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

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

\begin{enumerate}
    \item \label{dpll} Use DPLL with learning to show that $\phi$ is unsatisfiable. Decide variables in \textit{alphabetic order} and starting with the \textit{positive} phase.
    \item State and briefly explain the \textit{resolution rule}.
\item Using your results from \ref{dpll}, give a resolution proof of the unsatisfiability of $\phi$.
\end{enumerate}


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