## TPTP Problem File: SYO332^5.p

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```%------------------------------------------------------------------------------
% File     : SYO332^5 : TPTP v7.2.0. 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_1056 [Bro09]

% Status   : Theorem
% Rating   : 0.80 v7.2.0, 0.75 v7.1.0, 0.71 v7.0.0, 0.75 v6.4.0, 0.71 v6.3.0, 0.67 v5.5.0, 0.80 v5.4.0, 0.50 v5.3.0, 0.75 v5.2.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   32 (   0 equality;  32 variable)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :   31 (   0   ~;   0   |;   1   &;  20   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   18 (   0 sgn;  10   !;   8   ?;   0   ^)
%                                         (  18   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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
%          :
%------------------------------------------------------------------------------
thf(b_type,type,(
b: \$tType )).

thf(a_type,type,(
a: \$tType )).

thf(cTHM561,conjecture,
( ( ! [Xs: ( b > \$o ) > \$o] :
( ! [X: b > \$o] :
( ( Xs @ X )
=> ? [Xy: b] :
( X @ Xy ) )
=> ? [Xf: ( b > \$o ) > b] :
! [X: b > \$o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) )
=> ! [Xr: a > b > \$o] :
? [Xg: a > b] :
! [Xx: a] :
( ? [Xy: b] :
( Xr @ Xx @ Xy )
=> ( Xr @ Xx @ ( Xg @ Xx ) ) ) )
& ( ! [Xr: ( a > \$o ) > a > \$o] :
? [Xg: ( a > \$o ) > a] :
! [Xx: a > \$o] :
( ? [Xy: a] :
( Xr @ Xx @ Xy )
=> ( Xr @ Xx @ ( Xg @ Xx ) ) )
=> ! [Xs: ( a > \$o ) > \$o] :
( ! [X: a > \$o] :
( ( Xs @ X )
=> ? [Xt: a] :
( X @ Xt ) )
=> ? [Xf: ( a > \$o ) > a] :
! [X: a > \$o] :
( ( Xs @ X )
=> ( X @ ( Xf @ X ) ) ) ) ) )).

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