Dragon Ball Z: Zetsubou e no Hankou!! Nokosareta Chousenshi - Gohan to Trunks

It has been thirteen years since the Androids began their killing rampage and Son Gohan is the only person fighting back. He takes Bulma's son Trunks as a student and even gives his own life to save Trunks's. Now Trunks must figure out a way to change this apocalyptic future.
(Source: Anime News Network)