There are two dogs playing with each other.
Two dogs playing with a ball.
There are two dogs playing with each other does not imply that they are playing with a ball.
exists p1 x1 e1 x2 x3.((x1 = x2) & all x4.(n_other(x4) -> with(e1,x4)) & Actor(e1,x3) & v_play(e1) & (x2 = x3) & n_dog(x2) & card_eq_2(x2))
exists e1 x1 x2 x3.(a_topic(x1) & with(e1,x3) & n_ball(x3) & Actor(e1,x2) & v_play(e1) & (x1 = x2) & n_dog(x1) & card_eq_2(x1))