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SInE---0.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET955+1 : TPTP v5.0.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 03:54:11 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   59 (  12 unt;   0 def)
%            Number of atoms       :  255 (  81 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  319 ( 123   ~; 139   |;  49   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   4 con; 0-4 aty)
%            Number of variables   :  186 (   4 sgn  83   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmpStyPlQ/sel_SET955+1.p_1',d5_tarski) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( X3 = cartesian_product2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ? [X5,X6] :
              ( in(X5,X1)
              & in(X6,X2)
              & X4 = ordered_pair(X5,X6) ) ) ),
    file('/tmp/tmpStyPlQ/sel_SET955+1.p_1',d2_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> in(X3,X2) )
     => X1 = X2 ),
    file('/tmp/tmpStyPlQ/sel_SET955+1.p_1',t2_tarski) ).

fof(6,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpStyPlQ/sel_SET955+1.p_1',commutativity_k2_tarski) ).

fof(7,conjecture,
    ! [X1,X2,X3,X4] :
      ( ! [X5,X6] :
          ( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
        <=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
     => cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
    file('/tmp/tmpStyPlQ/sel_SET955+1.p_1',t108_zfmisc_1) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ! [X5,X6] :
            ( in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
          <=> in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
       => cartesian_product2(X1,X2) = cartesian_product2(X3,X4) ),
    inference(assume_negation,[status(cth)],[7]) ).

fof(14,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(15,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(16,plain,
    ! [X1,X2,X3] :
      ( ( X3 != cartesian_product2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ? [X5,X6] :
                  ( in(X5,X1)
                  & in(X6,X2)
                  & X4 = ordered_pair(X5,X6) ) )
            & ( ! [X5,X6] :
                  ( ~ in(X5,X1)
                  | ~ in(X6,X2)
                  | X4 != ordered_pair(X5,X6) )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ! [X5,X6] :
                  ( ~ in(X5,X1)
                  | ~ in(X6,X2)
                  | X4 != ordered_pair(X5,X6) ) )
            & ( in(X4,X3)
              | ? [X5,X6] :
                  ( in(X5,X1)
                  & in(X6,X2)
                  & X4 = ordered_pair(X5,X6) ) ) )
        | X3 = cartesian_product2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(17,plain,
    ! [X7,X8,X9] :
      ( ( X9 != cartesian_product2(X7,X8)
        | ! [X10] :
            ( ( ~ in(X10,X9)
              | ? [X11,X12] :
                  ( in(X11,X7)
                  & in(X12,X8)
                  & X10 = ordered_pair(X11,X12) ) )
            & ( ! [X13,X14] :
                  ( ~ in(X13,X7)
                  | ~ in(X14,X8)
                  | X10 != ordered_pair(X13,X14) )
              | in(X10,X9) ) ) )
      & ( ? [X15] :
            ( ( ~ in(X15,X9)
              | ! [X16,X17] :
                  ( ~ in(X16,X7)
                  | ~ in(X17,X8)
                  | X15 != ordered_pair(X16,X17) ) )
            & ( in(X15,X9)
              | ? [X18,X19] :
                  ( in(X18,X7)
                  & in(X19,X8)
                  & X15 = ordered_pair(X18,X19) ) ) )
        | X9 = cartesian_product2(X7,X8) ) ),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,plain,
    ! [X7,X8,X9] :
      ( ( X9 != cartesian_product2(X7,X8)
        | ! [X10] :
            ( ( ~ in(X10,X9)
              | ( in(esk1_4(X7,X8,X9,X10),X7)
                & in(esk2_4(X7,X8,X9,X10),X8)
                & X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)) ) )
            & ( ! [X13,X14] :
                  ( ~ in(X13,X7)
                  | ~ in(X14,X8)
                  | X10 != ordered_pair(X13,X14) )
              | in(X10,X9) ) ) )
      & ( ( ( ~ in(esk3_3(X7,X8,X9),X9)
            | ! [X16,X17] :
                ( ~ in(X16,X7)
                | ~ in(X17,X8)
                | esk3_3(X7,X8,X9) != ordered_pair(X16,X17) ) )
          & ( in(esk3_3(X7,X8,X9),X9)
            | ( in(esk4_3(X7,X8,X9),X7)
              & in(esk5_3(X7,X8,X9),X8)
              & esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9)) ) ) )
        | X9 = cartesian_product2(X7,X8) ) ),
    inference(skolemize,[status(esa)],[17]) ).

