I don’t think that a candidate solution to your problem statement can be deterministically verified in polynomial time.

Any candidate solution produced would be subjective to the interpreter who is verifying it as to whether it satisfies the requirements of a proof (maybe they want more definitions, less shorthand notation, maybe in french, references in APA style with full names, etc, all of which would effect the length of the proof).

So whereas a candidate solution to your question is difficult to verify, it is not in this P vs NP discussion.