Agatha hates Charles \& Agatha hates Agatha
\\[0ex]\& ($\forall$$p$:Person. $\neg$$p$ is richer than Agatha $\Rightarrow$ The Butler hates $p$)
\\[0ex]\& ($\forall$$p$:Person. Agatha hates $p$ $\Rightarrow$ $\neg$Charles hates $p$)
\\[0ex]\& ($\forall$$p$:Person. Agatha hates $p$ $\Rightarrow$ The Butler hates $p$)
\\[0ex]\& ($\forall$$p$:Person. $p$ likes Agatha $\vee$ $p$ likes The Butler $\vee$ $p$ likes Charles)
\\[0ex]\& ($\forall$$p$, $q$:Person. $p$ kills $q$ $\Rightarrow$ $\neg$$p$ is richer than $q$)
\\[0ex]\& ($\forall$$p$, $q$:Person. $p$ kills $q$ $\Rightarrow$ $p$ hates $q$)
\\[0ex]$\Rightarrow$ The Butler did not kill Agatha \& Charles did not kill Agatha