## TPTP Problem File: SYO294^5.p

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```%------------------------------------------------------------------------------
% File     : SYO294^5 : TPTP v7.1.0. 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_0727 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :    9 (   0 equality;   6 variable)
%            Maximal formula depth :    8 (   5 average)
%            Number of connectives :    8 (   0   ~;   0   |;   1   &;   5   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =)
%            Number of variables   :    2 (   0 sgn;   2   !;   0   ?;   0   ^)
%                                         (   2   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          :
%------------------------------------------------------------------------------
thf(cN,type,(
cN: ( \$i > \$o ) > \$o )).

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

thf(c0,type,(
c0: ( \$i > \$o ) > \$o )).

thf(cNATN1,conjecture,(
! [P: ( ( \$i > \$o ) > \$o ) > \$o] :
( ( ( P @ c0 )
& ! [X: ( \$i > \$o ) > \$o] :
( ( P @ X )
=> ( P @ ( cS @ X ) ) ) )
=> ( P @ cN ) ) )).

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