\item \prac \textbf{[3 Points]} Given the formula: 
    \begin{equation*} \varphi_{EUF} \quad := \quad  x=f(x,y) \land x \neq y \leftrightarrow z=f(x,y) \lor \\
    f(y,z) \neq z \land y \neq f(x,y) \lor y=f(x,z)
    \end{equation*}
Apply the \emph{Ackermann} reduction algorithm to compute an equisatisfiable formula in $\mathcal{T}_{E}$.