%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET045+1 : TPTP v5.0.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 02:39:28 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   20 (  11 unt;   0 def)
%            Number of atoms       :   49 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   51 (  22   ~;  17   |;  10   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   31 (   2 sgn  17   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( element(X3,X2)
    <=> ( element(X3,X1)
        & ~ element(X3,X3) ) ),
    file('/tmp/tmp77a_DQ/sel_SET045+1.p_1',pel41_1) ).

fof(2,conjecture,
    ~ ? [X1] :
      ! [X3] : element(X3,X1),
    file('/tmp/tmp77a_DQ/sel_SET045+1.p_1',pel41) ).

fof(3,negated_conjecture,
    ~ ~ ? [X1] :
        ! [X3] : element(X3,X1),
    inference(assume_negation,[status(cth)],[2]) ).

fof(4,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( element(X3,X2)
    <=> ( element(X3,X1)
        & ~ element(X3,X3) ) ),
    inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).

fof(5,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( ( ~ element(X3,X2)
        | ( element(X3,X1)
          & ~ element(X3,X3) ) )
      & ( ~ element(X3,X1)
        | element(X3,X3)
        | element(X3,X2) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(6,plain,
    ! [X4] :
    ? [X5] :
    ! [X6] :
      ( ( ~ element(X6,X5)
        | ( element(X6,X4)
          & ~ element(X6,X6) ) )
      & ( ~ element(X6,X4)
        | element(X6,X6)
        | element(X6,X5) ) ),
    inference(variable_rename,[status(thm)],[5]) ).

fof(7,plain,
    ! [X4,X6] :
      ( ( ~ element(X6,esk1_1(X4))
        | ( element(X6,X4)
          & ~ element(X6,X6) ) )
      & ( ~ element(X6,X4)
        | element(X6,X6)
        | element(X6,esk1_1(X4)) ) ),
    inference(skolemize,[status(esa)],[6]) ).

fof(8,plain,
    ! [X4,X6] :
      ( ( element(X6,X4)
        | ~ element(X6,esk1_1(X4)) )
      & ( ~ element(X6,X6)
        | ~ element(X6,esk1_1(X4)) )
      & ( ~ element(X6,X4)
        | element(X6,X6)
        | element(X6,esk1_1(X4)) ) ),
    inference(distribute,[status(thm)],[7]) ).

cnf(9,plain,
    ( element(X1,esk1_1(X2))
    | element(X1,X1)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[8]) ).

cnf(10,plain,
    ( ~ element(X1,esk1_1(X2))
    | ~ element(X1,X1) ),
    inference(split_conjunct,[status(thm)],[8]) ).

fof(12,negated_conjecture,
    ? [X1] :
    ! [X3] : element(X3,X1),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(13,negated_conjecture,
    ? [X4] :
    ! [X5] : element(X5,X4),
    inference(variable_rename,[status(thm)],[12]) ).

fof(14,negated_conjecture,
    ! [X5] : element(X5,esk2_0),
    inference(skolemize,[status(esa)],[13]) ).

cnf(15,negated_conjecture,
    element(X1,esk2_0),
    inference(split_conjunct,[status(thm)],[14]) ).

cnf(16,negated_conjecture,
    ( element(X1,esk1_1(esk2_0))
    | element(X1,X1) ),
    inference(spm,[status(thm)],[9,15,theory(equality)]) ).

cnf(17,negated_conjecture,
    element(esk1_1(esk2_0),esk1_1(esk2_0)),
    inference(ef,[status(thm)],[16,theory(equality)]) ).

cnf(27,negated_conjecture,
    ~ element(esk1_1(esk2_0),esk1_1(esk2_0)),
    inference(spm,[status(thm)],[10,17,theory(equality)]) ).

cnf(30,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[27,17,theory(equality)]) ).

cnf(31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[30,theory(equality)]) ).

cnf(32,negated_conjecture,
    $false,
    31,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET045+1.p
% --creating new selector for []
% -running prover on /tmp/tmp77a_DQ/sel_SET045+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET045+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET045+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET045+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
% 
%------------------------------------------------------------------------------