\item \self Consider the formula $\phi$ that consists of the conjunction of the following clauses:

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

Use the DPLL algorithm (\emph{without} BCP, PL and clause learning) to determine whether or not the set of clauses given is satisfiable. If the set of clauses resulted in \texttt{SAT}, give a satisfying model.
\begin{enumerate}
    \item \label{positive} Decide variables in alphabetical order starting with the \textit{positive} phase.
    \item \label{negative} Decide variables in alphabetical order starting with the \textit{negative} phase.
    \item What differences can you see between \ref{positive} and \ref{negative}? Explain in your own words, why for the DPLL algorithm making good decisions is very important.
\end{enumerate}

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