A band is practicing their routine.
A band rehearses for the battle of the band competiton.
We can't infer that they are practicing for the battle of the band competition, it could be for anything.
exists e1 x1 x2.(Theme(e1,x2) & Actor(e1,x1) & v_practice(e1) & n_routine(x2) & of(x2,x1) & n_thing(x1) & n_band(x1))
exists e1 x1 x2 x3.(n_battle(x2) & for(e1,x2) & of(x2,x3) & n_competiton(x3) & of(x3,x1) & n_band(x1) & n_band(x1) & Actor(e1,x1) & v_rehearse(e1))