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

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