The abundance conjecture for minimal models

Let $X$ be a minimal model, meaning a complex projective variety with at most terminal singularities and nef canonical divisor $K$. For a nef divisor $K$, its nef dimension $n(X,K)$ is the dimension of the target of the nef reduction map; $K$ has maximal nef dimension when $n(X,K)=\dim(X)$. Abundance conjecture. If $X$ is a minimal $4$-fold and $K$ has maximal nef dimension, then $K$ is big. This is the remaining numerical case needed for the four-dimensional Abundance Conjecture after the cases with smaller nef dimension are known; the supplied text gives no resolution of this statement.