\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{t21\_projpl\_1 (TMUQzvoqQb3Z8U5HyfwbcnrR3CEkdVXBoCK)}
\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 $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_projpl\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_zfmisc\_1~X0~X1~X2){\unicdbdjded}((X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X0{\unicdcdgdad}X2){\unicdcdcdhd}(X1{\unicdcdgdad}X2)))\end{array}
\label{hyp:egfdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}((v1\_projpl\_1~X0){\unicdbdjded}({\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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~\\
X3){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X4){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X4){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(X3{\unicdcdgdad}\\
X4)))))))))))\end{array}
\label{hyp:egedpfahchpgkgahmgpfbd}
\end{equation}
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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_incsp\_1~X0)){\unicdbdjdcd}((r3\_projpl\_1~X0~X1~X2~X3~X4){\unicdbdjded}((r1\_incsp\_1~X0~\\
X1~X2){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(r1\_incsp\_1~X0~X1~X4))))))))\end{array}
\label{hyp:egddpfahchpgkgahmgpfbd}
\end{equation}
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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}((r2\_projpl\_1~X0~X1~X2~X3){\unicdbdjded}((\\
r1\_incsp\_1~X0~X1~X2){\unicdcdcdhd}(r1\_incsp\_1~X0~X1~X3))))))\end{array}
\label{hyp:egcdpfahchpgkgahmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfahchpgkgahmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
(((v1\_projpl\_1~X0){\unicdcdcdhd}((r3\_projpl\_1~X0~X1~X5~X6~X7){\unicdcdcdhd}((r1\_zfmisc\_1~\\
X5~X6~X7){\unicdcdcdhd}((r2\_projpl\_1~X0~X2~X8~X5){\unicdcdcdhd}((r2\_projpl\_1~X0~X3~X8~X6){\unicdcdcdhd}(\\
r2\_projpl\_1~X0~X4~X8~X7)))))){\unicdbdjdcd}((r1\_incsp\_1~X0~X1~X8){\unicdcdcdid}(r1\_zfmisc\_1~\\
X2~X3~X4)))))))))))\end{array}$$
\end{theorem}
\end{document}
