\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{t108\_abcmiz\_1 (TMHsoN8e8pA9cjXZetNrUTnqb7WaGA77woX)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k28\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v9\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v10\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k40\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k38\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k45\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k47\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}((v4\_abcmiz\_1~\\
X1~X0~(k28\_abcmiz\_1~X0)){\unicdbdjded}(k45\_abcmiz\_1~X0~X1=k1\_xboole\_0)))\end{array}
\label{hyp:ehbdadhdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v9\_abcmiz\_1~X1~X0){\unicdcdcdhd}(m1\_abcmiz\_1~\\
X1~X0~(k12\_abcmiz\_1~X0))){\unicdbdjdcd}(k47\_abcmiz\_1~X0~(k40\_abcmiz\_1~X0~(k1\_subset\_1~\\
(k38\_abcmiz\_1~X0))~X1)=k45\_abcmiz\_1~X0~X1))\end{array}
\label{hyp:ehbdadgdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_xboole\_0}~{({{k1\_subset\_1}~{X0}})}}}\label{hyp:ggdgbdddpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}\\
((v3\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_abcmiz\_1~X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))))\end{array}
\label{hyp:egehpfngbdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~\\
X0){\unicdcdcdhd}((v3\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(((v1\_finset\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k38\_abcmiz\_1~X0)))){\unicdcdcdhd}((v9\_abcmiz\_1~\\
X2~X0){\unicdcdcdhd}(m1\_abcmiz\_1~X2~X0~(k12\_abcmiz\_1~X0))))){\unicdbdjdcd}(m3\_abcmiz\_1~\\
(k40\_abcmiz\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgedadpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k1\_subset\_1}~{X0}})}}~{({{k1\_zfmisc\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k12\_abcmiz\_1~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_abcmiz\_1~X1~X0){\unicdbdjdcd}((v10\_abcmiz\_1~\\
X1~X0){\unicdbdjded}(k47\_abcmiz\_1~X0~X1=k1\_xboole\_0)))\end{array}
\label{hyp:egfdadpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgbdpfggjgogdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadidpfbgcgdgngjgkhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_abcmiz\_1~X1~X0~(k28\_abcmiz\_1~\\
X0)){\unicdcdcdhd}((v9\_abcmiz\_1~X1~X0){\unicdcdcdhd}(m1\_abcmiz\_1~X1~X0~(k12\_abcmiz\_1~X0)))){\unicdbdjdcd}\\
(v10\_abcmiz\_1~(k40\_abcmiz\_1~X0~(k1\_subset\_1~(k38\_abcmiz\_1~X0))~\\
X1)~X0))\end{array}$$
\end{theorem}
\end{document}
