\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{t1\_group\_3 (TMK4L1WXnzs5sjVo5S9M6iHDkyKJrN2mgFP)}
\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 $ l3\_algstr\_0 : {{\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 $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_group\_1 : {{\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\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(((k6\_algstr\_0~X0~X1~X2=k6\_algstr\_0~\\
X0~X1~X3){\unicdcdcdid}(k6\_algstr\_0~X0~X2~X1=k6\_algstr\_0~X0~X3~X1)){\unicdbdjdcd}(X2=X3)))))\end{array}
\label{hyp:ehgdpfhgchpgfhahpfbd}
\end{equation}
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\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~X0~X1~X2=X3){\unicdbdjded}\\
(X2=k6\_algstr\_0~X0~(k2\_group\_1~X0~X1)~X3)))))\end{array}
\label{hyp:ehbdddpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}\\
((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k2\_group\_1~X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgcdpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v3\_group\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X1~X2)~X3=k6\_algstr\_0~X0~X1~(k6\_algstr\_0~X0~X2~\\
X3))))))\end{array}
\label{hyp:egddpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v2\_group\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k6\_algstr\_0~X0~X2~X1=X2){\unicdcdcdhd}((k6\_algstr\_0~X0~X1~X2=X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((k6\_algstr\_0~X0~X2~X3=X1){\unicdcdcdhd}\\
(k6\_algstr\_0~X0~X3~X2=X1))))))))\end{array}
\label{hyp:egcdpfhgchpgfhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfhgchpgfhahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X1~X2)~(k2\_group\_1~X0~X2)=X1){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X1~(k2\_group\_1~X0~X2))~X2=X1){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~(k2\_group\_1~X0~X2)~X2)~X1=X1){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X2~(k2\_group\_1~X0~X2))~X1=X1){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~X1~(k6\_algstr\_0~X0~X2~(k2\_group\_1~X0~X2))=X1){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~X1~(k6\_algstr\_0~X0~(k2\_group\_1~X0~X2)~X2)=X1){\unicdcdcdhd}((k6\_algstr\_0~\\
X0~(k2\_group\_1~X0~X2)~(k6\_algstr\_0~X0~X2~X1)=X1){\unicdcdcdhd}(k6\_algstr\_0~X0~\\
X2~(k6\_algstr\_0~X0~(k2\_group\_1~X0~X2)~X1)=X1))))))))))\end{array}$$
\end{theorem}
\end{document}
