TSTP Solution File: SEU354+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU354+2 : TPTP v5.0.0. Released v3.3.0.
% 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 07:42:41 EST 2010

% Result   : Theorem 13.67s
% Output   : CNFRefutation 13.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   28 (   9 unt;   0 def)
%            Number of atoms       :   77 (  36 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   86 (  37   ~;  34   |;   9   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   23 (   0 sgn  14   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(122,axiom,
    ! [X1] : union(powerset(X1)) = X1,
    file('/tmp/tmpwPEmX3/sel_SEU354+2.p_1',t99_zfmisc_1) ).

fof(204,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => ( proper_element(X2,powerset(X1))
      <=> X2 != X1 ) ),
    file('/tmp/tmpwPEmX3/sel_SEU354+2.p_1',t5_tex_2) ).

fof(412,axiom,
    ! [X1,X2] :
      ( element(X2,X1)
     => ( proper_element(X2,X1)
      <=> X2 != union(X1) ) ),
    file('/tmp/tmpwPEmX3/sel_SEU354+2.p_1',d2_tex_2) ).

fof(671,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(X1))
       => ( proper_element(X2,powerset(X1))
        <=> X2 != X1 ) ),
    inference(assume_negation,[status(cth)],[204]) ).

fof(1695,plain,
    ! [X2] : union(powerset(X2)) = X2,
    inference(variable_rename,[status(thm)],[122]) ).

cnf(1696,plain,
    union(powerset(X1)) = X1,
    inference(split_conjunct,[status(thm)],[1695]) ).

fof(2352,negated_conjecture,
    ? [X1,X2] :
      ( element(X2,powerset(X1))
      & ( ~ proper_element(X2,powerset(X1))
        | X2 = X1 )
      & ( proper_element(X2,powerset(X1))
        | X2 != X1 ) ),
    inference(fof_nnf,[status(thm)],[671]) ).

fof(2353,negated_conjecture,
    ? [X3,X4] :
      ( element(X4,powerset(X3))
      & ( ~ proper_element(X4,powerset(X3))
        | X4 = X3 )
      & ( proper_element(X4,powerset(X3))
        | X4 != X3 ) ),
    inference(variable_rename,[status(thm)],[2352]) ).

fof(2354,negated_conjecture,
    ( element(esk151_0,powerset(esk150_0))
    & ( ~ proper_element(esk151_0,powerset(esk150_0))
      | esk151_0 = esk150_0 )
    & ( proper_element(esk151_0,powerset(esk150_0))
      | esk151_0 != esk150_0 ) ),
    inference(skolemize,[status(esa)],[2353]) ).

cnf(2355,negated_conjecture,
    ( proper_element(esk151_0,powerset(esk150_0))
    | esk151_0 != esk150_0 ),
    inference(split_conjunct,[status(thm)],[2354]) ).

cnf(2356,negated_conjecture,
    ( esk151_0 = esk150_0
    | ~ proper_element(esk151_0,powerset(esk150_0)) ),
    inference(split_conjunct,[status(thm)],[2354]) ).

cnf(2357,negated_conjecture,
    element(esk151_0,powerset(esk150_0)),
    inference(split_conjunct,[status(thm)],[2354]) ).

fof(3664,plain,
    ! [X1,X2] :
      ( ~ element(X2,X1)
      | ( ( ~ proper_element(X2,X1)
          | X2 != union(X1) )
        & ( X2 = union(X1)
          | proper_element(X2,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[412]) ).

fof(3665,plain,
    ! [X3,X4] :
      ( ~ element(X4,X3)
      | ( ( ~ proper_element(X4,X3)
          | X4 != union(X3) )
        & ( X4 = union(X3)
          | proper_element(X4,X3) ) ) ),
    inference(variable_rename,[status(thm)],[3664]) ).

fof(3666,plain,
    ! [X3,X4] :
      ( ( ~ proper_element(X4,X3)
        | X4 != union(X3)
        | ~ element(X4,X3) )
      & ( X4 = union(X3)
        | proper_element(X4,X3)
        | ~ element(X4,X3) ) ),
    inference(distribute,[status(thm)],[3665]) ).

cnf(3667,plain,
    ( proper_element(X1,X2)
    | X1 = union(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[3666]) ).

cnf(3668,plain,
    ( ~ element(X1,X2)
    | X1 != union(X2)
    | ~ proper_element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[3666]) ).

cnf(6951,negated_conjecture,
    ( esk150_0 = esk151_0
    | union(powerset(esk150_0)) = esk151_0
    | ~ element(esk151_0,powerset(esk150_0)) ),
    inference(spm,[status(thm)],[2356,3667,theory(equality)]) ).

cnf(6955,negated_conjecture,
    ( esk150_0 = esk151_0
    | esk150_0 = esk151_0
    | ~ element(esk151_0,powerset(esk150_0)) ),
    inference(rw,[status(thm)],[6951,1696,theory(equality)]) ).

cnf(6956,negated_conjecture,
    ( esk150_0 = esk151_0
    | esk150_0 = esk151_0
    | $false ),
    inference(rw,[status(thm)],[6955,2357,theory(equality)]) ).

cnf(6957,negated_conjecture,
    esk150_0 = esk151_0,
    inference(cn,[status(thm)],[6956,theory(equality)]) ).

cnf(6958,negated_conjecture,
    ( union(powerset(esk150_0)) != esk151_0
    | ~ element(esk151_0,powerset(esk150_0))
    | esk150_0 != esk151_0 ),
    inference(spm,[status(thm)],[3668,2355,theory(equality)]) ).

cnf(6960,negated_conjecture,
    ( esk150_0 != esk151_0
    | ~ element(esk151_0,powerset(esk150_0))
    | esk150_0 != esk151_0 ),
    inference(rw,[status(thm)],[6958,1696,theory(equality)]) ).

cnf(6961,negated_conjecture,
    ( esk150_0 != esk151_0
    | $false
    | esk150_0 != esk151_0 ),
    inference(rw,[status(thm)],[6960,2357,theory(equality)]) ).

cnf(6962,negated_conjecture,
    esk150_0 != esk151_0,
    inference(cn,[status(thm)],[6961,theory(equality)]) ).

cnf(117482,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[6962,6957,theory(equality)]) ).

cnf(117483,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[117482,theory(equality)]) ).

cnf(117484,negated_conjecture,
    $false,
    117483,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU354+2.p
% --creating new selector for []
% -running prover on /tmp/tmpwPEmX3/sel_SEU354+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU354+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU354+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU354+2.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
% 
%------------------------------------------------------------------------------