\item Use the DPLL algorithm with \textit{Boolean Constrain Propagation} (\emph{without} PL and 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 $(\lnot f \lor \lnot b \lor \lnot a)$
        \item $(\lnot e \lor a \lor \lnot d)$
        \item $(\lnot a \lor c \lor b)$
        \item $(f \lor \lnot a \lor e)$
        \item $(d \lor \lnot a \lor \lnot b)$
        \item $(\lnot a \lor \lnot c \lor b)$
    \end{dpllCNFInput}