A man cooking food on the grill.
People having a cookout
A man cooking on  a grill does not mean he is cooking for other people, not does it mean that a cookout is occurring.
exists e1 x1 x2 x3 x4.(n_grill(x4) & a_topic(x1) & on(e1,x4) & Theme(e1,x3) & Actor(e1,x2) & v_cook(e1) & n_food(x3) & (x1 = x2) & n_man(x1))
exists e1 x1 x2 x3.(a_topic(x1) & Theme(e1,x3) & Actor(e1,x2) & v_have(e1) & n_cookout(x3) & (x1 = x2) & n_people(x1))