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Alasdair Urquhart, The Complexity of Propositional Proofs with the Substitution Rule, Logic Journal of the IGPL, Volume 13, Issue 3, May 2005, Pages 287–291, https://doi.org/10.1093/jigpal/jzi021
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Abstract
We prove that for sufficiently large N, there are tautologies of size O(N) that require proofs containing Ω(N) lines in axiomatic systems of propositional logic based on axioms and the rule of substitution for single variables. These tautologies have proofs with O(log2N) lines in systems with the multiple substitution rule.
© The Author, 2005. Published by Oxford University Press. All rights reserved.
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