\item \self For the following $\mathcal{T}_{EUF}$-formula, compute an equisatisfiable formula $\phi_{E}$ in the \textit{Theory of Equality} $\mathcal{T}_{E}$, by applying \textit{Ackermann's Reduction}.
    $$\phi_{EUF} \quad := \quad f(x,y)=g(x) \imp \left[f(g(y),z)=x \lor \lnot(g(z)=y)\right].$$