\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{t4\_ltlaxio1 (TMTwnHS2Fnmkm7kUVUEmBSntj8pRQtZk3g6)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_hilbert1 : {\iota}$ be given.
Let $ k2\_hilbert1 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_hilbert2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hilbert1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_hilbert2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_hilbert2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_hilbert2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}(\preoh (\preoh v1\_hilbert2~X0){\unicdcdcdhd}\\
((\preoh v2\_hilbert2~X0){\unicdcdcdhd}((\preoh v3\_hilbert2~X0){\unicdcdcdhd}(X0{\unicdcdgdad}k2\_hilbert1))))\end{array}
\label{hyp:ehjdpfigjgmgcgfgchehcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v3\_hilbert2~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}(X0=k1\_hilbert2~X1)))\end{array}
\label{hyp:egidpfigjgmgcgfgchehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v2\_hilbert2~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k1\_hilbert1){\unicdcdcdhd}(X0=k3\_hilbert1~X1~X2))))\end{array}
\label{hyp:eghdpfigjgmgcgfgchehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}((v1\_hilbert2~X0){\unicdbdjded}(\\
{\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k1\_hilbert1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~k1\_hilbert1){\unicdcdcdhd}(X0=k4\_hilbert1~X1~X2))))\end{array}
\label{hyp:eggdpfigjgmgcgfgchehcd}
\end{equation}
\begin{theorem}\label{thm:ehedpfmgehmgbgihjgpgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_hilbert1){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k2\_hilbert1){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_hilbert2~X1){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_hilbert1){\unicdbdjdcd}((X0{\unicdcdgdad}k3\_hilbert1~X2~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k1\_hilbert1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_hilbert1){\unicdbdjdcd}(X0{\unicdcdgdad}\\
k4\_hilbert1~X4~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
