\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\_ltlaxio1 (TMLyQAxL3MPCkm9pG6yxzzZxD6vvQ8sxJST)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_hilbert1 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r8\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ltlaxio1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_ltlaxio1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}(((r8\_ltlaxio1~X3~\\
(k3\_hilbert1~X0~X1)){\unicdcdcdhd}(r8\_ltlaxio1~X3~(k3\_hilbert1~X1~X2))){\unicdbdjdcd}(r8\_ltlaxio1~\\
X3~(k3\_hilbert1~X0~X2))))))\end{array}
\label{hyp:ehedhdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}((r8\_ltlaxio1~X3~\\
(k3\_hilbert1~X0~(k4\_ltlaxio1~X1~X2))){\unicdbdjdcd}((r8\_ltlaxio1~X3~(k3\_hilbert1~\\
X0~X1)){\unicdcdcdhd}(r8\_ltlaxio1~X3~(k3\_hilbert1~X0~X2)))))))\end{array}
\label{hyp:ehedgdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}\\
(((r8\_ltlaxio1~X2~X0){\unicdcdcdhd}(r8\_ltlaxio1~X2~(k3\_hilbert1~X0~X1))){\unicdbdjdcd}(\\
r8\_ltlaxio1~X2~X1))))\end{array}
\label{hyp:ehedddpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}(((X0 \in k13\_ltlaxio1){\unicdcdcdid}(X0 \in X1)){\unicdbdjdcd}\\
(r8\_ltlaxio1~X1~X0)))\end{array}
\label{hyp:ehedcdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}(k3\_hilbert1~\\
(k3\_hilbert1~X0~(k3\_hilbert1~X1~X2))~(k3\_hilbert1~(k3\_hilbert1~\\
X0~X1)~(k3\_hilbert1~X0~X2)) \in k13\_ltlaxio1)))\end{array}
\label{hyp:ehddfdpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}(k3\_hilbert1~X0~(k3\_hilbert1~X1~X0) \in k13\_ltlaxio1))\end{array}
\label{hyp:ehddedpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_hilbert1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_hilbert1)){\unicdbdjdcd}(m1\_subset\_1~(k4\_ltlaxio1~X0~X1)~k1\_hilbert1)\end{array}
\label{hyp:egehpflgedpfmgehmgbgihjgpgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_hilbert1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_hilbert1)){\unicdbdjdcd}(m1\_subset\_1~(k3\_hilbert1~X0~X1)~k1\_hilbert1)\end{array}
\label{hyp:egehpflgddpfigjgmgcgfgchehbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k13\_ltlaxio1}}~{({{k1\_zfmisc\_1}~{k1\_hilbert1}})}}\label{hyp:egehpflgbdddpfmgehmgbgihjgpgbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfmgehmgbgihjgpgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~k1\_hilbert1)){\unicdbdjdcd}((r8\_ltlaxio1~X3~\\
(k3\_hilbert1~X0~(k3\_hilbert1~X1~X2))){\unicdbdjdcd}(r8\_ltlaxio1~X3~(k3\_hilbert1~\\
(k4\_ltlaxio1~X0~X1)~X2))))))\end{array}$$
\end{theorem}
\end{document}
