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

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