The random k-SAT model is the most important and well-studied distribution over
k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for
satisfiablity algorithms, and lastly average-case hardness over this distribution has also
been linked to hardness of approximation via Feige’s hypothesis. In this paper, we prove
that any Cutting Planes refutation for random k-SAT requires exponential size, for k that
is logarithmic in the number of variables, and in the interesting regime where the number
of clauses guarantees that the formula is unsatisfiable with high probability.

- Re-wrote introduction.
- Numerical changes in proof of main theorem.
- Large editorial changes and notational simplification throughout.

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. In this paper, we prove that any Cutting Planes refutation for random k-SAT requires exponential size, for k that is logarithmic in the number of variables, and in the interesting regime where the number of clauses guarantees that the formula is unsatisfiable with high probability.

Minor edits throughout. Expanded Section 4.2, added Appendix and Conclusion.

The random k-SAT model is the most important and well-studied distribution over
k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for
satisfiablity algorithms, and lastly average-case hardness over this distribution has also
been linked to hardness of approximation via Feige’s hypothesis. In this paper, we prove
that any Cutting Planes refutation for random k-SAT requires exponential size, for k that
is logarithmic in the number of variables, and in the interesting regime where the number
of clauses guarantees that the formula is unsatisfiable with high probability.