\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{t21\_group\_9 (TMYzgyYNMLAPEQkeBiAcbXtdZWNP3As1ZxM)}
\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 $ k17\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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 .  (m1\_group\_9~X2~X0~X1){\unicdbdjdcd}(m1\_group\_9~(k4\_group\_9~X0~X1)~\\
X0~X2))\end{array}
\label{hyp:ehbdgdpfhgchpgfhahpfjd}
\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 .  (m1\_group\_9~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v2\_group\_9~X3~X0){\unicdcdcdhd}\\
(m1\_group\_9~X3~X0~X1)){\unicdbdjdcd}((m1\_group\_9~X3~X0~X2){\unicdbdjded}(k17\_group\_9~X0~X1~\\
X3~X2=X3))))\end{array}
\label{hyp:mggdjdpfhgchpgfhahpfjd}
\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}(\\
(v2\_group\_9~(k4\_group\_9~X0~X1)~X0){\unicdcdcdhd}(m1\_group\_9~(k4\_group\_9~X0~\\
X1)~X0~X1))\end{array}
\label{hyp:egehpflgedpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\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\_group\_9~X2~X0~X1){\unicdcdcdhd}(m1\_group\_9~X3~X0~\\
X1))){\unicdbdjdcd}(k17\_group\_9~X0~X1~X2~X3=k17\_group\_9~X0~X1~X3~X2)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdhdpfhgchpgfhahpfjd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_group\_9~X2~X0~X1){\unicdbdjdcd}((k17\_group\_9~X0~X1~(k4\_group\_9~\\
X0~X1)~X2=k4\_group\_9~X0~X1){\unicdcdcdhd}(k17\_group\_9~X0~X1~X2~(k4\_group\_9~X0~\\
X1)=k4\_group\_9~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
