## TPTP Problem File: SYO165^5.p

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```%------------------------------------------------------------------------------
% File     : SYO165^5 : TPTP v7.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-FO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0951 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   27 (   0 equality;  16 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   27 (   1   ~;   0   |;   3   &;  17   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   7   !;   1   ?;   0   ^)
%                                         (   8   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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(cP,type,(
cP: \$i > \$o )).

thf(s,type,(
s: \$i )).

thf(cE,type,(
cE: \$i > \$i > \$o )).

thf(cR,type,(
cR: \$i > \$i > \$o )).

thf(cTHM117A,conjecture,
( ( ! [Xx: \$i,Xz: \$i] :
( ( cE @ Xz @ Xx )
=> ? [Xy: \$i] :
( ( cE @ Xy @ Xx )
& ! [Xw: \$i] :
( ( cR @ Xy @ Xw )
=> ~ ( cE @ Xw @ Xx ) ) ) )
& ! [Xs0: \$i,Xx: \$i] :
( ! [Xy: \$i] :
( ( ( cE @ Xy @ Xs0 )
& ( cR @ Xx @ Xy ) )
=> ( cP @ Xy ) )
=> ( cP @ Xx ) ) )
=> ! [Xx: \$i] :
( ( cE @ Xx @ s )
=> ( cP @ Xx ) ) )).

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