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MaxSAT Resolution is a version of Resolution designed to solve the MaxSAT problem. However, it is also possible to use it as a refutation system.

We analyze MaxSAT Resolution (MaxRes), MaxRes with weakening (MaxResW), and a related proof system, SubCubeSums, which is a special case of Sherali–Adams:

• We show that Res p-simulates MaxResW and that MaxResW p-simulates treelike Res, and separate MaxRes from TreeRes.
• We show that SubCubeSums p-simulates MaxResW and is not p-simulated by Res.
• We show that Tseitin contradictions on expanders are hard for SubCubeSums and so for MaxResW. While it is already known that these contradictions are hard for Res, our proof is different. We hope that it could be used to separate Res and MaxResW.