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\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 \lor c) \item (\lnot a \lor \lnot b) \item (\lnot a \lor \lnot c) \item (b \lor \lnot c) \item (\lnot b \lor c)\end{dpllCNFInput}
% (a or b or c) and (not a or not b) and (not a or not c) and (b or not c) and (not b or c)
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