No, not learning. And the 'do nothing else' parts can't be left out.

This shouldn't be a general automatic programing method, just something that goes through the motions of solving this one problem. It should already 'know' whatever principles lead to that solution. The outcome should be obvious to the programmer, and I suspect realistically hand-traceable. My goal is a solid understanding of a toy program exactly one meta-level above hanoi.

This does seem like something Prolog could do well, if there is already a static program that does this I'd love to see it.