%------------------------------------------------------------------------------
% File     : SYO213^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-PROP-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0760 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.78 v7.2.0, 0.75 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    2 (   2 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :    5 (   1   ~;   0   |;   0   &;   3   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :    4 (   0   ^;   2   !;   2   ?;   4   :)
% SPC      : TH0_THM_EQU_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(cCT30,conjecture,
    ~ ? [Xg: a > a > $o] :
      ! [Xf: a > $o] :
      ? [Xj: a] :
      ! [Xp: $o > $o] :
        ( ( Xp
          @ ( ( Xg @ Xj )
            = Xf ) )
       => ( Xp @ ( Xf = Xf ) ) ) ).

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