On the maximal minimal cube lengths in distinct DNF tautologies

Inspired by a recent article by Anthony Zaleski and Doron Zeilberger, we investigate the question of determining the largest k for which there exists boolean formulas in disjunctive normal form (DNF) with n variables, none of whose conjunctions are `parallel', and such that all of them have at least k literals. Using a SAT solver, we answer some of the questions they left open. We also determine the corresponding numbers for DNFs obeying certain symmetries.