This is no problem with XeTeX if you load a font that contains these characters:
\documentclass{minimal}
\usepackage{fontspec}
\setmainfont{DejaVu Serif}
\setsansfont{DejaVu Sans}
\setmonofont{DejaVu Sans Mono}
\begin{document}
\texttt{∀x(∃y((f(x)=y)∧(¬(g(y)=y))))}
If $\phi$ is a formula of first-order logic and $x$ is a variable, then
\texttt{∀$x$($\phi$)} is again a formula of first-order logic.
\end{document}
Note: Never load the inputenc package when compiling with XeTeX.
Best Answer
This keeps the "S" and "L" in non-italic upshape, as given in your example.