The main idea of eager encoding is that the input formula is translated into a
propositional formula with all relevant theory-specific information encoded into
the formula.

\begin{enumerate}[label=(\Roman*)]
  \item Replace any unique $\Theory$-atom in the original formula $\varphi$ with a fresh propositional variable to get a propositional formula $\hat{\varphi}$. \label{item:varphi_prop}
\item Generate a propositional formula $\varphi_{cons}$ that constrains the values of the introduced
  propositional variables to preserve the information of the theory. \label{item:varphi_cons}

\item Invoke a SAT solver on the propositional formula $\varphi_{prop} \coloneqq \hat{\varphi} \land \varphi_{cons}$
that corresponds to an equisatisfiable propositional formula to $\varphi$.
\end{enumerate}