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

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