\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{t12\_yellow\_7 (TMLmkX1P5Yj7CnKmGg1ts95eeLNpXkPbM2q)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k7\_lattice3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((r1\_lattice3~(k7\_lattice3~X0)~\\
X2~X1){\unicdbdjdcd}(r2\_lattice3~X0~X2~(k9\_lattice3~X0~X1))){\unicdcdcdhd}(((r2\_lattice3~\\
X0~X2~(k9\_lattice3~X0~X1)){\unicdbdjdcd}(r1\_lattice3~(k7\_lattice3~X0)~X2~X1)){\unicdcdcdhd}\\
(((r2\_lattice3~(k7\_lattice3~X0)~X2~X1){\unicdbdjdcd}(r1\_lattice3~X0~X2~(k9\_lattice3~\\
X0~X1))){\unicdcdcdhd}((r1\_lattice3~X0~X2~(k9\_lattice3~X0~X1)){\unicdbdjdcd}(r2\_lattice3~\\
(k7\_lattice3~X0)~X2~X1))))))\end{array}
\label{hyp:ehjdpfjhfgmgmgpghhpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k7\_lattice3~X0))){\unicdbdjdcd}\\
(((r1\_orders\_2~X0~X1~(k9\_lattice3~X0~X2)){\unicdbdjdcd}(r1\_orders\_2~(k7\_lattice3~\\
X0)~X2~(k8\_lattice3~X0~X1))){\unicdcdcdhd}(((r1\_orders\_2~(k7\_lattice3~X0)~X2~\\
(k8\_lattice3~X0~X1)){\unicdbdjdcd}(r1\_orders\_2~X0~X1~(k9\_lattice3~X0~X2))){\unicdcdcdhd}\\
(((r1\_orders\_2~X0~(k9\_lattice3~X0~X2)~X1){\unicdbdjdcd}(r1\_orders\_2~(k7\_lattice3~\\
X0)~(k8\_lattice3~X0~X1)~X2)){\unicdcdcdhd}((r1\_orders\_2~(k7\_lattice3~X0)~(k8\_lattice3~\\
X0~X1)~X2){\unicdbdjdcd}(r1\_orders\_2~X0~(k9\_lattice3~X0~X2)~X1)))))))\end{array}
\label{hyp:ehcdpfjhfgmgmgpghhpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_yellow\_0~X0~X1){\unicdbdjded}\\
(r2\_yellow\_0~(k7\_lattice3~X0)~X1))\end{array}
\label{hyp:ehbdadpfjhfgmgmgpghhpfhd}
\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}(k3\_relset\_1~X0~X1~X2=k2\_relat\_1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_orders\_2~X0~X1=g1\_orders\_2~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(u1\_orders\_2~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpffhbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
(k7\_lattice3~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k9\_lattice3~X0~X1)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgjdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:egehpflghdpfmgbgehehjgdgfgdd}
\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}(m1\_subset\_1~(k3\_relset\_1~X0~X1~X2)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X0)))\end{array}
\label{hyp:egehpflgddpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_yellow\_0~\\
X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_yellow\_0~X0~X1){\unicdbdjdcd}((X2=k1\_yellow\_0~X0~\\
X1){\unicdbdjded}((r2\_lattice3~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r2\_lattice3~X0~X1~X3){\unicdbdjdcd}(r1\_orders\_2~X0~X2~X3)))))))\end{array}
\label{hyp:egjdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k7\_lattice3~X0))){\unicdbdjdcd}(k9\_lattice3~X0~X1=X1))\end{array}
\label{hyp:eghdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k8\_lattice3~X0~X1=X1))\end{array}
\label{hyp:eggdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(k7\_lattice3~X0=g1\_orders\_2~(u1\_struct\_0~\\
X0)~(k3\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_orders\_2~\\
X0)))\end{array}
\label{hyp:egfdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_yellow\_0~X0~X1){\unicdbdjdcd}((X2=k2\_yellow\_0~X0~\\
X1){\unicdbdjded}((r1\_lattice3~X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_lattice3~X0~X1~X3){\unicdbdjdcd}(r1\_orders\_2~X0~X3~X2)))))))\end{array}
\label{hyp:egbdadpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~X0){\unicdbdjdcd}(X0=g1\_orders\_2~\\
(u1\_struct\_0~X0)~(u1\_orders\_2~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfpgchegfgchdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfjhfgmgmgpghhpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((r1\_yellow\_0~X0~X1){\unicdcdcdid}(r2\_yellow\_0~(k7\_lattice3~X0)~X1)){\unicdbdjdcd}(k1\_yellow\_0~\\
X0~X1=k2\_yellow\_0~(k7\_lattice3~X0)~X1))\end{array}$$
\end{theorem}
\end{document}
