\begin{frame}[t]{Not Valid Formula (Example)}
  \exampleloverlover
  \pause\bigskip
  
  The formula $\aform$ is \emph{not valid}:
  \pause
  \begin{exampleblock}{}
    Let $\model{\amodeli{2}}$ have domain $\model{\adomaini{2}} = \setexp{ a, g, f, w }$,
    $ \intin{\const{alma}}{\model{\amodeli{1}}} = a$, and:
    \begin{talign}
      \intin{\sbinpred{loves}}{\model{\amodeli{2}}} 
      & = \setexp{ \pair{a}{g}, \pair{a}{f}, \pair {a}{w}, \pair{a}{a},
                   \pair{g}{a}, \pair{f}{a}, \pair{w}{a} } 
%       \\[-0.5ex] & \supseteq \setexp{ \pair{g}{a}, \pair{a}{g}, \pair{a}{a} }
    \end{talign}
    \pause
    In this model:
    \begin{itemize}
      \item Alma herself is a lover of a lover of herself.
    \pause
      \item Alma loves herself.
    \pause   
    \end{itemize} 
    Hence: $\model{\amodeli{2}} \satisfiesnot \aform$.   
  \end{exampleblock}
  \vspace{10cm}
\end{frame}