhlvq/sel_SET574+3.p_1',prove_th13) ).

fof(3,axiom,
    ! [X1,X2] :
      ( intersect(X1,X2)
    <=> ? [X3] :
          ( member(X3,X1)
          & member(X3,X2) ) ),
    file('/tmp/tmp4lhlvq/sel_SET574+3.p_1',intersect_defn) ).

fof(4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( member(X1,X2)
          & member(X1,X3) )
       => intersect(X2,X3) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(8,negated_conjecture,
    ? [X1,X2,X3] :
      ( member(X1,X2)
      & member(X1,X3)
      & ~ intersect(X2,X3) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(9,negated_conjecture,
    ? [X4,X5,X6] :
      ( member(X4,X5)
      & member(X4,X6)
      & ~ intersect(X5,X6) ),
    inference(variable_rename,[status(thm)],[8]) ).

fof(10,negated_conjecture,
    ( member(esk1_0,esk2_0)
    & member(esk1_0,esk3_0)
    & ~ intersect(esk2_0,esk3_0) ),
    inference(skolemize,[status(esa)],[9]) ).

cnf(11,negated_conjecture,
    ~ intersect(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(12,negated_conjecture,
    member(esk1_0,esk3_0),
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(13,negated_conjecture,
    member(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[10]) ).

fof(14,plain,
    ! [X1,X2] :
      ( ( ~ intersect(X1,X2)
        | ? [X3] :
            ( member(X3,X1)
            & member(X3,X2) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | ~ member(X3,X2) )
        | intersect(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(15,plain,
    ! [X4,X5] :
      ( ( ~ intersect(X4,X5)
        | ? [X6] :
            ( member(X6,X4)
            & member(X6,X5) ) )
      & ( ! [X7] :
            ( ~ member(X7,X4)
            | ~ member(X7,X5) )
        | intersect(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[14]) ).

fof(16,plain,
    ! [X4,X5] :
      ( ( ~ intersect(X4,X5)
        | ( member(esk4_2(X4,X5),X4)
          & member(esk4_2(X4,X5),X5) ) )
      & ( ! [X7] :
            ( ~ member(X7,X4)
            | ~ member(X7,X5) )
        | intersect(X4,X5) ) ),
    inference(skolemize,[status(esa)],[15]) ).

fof(17,plain,
    ! [X4,X5,X7] :
      ( ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(X4,X5) )
      & ( ~ intersect(X4,X5)
        | ( member(esk4_2(X4,X5),X4)
          & member(esk4_2(X4,X5),X5) ) ) ),
    inference(shift_quantors,[status(thm)],[16]) ).

fof(18,plain,
    ! [X4,X5,X7] :
      ( ( ~ member(X7,X4)
        | ~ member(X7,X5)
        | intersect(X4,X5) )
      & ( member(esk4_2(X4,X5),X4)
        | ~ intersect(X4,X5) )
      & ( member(esk4_2(X4,X5),X5)
        | ~ intersect(X4,X5) ) ),
    inference(distribute,[status(thm)],[17]) ).

cnf(21,plain,
    ( intersect(X1,X2)
    | ~ member(X3,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[18]) ).

cnf(23,negated_conjecture,
    ( intersect(X1,esk3_0)
    | ~ member(esk1_0,X1) ),
    inference(spm,[status(thm)],[21,12,theory(equality)]) ).

cnf(30,negated_conjecture,
    intersect(esk2_0,esk3_0),
    inference(spm,[status(thm)],[23,13,theory(equality)]) ).

cnf(32,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[30,11,theory(equality)]) ).

cnf(33,negated_conjecture,
    $false,
    32,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET574+3.p
% --creating new selector for []
% -running prover on /tmp/tmp4lhlvq/sel_SET574+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET574+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET574+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET574+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
% 
%------------------------------------------------------------------------------