\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{t48\_graph\_3 (TMURx6b3Tzk51KkcWqa634LWpisaQsDF4Cw)}
\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 $ k8\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_graph\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k8\_graph\_3~X1~\\
X4~X2))){\unicdbdjdcd}((X5=X3){\unicdbdjdcd}((X3=X4){\unicdcdcdid}(k3\_graph\_3~(k8\_graph\_3~X1~X4~X2)~\\
X5~X0=k3\_graph\_3~X1~X3~X0)))))))\end{array}
\label{hyp:ehededpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k8\_graph\_3~X1~\\
X2~X4))){\unicdbdjdcd}((X5=X3){\unicdbdjdcd}((X3=X4){\unicdcdcdid}(k2\_graph\_3~(k8\_graph\_3~X1~X2~X4)~\\
X5~X0=k2\_graph\_3~X1~X3~X0)))))))\end{array}
\label{hyp:ehedddpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_graph\_1~\\
X0){\unicdcdcdhd}(l1\_graph\_1~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_graph\_3~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_graph\_1~(k8\_graph\_3~X0~X1~X2)){\unicdcdcdhd}(v6\_graph\_1~(k8\_graph\_3~X0~\\
X1~X2))))\end{array}
\label{hyp:ggdgbdadpfhgchbgahigpfdd}
\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)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_graph\_3~X0~X1~X2)){\unicdcdcdhd}((v1\_graph\_1~(k8\_graph\_3~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_graph\_1~(k8\_graph\_3~X0~X1~X2))))\end{array}
\label{hyp:egehpflgidpfhgchbgahigpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_graph\_1~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
k7\_graph\_3~X0~X1~X2=k2\_nat\_1~(k5\_card\_1~(k2\_graph\_3~X0~X1~X2))~(\\
k5\_card\_1~(k3\_graph\_3~X0~X1~X2))))\end{array}
\label{hyp:eggdpfhgchbgahigpfdd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfhgchbgahigpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v6\_graph\_1~X1){\unicdcdcdhd}(\\
l1\_graph\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
(k8\_graph\_3~X1~X3~X4))){\unicdbdjdcd}((X5=X2){\unicdbdjdcd}((X2=X3){\unicdcdcdid}((X2=X4){\unicdcdcdid}(k7\_graph\_3~\\
(k8\_graph\_3~X1~X3~X4)~X5~X0=k7\_graph\_3~X1~X2~X0))))))))\end{array}$$
\end{theorem}
\end{document}
