\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{l44\_group\_9 (TMYVf69ZbLhd3obEhmW7qPsmKvhYgdfpSBe)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ 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}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_group\_2~X2~X0){\unicdbdjdcd}((r1\_struct\_0~X2~X1){\unicdbdjdcd}(r1\_struct\_0~\\
X2~(k2\_group\_1~X0~X1)))))\end{array}
\label{hyp:ehfdbdpfhgchpgfhahpfcd}
\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}((\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))))))\end{array}
\label{hyp:egehpfngbdpfhgchpgfhahpfjd}
\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 .  ((\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}
\begin{theorem}\label{thm:mgededpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_group\_9~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_struct\_0~X2~X3){\unicdbdjdcd}(r1\_struct\_0~X2~(k2\_group\_1~\\
X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
