  L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local
formations $\mathfrak{F}$ of finite groups such that every finite minimal
non-$\mathfrak{F}$-group is either a Schmidt group or a group of prime order.
All known solutions to this problem are obtained under the assumption that
every minimal non-$\mathfrak{F}$-group is soluble. Using the above mentioned
solutions we present a polynomial in $n$ time check for a local formation
$\mathfrak{F}$ with bounded $\pi(\mathfrak{F})$ to be a formation of soluble
groups with the Shemtkov property where $n=\max \pi(\mathfrak{F})$.
