\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{t64\_classes2 (TMNXz68yKdyUiEWgNtQVsjhEMoSjX8h8851)}
\maketitle
Let $ k13\_classes2 : {\iota}$ be given.
Let $ k4\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v2\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_classes1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{X0}{\unicdcdgdad}{k1\_xboole\_0}})}{\unicdbdjdcd}{({{k1\_xboole\_0} \in {X0}})}})}}}\label{hyp:ehidpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
{{v2\_classes1}~{({{k4\_classes1}~{k4\_ordinal1}})}}\label{hyp:ehgdddpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}((k2\_ordinal1~\\
X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(v4\_ordinal1~(k2\_ordinal1~X0)))\end{array}
\label{hyp:ehfdbdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(X0=k4\_classes1~\\
(k2\_ordinal1~X0))\end{array}
\label{hyp:ehfdadpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\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}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{r1\_tarski}~{X0}}~{({{k4\_classes1}~{X0}})}})}}}\label{hyp:ehddidpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_ordinal1~X0~X1){\unicdbdjded}(r1\_tarski~(k4\_classes1~X0)~(k4\_classes1~X1))))\end{array}
\label{hyp:ehddhdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_ordinal1~X0~X1){\unicdbdjded}(r1\_tarski~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(v3\_ordinal1~\\
(k2\_ordinal1~X0))\end{array}
\label{hyp:ggdgcdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k13\_classes2}}}})}{\unicdcdcdhd}{({{v1\_classes2}~{k13\_classes2}})}}\label{hyp:egehpflgbdddpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_classes1~X0){\unicdbdjded}((r1\_classes1~X0~X1){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (r1\_classes1~X0~X2){\unicdbdjdcd}(r1\_tarski~X1~X2)))\end{array}
\label{hyp:egedpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_classes1~X0~X1){\unicdbdjded}((X0 \in X1){\unicdcdcdhd}(v2\_classes1~\\
X1))\end{array}
\label{hyp:egddpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{k13\_classes2}={{k1\_classes1}~{k1\_xboole\_0}}}\label{hyp:egcdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (X0=k4\_ordinal1){\unicdbdjded}((k1\_xboole\_0 \in X0){\unicdcdcdhd}((v4\_ordinal1~\\
X0){\unicdcdcdhd}((v3\_ordinal1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(((k1\_xboole\_0 \in \\
X1){\unicdcdcdhd}(v4\_ordinal1~X1)){\unicdbdjdcd}(r1\_tarski~X0~X1))))))\end{array}
\label{hyp:egbdbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehgdedpfdgmgbgdhdhfgdhcd}
${{k13\_classes2}={{k4\_classes1}~{k4\_ordinal1}}}$.
\end{theorem}
\end{document}
