\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{t23\_graph\_3 (TMdiD4WPTPBx6CDVGPnfTY1FjmVd6pFtKCP)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_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 $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_graph\_1~X0){\unicdcdcdhd}\\
(l1\_graph\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(v1\_finset\_1~\\
(k6\_graph\_3~X0~X1))\end{array}
\label{hyp:ggdgjdpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k6\_graph\_3~\\
X0~X1)~(k1\_zfmisc\_1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpflggdpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{({{k5\_card\_1}~{X0}})}}~{k4\_ordinal1}})}}}\label{hyp:egehpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_graph\_3~X0~X1=k3\_graph\_3~\\
X0~X1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egfdpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u4\_struct\_0~X0))){\unicdbdjdcd}((X3=k3\_graph\_3~X0~X1~X2){\unicdbdjded}\\
({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}((X4 \in u4\_struct\_0~X0){\unicdcdcdhd}((X4 \in X2){\unicdcdcdhd}(k1\_funct\_1~\\
(u1\_graph\_1~X0)~X4=X1)))))))\end{array}
\label{hyp:egcdpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}((X2=k9\_graph\_1~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(v1\_finset\_1~X3){\unicdcdcdhd}(({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}((X4 \in u4\_struct\_0~X0){\unicdcdcdhd}\\
(k1\_funct\_1~(u1\_graph\_1~X0)~X4=X1))){\unicdcdcdhd}(X2=k5\_card\_1~X3))))))\end{array}
\label{hyp:egcdcdpfhgchbgahigpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfhgchbgahigpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k5\_card\_1~\\
(k6\_graph\_3~X0~X1)=k9\_graph\_1~X0~X1))\end{array}$$
\end{theorem}
\end{document}
