\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{t4\_waybel29 (TMSkAT81g1YXo2VeFyucMTQLN5QDBxGtqm8)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_yellow\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_waybel27 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v23\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_waybel27 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
(((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~X2~(u1\_struct\_0~X1))){\unicdbdjdcd}((r2\_funct\_2~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(k1\_partfun1~(u1\_struct\_0~X1)~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~X2)~(k3\_struct\_0~X1)){\unicdcdcdhd}((\\
r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k1\_partfun1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X2~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2))~(k3\_struct\_0~X0)){\unicdcdcdhd}((v2\_funct\_1~\\
(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)){\unicdcdcdhd}(v2\_funct\_2~\\
(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~(u1\_struct\_0~\\
X0))))))))\end{array}
\label{hyp:ehedbdpfhgchdgbgehpfbd}
\end{equation}
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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}(m1\_yellow\_0~X3~(k6\_yellow\_1~(k2\_zfmisc\_1~\\
X0~X1)~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}(m1\_yellow\_0~X4~(\\
k6\_yellow\_1~X0~(k6\_yellow\_1~X1~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~X4)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X4)~(u1\_struct\_0~X3)))))){\unicdbdjdcd}\\
(((v1\_waybel27~X5){\unicdcdcdhd}((v2\_funct\_1~X5){\unicdcdcdhd}(v2\_funct\_2~X5~(u1\_struct\_0~\\
X3)))){\unicdbdjdcd}(v2\_waybel27~(k2\_tops\_2~(u1\_struct\_0~X4)~(u1\_struct\_0~\\
X3)~X5))))))))\end{array}
\label{hyp:ehcdpfhhbgjhcgfgmgcdjd}
\end{equation}
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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_orders\_2~X2){\unicdcdcdhd}((v4\_orders\_2~\\
X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh \\
v2\_struct\_0~X3){\unicdcdcdhd}((v4\_yellow\_0~X3~(k6\_yellow\_1~X0~(k6\_yellow\_1~\\
X1~X2))){\unicdcdcdhd}(m1\_yellow\_0~X3~(k6\_yellow\_1~X0~(k6\_yellow\_1~X1~X2))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((v4\_yellow\_0~X4~(k6\_yellow\_1~\\
(k2\_zfmisc\_1~X0~X1)~X2)){\unicdcdcdhd}(m1\_yellow\_0~X4~(k6\_yellow\_1~(k2\_zfmisc\_1~\\
X0~X1)~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~\\
X4)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X4)~(u1\_struct\_0~X3)))))){\unicdbdjdcd}((v2\_waybel27~X5){\unicdbdjdcd}(v5\_orders\_3~\\
X5~X4~X3)))))))\end{array}
\label{hyp:ehcdbdpfhhbgjhcgfgmgcdhd}
\end{equation}
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 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_orders\_2~X2){\unicdcdcdhd}((v4\_orders\_2~\\
X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh \\
v2\_struct\_0~X3){\unicdcdcdhd}((v4\_yellow\_0~X3~(k6\_yellow\_1~X0~(k6\_yellow\_1~\\
X1~X2))){\unicdcdcdhd}(m1\_yellow\_0~X3~(k6\_yellow\_1~X0~(k6\_yellow\_1~X1~X2))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((v4\_yellow\_0~X4~(k6\_yellow\_1~\\
(k2\_zfmisc\_1~X0~X1)~X2)){\unicdcdcdhd}(m1\_yellow\_0~X4~(k6\_yellow\_1~(k2\_zfmisc\_1~\\
X0~X1)~X2)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~\\
X3)~(u1\_struct\_0~X4)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X3)~(u1\_struct\_0~X4)))))){\unicdbdjdcd}((v1\_waybel27~X5){\unicdbdjdcd}(v5\_orders\_3~\\
X5~X3~X4)))))))\end{array}
\label{hyp:ehcdadpfhhbgjhcgfgmgcdhd}
