## TPTP Problem File: NUM807^5.p

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```%------------------------------------------------------------------------------
% File     : NUM807^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Number Theory (Induction on naturals)
% Problem  : TPS problem from NATS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0860 [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    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   22 (   4 equality;  14 variable)
%            Maximal formula depth :   10 (   4 average)
%            Number of connectives :   13 (   0   ~;   0   |;   1   &;  10   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   4   !;   0   ?;   0   ^)
%                                         (   4   :;   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
%          :
%------------------------------------------------------------------------------
thf(n_type,type,(
n: \$tType )).

thf(cS,type,(
cS: n > n )).

thf(c0,type,(
c0: n )).

thf(cPA_IND_EQ,conjecture,(
! [Xp: n > n,Xq: n > n] :
( ( ( ( Xp @ c0 )
= ( Xq @ c0 ) )
& ! [Xx: n] :
( ( ( Xp @ Xx )
= ( Xq @ Xx ) )
=> ( ( Xp @ ( cS @ Xx ) )
= ( Xq @ ( cS @ Xx ) ) ) ) )
=> ! [Xx: n] :
( ( Xp @ Xx )
= ( Xq @ Xx ) ) ) )).

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