Non-Elementary Speed-Ups in Proof Length by Different Variants of Classical Analytic Calculi

. In this paper, different variants of classical analytic calculi for first-order logic are compared with respect to the length of proofs possible in such calculi. A cut-free sequent calculus is used as a prototype for different other analytic calculi like analytic tableau or various connection calculi. With modified branching rules (fi--rules), non-elementary shorter minimal proofs can be obtained for a class of formulae. Moreover, by a simple translation technique and a standard sequent calculus, analytic cuts, i.e., cuts where the cut formulae occur as subformulae in the input formula, can be polynomially simulated. 1 Introduction Analytic first-order calculi like (free-variable) analytic tableaux [4, 15, 23] or various connection calculi [5] are well suited for implementing automated deduction on a computer. In order to search for a proof in such calculi, only subformulae of the input formula have to be considered. This property, often referred to as the subformula property, makes..