Cheerleaders are on the field cheering.
Cheerleaders cheer for the football team.
Many different sports teams have cheerleaders, so it can't be inferred from sentence 1 that they are cheering for a football team.
exists p1 x1 x2 x3.(n_cheering(x2) & of(x2,x3) & n_field(x3) & on(x1,x2) & n_cheerleader(x1))
exists x1 x2 x3 x4.(n_team(x3) & of(x3,x4) & n_football(x4) & a_topic(x1) & for(x1,x3) & n_cheer(x1) & of(x1,x2) & n_cheerleader(x2))