%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU090+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 04:34:04 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   31 (  12 unt;   0 def)
%            Number of atoms       :   81 (   3 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   81 (  31   ~;  25   |;  21   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-4 aty)
%            Number of variables   :   48 (   0 sgn  31   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1,X2] :
      ( ( finite(X1)
        & finite(X2) )
     => finite(cartesian_product2(X1,X2)) ),
    file('/tmp/tmpbHXUOl/sel_SEU090+1.p_1',t19_finset_1) ).

fof(15,axiom,
    ! [X1,X2,X3] :
      ( ( finite(X1)
        & finite(X2)
        & finite(X3) )
     => finite(cartesian_product3(X1,X2,X3)) ),
    file('/tmp/tmpbHXUOl/sel_SEU090+1.p_1',t20_finset_1) ).

fof(27,axiom,
    ! [X1,X2,X3,X4] : cartesian_product4(X1,X2,X3,X4) = cartesian_product2(cartesian_product3(X1,X2,X3),X4),
    file('/tmp/tmpbHXUOl/sel_SEU090+1.p_1',d4_zfmisc_1) ).

fof(39,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( finite(X1)
        & finite(X2)
        & finite(X3)
        & finite(X4) )
     => finite(cartesian_product4(X1,X2,X3,X4)) ),
    file('/tmp/tmpbHXUOl/sel_SEU090+1.p_1',t21_finset_1) ).

fof(64,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( finite(X1)
          & finite(X2)
          & finite(X3)
          & finite(X4) )
       => finite(cartesian_product4(X1,X2,X3,X4)) ),
    inference(assume_negation,[status(cth)],[39]) ).

fof(104,plain,
    ! [X1,X2] :
      ( ~ finite(X1)
      | ~ finite(X2)
      | finite(cartesian_product2(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(105,plain,
    ! [X3,X4] :
      ( ~ finite(X3)
      | ~ finite(X4)
      | finite(cartesian_product2(X3,X4)) ),
    inference(variable_rename,[status(thm)],[104]) ).

cnf(106,plain,
    ( finite(cartesian_product2(X1,X2))
    | ~ finite(X2)
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

fof(140,plain,
    ! [X1,X2,X3] :
      ( ~ finite(X1)
      | ~ finite(X2)
      | ~ finite(X3)
      | finite(cartesian_product3(X1,X2,X3)) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(141,plain,
    ! [X4,X5,X6] :
      ( ~ finite(X4)
      | ~ finite(X5)
      | ~ finite(X6)
      | finite(cartesian_product3(X4,X5,X6)) ),
    inference(variable_rename,[status(thm)],[140]) ).

cnf(142,plain,
    ( finite(cartesian_product3(X1,X2,X3))
    | ~ finite(X3)
    | ~ finite(X2)
    | ~ finite(X1) ),
    inference(split_conjunct,[status(thm)],[141]) ).

fof(197,plain,
    ! [X5,X6,X7,X8] : cartesian_product4(X5,X6,X7,X8) = cartesian_product2(cartesian_product3(X5,X6,X7),X8),
    inference(variable_rename,[status(thm)],[27]) ).

cnf(198,plain,
    cartesian_product4(X1,X2,X3,X4) = cartesian_product2(cartesian_product3(X1,X2,X3),X4),
    inference(split_conjunct,[status(thm)],[197]) ).

fof(238,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( finite(X1)
      & finite(X2)
      & finite(X3)
      & finite(X4)
      & ~ finite(cartesian_product4(X1,X2,X3,X4)) ),
    inference(fof_nnf,[status(thm)],[64]) ).

fof(239,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( finite(X5)
      & finite(X6)
      & finite(X7)
      & finite(X8)
      & ~ finite(cartesian_product4(X5,X6,X7,X8)) ),
    inference(variable_rename,[status(thm)],[238]) ).

fof(240,negated_conjecture,
    ( finite(esk15_0)
    & finite(esk16_0)
    & finite(esk17_0)
    & finite(esk18_0)
    & ~ finite(cartesian_product4(esk15_0,esk16_0,esk17_0,esk18_0)) ),
    inference(skolemize,[status(esa)],[239]) ).

cnf(241,negated_conjecture,
    ~ finite(cartesian_product4(esk15_0,esk16_0,esk17_0,esk18_0)),
    inference(split_conjunct,[status(thm)],[240]) ).

cnf(242,negated_conjecture,
    finite(esk18_0),
    inference(split_conjunct,[status(thm)],[240]) ).

cnf(243,negated_conjecture,
    finite(esk17_0),
    inference(split_conjunct,[status(thm)],[240]) ).

cnf(244,negated_conjecture,
    finite(esk16_0),
    inference(split_conjunct,[status(thm)],[240]) ).

cnf(245,negated_conjecture,
    finite(esk15_0),
    inference(split_conjunct,[status(thm)],[240]) ).

cnf(357,negated_conjecture,
    ~ finite(cartesian_product2(cartesian_product3(esk15_0,esk16_0,esk17_0),esk18_0)),
    inference(rw,[status(thm)],[241,198,theory(equality)]),
    [unfolding] ).

cnf(372,negated_conjecture,
    ( ~ finite(esk18_0)
    | ~ finite(cartesian_product3(esk15_0,esk16_0,esk17_0)) ),
    inference(spm,[status(thm)],[357,106,theory(equality)]) ).

cnf(373,negated_conjecture,
    ( $false
    | ~ finite(cartesian_product3(esk15_0,esk16_0,esk17_0)) ),
    inference(rw,[status(thm)],[372,242,theory(equality)]) ).

cnf(374,negated_conjecture,
    ~ finite(cartesian_product3(esk15_0,esk16_0,esk17_0)),
    inference(cn,[status(thm)],[373,theory(equality)]) ).

cnf(486,negated_conjecture,
    ( ~ finite(esk17_0)
    | ~ finite(esk16_0)
    | ~ finite(esk15_0) ),
    inference(spm,[status(thm)],[374,142,theory(equality)]) ).

cnf(487,negated_conjecture,
    ( $false
    | ~ finite(esk16_0)
    | ~ finite(esk15_0) ),
    inference(rw,[status(thm)],[486,243,theory(equality)]) ).

cnf(488,negated_conjecture,
    ( $false
    | $false
    | ~ finite(esk15_0) ),
    inference(rw,[status(thm)],[487,244,theory(equality)]) ).

cnf(489,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[488,245,theory(equality)]) ).

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

cnf(491,negated_conjecture,
    $false,
    490,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU090+1.p
% --creating new selector for []
% -running prover on /tmp/tmpbHXUOl/sel_SEU090+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU090+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU090+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU090+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
% 
%------------------------------------------------------------------------------