%------------------------------------------------------------------------------
% File     : SYO159^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-FO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0855 [Bro09]

% 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       :    6 (   0 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives :   17 (   4   ~;   0   |;   2   &;   8   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    4 (   0   ^;   1   !;   3   ?;   4   :)
% 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(cC,type,
    cC: $i > $o ).

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

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

thf(cNNF_EXAMPLE,conjecture,
    ( ~ ! [Xx: $i] :
          ( ( cA @ Xx )
         => ? [Xy: $i] :
              ( ( cB @ Xx @ Xy )
              & ( cC @ Xy ) ) )
   => ? [Xu: $i] :
        ( ( cA @ Xu )
        & ~ ? [Xv: $i] :
              ~ ( ( cB @ Xu @ Xv )
               => ~ ( cC @ Xv ) ) ) ) ).

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