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DPLL algorithm:
\begin{tabular}{|l|c|c|c|c|c|}\hlineStep & 1 & 2 & 3 & 4 & 5 \\ \hline \hlineDecision Level & 0 & 0 & 0 & 0 & 0 \\ \hlineAssignment & - & $\lnot a$ & $\lnot a,\lnot b$ & $\lnot a,\lnot b,\lnot c$ & $\lnot a,\lnot b,\lnot c,\lnot d$ \\ \hlineCl. 1: $\lnot a, b$ & 1 & \cmark & \cmark & \cmark & \cmark \\ \hlineCl. 2: $\lnot b, c$ & 2 & 2 & \cmark & \cmark & \cmark \\ \hlineCl. 3: $\lnot c, d$ & 3 & 3 & 3 & \cmark & \cmark \\ \hlineCl. 4: $\lnot d, e$ & 4 & 4 & 4 & 4 & \cmark \\ \hlineCl. 5: $\lnot e, \lnot a$ & 5 &\cmark& \cmark & \cmark& \cmark\\ \hline \hlineBCP & - & - & - & - & - \\ \hlinePL & $\lnot a$ & $\lnot b$ & $\lnot c$ & $\lnot d$ & - \\ \hlineDecision & - & - & - & - & SAT \\ \hline\end{tabular}
Model:
$a$ = F, $b$ = F, $c$ = F, $d$ = F, $e$ = F
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