I recently refereed a paper that I returned to the author(s) for revision. The thrust of their argument relied on a claim whose justification I felt was lacking. I dutifully raised the issue in my report and, in addition, I corrected another portion of their proof.

The author(s) have yet to revise their work and, in the interim, I came up with a justification for their claim. I now have a proof of this result (which is important for another paper I'm working on) and would like to publish it.

What are the ethics/options here? Do I need to provide them with the correct proof? May I submit the result as my own after their revision? Should I recuse myself from serving as the referee?

**EDIT:** Not sure if this makes a difference, but the conjecture the author(s) purports to resolve is one that I raised in a previous a paper and one for which I obtained partial results with similar methods. Although, I have worked on the problem and obtained partial results, I would not have obtained a proof without refereeing their work.