fof(19,plain,
    ! [X7,X8,X9,X10,X13,X14,X16,X17] :
      ( ( ( ( ~ in(X16,X7)
            | ~ in(X17,X8)
            | esk3_3(X7,X8,X9) != ordered_pair(X16,X17)
            | ~ in(esk3_3(X7,X8,X9),X9) )
          & ( in(esk3_3(X7,X8,X9),X9)
            | ( in(esk4_3(X7,X8,X9),X7)
              & in(esk5_3(X7,X8,X9),X8)
              & esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9)) ) ) )
        | X9 = cartesian_product2(X7,X8) )
      & ( ( ( ~ in(X13,X7)
            | ~ in(X14,X8)
            | X10 != ordered_pair(X13,X14)
            | in(X10,X9) )
          & ( ~ in(X10,X9)
            | ( in(esk1_4(X7,X8,X9,X10),X7)
              & in(esk2_4(X7,X8,X9,X10),X8)
              & X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10)) ) ) )
        | X9 != cartesian_product2(X7,X8) ) ),
    inference(shift_quantors,[status(thm)],[18]) ).

fof(20,plain,
    ! [X7,X8,X9,X10,X13,X14,X16,X17] :
      ( ( ~ in(X16,X7)
        | ~ in(X17,X8)
        | esk3_3(X7,X8,X9) != ordered_pair(X16,X17)
        | ~ in(esk3_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( in(esk4_3(X7,X8,X9),X7)
        | in(esk3_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( in(esk5_3(X7,X8,X9),X8)
        | in(esk3_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( esk3_3(X7,X8,X9) = ordered_pair(esk4_3(X7,X8,X9),esk5_3(X7,X8,X9))
        | in(esk3_3(X7,X8,X9),X9)
        | X9 = cartesian_product2(X7,X8) )
      & ( ~ in(X13,X7)
        | ~ in(X14,X8)
        | X10 != ordered_pair(X13,X14)
        | in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( in(esk1_4(X7,X8,X9,X10),X7)
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( in(esk2_4(X7,X8,X9,X10),X8)
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) )
      & ( X10 = ordered_pair(esk1_4(X7,X8,X9,X10),esk2_4(X7,X8,X9,X10))
        | ~ in(X10,X9)
        | X9 != cartesian_product2(X7,X8) ) ),
    inference(distribute,[status(thm)],[19]) ).

cnf(21,plain,
    ( X4 = ordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,plain,
    ( in(esk2_4(X2,X3,X1,X4),X3)
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(23,plain,
    ( in(esk1_4(X2,X3,X1,X4),X2)
    | X1 != cartesian_product2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(24,plain,
    ( in(X4,X1)
    | X1 != cartesian_product2(X2,X3)
    | X4 != ordered_pair(X5,X6)
    | ~ in(X6,X3)
    | ~ in(X5,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(29,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X2) ) )
      | X1 = X2 ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(30,plain,
    ! [X4,X5] :
      ( ? [X6] :
          ( ( ~ in(X6,X4)
            | ~ in(X6,X5) )
          & ( in(X6,X4)
            | in(X6,X5) ) )
      | X4 = X5 ),
    inference(variable_rename,[status(thm)],[29]) ).

fof(31,plain,
    ! [X4,X5] :
      ( ( ( ~ in(esk6_2(X4,X5),X4)
          | ~ in(esk6_2(X4,X5),X5) )
        & ( in(esk6_2(X4,X5),X4)
          | in(esk6_2(X4,X5),X5) ) )
      | X4 = X5 ),
    inference(skolemize,[status(esa)],[30]) ).

fof(32,plain,
    ! [X4,X5] :
      ( ( ~ in(esk6_2(X4,X5),X4)
        | ~ in(esk6_2(X4,X5),X5)
        | X4 = X5 )
      & ( in(esk6_2(X4,X5),X4)
        | in(esk6_2(X4,X5),X5)
        | X4 = X5 ) ),
    inference(distribute,[status(thm)],[31]) ).

cnf(33,plain,
    ( X1 = X2
    | in(esk6_2(X1,X2),X2)
    | in(esk6_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[32]) ).

