The $3$-closure of a solvable permutation group is solvable

Let $m$ be a positive integer and let $\mathrm{\Omega }$ be a finite set. The $m$-closure of $G\le \mathrm{Sym}(\mathrm{\Omega })$ is the largest permutation group on $\mathrm{\Omega }$ having the same orbits as $G$ in its induced action on the Cartesian product ${\mathrm{\Omega }}^m$. The $1$-closure and $2$-closure of a solvable permutation group need not be solvable. We prove that the $m$-closure of a solvable permutation group is always solvable for $m\ge 3$.