\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t66\_arytm\_3 (TMUB9fQQP9bP2aWPSooQhQxqzwvv5MpGU4a)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ 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}((k9\_arytm\_3~X0~X1=k11\_arytm\_3){\unicdbdjdcd}(X0=k11\_arytm\_3)))\end{array}
\label{hyp:ehgdddpfbgchjhehngpfdd}
\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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}((k9\_arytm\_3~\\
X0~X1=k9\_arytm\_3~X2~X1){\unicdbdjdcd}(X0=X2))))\end{array}
\label{hyp:ehgdcdpfbgchjhehngpfdd}
\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}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}(k9\_arytm\_3~\\
(k9\_arytm\_3~X0~X1)~X2=k9\_arytm\_3~X0~(k9\_arytm\_3~X1~X2))))\end{array}
\label{hyp:ehfdbdpfbgchjhehngpfdd}
\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}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\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}
\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~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k5\_arytm\_3){\unicdcdcdhd}(X1=k9\_arytm\_3~X0~X2))))\end{array}
\label{hyp:egbdddpfbgchjhehngpfdd}
\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}
\begin{theorem}\label{thm:ehgdgdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}(((r3\_arytm\_3~X0~X1){\unicdcdcdhd}(r3\_arytm\_3~X1~X0)){\unicdbdjdcd}(X0=\\
X1)))\end{array}$$
\end{theorem}
\end{document}