cnf(34,plain,
    ( X1 = X2
    | ~ in(esk6_2(X1,X2),X2)
    | ~ in(esk6_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(40,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(41,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(42,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( ! [X5,X6] :
          ( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X1,X2))
            | in(ordered_pair(X5,X6),cartesian_product2(X3,X4)) )
          & ( ~ in(ordered_pair(X5,X6),cartesian_product2(X3,X4))
            | in(ordered_pair(X5,X6),cartesian_product2(X1,X2)) ) )
      & cartesian_product2(X1,X2) != cartesian_product2(X3,X4) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(43,negated_conjecture,
    ? [X7,X8,X9,X10] :
      ( ! [X11,X12] :
          ( ( ~ in(ordered_pair(X11,X12),cartesian_product2(X7,X8))
            | in(ordered_pair(X11,X12),cartesian_product2(X9,X10)) )
          & ( ~ in(ordered_pair(X11,X12),cartesian_product2(X9,X10))
            | in(ordered_pair(X11,X12),cartesian_product2(X7,X8)) ) )
      & cartesian_product2(X7,X8) != cartesian_product2(X9,X10) ),
    inference(variable_rename,[status(thm)],[42]) ).

fof(44,negated_conjecture,
    ( ! [X11,X12] :
        ( ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk8_0,esk9_0))
          | in(ordered_pair(X11,X12),cartesian_product2(esk10_0,esk11_0)) )
        & ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk10_0,esk11_0))
          | in(ordered_pair(X11,X12),cartesian_product2(esk8_0,esk9_0)) ) )
    & cartesian_product2(esk8_0,esk9_0) != cartesian_product2(esk10_0,esk11_0) ),
    inference(skolemize,[status(esa)],[43]) ).

fof(45,negated_conjecture,
    ! [X11,X12] :
      ( ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk8_0,esk9_0))
        | in(ordered_pair(X11,X12),cartesian_product2(esk10_0,esk11_0)) )
      & ( ~ in(ordered_pair(X11,X12),cartesian_product2(esk10_0,esk11_0))
        | in(ordered_pair(X11,X12),cartesian_product2(esk8_0,esk9_0)) )
      & cartesian_product2(esk8_0,esk9_0) != cartesian_product2(esk10_0,esk11_0) ),
    inference(shift_quantors,[status(thm)],[44]) ).

cnf(46,negated_conjecture,
    cartesian_product2(esk8_0,esk9_0) != cartesian_product2(esk10_0,esk11_0),
    inference(split_conjunct,[status(thm)],[45]) ).

cnf(47,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk8_0,esk9_0))
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk10_0,esk11_0)) ),
    inference(split_conjunct,[status(thm)],[45]) ).

cnf(48,negated_conjecture,
    ( in(ordered_pair(X1,X2),cartesian_product2(esk10_0,esk11_0))
    | ~ in(ordered_pair(X1,X2),cartesian_product2(esk8_0,esk9_0)) ),
    inference(split_conjunct,[status(thm)],[45]) ).

cnf(56,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk8_0,esk9_0))
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk10_0,esk11_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[47,15,theory(equality)]),15,theory(equality)]),
    [unfolding] ).

cnf(57,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk10_0,esk11_0))
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk8_0,esk9_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[48,15,theory(equality)]),15,theory(equality)]),
    [unfolding] ).

cnf(58,plain,
    ( unordered_pair(unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4)),singleton(esk1_4(X2,X3,X1,X4))) = X4
    | cartesian_product2(X2,X3) != X1
    | ~ in(X4,X1) ),
    inference(rw,[status(thm)],[21,15,theory(equality)]),
    [unfolding] ).

cnf(59,plain,
    ( in(X4,X1)
    | unordered_pair(unordered_pair(X5,X6),singleton(X5)) != X4
    | cartesian_product2(X2,X3) != X1
    | ~ in(X6,X3)
    | ~ in(X5,X2) ),
    inference(rw,[status(thm)],[24,15,theory(equality)]),
    [unfolding] ).

cnf(82,negated_conjecture,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk10_0,esk11_0))
    | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk8_0,esk9_0)) ),
    inference(spm,[status(thm)],[57,41,theory(equality)]) ).

cnf(87,plain,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
    | cartesian_product2(X4,X5) != X3
    | ~ in(X2,X5)
    | ~ in(X1,X4) ),
    inference(er,[status(thm)],[59,theory(equality)]) ).

cnf(94,plain,
    ( unordered_pair(singleton(esk1_4(X2,X3,X1,X4)),unordered_pair(esk1_4(X2,X3,X1,X4),esk2_4(X2,X3,X1,X4))) = X4
    | cartesian_product2(X2,X3) != X1
    | ~ in(X4,X1) ),
    inference(rw,[status(thm)],[58,41,theory(equality)]) ).

cnf(172,negated_conjecture,
    ( in(X4,cartesian_product2(esk10_0,esk11_0))
    | ~ in(X4,cartesian_product2(esk8_0,esk9_0))
    | cartesian_product2(X1,X2) != X3
    | ~ in(X4,X3) ),
    inference(spm,[status(thm)],[82,94,theory(equality)]) ).

