The mating paradigm for automated theorem provers was proposed by Andrews to avoid some of the shortcomings in resolution. It facilitates automated deduction in higher-order and non-classical logics. Moreover, there are procedures which translate back and forth between refutations by the mating method and proofs in a natural deduction system. We describe a search procedure, called path-focused duplication, for finding refutations by the mating method. This procedure, which is a complete strategy for the mating method, addresses two crucial issues (inadequately handled in current implementations) that arise in the search for refutations: when and how to expand the search space. It focuses on a particular path that seems to cause an impasse in the search and expands the search space relative to this path in a way that allows the search to immediately resolve the impasse. The search space grows and shrinks dynamically to respond to the requirements that have arisen or have been met in the search process, thus avoiding an explosion in the size of the search space. We have implemented a prototype of this procedure and have been able to easily solve many problems that an earlier program found difficult.