Happy man grilling meat on his barbecue.
The father prepares dinner in the back yard.
A man does not have to be a father.  Just because a man is grilling it does not mean he prepares dinner.
exists e1 s1 x1 x2 x3.(a_topic(x1) & on(x1,x3) & n_barbecue(x3) & of(x3,x1) & n_male(x1) & n_meat(x1) & Actor(e1,x1) & v_grill(e1) & of(x1,x2) & n_man(x2) & a_happy(s1) & Theme(s1,x1))
exists e1 s1 x1 x2 x3.(n_yard(x3) & a_back(s1) & Theme(s1,x3) & n_father(x1) & Theme(e1,x2) & Actor(e1,x1) & v_prepare(e1) & in(x2,x3) & n_dinner(x2))