Lower bounds for Lovasz-Schrijver systems and beyond follow from multiparty communication complexity

We prove that an omega(log(3)n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-disjointness function implies an n omega((1)) size lower bound for tree-like Lovasz-Schrijver systems that refute unsatistiable CNFs. More generally, we prove that an n(Omega(1)) lower bound for the (k + I) -party NOF communication complexity of set-disjointness implies a 2(n Omega(1)) size lower bound for all tree-like proof systems whose formulas are degree k polynomial inequalities.