\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\_1 (TMKCTt4Dmy1iYe34xy8CaSq4QJtQwGm1MEE)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\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 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(((r1\_partfun1~(u1\_graph\_1~\\
X0)~(u1\_graph\_1~X1)){\unicdcdcdhd}(r1\_partfun1~(u2\_graph\_1~X0)~(u2\_graph\_1~\\
X1))){\unicdbdjdcd}(k5\_graph\_1~X0~X1=k5\_graph\_1~X1~X0)))\end{array}
\label{hyp:ehidpfhgchbgahigpfbd}
\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}(((r1\_partfun1~(u1\_graph\_1~\\
X0)~(u1\_graph\_1~X1)){\unicdcdcdhd}(r1\_partfun1~(u2\_graph\_1~X0)~(u2\_graph\_1~\\
X1))){\unicdbdjdcd}((r4\_graph\_1~X0~(k5\_graph\_1~X0~X1)){\unicdcdcdhd}(r4\_graph\_1~X1~(k5\_graph\_1~\\
X0~X1)))))\end{array}
\label{hyp:ehbdjdpfhgchbgahigpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfhgchbgahigpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(((r1\_partfun1~(u1\_graph\_1~\\
X0)~(u1\_graph\_1~X1)){\unicdcdcdhd}(r1\_partfun1~(u2\_graph\_1~X0)~(u2\_graph\_1~\\
X1))){\unicdbdjdcd}(((k5\_graph\_1~X0~X1{\unicdcdgdad}X1){\unicdcdcdhd}(k5\_graph\_1~X1~X0{\unicdcdgdad}X1)){\unicdcdcdid}(r4\_graph\_1~\\
X0~X1))))\end{array}$$
\end{theorem}
\end{document}
