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\begin{itemize} \item We start by construction $\varphi$: \\ \begin{align*} \varphi &= \varphi_1 \oplus \varphi_2 \\ &= [\varphi_1 \lor \varphi_2] \land \lnot [\varphi_1 \land \varphi_2] = \\ &= [(a \land \lnot b) \lor (\lnot(\lnot a \lor b))] \land \lnot [(a \land \lnot b) \land (\lnot(\lnot a \lor b))] \end{align*}\end{itemize}
$$
\underbracket{ \underbracket{\Big[ \underbracket{\big( a \land \underbracket{\lnot b}_{x_{10}} \big)}_{x_4} \lor \underbracket{\big( \lnot \underbracket{( \underbracket{\lnot a}_{x_{11}} \lor b )}_{x_8} \big)}_{x_5} \Big]}_{x_1} \land \underbracket{ \lnot \underbracket{\Big[ \underbracket{\big( a \land \underbracket{\lnot b}_{x_{12}} \big)}_{x_6} \lor \underbracket{\big( \lnot \underbracket{( \underbracket{\lnot a}_{x_{13}} \lor b )}_{x_9} \big)}_{x_7} \Big]}_{x_3} }_{x_2} }_{x_\varphi} $$
\begin{align*} CNF(\phi) = \ &x_\phi \land \\ &\tseitinAnd{x_{\varphi}}{x_1}{x_2} \land \\ &\tseitinNot{x_2}{x_3} \land \\ &\tseitinOr{x_1}{x_4}{x_5} \land \\ &\tseitinOr{x_3}{x_6}{x_7} \land \\ &\tseitinAnd{x_4}{a}{x_{10}} \land \\ &\tseitinNot{x_5}{x_8} \land \\ &\tseitinAnd{x_6}{a}{x_{12}} \land \\ &\tseitinNot{x_7}{x_9} \land \\ &\tseitinOr{x_8}{x_{11}}{b} \land \\ &\tseitinOr{x_9}{x_{13}}{b} \land \\ &\tseitinNot{x_{10}}{b} \land \\ &\tseitinNot{x_{11}}{a} \land \\ &\tseitinNot{x_{12}}{b} \land \\ &\tseitinNot{x_{13}}{a}\end{align*}
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