\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{t10\_group\_9 (TMT7xTYrBgs1mqgy49KLsLckocaL8eBECSw)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}(m1\_group\_2~X0~X0)\end{array}
\label{hyp:ehfdedpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_partfun1~\\
X0~X1~X2~X3=k5\_relat\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k5\_relat\_1~X1~X0=X1)\end{array}
\label{hyp:chegidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{l1\_group\_9}~{X1}}~{X0}})}{\unicdbdjdcd}{({{l3\_algstr\_0}~{X1}})}}}}\label{hyp:egehpfmgbdpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~X0)){\unicdbdjdcd}((v1\_funct\_1~(k3\_group\_9~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~\\
(k3\_group\_9~X0~X1~X2)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_group\_6~\\
(k3\_group\_9~X0~X1~X2)~X1~X1){\unicdcdcdhd}(m1\_subset\_1~(k3\_group\_9~X0~X1~X2)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpflgddpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_group\_1~X2){\unicdcdcdhd}((v3\_group\_1~\\
X2){\unicdcdcdhd}((v3\_group\_9~X2~X0){\unicdcdcdhd}(l1\_group\_9~X2~X0))))){\unicdbdjdcd}((m1\_group\_9~\\
X2~X0~X1){\unicdbdjded}((m1\_group\_2~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
(k3\_group\_9~X0~X2~X3=k2\_partfun1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1)~(k3\_group\_9~X0~X1~X3)~(u1\_struct\_0~X2))))))\end{array}
\label{hyp:eghdpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
m1\_group\_9~X1~X0~X1)\end{array}$$
\end{theorem}
\end{document}
