## TPTP Problem File: SYO166^5.p

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```%------------------------------------------------------------------------------
% File     : SYO166^5 : TPTP v7.1.0. 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_0972 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v5.4.0, 1.00 v5.0.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unit;   4 type;   0 defn)
%            Number of atoms       :   44 (   0 equality;  18 variable)
%            Maximal formula depth :   13 (   5 average)
%            Number of connectives :   43 (   0   ~;   0   |;   4   &;  37   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   3   !;   0   ?;   0   ^)
%                                         (   3   :;   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(n,type,(
n: \$i > \$i )).

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

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

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

thf(cPELL67,conjecture,
( ! [Xx: \$i,Xy: \$i] :
( ( cT @ ( i @ Xx @ ( i @ Xy @ Xx ) ) )
& ( cT @ ( i @ ( i @ Xx @ ( i @ Xy @ z ) ) @ ( i @ ( i @ Xx @ Xy ) @ ( i @ Xx @ z ) ) ) )
& ( cT @ ( i @ ( i @ ( n @ Xx ) @ ( n @ Xy ) ) @ ( i @ Xy @ Xx ) ) )
& ( ( ( cT @ ( i @ Xx @ Xy ) )
& ( cT @ Xx ) )
=> ( cT @ Xy ) ) )
=> ! [Xx: \$i] :
( cT @ ( i @ ( n @ ( n @ Xx ) ) @ Xx ) ) )).

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