A woman with a Nike hat on is cooking.
A woman wearing a hat is making breakfast.
Because someone is cooking does not mean its breakfast
exists p1 s1 s2 x1 x2 x3.(exists x4.((x1 = x4) & n_cooking(x4)) & Theme(s2,x3) & a_on(s2) & (x1 = x3) & with(x1,x2) & n_hat(x2) & a_nike(s1) & Theme(s1,x2) & n_woman(x1))
exists e1 e2 x1 x2 x3 x4.(Theme(e2,x4) & Actor(e2,x1) & v_make(e2) & n_breakfast(x4) & Theme(e1,x3) & Actor(e1,x2) & v_wear(e1) & n_hat(x3) & (x1 = x2) & n_woman(x1))