\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t67\_classes2 (TMJLuKEgk4AKwQaiVEz72dmbWxNSrVVpZoJ)}
\maketitle
Let $ k16\_classes2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k14\_classes2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_classes2 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_classes2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_ordinal1}~{np\_\_0}}={np\_\_1}}\label{hyp:chbhdffhdgdgpfpflgbdpfpgchegjgogbgmgbdpfpfchadpfchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k16\_classes2~k1\_xboole\_0=k13\_classes2){\unicdcdcdhd}(({\unicdcdadad} X0 .  (v3\_ordinal1~\\
X0){\unicdbdjdcd}(k16\_classes2~(k1\_ordinal1~X0)=k1\_classes1~(k16\_classes2~\\
X0))){\unicdcdcdhd}({\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}(((v4\_ordinal1~X0){\unicdcdcdhd}\\
((k9\_xtuple\_0~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}\\
(k1\_funct\_1~X1~X2=k16\_classes2~X2))))){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}(\\
k16\_classes2~X0=k15\_classes2~(k3\_card\_3~X1)))))))\end{array}
\label{hyp:mghdfdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{k14\_classes2}={{k1\_classes1}~{k13\_classes2}}}\label{hyp:egddpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_ordinal1}~{X0}}={{{k2\_xboole\_0}~{X0}}~{({{k1\_tarski}~{X0}})}}}}\label{hyp:egbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgddpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdhdpfdgmgbgdhdhfgdhcd}
${{{k16\_classes2}~{np\_\_1}}={k14\_classes2}}$.
\end{theorem}
\end{document}
