<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[convert={outfile=\jobname.svg}]{standalone}

\usepackage{proof}
\usepackage{amsmath}
\usepackage{utf8}

\begin{document}

$$
\infer[â†’~intro]{âŠ¢ Â¬(Pâˆ§Q) â†’ Â¬Pâˆ¨Â¬Q}{
  \infer[âˆ¨~elim]{Â¬(Pâˆ§Q) âŠ¢ Â¬Pâˆ¨Â¬Q}{
    \infer[excl.~mid.]{Â¬(Pâˆ§Q) âŠ¢ Pâˆ¨Â¬P}{}
    &amp;
    \infer[âˆ¨~elim]{Â¬(Pâˆ§Q), P âŠ¢ Â¬Pâˆ¨Â¬Q}{
      \infer[excl.~mid.]{Â¬(Pâˆ§Q),P âŠ¢ Qâˆ¨Â¬Q}{}
      &amp;
      \infer[absurd]{Â¬(Pâˆ§Q),P,Q âŠ¢ Â¬Pâˆ¨Â¬Q}{
        \infer[âˆ§~intro]{Â¬(Pâˆ§Q),P,Q âŠ¢ Pâˆ§Q}{
          \infer[assum]{Â¬(Pâˆ§Q),P,Q âŠ¢ P}{}
          &amp;
	  \infer[assum]{Â¬(Pâˆ§Q),P,Q âŠ¢ Q}{}
        }
        &amp;
	\infer[assum]{Â¬(Pâˆ§Q),P,Q âŠ¢ Â¬(Pâˆ§Q)}{}
      }
      &amp;
      \infer[âˆ¨~intro]{Â¬(Pâˆ§Q), P, Â¬Q âŠ¢ Â¬Pâˆ¨Â¬Q}{
	\infer[assum]{Â¬(Pâˆ§Q), P, Â¬Q âŠ¢ Â¬Q}{} 
      }
    }
    &amp;
    \infer[âˆ¨~intro]{Â¬(Pâˆ§Q), Â¬P âŠ¢ Â¬Pâˆ¨Â¬Q}{
      \infer[assum]{Â¬(Pâˆ§Q), Â¬P âŠ¢ Â¬P}{} 
    }
  }
}
$$

\end{document}
</pre></body></html>