N1
ずにはすまない
Won't get away without, Won't get off without, Have to, Have no choice but to, Can’t not
取引先のお偉いさんに飲みに誘われたから、行かずにはすまない。
A high-ranking business partner invited me out for a drink, so I have no choice but to go.
Explanation
「Vずにはすまない」 means 'you cannot get away without doing ...'. It is not that you want to; given social duty, rules or responsibility, the matter cannot be settled unless you do it: 「他人にこれだけの損害を与えた以上、弁償せずにはすまない」 (Having caused this much damage to others, I can't get off without compensating them). It is heavy, formal language; speech often uses 「〜ないではすまない」. The verb 「する」 becomes 「せずにはすまない」 and 「来る」 becomes 「来ずにはすまない」.
Mixed up with
「〜ずにはすまない」: social duty or responsibility; things can't be settled unless you do it (apologize, compensate, be punished).
「〜ずにはいられない」: an urge you can't hold back (laughing, crying).
「〜ざるを得ない」: circumstances leave no other choice; you have to do it against your will, e.g. have to resign.