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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 $\{\lnot a, \lnot d\}$
  5. \item $\{a, b, c\}$
  6. \item $\{\lnot a, b\}$
  7. \item $\{\lnot b, c\}$
  8. \item $\{\lnot c, d\}$
  9. \item $\{\lnot c, e\}$
  10. \item $\{\lnot d, \lnot e\}$
  11. \end{dpllCNFInput}
  12. % (not a or not d) and (a or b or c) and (not a or b) and (not b or c) and (not c or d) and (not c or e) and (not d or not e)