The planetary crust contains life 30 kms down. Even if the surface was sterilized and the oceans boild away, life would return from the life in the crust. It would take a long time to "rediscover" the innovations like chlorophyll, but in the end, life would recover completely.
This is self-contradictory. If the oceans boiled away it would be because of rising temperatures that caused evaporation, but the temperature would rise everywhere (even 30 kms down), meaning that the crust would also be inhospitable to life due to drying out.
