\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{t39\_waybel20 (TMZbFm2gD65CgqcKXjkNKxV5icz4TjxkoFM)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\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 $ v8\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_waybel20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k16\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_waybel20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k15\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}((v1\_partfun1~(k8\_relset\_1~\\
(k2\_zfmisc\_1~X0~X0)~(k2\_zfmisc\_1~X1~X1)~(k16\_funct\_3~X0~X0~X1~X1~X2~\\
X2)~(k6\_partfun1~X1))~X0){\unicdcdcdhd}((v3\_relat\_2~(k8\_relset\_1~(k2\_zfmisc\_1~\\
X0~X0)~(k2\_zfmisc\_1~X1~X1)~(k16\_funct\_3~X0~X0~X1~X1~X2~X2)~(k6\_partfun1~\\
X1))){\unicdcdcdhd}((v8\_relat\_2~(k8\_relset\_1~(k2\_zfmisc\_1~X0~X0)~(k2\_zfmisc\_1~\\
X1~X1)~(k16\_funct\_3~X0~X0~X1~X1~X2~X2)~(k6\_partfun1~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
(k8\_relset\_1~(k2\_zfmisc\_1~X0~X0)~(k2\_zfmisc\_1~X1~X1)~(k16\_funct\_3~\\
X0~X0~X1~X1~X2~X2)~(k6\_partfun1~X1))~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
X0))))))))\end{array}
\label{hyp:ehcdpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(k8\_relset\_1~X0~X1~X2~X3=k8\_relat\_1~\\
X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((l1\_orders\_2~X0){\unicdcdcdhd}((l1\_orders\_2~X1){\unicdcdcdhd}((l1\_orders\_2~X2){\unicdcdcdhd}((l1\_orders\_2~\\
X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X2)))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(\\
u1\_struct\_0~X1)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X3))))))))))){\unicdbdjdcd}(k1\_waybel20~\\
X0~X1~X2~X3~X4~X5=k15\_funct\_3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~X2){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X2))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3)))))){\unicdbdjdcd}(k16\_funct\_3~\\
X0~X1~X2~X3~X4~X5=k15\_funct\_3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdgdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_relat\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k4\_relat\_1~\\
X0)~X0){\unicdcdcdhd}(v5\_relat\_1~(k4\_relat\_1~X0)~X0))\end{array}
\label{hyp:ggdgcdidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_xboole\_0~X1)){\unicdbdjdcd}(v1\_xboole\_0~\\
(k8\_relat\_1~X0~X1))\end{array}
\label{hyp:ggdgcdbdpfchfgmgbgehpfbd}
\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}\\
(l1\_orders\_2~X0))){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v8\_waybel\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k4\_waybel20~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k4\_waybel20~X0~X1)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_3~X0~X0)))))\end{array}
\label{hyp:egehpflgedpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((l1\_orders\_2~X0){\unicdcdcdhd}((l1\_orders\_2~X1){\unicdcdcdhd}((l1\_orders\_2~X2){\unicdcdcdhd}((l1\_orders\_2~\\
X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X2)){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X2)))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(\\
u1\_struct\_0~X1)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X3))))))))))){\unicdbdjdcd}((\\
v1\_funct\_1~(k1\_waybel20~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}((v1\_funct\_2~(k1\_waybel20~\\
X0~X1~X2~X3~X4~X5)~(u1\_struct\_0~(k3\_yellow\_3~X0~X1))~(u1\_struct\_0~\\
(k3\_yellow\_3~X2~X3))){\unicdcdcdhd}(m1\_subset\_1~(k1\_waybel20~X0~X1~X2~X3~X4~X5)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~X1))~(\\
u1\_struct\_0~(k3\_yellow\_3~X2~X3)))))))\end{array}
\label{hyp:egehpflgbdpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~X2){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X2))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X3)))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k16\_funct\_3~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}((v1\_funct\_2~(k16\_funct\_3~X0~X1~\\
X2~X3~X4~X5)~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
(k16\_funct\_3~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)~(k2\_zfmisc\_1~X2~X3))))))\end{array}
\label{hyp:egehpflgbdgdpfggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_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}((v8\_waybel\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}(k4\_waybel20~\\
X0~X1=k8\_relset\_1~(u1\_struct\_0~(k3\_yellow\_3~X0~X0))~(u1\_struct\_0~\\
(k3\_yellow\_3~X0~X0))~(k1\_waybel20~X0~X0~X0~X0~X1~X1)~(k6\_partfun1~\\
(u1\_struct\_0~X0))))\end{array}
\label{hyp:egedpfhhbgjhcgfgmgcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdgidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfhhbgjhcgfgmgcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v8\_waybel\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((v1\_partfun1~\\
(k4\_waybel20~X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v3\_relat\_2~(k4\_waybel20~\\
X0~X1)){\unicdcdcdhd}((v8\_relat\_2~(k4\_waybel20~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k4\_waybel20~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))))\end{array}$$
\end{theorem}
\end{document}
