Learn Russian: Если воинам не одолеть колдуна, быть великой беде и гибели! - If the warriors cannot defeat the sorcerer, great trouble and ruin are inevitable!

This is the classic structure for independent infinitive clauses. When you combine a logical subject in the Dative case (воинам, беде и гибели) with an infinitive verb (одолеть, быть), it expresses that an action is either completely impossible or absolutely inevitable, depending on the context and whether there is a negative particle.

How does не одолеть translate to 'cannot defeat' instead of just 'not to defeat'?

When you use the negative particle не followed by a perfective infinitive like одолеть, it creates a strong sense of impossibility. It means the action simply cannot be accomplished by the Dative subject. If you wanted to state a simple future fact like 'they will not defeat him', you would use a standard conjugated verb.

Would the meaning change if the imperfective verb одолевать was used instead of the perfective одолеть?

Yes, drastically! In infinitive clauses, не plus an imperfective infinitive usually expresses prohibition (you must not do it) or lack of necessity (there is no need to do it). Using the perfective одолеть is what locks in the meaning of physical or circumstantial impossibility.

How does the single word быть mean 'are inevitable' in the second clause?