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\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.
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