## TPTP Problem File: SYO213^5.p

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```%------------------------------------------------------------------------------
% File     : SYO213^5 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-PROP-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0760 [Bro09]

% Status   : Theorem
% Rating   : 0.75 v7.1.0, 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.71 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :    9 (   2 equality;   7 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :    5 (   1   ~;   0   |;   0   &;   3   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   2   !;   2   ?;   0   ^)
%                                         (   4   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%          :
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cCT30,conjecture,(
~ ( ? [Xg: a > a > \$o] :
! [Xf: a > \$o] :
? [Xj: a] :
! [Xp: \$o > \$o] :
( ( Xp
@ ( ( Xg @ Xj )
= Xf ) )
=> ( Xp @ ( Xf = Xf ) ) ) ) )).

%------------------------------------------------------------------------------
```