\documentclass{slides}

\usepackage{exptrees}

\pagestyle{empty}

\begin{document}
\begin{slide} %\setlength\parskip{0.7\parskip}
\begin{center} %{\bfseries Cut elimination} 

%\vspace{-2ex}
\bpf
\A "$A \vdash A$"
\U "$A, B \vdash A$"
\U "$A \land B \vdash A$"
\U "$\bullet A \land B \vdash \bullet A$"
\U "$\bullet A \land B \vdash \smile A$"
\U "$\smile (A \land B) \vdash \smile A$"
\A "$A \vdash A$"
\U "$A \vdash A, C$"
\U "$A \vdash A \lor C$"
\U "$\bullet A \vdash \bullet A \lor C$"
\U "$\smile A \vdash \bullet A \lor C$"
\U "$\smile A \vdash \smile (A \lor C)$"
\B "$\smile (A \land B) \vdash \smile (A \lor C)$"
\epf

\end{center} 
\end{slide}
\begin{slide}
\begin{center} %{\bfseries Cut elimination} 

%\vspace{-2ex}
\bpf
\A "$A \vdash A$"
\U "$A \vdash A, C$"
\U "$A \vdash A \lor C$"
\U "$\bullet A \vdash \bullet A \lor C$"
\U "$A \vdash \bullet \bullet A \lor C$"
\U "$A, B \vdash \bullet \bullet A \lor C$"
\U "$A \land B \vdash \bullet \bullet A \lor C$"
\U "$\bullet A \land B \vdash \bullet \bullet \bullet A \lor C$"
\U "$\bullet \bullet A \land B \vdash \bullet \bullet A \lor C$"
\U "$\bullet A \land B \vdash \bullet A \lor C$"
\U "$\bullet A \land B \vdash \smile (A \lor C)$"
\U "$\smile (A \land B) \vdash \smile (A \lor C)$"
\epf
\end{center}
\end{slide}
  
\end{document}

