\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{t10\_yellow\_3 (TMMkg2uzrfbAXSdthH2esTjQ7jJ5sJJvRuB)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k1\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X0}}}}\label{hyp:chegbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_relat\_1~X1)){\unicdbdjdcd}(v1\_relat\_1~\\
(k1\_yellow\_3~X0~X1))\end{array}
\label{hyp:egehpflgbdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}((X2=k1\_yellow\_3~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
(k4\_tarski~X3~X4 \in X2){\unicdbdjded}({\unicdcdaddd} X5 .  {\unicdcdaddd} X6 .  {\unicdcdaddd} X7 .  {\unicdcdaddd} X8 .  \\
(X3=k4\_tarski~X5~X6){\unicdcdcdhd}((X4=k4\_tarski~X7~X8){\unicdcdcdhd}((k4\_tarski~X5~X7 \in \\
X0){\unicdcdcdhd}(k4\_tarski~X6~X8 \in X1))))))))\end{array}
\label{hyp:egbdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  X1{\unicdcdgdad}k4\_tarski~X2~X3))\end{array}
\label{hyp:egbdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfjhfgmgmgpghhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(X2 \in k1\_yellow\_3~X0~X1){\unicdbdjded}((k4\_tarski~(k1\_xtuple\_0~(k1\_xtuple\_0~\\
X2))~(k1\_xtuple\_0~(k2\_xtuple\_0~X2)) \in X0){\unicdcdcdhd}((k4\_tarski~(k2\_xtuple\_0~\\
(k1\_xtuple\_0~X2))~(k2\_xtuple\_0~(k2\_xtuple\_0~X2)) \in X1){\unicdcdcdhd}(({\unicdcdaddd} X3 .  \\
{\unicdcdaddd} X4 .  X2=k4\_tarski~X3~X4){\unicdcdcdhd}(({\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  k1\_xtuple\_0~\\
X2=k4\_tarski~X3~X4){\unicdcdcdhd}({\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  k2\_xtuple\_0~X2=k4\_tarski~\\
X3~X4)))))))\end{array}$$
\end{theorem}
\end{document}
