Two brown dogs playing.
Two dogs are playing with a rope.
Just because two dogs are playing doesn't reveal any information to suggest that they are playing with a rope.
exists e1 s1 x1.(Actor(e1,x1) & v_play(e1) & n_dog(x1) & a_brown(s1) & Theme(s1,x1) & card_eq_2(x1))
exists e1 x1 x2.(with(e1,x2) & n_rope(x2) & Actor(e1,x1) & v_play(e1) & n_dog(x1) & card_eq_2(x1))