Shokurov's toric equality conjecture for log canonical pairs

Let $X$ be a normal $\mathbb{Q}$-factorial algebraic variety with a $\mathbb{Q}$-boundary divisor $D=\sum d_iD_i$, where $0\leq d_i\leq 1$ and the $D_i$ are prime Weil divisors. Assume that $-(K_X+D)$ is nef and that the pair $(X,D)$ is log canonical. Shokurov's toric equality conjecture. The estimate

$$\sum d_i\leq \operatorname{rk}\operatorname{Pic}(X)+\dim X$$

holds. Moreover, equality is achieved if and only if $(X,\lfloor D\rfloor)$ is toric, meaning that $X$ is toric and $\lfloor D\rfloor$ is its boundary. This gives a numerical criterion for recognizing toric varieties among log canonical pairs, but the supplied text does not state whether the claim has been resolved.