\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{t10\_graphsp (TMXQwdZwNFpYAjsL1vFfm77jTFZjW78P1wa)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_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 $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ 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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}((v2\_graph\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in u4\_struct\_0~X0){\unicdcdcdhd}((X2 \in u4\_struct\_0~\\
X0){\unicdcdcdhd}((k1\_funct\_1~(u1\_graph\_1~X0)~X1=k1\_funct\_1~(u1\_graph\_1~X0)~\\
X2){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X0)~X1=k1\_funct\_1~(u2\_graph\_1~X0)~\\
X2)))){\unicdbdjdcd}(X1=X2)))\end{array}
\label{hyp:eghdpfhgchbgahigpfbd}
\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 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (r1\_graph\_4~X0~X1~X2~X3){\unicdbdjded}((k1\_funct\_1~\\
(u1\_graph\_1~X0)~X3=X1){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X0)~X3=X2)))))\end{array}
\label{hyp:egbdpfhgchbgahigpfed}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfhgchbgahigdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X3 \in \\
u4\_struct\_0~X0){\unicdcdcdhd}((X4 \in u4\_struct\_0~X0){\unicdcdcdhd}((r1\_graph\_4~X0~X1~X2~X3){\unicdcdcdhd}\\
(r1\_graph\_4~X0~X1~X2~X4)))){\unicdbdjdcd}(X3=X4))))\end{array}$$
\end{theorem}
\end{document}
