/usr/share/lhs2tex-1.15/exists.fmt is in lhs2tex 1.15-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% exists.fmt
%
% Format exists x. y as \exists x. y in TeX, not as compose
% Based on forall.fmt; look there for slightly more
% documentation.
%
% Andres Loeh, September 2008, version 1.1
% Duncan Coutts, September 2008, copy'n'pasted from lambda.fmt
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%endif
%if not lhs2tex_exists_fmt_read
%let lhs2tex_exists_fmt_read = True
%include lhs2TeX.fmt
%include forall.fmt
%
%if style /= newcode
%format exists(x) = exists_ x "\hsexists "
%format exists_ = "\exists "
%
\ReadOnlyOnce{exists.fmt}%
\makeatletter
\newcommand\hsexists{\global\let\hsdot=\hsperiodonce}
\AtHaskellReset{\global\let\hsdot=\hscompose}
% In the beginning, we should reset Haskell once.
\HaskellReset
\makeatother
\EndFmtInput
%endif
%endif
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