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