Could life at TRAPPIST-1 survive the star's superflares?

The TRAPPIST-1 system is a science-fiction writer's dream. Seven Earth-sized worlds orbit a red dwarf star just 40 light-years away. Three of those worlds are within the habitable zone of the star. The system spans a distance less than 25 times that of the distance from the Earth to the moon. Oh, what epic tales a TRAPPIST civilization would have. That is, if life in such a system is even possible.