\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{t107\_group\_3 (TMbowoQKRLnY3knWzxU8KPnNSA1adJspH2P)}
\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 $ k9\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r6\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r5\_group\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_group\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(((v15\_algstr\_0~X1){\unicdcdcdhd}\\
(m1\_group\_2~X1~X0)){\unicdcdcdhd}((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~X2~X0)))){\unicdbdjdcd}\\
((r6\_group\_3~X0~X1~X2){\unicdbdjdcd}(r6\_group\_3~X0~X2~X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchgdpfhgchpgfhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdcdcdhd}(((v15\_algstr\_0~X1){\unicdcdcdhd}\\
(m1\_group\_2~X1~X0)){\unicdcdcdhd}((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~X2~X0)))){\unicdbdjdcd}\\
((r6\_group\_3~X0~X1~X2){\unicdbdjded}(r5\_group\_3~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchgdpfhgchpgfhahpfdd}
\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}(m1\_subset\_1~\\
(k9\_group\_3~X0~X1)~(k1\_zfmisc\_1~(k1\_group\_3~X0)))\end{array}
\label{hyp:egehpflgjdpfhgchpgfhahpfdd}
\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}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_group\_3~X0))){\unicdbdjdcd}((X2=k9\_group\_3~\\
X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v15\_algstr\_0~X4){\unicdcdcdhd}(\\
m1\_group\_2~X4~X0)){\unicdcdcdhd}((X3=X4){\unicdcdcdhd}(r5\_group\_3~X0~X1~X4)))))))\end{array}
\label{hyp:egbdcdpfhgchpgfhahpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdadhdpfhgchpgfhahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v15\_algstr\_0~X1){\unicdcdcdhd}(m1\_group\_2~\\
X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_algstr\_0~X2){\unicdcdcdhd}(m1\_group\_2~X2~X0)){\unicdbdjdcd}(\\
(X1 \in k9\_group\_3~X0~X2){\unicdbdjded}(r6\_group\_3~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
