%--------------------------------------------------------------------------
% File     : SYN036+1 : TPTP v8.2.0. Released v2.0.0.
% Domain   : Syntactic
% Problem  : Andrews Challenge Problem
% Version  : Especial.
%            Theorem formulation : Erroneous, as in [Pel86]
% English  :

% Refs     : [And86] Andrews (1986), An Introduction to Mathematical Logic
%          : [DeC79] DeChampeaux (1979), Sub-problem Finder and Instance Ch
%          : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
%          : [Pel88] Pelletier (1988), Errata
%          : [Hah94] Haehnle (1994), Email to G. Sutcliffe
% Source   : [Hah94]
% Names    : Pelletier 34 [Pel86]

% Status   : Theorem
% Rating   : 0.00 v8.2.0, 0.07 v8.1.0, 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.22 v5.2.0, 0.21 v5.0.0, 0.10 v4.1.0, 0.11 v4.0.1, 0.16 v4.0.0, 0.20 v3.7.0, 0.33 v3.5.0, 0.25 v3.4.0, 0.08 v3.3.0, 0.11 v3.2.0, 0.33 v3.1.0, 0.50 v2.7.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1, 0.50 v2.2.0, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :    8 (   0 equ)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives :    7 (   0   ~;   0   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 1-1 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    8 (   4   !;   4   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : This problem is incorrect in [Pel86] and is corrected in [Pel88].
%--------------------------------------------------------------------------
fof(pel34,conjecture,
    ( ( ? [X] :
        ! [Y] :
          ( big_p(X)
        <=> big_p(Y) )
    <=> ( ? [U] : big_q(U)
      <=> ! [W] : big_q(W) ) )
  <=> ( ? [X1] :
        ! [Y1] :
          ( big_q(X1)
        <=> big_q(Y1) )
    <=> ( ? [U1] : big_p(U1)
      <=> ! [W1] : big_p(W1) ) ) ) ).

%--------------------------------------------------------------------------