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\usepackage{amsfonts}  % Gives funny symbols like the sets N, Q, R, Z.
\usepackage{latexsym}  % Gives funny symbols like /Box for end of proof.
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\usepackage{amsmath}   % Good karma.

\begin{document}

\centerline{\LARGE{A Hard Problem in Propositional Logic}}

\vspace{0.5in}

In the proposition below, there is one variable $V_{i,j}$ for every
pair $i, j \in \{1, \ldots, 45\}$ such that $i < j$.  Is there a
setting of the variables that makes the proposition true?  At present,
no one knows.

\[
\left(
\bigwedge_{
\begin{array}{c}
\scriptstyle{S \subset \{1, \ldots, 45\},} \\
\scriptstyle{|S| = 5}
\end{array}
}
\bigvee_{
\begin{array}{c}
{\scriptstyle i,j \in S,} \\
{\scriptstyle i < j}
\end{array}
} V_{i,j}
\right)
\bigwedge
\left(
\bigwedge_{
\begin{array}{c}
\scriptstyle{S \subset \{1, \ldots, 45\},} \\
\scriptstyle{|S| = 5}
\end{array}
}
\bigvee_{
\begin{array}{c}
{\scriptstyle i,j \in S,} \\
{\scriptstyle i < j}
\end{array}} \neg V_{i,j}
\right)
\]

\end{document}