\item Use the DPLL algorithm with no explicit heuristics to determine whether or not the set of clauses given is satisfiable. Decide variables in alphabetical order starting with the \textit{negative} phase.\\
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 b \lor c)
  \item (\lnot a \lor \lnot b)
  \item (\lnot a \lor \lnot c)
  \item (b \lor \lnot c)
  \item (\lnot b \lor c)
\end{dpllCNFInput}

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