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\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 $\phi_{prop}$.