They are playing ice-hockey.
The home team is currently winning the game.
Just because they are playing ice-hockey it doesn't mean the home team is winning the game. The home team may be losing.
exists e1 x1 x2.(n_thing(x1) & Theme(e1,x2) & Actor(e1,x1) & v_play(e1) & n_ice-hockey(x2))
exists e1 s1 x1 x2 x3.(n_game(x3) & n_team(x1) & of(x1,x2) & n_home(x2) & a_currently(s1) & Manner(e1,s1) & Theme(e1,x3) & Actor(e1,x1) & v_win(e1))