Participants are on horses competing in a game
A group is horseback riding.
Not all participants competing in a game are a group.
exists p1 x1.(exists e1 x2 x3 x4.(on(x1,x2) & in(e1,x4) & n_game(x4) & Actor(e1,x3) & v_compete(e1) & (x2 = x3) & n_horse(x2)) & n_participant(x1))
exists p1 x1.(exists s1 x2.((x1 = x2) & n_riding(x2) & a_horseback(s1) & Theme(s1,x2)) & n_group(x1))