%------------------------------------------------------------------------------
% File     : SYO084^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM75
% Version  : Especial.
% English  : Related to THM87, which was used for CADE-6.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0116 [Bro09]
%          : THM75 [TPS]

% Status   : Theorem
% Rating   : 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.5.0, 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    :    5 (   0 unt;   4 typ;   0 def)
%            Number of atoms       :    3 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :   13 (   0   ~;   1   |;   0   &;  11   @)
%                                         (   0 <=>;   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     :    4 (   4 usr;   1 con; 0-3 aty)
%            Number of variables   :    3 (   0   ^;   1   !;   2   ?;   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(cP,type,
    cP: $i > $i > $i > $o ).

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

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

thf(a,type,
    a: $i ).

thf(cTHM75,conjecture,
    ? [Xv: $i] :
    ! [Xj: $i] :
    ? [Xq: $i] :
      ( ( ( cP @ a @ Xj @ ( h @ Xj ) )
        | ( cP @ Xv @ Xj @ ( k @ Xj ) ) )
     => ( cP @ Xv @ Xj @ Xq ) ) ).

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