Random \( \Theta (\log n) \) -CNFs are Hard for Cutting Planes

Abstract

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 \( k = \Theta (\log n) \), 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.