\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{t3\_graph\_1 (TMNYteLPNyzLwkfGQH8q8GZwjCMtp83LqoW)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_struct\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1))){\unicdbdjdcd}(r4\_graph\_1~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchedpfhgchbgahigpfbd}
\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 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}((r4\_graph\_1~X0~X1){\unicdbdjded}(m3\_graph\_1~\\
X0~X1)))\end{array}
\label{hyp:egcdedpfhgchbgahigpfbd}
\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 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}((m3\_graph\_1~X1~X0){\unicdbdjded}((r1\_tarski~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_tarski~(u4\_struct\_0~\\
X1)~(u4\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in u4\_struct\_0~X1){\unicdbdjdcd}((k1\_funct\_1~\\
(u1\_graph\_1~X1)~X2=k1\_funct\_1~(u1\_graph\_1~X0)~X2){\unicdcdcdhd}((k1\_funct\_1~\\
(u2\_graph\_1~X1)~X2=k1\_funct\_1~(u2\_graph\_1~X0)~X2){\unicdcdcdhd}((k1\_funct\_1~\\
(u1\_graph\_1~X0)~X2 \in u1\_struct\_0~X1){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X0)~\\
X2 \in u1\_struct\_0~X1)))))))))\end{array}
\label{hyp:egbdidpfhgchbgahigpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddpfhgchbgahigpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(X1 \in u4\_struct\_0~X0){\unicdbdjdcd}((k1\_funct\_1~(u1\_graph\_1~X0)~X1 \in u1\_struct\_0~\\
X0){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X0)~X1 \in u1\_struct\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
