\item \self Use the DPLL algorithm with \textit{Boolean Constrain Propagation} and \textit{Pure Literals} (\emph{without} 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. If the set of clauses resulted in \texttt{SAT}, give a satisfying model.

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

% (not c or d) and (a or not d or not e) and (b or not c) and (c or e) and (not b or not c) and (a or b)