\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t4\_metric\_6 (TMJ42h27Tet24JkeY1XQyf422Z5HVnG1yAG)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_metric\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}((v9\_metric\_1~X0){\unicdbdjded}(v5\_metric\_1~\\
(u1\_metric\_1~X0)~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egjdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}((v8\_metric\_1~X0){\unicdbdjded}(v4\_metric\_1~\\
(u1\_metric\_1~X0)~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egidpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}((v7\_metric\_1~X0){\unicdbdjded}(v3\_metric\_1~\\
(u1\_metric\_1~X0)~(u1\_struct\_0~X0)))\end{array}
\label{hyp:eghdpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_metric\_1~X0){\unicdbdjdcd}((v6\_metric\_1~X0){\unicdbdjded}(v2\_metric\_1~\\
(u1\_metric\_1~X0)~(u1\_struct\_0~X0)))\end{array}
\label{hyp:eggdpfngfgehchjgdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfngfgehchjgdgpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_metric\_1~X0){\unicdcdcdhd}((v6\_metric\_1~\\
X0){\unicdcdcdhd}((v7\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}\\
(l1\_metric\_1~X0))))))){\unicdbdjdcd}((v2\_metric\_1~(u1\_metric\_1~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v3\_metric\_1~(u1\_metric\_1~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v4\_metric\_1~\\
(u1\_metric\_1~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(v5\_metric\_1~(u1\_metric\_1~\\
X0)~(u1\_struct\_0~X0)))))\end{array}$$
\end{theorem}
\end{document}
