\item \self Consider the following formula from $\mathcal{T}_{E}$.
    \begin{equation*}
        \phi_{EUF}  :=    \big[ f_y = g_x \land f_y = y \big] \lor \big[ f_y = f_x \land y \neq f_{gy} \big] \lor \big[ f_x = f_y \land f_y = y \big] \lor \big[ f_x = f_{gy} \land f_y \neq y \big]
    \end{equation*}
    
    Use the graph-based algorithm to construct an equisatisfiable propositional formula $\phi_{prop}$.

    What would you have to change if you would want to check $\phi_E$ for \textit{validity} instead of satisfiability?