\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{t36\_yellow18 (TMSYZXLBf2qWeLmLwD6fUE5eQsMVShp5ETy)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow18 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_altcat\_1~X0){\unicdbdjdcd}((v2\_altcat\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(k1\_altcat\_1~X0~X1~X3=k1\_xboole\_0)))))))\end{array}
\label{hyp:egcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}((v9\_altcat\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~\\
X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~X0~X1~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(k1\_altcat\_1~X0~X1~X2)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(k1\_altcat\_1~X0~X2~X3)){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~\\
X6)){\unicdcdcdhd}({\unicdcdaddd} X7 .  ((v1\_relat\_1~X7){\unicdcdcdhd}(v1\_funct\_1~X7)){\unicdcdcdhd}((X4=X6){\unicdcdcdhd}\\
((X5=X7){\unicdcdcdhd}(k5\_altcat\_1~X0~X1~X2~X3~X4~X5{\unicdcdgdad}k3\_relat\_1~X6~X7))))))))))))))\end{array}
\label{hyp:egbdcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~\\
X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v2\_yellow18~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0)))))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_altcat\_1~\\
X0~X1~X2)){\unicdbdjdcd}((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)))\end{array}
\label{hyp:dgdgedpfjhfgmgmgpghhbdid}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v9\_altcat\_1~\\
X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v2\_yellow18~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(\preoh {\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_altcat\_1~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_altcat\_1~\\
X0~X2~X3)){\unicdbdjdcd}(k5\_altcat\_1~X0~X1~X2~X3~X4~X5=k3\_relat\_1~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
