Entropicity conjecture for polymatroids satisfying Ingleton and strong union inequalities

Let $h$ be a polymatroid function on a lattice. The entropicity conjecture. If $h$ satisfies all Ingleton inequalities and all strong union inequalities, then $h$ is entropic. The conjecture is motivated by computer experiments and would characterize entropic polymatroid functions using these two classes of inequalities; the supplied text gives no resolution.