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\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}
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