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

We prove that an omega (log(4) n) lower bound for the three- party number- on- the- forehead ( NOF) communication complexity of the set- disjointness function implies an n.( 1) size lower bound for treelike Lovasz - Schrijver systems that refute unsatisfiable formulas in conjunctive normal form (CNFs). More generally, we prove that an n(Omega(1)) lower bound for the ( k + 1)- party NOF communication complexity of set disjointness implies a 2(n Omega(1)) size lower bound for all treelike proof systems whose formulas are degree k polynomial inequalities.