\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{t9\_grcat\_1 (TMLRvCQCiJnhSyzAukFsRpvZ8SpH1wqNFnU)}
\maketitle
Let $ v2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_grcat\_1}~{X0}})}{\unicdbdjdcd}{({{{k7\_grcat\_1}~{X0}}={{u1\_grcat\_1}~{X0}}})}}}\label{hyp:egjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_grcat\_1~X0){\unicdbdjdcd}((v2\_grcat\_1~X0){\unicdbdjded}(v13\_vectsp\_1~(\\
k9\_grcat\_1~X0)~(k7\_grcat\_1~X0)~(k8\_grcat\_1~X0)))\end{array}
\label{hyp:egbdddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_grcat\_1}~{X0}})}{\unicdbdjdcd}{({{{k9\_grcat\_1}~{X0}}={{u3\_grcat\_1}~{X0}}})}}}\label{hyp:egbdbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_grcat\_1}~{X0}})}{\unicdbdjdcd}{({{{k8\_grcat\_1}~{X0}}={{u2\_grcat\_1}~{X0}}})}}}\label{hyp:egbdadpfhgchdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_grcat\_1~X0){\unicdcdcdhd}(l1\_grcat\_1~X0)){\unicdbdjdcd}(v13\_vectsp\_1~\\
(u3\_grcat\_1~X0)~(u1\_grcat\_1~X0)~(u2\_grcat\_1~X0))\end{array}$$
\end{theorem}
\end{document}
