Universal abstract consistency class and universal refutation

Refutation methods based on the resolution principle are generally applied to a (finite) set of sentences, which must have a series of pre-transformations (prenex normalization, Skolemization and conjunction normalization) before starting the refutation. In this paper, the authors first generalize the concept to abstract consistency class to the most general form—universal abstract consistency class, and prove its universal unifying principle. Then, based on theR-refutation, a universal refutation method is proposed and its soundness and completeness are proved by means of the universal unifying principle. This method can be applied directly to any finite set of wffs without preprocessing the wffs at all so that the refutation procedure is more natural.