TSTP Solution File: SET983+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET983+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 04:02:50 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   25 (   8 unt;   0 def)
%            Number of atoms       :  119 (  19 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  147 (  53   ~;  56   |;  34   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   70 (   0 sgn  42   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2,X3,X4,X5] :
      ( ( in(X1,cartesian_product2(X2,X3))
        & in(X1,cartesian_product2(X4,X5)) )
     => in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
    file('/tmp/tmpW9eT86/sel_SET983+1.p_1',t137_zfmisc_1) ).

fof(5,axiom,
    ! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    file('/tmp/tmpW9eT86/sel_SET983+1.p_1',t123_zfmisc_1) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/tmp/tmpW9eT86/sel_SET983+1.p_1',d3_xboole_0) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2,X3,X4,X5] :
        ( ( in(X1,cartesian_product2(X2,X3))
          & in(X1,cartesian_product2(X4,X5)) )
       => in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(14,negated_conjecture,
    ? [X1,X2,X3,X4,X5] :
      ( in(X1,cartesian_product2(X2,X3))
      & in(X1,cartesian_product2(X4,X5))
      & ~ in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(15,negated_conjecture,
    ? [X6,X7,X8,X9,X10] :
      ( in(X6,cartesian_product2(X7,X8))
      & in(X6,cartesian_product2(X9,X10))
      & ~ in(X6,cartesian_product2(set_intersection2(X7,X9),set_intersection2(X8,X10))) ),
    inference(variable_rename,[status(thm)],[14]) ).

fof(16,negated_conjecture,
    ( in(esk1_0,cartesian_product2(esk2_0,esk3_0))
    & in(esk1_0,cartesian_product2(esk4_0,esk5_0))
    & ~ in(esk1_0,cartesian_product2(set_intersection2(esk2_0,esk4_0),set_intersection2(esk3_0,esk5_0))) ),
    inference(skolemize,[status(esa)],[15]) ).

cnf(17,negated_conjecture,
    ~ in(esk1_0,cartesian_product2(set_intersection2(esk2_0,esk4_0),set_intersection2(esk3_0,esk5_0))),
    inference(split_conjunct,[status(thm)],[16]) ).

cnf(18,negated_conjecture,
    in(esk1_0,cartesian_product2(esk4_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[16]) ).

cnf(19,negated_conjecture,
    in(esk1_0,cartesian_product2(esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(25,plain,
    ! [X5,X6,X7,X8] : cartesian_product2(set_intersection2(X5,X6),set_intersection2(X7,X8)) = set_intersection2(cartesian_product2(X5,X7),cartesian_product2(X6,X8)),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(26,plain,
    cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(30,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_intersection2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | ~ in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) ) )
        | X3 = set_intersection2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(31,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | ~ in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & in(X9,X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[30]) ).

fof(32,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
            | ~ in(esk8_3(X5,X6,X7),X5)
            | ~ in(esk8_3(X5,X6,X7),X6) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | ( in(esk8_3(X5,X6,X7),X5)
              & in(esk8_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[31]) ).

fof(33,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | ~ in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_intersection2(X5,X6) )
      & ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
            | ~ in(esk8_3(X5,X6,X7),X5)
            | ~ in(esk8_3(X5,X6,X7),X6) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | ( in(esk8_3(X5,X6,X7),X5)
              & in(esk8_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[32]) ).

fof(34,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(X8,X5)
        | ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(esk8_3(X5,X6,X7),X7)
        | ~ in(esk8_3(X5,X6,X7),X5)
        | ~ in(esk8_3(X5,X6,X7),X6)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk8_3(X5,X6,X7),X5)
        | in(esk8_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk8_3(X5,X6,X7),X6)
        | in(esk8_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) ) ),
    inference(distribute,[status(thm)],[33]) ).

cnf(38,plain,
    ( in(X4,X1)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(60,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[38,theory(equality)]) ).

cnf(103,plain,
    ( in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5)))
    | ~ in(X1,cartesian_product2(X4,X5))
    | ~ in(X1,cartesian_product2(X2,X3)) ),
    inference(spm,[status(thm)],[60,26,theory(equality)]) ).

cnf(691,negated_conjecture,
    ( ~ in(esk1_0,cartesian_product2(esk4_0,esk5_0))
    | ~ in(esk1_0,cartesian_product2(esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[17,103,theory(equality)]) ).

cnf(715,negated_conjecture,
    ( $false
    | ~ in(esk1_0,cartesian_product2(esk2_0,esk3_0)) ),
    inference(rw,[status(thm)],[691,18,theory(equality)]) ).

cnf(716,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[715,19,theory(equality)]) ).

cnf(717,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[716,theory(equality)]) ).

cnf(718,negated_conjecture,
    $false,
    717,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET983+1.p
% --creating new selector for []
% -running prover on /tmp/tmpW9eT86/sel_SET983+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET983+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET983+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET983+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
% 
%------------------------------------------------------------------------------