Random Θ(log n)-CNFs Are Hard for Cutting Planes

The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics and is a benchmark for satisfiability algorithms. We show that when k = Θ(log n), any Cutting Planes refutation for random k-SAT requires exponential size in the interesting regime where the number of clauses guarantees that the formula is unsatisfiable with high probability. Keywords-Proof complexity; random k-SAT; Cutting Planes;