\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{t9\_euclmetr (TMF2TvhJHpMWXJiYPSpyquwabLE2yjLeWvR)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_conaffm : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v7\_euclmetr~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r4\_analmetr~X0~X1~X2~X1~X3){\unicdcdcdhd}((r4\_analmetr~\\
X0~X1~X4~X1~X5){\unicdcdcdhd}((r4\_analmetr~X0~X1~X6~X1~X7){\unicdcdcdhd}((r4\_analmetr~X0~X2~X4~\\
X3~X5){\unicdcdcdhd}(r4\_analmetr~X0~X2~X6~X3~X7))))){\unicdbdjdcd}((r2\_analoaf~X0~X1~X6~X1~X2){\unicdcdcdid}\\
((r2\_analoaf~X0~X1~X2~X1~X4){\unicdcdcdid}(r4\_analmetr~X0~X4~X6~X5~X7))))))))))))\end{array}
\label{hyp:eghdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v4\_conaffm~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r4\_analmetr~X0~X1~X2~X1~X3){\unicdcdcdhd}((r4\_analmetr~\\
X0~X1~X4~X1~X5){\unicdcdcdhd}((r4\_analmetr~X0~X1~X6~X1~X7){\unicdcdcdhd}((r4\_analmetr~X0~X2~X4~\\
X3~X5){\unicdcdcdhd}(r4\_analmetr~X0~X2~X6~X3~X7))))){\unicdbdjdcd}((r2\_analoaf~X0~X1~X6~X1~X2){\unicdcdcdid}\\
((r2\_analoaf~X0~X1~X2~X1~X4){\unicdcdcdid}(r4\_analmetr~X0~X4~X6~X5~X7))))))))))))\end{array}
\label{hyp:egedpfdgpgogbgggggng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analmetr~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_analmetr~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v2\_analmetr~X0)))\end{array}
\label{hyp:dgdgbdpfbgogbgmgngfgehch}
\end{equation}
\begin{theorem}\label{thm:ehjdpffgfhdgmgngfgehch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v7\_euclmetr~X0){\unicdbdjded}(v4\_conaffm~X0))\end{array}$$
\end{theorem}
\end{document}
