Abstract. In 1980 Monien and Speckenmeyer proved that satisfiability of a propositional formula consisting of K clauses (of arbitrary length) can be checked in time of the order 2K/3. Recently Kullmann and Luckhardt proved the worst-case upper bound 2L/9, where L is the length of the input formula. The algorithms leading to these bounds are based on the splitting method which goes back to the Davis-Putnam procedure. Transformation rules (pure literal elimination, unit propagation etc.) constitute a substantial part of this method. In this paper we present a new transformation rule and two algorithms using this rule. We prove that these algorithms have the worst-case upper bounds 20.30897K and 20.10299L respectively.
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