\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{t20\_waybel34 (TMcYmcDBTcEu1dEJZc7KXFcDotTgs1UECdP)}
\maketitle
Let $ v2\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_waybel34 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v16\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v21\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_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 $ v2\_yellow21 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}((v9\_functor0~(k6\_waybel34~X0)~\\
(k4\_waybel34~X0)~(k5\_waybel34~X0)){\unicdcdcdhd}((v16\_functor0~(k6\_waybel34~\\
X0)~(k4\_waybel34~X0)~(k5\_waybel34~X0)){\unicdcdcdhd}(v21\_functor0~(k6\_waybel34~\\
X0)~(k4\_waybel34~X0)~(k5\_waybel34~X0))))\end{array}
\label{hyp:ggdghdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}((v9\_functor0~(k6\_waybel34~X0)~\\
(k4\_waybel34~X0)~(k5\_waybel34~X0)){\unicdcdcdhd}((v16\_functor0~(k6\_waybel34~\\
X0)~(k4\_waybel34~X0)~(k5\_waybel34~X0)){\unicdcdcdhd}(m2\_functor0~(k6\_waybel34~\\
X0)~(k4\_waybel34~X0)~(k5\_waybel34~X0))))\end{array}
\label{hyp:egehpflggdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_waybel34~X0)){\unicdcdcdhd}\\
((v2\_altcat\_1~(k5\_waybel34~X0)){\unicdcdcdhd}((v6\_altcat\_1~(k5\_waybel34~\\
X0)){\unicdcdcdhd}((v11\_altcat\_1~(k5\_waybel34~X0)){\unicdcdcdhd}((v12\_altcat\_1~(k5\_waybel34~\\
X0)){\unicdcdcdhd}((v2\_yellow21~(k5\_waybel34~X0)){\unicdcdcdhd}(l2\_altcat\_1~(k5\_waybel34~\\
X0))))))))\end{array}
\label{hyp:egehpflgfdpfhhbgjhcgfgmgdded}
\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\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}((r2\_functor0~X0~\\
X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_functor0~X2~X0~X1){\unicdcdcdhd}((v21\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(v16\_functor0~X2~X0~X1)))))\end{array}
\label{hyp:egedadpfggfhogdgehpgchad}
\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}
\begin{theorem}\label{thm:ehcdadpfhhbgjhcgfgmgdded}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_setfam\_1~X0){\unicdbdjdcd}(r2\_functor0~(k4\_waybel34~X0)~(\\
k5\_waybel34~X0))\end{array}$$
\end{theorem}
\end{document}
