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