\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{t50\_eqrel\_1 (TMFLhKncbwhxnYZQ5yjZuBN6Tpqhn2iovPi)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}((k8\_mcart\_1~\\
X0~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k7\_relset\_1~(k2\_zfmisc\_1~X0~X1)~X0~(\\
k9\_funct\_3~X0~X1)~(k8\_mcart\_1~X0~X1~X2~X3)=X2){\unicdcdcdhd}(k7\_relset\_1~(k2\_zfmisc\_1~\\
X0~X1)~X1~(k10\_funct\_3~X0~X1)~(k8\_mcart\_1~X0~X1~X2~X3)=X3))))\end{array}
\label{hyp:ehedjdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~(k2\_zfmisc\_1~X1~\\
X2)){\unicdbdjdcd}(k1\_funct\_1~(k1\_funct\_3~(k10\_funct\_3~X1~X2))~X0=k7\_relset\_1~\\
(k2\_zfmisc\_1~X1~X2)~X2~(k10\_funct\_3~X1~X2)~X0)\end{array}
\label{hyp:ehedidpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~(k2\_zfmisc\_1~X1~\\
X2)){\unicdbdjdcd}(k1\_funct\_1~(k1\_funct\_3~(k9\_funct\_3~X1~X2))~X0=k7\_relset\_1~\\
(k2\_zfmisc\_1~X1~X2)~X1~(k9\_funct\_3~X1~X2)~X0)\end{array}
\label{hyp:ehedhdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}(m1\_subset\_1~\\
(k8\_mcart\_1~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))\end{array}
\label{hyp:egehpflgidpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpffgbhchfgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}((k8\_mcart\_1~\\
X0~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k1\_funct\_1~(k1\_funct\_3~(k9\_funct\_3~\\
X0~X1))~(k8\_mcart\_1~X0~X1~X2~X3)=X2){\unicdcdcdhd}(k1\_funct\_1~(k1\_funct\_3~(k10\_funct\_3~\\
X0~X1))~(k8\_mcart\_1~X0~X1~X2~X3)=X3))))\end{array}$$
\end{theorem}
\end{document}
