A group of girls playing a game on horseback.
The horses have riders.
One rides a horse on its back so girls on horseback, meaning girls on horses backs, are riding the horses; one is only able to ride a horse if that horse has a rider; one cannot happen without the other; therefore girls on horseback expresses the same idea without specifying who is actually on the horse.
exists e1 x1 x2 x3 x4 x5.(a_topic(x1) & Theme(e1,x4) & Actor(e1,x3) & v_play(e1) & on(x4,x5) & n_horseback(x5) & n_game(x4) & (x1 = x3) & of(x1,x2) & n_girl(x2) & n_group(x1))
exists e1 x1 x2.(n_horse(x1) & Theme(e1,x2) & Actor(e1,x1) & v_have(e1) & n_rider(x2))