\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{t25\_incsp\_1 (TMJY5RHa4yBvn824ZZwr9YetUuUuBNZgU2w)}
\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 $ 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 $ u4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r5\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v10\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_incsp\_1~X0){\unicdbdjdcd}((v10\_incsp\_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~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u4\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u4\_incsp\_1~X0)){\unicdbdjdcd}\\
(((r5\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X4){\unicdcdcdhd}(r5\_incsp\_1~\\
X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X5)){\unicdbdjdcd}((v3\_incsp\_1~(k8\_domain\_1~\\
(u1\_incsp\_1~X0)~X1~X2~X3)~X0){\unicdcdcdid}(X4=X5)))))))))\end{array}
\label{hyp:egbdddpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_incsp\_1~X0){\unicdbdjdcd}((v9\_incsp\_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~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(u4\_incsp\_1~X0)){\unicdcdcdhd}(r5\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~\\
X1~X2~X3)~X4))))))\end{array}
\label{hyp:egbdcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_incsp\_1~X0){\unicdbdjdcd}((v15\_incsp\_1~X0){\unicdbdjdcd}((v5\_incsp\_1~X0){\unicdcdcdhd}\\
((v6\_incsp\_1~X0){\unicdcdcdhd}((v7\_incsp\_1~X0){\unicdcdcdhd}((v8\_incsp\_1~X0){\unicdcdcdhd}((v9\_incsp\_1~\\
X0){\unicdcdcdhd}((v10\_incsp\_1~X0){\unicdcdcdhd}((v11\_incsp\_1~X0){\unicdcdcdhd}((v12\_incsp\_1~X0){\unicdcdcdhd}\\
((v13\_incsp\_1~X0){\unicdcdcdhd}(v14\_incsp\_1~X0)))))))))))\end{array}
\label{hyp:dgdgbdpfjgogdgdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfjgogdgdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
(\preoh (\preoh v3\_incsp\_1~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X0){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u4\_incsp\_1~X0)){\unicdbdjdcd}(\preoh {\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u4\_incsp\_1~X0)){\unicdbdjdcd}((r5\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~\\
X1~X2~X3)~X5){\unicdbdjded}(X4=X5))))))))\end{array}$$
\end{theorem}
\end{document}
