A group of children playing a game.
A group of children playing a game of football outside.
There are different types of games not just football therefore playing a game does not imply it is football.
exists e1 x1 x2 x3 x4.(a_topic(x1) & of(x1,x2) & Theme(e1,x4) & Actor(e1,x3) & v_play(e1) & n_game(x4) & (x2 = x3) & n_child(x2) & n_group(x1))
exists e1 x1 x2 x3 x4 x5 x6.(a_topic(x1) & of(x1,x2) & Theme(e1,x4) & Actor(e1,x3) & v_play(e1) & of(x4,x5) & n_outside(x5) & of(x5,x6) & n_football(x6) & n_game(x4) & (x2 = x3) & n_child(x2) & n_group(x1))