Semi-ampleness conjecture for nef line bundles on Calabi–Yau manifolds

Let $X$ be a projective manifold with torsion canonical bundle, and let $L$ be a nef line bundle on $X$. Semi-ampleness conjecture. The line bundle $L$ is numerically equivalent to a semiample line bundle. This is a consequence of the log abundance conjecture if $L$ is numerically equivalent to a $\mathbb{Q}$-effective line bundle, but it is open even in dimension $3$.