  Using Isabelle/HOL, we verify the state-of-the-art decision procedure for
multi-level syllogistic with singleton (MLSS for short), which is a
quantifier-free fragment of set theory. We formalise its syntax and semantics
as well as a sound and complete tableau calculus for it. We also provide an
executable specification of a decision procedure that exhaustively applies the
rules of the calculus and prove its termination. Furthermore, we extend the
calculus with a lightweight type system that paves the way for an integration
of the procedure into Isabelle/HOL.
