%------------------------------------------------------------------------------
% File     : SEU933^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM196B
% Version  : Especial.
% English  : It is not true that if [k COMPOSE j] is an iterate of j, then k 
%            must be an iterate of j, provided  we have distinct elements a 
%            and b.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0273 [Bro09]
%          : THM196B [TPS]

% Status   : Theorem
% Rating   : 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   25 (   1 equality;  22 variable)
%            Maximal formula depth :   15 (   6 average)
%            Number of connectives :   24 (   2   ~;   0   |;   2   &;  14   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    9 (   0 sgn;   6   !;   0   ?;   3   ^)
%                                         (   9   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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/
%          : Polymorphic definitions expanded.
%          : 
%------------------------------------------------------------------------------
thf(b,type,(
    b: $i )).

thf(a,type,(
    a: $i )).

thf(cTHM196B_pme,conjecture,
    ( ( a != b )
   => ~ ( ! [Xj: $i > $i,Xk: $i > $i] :
            ( ! [Xp: ( $i > $i ) > $o] :
                ( ( ( Xp @ Xj )
                  & ! [Xj_2: $i > $i] :
                      ( ( Xp @ Xj_2 )
                     => ( Xp
                        @ ^ [Xx: $i] :
                            ( Xj @ ( Xj_2 @ Xx ) ) ) ) )
               => ( Xp
                  @ ^ [Xx: $i] :
                      ( Xk @ ( Xj @ Xx ) ) ) )
           => ! [Xp: ( $i > $i ) > $o] :
                ( ( ( Xp @ Xj )
                  & ! [Xj_3: $i > $i] :
                      ( ( Xp @ Xj_3 )
                     => ( Xp
                        @ ^ [Xx: $i] :
                            ( Xj @ ( Xj_3 @ Xx ) ) ) ) )
               => ( Xp @ Xk ) ) ) ) )).

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