People search for their seats in a stadium.
People are going to see a baseball game.
You cannot assume they are at a baseball game, and it is not implied. Not all games are that of baseball.
exists x1 x2 x3 x4.(a_topic(x1) & for(x1,x3) & in(x3,x4) & n_stadium(x4) & n_seat(x3) & of(x3,x1) & n_thing(x1) & n_search(x1) & of(x1,x2) & n_people(x2))
exists e1 p1 x1.(Topic(e1,p1) & Actor(e1,x1) & v_go(e1) & exists e2 x2 x3.(Theme(e2,x2) & Actor(e2,x1) & v_see(e2) & n_game(x2) & of(x2,x3) & n_baseball(x3)) & n_people(x1))