\item Use the DPLL algorithm with BCP 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 $(\lnot x \lor y)$
  \item $(\lnot y \lor \lnot z)$
  \item $(x \lor \lnot w)$
  \item $(w \lor z)$
  \item $(\lnot z \lor u)$
  \item $(\lnot u \lor \lnot x)$
  \end{dpllCNFInput}