\item Use the DPLL algorithm with BCP and PL to determine whether or not the set of clauses given is satisfiable. Decide variables in alphabetical order starting with the \textit{negative} phase.\\
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 \lor b)
  \item (a \lor c)
  \item (d \lor e)
  \item (\lnot b \lor \lnot c)
  \item (e \lor \lnot f)
  \item (\lnot d \lor \lnot f)
  \item (d \lor \lnot f)
  \item (b \lor e)
  \item (a \lor \lnot f)
\end{dpllCNFInput}