\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{t8\_waybel20 (TMNA678DeazPJgVz37j6X4yR46qZe68VZMT)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k9\_xtuple\_0~k1\_xboole\_0=k1\_xboole\_0){\unicdcdcdhd}(k10\_xtuple\_0~k1\_xboole\_0=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehidpfggfhogdgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}((r1\_yellow\_0~X0~k1\_xboole\_0){\unicdbdjdcd}(v1\_yellow\_0~X0))\end{array}
\label{hyp:ehgdpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_yellow\_0~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}((v1\_yellow\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~X1)))){\unicdbdjdcd}(((v3\_lattice3~\\
(k3\_yellow\_3~X0~X1)){\unicdcdcdid}(r1\_yellow\_0~(k3\_yellow\_3~X0~X1)~X2)){\unicdbdjdcd}(k1\_yellow\_0~\\
(k3\_yellow\_3~X0~X1)~X2=k7\_yellow\_3~X0~X1~(k1\_yellow\_0~X0~(k4\_yellow\_3~\\
X0~X1~X2))~(k1\_yellow\_0~X1~(k5\_yellow\_3~X0~X1~X2))))))\end{array}
\label{hyp:ehfdpfjhfgmgmgpghhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_3~X0~X1))))){\unicdbdjdcd}(((v3\_lattice3~(k3\_yellow\_3~\\
X0~X1)){\unicdcdcdid}(r1\_yellow\_0~(k3\_yellow\_3~X0~X1)~X2)){\unicdbdjdcd}(k1\_yellow\_0~(k3\_yellow\_3~\\
X0~X1)~X2=k7\_yellow\_3~X0~X1~(k1\_yellow\_0~X0~(k4\_yellow\_3~X0~X1~X2))~\\
(k1\_yellow\_0~X1~(k5\_yellow\_3~X0~X1~X2))))))\end{array}
\label{hyp:ehedgdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k3\_yellow\_3~X0~X1)))){\unicdbdjdcd}(((r1\_yellow\_0~X0~(k4\_yellow\_3~X0~X1~X2)){\unicdcdcdhd}\\
(r1\_yellow\_0~X1~(k5\_yellow\_3~X0~X1~X2))){\unicdbdjded}(r1\_yellow\_0~(k3\_yellow\_3~\\
X0~X1)~X2))))\end{array}
\label{hyp:ehedbdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_orders\_2~X0){\unicdcdcdhd}((l1\_orders\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~\\
X1)))))){\unicdbdjdcd}(k5\_yellow\_3~X0~X1~X2=k10\_xtuple\_0~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_orders\_2~X0){\unicdcdcdhd}((l1\_orders\_2~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~\\
X1)))))){\unicdbdjdcd}(k4\_yellow\_3~X0~X1~X2=k9\_xtuple\_0~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfjhfgmgmgpghhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehidpfhhbgjhcgfgmgcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k3\_yellow\_3~X0~X1)))){\unicdbdjdcd}((r1\_yellow\_0~(k3\_yellow\_3~X0~X1)~X2){\unicdbdjdcd}\\
(k1\_yellow\_0~(k3\_yellow\_3~X0~X1)~X2=k7\_yellow\_3~X0~X1~(k1\_yellow\_0~\\
X0~(k4\_yellow\_3~X0~X1~X2))~(k1\_yellow\_0~X1~(k5\_yellow\_3~X0~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
