\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{t1\_seq\_4 (TMKy8ompCUHns77w2ro39mEbjfg1mF3rvGt)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(\preoh ({\unicdcdadad} X2 .  (v1\_xreal\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(((X2 \in X0){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}(r1\_xxreal\_0~\\
X2~X3)))){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdaddd} X3 .  (v1\_xreal\_0~\\
X3){\unicdcdcdhd}({\unicdcdaddd} X4 .  (v1\_xreal\_0~X4){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}(\preoh (r1\_xxreal\_0~\\
X3~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~X4)))))))))\end{array}
\label{hyp:ehbdpfbgihjgpgngdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfdhfgbhpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(\preoh ({\unicdcdadad} X2 .  (v1\_xreal\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}(\preoh (X2 \in X0){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}(r1\_xxreal\_0~\\
X3~X2))))){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdaddd} X3 .  (v1\_xreal\_0~\\
X3){\unicdcdcdhd}({\unicdcdaddd} X4 .  (v1\_xreal\_0~X4){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}(\preoh (r1\_xxreal\_0~\\
X3~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
