ずにはおかない・ずにはすまない: the difference
ずにはおかないN1
Meaning
Will definitely, Will certainly, Bound to, Not fail to
Past papers
Example
小説、勇者：「どんな手段を用いても、かならず魔王を倒さずにはおかない。」
Novel, Hero: 'No matter what it takes, I will not fail to defeat the Demon Lord!'
ずにはすまないN1
Meaning
Won't get away without, Won't get off without, Have to, Have no choice but to, Can’t not
Past papers
Example
重要な会議だから、間に合わないではすまない。
It's an important meeting, so I won't get away without making it on time.
How to tell them apart
「〜ずにはおかない」: the subject forcibly affects the object; a person won't rest, a thing inevitably moves people.
「〜ずにはすまない」: under social duty and responsibility, you can't get away without doing it.
「〜てやまない」: a sincere, lasting hope or wish, e.g. 「祈ってやまない」 (I sincerely pray).