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The addition of the symmetry rule to the resolution system sometimes allows considerable shortening in the length of refutations. We prove exponential lower bounds on the size of resolution refutations using two forms of a global symmetry rule. The paper also discusses the relationship of symmetry rules to the extension rule that allows the use of abbreviative deÿnitions in proofs. ? . (A. Urquhart) 0166-218X/99/$ -see front matter ? 1999 Elsevier Science B.V. All rights reserved PII: S 0 1 6 6 -2 1 8 X ( 9 9 ) 0 0 0 3 9 -6doi:10.1016/s0166-218x(99)00039-6 fatcat:kdogbbz7wjhfhgykzstqxsicei