\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{t42\_modal\_1 (TMc4KA3eg6hYJ6Q3yPmPbGmVTBqfEbKYEXp)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_modal\_1 : {\iota}$ be given.
Let $ k17\_modal\_1 : {\iota}$ be given.
Let $ k3\_modal\_1 : {\iota}$ be given.
Let $ k16\_modal\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_modal\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_modal\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_modal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_modal\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_modal\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_modal\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_modal\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_modal\_1){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k17\_modal\_1){\unicdcdcdhd}\\
((\preoh (v1\_modal\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~k6\_modal\_1)){\unicdcdcdhd}((\preoh (v2\_modal\_1~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~k6\_modal\_1)){\unicdcdcdhd}((\preoh (v3\_modal\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~k6\_modal\_1)){\unicdcdcdhd}(\preoh (v4\_modal\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~k6\_modal\_1))))))\end{array}
\label{hyp:ehedbdpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_modal\_1){\unicdbdjdcd}((v4\_modal\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k6\_modal\_1){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k6\_modal\_1){\unicdcdcdhd}\\
(X0=k12\_modal\_1~X1~X2))))\end{array}
\label{hyp:egbdjdpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_modal\_1){\unicdbdjdcd}((v3\_modal\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k6\_modal\_1){\unicdcdcdhd}(X0=k11\_modal\_1~X1)))\end{array}
\label{hyp:egbdidpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_modal\_1){\unicdbdjdcd}((v2\_modal\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k6\_modal\_1){\unicdcdcdhd}(X0=k10\_modal\_1~X1)))\end{array}
\label{hyp:egbdhdpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_modal\_1){\unicdbdjdcd}((v1\_modal\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k3\_modal\_1){\unicdcdcdhd}(X0=k16\_modal\_1~X1)))\end{array}
\label{hyp:egbdgdpfngpgegbgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfngpgegbgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_modal\_1){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k17\_modal\_1){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k3\_modal\_1){\unicdbdjdcd}(X0{\unicdcdgdad}k16\_modal\_1~X1)){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_modal\_1){\unicdbdjdcd}(X0{\unicdcdgdad}k10\_modal\_1~X1)){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_modal\_1){\unicdbdjdcd}(X0{\unicdcdgdad}k11\_modal\_1~X1)){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k6\_modal\_1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k6\_modal\_1){\unicdbdjdcd}(X0{\unicdcdgdad}k12\_modal\_1~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
