\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t20\_arytm\_1 (TMGzREED7BrLzASkNPJuf519UC3HiFCYYgv)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ r1\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_arytm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_arytm\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_arytm\_2){\unicdbdjdcd}(((r1\_arytm\_2~\\
X0~X1){\unicdcdcdhd}(r1\_arytm\_2~X1~X2)){\unicdbdjdcd}(r1\_arytm\_2~X0~X2))))\end{array}
\label{hyp:ehddpfbgchjhehngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_arytm\_2){\unicdbdjdcd}((X0=\\
k7\_arytm\_2~X1~X2){\unicdbdjdcd}(r1\_arytm\_2~X2~X0))))\end{array}
\label{hyp:ehbdjdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_arytm\_2){\unicdbdjdcd}((r1\_arytm\_2~\\
X0~X1){\unicdbdjdcd}(k7\_arytm\_2~X2~(k1\_arytm\_1~X1~X0)=k1\_arytm\_1~(k7\_arytm\_2~\\
X2~X1)~X0))))\end{array}
\label{hyp:ehbdddpfbgchjhehngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k2\_arytm\_2){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k2\_arytm\_2)){\unicdbdjdcd}(m1\_subset\_1~(k7\_arytm\_2~X0~X1)~k2\_arytm\_2)\end{array}
\label{hyp:egehpflghdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}(((r1\_arytm\_2~X1~X0){\unicdbdjdcd}(k2\_arytm\_1~X0~X1=k1\_arytm\_1~\\
X0~X1)){\unicdcdcdhd}((\preoh r1\_arytm\_2~X1~X0){\unicdbdjdcd}(k2\_arytm\_1~X0~X1=k4\_tarski~k11\_arytm\_3~\\
(k1\_arytm\_1~X1~X0)))))\end{array}
\label{hyp:egcdpfbgchjhehngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfbgchjhehngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_arytm\_2){\unicdbdjdcd}((r1\_arytm\_2~\\
X0~X1){\unicdbdjdcd}(k7\_arytm\_2~X2~(k1\_arytm\_1~X1~X0)=k2\_arytm\_1~(k7\_arytm\_2~\\
X2~X1)~X0))))\end{array}$$
\end{theorem}
\end{document}
