\item \prac \textbf{[5 Points]} Consider the following formula in $\mathcal{T}_{EUF}$:
    \begin{equation*}
           \varphi_{EUF} \quad := (y = z \lor f(x) = f(y)) \imp ( x = z \vee f(x) = x \wedge f(x) = y)
    \end{equation*}
        
    Use Ackermann's reduction to compute an equisatisfiable formula in $\mathcal{T}_{E}$.
    
    Then perform the graph-based reduction on the outcome of Ackermann's reduction to construct an equisatisfiable propositional formula.