\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{t41\_abcmiz\_a (TMbF8yqmYaSRzhpKt7uPWjPg79R5njNoEJK)}
\maketitle
Let $ k41\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k27\_abcmiz\_1 : {\iota}$ be given.
Let $ k15\_abcmiz\_a : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k42\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_abcmiz\_a : {\iota}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
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 $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k38\_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 $ k40\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_abcmiz\_a : {\iota}$ be given.
Let $ k13\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_abcmiz\_1 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_abcmiz\_1 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_abcmiz\_a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_abcmiz\_1 : {\iota}$ be given.
Let $ k1\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\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}\\
(k42\_abcmiz\_1~X0~X1=k2\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedcdpfbgcgdgngjgkhpfbd}
\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}\\
(k41\_abcmiz\_1~X0~X1=k1\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedbdpfbgcgdgngjgkhpfbd}
\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}(k40\_abcmiz\_1~\\
X0~X1~X2=k4\_tarski~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedadpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_abcmiz\_a){\unicdbdjdcd}(k14\_abcmiz\_a~X0=k13\_abcmiz\_a~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdedpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (m1\_subset\_1~X0~k4\_abcmiz\_1){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdcdcdhd}(\\
(v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~\\
k2\_abcmiz\_1){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v2\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_finseq\_1~X0)))))))))\end{array}
\label{hyp:chdgbdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_abcmiz\_1~(k13\_abcmiz\_a~k8\_abcmiz\_a)~k27\_abcmiz\_1){\unicdcdcdhd}(v4\_abcmiz\_a~\\
(k13\_abcmiz\_a~k8\_abcmiz\_a)~k27\_abcmiz\_1)\end{array}
\label{hyp:ggdgbdadpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_msualg\_1~k27\_abcmiz\_1){\unicdcdcdhd}((v1\_instalg1~k27\_abcmiz\_1){\unicdcdcdhd}((\\
v1\_abcmiz\_1~k27\_abcmiz\_1){\unicdcdcdhd}(v3\_abcmiz\_1~k27\_abcmiz\_1)))\end{array}
\label{hyp:ggdgbdadpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{m2\_subset\_1}~{k8\_abcmiz\_a}}~{k20\_abcmiz\_1}}~{k5\_abcmiz\_a}}\label{hyp:egehpflgidpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~k5\_abcmiz\_a){\unicdcdcdhd}(m1\_subset\_1~k5\_abcmiz\_a~(k1\_zfmisc\_1~\\
k20\_abcmiz\_1))\end{array}
\label{hyp:egehpflgfdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_msualg\_1~k27\_abcmiz\_1){\unicdcdcdhd}((v1\_instalg1~k27\_abcmiz\_1){\unicdcdcdhd}((\\
v1\_abcmiz\_1~k27\_abcmiz\_1){\unicdcdcdhd}(l1\_msualg\_1~k27\_abcmiz\_1)))\end{array}
\label{hyp:egehpflgcdhdpfbgcgdgngjgkhpfbd}
\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}
{{{m3\_abcmiz\_1}~{k15\_abcmiz\_a}}~{k27\_abcmiz\_1}}\label{hyp:egehpflgbdfdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_abcmiz\_a){\unicdbdjdcd}((v2\_abcmiz\_1~(k14\_abcmiz\_a~\\
X0)~k27\_abcmiz\_1){\unicdcdcdhd}(m2\_abcmiz\_1~(k14\_abcmiz\_a~X0)~k27\_abcmiz\_1~\\
(k12\_abcmiz\_1~k27\_abcmiz\_1)))\end{array}
\label{hyp:egehpflgbdedpfbgcgdgngjgkhpfbg}
\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}((v2\_abcmiz\_1~X1~X0){\unicdcdcdhd}\\
((v4\_abcmiz\_a~X1~X0){\unicdcdcdhd}(m2\_abcmiz\_1~X1~X0~(k12\_abcmiz\_1~X0))))){\unicdbdjdcd}\\
((v9\_abcmiz\_1~(k12\_abcmiz\_a~X0~X1)~X0){\unicdcdcdhd}(m1\_abcmiz\_1~(k12\_abcmiz\_a~\\
X0~X1)~X0~(k12\_abcmiz\_1~X0)))\end{array}
\label{hyp:egehpflgbdcdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_subset\_1}~{X0}}={k1\_xboole\_0}}}\label{hyp:egcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k15\_abcmiz\_a=k40\_abcmiz\_1~k27\_abcmiz\_1~(k1\_subset\_1~(k38\_abcmiz\_1~\\
k27\_abcmiz\_1))~(k12\_abcmiz\_a~k27\_abcmiz\_1~(k14\_abcmiz\_a~k8\_abcmiz\_a))\end{array}
\label{hyp:egbdhdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k20\_abcmiz\_1}})}{\unicdbdjdcd}{({{{k13\_abcmiz\_a}~{X0}}={X0}})}}}\label{hyp:egbdgdpfbgcgdgngjgkhpfbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfbgcgdgngjgkhpfbg}
$$\begin{array}{c}(k41\_abcmiz\_1~k27\_abcmiz\_1~k15\_abcmiz\_a=k1\_xboole\_0){\unicdcdcdhd}(k42\_abcmiz\_1~\\
k27\_abcmiz\_1~k15\_abcmiz\_a=k12\_abcmiz\_a~k27\_abcmiz\_1~(k14\_abcmiz\_a~\\
k8\_abcmiz\_a))\end{array}$$
\end{theorem}
\end{document}
