TSTP Solution File: SET978+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET978+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 03:57:36 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   24 (   5 unt;   0 def)
%            Number of atoms       :   53 (  14 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   55 (  26   ~;  17   |;   8   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   56 (   8 sgn  30   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2] :
      ( X1 != X2
     => disjoint(singleton(X1),singleton(X2)) ),
    file('/tmp/tmpCOK0C4/sel_SET978+1.p_1',t17_zfmisc_1) ).

fof(4,conjecture,
    ! [X1,X2,X3,X4] :
      ( X1 != X2
     => ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
        & disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
    file('/tmp/tmpCOK0C4/sel_SET978+1.p_1',t131_zfmisc_1) ).

fof(6,axiom,
    ! [X1,X2,X3,X4] :
      ( ( disjoint(X1,X2)
        | disjoint(X3,X4) )
     => disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    file('/tmp/tmpCOK0C4/sel_SET978+1.p_1',t127_zfmisc_1) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( X1 != X2
       => ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
          & disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(15,plain,
    ! [X1,X2] :
      ( X1 = X2
      | disjoint(singleton(X1),singleton(X2)) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(16,plain,
    ! [X3,X4] :
      ( X3 = X4
      | disjoint(singleton(X3),singleton(X4)) ),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(17,plain,
    ( disjoint(singleton(X1),singleton(X2))
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(18,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( X1 != X2
      & ( ~ disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
        | ~ disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(19,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( X5 != X6
      & ( ~ disjoint(cartesian_product2(singleton(X5),X7),cartesian_product2(singleton(X6),X8))
        | ~ disjoint(cartesian_product2(X7,singleton(X5)),cartesian_product2(X8,singleton(X6))) ) ),
    inference(variable_rename,[status(thm)],[18]) ).

fof(20,negated_conjecture,
    ( esk2_0 != esk3_0
    & ( ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0))
      | ~ disjoint(cartesian_product2(esk4_0,singleton(esk2_0)),cartesian_product2(esk5_0,singleton(esk3_0))) ) ),
    inference(skolemize,[status(esa)],[19]) ).

cnf(21,negated_conjecture,
    ( ~ disjoint(cartesian_product2(esk4_0,singleton(esk2_0)),cartesian_product2(esk5_0,singleton(esk3_0)))
    | ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0)) ),
    inference(split_conjunct,[status(thm)],[20]) ).

cnf(22,negated_conjecture,
    esk2_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[20]) ).

fof(26,plain,
    ! [X1,X2,X3,X4] :
      ( ( ~ disjoint(X1,X2)
        & ~ disjoint(X3,X4) )
      | disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(27,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ disjoint(X5,X6)
        & ~ disjoint(X7,X8) )
      | disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
    inference(variable_rename,[status(thm)],[26]) ).

fof(28,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ disjoint(X5,X6)
        | disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) )
      & ( ~ disjoint(X7,X8)
        | disjoint(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ) ),
    inference(distribute,[status(thm)],[27]) ).

cnf(29,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X2,X4) ),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(30,plain,
    ( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ disjoint(X1,X3) ),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(31,plain,
    ( disjoint(cartesian_product2(X1,singleton(X2)),cartesian_product2(X3,singleton(X4)))
    | X2 = X4 ),
    inference(spm,[status(thm)],[29,17,theory(equality)]) ).

cnf(32,plain,
    ( disjoint(cartesian_product2(singleton(X1),X2),cartesian_product2(singleton(X3),X4))
    | X1 = X3 ),
    inference(spm,[status(thm)],[30,17,theory(equality)]) ).

cnf(34,negated_conjecture,
    ( esk2_0 = esk3_0
    | ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0)) ),
    inference(spm,[status(thm)],[21,31,theory(equality)]) ).

cnf(38,negated_conjecture,
    ~ disjoint(cartesian_product2(singleton(esk2_0),esk4_0),cartesian_product2(singleton(esk3_0),esk5_0)),
    inference(sr,[status(thm)],[34,22,theory(equality)]) ).

cnf(54,negated_conjecture,
    esk2_0 = esk3_0,
    inference(spm,[status(thm)],[38,32,theory(equality)]) ).

cnf(55,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[54,22,theory(equality)]) ).

cnf(56,negated_conjecture,
    $false,
    55,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET978+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCOK0C4/sel_SET978+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET978+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET978+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET978+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
% 
%------------------------------------------------------------------------------