\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{t24\_catalg\_1 (TMGPBtQ21BDnqEa9kvfwy7EUAiSWiy6Pv1M)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u4\_struct\_0~X0)){\unicdbdjdcd}((k1\_msualg\_1~X0~X2=k1\_xboole\_0){\unicdbdjdcd}(k3\_msualg\_1~\\
X0~X2~X1=k1\_tarski~k1\_xboole\_0))))\end{array}
\label{hyp:ehedpfahchbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
((k1\_msualg\_1~(k3\_catalg\_1~X0)~(k8\_catalg\_1~X0~X1)=k1\_xboole\_0){\unicdcdcdhd}\\
(k2\_msualg\_1~(k3\_catalg\_1~X0)~(k8\_catalg\_1~X0~X1)=k9\_catalg\_1~\\
X0~X1~X1)))\end{array}
\label{hyp:ehbdidpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_catalg\_1}~{X0}}={{k2\_catalg\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_catalg\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k2\_catalg\_1~X0)){\unicdcdcdhd}(v1\_msualg\_1~(k2\_catalg\_1~\\
X0))))\end{array}
\label{hyp:ggdgddpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k8\_catalg\_1~X0~X1)~(u4\_struct\_0~(k3\_catalg\_1~X0)))\end{array}
\label{hyp:egehpflgidpfdgbgehbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_msualg\_1~(k2\_catalg\_1~X0)){\unicdcdcdhd}(l1\_msualg\_1~(k2\_catalg\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdgbgehbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfdgbgehbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~(k3\_catalg\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(k3\_msualg\_1~(k3\_catalg\_1~\\
X0)~(k8\_catalg\_1~X0~X2)~X1=k1\_tarski~k1\_xboole\_0)))\end{array}$$
\end{theorem}
\end{document}
