  We prove that for any free lattice F with at least $\aleph\_2$ generators in
any non-distributive variety of lattices, there exists no sectionally
complemented lattice L with congruence lattice isomorphic to the one of F. This
solves a question formulated by Gr\"{a}tzer and Schmidt in 1962. This yields in
turn further examples of simply constructed distributive semilattices that are
not isomorphic to the semilattice of &#64257;nitely generated two-sided ideals
in any von Neumann regular ring.
