I'm making a research on computational complexity theory and have so far been unable to find solution for the following problem:
Find two $\mathbf{NP}$-hard languages $A$ and $B$ such that $A \cap B$ is $\mathbf{coNP}$-complete.
A reminder: $\mathbf{coNP}=\{L|\overline{L}\in \mathbf{NP}\}$.
Usually, such tasks are solved by providing examples of two common $\mathbf{NP}$-hard problems, which are easily to intersect and get the result, but nothing comes to mind in this case.