\begin{frame}[t]{Rutte, Samsom, and the Parliament}
  \begin{block}{\sentence{Only Rutte and Samsom vote for themselves}}
    \pause
    Two solutions:
    \pause
     \begin{itemize}
       \item 
         $\formula{ \binpred{V}{\const{r}}{\const{r}} \logandinf \binpred{V}{\const{s}}{\const{s}} \logandinf 
           \forallst{x}{\big(\, \binpred{V}{x}{x} \;\logimpinf\; \equalto{x}{\const{r}} \logorinf \equalto{x}{\const{s}} \,\big)}}$   
       \item
         $\formula{ \forallst{x}{\big(\, \binpred{V}{x}{x} \;\logbiimpinf\;
            \equalto{x}{\const{r}} \logorinf \equalto{x}{\const{s}} \,\big)}}$
    \end{itemize}
  \end{block} 
  \pause\medskip
  
  \begin{block}{\sentence{All members of parliament except for one vote for Rutte}}
    \pause
    Again two solutions:\pause{} 
    \begin{itemize}
      \item  
        \sentence{There is a member who does not vote for Rutte,}\\
        \sentence{but all others do:}\\[0.75ex]
        \pause
        $\formula{\existsst{x}{\big(\, \unpred{MP}{x} \logandinf \lognot{\binpred{V}{x}{\const{r}}} \logandinf
             \forallst{y}{( \unpred{MP}{y} \logandinf \notequalto{y}{x} \logimpinf \binpred{V}{y}{\const{r}} )}    
         \,\big)}}$
      \pause\smallskip
      \item 
        \sentence{Precisely one human being is a member of parliament}\\ 
        \sentence{and does not vote for Rutte:}\\[0.75ex]  
        \pause
        $\formula{ \existsst{x}{\forallst{y}{\big(\,
           \unpred{MP}{y} \logandinf \lognot{\binpred{V}{y}{\const{r}}}
           \mathrel{\alert{\slogbiimp}}
           \equalto{y}{x}
          \,\big)}}}$
    \end{itemize}
  \end{block} 
\end{frame}