Random Θ(log n)-CNFs are hard for Cutting Planes - Fleming, Noah ; 0000-0002-8636-1290; Pankratov, Denis; Pitassi, Toniann; Robere, Robert (Journal of the ACM, 2022)
The random k-SAT model is one of the most important and well-studied distributions 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 length in the regime where the number of clauses guarantees that the formula is unsatisfiable with high probability.