MaxSAT Resolution and Subcube Sums

We study the MaxSAT Resolution (MaxRes) rule in context of certifying unsatisfiability. show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p -simulates resolution. In devising a lower bound technique specific to MaxRes (and not merely inheriting bounds from Res), we define new proof called SubCubeSums system. This system, which MaxResW, viewed as special case semi-algebraic Sherali–Adams expressivity, is integral restriction conical juntas studied contexts communication complexity extension complexity. simulated by Res. Using qualitatively different MaxResW inherits Res, Tseitin contradictions on expander graphs are hard refute SubCubeSums. also establish via lifting: for formulas requiring large degree SubCubeSums, their XOR-ification requires size