\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{t64\_graph\_5 (TMV56LhYzc7NAYEH2SiwyaWzRvbCbQHJ7g1)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ v7\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ r5\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r8\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r7\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r2\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v6\_graph\_1~X2){\unicdcdcdhd}(l1\_graph\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v7\_graph\_1~X3~X2){\unicdcdcdhd}(m2\_graph\_1~X3~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}(((r5\_graph\_5~X2~X1){\unicdcdcdhd}((r8\_graph\_5~X2~X4~X5~X3~X0~X1){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
((v7\_graph\_1~X6~X2){\unicdcdcdhd}(m2\_graph\_1~X6~X2)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X2)){\unicdbdjdcd}((r8\_graph\_5~X2~X4~X7~X6~X0~X1){\unicdbdjdcd}((X7 \in X0){\unicdcdcdid}(\\
r1\_xxreal\_0~(k10\_graph\_5~X2~X3~X1)~(k10\_graph\_5~X2~X6~X1)))))))){\unicdbdjdcd}\\
((X4=X5){\unicdcdcdid}(r7\_graph\_5~X2~X4~X5~X3~X1)))))))\end{array}
\label{hyp:ehgdddpfhgchbgahigpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_graph\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v7\_graph\_1~X5~\\
X2){\unicdcdcdhd}(m2\_graph\_1~X5~X2)){\unicdbdjdcd}(((r2\_graph\_5~X2~X3~X4~X5~X0){\unicdcdcdhd}(r1\_tarski~\\
X0~X1)){\unicdbdjdcd}(r2\_graph\_5~X2~X3~X4~X5~X1)))))\end{array}
\label{hyp:ehddcdpfhgchbgahigpffd}
\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 .  ((v7\_graph\_1~X3~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (r2\_graph\_5~X0~X1~X2~X3~X4){\unicdbdjded}((r1\_graph\_5~X0~\\
X3~X1~X2){\unicdcdcdhd}(r1\_tarski~(k7\_subset\_1~(u1\_struct\_0~X0)~(k2\_graph\_5~\\
X0~X3)~(k1\_tarski~X2))~X4))))))\end{array}
\label{hyp:egedpfhgchbgahigpffd}
\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 .  ((v7\_graph\_1~X3~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(v1\_funct\_1~\\
X5)){\unicdbdjdcd}((r8\_graph\_5~X0~X1~X2~X3~X4~X5){\unicdbdjded}((r2\_graph\_5~X0~X1~X2~X3~X4){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  ((v7\_graph\_1~X6~X0){\unicdcdcdhd}(m2\_graph\_1~X6~X0)){\unicdbdjdcd}((r2\_graph\_5~\\
X0~X1~X2~X6~X4){\unicdbdjdcd}(r1\_xxreal\_0~(k10\_graph\_5~X0~X3~X5)~(k10\_graph\_5~\\
X0~X6~X5))))))))))\end{array}
\label{hyp:egbdidpfhgchbgahigpffd}
\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 .  ((v7\_graph\_1~X3~X0){\unicdcdcdhd}(m2\_graph\_1~\\
X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}((r7\_graph\_5~\\
X0~X1~X2~X3~X4){\unicdbdjded}((r1\_graph\_5~X0~X3~X1~X2){\unicdcdcdhd}({\unicdcdadad} X5 .  ((v7\_graph\_1~\\
X5~X0){\unicdcdcdhd}(m2\_graph\_1~X5~X0)){\unicdbdjdcd}((r1\_graph\_5~X0~X5~X1~X2){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k10\_graph\_5~X0~X3~X4)~(k10\_graph\_5~X0~X5~X4))))))))))\end{array}
\label{hyp:egbdhdpfhgchbgahigpffd}
\end{equation}
\begin{theorem}\label{thm:ehgdedpfhgchbgahigpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v6\_graph\_1~X3){\unicdcdcdhd}(l1\_graph\_1~\\
X3))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v7\_graph\_1~X4~X3){\unicdcdcdhd}(m2\_graph\_1~X4~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X3)){\unicdbdjdcd}(((r5\_graph\_5~X3~X2){\unicdcdcdhd}((r8\_graph\_5~X3~X5~X6~X4~\\
X0~X2){\unicdcdcdhd}((r1\_tarski~X0~X1){\unicdcdcdhd}({\unicdcdadad} X7 .  ((v7\_graph\_1~X7~X3){\unicdcdcdhd}(m2\_graph\_1~\\
X7~X3)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X3)){\unicdbdjdcd}((r8\_graph\_5~\\
X3~X5~X8~X7~X0~X2){\unicdbdjdcd}((X8 \in X0){\unicdcdcdid}(r1\_xxreal\_0~(k10\_graph\_5~X3~X4~X2)~(\\
k10\_graph\_5~X3~X7~X2))))))))){\unicdbdjdcd}((X5=X6){\unicdcdcdid}(r8\_graph\_5~X3~X5~X6~X4~\\
X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
