\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\_sgraph1 (TMRzQ2nmULcsxNoN3Wv1DZsMXxFFtUzhWCM)}
\maketitle
Let $ m1\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_sgraph1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sgraph1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k3\_sgraph1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_sgraph1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sgraph1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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 .  (X1 \in k3\_sgraph1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_finset\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_finset\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_sgraph1~X2)))){\unicdcdcdhd}(X1=g1\_sgraph1~\\
X2~X3)))\end{array}
\label{hyp:ehbdhdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_sgraph1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_sgraph1~X0~X1=g1\_sgraph1~X2~\\
X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k3\_sgraph1}~{X0}})}}}}}\label{hyp:ggdgcdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_sgraph1~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_sgraph1~X0)~(k1\_zfmisc\_1~\\
(k2\_sgraph1~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}((v1\_sgraph1~X1){\unicdcdcdhd}(l1\_sgraph1~\\
X1))\end{array}
\label{hyp:egehpfngbdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_sgraph1~X1){\unicdcdcdhd}(l1\_sgraph1~X1)){\unicdbdjdcd}((m1\_sgraph1~\\
X1~X0){\unicdbdjded}(m1\_subset\_1~X1~(k3\_sgraph1~X0)))\end{array}
\label{hyp:egedpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_sgraph1~X0){\unicdbdjdcd}((v1\_sgraph1~X0){\unicdbdjdcd}(X0=g1\_sgraph1~\\
(u1\_struct\_0~X0)~(u1\_sgraph1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdhhgchbgahigbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfdhhgchbgahigbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}((r1\_tarski~(u1\_struct\_0~\\
X1)~X0){\unicdcdcdhd}(r1\_tarski~(u1\_sgraph1~X1)~(k2\_sgraph1~(u1\_struct\_0~X1))))\end{array}$$
\end{theorem}
\end{document}
