DPLL algorithm:

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\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline
Step                        & 1 & 2       & 3         & 4         & 5         & 6             & 7                     & 8                 & 9             & 10            \\ \hline \hline
Decision Level              & 0 & 1       & 2         & 3         & 4         & 5             & 5                     & 4                 & 3             & 2             \\ \hline
Assignment                  & - & $a$     & $a,b$     & $a,b,c$   & $a,b,c,d$ & $a,b,c,d,e$   & $a,b,c,d, \lnot e$    & $a,b,c,\lnot d$   & $a,b,\lnot c$ & $a,\lnot b$   \\ \hline
Cl. 1: $\lnot a, b$         & 1 & $b$     & \cmark    & \cmark    & \cmark    & \cmark        & \cmark                & \cmark            & \cmark        & $\{\}$ \xmark \\ \hline
Cl. 2: $\lnot b, c$         & 2 & 2       & $c$       & \cmark    & \cmark    & \cmark        & \cmark                & \cmark            & $\{\}$ \xmark & \cmark        \\ \hline
Cl. 3: $\lnot c, d$         & 3 & 3       & 3         & $d$       & \cmark    & \cmark        & \cmark                & $\{\}$ \xmark     & \cmark        & 3             \\ \hline
Cl. 4: $\lnot d, e$         & 4 & 4       & 4         & 4         & $e$       & \cmark        & $\{\}$ \xmark         & \cmark            & 4             & 4             \\ \hline
Cl. 5: $\lnot e, \lnot a$   & 5 &$\lnot e$&$\lnot e$  & $\lnot e$ & $\lnot e$ & $\{\}$ \xmark & \cmark                & $\lnot e$         & $\lnot e$     & $\lnot e$     \\ \hline \hline
Decision                    &$a$&$b$      & $c$       &  $d$      & $e$       & $\lnot e$     & $\lnot d$             & $\lnot c$         & $\lnot b$     & $\lnot a$     \\ \hline
\end{tabular}}

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\begin{tabular}{|l|c|c|c|c|c|}
\hline
Step                        & 11        & 12            & 13                & 14                    & 15 \\ \hline \hline
Decision Level              & 1         & 2             & 3                 & 4                     & 5 \\ \hline
Assignment                  & $\lnot a$ & $\lnot a, b$  & $\lnot a, b, c$   & $\lnot a, b, c, d$    & $\lnot a, b, c, d, e$ \\ \hline
Cl. 1: $\lnot a, b$         & \cmark    & \cmark              & \cmark                  & \cmark                      & \cmark \\ \hline
Cl. 2: $\lnot b, c$         & 2          &   $c$            &  \cmark                 &  \cmark                     & \cmark  \\ \hline
Cl. 3: $\lnot c, d$         &  3         &  3             &   $d$                &  \cmark                     & \cmark \\ \hline
Cl. 4: $\lnot d, e$         & 4          & 4              & 4                  & $e$                      & \cmark \\ \hline
Cl. 5: $\lnot e, \lnot a$   & \cmark          &  \cmark             & \cmark                  &  \cmark                     & \cmark \\ \hline \hline
Decision                    & $b$          & $c$              & $d$                  &  $e$                     & SAT  \\ \hline
\end{tabular}}

Model:

$a$ = F, $b$ = T, $c$ = T, $d$ = T, $e$ = T
