## TPTP Problem File: ALG285^5.p

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```%------------------------------------------------------------------------------
% File     : ALG285^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : General Algebra
% Problem  : TPS problem from GRP-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1023 [Bro09]

% Status   : Theorem
% Rating   : 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   43 (   6 equality;  22 variable)
%            Maximal formula depth :   11 (   4 average)
%            Number of connectives :   30 (   0   ~;   0   |;   4   &;  25   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   4   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  10   !;   2   ?;   0   ^)
%                                         (  12   :;   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(cP,type,(
cP: a > a > a )).

thf(cE,type,(
cE: a )).

thf(cJ,type,(
cJ: a > a )).

thf(cTHM22_pme,conjecture,
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [Xx: a] :
( ( cP @ cE @ Xx )
= Xx )
& ! [Xy: a] :
( ( cP @ ( cJ @ Xy ) @ Xy )
= cE ) )
=> ( ! [Xx: a,Xy: a,Xz: a] :
( ( cP @ ( cP @ Xx @ Xy ) @ Xz )
= ( cP @ Xx @ ( cP @ Xy @ Xz ) ) )
& ! [X: a,Y: a] :
( ? [U: a] :
( ( cP @ X @ U )
= Y )
& ? [V: a] :
( ( cP @ V @ X )
= Y ) ) ) )).

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