\item \self Consider the following formula from $\mathcal{T}_{E}$.
    \begin{equation*}
        \phi_{EUF} \quad := \quad  x \neq y \land y = g_x \lor g_x = g_y \rightarrow \neg (g_y \neq z \lor z = f_x) \land \neg (f_x = f_y \land x \neq z)
    \end{equation*}

    Use the graph-based algorithm to construct an equisatisfiable propositional formula $\phi_{prop}$.