The $(-\infty)$-conjecture

Let $X$ be a smooth projective variety. A variety is uniruled if there are a variety $B$ of dimension $\dim X-1$ and a dominant rational map $B\times \mathbb{P}^1 \dashrightarrow X$. The $(-\infty)$-conjecture. If $X$ is not uniruled, then $\kappa(X)\geq 0$. This is the converse to the fact that uniruled varieties have Kodaira dimension $-\infty$, and is stated as a consequence of the good minimal model conjecture; its resolution is not supplied here.