\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{t25\_yellow20 (TMNLs1PapJ6GiJoB8jhWQKwymCHmGMaB7fo)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_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 $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_yellow20 : {{\iota}{\unicdbdjdcd}{{\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 $ k8\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_yellow20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~X2~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ehcdjdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}((r1\_yellow20~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~(k2\_yellow20~X0~X1))){\unicdbdjdcd}(((X4=X2){\unicdcdcdhd}\\
((X4=X3){\unicdcdcdhd}(k8\_altcat\_1~X0~X2=k8\_altcat\_1~X1~X3))){\unicdbdjdcd}(k8\_altcat\_1~\\
X0~X2 \in k1\_altcat\_1~(k2\_yellow20~X0~X1)~X4~X4)))))))\end{array}
\label{hyp:ehcdedpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v2\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}((r1\_yellow20~X0~X1){\unicdbdjdcd}(v2\_altcat\_1~\\
(k2\_yellow20~X0~X1))))\end{array}
\label{hyp:ehcdcdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_altcat\_1~X1){\unicdbdjdcd}((\\
r1\_yellow20~X0~X1){\unicdbdjdcd}(m1\_altcat\_2~(k2\_yellow20~X0~X1)~X0)))\end{array}
\label{hyp:ehcdadpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l2\_altcat\_1~X1){\unicdbdjdcd}((\\
r1\_yellow20~X0~X1){\unicdbdjdcd}(k2\_yellow20~X0~X1=k2\_yellow20~X1~X0)))\end{array}
\label{hyp:ehbdjdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}(\\
(r1\_yellow20~X0~X1){\unicdbdjdcd}(r1\_yellow20~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X1){\unicdbdjdcd}(\\
(v3\_altcat\_2~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}\\
(k8\_altcat\_1~X0~X3 \in k1\_altcat\_1~X1~X2~X2)))))){\unicdcdcdhd}((v2\_struct\_0~X1){\unicdbdjdcd}\\
(v3\_altcat\_2~X1~X0))))\end{array}
\label{hyp:egbdedpfbgmgehdgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfjhfgmgmgpghhcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}(((r1\_yellow20~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k8\_altcat\_1~X0~X2=k8\_altcat\_1~X1~\\
X3))))){\unicdbdjdcd}((v2\_struct\_0~(k2\_yellow20~X0~X1)){\unicdcdcdid}((v2\_altcat\_1~(k2\_yellow20~\\
X0~X1)){\unicdcdcdhd}((v3\_altcat\_2~(k2\_yellow20~X0~X1)~X0){\unicdcdcdhd}(m1\_altcat\_2~(k2\_yellow20~\\
X0~X1)~X0))))))\end{array}$$
\end{theorem}
\end{document}
