\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{t9\_quaterni (TMbLu6cgRYie2mBSrULxhU57chF2jGUHYYG)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}(\preoh (\preoh r3\_arytm\_3~X1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_arytm\_3){\unicdbdjdcd}(\preoh (\preoh r3\_arytm\_3~X2~X0){\unicdcdcdhd}(\preoh r3\_arytm\_3~X1~X2)))))\end{array}
\label{hyp:ehjdddpfbgchjhehngpfdd}
\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 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}(r3\_arytm\_3~X0~(k9\_arytm\_3~X0~X1)))\end{array}
\label{hyp:ehhdhdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}(\preoh (\preoh r3\_arytm\_3~X0~X1){\unicdcdcdhd}\\
(\preoh X1 \in k4\_ordinal1))))\end{array}
\label{hyp:ehhdddpfbgchjhehngpfdd}
\end{equation}
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}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}((\preoh r3\_arytm\_3~X1~X0){\unicdbdjded}((r3\_arytm\_3~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}\\
X1))))\end{array}
\label{hyp:ehgdidpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k5\_arytm\_3}})}{\unicdbdjdcd}{({{{r3\_arytm\_3}~{k11\_arytm\_3}}~{X0}})}}}\label{hyp:ehgdedpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(k9\_arytm\_3~X0~k11\_arytm\_3=\\
X0)\end{array}
\label{hyp:ehfdadpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{X0} \in {k5\_arytm\_3}})}{\unicdbdjdcd}{({{X0} \in {k4\_ordinal1}})}})}}}\label{hyp:ehddbdpfbgchjhehngpfdd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k5\_arytm\_3}}}}\label{hyp:ggdgddpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_arytm\_3)){\unicdbdjdcd}(m1\_subset\_1~(k9\_arytm\_3~X0~X1)~k5\_arytm\_3)\end{array}
\label{hyp:egehpflgjdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k11\_arytm\_3}}~{k5\_arytm\_3}}\label{hyp:egehpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_arytm\_3)){\unicdbdjdcd}(k9\_arytm\_3~X0~X1=k9\_arytm\_3~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgjdpfbgchjhehngpfdd}
\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:ehjdpfbhfhbgehfgchogjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k5\_arytm\_3)){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k5\_arytm\_3){\unicdcdcdhd}((X1 \in X0){\unicdcdcdhd}(X1{\unicdcdgdad}k11\_arytm\_3))){\unicdcdcdhd}(\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_arytm\_3){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}(r3\_arytm\_3~X2~X1)){\unicdbdjdcd}(X2 \in X0)))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k5\_arytm\_3){\unicdbdjdcd}(\preoh (X1 \in \\
X0){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}((X4 \in X0){\unicdcdcdhd}((X5 \in X0){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X3){\unicdcdcdhd}\\
((X1{\unicdcdgdad}X4){\unicdcdcdhd}((X1{\unicdcdgdad}X5){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}((X2{\unicdcdgdad}X4){\unicdcdcdhd}((X2{\unicdcdgdad}X5){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}(\\
(X3{\unicdcdgdad}X5){\unicdcdcdhd}(X4{\unicdcdgdad}X5))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
