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\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 e \land \; e \neq d)
\end{equation*}