\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{t18\_projpl\_1 (TMFNJ7QQhqK6L1UKWhWJNTb1DsrjCE8en7x)}
\maketitle
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r5\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r4\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}((r5\_projpl\_1~X0~X1~X2~X3~X4){\unicdbdjded}((\preoh r4\_projpl\_1~\\
X0~X1~X2~X3){\unicdcdcdhd}((\preoh r4\_projpl\_1~X0~X2~X3~X4){\unicdcdcdhd}((\preoh r4\_projpl\_1~X0~X3~X4~X1){\unicdcdcdhd}\\
(\preoh r4\_projpl\_1~X0~X4~X1~X2)))))))))\end{array}
\label{hyp:eggdpfahchpgkgahmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfahchpgkgahmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}(r5\_projpl\_1~X0~X1~X2~X3~X4))))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
(r4\_projpl\_1~X0~X1~X2~X3)))))\end{array}$$
\end{theorem}
\end{document}
