There are two dogs playing with each other.
The dogs are chasing each other.
There are two dogs playing with each other does not necessary that they are chasing each other.
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 x1.(n_dog(x1) & all x2.(n_other(x2) -> exists e1.(Theme(e1,x2) & Actor(e1,x1) & v_chase(e1))))