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\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{positive} phase. For conflicts, draw conflict graphs after the end of the table, and add the learned clause to the table.\\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 $\{\lnot a, d\}$ \item $\{\lnot d, c, \lnot a\}$ \item $\{\lnot b, e\}$ \item $\{\lnot b, \lnot e\}$ \item $\{\lnot b, f\}$ \item $\{b, \lnot f\}$\end{dpllCNFInput}
% (not a or d) and (not d or c or not a) and (not b or e) and (not b or not e) and (not b or f) and (b or not f)
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