\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\unicdbdjded{\Leftrightarrow}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t61\_stirl2\_1 (TMYFJrYU82j7u7QY1BT5s6KnTBNef2ERa6M)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X1 .  \preoh \\
(X1 \in k10\_xtuple\_0~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  k8\_relat\_1~X0~(k1\_tarski~X1){\unicdcdgdad}\\
k1\_tarski~X2)){\unicdbdjded}(v2\_funct\_1~X0))\end{array}
\label{hyp:ehhdedpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((X0 \in k10\_xtuple\_0~X1){\unicdbdjded}\\
(k8\_relat\_1~X1~(k1\_tarski~X0){\unicdcdgdad}k1\_xboole\_0))\end{array}
\label{hyp:ehhdcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
(k8\_relat\_1~X0~(k1\_tarski~X2)=k1\_tarski~X1){\unicdbdjdcd}((X1 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}((X2 \in k10\_xtuple\_0~X0){\unicdcdcdhd}(k1\_funct\_1~X0~X1=X2))))\end{array}
\label{hyp:ehddpfggjgogdhfgbhpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((X0 \in k10\_xtuple\_0~(k3\_relat\_1~\\
X2~X1)){\unicdbdjdcd}(X0 \in k10\_xtuple\_0~X1)))\end{array}
\label{hyp:ehbdedpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_relat\_1~\\
X2){\unicdbdjdcd}(k8\_relat\_1~(k3\_relat\_1~X1~X2)~X0=k8\_relat\_1~X1~(k8\_relat\_1~\\
X2~X0)))\end{array}
\label{hyp:ehbdedgdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k3\_relat\_1}~{X0}}~{X1}})}}}}\label{hyp:egehpflgddpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdbdpfdhehjgchmgcdpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \preoh (X2 \in k10\_xtuple\_0~\\
(k3\_relat\_1~X0~X1)){\unicdcdcdhd}((v2\_funct\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \preoh (X3 \in k9\_xtuple\_0~\\
X1){\unicdcdcdhd}((X3 \in k10\_xtuple\_0~X0){\unicdcdcdhd}((k8\_relat\_1~X1~(k1\_tarski~X2)=k1\_tarski~\\
X3){\unicdcdcdhd}(k8\_relat\_1~X0~(k1\_tarski~X3)=k8\_relat\_1~(k3\_relat\_1~X0~X1)~\\
(k1\_tarski~X2))))))))\end{array}$$
\end{theorem}
\end{document}
