\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{t35\_waybel34 (TMXqxukVwghUN1iGMHZk2vFWEWJpxFvS1jQ)}
\maketitle
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 $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\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 $ v7\_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 $ v18\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v17\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_waybel34 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_waybel34 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v3\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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}\\
((v7\_waybel\_1~X1~X0){\unicdbdjdcd}((v18\_waybel\_0~(k2\_waybel\_1~X0~X0~X1)~X0~(\\
k1\_yellow\_2~X0~X0~X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((r1\_tarski~X2~(u1\_struct\_0~(k1\_yellow\_2~\\
X0~X0~X1))){\unicdcdcdhd}(r1\_yellow\_0~X0~X2)){\unicdbdjdcd}((r1\_yellow\_0~(k1\_yellow\_2~X0~\\
X0~X1)~X2){\unicdcdcdhd}(k1\_yellow\_0~(k1\_yellow\_2~X0~X0~X1)~X2=k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~X1~(k1\_yellow\_0~X0~X2))))))))\end{array}
\label{hyp:ehfdfdpfhhbgjhcgfgmgpfbd}
\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}\\
((v7\_waybel\_1~X1~X0){\unicdbdjdcd}(v3\_waybel\_1~(k1\_waybel\_1~(k1\_yellow\_2~\\
X0~X0~X1)~X0~(k3\_waybel\_1~X0~X0~X1)~(k2\_waybel\_1~X0~X0~X1))~(k1\_yellow\_2~\\
X0~X0~X1)~X0)))\end{array}
\label{hyp:ehddgdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_yellow\_0~\\
X1~X0){\unicdcdcdhd}((v7\_yellow\_0~X1~X0){\unicdcdcdhd}(m1\_yellow\_0~X1~X0)))){\unicdbdjdcd}((v3\_orders\_2~\\
X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}\\
((v2\_lattice3~X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))))\end{array}
\label{hyp:ehddadpfjhfgmgmgpghhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~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}((v18\_waybel\_0~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))))))){\unicdbdjdcd}(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~(k1\_waybel34~X1~X0~(k2\_waybel34~X1~X0~X2))~X2)))\end{array}
\label{hyp:ehbdbdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~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}((v17\_waybel\_0~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))))))){\unicdbdjdcd}(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~(k2\_waybel34~X0~X1~(k1\_waybel34~X0~X1~X2))~X2)))\end{array}
\label{hyp:ehbdadpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))){\unicdbdjdcd}\\
(((v3\_lattice3~X0){\unicdcdcdhd}(v3\_lattice3~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}\\
((v18\_waybel\_0~X2~X0~X1){\unicdbdjdcd}((v5\_orders\_3~(k2\_waybel34~X1~X0~X2)~X1~\\
X0){\unicdcdcdhd}((v4\_waybel\_1~(k2\_waybel34~X1~X0~X2)~X1~X0){\unicdcdcdhd}(v17\_waybel\_0~\\
(k2\_waybel34~X1~X0~X2)~X1~X0)))))))\end{array}
\label{hyp:mgfdpfhhbgjhcgfgmgdded}
\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}\\
((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_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}((v7\_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\_orders\_2~(k1\_yellow\_2~\\
X0~X0~X1)){\unicdcdcdhd}((v4\_yellow\_0~(k1\_yellow\_2~X0~X0~X1)~X0){\unicdcdcdhd}(v7\_yellow\_0~\\
(k1\_yellow\_2~X0~X0~X1)~X0)))\end{array}
\label{hyp:ggdgjdpfhhbgjhcgfgmgbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((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}\\
((v1\_funct\_1~(k3\_waybel\_1~X0~X1~X2)){\unicdcdcdhd}((v2\_funct\_1~(k3\_waybel\_1~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k3\_waybel\_1~X0~X1~X2)~(u1\_struct\_0~(k1\_yellow\_2~\\
X0~X1~X2))~(u1\_struct\_0~X1)){\unicdcdcdhd}(v5\_orders\_3~(k3\_waybel\_1~X0~X1~X2)~\\
(k1\_yellow\_2~X0~X1~X2)~X1))))\end{array}
\label{hyp:ggdghdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((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}\\
((\preoh v2\_struct\_0~(k1\_yellow\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_orders\_2~(k1\_yellow\_2~\\
X0~X1~X2)){\unicdcdcdhd}(v4\_yellow\_0~(k1\_yellow\_2~X0~X1~X2)~X1)))\end{array}
\label{hyp:ggdgcdpfjhfgmgmgpghhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
