%------------------------------------------------------------------------------
% File     : SYN355^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem X2106
% Version  : Especial.
% English  : 

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0120 [Bro09]
%          : X2106 [TPS]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :    6 (   0 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives :   12 (   1   ~;   1   |;   1   &;   6   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   7 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   :    3 (   0   ^;   3   !;   0   ?;   3   :)
% 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(cQ,type,
    cQ: $i > $o ).

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

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

thf(cX2106,conjecture,
    ( ( ! [Xx: $i] :
          ( ( cR @ Xx )
         => ( cP @ Xx ) )
      & ! [Xx: $i] :
          ( ~ ( cQ @ Xx )
         => ( cR @ Xx ) ) )
   => ! [Xx: $i] :
        ( ( cP @ Xx )
        | ( cQ @ Xx ) ) ) ).

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