%------------------------------------------------------------------------------
% File     : SYO309^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0833 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v8.2.0, 0.55 v8.1.0, 0.42 v7.4.0, 0.44 v7.3.0, 0.50 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.43 v6.3.0, 0.33 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.67 v5.5.0, 0.80 v5.4.0, 0.75 v5.2.0, 0.50 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :    2 (   0 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   15 (   2   ~;   0   |;   0   &;  10   @)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    5 (   0   ^;   2   !;   3   ?;   5   :)
% 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(cS,type,
    cS: $i > $i ).

thf(cQ,type,
    cQ: $i > $i ).

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

thf(cEO1,conjecture,
    ( ! [Xx: $i] :
        ( ? [Xu: $i] : ( cR @ Xx @ ( cQ @ Xu ) )
      <=> ~ ? [Xv: $i] : ( cR @ ( cS @ Xx ) @ ( cQ @ Xv ) ) )
   => ? [A: $i > $o] :
      ! [Xx: $i] :
        ( ( A @ Xx )
      <=> ~ ( A @ ( cS @ Xx ) ) ) ) ).

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