\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{t32\_waybel20 (TMGbLEdEe3ewDkahHX7jrpZ99hEDHjceUHR)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_yellow\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_waybel\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_yellow\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v2\_yellow\_0~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(r1\_orders\_2~X0~X1~(k4\_yellow\_0~X0)))\end{array}
\label{hyp:ehedfdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v2\_yellow\_0~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_orders\_2~X0~(k4\_yellow\_0~X0)~X1){\unicdbdjdcd}(X1=k4\_yellow\_0~X0)))\end{array}
\label{hyp:ehddpfhhbgjhcgfgmgbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_yellow\_1~\\
X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}\\
(v5\_orders\_2~(k3\_waybel\_3~X0~X1~X2))){\unicdbdjdcd}(v5\_orders\_2~(k5\_yellow\_1~\\
X0~X1))))\end{array}
\label{hyp:ehddadpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_yellow\_1~\\
X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}\\
((v5\_orders\_2~(k3\_waybel\_3~X0~X1~X2)){\unicdcdcdhd}((v2\_yellow\_0~(k3\_waybel\_3~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_orders\_2~(k3\_waybel\_3~X0~X1~X2))))){\unicdbdjdcd}(v2\_yellow\_0~\\
(k5\_yellow\_1~X0~X1))))\end{array}
\label{hyp:ehddadpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_yellow\_1~\\
X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_yellow\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k5\_yellow\_1~X0~X1))){\unicdbdjdcd}((r1\_orders\_2~(k5\_yellow\_1~X0~X1)~X2~X3){\unicdbdjded}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}(r1\_orders\_2~(k3\_waybel\_3~X0~\\
X1~X4)~(k4\_waybel\_3~X0~X1~X2~X4)~(k4\_waybel\_3~X0~X1~X3~X4)))))))\end{array}
\label{hyp:ehcdidpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_yellow\_1~\\
X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((m1\_subset\_1~X2~(u1\_struct\_0~(k5\_yellow\_1~X0~X1))){\unicdbdjded}((k9\_xtuple\_0~\\
X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_funct\_1~\\
X2~X3)~(u1\_struct\_0~(k3\_waybel\_3~X0~X1~X3))))))))\end{array}
\label{hyp:ehcdhdpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 .  {\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(\\
(v4\_relat\_1~X2~X1){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X1)))){\unicdcdcdhd}(\\
{\unicdcdadad} X3 .  (m1\_subset\_1~X3~X1){\unicdbdjdcd}(k1\_funct\_1~X2~X3=X0~X3))\end{array}
\label{hyp:dhfdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}((v1\_yellow\_1~X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(u1\_struct\_0~(k5\_yellow\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}\\
(k4\_waybel\_3~X0~X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(v1\_yellow\_1~X1))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k3\_waybel\_3~X0~X1~\\
X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
((v1\_yellow\_1~X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}\\
(\preoh v2\_struct\_0~(k1\_funct\_1~X1~X2))\end{array}
\label{hyp:ggdgidpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_yellow\_1~X1){\unicdcdcdhd}(v4\_waybel\_3~\\
X1)))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_yellow\_1~X0~X1)){\unicdcdcdhd}(v1\_orders\_2~(\\
k5\_yellow\_1~X0~X1)))\end{array}
\label{hyp:ggdghdpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_yellow\_1~X1))))){\unicdbdjdcd}(\\
(v1\_orders\_2~(k5\_yellow\_1~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k5\_yellow\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflgfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(m1\_subset\_1~(k4\_yellow\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgedpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}((v1\_yellow\_1~X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(u1\_struct\_0~(k5\_yellow\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_waybel\_3~X0~X1~X2~X3)~(u1\_struct\_0~(k3\_waybel\_3~\\
X0~X1~X3)))\end{array}
\label{hyp:egehpflgedpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
(v1\_partfun1~X1~X0){\unicdbdjded}(k1\_relset\_1~X0~X1=X0))\end{array}
\label{hyp:egcdpfahbgchehggfhogbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfhhbgjhcgfgmgcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_yellow\_1~\\
X1){\unicdcdcdhd}(v4\_waybel\_3~X1)))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}\\
((v5\_orders\_2~(k3\_waybel\_3~X0~X1~X2)){\unicdcdcdhd}((v2\_yellow\_0~(k3\_waybel\_3~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_orders\_2~(k3\_waybel\_3~X0~X1~X2))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}(k4\_waybel\_3~X0~X1~(k4\_yellow\_0~(k5\_yellow\_1~\\
X0~X1))~X2=k4\_yellow\_0~(k3\_waybel\_3~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
