\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{t17\_group\_8 (TML8G7Jf2yQqkcSzQe7J32Bovqn5Urc8ktn)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_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 $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\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}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_group\_2~X3~\\
X1){\unicdbdjdcd}((X0 \in k11\_group\_2~X1~X3~X2){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((X0=k6\_algstr\_0~\\
X1~X4~X5){\unicdcdcdhd}((X4 \in X2){\unicdcdcdhd}(r1\_struct\_0~X3~X5))))))))\end{array}
\label{hyp:ehjdedpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\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}(l3\_algstr\_0~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_group\_2~X3~X1){\unicdbdjdcd}((X0 \in k14\_group\_2~\\
X1~X3~X2){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdcdcdhd}((X0=\\
k6\_algstr\_0~X1~X4~X2){\unicdcdcdhd}(r1\_struct\_0~X3~X4))))))\end{array}
\label{hyp:ehbdadedpfhgchpgfhahpfcd}
\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}((m1\_group\_2~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k14\_group\_2~\\
X0~X1~X2)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgbdedpfhgchpgfhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfhgchpgfhahpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v15\_algstr\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_algstr\_0~X3){\unicdcdcdhd}(m1\_group\_2~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v15\_algstr\_0~X4){\unicdcdcdhd}(m1\_group\_2~X4~X0)){\unicdbdjdcd}((X1 \in k11\_group\_2~X0~X4~\\
(k14\_group\_2~X0~X3~X2)){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}((X1=k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X5~X2)~X6){\unicdcdcdhd}((r1\_struct\_0~X3~X5){\unicdcdcdhd}(r1\_struct\_0~\\
X4~X6))))))))))\end{array}$$
\end{theorem}
\end{document}