cnf(181,negated_conjecture,
    ( in(X1,cartesian_product2(esk10_0,esk11_0))
    | ~ in(X1,cartesian_product2(esk8_0,esk9_0))
    | ~ in(X1,cartesian_product2(X2,X3)) ),
    inference(er,[status(thm)],[172,theory(equality)]) ).

cnf(240,plain,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
    | ~ in(X2,X4)
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[87,theory(equality)]) ).

cnf(246,negated_conjecture,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(esk8_0,esk9_0))
    | ~ in(X2,esk11_0)
    | ~ in(X1,esk10_0) ),
    inference(spm,[status(thm)],[56,240,theory(equality)]) ).

cnf(256,negated_conjecture,
    ( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(esk8_0,esk9_0))
    | ~ in(X2,esk11_0)
    | ~ in(X1,esk10_0) ),
    inference(spm,[status(thm)],[246,41,theory(equality)]) ).

cnf(302,negated_conjecture,
    ( in(X4,cartesian_product2(esk8_0,esk9_0))
    | ~ in(esk2_4(X1,X2,X3,X4),esk11_0)
    | ~ in(esk1_4(X1,X2,X3,X4),esk10_0)
    | cartesian_product2(X1,X2) != X3
    | ~ in(X4,X3) ),
    inference(spm,[status(thm)],[256,94,theory(equality)]) ).

cnf(575,negated_conjecture,
    ( in(X1,cartesian_product2(esk8_0,esk9_0))
    | cartesian_product2(X2,esk11_0) != X3
    | ~ in(esk1_4(X2,esk11_0,X3,X1),esk10_0)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[302,22,theory(equality)]) ).

cnf(576,negated_conjecture,
    ( in(X1,cartesian_product2(esk8_0,esk9_0))
    | cartesian_product2(esk10_0,esk11_0) != X2
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[575,23,theory(equality)]) ).

cnf(577,negated_conjecture,
    ( in(X1,cartesian_product2(esk8_0,esk9_0))
    | ~ in(X1,cartesian_product2(esk10_0,esk11_0)) ),
    inference(er,[status(thm)],[576,theory(equality)]) ).

cnf(582,negated_conjecture,
    ( in(esk6_2(X1,cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0))
    | X1 = cartesian_product2(esk10_0,esk11_0)
    | in(esk6_2(X1,cartesian_product2(esk10_0,esk11_0)),X1) ),
    inference(spm,[status(thm)],[577,33,theory(equality)]) ).

cnf(637,negated_conjecture,
    ( cartesian_product2(esk8_0,esk9_0) = cartesian_product2(esk10_0,esk11_0)
    | in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0)) ),
    inference(ef,[status(thm)],[582,theory(equality)]) ).

cnf(646,negated_conjecture,
    in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0)),
    inference(sr,[status(thm)],[637,46,theory(equality)]) ).

cnf(649,negated_conjecture,
    ( in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk10_0,esk11_0))
    | ~ in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0)) ),
    inference(spm,[status(thm)],[181,646,theory(equality)]) ).

cnf(651,negated_conjecture,
    ( in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk10_0,esk11_0))
    | $false ),
    inference(rw,[status(thm)],[649,646,theory(equality)]) ).

cnf(652,negated_conjecture,
    in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk10_0,esk11_0)),
    inference(cn,[status(thm)],[651,theory(equality)]) ).

cnf(654,negated_conjecture,
    ( cartesian_product2(esk8_0,esk9_0) = cartesian_product2(esk10_0,esk11_0)
    | ~ in(esk6_2(cartesian_product2(esk8_0,esk9_0),cartesian_product2(esk10_0,esk11_0)),cartesian_product2(esk8_0,esk9_0)) ),
    inference(spm,[status(thm)],[34,652,theory(equality)]) ).

cnf(658,negated_conjecture,
    ( cartesian_product2(esk8_0,esk9_0) = cartesian_product2(esk10_0,esk11_0)
    | $false ),
    inference(rw,[status(thm)],[654,646,theory(equality)]) ).

cnf(659,negated_conjecture,
    cartesian_product2(esk8_0,esk9_0) = cartesian_product2(esk10_0,esk11_0),
    inference(cn,[status(thm)],[658,theory(equality)]) ).

cnf(660,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[659,46,theory(equality)]) ).

cnf(661,negated_conjecture,
    $false,
    660,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET955+1.p
% --creating new selector for []
% -running prover on /tmp/tmpStyPlQ/sel_SET955+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET955+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET955+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET955+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
% 
%------------------------------------------------------------------------------