TPTP Problem File: SET043+1.p

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% File     : SET043+1 : TPTP v8.1.0. Released v2.0.0.
% Domain   : Set Theory
% Problem  : Russell's Paradox
% Version  : Especial.
% English  : Russell's paradox : there is no Russell set (a set which
%            contains exactly those sets which are not members
%            of themselves).

% Refs     : [KM64]  Kalish & Montegue (1964), Logic: Techniques of Formal
%          : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
%          : [Hah94] Haehnle (1994), Email to G. Sutcliffe
% Source   : [Hah94]
% Names    : Pelletier 39 [Pel86]

% Status   : Theorem
% Rating   : 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :    2 (   0 equ)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :    3 (   2   ~;   0   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    2 (   1   !;   1   ?)
% SPC      : FOF_THM_EPR_NEQ

% Comments :
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fof(pel39,conjecture,
    ~ ? [X] :
      ! [Y] :
        ( element(Y,X)
      <=> ~ element(Y,Y) ) ).

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