  Usuba has asked whether the $\kappa$-mantle, the intersection of all grounds
that extend to $V$ via a forcing of size ${<}\kappa$, is always a model of ZFC.
We give a negative answers by constructing counterexamples where $\kappa$ is a
Mahlo cardinal, $\kappa=\omega_1$ and where $\kappa$ is the successor of a
regular uncountable cardinal.
