\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{t30\_graph\_3 (TMLhwXG86fC9X6fYxzQ5H4cwHZ9qySHeWqQ)}
\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 $ k2\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\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\_zfmisc\_1 : {{\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.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k3\_graph\_3~\\
X0~X1~X2)~(k1\_zfmisc\_1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgddpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~(k2\_graph\_3~\\
X0~X1~X2)~(k1\_zfmisc\_1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgcdpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\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}(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=k2\_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~\\
(u2\_graph\_1~X0)~X4=X1)))))))\end{array}
\label{hyp:egbdpfhgchbgahigpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfhgchbgahigpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v6\_graph\_1~X1){\unicdcdcdhd}(\\
l1\_graph\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}\\
((k2\_graph\_3~X1~X2~X0=k2\_graph\_3~X1~X2~(k3\_xboole\_0~X0~(u4\_struct\_0~\\
X1))){\unicdcdcdhd}(k3\_graph\_3~X1~X2~X0=k3\_graph\_3~X1~X2~(k3\_xboole\_0~X0~(u4\_struct\_0~\\
X1)))))\end{array}$$
\end{theorem}
\end{document}
