TPTP Problem File: SYO242^5.p

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```%------------------------------------------------------------------------------
% File     : SYO242^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-EQ-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0927 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   21 (   1 equality;  20 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :   18 (   0   ~;   0   |;   3   &;  11   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   5   !;   5   ?;   0   ^)
%                                         (  10   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_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(a_type,type,(
a: \$tType )).

thf(cTHM539,conjecture,
( ? [Xf: ( a > \$o ) > a] :
! [X: a > \$o] :
( ? [Xt: a] :
( X @ Xt )
=> ( X @ ( Xf @ X ) ) )
=> ? [R: a > a > \$o] :
( ! [Xx: a,Xy: a] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xx ) )
=> ( Xx = Xy ) )
& ! [S: a > \$o] :
( ? [Xu: a] :
( S @ Xu )
=> ? [Xv: a] :
( ( S @ Xv )
& ! [Xz: a] :
( R @ Xv @ Xz ) ) ) ) )).

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