\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{t15\_domain\_1 (TMNmSu8jkFo4neTaHt7U4MyP65JZ3qmReAx)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ k6\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k8\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k7\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (k6\_xtuple\_0~X0~X1~X2~X3=k6\_xtuple\_0~X4~X5~\\
X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7))))\end{array}
\label{hyp:ehfdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(k7\_mcart\_1~X0~X1~\\
X2~X3~X4=k2\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(k6\_mcart\_1~X0~X1~\\
X2~X3~X4=k5\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(k5\_mcart\_1~X0~X1~\\
X2~X3~X4=k8\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((m1\_subset\_1~X4~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X5~X1){\unicdcdcdhd}((m1\_subset\_1~X6~X2){\unicdcdcdhd}(m1\_subset\_1~X7~X3)))))))){\unicdbdjdcd}\\
(k5\_domain\_1~X0~X1~X2~X3~X4~X5~X6~X7=k6\_xtuple\_0~X4~X5~X6~X7)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(k4\_mcart\_1~X0~X1~\\
X2~X3~X4=k7\_xtuple\_0~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_xtuple\_0~X0){\unicdbdjdcd}(k6\_xtuple\_0~(k7\_xtuple\_0~X0)~(k8\_xtuple\_0~\\
X0)~(k5\_xtuple\_0~X0)~(k2\_xtuple\_0~X0)=X0)\end{array}
\label{hyp:chegbdcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(m1\_subset\_1~(k7\_mcart\_1~\\
X0~X1~X2~X3~X4)~X3)\end{array}
\label{hyp:egehpflghdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(m1\_subset\_1~(k6\_mcart\_1~\\
X0~X1~X2~X3~X4)~X2)\end{array}
\label{hyp:egehpflggdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(m1\_subset\_1~(k5\_mcart\_1~\\
X0~X1~X2~X3~X4)~X1)\end{array}
\label{hyp:egehpflgfdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_mcart\_1~\\
X0~X1~X2~X3~X4)~X0)\end{array}
\label{hyp:egehpflgedpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(\preoh v1\_xboole\_0~X3)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k4\_zfmisc\_1~X0~X1~X2~X3)){\unicdbdjdcd}(v3\_xtuple\_0~\\
X4))\end{array}
\label{hyp:dgdgcdpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfegpgngbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\preoh v1\_xboole\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k4\_zfmisc\_1~X1~X2~X3~X4)){\unicdbdjdcd}((X0=\\
k6\_mcart\_1~X1~X2~X3~X4~X5){\unicdbdjded}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~X2){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X3){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~X4){\unicdbdjdcd}((X5=k5\_domain\_1~X1~X2~X3~X4~X6~X7~X8~X9){\unicdbdjdcd}(X0=\\
X8)))))))))))\end{array}$$
\end{theorem}
\end{document}
