\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t1\_msualg\_9 (TMWe2SPdNuY82zgE7X3UNhdRQ92HazZjkZE)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_mcart\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_mcart\_1 : {{\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((X0 \in X1){\unicdbdjdcd}(X0=k4\_tarski~\\
(k1\_xtuple\_0~X0)~(k2\_xtuple\_0~X0)))\end{array}
\label{hyp:ehcdbdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k12\_mcart\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k12\_mcart\_1~X0)))\end{array}
\label{hyp:egehpflgbdcdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k11\_mcart\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k11\_mcart\_1~X0)))\end{array}
\label{hyp:egehpflgbdbdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k12\_mcart\_1~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k9\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k2\_xtuple\_0~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egbdddpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((X1=k11\_mcart\_1~X0){\unicdbdjded}((k9\_xtuple\_0~\\
X1=k9\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~\\
X1~X2=k1\_xtuple\_0~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egbdcdpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfngdhfhbgmghgpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
(v1\_funct\_1~X3)){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~X3){\unicdcdcdhd}(k1\_funct\_1~X3~X0 \in k2\_zfmisc\_1~\\
X1~X2)){\unicdbdjdcd}(k1\_funct\_1~X3~X0=k4\_tarski~(k1\_funct\_1~(k11\_mcart\_1~\\
X3)~X0)~(k1\_funct\_1~(k12\_mcart\_1~X3)~X0)))\end{array}$$
\end{theorem}
\end{document}
