\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{t24\_graph\_4 (TMG2oDBzagYSnt9YW8GroqXi43Fn24kXdFc)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_graph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}\\
((v2\_funct\_1~X1){\unicdcdcdhd}((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))))\end{array}
\label{hyp:ehcdddpfhgchbgahigpfed}
\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 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}((v1\_graph\_4~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}\\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))))\end{array}
\label{hyp:ehbdjdpfhgchbgahigpfed}
\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 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v7\_graph\_1~X2~X0){\unicdcdcdhd}(m2\_graph\_1~X2~X0)){\unicdbdjdcd}((X2=X1){\unicdbdjdcd}\\
(v1\_graph\_4~X2~X0))))\end{array}
\label{hyp:ehbdidpfhgchbgahigpfed}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfhgchbgahigpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v1\_graph\_4~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)))){\unicdcdcdhd}((((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v1\_graph\_4~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)))){\unicdcdcdhd}(((v7\_graph\_1~\\
X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}((v2\_funct\_1~\\
X1){\unicdcdcdhd}((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)))))))\end{array}$$
\end{theorem}
\end{document}
