How to write neither ___ nor ___ in First Order Logic? If X exists, it is neither Y nor Z.

Would this be written as X ⇒ ¬Y ∨ ¬Z  ?

Or would it be X ⇒ ¬(Y ∨ Z)  ?
\begin{equation}
(\exists x \in S)(\exists y, z \in S) \Rightarrow x \neq y \wedge x \neq z
\end{equation}

Where S is some arbitrary set
\begin{equation}
(\exists x \in S)(\exists y, z \in S) \Rightarrow x \neq y \wedge x \neq z
\end{equation}

Where S is some arbitrary set