\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\_4 (TMMSJFGT6D3aQvEnhQ1i2nUunu957Py1z3q)}
\maketitle
Let $ v2\_struct\_0 : {{\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 $ v3\_graph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_graph\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_graph\_4 : {{\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 $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_graph\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\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 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m2\_finseq\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(r3\_graph\_4~X0~X2~X1)))\end{array}
\label{hyp:ehjdpfhgchbgahigpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0 \in X1){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~X2)){\unicdcdcdhd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:ehfdpfdhfhcgdhfgeh}
\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 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v7\_graph\_1~X2~\\
X0){\unicdcdcdhd}(m2\_graph\_1~X2~X0)){\unicdbdjdcd}((r3\_graph\_4~X0~X1~X2){\unicdbdjdcd}(r1\_graph\_2~X0~\\
X1~X2))))\end{array}
\label{hyp:ehedpfhgchbgahigpfed}
\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 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v3\_graph\_2~X2~\\
X0){\unicdcdcdhd}(m2\_graph\_1~X2~X0)){\unicdbdjdcd}((r1\_graph\_2~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~X4~(k3\_finseq\_1~\\
X1)){\unicdcdcdhd}(k1\_funct\_1~X1~X3=k1\_funct\_1~X1~X4))){\unicdbdjdcd}((r1\_xxreal\_0~X4~X3){\unicdcdcdid}\\
((X3=np\_\_1){\unicdcdcdhd}(X4=k3\_finseq\_1~X1)))))))))\end{array}
\label{hyp:ehedhdpfhgchbgahigpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\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 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0)){\unicdbdjdcd}((v1\_graph\_4~X1~X0){\unicdbdjded}(\\
{\unicdcdaddd} X2 .  (m2\_finseq\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((r3\_graph\_4~X0~\\
X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
X4~(k3\_finseq\_1~X2)){\unicdcdcdhd}(k1\_funct\_1~X2~X3=k1\_funct\_1~X2~X4))){\unicdbdjdcd}((\\
r1\_xxreal\_0~X4~X3){\unicdcdcdid}((X3=np\_\_1){\unicdcdcdhd}(X4=k3\_finseq\_1~X2))))))))))\end{array}
\label{hyp:eghdpfhgchbgahigpfed}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfhgchbgahigpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v7\_graph\_1~X1~X0){\unicdcdcdhd}((v3\_graph\_2~X1~X0){\unicdcdcdhd}(m2\_graph\_1~X1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v7\_graph\_1~X2~X0){\unicdcdcdhd}(m2\_graph\_1~X2~X0)){\unicdbdjdcd}((X2=X1){\unicdbdjdcd}\\
(v1\_graph\_4~X2~X0))))\end{array}$$
\end{theorem}
\end{document}
