%------------------------------------------------------------------------------
% File     : ARI595_1 : TPTP v9.0.0. Released v5.1.0.
% Domain   : Arithmetic
% Problem  : There is a number in [a,...,a+2] that is divisible by 3
% Version  : Especial.
% English  :

% Refs     : [Wal10] Waldmann (2010), Email to Geoff Sutcliffe
% Source   : [Wal10]
% Names    :

% Status   : Theorem
% Rating   : 0.60 v9.0.0, 0.50 v8.2.0, 0.67 v7.5.0, 0.60 v7.4.0, 0.67 v7.3.0, 0.75 v7.1.0, 0.67 v7.0.0, 0.50 v6.4.0, 0.67 v6.3.0, 0.25 v6.2.0, 0.80 v6.1.0, 0.89 v6.0.0, 0.88 v5.3.0, 1.00 v5.1.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :    4 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :    3 (   0   ~;   0   |;   1   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :    8 (   2 atm;   2 fun;   2 num;   2 var)
%            Number of types       :    2 (   0 usr;   1 ari)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :    5 (   1 usr;   3 con; 0-2 aty)
%            Number of variables   :    2 (   1   !;   1   ?;   2   :)
% SPC      : TF0_THM_NEQ_ARI

% Comments : Also a theorem for $rat and $real, but much easier
%------------------------------------------------------------------------------
tff(p_type,type,
    p: $int > $o ).

tff(a_type,type,
    a: $int ).

tff(exists_X_in_a_to_aplus2_div_3,conjecture,
    ( ! [Z: $int] :
        ( ( $lesseq(a,Z)
          & $lesseq(Z,$sum(a,2)) )
       => p(Z) )
   => ? [X: $int] : p($product(3,X)) ) ).

%------------------------------------------------------------------------------