\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{t18\_graph\_1 (TMEpVZQhb3DUtQZ1kHzaF6JS698WSPG5kGi)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ 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 $ g1\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{({{{k2\_xboole\_0}~{X0}}~{X1}})}}}}\label{hyp:ehhdpfihcgpgpgmgfgpfbd}
\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}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_graph\_1~X2)){\unicdbdjdcd}((r1\_graph\_1~X0~X1~X2){\unicdbdjdcd}(r1\_graph\_1~X0~X2~\\
X1))))\end{array}
\label{hyp:ehbdadpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1))){\unicdbdjdcd}(r4\_graph\_1~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchedpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (g1\_graph\_1~X0~X1~X2~X3=g1\_graph\_1~X4~X5~X6~\\
X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_graph\_1~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(u2\_graph\_1~X0)~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(u2\_graph\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_graph\_1~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(u1\_graph\_1~X0)~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(u1\_graph\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_graph\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_graph\_1~(k5\_graph\_1~X0~X1)){\unicdcdcdhd}(l1\_graph\_1~(k5\_graph\_1~\\
X0~X1))))\end{array}
\label{hyp:egehpflgfdpfhgchbgahigpfbd}
\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}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_graph\_1~X2)){\unicdbdjdcd}((r1\_graph\_1~X0~X1~X2){\unicdbdjded}((r1\_partfun1~(u2\_graph\_1~\\
X1)~(u2\_graph\_1~X2)){\unicdcdcdhd}((r1\_partfun1~(u1\_graph\_1~X1)~(u1\_graph\_1~\\
X2)){\unicdcdcdhd}(g1\_graph\_1~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~\\
X0)~(u2\_graph\_1~X0)=k5\_graph\_1~X1~X2))))))\end{array}
\label{hyp:eggdpfhgchbgahigpfbd}
\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}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_graph\_1~X2){\unicdcdcdhd}(l1\_graph\_1~\\
X2))){\unicdbdjdcd}((X2=k5\_graph\_1~X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k2\_xboole\_0~(\\
u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((u4\_struct\_0~X2=k2\_xboole\_0~\\
(u4\_struct\_0~X0)~(u4\_struct\_0~X1)){\unicdcdcdhd}(({\unicdcdadad} X3 .  (X3 \in u4\_struct\_0~\\
X0){\unicdbdjdcd}((k1\_funct\_1~(u1\_graph\_1~X2)~X3=k1\_funct\_1~(u1\_graph\_1~X0)~\\
X3){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X2)~X3=k1\_funct\_1~(u2\_graph\_1~X0)~\\
X3))){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in u4\_struct\_0~X1){\unicdbdjdcd}((k1\_funct\_1~(u1\_graph\_1~\\
X2)~X3=k1\_funct\_1~(u1\_graph\_1~X1)~X3){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~\\
X2)~X3=k1\_funct\_1~(u2\_graph\_1~X1)~X3))))))))))\end{array}
\label{hyp:egfdpfhgchbgahigpfbd}
\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}((r4\_graph\_1~X0~X1){\unicdbdjded}(m3\_graph\_1~\\
X0~X1)))\end{array}
\label{hyp:egcdedpfhgchbgahigpfbd}
\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}((m3\_graph\_1~X1~X0){\unicdbdjded}((r1\_tarski~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_tarski~(u4\_struct\_0~\\
X1)~(u4\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in u4\_struct\_0~X1){\unicdbdjdcd}((k1\_funct\_1~\\
(u1\_graph\_1~X1)~X2=k1\_funct\_1~(u1\_graph\_1~X0)~X2){\unicdcdcdhd}((k1\_funct\_1~\\
(u2\_graph\_1~X1)~X2=k1\_funct\_1~(u2\_graph\_1~X0)~X2){\unicdcdcdhd}((k1\_funct\_1~\\
(u1\_graph\_1~X0)~X2 \in u1\_struct\_0~X1){\unicdcdcdhd}(k1\_funct\_1~(u2\_graph\_1~X0)~\\
X2 \in u1\_struct\_0~X1)))))))))\end{array}
\label{hyp:egbdidpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}((v1\_graph\_1~X0){\unicdbdjdcd}(X0=g1\_graph\_1~\\
(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfhgchbgahigpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfhgchbgahigpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_graph\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_graph\_1~X2)){\unicdbdjdcd}((r1\_graph\_1~X0~X1~X2){\unicdbdjdcd}((r4\_graph\_1~X1~X0){\unicdcdcdhd}\\
(r4\_graph\_1~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
