%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET924+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 03:52:11 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   21 (   6 unt;   0 def)
%            Number of atoms       :   46 (  20 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   47 (  22   ~;  15   |;   5   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn  14   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    file('/tmp/tmpKf6TID/sel_SET924+1.p_1',l34_zfmisc_1) ).

fof(5,conjecture,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    file('/tmp/tmpKf6TID/sel_SET924+1.p_1',t67_zfmisc_1) ).

fof(6,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(singleton(X1),X2) = singleton(X1)
      <=> ~ in(X1,X2) ),
    inference(assume_negation,[status(cth)],[5]) ).

fof(9,plain,
    ! [X1,X2] :
      ( set_difference(singleton(X1),X2) = singleton(X1)
    <=> ~ in(X1,X2) ),
    inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(singleton(X1),X2) = singleton(X1)
      <=> ~ in(X1,X2) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(20,plain,
    ! [X1,X2] :
      ( ( set_difference(singleton(X1),X2) != singleton(X1)
        | ~ in(X1,X2) )
      & ( in(X1,X2)
        | set_difference(singleton(X1),X2) = singleton(X1) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(21,plain,
    ! [X3,X4] :
      ( ( set_difference(singleton(X3),X4) != singleton(X3)
        | ~ in(X3,X4) )
      & ( in(X3,X4)
        | set_difference(singleton(X3),X4) = singleton(X3) ) ),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(22,plain,
    ( set_difference(singleton(X1),X2) = singleton(X1)
    | in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(23,plain,
    ( ~ in(X1,X2)
    | set_difference(singleton(X1),X2) != singleton(X1) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(24,negated_conjecture,
    ? [X1,X2] :
      ( ( set_difference(singleton(X1),X2) != singleton(X1)
        | in(X1,X2) )
      & ( set_difference(singleton(X1),X2) = singleton(X1)
        | ~ in(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(25,negated_conjecture,
    ? [X3,X4] :
      ( ( set_difference(singleton(X3),X4) != singleton(X3)
        | in(X3,X4) )
      & ( set_difference(singleton(X3),X4) = singleton(X3)
        | ~ in(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[24]) ).

fof(26,negated_conjecture,
    ( ( set_difference(singleton(esk3_0),esk4_0) != singleton(esk3_0)
      | in(esk3_0,esk4_0) )
    & ( set_difference(singleton(esk3_0),esk4_0) = singleton(esk3_0)
      | ~ in(esk3_0,esk4_0) ) ),
    inference(skolemize,[status(esa)],[25]) ).

cnf(27,negated_conjecture,
    ( set_difference(singleton(esk3_0),esk4_0) = singleton(esk3_0)
    | ~ in(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(28,negated_conjecture,
    ( in(esk3_0,esk4_0)
    | set_difference(singleton(esk3_0),esk4_0) != singleton(esk3_0) ),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(30,negated_conjecture,
    set_difference(singleton(esk3_0),esk4_0) = singleton(esk3_0),
    inference(csr,[status(thm)],[27,22]) ).

cnf(31,negated_conjecture,
    ~ in(esk3_0,esk4_0),
    inference(spm,[status(thm)],[23,30,theory(equality)]) ).

cnf(32,negated_conjecture,
    ( in(esk3_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[28,30,theory(equality)]) ).

cnf(33,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(cn,[status(thm)],[32,theory(equality)]) ).

cnf(35,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[31,33,theory(equality)]) ).

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

cnf(37,negated_conjecture,
    $false,
    36,
    [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/SET924+1.p
% --creating new selector for []
% -running prover on /tmp/tmpKf6TID/sel_SET924+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET924+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET924+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET924+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
% 
%------------------------------------------------------------------------------