\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{l28\_waybel13 (TMXV8wDdN8G7aG79S3eRDMBwvD9r5hjoPwQ)}
\maketitle
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 $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_waybel\_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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v22\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_waybel10 : {{\iota}{\unicdbdjdcd}{{\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 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_orders\_2~X2){\unicdbdjdcd}(((r5\_waybel\_1~X0~X1){\unicdcdcdhd}(r5\_waybel\_1~X1~X2)){\unicdbdjdcd}\\
(r5\_waybel\_1~X0~X2))))\end{array}
\label{hyp:ehhdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}((g1\_orders\_2~(u1\_struct\_0~\\
X0)~(u1\_orders\_2~X0)=g1\_orders\_2~(u1\_struct\_0~X1)~(u1\_orders\_2~\\
X1)){\unicdbdjdcd}(r5\_waybel\_1~X0~X1)))\end{array}
\label{hyp:ehcdgdpfhhbgjhcgfgmgbddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_yellow\_0~X1~X0){\unicdcdcdhd}((v7\_yellow\_0~\\
X1~X0){\unicdcdcdhd}(m1\_yellow\_0~X1~X0))){\unicdbdjdcd}(k1\_yellow\_2~X0~X0~(k6\_waybel10~X0~\\
X1)=g1\_orders\_2~(u1\_struct\_0~X1)~(u1\_orders\_2~X1)))\end{array}
\label{hyp:ehbdidpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(v3\_lattice3~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:ggdgidpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k3\_yellow\_1~X0)){\unicdcdcdhd}((v1\_orders\_2~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}((v3\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}(v5\_orders\_2~(k3\_yellow\_1~X0)))))\end{array}
\label{hyp:ggdghdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k1\_yellow\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_orders\_2~(k1\_yellow\_2~\\
X0~X1~X2)){\unicdcdcdhd}(v4\_yellow\_0~(k1\_yellow\_2~X0~X1~X2)~X1)))\end{array}
\label{hyp:ggdgcdpfjhfgmgmgpghhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))))))){\unicdcdcdhd}((v4\_yellow\_0~X1~X0){\unicdcdcdhd}((v7\_yellow\_0~\\
X1~X0){\unicdcdcdhd}((v4\_waybel\_0~X1~X0){\unicdcdcdhd}(m1\_yellow\_0~X1~X0))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k6\_waybel10~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k6\_waybel10~X0~X1)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(v22\_waybel\_0~(k6\_waybel10~X0~X1)~X0~X0)))\end{array}
\label{hyp:ggdgbdddpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))))))){\unicdcdcdhd}((v4\_yellow\_0~X1~X0){\unicdcdcdhd}((v7\_yellow\_0~\\
X1~X0){\unicdcdcdhd}(m1\_yellow\_0~X1~X0)))){\unicdbdjdcd}((v1\_funct\_1~(k6\_waybel10~X0~X1)){\unicdcdcdhd}\\
((v1\_funct\_2~(k6\_waybel10~X0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(v7\_waybel\_1~(k6\_waybel10~X0~X1)~X0)))\end{array}
\label{hyp:ggdgbdadpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_yellow\_0~X1~X0){\unicdbdjdcd}\\
(l1\_orders\_2~X1))\end{array}
\label{hyp:egehpfngbdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}\\
(m1\_yellow\_0~X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k6\_waybel10~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~\\
(k6\_waybel10~X0~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k6\_waybel10~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflggdpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))))){\unicdbdjdcd}\\
((v1\_orders\_2~(k1\_yellow\_2~X0~X1~X2)){\unicdcdcdhd}((v4\_yellow\_0~(k1\_yellow\_2~\\
X0~X1~X2)~X1){\unicdcdcdhd}(m1\_yellow\_0~(k1\_yellow\_2~X0~X1~X2)~X1)))\end{array}
\label{hyp:egehpflgbdpfjhfgmgmgpghhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_yellow\_0~X1~X0){\unicdbdjdcd}((v7\_yellow\_0~\\
X1~X0){\unicdbdjdcd}(\preoh v2\_struct\_0~X1)))\end{array}
\label{hyp:dgdgcdpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_lattice3~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}(v2\_lattice3~X0))))\end{array}
\label{hyp:dgdgbdpfjhfgmgmgpghhpfad}
\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:mgcdidpfhhbgjhcgfgmgbddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
(\preoh ({\unicdcdaddd} X1 .  (\preoh v1\_xboole\_0~X1){\unicdcdcdhd}({\unicdcdaddd} X2 .  ((v4\_yellow\_0~X2~\\
(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_yellow\_0~X2~(k3\_yellow\_1~X1))){\unicdcdcdhd}((v7\_yellow\_0~\\
X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}((v4\_waybel\_0~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(r5\_waybel\_1~\\
X0~X2))))){\unicdcdcdhd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~(k3\_yellow\_1~X1))~(u1\_struct\_0~\\
(k3\_yellow\_1~X1))){\unicdcdcdhd}((v7\_waybel\_1~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_1~X1))~(\\
u1\_struct\_0~(k3\_yellow\_1~X1)))))))){\unicdbdjdcd}(\preoh (v22\_waybel\_0~X2~(k3\_yellow\_1~\\
X1)~(k3\_yellow\_1~X1)){\unicdcdcdhd}(r5\_waybel\_1~X0~(k1\_yellow\_2~(k3\_yellow\_1~\\
X1)~(k3\_yellow\_1~X1)~X2))))))\end{array}$$
\end{theorem}
\end{document}
