%------------------------------------------------------------------------------
% File     : SEU927^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM92
% Version  : Especial.
% English  : Trivial theorem which gives nice simple example of an expansion
%            proof.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0233 [Bro09]
%          : THM92 [TPS]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    0 (   0 equ;   0 cnn)
%            Maximal formula atoms :    0 (   0 avg)
%            Number of connectives :   11 (   0   ~;   0   |;   1   &;   8   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (  11 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    6 (   3   ^;   3   !;   0   ?;   6   :)
% 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/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cTHM92_pme,conjecture,
    ! [Xf: a > a,Xp: ( a > a ) > $o] :
      ( ( ( Xp
          @ ^ [Xu: a] : Xu )
        & ! [Xj: a > a] :
            ( ( Xp @ Xj )
           => ( Xp
              @ ^ [Xx: a] : ( Xf @ ( Xj @ Xx ) ) ) ) )
     => ( Xp
        @ ^ [Xx: a] : ( Xf @ ( Xf @ Xx ) ) ) ) ).

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