\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{t30\_group\_9 (TMUiYbmeHhkteSroojn3GPTrvCUcpmZXVNN)}
\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 $ k16\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k18\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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}({\unicdcdadad} X3 .  (m1\_group\_9~X3~X0~\\
X1){\unicdbdjdcd}(k19\_group\_9~X0~X1~X2~X3=k18\_group\_9~X0~X1~(k16\_group\_9~X0~X1~\\
X2~X3))))\end{array}
\label{hyp:ehcdjdpfhgchpgfhahpfjd}
\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 .  ((v2\_group\_9~X2~X0){\unicdcdcdhd}(m1\_group\_9~X2~X0~X1)){\unicdbdjdcd}(k18\_group\_9~\\
X0~X1~(k15\_group\_9~X0~X1~X2)=X2))\end{array}
\label{hyp:ehcdfdpfhgchpgfhahpfjd}
\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 .  (m1\_group\_9~X3~X0~\\
X1){\unicdbdjdcd}(\preoh (k2\_group\_2~X1~(k15\_group\_9~X0~X1~X2)~(k15\_group\_9~X0~X1~X3)=\\
k2\_group\_2~X1~(k15\_group\_9~X0~X1~X3)~(k15\_group\_9~X0~X1~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
((v2\_group\_9~X4~X0){\unicdcdcdhd}(m1\_group\_9~X4~X0~X1)){\unicdbdjdcd}(u1\_struct\_0~X4{\unicdcdgdad}k2\_group\_2~\\
X1~(k15\_group\_9~X0~X1~X2)~(k15\_group\_9~X0~X1~X3))))))\end{array}
\label{hyp:ehbdhdpfhgchpgfhahpfjd}
\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 .  (m1\_group\_9~X3~X0~\\
X1){\unicdbdjdcd}(k16\_group\_9~X0~X1~X2~X3=k2\_group\_2~X1~(k15\_group\_9~X0~X1~X2)~\\
(k15\_group\_9~X0~X1~X3))))\end{array}
\label{hyp:egcdedpfhgchpgfhahpfjd}
\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}(k15\_group\_9~X0~X1~X2=u1\_struct\_0~\\
X2))\end{array}
\label{hyp:egcdddpfhgchpgfhahpfjd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_group\_9~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_group\_9~X3~X0~\\
X1){\unicdbdjdcd}((k16\_group\_9~X0~X1~X2~X3=k16\_group\_9~X0~X1~X3~X2){\unicdbdjdcd}(u1\_struct\_0~\\
(k19\_group\_9~X0~X1~X2~X3)=k16\_group\_9~X0~X1~X2~X3))))\end{array}$$
\end{theorem}
\end{document}
