Are hitting formulas hard for resolution?

Hitting formulas, introduced by Iwama, are an unusual class of propositional CNF formulas. Not only is their satisfiability decidable in polynomial time, but even models can be counted closed form. This stands stark contrast with other polynomial-time classes, which usually have algorithms based on backtracking and resolution for model counting remains hard, like 2-SAT Horn-SAT. However, those resolution-based easily imply upper bound complexity, missing hitting Are formulas hard resolution? In this paper we take the first steps towards answering question. We show that complexity dominated so-called irreducible studied Kullmann Zhao, cannot composed smaller definition, large unsatisfiable difficult to construct; it not known whether infinitely many exist. Building upon our theoretical results, implement efficient algorithm top Nauty software package enumerate all up 14 clauses. also determine exact generated 13 clauses extending a SAT encoding purposes. Our experimental results suggest indeed resolution.