This paper considers the length of resolution proofs when using
Krishnamurthy's classic symmetry rules. We show that inconsistent linear
equation systems of bounded width over a fixed finite field Fp with
p a prime have, in their standard encoding as CNFs, polynomial length
resolutions when using the local symmetry rule (SRC-II).
As a consequence it follows that the multipede instances for the graph
isomorphism problem encoded as CNF formula have polynomial length resolution
proofs. This contrasts exponential lower bounds for
individualization-refinement algorithms on these graphs.
For the Cai-F\"urer-Immerman graphs, for which Tor\'an showed exponential
lower bounds for resolution proofs (SAT 2013), we also show that already the
global symmetry rule (SRC-I) suffices to allow for polynomial length proofs.Comment: 18 pages, to be published in STACS 202