\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{t23\_abcmiz\_a (TMNNDDenwE9XwD1rSN4RpMvP42VbwvrGaRj)}
\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 $ 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 $ k20\_abcmiz\_1 : {\iota}$ be given.
Let $ k8\_abcmiz\_1 : {\iota}$ be given.
Let $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ v5\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ 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}((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}
\label{hyp:ehcdcdpfbgcgdgngjgkhpfbg}
\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\_abcmiz\_1~\\
X1~X0~(k14\_abcmiz\_1~X0)){\unicdbdjdcd}((v5\_abcmiz\_1~X1~X0~(k28\_abcmiz\_1~X0)){\unicdbdjded}\\
((k1\_xtuple\_0~(k1\_funct\_1~X1~k1\_xboole\_0) \in k20\_abcmiz\_1){\unicdcdcdhd}(k1\_xtuple\_0~\\
(k1\_xtuple\_0~(k1\_funct\_1~X1~k1\_xboole\_0))=k8\_abcmiz\_1))))\end{array}
\label{hyp:ehcdbdpfbgcgdgngjgkhpfbg}
\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 k20\_abcmiz\_1){\unicdcdcdhd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X2=k1\_xtuple\_0~\\
(k1\_funct\_1~X1~k1\_xboole\_0)){\unicdcdcdhd}((k2\_msualg\_1~X0~X2=k1\_xtuple\_0~\\
X2){\unicdcdcdhd}(m1\_abcmiz\_1~X1~X0~(k2\_msualg\_1~X0~X2)))))))\end{array}
\label{hyp:ehcdadpfbgcgdgngjgkhpfbg}
\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 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}(k14\_abcmiz\_1~X0=k8\_abcmiz\_1)\end{array}
\label{hyp:egbdfdpfbgcgdgngjgkhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}((v1\_abcmiz\_a~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
((m1\_abcmiz\_1~X1~X0~(k14\_abcmiz\_1~X0)){\unicdbdjded}(((k1\_xtuple\_0~(k1\_funct\_1~\\
X1~k1\_xboole\_0) \in k20\_abcmiz\_1){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_xtuple\_0~(k1\_funct\_1~\\
X1~k1\_xboole\_0))=k8\_abcmiz\_1)){\unicdcdcdid}(k1\_xtuple\_0~(k1\_funct\_1~X1~\\
k1\_xboole\_0) \in k2\_abcmiz\_1))))\end{array}$$
\end{theorem}
\end{document}
