\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{t10\_waybel\_9 (TMYQUV3yH4qjsYha8yds19RR55hx4uLDDEa)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_waybel\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_waybel\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ v6\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((v4\_orders\_2~\\
X0){\unicdbdjded}(v4\_orders\_2~(g1\_orders\_2~(u1\_struct\_0~X0)~(u1\_orders\_2~\\
X0))))\end{array}
\label{hyp:mghdpfjhfgmgmgpghhpfgd}
\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}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((v7\_waybel\_0~X2){\unicdcdcdhd}(l1\_waybel\_0~X2~X0))))){\unicdbdjdcd}((v6\_waybel\_0~(k3\_waybel\_2~\\
X0~X1~X2)~X0){\unicdcdcdhd}(v7\_waybel\_0~(k3\_waybel\_2~X0~X1~X2)))\end{array}
\label{hyp:ggdggdpfhhbgjhcgfgmgpfcd}
\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}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
(l1\_waybel\_0~X2~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k3\_waybel\_2~X0~X1~X2)){\unicdcdcdhd}\\
(v6\_waybel\_0~(k3\_waybel\_2~X0~X1~X2)~X0))\end{array}
\label{hyp:ggdgfdpfhhbgjhcgfgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_waybel\_0~X1~X0){\unicdbdjdcd}\\
(l1\_orders\_2~X1))\end{array}
\label{hyp:egehpfmgbdpfhhbgjhcgfgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\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}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
(l1\_waybel\_0~X2~X0)))){\unicdbdjdcd}((v6\_waybel\_0~(k3\_waybel\_2~X0~X1~X2)~X0){\unicdcdcdhd}\\
(l1\_waybel\_0~(k3\_waybel\_2~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflgddpfhhbgjhcgfgmgpfcd}
\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 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l1\_waybel\_0~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v6\_waybel\_0~X3~X0){\unicdcdcdhd}(l1\_waybel\_0~\\
X3~X0)){\unicdbdjdcd}((X3=k3\_waybel\_2~X0~X1~X2){\unicdbdjded}((g1\_orders\_2~(u1\_struct\_0~\\
X3)~(u1\_orders\_2~X3)=g1\_orders\_2~(u1\_struct\_0~X2)~(u1\_orders\_2~\\
X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((X5=k1\_funct\_1~(u1\_waybel\_0~\\
X0~X2)~X4){\unicdcdcdhd}(k1\_funct\_1~(u1\_waybel\_0~X0~X3)~X4=k11\_lattice3~X0~X1~\\
X5)))))))))\end{array}
\label{hyp:egddpfhhbgjhcgfgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfhhbgjhcgfgmgpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v4\_orders\_2~X2){\unicdcdcdhd}((v7\_waybel\_0~X2){\unicdcdcdhd}(l1\_waybel\_0~X2~X0)))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k3\_waybel\_2~X0~X1~X2)){\unicdcdcdhd}((v4\_orders\_2~(k3\_waybel\_2~\\
X0~X1~X2)){\unicdcdcdhd}((v7\_waybel\_0~(k3\_waybel\_2~X0~X1~X2)){\unicdcdcdhd}(l1\_waybel\_0~\\
(k3\_waybel\_2~X0~X1~X2)~X0))))))\end{array}$$
\end{theorem}
\end{document}