\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}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_orders\_2~\\
X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}\\
((v23\_waybel\_0~X2~X0~X1){\unicdbdjded}((v5\_orders\_3~X2~X0~X1){\unicdcdcdhd}({\unicdcdaddd} X3 .  (\\
(v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v5\_orders\_3~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0))))))){\unicdcdcdhd}((r2\_funct\_2~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1)~(k1\_partfun1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X3~X2)~(k3\_struct\_0~X1)){\unicdcdcdhd}\\
(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k1\_partfun1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~X2~X3)~(k3\_struct\_0~\\
X0))))))))\end{array}
\label{hyp:ehbdfdpfjhfgmgmgpghhbdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}\\
(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k6\_yellow\_1~X0~X1)){\unicdcdcdhd}(v4\_orders\_2~\\
(k6\_yellow\_1~X0~X1)))\end{array}
\label{hyp:ggdgbdfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}\\
(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k6\_yellow\_1~X0~X1)){\unicdcdcdhd}(v3\_orders\_2~\\
(k6\_yellow\_1~X0~X1)))\end{array}
\label{hyp:ggdgbdcdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k6\_yellow\_1~X0~X1)){\unicdcdcdhd}(v1\_orders\_2~(k6\_yellow\_1~\\
X0~X1)))\end{array}
\label{hyp:ggdgbdbdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_yellow\_0~X1~X0){\unicdbdjdcd}\\
(l1\_orders\_2~X1))\end{array}
\label{hyp:egehpfngbdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}((v1\_orders\_2~(k6\_yellow\_1~\\
X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k6\_yellow\_1~X0~X1)))\end{array}
\label{hyp:egehpflggdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\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\_funct\_1~(k2\_tops\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_tops\_2~X0~\\
X1~X2)~X1~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_tops\_2~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0)))))\end{array}
\label{hyp:egehpflgcdpfehpgahdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_yellow\_0~X1~X0){\unicdbdjdcd}((v4\_yellow\_0~X1~X0){\unicdbdjdcd}((v4\_orders\_2~X1){\unicdcdcdhd}(\\
v4\_yellow\_0~X1~X0))))\end{array}
\label{hyp:dgdghdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_yellow\_0~X1~X0){\unicdbdjdcd}((v4\_yellow\_0~X1~X0){\unicdbdjdcd}((v3\_orders\_2~X1){\unicdcdcdhd}(\\
v4\_yellow\_0~X1~X0))))\end{array}
\label{hyp:dgdggdpfjhfgmgmgpghhpfad}
\end{equation}
\begin{theorem}\label{thm:ehedpfhhbgjhcgfgmgcdjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v3\_orders\_2~X2){\unicdcdcdhd}((v4\_orders\_2~\\
X2){\unicdcdcdhd}((v5\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh \\
v2\_struct\_0~X3){\unicdcdcdhd}((v4\_yellow\_0~X3~(k6\_yellow\_1~(k2\_zfmisc\_1~X0~\\
X1)~X2)){\unicdcdcdhd}(m1\_yellow\_0~X3~(k6\_yellow\_1~(k2\_zfmisc\_1~X0~X1)~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~X4){\unicdcdcdhd}((v4\_yellow\_0~X4~(k6\_yellow\_1~\\
X0~(k6\_yellow\_1~X1~X2))){\unicdcdcdhd}(m1\_yellow\_0~X4~(k6\_yellow\_1~X0~(k6\_yellow\_1~\\
X1~X2))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~\\
X4)~(u1\_struct\_0~X3)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X4)~(u1\_struct\_0~X3)))))){\unicdbdjdcd}(((v1\_waybel27~X5){\unicdcdcdhd}(\\
(v2\_funct\_1~X5){\unicdcdcdhd}(v2\_funct\_2~X5~(u1\_struct\_0~X3)))){\unicdbdjdcd}(v23\_waybel\_0~\\
X5~X4~X3)))))))\end{array}$$
\end{theorem}
\end{document}
