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\item \lect 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 $(\lnot a \lor d)$ \item $(\lnot d \lor c)$ \item $(\lnot b \lor e)$ \item $(\lnot b \lor \lnot e)$ \item $(b \lor f)$ \item $(b \lor \lnot f)$\end{dpllCNFInput}
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