TSTP Solution File: SET974+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET974+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 03:56:35 EST 2010

% Result   : Theorem 0.28s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   32 (   7 unt;   0 def)
%            Number of atoms       :   86 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   95 (  41   ~;  28   |;  24   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-5 aty)
%            Number of variables   :  102 (  11 sgn  53   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,conjecture,
    ! [X1,X2,X3,X4] :
      ( ( disjoint(X1,X2)
        | disjoint(X3,X4) )
     => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    file('/tmp/tmpsBIjTG/sel_SET974+1.p_1',t127_zfmisc_1) ).

fof(11,axiom,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/tmp/tmpsBIjTG/sel_SET974+1.p_1',t4_xboole_0) ).

fof(12,axiom,
    ! [X1,X2,X3,X4,X5] :
      ~ ( in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
        & ! [X6,X7] :
            ~ ( X1 = ordered_pair(X6,X7)
              & in(X6,set_intersection2(X2,X4))
              & in(X7,set_intersection2(X3,X5)) ) ),
    file('/tmp/tmpsBIjTG/sel_SET974+1.p_1',t104_zfmisc_1) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ( disjoint(X1,X2)
          | disjoint(X3,X4) )
       => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(17,plain,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(22,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( ( disjoint(X1,X2)
        | disjoint(X3,X4) )
      & ~ disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(23,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( ( disjoint(X5,X6)
        | disjoint(X7,X8) )
      & ~ disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
    inference(variable_rename,[status(thm)],[22]) ).

fof(24,negated_conjecture,
    ( ( disjoint(esk1_0,esk2_0)
      | disjoint(esk3_0,esk4_0) )
    & ~ disjoint(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[23]) ).

cnf(25,negated_conjecture,
    ~ disjoint(cartesian_product2(esk1_0,esk3_0),cartesian_product2(esk2_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[24]) ).

cnf(26,negated_conjecture,
    ( disjoint(esk3_0,esk4_0)
    | disjoint(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(45,plain,
    ! [X1,X2] :
      ( ( disjoint(X1,X2)
        | ? [X3] : in(X3,set_intersection2(X1,X2)) )
      & ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
        | ~ disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(46,plain,
    ! [X4,X5] :
      ( ( disjoint(X4,X5)
        | ? [X6] : in(X6,set_intersection2(X4,X5)) )
      & ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[45]) ).

fof(47,plain,
    ! [X4,X5] :
      ( ( disjoint(X4,X5)
        | in(esk7_2(X4,X5),set_intersection2(X4,X5)) )
      & ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    inference(skolemize,[status(esa)],[46]) ).

fof(48,plain,
    ! [X4,X5,X7] :
      ( ( ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) )
      & ( disjoint(X4,X5)
        | in(esk7_2(X4,X5),set_intersection2(X4,X5)) ) ),
    inference(shift_quantors,[status(thm)],[47]) ).

cnf(49,plain,
    ( in(esk7_2(X1,X2),set_intersection2(X1,X2))
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(51,plain,
    ! [X1,X2,X3,X4,X5] :
      ( ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
      | ? [X6,X7] :
          ( X1 = ordered_pair(X6,X7)
          & in(X6,set_intersection2(X2,X4))
          & in(X7,set_intersection2(X3,X5)) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(52,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12)))
      | ? [X13,X14] :
          ( X8 = ordered_pair(X13,X14)
          & in(X13,set_intersection2(X9,X11))
          & in(X14,set_intersection2(X10,X12)) ) ),
    inference(variable_rename,[status(thm)],[51]) ).

fof(53,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12)))
      | ( X8 = ordered_pair(esk8_5(X8,X9,X10,X11,X12),esk9_5(X8,X9,X10,X11,X12))
        & in(esk8_5(X8,X9,X10,X11,X12),set_intersection2(X9,X11))
        & in(esk9_5(X8,X9,X10,X11,X12),set_intersection2(X10,X12)) ) ),
    inference(skolemize,[status(esa)],[52]) ).

fof(54,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( X8 = ordered_pair(esk8_5(X8,X9,X10,X11,X12),esk9_5(X8,X9,X10,X11,X12))
        | ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) )
      & ( in(esk8_5(X8,X9,X10,X11,X12),set_intersection2(X9,X11))
        | ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) )
      & ( in(esk9_5(X8,X9,X10,X11,X12),set_intersection2(X10,X12))
        | ~ in(X8,set_intersection2(cartesian_product2(X9,X10),cartesian_product2(X11,X12))) ) ),
    inference(distribute,[status(thm)],[53]) ).

cnf(55,plain,
    ( in(esk9_5(X1,X2,X3,X4,X5),set_intersection2(X3,X5))
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[54]) ).

cnf(56,plain,
    ( in(esk8_5(X1,X2,X3,X4,X5),set_intersection2(X2,X4))
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(split_conjunct,[status(thm)],[54]) ).

cnf(81,plain,
    ( ~ disjoint(X2,X4)
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(spm,[status(thm)],[50,56,theory(equality)]) ).

cnf(86,plain,
    ( ~ disjoint(X3,X5)
    | ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
    inference(spm,[status(thm)],[50,55,theory(equality)]) ).

cnf(166,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X1,X3) ),
    inference(spm,[status(thm)],[81,49,theory(equality)]) ).

cnf(173,negated_conjecture,
    ~ disjoint(esk1_0,esk2_0),
    inference(spm,[status(thm)],[25,166,theory(equality)]) ).

cnf(177,negated_conjecture,
    disjoint(esk3_0,esk4_0),
    inference(sr,[status(thm)],[26,173,theory(equality)]) ).

cnf(197,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X2,X4) ),
    inference(spm,[status(thm)],[86,49,theory(equality)]) ).

cnf(204,negated_conjecture,
    ~ disjoint(esk3_0,esk4_0),
    inference(spm,[status(thm)],[25,197,theory(equality)]) ).

cnf(206,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[204,177,theory(equality)]) ).

cnf(207,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[206,theory(equality)]) ).

cnf(208,negated_conjecture,
    $false,
    207,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET974+1.p
% --creating new selector for []
% -running prover on /tmp/tmpsBIjTG/sel_SET974+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET974+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET974+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET974+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
% 
%------------------------------------------------------------------------------