Shokurov's Gorensteinness conjecture for quotient singularities

Let $X$ be an $n$-dimensional $\mathbb{Q}$-Gorenstein variety, let $p\in X$ be a closed point, and let $\operatorname{mld}_p(X)$ denote the minimal log discrepancy at $p$.

Shokurov's Gorensteinness conjecture. The following assertions hold:

1. $\operatorname{mld}_p(X)\leq n$.
2. If $\operatorname{mld}_p(X)>n-1$, then $X$ is smooth at $p$.
3. If $\operatorname{mld}_p(X)=n-1$, then $X$ is Gorenstein at $p$.

The source states that this conjecture is proved for quotient singularities, including the assertion that one can take $r(n,n-1)=1$ in the index conjecture.