%------------------------------------------------------------------------------
% File     : SYO268^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem X5308
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0240 [Bro09]
%          : X5308 [TPS]

% Status   : Theorem
% Rating   : 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.00 v7.3.0, 0.10 v7.2.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :    2 (   0 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   11 (   0   ~;   0   |;   0   &;   8   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   7 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    7 (   0   ^;   3   !;   4   ?;   7   :)
% SPC      : TH0_THM_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(b_type,type,
    b: $tType ).

thf(r,type,
    r: a > b > $o ).

thf(cX5308,conjecture,
    ( ? [Xj: ( b > $o ) > b] :
      ! [Xp: b > $o] :
        ( ? [Xx: b] : ( Xp @ Xx )
       => ( Xp @ ( Xj @ Xp ) ) )
   => ( ! [Xx: a] :
        ? [Xy: b] : ( r @ Xx @ Xy )
    <=> ? [Xf: a > b] :
        ! [Xx: a] : ( r @ Xx @ ( Xf @ Xx ) ) ) ) ).

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