\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{t63\_rewrite1 (TMPow1eEGHU88kYbj6kNaqDCZfEFu6twyjM)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r12\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r6\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v10\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r5\_rewrite1~\\
X0~X1~X2){\unicdcdcdid}(r6\_rewrite1~X0~X1~X2)){\unicdbdjdcd}(r2\_rewrite1~X0~X1~X2))\end{array}
\label{hyp:ehddhdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_rewrite1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v10\_rewrite1~X1)))\end{array}
\label{hyp:egehpfngcdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v10\_rewrite1~\\
X1)){\unicdbdjdcd}((m2\_rewrite1~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (r2\_rewrite1~\\
X0~X2~X3){\unicdbdjded}(r5\_rewrite1~X1~X2~X3))))\end{array}
\label{hyp:egcdidpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r12\_rewrite1~\\
X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (r2\_rewrite1~X0~X2~X3){\unicdbdjded}(r2\_rewrite1~\\
X1~X2~X3))))\end{array}
\label{hyp:egcdgdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v8\_rewrite1~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
(r2\_rewrite1~X0~X1~X2){\unicdbdjdcd}(r5\_rewrite1~X0~X1~X2)))\end{array}
\label{hyp:egcdddpfchfghhchjgehfgbd}
\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){\unicdcdcdhd}(v10\_rewrite1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}((v3\_rewrite1~X0){\unicdcdcdhd}(v7\_rewrite1~X0)))\end{array}
\label{hyp:dgdgbdedpfchfghhchjgehfgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdddpfchfghhchjgehfgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_rewrite1~X1~X0){\unicdbdjdcd}(\\
r12\_rewrite1~X0~X1))\end{array}$$
\end{theorem}
\end{document}
