\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{t22\_abcmiz\_a (TMXb8dzBCFBi9bmkZXjgXJk7PF43FQH5zet)}
\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 $ v1\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k28\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k14\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_trees\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_trees\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k35\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_abcmiz\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_xtuple\_0~(k4\_tarski~X0~X1)=X0){\unicdcdcdhd}(k2\_xtuple\_0~\\
(k4\_tarski~X0~X1)=X1)\end{array}
\label{hyp:ehhdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (k9\_xtuple\_0~(k1\_trees\_4~X0)=k2\_trees\_1~k6\_numbers){\unicdcdcdhd}\\
(k1\_funct\_1~(k1\_trees\_4~X0)~k1\_xboole\_0=X0)\end{array}
\label{hyp:ehddpfehchfgfgdhpfed}
\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 .  (m1\_subset\_1~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}((v5\_abcmiz\_1~\\
X1~X0~(k28\_abcmiz\_1~X0)){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_abcmiz\_1){\unicdbdjdcd}\\
(X1{\unicdcdgdad}k35\_abcmiz\_1~X2~X0))))\end{array}
\label{hyp:ehddpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\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}((v1\_abcmiz\_a~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}\\
(\preoh (k1\_xtuple\_0~(k1\_funct\_1~X1~k1\_xboole\_0) \in k2\_abcmiz\_1){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k2\_abcmiz\_1){\unicdbdjdcd}(\preoh (X2=k1\_xtuple\_0~(k1\_funct\_1~\\
X1~k1\_xboole\_0)){\unicdcdcdhd}(X1=k35\_abcmiz\_1~X2~X0)))))\end{array}
\label{hyp:ehbdhdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_abcmiz\_1}}}}\label{hyp:ggdgcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k2\_abcmiz\_1){\unicdcdcdhd}((v1\_instalg1~\\
X1){\unicdcdcdhd}((v1\_abcmiz\_1~X1){\unicdcdcdhd}((v3\_abcmiz\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))))){\unicdbdjdcd}\\
(\preoh v5\_abcmiz\_1~(k35\_abcmiz\_1~X0~X1)~X1~(k28\_abcmiz\_1~X1))\end{array}
\label{hyp:ggdgbdgdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k2\_abcmiz\_1){\unicdcdcdhd}((v1\_instalg1~\\
X1){\unicdcdcdhd}((v1\_abcmiz\_1~X1){\unicdcdcdhd}((v3\_abcmiz\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))))){\unicdbdjdcd}\\
(m1\_abcmiz\_1~(k35\_abcmiz\_1~X0~X1)~X1~(k14\_abcmiz\_1~X1))\end{array}
\label{hyp:egehpflgddfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_abcmiz\_1}={np\_\_2}}\label{hyp:eggdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_abcmiz\_1){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_instalg1~\\
X1){\unicdcdcdhd}((v1\_abcmiz\_1~X1){\unicdcdcdhd}((v3\_abcmiz\_1~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}\\
(k35\_abcmiz\_1~X0~X1=k1\_trees\_4~(k4\_tarski~X0~k8\_abcmiz\_1)))\end{array}
\label{hyp:egddedpfbgcgdgngjgkhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}((v1\_abcmiz\_a~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
(((\preoh v5\_abcmiz\_1~X1~X0~(k28\_abcmiz\_1~X0)){\unicdcdcdhd}(m1\_abcmiz\_1~X1~X0~(k14\_abcmiz\_1~\\
X0))){\unicdbdjded}(k1\_xtuple\_0~(k1\_funct\_1~X1~k1\_xboole\_0) \in k2\_abcmiz\_1)))\end{array}$$
\end{theorem}
\end{document}
