\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{t48\_waybel34 (TMKVX8Vm3Lf3RCTjpHZQAh1k7x9TdgF3PTK)}
\maketitle
Let $ v2\_setfam\_1 : {{\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 $ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_yellow21 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_yellow21 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow21 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_yellow21 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_yellow21 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))){\unicdbdjdcd}((m1\_subset\_1~X1~(u1\_struct\_0~(k8\_waybel34~\\
X0))){\unicdbdjded}((v1\_orders\_2~X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(u1\_struct\_0~X1 \in \\
X0)))))\end{array}
\label{hyp:ehedddpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~X2~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ehcdjdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v3\_yellow21~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0)))))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(k4\_yellow21~X0~\\
X1=k1\_yellow21~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfjhfgmgmgpghhcdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v2\_yellow21~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0)))))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(k3\_yellow21~X0~\\
X1=k1\_yellow21~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfjhfgmgmgpghhcdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k4\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k4\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}((v11\_altcat\_1~(k4\_waybel34~X0)){\unicdcdcdhd}((v12\_altcat\_1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}((v2\_yellow21~(k4\_waybel34~X0)){\unicdcdcdhd}(v3\_yellow21~(k4\_waybel34~\\
X0))))))))\end{array}
\label{hyp:ggdgfdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}\\
(l2\_altcat\_1~X1))\end{array}
\label{hyp:egehpfngbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k8\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k8\_waybel34~\\
X0)){\unicdcdcdhd}((v3\_altcat\_2~(k8\_waybel34~X0)~(k4\_waybel34~X0)){\unicdcdcdhd}(m1\_altcat\_2~\\
(k8\_waybel34~X0)~(k4\_waybel34~X0))))))\end{array}
\label{hyp:egehpflgidpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k4\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k4\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}((v11\_altcat\_1~(k4\_waybel34~X0)){\unicdcdcdhd}((v12\_altcat\_1~(k4\_waybel34~\\
X0)){\unicdcdcdhd}((v2\_yellow21~(k4\_waybel34~X0)){\unicdcdcdhd}(l2\_altcat\_1~(k4\_waybel34~\\
X0))))))))\end{array}
\label{hyp:egehpflgedpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k10\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k10\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k10\_waybel34~\\
X0)){\unicdcdcdhd}((v2\_altcat\_2~(k10\_waybel34~X0)~(k8\_waybel34~X0)){\unicdcdcdhd}((v3\_altcat\_2~\\
(k10\_waybel34~X0)~(k8\_waybel34~X0)){\unicdcdcdhd}(m1\_altcat\_2~(k10\_waybel34~\\
X0)~(k8\_waybel34~X0)))))))\end{array}
\label{hyp:egehpflgbdadpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v2\_yellow21~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_yellow21~X0~\\
X1=X1))\end{array}
\label{hyp:eggdpfjhfgmgmgpghhcdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_altcat\_1~X1){\unicdcdcdhd}((v6\_altcat\_1~X1){\unicdcdcdhd}((v2\_altcat\_2~X1~(k8\_waybel34~\\
X0)){\unicdcdcdhd}((v3\_altcat\_2~X1~(k8\_waybel34~X0)){\unicdcdcdhd}(m1\_altcat\_2~X1~(k8\_waybel34~\\
X0))))))){\unicdbdjdcd}((X1=k10\_waybel34~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~(k8\_waybel34~X0))){\unicdbdjdcd}((m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjded}(v3\_waybel\_3~(k4\_yellow21~(k8\_waybel34~X0)~X2))))))\end{array}
\label{hyp:egbdcdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v2\_yellow21~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}(v3\_altcat\_2~X1~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v3\_altcat\_2~X1~X0){\unicdcdcdhd}(v2\_yellow21~X1))))))\end{array}
\label{hyp:dgdgidpfjhfgmgmgpghhcdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(v3\_altcat\_2~X1~X0))){\unicdbdjdcd}((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}(v12\_altcat\_1~X1))))\end{array}
\label{hyp:dgdgedpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}(v2\_altcat\_1~X1)){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(v11\_altcat\_1~\\
X1))))\end{array}
\label{hyp:dgdgddpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v2\_setfam\_1}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X0}}}})}}}\label{hyp:dgdgcdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v3\_yellow21~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}(v3\_altcat\_2~X1~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v3\_altcat\_2~X1~X0){\unicdcdcdhd}(v3\_yellow21~X1))))))\end{array}
\label{hyp:dgdgbdadpfjhfgmgmgpghhcdbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfhhbgjhcgfgmgdded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))){\unicdbdjdcd}((u1\_struct\_0~X1 \in X0){\unicdbdjdcd}((m1\_subset\_1~\\
X1~(u1\_struct\_0~(k10\_waybel34~X0))){\unicdbdjded}((v1\_orders\_2~X1){\unicdcdcdhd}((v3\_lattice3~\\
X1){\unicdcdcdhd}(v3\_waybel\_3~X1))))))\end{array}$$
\end{theorem}
\end{document}
