\item \self 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 $\{a, b, \lnot c\}$
    \item $\{\lnot b, c, d\}$
    \item $\{c, d, \lnot e\}$
    \item $\{\lnot a, d, \lnot e\}$
    \item $\{a, b, \lnot d\}$
    \item $\{c, \lnot d, e\}$
\end{dpllCNFInput}

% (a or b or not c) and (not b or c or d) and (c or d or not e) and (not a or d or not e) and (a or b or not d) and (c or not d or e)