\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{t5\_yellow\_9 (TMbEs1APfXnNVWbvRexqmQgZeLkXtRDU4kH)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k8\_setfam\_1~(u1\_struct\_0~\\
X0)~(k7\_setfam\_1~(u1\_struct\_0~X0)~X1)=k3\_subset\_1~(u1\_struct\_0~\\
X0)~(k5\_setfam\_1~(u1\_struct\_0~X0)~X1)))\end{array}
\label{hyp:ehgdpfjhfgmgmgpghhpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((k4\_waybel\_0~\\
X0~X1=k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))~({\uniddcgcg} X2 : \iota .  X2 \in X1)~({\uniddcgcg} X2 : \iota .  k6\_waybel\_0~X0~X2))){\unicdcdcdhd}(\\
k3\_waybel\_0~X0~X1=k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  X2 \in X1)~({\uniddcgcg} X2 : \iota .  k5\_waybel\_0~\\
X0~X2)))))\end{array}
\label{hyp:ehedpfjhfgmgmgpghhpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X3){\unicdcdcdhd}(l1\_orders\_2~X3)){\unicdcdcdhd}((m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X3)))){\unicdcdcdhd}({\unicdcdadad} X4 .  m1\_subset\_1~(X1~X4)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X3))))){\unicdbdjdcd}((X2=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~(u1\_struct\_0~X3)))~({\uniddcgcg} X4 : \iota .  X4 \in X0)~({\uniddcgcg} X4 : \iota .  k3\_subset\_1~\\
(u1\_struct\_0~X3)~(X1~X4))){\unicdbdjdcd}(k7\_setfam\_1~(u1\_struct\_0~X3)~X2=ReplSep~\\
(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(u1\_struct\_0~X3)))~({\uniddcgcg} X4 : \\
\iota .  X4 \in X0)~({\uniddcgcg} X4 : \iota .  X1~X4)))\end{array}
\label{hyp:dhddpfjhfgmgmgpghhpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(k5\_setfam\_1~X0~X1=k3\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(k7\_setfam\_1~X0~(k7\_setfam\_1~X0~X1)=X1)\end{array}
\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflghdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k7\_setfam\_1~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))\end{array}
\label{hyp:egehpflghdpfdhfgehggbgngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfjhfgmgmgpghhpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((X1=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)))~({\uniddcgcg} X3 : \iota .  X3 \in X2)~({\uniddcgcg} X3 : \iota .  k3\_subset\_1~(u1\_struct\_0~\\
X0)~(k6\_waybel\_0~X0~X3))){\unicdbdjdcd}(k8\_setfam\_1~(u1\_struct\_0~X0)~X1=k3\_subset\_1~\\
(u1\_struct\_0~X0)~(k4\_waybel\_0~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
