\begin{definition}[Definition:Contradictory/Branch]
Let $T$ be a labeled tree for propositional logic.
Let $\Gamma$ be a branch of $T$.
Then $\Gamma$ is a '''contradictory branch''' {{iff}}, for some WFF of propositional logic $\mathbf A$, both $\mathbf A$ and $\neg \mathbf A$ occur along $\Gamma$.
\end{definition}