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 (β-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.

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