\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{t3\_grcat\_1 (TMNRJW4mTbeYhyxzTVUwohcwaoUx4p1hRLB)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_funct\_5 : {\iota}$ be given.
Let $ k8\_funct\_5 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
(((X1=k1\_xboole\_0){\unicdbdjdcd}(X0=k1\_xboole\_0)){\unicdbdjdcd}(X2 \in k1\_funct\_2~X0~X1))\end{array}
\label{hyp:ehidpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(v1\_classes2~\\
X2)){\unicdbdjdcd}(((X0 \in X2){\unicdcdcdhd}(X1 \in X2)){\unicdbdjdcd}((k2\_zfmisc\_1~X0~X1 \in X2){\unicdcdcdhd}(k1\_funct\_2~\\
X0~X1 \in X2)))\end{array}
\label{hyp:ehgdbdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(v1\_classes2~\\
X2)){\unicdbdjdcd}(((X0 \in X2){\unicdcdcdhd}(X1 \in X2)){\unicdbdjdcd}((k2\_tarski~X0~X1 \in X2){\unicdcdcdhd}(k4\_tarski~X0~\\
X1 \in X2)))\end{array}
\label{hyp:ehfdidpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_classes2~X1)){\unicdbdjdcd}\\
((X0 \in X1){\unicdbdjdcd}(k1\_tarski~X0 \in X1))\end{array}
\label{hyp:ehfdhdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v1\_classes2}~{X0}})}})}{\unicdbdjdcd}{({{k1\_xboole\_0} \in {X0}})}}}\label{hyp:ehfdgdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
{{np\_\_1}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehedjdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_ordinal1~X2){\unicdbdjdcd}(((X0 \in X1){\unicdcdcdhd}\\
(X1 \in X2)){\unicdbdjdcd}(X0 \in X2))\end{array}
\label{hyp:ehbdadpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k9\_funct\_5){\unicdcdcdhd}((v1\_funct\_2~k9\_funct\_5~(k2\_zfmisc\_1~\\
np\_\_1~np\_\_1)~np\_\_1){\unicdcdcdhd}(m1\_subset\_1~k9\_funct\_5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~np\_\_1~np\_\_1)~np\_\_1))))\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k8\_funct\_5){\unicdcdcdhd}((v1\_funct\_2~k8\_funct\_5~np\_\_1~np\_\_1){\unicdcdcdhd}\\
(m1\_subset\_1~k8\_funct\_5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~np\_\_1~np\_\_1))))\end{array}
\label{hyp:egehpflgidpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_classes2}~{X0}})}{\unicdbdjdcd}{({{({{v1\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v2\_classes1}~{X0}})}})}}}\label{hyp:dgdgcdpfdgmgbgdhdhfgdhcd}
\end{equation}
\begin{theorem}\label{thm:ehddpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}((k1\_tarski~\\
k1\_xboole\_0 \in X0){\unicdcdcdhd}((k4\_tarski~(k1\_tarski~k1\_xboole\_0)~(k1\_tarski~\\
k1\_xboole\_0) \in X0){\unicdcdcdhd}((k2\_zfmisc\_1~(k1\_tarski~k1\_xboole\_0)~(k1\_tarski~\\
k1\_xboole\_0) \in X0){\unicdcdcdhd}((k9\_funct\_5 \in X0){\unicdcdcdhd}(k8\_funct\_5 \in X0)))))\end{array}$$
\end{theorem}
\end{document}
