Questionnaire-2024/sat_solvers_dpll/0008_sol.tex

\begin{prooftree}
\AxiomC{$ \circled{6} \; c \lor \lnot e$}
\AxiomC{$ \circled{7} \; c \lor e$}
	\BinaryInfC{$c$}
	\AxiomC{$\circled{1} \; \lnot a \lor \lnot c \lor \lnot d$}
		\BinaryInfC{$\lnot a \lor \lnot d$}
		\AxiomC{$\circled{3} \; b \lor d$}
			\BinaryInfC{$\lnot a \lor b$}
\end{prooftree}

The new learned clause is therefore Cl. 8: $\lnot a \lor b$