\documentclass{article}
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\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}
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\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t20\_trees\_9 (TMTqx2ZaTkTpC7u413AnWNPgf31xEcAR4ta)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_trees\_9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_trees\_9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v3\_trees\_3~X1)){\unicdbdjdcd}(\\
(X0 \in k9\_trees\_9~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~X1){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_trees\_1~X3~(k9\_xtuple\_0~X2)){\unicdcdcdhd}(X0=k5\_trees\_2~X2~X3))))\end{array}
\label{hyp:ehbdjdpfehchfgfgdhpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
(X0 \in k3\_trees\_9~X0)\end{array}
\label{hyp:ehbdbdpfehchfgfgdhpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~\\
X1))){\unicdbdjdcd}((X0 \in k3\_trees\_9~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_trees\_1~X2~(k9\_xtuple\_0~\\
X1)){\unicdcdcdhd}(X0=k5\_trees\_2~X1~X2)))\end{array}
\label{hyp:ehbdadpfehchfgfgdhpfjd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfehchfgfgdhpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v3\_trees\_3~X1)){\unicdbdjdcd}((X0 \in X1){\unicdbdjdcd}(\\
X0 \in k9\_trees\_9~X1)))\end{array}$$
\end{theorem}
\end{document}
