Conforti–Cornuéjols conjecture for square-free monomial ideals

Let $I$ be a square-free monomial ideal. The packing property means that every minor of the clutter associated to $I$ has the König property, namely, its minimum vertex-cover number equals its maximum matching number. The symbolic power $I^{(s)}$ is defined by

$$I^{(s)} = \bigcap_{\mathfrak{p} \in \operatorname{Ass}(I)} I^s R_{\mathfrak{p}} \cap R.$$

Conforti–Cornuéjols conjecture. All symbolic powers and ordinary powers of $I$ coincide if and only if $I$ has the packing property:

$$I^{(s)}=I^s \quad\text{for every }s\geq 1.$$

This is the commutative-algebra formulation of the Conforti–Cornuéjols packing problem, relating equality of symbolic and ordinary powers to a combinatorial property of the associated clutter. The supplied text states that the conjecture is proved for the class of Alexander duals of connected ideals considered in the paper, but gives no general resolution, so its overall status is left open.