%------------------------------------------------------------------------------
% File     : NUM800^1 : TPTP v8.2.0. Released v3.7.0.
% Domain   : Number Theory
% Problem  : Some function of two and three is six, and of one and two is two
% Version  : Especial.
% English  :

% Refs     : [BB05]  Benzmueller & Brown (2005), A Structured Set of Higher
%          : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% Source   : [Ben09]
% Names    : Example 1c [BB05]

% Status   : Theorem
% Rating   : 0.50 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.71 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 0.86 v6.4.0, 1.00 v6.2.0, 0.86 v6.1.0, 0.71 v6.0.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0, 1.00 v3.7.0
% Syntax   : Number of formulae    :   29 (  14 unt;  14 typ;  14 def)
%            Number of atoms       :   26 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   70 (   0   ~;   0   |;   1   &;  69   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :  102 ( 102   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  18 usr;   4 con; 0-4 aty)
%            Number of variables   :   34 (  33   ^;   0   !;   1   ?;  34   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : 
%------------------------------------------------------------------------------
%----Include Church numerals definitions
include('Axioms/NUM006^0.ax').
%------------------------------------------------------------------------------
thf(thm,conjecture,
    ? [H: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
      ( ( ( H @ two @ three )
        = six )
      & ( ( H @ one @ two )
        = two ) ) ).

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