Brown dog runs through snow with a snow covered branch in its mouth.
The dog is fetching the branch for his owner.
Just because the dog has a branch does not mean he was fetching it for his owner.
exists e1 e2 s1 x1 x2 x3 x4 x5.(with(e1,x3) & in(x3,x5) & n_mouth(x5) & of(x5,x1) & n_thing(x1) & n_branch(x3) & Theme(e2,x3) & v_cover(e2) & of(x3,x4) & n_snow(x4) & through(e1,x2) & n_snow(x2) & Actor(e1,x1) & v_run(e1) & n_dog(x1) & a_brown(s1) & Theme(s1,x1))
exists e1 x1 x2 x3.(n_owner(x3) & of(x3,x2) & n_male(x2) & n_branch(x2) & n_dog(x1) & Theme(e1,x2) & Actor(e1,x1) & v_fetch(e1) & for(x2,x3))