Abstract

Resolution and cut-free LK are the most popular propositional systems used for logical automated reasoning. The question whether or not resolution and cut-free LK have the same efficiency on the system of CNF formulas has been asked and studied since 1960 425–467). It was shown in Cook and Reckhow, J. Symbolic Logic 44 36–50 that tree resolution has super-polynomial speed-up over cut-free LK. Naturally, the current issue is whether or not resolution and cut-free LK expressed as directed acyclic graphs have the same efficiency. In this paper, we introduce a new algorithm to eliminate atomic cuts and show that cut-free LK polynomially simulates resolution when the input formula is expressed as a k-CNF formula. As a corollary, we show that regular resolution does not polynomially simulate cut-free LK . We also show that cut-free LK polynomially simulates regular resolution