A resolution lower bound for a principle capturing the hardness of depth-1 LK
نویسندگان
چکیده
We introduce principles 2VR and 2VR which imply reflection for, respectively, the CNFs and the narrow CNFs refutable in the depth-1 propositional LK system PK1. We give a polynomial-size refutation of their negations 2VR and 2VR in the system PK1 and show an exponential lower bound on the size of their resolution refutations. We conjecture that they have no small Res(log) refutations; this would be the first such lower bound for a principle with bounded depth refutations. We also show that if any CNF with a small PK1 refutation is exponentially hard for Res(log) then 2VR is as well.
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