\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}