\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{t9\_cat\_4 (TMUFwnHtnf1rStiXBYaMEpQPmPntJ6nJX9b)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_cat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u4\_struct\_0~(k5\_cat\_4~\\
X0~X1))){\unicdbdjdcd}(X4 \in k2\_cat\_1~(k5\_cat\_4~X0~X1)~X2~X3)))\end{array}
\label{hyp:ehfdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~(\\
k5\_cat\_4~X0~X1))){\unicdbdjdcd}(X2=X3))\end{array}
\label{hyp:ehedpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k5\_cat\_4~X0~X1))){\unicdbdjdcd}(X2=X3))\end{array}
\label{hyp:ehddpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v2\_cat\_1}~{({{{k5\_cat\_4}~{X0}}~{X1}})}}}}\label{hyp:mgbdadpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v2\_struct\_0~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((v2\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((v3\_cat\_1~(k5\_cat\_4~\\
X0~X1)){\unicdcdcdhd}((v4\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((v5\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}\\
((v6\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}(v2\_cat\_4~(k5\_cat\_4~X0~X1))))))))\end{array}
\label{hyp:ggdgcdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_cat\_4}~{X0}})}{\unicdbdjdcd}{({{l1\_cat\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_cat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_graph\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v2\_cat\_4~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}(l1\_cat\_4~(\\
k5\_cat\_4~X0~X1))\end{array}
\label{hyp:egehpflgfdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_graph\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k3\_graph\_1~X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgddpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_cat\_1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u4\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_cat\_1~X0~X1~X2)~(u4\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u4\_struct\_0~X0)){\unicdbdjdcd}((r2\_cat\_3~X0~X1~X2~X3){\unicdbdjded}((k3\_graph\_1~\\
X0~X2=X1){\unicdcdcdhd}((k3\_graph\_1~X0~X3=X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u4\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u4\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X5 \in k2\_cat\_1~\\
X0~X4~(k4\_graph\_1~X0~X2)){\unicdcdcdhd}((X6 \in k2\_cat\_1~X0~X4~(k4\_graph\_1~X0~X3)){\unicdcdcdhd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u4\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X7 \in k2\_cat\_1~\\
X0~X4~X1){\unicdcdcdhd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u4\_struct\_0~X0)){\unicdbdjdcd}((X8 \in \\
k2\_cat\_1~X0~X4~X1){\unicdbdjdcd}(((k1\_cat\_1~X0~X8~X2=X5){\unicdcdcdhd}(k1\_cat\_1~X0~X8~X3=X6)){\unicdbdjded}\\
(X7=X8)))))))))))))))))\end{array}
\label{hyp:egbdfdpfdgbgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfdgbgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~(\\
k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u4\_struct\_0~(k5\_cat\_4~\\
X0~X1))){\unicdbdjdcd}(r2\_cat\_3~(k5\_cat\_4~X0~X1)~X2~X3~X4)))\end{array}$$
\end{theorem}
\end{document}
