a b s t r a c tWe consider a proof (more accurately, refutation) system based on the Sherali-Adams (SA) operator associated with integer linear programming. If F is a CNF contradiction that admits a Resolution refutation of width k and size s, then we prove that the SA rank of F is ≤ k and the SA size of F is ≤ (k + 1)s + 1. We establish that the SA rank of both the Pigeonhole Principle PHP n n−1 and the Least Number Principle LNP n is n − 2. Since the SA refutation system rank-simulates the refutation system of Lovász-Schrijver without semidefinite cuts (LS), we obtain as a corollary linear rank lower bounds for both of these principles in LS.

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