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  1. \item Use the DPLL algorithm with conflict-driven clause learning to determine whether or not the set of clauses given is satisfiable. Decide variables in alphabetical order starting with the \textit{negative} phase. For conflicts, draw conflict graphs after the end of the table, and add the learned clause to the table.\\
  2. 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.
  3. \begin{dpllCNFInput}
  4. \item $\{b, c, d\}$
  5. \item $\{\lnot a, \lnot c\}$
  6. \item $\{b, c\}$
  7. \item $\{\lnot b, \lnot d\}$
  8. \item $\{\lnot d, e\}$
  9. \item $\{d, e\}$
  10. \item $\{\lnot c, \lnot e\}$
  11. \item $\{\lnot b, c, \lnot d\}$
  12. \end{dpllCNFInput}
  13. % (b or c or d) and (not a or not c) and (b or c) and (not b or not d) and (not d or e) and (d or e) and (not c or not e) and (not b or c or d)