Refutations by Matings

Occurrences of literals in the initial clauses of a refutation by resolution (with each clause-occurrence used only once) are mated iff their descendants are resolved with each other. This leads to an abstract notion of a mating as a relation between: occurrences of literals in a set of clause-occurrences. The existence of many refutations with the same mating leads to wasteful redundancy in the search for a refutation, so it is natural to focus on the essential problem of finding appropriate matings.