\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{t136\_group\_3 (TMX6jpq9jk1fZXNVNdJSsDpKXkpVsrUSta4)}
\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 $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_card\_1 : {{\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}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}((v1\_finset\_1~\\
(k15\_group\_2~X0~X1)){\unicdbdjdcd}(({\unicdcdaddd} X2 .  (v1\_finset\_1~X2){\unicdcdcdhd}((X2=k15\_group\_2~\\
X0~X1){\unicdcdcdhd}(k18\_group\_2~X0~X1=k5\_card\_1~X2))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (v1\_finset\_1~\\
X2){\unicdcdcdhd}((X2=k16\_group\_2~X0~X1){\unicdcdcdhd}(k18\_group\_2~X0~X1=k5\_card\_1~X2))))))\end{array}
\label{hyp:ehbdedgdpfhgchpgfhahpfcd}
\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 .  ((v15\_algstr\_0~X1){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0)){\unicdbdjdcd}(k1\_card\_1~(k9\_group\_3~X0~X1)=k17\_group\_2~X0~(k11\_group\_3~\\
X0~X1)))\end{array}
\label{hyp:ehbdddfdpfhgchpgfhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{X0}}={{k1\_card\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_finset\_1~X0){\unicdbdjdcd}((\preoh v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}\\
(v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdgidpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}((v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}(\\
v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdggdpfdgbgchegpfbd}
\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\_group\_2~X1~X0)){\unicdbdjdcd}((\\
v15\_algstr\_0~(k11\_group\_3~X0~X1)){\unicdcdcdhd}(m1\_group\_2~(k11\_group\_3~X0~\\
X1)~X0))\end{array}
\label{hyp:egehpflgbdbdpfhgchpgfhahpfdd}
\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\_group\_2~X1~X0){\unicdbdjdcd}(k17\_group\_2~\\
X0~X1=k1\_card\_1~(k15\_group\_2~X0~X1)))\end{array}
\label{hyp:egbdhdpfhgchpgfhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdddgdpfhgchpgfhahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v15\_algstr\_0~X1){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0)){\unicdbdjdcd}(\preoh ((v1\_finset\_1~(k9\_group\_3~X0~X1)){\unicdcdcdid}(v1\_finset\_1~(k15\_group\_2~\\
X0~(k11\_group\_3~X0~X1)))){\unicdcdcdhd}({\unicdcdadad} X2 .  (v1\_finset\_1~X2){\unicdbdjdcd}(\preoh (X2=\\
k9\_group\_3~X0~X1){\unicdcdcdhd}(k5\_card\_1~X2=k18\_group\_2~X0~(k11\_group\_3~X0~\\
X1))))))\end{array}$$
\end{theorem}
\end{document}
