[verb ない-form 〜ない → 〜] + ずにはおかない する → せずにはおかない [verb ない-form] + ではおかない
ずにはおかない means "cannot fail to": something – a film, a speech, an event – is bound to have an effect on people. Take the ない-form and replace ない with ずにはおかない; する becomes せずにはおかない.
The subject is the thing that causes the effect, and the verb is usually a causative of feeling – かんどう感動させる, なかせる泣かせる, おこらせる怒らせる – or a verb like あたえる与える or かえる変える.
ないではおかない goes on the ない-form as it is and means the same; the ず form is the more written. Both are literary – essays, reviews, news commentary. In speech you would say きっと〜~だろう or かならず必ずから~する.With a person as the subject and a deliberate action, the pattern says that person won't rest until it is done. It sounds determined, sometimes threatening.