Sadaharu: I think John is correct. The problem seems to be assuming that black needs to take the stone, but black may ignore the atari depending on the situation. Maybe it will be better to just exchange the atari first.
John: The counting of liberties is wrong in this problem - Black can sacrifice O14 stones and be in time to kill White. See sgf for the position I had, it was marked as seki. Did I miss something?
Thank you.