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\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 $\{b, d\}$ \item $\{b, c\}$ \item $\{\lnot b, \lnot e\}$ \item $\{\lnot a, \lnot c\}$ \item $\{\lnot c, \lnot d\}$ \item $\{\lnot b, c\}$ \item $\{a, b\}$ \item $\{\lnot b, d, e\}$\end{dpllCNFInput}
% (b or d) and (b or c) and (not b or not e) and (not a or not c) and (not c or not d) and (not b or c) and (a or b) and (not b or d or e)
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