DPLL algorithm:

\scalebox{0.9}{
\setlength\tabcolsep{3pt}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Step                        & 1 & 2       & 3         & 4         & 5         & 6             & 7                     & 8                 & 9             & 10              & 11 \\ \hline \hline
Decision Level              & 0 & 1       & 1         & 1         & 1         & 1             & 1                     & 2                 & 2             & 2               & 2  \\ \hline
Assignment                  & - & $a$     & $a,b$     & $a,b,c$   & $a,b,c,d$ & $a,b,c,d,e$   & $\lnot a$             & $\lnot a, b$      & $\lnot a,b,c$ & $\lnot a,b,c,d$ & $\lnot a,b,c,d,e$ \\ \hline
Cl. 1: $\lnot a, b$         & 1 & $b$     & \cmark    & \cmark    & \cmark    & \cmark        & \cmark                & \cmark            & \cmark        & \cmark          & \cmark \\ \hline
Cl. 2: $\lnot b, c$         & 2 & 2       & $c$       & \cmark    & \cmark    & \cmark        & 2                     & $c$               & \cmark        & \cmark          & \cmark \\ \hline
Cl. 3: $\lnot c, d$         & 3 & 3       & 3         & $d$       & \cmark    & \cmark        & 3                     & 3                 & $d$           & \cmark          & \cmark \\ \hline
Cl. 4: $\lnot d, e$         & 4 & 4       & 4         & 4         & $e$       & \cmark        & 4                     & 4                 & 4             & $e$             & \cmark \\ \hline
Cl. 5: $\lnot e, \lnot a$   & 5 &$\lnot e$& $\lnot e$ & $\lnot e$ & $\lnot e$ & $\{\}$ \xmark & \cmark                & \cmark            & \cmark        & \cmark          & \cmark \\ \hline \hline
BCP                         & - & $b$     & $c$       &  $d$      & $e$       &   -           &     -                 & $c$               & $d$           & $e$             & \cmark \\ \hline
Decision                    &$a$&   -     &     -     &       -   &    -      & $\lnot a$     & $b$                   &    -              &   -           &     -           & SAT \\ \hline
\end{tabular}}

Model:

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