Friedman's $ \mathsf{WD} $ is not parameter-free sequential

Harvey Friedman's $\mathsf{WD}$ is a weak set theory given by the following non-logical axioms: $\mathsf{(W)} \; \forall x y \, \exists z \, \forall u \left[ \, u \in z \leftrightarrow ( \, u \in x \; \vee \; u = y \, ) \, \right]$; $\mathsf{(D)} \; \forall x y \, \exists z \, \forall u \, \left[ \, u \in z \leftrightarrow ( \, u \in x \; \wedge \; u \neq y \, ) \, \right]$. We answer a question raised by Albert Visser which asks whether $\mathsf{WD}$ is parameter-free sequential. Let $\mathsf{WD} + \mathsf{EXT}$ denote the theory we obtain by extending $\mathsf{WD}$ with the axiom of extensionality. We show that $\mathsf{WD} + \mathsf{EXT}$, and hence also $\mathsf{WD}$, is not parameter-free sequential by using forcing to construct a model $\mathcal{V}^{ \star }$ of $\mathsf{WD} + \mathsf{EXT}$ where $\left( \mathcal{V}^{ \star } , a \right) \simeq \left( \mathcal{V}^{ \star } , b \right)$ for any two elements $a, b$ of $\mathcal{V}^{ \star }$.