\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{t13\_groeb\_1 (TMPoQ3gpqwXteHams1xTySfBmjAz4RyxZ1y)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_pre\_poly : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_polynom1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_polyred : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v4\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v8\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v3\_ordinal1~X0){\unicdcdcdhd}\\
(((v1\_partfun1~X1~(k15\_pre\_poly~X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~\\
X1){\unicdcdcdhd}((v6\_relat\_2~X1){\unicdcdcdhd}((v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k15\_pre\_poly~X0)~(k15\_pre\_poly~X0))))))))){\unicdcdcdhd}((\\
(\preoh v7\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((\\
v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~\\
X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k11\_polynom1~X0~X2))))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k3\_polyred~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k8\_struct\_0~(k11\_polynom1~X0~X2))~(u1\_struct\_0~(k11\_polynom1~\\
X0~X2)))))\end{array}
\label{hyp:egehpflgddpfahpgmgjhchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v8\_rewrite1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v5\_rewrite1~X0))\end{array}
\label{hyp:dgdgjdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v7\_rewrite1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}((v8\_rewrite1~X0){\unicdcdcdhd}(v9\_rewrite1~X0)))\end{array}
\label{hyp:dgdghdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_relat\_1~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v5\_rewrite1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v4\_rewrite1~X0))\end{array}
\label{hyp:dgdgbdadpfchfghhchjgehfgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfhgchpgfgcgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~(k15\_pre\_poly~\\
X0)){\unicdcdcdhd}((v1\_relat\_2~X1){\unicdcdcdhd}((v4\_relat\_2~X1){\unicdcdcdhd}((v6\_relat\_2~X1){\unicdcdcdhd}((\\
v8\_relat\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k15\_pre\_poly~\\
X0)~(k15\_pre\_poly~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v7\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~\\
X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k11\_polynom1~X0~X2)))){\unicdbdjdcd}((v7\_rewrite1~\\
(k3\_polyred~X0~X1~X2~X3)){\unicdbdjdcd}(v4\_rewrite1~(k3\_polyred~X0~X1~X2~X3))))))\end{array}$$
\end{theorem}
\end{document}
