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