\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{t15\_yellow17 (TMTQWF7EcQyzrQWCuGXZtrDPix8NGebLdtf)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_cantor\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_compts\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_waybel\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_waybel\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k2\_yellow\_1~\\
(u1\_pre\_topc~X0)))){\unicdbdjdcd}((X1=u1\_struct\_0~X0){\unicdbdjdcd}((v1\_waybel\_3~X1~(\\
k2\_yellow\_1~(u1\_pre\_topc~X0))){\unicdbdjded}(v1\_compts\_1~X0))))\end{array}
\label{hyp:ehddhdpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_tops\_2~X1~X0){\unicdcdcdhd}((v2\_cantor\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k2\_yellow\_1~(u1\_pre\_topc~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k2\_yellow\_1~(u1\_pre\_topc~\\
X0)))){\unicdbdjdcd}((r1\_tarski~X2~X3){\unicdbdjdcd}((r1\_waybel\_3~(k2\_yellow\_1~(u1\_pre\_topc~\\
X0))~X2~X3){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}(\preoh (\\
r1\_tarski~X3~(k3\_tarski~X4)){\unicdcdcdhd}({\unicdcdadad} X5 .  ((v1\_finset\_1~X5){\unicdcdcdhd}(\\
m1\_subset\_1~X5~(k1\_zfmisc\_1~X4))){\unicdbdjdcd}(\preoh r1\_tarski~X2~(k3\_tarski~X5))))))))))\end{array}
\label{hyp:ehddbdpfhhbgjhcgfgmgpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (u1\_struct\_0~(k2\_yellow\_1~X0)=X0){\unicdcdcdhd}(u1\_orders\_2~(\\
k2\_yellow\_1~X0)=k1\_yellow\_1~X0)\end{array}
\label{hyp:ehbdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_yellow\_1~X0)){\unicdcdcdhd}\\
(v1\_orders\_2~(k2\_yellow\_1~X0)))\end{array}
\label{hyp:ggdggdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}((v3\_orders\_2~(k2\_yellow\_1~\\
X0)){\unicdcdcdhd}((v4\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(v5\_orders\_2~(k2\_yellow\_1~\\
X0))))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_pre\_topc~X0))\end{array}
\label{hyp:ggdgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k2\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_struct\_0}~{X0}}={{u1\_struct\_0}~{X0}}})}}}\label{hyp:egddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((v1\_waybel\_3~\\
X1~X0){\unicdbdjded}(r1\_waybel\_3~X0~X1~X1)))\end{array}
\label{hyp:egcdpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v2\_pre\_topc~X0){\unicdbdjded}((u1\_struct\_0~\\
X0 \in u1\_pre\_topc~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r1\_tarski~X1~(u1\_pre\_topc~\\
X0)){\unicdbdjdcd}(k5\_setfam\_1~(u1\_struct\_0~X0)~X1 \in u1\_pre\_topc~X0))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((X1 \in u1\_pre\_topc~\\
X0){\unicdcdcdhd}(X2 \in u1\_pre\_topc~X0)){\unicdbdjdcd}(k9\_subset\_1~(u1\_struct\_0~X0)~X1~X2 \in \\
u1\_pre\_topc~X0)))))))\end{array}
\label{hyp:egbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfjhfgmgmgpghhbdhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_tops\_2~X1~X0){\unicdcdcdhd}((v2\_cantor\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v1\_compts\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~X1)){\unicdbdjdcd}(\preoh (r1\_tarski~\\
(k2\_struct\_0~X0)~(k3\_tarski~X2)){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_finset\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~X2))){\unicdbdjdcd}(\preoh r1\_tarski~(k2\_struct\_0~\\
X0)~(k3\_tarski~X3)))))))\end{array}$$
\end{theorem}
\end{document}
