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

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