%------------------------------------------------------------------------------
% File     : SYO111^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM80
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0465 [Bro09]
%          : tps_1015 [Bro09]
%          : THM80 [TPS]

% Status   : Theorem
% Rating   : 0.17 v8.2.0, 0.18 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :   12 (   0 equ;   0 cnn)
%            Maximal formula atoms :   12 (  12 avg)
%            Number of connectives :   33 (  10   ~;  10   |;   0   &;  12   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   3 usr;   0 con; 1-1 aty)
%            Number of variables   :   12 (   0   ^;   8   !;   4   ?;  12   :)
% 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(cG,type,
    cG: $i > $o ).

thf(cN,type,
    cN: $i > $o ).

thf(cM,type,
    cM: $i > $o ).

thf(cTHM80,conjecture,
    ( ( ! [R: $i] : ( cM @ R )
      | ? [X: $i] :
          ~ ( cG @ X )
      | ~ ( ! [Y: $i] : ( cM @ Y )
          | ? [S: $i] : ( cN @ S ) )
      | ~ ( ! [Z: $i] :
              ~ ( cN @ Z )
          | ~ ! [T: $i] : ( cG @ T ) ) )
   => ( ! [R: $i] : ( cM @ R )
      | ? [X: $i] :
          ~ ( cG @ X )
      | ~ ! [Y: $i] :
            ( ( cM @ Y )
            | ? [S: $i] : ( cN @ S ) )
      | ~ ! [Z: $i] :
            ( ~ ( cN @ Z )
            | ~ ! [T: $i] : ( cG @ T ) ) ) ) ).

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