\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{t6\_yellow16 (TMNmqE5dvaWAZ7cu3XAMkWBhiA8XnXj9PTR)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v24\_waybel\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v11\_quantal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v22\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v6\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v18\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v8\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((v6\_waybel\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X2=ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X3 : \iota .  r3\_orders\_2~\\
X0~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X3)~X3)~({\uniddcgcg} X3 : \\
\iota .  X3)){\unicdbdjdcd}(((v18\_waybel\_0~X1~X0~X0){\unicdbdjdcd}((v8\_yellow\_0~(k5\_yellow\_0~\\
X0~X2)~X0){\unicdcdcdhd}(v8\_yellow\_0~(k1\_yellow\_2~X0~X0~X1)~X0))){\unicdcdcdhd}((v22\_waybel\_0~\\
X1~X0~X0){\unicdbdjdcd}((v4\_waybel\_0~(k5\_yellow\_0~X0~X2)~X0){\unicdcdcdhd}(v4\_waybel\_0~(\\
k1\_yellow\_2~X0~X0~X1)~X0))))))))\end{array}
\label{hyp:ehfdcdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((v6\_waybel\_1~X1~X0){\unicdbdjdcd}(((\preoh v1\_xboole\_0~(ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  r3\_orders\_2~\\
X0~X2~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2))~({\uniddcgcg} X2 : \\
\iota .  X2))){\unicdcdcdhd}(m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  r3\_orders\_2~X0~X2~(k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2))~({\uniddcgcg} X2 : \iota .  X2))~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdcdcdhd}((\preoh v1\_xboole\_0~(ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  r3\_orders\_2~\\
X0~(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2)~X2)~({\uniddcgcg} X2 : \\
\iota .  X2))){\unicdcdcdhd}(m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X2 : \iota .  r3\_orders\_2~X0~(k3\_funct\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2)~X2)~({\uniddcgcg} X2 : \iota .  X2))~(\\
k1\_zfmisc\_1~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:ehedddpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  {\unicdcdadad} X1 .  m1\_subset\_1~(ReplSep~(toset~(\\
{\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~X1))~({\uniddcgcg} X2 : \iota .  X0~X2)~({\uniddcgcg} X2 : \iota .  \\
X2))~(k1\_zfmisc\_1~X1)\end{array}
\label{hyp:dhhdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((v6\_waybel\_1~X1~X0){\unicdbdjded}((v11\_quantal1~\\
X1){\unicdcdcdhd}(v5\_orders\_3~X1~X0~X0))))\end{array}
\label{hyp:egbdddpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(\\
(v3\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)))){\unicdbdjdcd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(v22\_waybel\_0~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(v5\_orders\_3~X2~X0~X1)))))\end{array}
\label{hyp:dgdgbdpfhhbgjhcgfgmgbdhd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfjhfgmgmgpghhbdgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v24\_waybel\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}(((v11\_quantal1~X1){\unicdcdcdhd}\\
(v22\_waybel\_0~X1~X0~X0)){\unicdbdjdcd}(v4\_waybel\_0~(k1\_yellow\_2~X0~X0~X1)~X0)))\end{array}$$
\end{theorem}
\end{document}
