\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{t50\_aofa\_000 (TMT9M2itwS7dg5uqHn8QKPPdPksvGGws5kK)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_aofa\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_aofa\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_aofa\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_aofa\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_pua2mss1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~(k7\_subset\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflghdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  m1\_subset\_1~(k6\_subset\_1~X0~X1)~(k1\_zfmisc\_1~\\
X0)\end{array}
\label{hyp:egehpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k4\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(\preoh X3 \in X1)))\end{array}
\label{hyp:egfdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}((v4\_aofa\_000~X0){\unicdcdcdhd}\\
((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))))))){\unicdbdjdcd}\\
(k18\_aofa\_000~X0=k7\_subset\_1~(u1\_struct\_0~X0)~(k7\_subset\_1~(\\
u1\_struct\_0~X0)~(k7\_subset\_1~(u1\_struct\_0~X0)~(k6\_subset\_1~(u1\_struct\_0~\\
X0)~(k1\_tarski~(k12\_aofa\_000~X0)))~(k2\_relset\_1~(u1\_struct\_0~\\
X0)~(k2\_pua2mss1~X0~(k1\_funct\_7~np\_\_3~(k4\_finseq\_1~(u1\_unialg\_1~\\
X0))))))~(k2\_relset\_1~(u1\_struct\_0~X0)~(k2\_pua2mss1~X0~(k1\_funct\_7~\\
np\_\_4~(k4\_finseq\_1~(u1\_unialg\_1~X0))))))~(ReplSep2~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~(u1\_struct\_0~X0)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  \\
(X1{\unicdcdgdad}k13\_aofa\_000~X0~X1~X2){\unicdcdcdhd}(X2{\unicdcdgdad}k13\_aofa\_000~X0~X1~X2))~({\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  k13\_aofa\_000~X0~X1~X2)))\end{array}
\label{hyp:egcdcdpfbgpgggbgpfadadad}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfbgpgggbgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v3\_aofa\_000~X0){\unicdcdcdhd}((v4\_aofa\_000~X0){\unicdcdcdhd}\\
((v5\_aofa\_000~X0){\unicdcdcdhd}((v6\_aofa\_000~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k13\_aofa\_000~X0~X1~X2){\unicdcdcdhd}((X2{\unicdcdgdad}k13\_aofa\_000~\\
X0~X1~X2){\unicdcdcdhd}(k13\_aofa\_000~X0~X1~X2 \in k18\_aofa\_000~X0)))))\end{array}$$
\end{theorem}
\end{document}
