cannot possibly be ~
Expresses that something cannot possibly be the case, often due to obvious reasons or lack of possibility.
This pattern is used to strongly deny the possibility of something. It often appears in written or formal contexts, expressing that something is unthinkable or beyond reach. The nuance is that the event is not just unlikely, but logically or evidently impossible.
It is frequently used with verbs like ある (to exist) or できる (to be possible) to say something like 'cannot possibly exist' or 'cannot possibly be done.' For example, 成功するべくもない means 'there is no way it can succeed.' Note that it is not used in casual conversation; it sounds stiff and literary.
When using with a noun or na-adjective, you need to add である: 彼が犯人であるべくもない (He cannot possibly be the culprit). The pattern is often preceded by phrases that give a reason, like 予想するべくもない (could not have anticipated).