\item \lect Perform graph-based reduction to translate the following formula in $\mathcal{T}_{E}$ into an
 equisatisfiable formula in propositional logic.
    \begin{equation*}
        \phi_E \;\; := \;\; (a=b \; \lor \; a=d) \imp (b=c \; \land \; c \neq d)
    \end{equation*}