\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{t19\_altcat\_2 (TMXNfDh6MHSKYLaswjsqb795RkSZTJsZfux)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_altcat\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)){\unicdbdjdcd}(((v1\_xboole\_0~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(v1\_xboole\_0~(u1\_struct\_0~X1))){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:mgcdidpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v2\_struct\_0}~{k5\_altcat\_2}})}{\unicdcdcdhd}{({{v6\_altcat\_1}~{k5\_altcat\_2}})}}\label{hyp:ggdgidpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgbdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v6\_altcat\_1}~{k5\_altcat\_2}})}{\unicdcdcdhd}{({{l2\_altcat\_1}~{k5\_altcat\_2}})}}\label{hyp:egehpflgfdpfbgmgehdgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfbgmgehdgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_struct\_0~X0){\unicdcdcdhd}((v6\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}(X0=k5\_altcat\_2)\end{array}$$
\end{theorem}
\end{document}
