Here, we are given an $n\times n$ Boolean matrix $A$ and an $n\times n$ Boolean matrix $B$ and a mapping $color : [n] \to \Gamma$. For each $i\in [n]$ and $j\in [n]$, we want to decide whether $\{color(k) : A[i, k] \wedge B[k, j], k \in [n]\} = \Gamma$. In other words, for every pair of $i$, $j$, we want to determine whether the witnesses cover all the colors.