%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU089+1 : TPTP v5.0.0. Released v3.2.0.
% 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 04:33:57 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   25 (  11 unt;   0 def)
%            Number of atoms       :   53 (   3 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   47 (  19   ~;  11   |;  14   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 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; 0-3 aty)
%            Number of variables   :   29 (   0 sgn  18   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1,X2] :
      ( ( finite(X1)
        & finite(X2) )
     => finite(cartesian_product2(X1,X2)) ),
    file('/tmp/tmp9mzlYb/sel_SEU089+1.p_1',t19_finset_1) ).

fof(15,conjecture,
    ! [X1,X2,X3] :
      ( ( finite(X1)
        & finite(X2)
        & finite(X3) )
     => finite(cartesian_product3(X1,X2,X3)) ),
    file('/tmp/tmp9mzlYb/sel_SEU089+1.p_1',t20_finset_1) ).

fof(47,axiom,
    ! [X1,X2,X3] : cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
    file('/tmp/tmp9mzlYb/sel_SEU089+1.p_1',d3_zfmisc_1) ).

fof(61,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( finite(X1)
          & finite(X2)
          & finite(X3) )
       => finite(cartesian_product3(X1,X2,X3)) ),
    inference(assume_negation,[status(cth)],[15]) ).

fof(100,plain,
    ! [X1,X2] :
      ( ~ finite(X1)
      | ~ finite(X2)
      | finite(cartesian_product2(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(101,plain,
    ! [X3,X4] :
      ( ~ finite(X3)
      | ~ finite(X4)
      | finite(cartesian_product2(X3,X4)) ),
    inference(variable_rename,[status(thm)],[100]) ).

cnf(102,plain,
    ( finite(cartesian_product2(X1,X2))
    | ~ finite(X2)
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[101]) ).

fof(136,negated_conjecture,
    ? [X1,X2,X3] :
      ( finite(X1)
      & finite(X2)
      & finite(X3)
      & ~ finite(cartesian_product3(X1,X2,X3)) ),
    inference(fof_nnf,[status(thm)],[61]) ).

fof(137,negated_conjecture,
    ? [X4,X5,X6] :
      ( finite(X4)
      & finite(X5)
      & finite(X6)
      & ~ finite(cartesian_product3(X4,X5,X6)) ),
    inference(variable_rename,[status(thm)],[136]) ).

fof(138,negated_conjecture,
    ( finite(esk7_0)
    & finite(esk8_0)
    & finite(esk9_0)
    & ~ finite(cartesian_product3(esk7_0,esk8_0,esk9_0)) ),
    inference(skolemize,[status(esa)],[137]) ).

cnf(139,negated_conjecture,
    ~ finite(cartesian_product3(esk7_0,esk8_0,esk9_0)),
    inference(split_conjunct,[status(thm)],[138]) ).

cnf(140,negated_conjecture,
    finite(esk9_0),
    inference(split_conjunct,[status(thm)],[138]) ).

cnf(141,negated_conjecture,
    finite(esk8_0),
    inference(split_conjunct,[status(thm)],[138]) ).

cnf(142,negated_conjecture,
    finite(esk7_0),
    inference(split_conjunct,[status(thm)],[138]) ).

fof(284,plain,
    ! [X4,X5,X6] : cartesian_product3(X4,X5,X6) = cartesian_product2(cartesian_product2(X4,X5),X6),
    inference(variable_rename,[status(thm)],[47]) ).

cnf(285,plain,
    cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[284]) ).

cnf(343,negated_conjecture,
    ~ finite(cartesian_product2(cartesian_product2(esk7_0,esk8_0),esk9_0)),
    inference(rw,[status(thm)],[139,285,theory(equality)]),
    [unfolding] ).

cnf(358,negated_conjecture,
    ( ~ finite(esk9_0)
    | ~ finite(cartesian_product2(esk7_0,esk8_0)) ),
    inference(spm,[status(thm)],[343,102,theory(equality)]) ).

cnf(359,negated_conjecture,
    ( $false
    | ~ finite(cartesian_product2(esk7_0,esk8_0)) ),
    inference(rw,[status(thm)],[358,140,theory(equality)]) ).

cnf(360,negated_conjecture,
    ~ finite(cartesian_product2(esk7_0,esk8_0)),
    inference(cn,[status(thm)],[359,theory(equality)]) ).

cnf(488,negated_conjecture,
    ( ~ finite(esk8_0)
    | ~ finite(esk7_0) ),
    inference(spm,[status(thm)],[360,102,theory(equality)]) ).

cnf(489,negated_conjecture,
    ( $false
    | ~ finite(esk7_0) ),
    inference(rw,[status(thm)],[488,141,theory(equality)]) ).

cnf(490,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[489,142,theory(equality)]) ).

cnf(491,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[490,theory(equality)]) ).

cnf(492,negated_conjecture,
    $false,
    491,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU089+1.p
% --creating new selector for []
% -running prover on /tmp/tmp9mzlYb/sel_SEU089+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU089+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU089+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU089+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
% 
%------------------------------------------------------------------------------