An elderly man is cooking hotdogs outside.
A man is cooking.
An elderly man is a man.  Cooking is a restatement of cooking hotdogs.
exists p1 s1 s2 x1.(a_outside(s2) & Manner(p1,s2) & exists s3 x2.((x1 = x2) & n_hotdog(x2) & a_cooking(s3) & Theme(s3,x2)) & n_man(x1) & a_elderly(s1) & Theme(s1,x1))
exists s1 x1.(Theme(s1,x1) & a_cooking(s1) & n_man(x1))