\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{t103\_abcmiz\_1 (TMdqVUfXs4NsSmDT8PFaJiHGokwLedJ1wmE)}
\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 $ m3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k13\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k48\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k43\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ k46\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k47\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k45\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k1\_abcmiz\_1~(k2\_xboole\_0~X0~X1)=k2\_xboole\_0~\\
(k1\_abcmiz\_1~X0)~(k1\_abcmiz\_1~X1)\end{array}
\label{hyp:ehbdbdpfbgcgdgngjgkhpfbd}
\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}({\unicdcdadad} X2 .  \\
((v8\_abcmiz\_1~X2~X0){\unicdcdcdhd}(m1\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~X0))){\unicdbdjdcd}(\\
k47\_abcmiz\_1~X0~(k43\_abcmiz\_1~X0~X1~X2)=k4\_subset\_1~k2\_abcmiz\_1~\\
(k45\_abcmiz\_1~X0~X2)~(k47\_abcmiz\_1~X0~X1))))\end{array}
\label{hyp:ehbdadcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\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 .  (((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}\\
((v3\_abcmiz\_1~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdcdcdhd}(m3\_abcmiz\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_finset\_1~(k48\_abcmiz\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k48\_abcmiz\_1~\\
X0~X1)~(k1\_zfmisc\_1~k2\_abcmiz\_1)))\end{array}
\label{hyp:egehpflgedidpfbgcgdgngjgkhpfbd}
\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}(m3\_abcmiz\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k47\_abcmiz\_1~X0~X1)~(k1\_zfmisc\_1~k2\_abcmiz\_1))\end{array}
\label{hyp:egehpflgedhdpfbgcgdgngjgkhpfbd}
\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~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0)))))){\unicdbdjdcd}((v1\_finset\_1~\\
(k46\_abcmiz\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k46\_abcmiz\_1~X0~X1)~(k1\_zfmisc\_1~\\
k2\_abcmiz\_1)))\end{array}
\label{hyp:egehpflgedgdpfbgcgdgngjgkhpfbd}
\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~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0)))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k45\_abcmiz\_1~X0~X1)~(k1\_zfmisc\_1~k2\_abcmiz\_1))\end{array}
\label{hyp:egehpflgedfdpfbgcgdgngjgkhpfbd}
\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}((m3\_abcmiz\_1~X1~\\
X0){\unicdcdcdhd}((v8\_abcmiz\_1~X2~X0){\unicdcdcdhd}(m1\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
(m3\_abcmiz\_1~(k43\_abcmiz\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgedddpfbgcgdgngjgkhpfbd}
\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~(k13\_abcmiz\_1~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdddpfbgcgdgngjgkhpfbd}
\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}(k48\_abcmiz\_1~\\
X0~X1=k1\_abcmiz\_1~(k47\_abcmiz\_1~X0~X1)))\end{array}
\label{hyp:egedjdpfbgcgdgngjgkhpfbd}
\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}(k46\_abcmiz\_1~\\
X0~X1=k1\_abcmiz\_1~(k45\_abcmiz\_1~X0~X1)))\end{array}
\label{hyp:egedhdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdadddpfbgcgdgngjgkhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_abcmiz\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v8\_abcmiz\_1~X2~X0){\unicdcdcdhd}(m1\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~X0))){\unicdbdjdcd}(\\
k48\_abcmiz\_1~X0~(k43\_abcmiz\_1~X0~X1~X2)=k4\_subset\_1~k2\_abcmiz\_1~\\
(k46\_abcmiz\_1~X0~X2)~(k48\_abcmiz\_1~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
