a.)\\ \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{5} \dpllStep{1|2|3|4|5} \dpllDecL{0|1|2|3|4} \dpllAssi{ - |$a$|$a, b$|$a, b, c$|\makecell{$a, b, c, $ \\ $d$}} \dpllClause{1}{$\lnot a, b$}{$\lnot a, b$|$b$|\done|\done|\done} \dpllClause{2}{$\lnot a, \lnot d$}{$\lnot a, \lnot d$|$\lnot d$|$\lnot d$|$\lnot d$|\conflict} \dpllClause{3}{$c, \lnot b$}{$c, \lnot b$|$c, \lnot b$|$c$|\done|\done} \dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\done} \dpllBCP{ - | - | - | - | - } \dpllPL{ - | - | - | - | - } \dpllDeci{$a$|$b$|$c$|$d$| - } \end{dplltabular} } \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{2} \dpllStep{6|7} \dpllDecL{3|4} \dpllAssi{$a, b, c$|\makecell{$a, b, c, $ \\ $\lnot d$}} \dpllClause{1}{$\lnot a, b$}{\done|\done} \dpllClause{2}{$\lnot a, \lnot d$}{$\lnot d$|\done} \dpllClause{3}{$c, \lnot b$}{\done|\done} \dpllClause{4}{$\lnot c, d$}{$d$|\conflict} \dpllBCP{ - | - } \dpllPL{ - | - } \dpllDeci{$\lnot d$| - } \end{dplltabular} } \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{2} \dpllStep{8|9} \dpllDecL{2|3} \dpllAssi{$a, b$|$a, b, \lnot c$} \dpllClause{1}{$\lnot a, b$}{\done|\done} \dpllClause{2}{$\lnot a, \lnot d$}{$\lnot d$|$\lnot d$} \dpllClause{3}{$c, \lnot b$}{$c$|\conflict} \dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|\done} \dpllBCP{ - | - } \dpllPL{ - | - } \dpllDeci{$\lnot c$| - } \end{dplltabular} } \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{2} \dpllStep{10|11} \dpllDecL{1|2} \dpllAssi{$a$|$a, \lnot b$} \dpllClause{1}{$\lnot a, b$}{$b$|\conflict} \dpllClause{2}{$\lnot a, \lnot d$}{$\lnot d$|$\lnot d$} \dpllClause{3}{$c, \lnot b$}{$c, \lnot b$|\done} \dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$} \dpllBCP{ - | - } \dpllPL{ - | - } \dpllDeci{$\lnot b$| - } \end{dplltabular} } \hspace{-0.09cm}\scalebox{0.85}{ \begin{dplltabular}{5} \dpllStep{12|13|14|15|16} \dpllDecL{0|1|2|3|4} \dpllAssi{ - |$\lnot a$|$\lnot a, b$|$\lnot a, b, c$|\makecell{$\lnot a, b, c, $ \\ $d$}} \dpllClause{1}{$\lnot a, b$}{$\lnot a, b$|\done|\done|\done|\done} \dpllClause{2}{$\lnot a, \lnot d$}{$\lnot a, \lnot d$|\done|\done|\done|\done} \dpllClause{3}{$c, \lnot b$}{$c, \lnot b$|$c, \lnot b$|$c$|\done|\done} \dpllClause{4}{$\lnot c, d$}{$\lnot c, d$|$\lnot c, d$|$\lnot c, d$|$d$|\done} \dpllBCP{ - | - | - | - | - } \dpllPL{ - | - | - | - | - } \dpllDeci{$\lnot a$|$b$|$c$|$d$|SAT} \end{dplltabular} }