%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET583+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 02:58:14 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   18 (   6 unt;   0 def)
%            Number of atoms       :   50 (  18 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   50 (  18   ~;  14   |;  15   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   18 (   0 sgn  12   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpVLm3N0/sel_SET583+3.p_1',equal_defn) ).

fof(2,conjecture,
    ! [X1,X2] :
      ( ( subset(X1,X2)
        & subset(X2,X1) )
     => X1 = X2 ),
    file('/tmp/tmpVLm3N0/sel_SET583+3.p_1',prove_extensionality) ).

fof(5,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( subset(X1,X2)
          & subset(X2,X1) )
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(6,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(7,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[6]) ).

fof(8,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[7]) ).

cnf(9,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[8]) ).

fof(12,negated_conjecture,
    ? [X1,X2] :
      ( subset(X1,X2)
      & subset(X2,X1)
      & X1 != X2 ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(13,negated_conjecture,
    ? [X3,X4] :
      ( subset(X3,X4)
      & subset(X4,X3)
      & X3 != X4 ),
    inference(variable_rename,[status(thm)],[12]) ).

fof(14,negated_conjecture,
    ( subset(esk1_0,esk2_0)
    & subset(esk2_0,esk1_0)
    & esk1_0 != esk2_0 ),
    inference(skolemize,[status(esa)],[13]) ).

cnf(15,negated_conjecture,
    esk1_0 != esk2_0,
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,negated_conjecture,
    subset(esk2_0,esk1_0),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(17,negated_conjecture,
    subset(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(32,negated_conjecture,
    ( esk2_0 = esk1_0
    | ~ subset(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[9,17,theory(equality)]) ).

cnf(34,negated_conjecture,
    ( esk2_0 = esk1_0
    | $false ),
    inference(rw,[status(thm)],[32,16,theory(equality)]) ).

cnf(35,negated_conjecture,
    esk2_0 = esk1_0,
    inference(cn,[status(thm)],[34,theory(equality)]) ).

cnf(36,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[35,15,theory(equality)]) ).

cnf(37,negated_conjecture,
    $false,
    36,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET583+3.p
% --creating new selector for []
% -running prover on /tmp/tmpVLm3N0/sel_SET583+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET583+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET583+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET583+3.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
% 
%------------------------------------------------------------------------------