  We prove a sufficient condition under which a semigroup admits no finite
identity basis. As an application, it is shown that the identities of the
Kauffman monoid $\mathcal{K}_n$ are nonfinitely based for each $n\ge 3$. This
result holds also for the case when $\mathcal{K}_n$ is considered as an
involution semigroup under either of its natural involutions.
