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\item Use the DPLL algorithm with conflict-driven clause learning to determine whether or not the set of clauses given is satisfiable. Decide variables in alphabetical order starting with the \textit{negative} phase. For conflicts, draw conflict graphs after the end of the table, and add the learned clause to the table.\\
If the set of clauses resulted in \texttt{SAT}, give a satisfying model. If the set of clauses resulted in \texttt{UNSAT}, give a resolution proof that shows that the conjunction of the clauses from the table is unsatisfiable.
\begin{dpllCNFInput}
\item $\{\lnot c, \lnot d\}$
\item $\{c, e\}$
\item $\{\lnot d, c\}$
\item $\{d, \lnot e\}$
\item $\{b, \lnot d\}$
\item $\{\lnot d, \lnot e\}$
\item $\{a, c\}$
\end{dpllCNFInput}