%------------------------------------------------------------------------------
% File     : ARI611_1 : TPTP v8.2.0. Released v5.1.0.
% Domain   : Arithmetic
% Problem  : Intervals (5,15) and (8,18) intersect
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.00 v7.3.0, 0.12 v7.1.0, 0.00 v6.2.0, 0.60 v6.1.0, 0.56 v6.0.0, 0.62 v5.5.0, 0.50 v5.3.0, 0.43 v5.2.0, 0.40 v5.1.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :    8 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :    7 (   0   ~;   0   |;   4   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number arithmetic     :   11 (   4 atm;   0 fun;   4 num;   3 var)
%            Number of types       :    2 (   0 usr;   1 ari)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   0 usr;   4 con; 0-0 aty)
%            Number of variables   :    3 (   2   !;   1   ?;   3   :)
% SPC      : TF0_THM_NEQ_ARI

% Comments :
%------------------------------------------------------------------------------
tff(p_type,type,
    p: $int > $o ).

tff(q_type,type,
    q: $int > $o ).

tff(interv_5_15_and_8_18_intersect,conjecture,
    ( ( ! [X: $int] :
          ( ( $less(5,X)
            & $less(X,15) )
        <=> p(X) )
      & ! [X: $int] :
          ( ( $less(8,X)
            & $less(X,18) )
        <=> q(X) ) )
   => ? [X: $int] :
        ( p(X)
        & q(X) ) ) ).

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