Quantum algorithms for Prolog or automated theorem proving?

Are there quantum algorithms for Prolog (SLD resolution – unification and depth-first-search) or for automated theorem proving in general (negation, resolution, and SAT)?

Usually automated theorem proving involves SAT problem for the negation of the initial statement and there is some better (but no exceptionally better) algorithms for that, e.g. Do any quantum algorithms improve on classical SAT?. But maybe there are some new ideas, some holistic approaches that involve the parallel search available on quantum computers? Google is of no help (“automated theorem proving quantum algorithm” no any result).