\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{t16\_graphsp (TMWxk9geKvyzC89eP1gAhHz4ZAimRHJ1Zdh)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_graph\_1 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_graph\_5 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ r7\_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 $ r2\_graph\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_tarski : {{\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.
Let $ v1\_relat\_1 : {{\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.
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}(m2\_graph\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(((u1\_struct\_0~X0=k2\_xboole\_0~X2~X3){\unicdcdcdhd}((\\
X4 \in X2){\unicdcdcdhd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X6 \in X2){\unicdcdcdhd}(X7 \in X3)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
\preoh (X8 \in u4\_struct\_0~X0){\unicdcdcdhd}(r1\_graph\_4~X0~X6~X7~X8))))){\unicdcdcdhd}(r1\_graph\_5~\\
X0~X1~X4~X5)))){\unicdbdjdcd}(r2\_graph\_5~X0~X4~X5~X1~X2)))))\end{array}
\label{hyp:ehbdcdpfhgchbgahigdhah}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfhgchbgahigdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_graph\_1~\\
X2){\unicdcdcdhd}((v6\_graph\_1~X2){\unicdcdcdhd}(l1\_graph\_1~X2)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v7\_graph\_1~\\
X3~X2){\unicdcdcdhd}(m2\_graph\_1~X3~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~\\
X4~(u4\_struct\_0~X2)~k8\_graph\_5){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u4\_struct\_0~X2)~k8\_graph\_5))))){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
m1\_subset\_1~X5~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X2)){\unicdbdjdcd}(((u1\_struct\_0~X2=k2\_xboole\_0~X0~X1){\unicdcdcdhd}((X5 \in \\
X0){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X2)){\unicdbdjdcd}(((X7 \in X0){\unicdcdcdhd}(X8 \in X1)){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
\preoh (X9 \in u4\_struct\_0~X2){\unicdcdcdhd}(r1\_graph\_4~X2~X7~X8~X9))))))){\unicdbdjdcd}((r8\_graph\_5~\\
X2~X5~X6~X3~X0~X4){\unicdbdjded}(r7\_graph\_5~X2~X5~X6~X3~X4)))))))\end{array}$$
\end{theorem}
\end{document}
