\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l12\_jgraph\_5 (TMN3s4AHmqUzGGz5KYig5fxhzE6PrD71FdP)}
\maketitle
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k6\_numbers \in k1\_rcomp\_1~k6\_numbers~np\_\_1){\unicdcdcdhd}(np\_\_1 \in k1\_rcomp\_1~\\
k6\_numbers~np\_\_1)\end{array}
\label{hyp:mgbdpfkgpgchegbgogbd}
\end{equation}
\begin{theorem}\label{thm:mgbdcdpfkghgchbgahigpffd}
${{k6\_numbers} \in {{{k1\_rcomp\_1}~{k6\_numbers}}~{np\_\_1}}}$.
\end{theorem}
\end{document}
