\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{t46\_incsp\_1 (TMURMH1aJPUhXdDcfeF94w8QHRshKpvbiqv)}
\maketitle
Let $ v15\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_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 $ u4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r5\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_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~\\
(u4\_incsp\_1~X0)){\unicdbdjdcd}((r5\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~\\
X1~X2~X3)~X4){\unicdbdjded}((r2\_incsp\_1~X0~X1~X4){\unicdcdcdhd}((r2\_incsp\_1~X0~X2~X4){\unicdcdcdhd}(r2\_incsp\_1~\\
X0~X3~X4))))))))\end{array}
\label{hyp:ehedpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_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~(u4\_incsp\_1~X0)){\unicdbdjdcd}\\
(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r2\_incsp\_1~\\
X0~X4~X3){\unicdcdcdhd}(\preoh v3\_incsp\_1~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X4)~X0)))))))\end{array}
\label{hyp:ehededpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u4\_incsp\_1~X0)){\unicdbdjdcd}({\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\_incsp\_1~X0~\\
(k8\_domain\_1~(u1\_incsp\_1~X0)~X2~X3~X4)~X1){\unicdcdcdhd}(\preoh v3\_incsp\_1~(k8\_domain\_1~\\
(u1\_incsp\_1~X0)~X2~X3~X4)~X0))))))\end{array}
\label{hyp:ehedbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_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~(u4\_incsp\_1~X0)){\unicdbdjdcd}((r5\_incsp\_1~X0~(k7\_domain\_1~\\
(u1\_incsp\_1~X0)~X1~X2)~X3){\unicdbdjded}((r2\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(r2\_incsp\_1~X0~\\
X2~X3))))))\end{array}
\label{hyp:ehddpfjgogdgdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfjgogdgdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u4\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r5\_incsp\_1~X0~\\
(k7\_domain\_1~(u1\_incsp\_1~X0)~X3~X4)~X2){\unicdcdcdhd}(\preoh v3\_incsp\_1~(k8\_domain\_1~\\
(u1\_incsp\_1~X0)~X1~X3~X4)~X0))))))\end{array}$$
\end{theorem}
\end{document}
