Abstract
In this paper, we propose different new techniques for introducing additional clauses in a rather restricted way. Most of the new techniques are based on the introduction of a formula C → C and a simple decomposition technique. In order to restrict the introduction of such formulae, we choose C from redundant clauses like clauses C ∀ L with a pure literal L which are derived in the deduction. We prove the correctness of these techniques and introduce a class of propositional formulae for which any resolution refutation has length super-polynomially related to the length of the input formula. We demonstrate how a super-polynomial decrease of proof length can be achieved for these formulae by applying our new techniques in combination with resolution.
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© 1995 Springer-Verlag Berlin Heidelberg
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Egly, U. (1995). Super-polynomial speed-ups in proof length by new tautologies. In: Pinto-Ferreira, C., Mamede, N.J. (eds) Progress in Artificial Intelligence. EPIA 1995. Lecture Notes in Computer Science, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60428-6_3
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DOI: https://doi.org/10.1007/3-540-60428-6_3
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