((v3\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0))))))){\unicdcdcdhd}(((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v18\_waybel\_0~\\
X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X0))))))))){\unicdbdjdcd}((v1\_funct\_1~(k2\_waybel34~X0~X1~\\
X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_waybel34~X0~X1~X2)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(v4\_waybel\_1~(k2\_waybel34~X0~X1~X2)~X0~X1)))\end{array}
\label{hyp:ggdgcdpfhhbgjhcgfgmgdded}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((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}\\
((v1\_funct\_1~(k3\_waybel\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k3\_waybel\_1~\\
X0~X1~X2)~(u1\_struct\_0~(k1\_yellow\_2~X0~X1~X2))~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_waybel\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_yellow\_2~X0~X1~X2))~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgddpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((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}\\
((v1\_funct\_1~(k2\_waybel\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_waybel\_1~\\
X0~X1~X2)~(u1\_struct\_0~X0)~(u1\_struct\_0~(k1\_yellow\_2~X0~X1~X2))){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_waybel\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k1\_yellow\_2~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0)))))){\unicdcdcdhd}(((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}\\
((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1)))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X1)~(\\
u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))))){\unicdbdjdcd}((v1\_funct\_1~(k2\_waybel34~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_waybel34~X0~X1~X2)~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k2\_waybel34~X0~X1~X2)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}((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}\\
((v1\_orders\_2~(k1\_yellow\_2~X0~X1~X2)){\unicdcdcdhd}((v4\_yellow\_0~(k1\_yellow\_2~\\
X0~X1~X2)~X1){\unicdcdcdhd}(m1\_yellow\_0~(k1\_yellow\_2~X0~X1~X2)~X1)))\end{array}
\label{hyp:egehpflgbdpfjhfgmgmgpghhpfcd}
\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 .  \\
((\preoh v2\_struct\_0~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}\\
(k1\_yellow\_2~X0~X1~X2=k5\_yellow\_0~X1~(k2\_relset\_1~(u1\_struct\_0~\\
X1)~X2))))\end{array}
\label{hyp:egcdpfjhfgmgmgpghhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X1)~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}(((v3\_lattice3~X1){\unicdcdcdhd}(\\
v18\_waybel\_0~X2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((X3=k2\_waybel34~\\
X0~X1~X2){\unicdbdjded}(v3\_waybel\_1~(k1\_waybel\_1~X0~X1~X3~X2)~X0~X1))))))\end{array}
\label{hyp:egcdpfhhbgjhcgfgmgdded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(l1\_orders\_2~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~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}(((v3\_lattice3~X0){\unicdcdcdhd}(\\
v17\_waybel\_0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}((X3=k1\_waybel34~\\
X0~X1~X2){\unicdbdjded}(v3\_waybel\_1~(k1\_waybel\_1~X0~X1~X2~X3)~X0~X1))))))\end{array}
\label{hyp:egbdpfhhbgjhcgfgmgdded}
\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 .  \\
((\preoh v2\_struct\_0~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}\\
(k3\_waybel\_1~X0~X1~X2=k3\_struct\_0~(k1\_yellow\_2~X0~X1~X2))))\end{array}
\label{hyp:egbdhdpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v1\_lattice3}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgbdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfhhbgjhcgfgmgdded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v7\_waybel\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
((v18\_waybel\_0~(k2\_waybel\_1~X0~X0~X1)~X0~(k1\_yellow\_2~X0~X0~X1)){\unicdcdcdhd}\\
((v17\_waybel\_0~(k3\_waybel\_1~X0~X0~X1)~(k1\_yellow\_2~X0~X0~X1)~X0){\unicdcdcdhd}\\
((r2\_funct\_2~(u1\_struct\_0~(k1\_yellow\_2~X0~X0~X1))~(u1\_struct\_0~\\
X0)~(k2\_waybel34~(k1\_yellow\_2~X0~X0~X1)~X0~(k2\_waybel\_1~X0~X0~X1))~\\
(k3\_waybel\_1~X0~X0~X1)){\unicdcdcdhd}(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k1\_yellow\_2~X0~X0~X1))~(k1\_waybel34~(k1\_yellow\_2~X0~X0~X1)~X0~(k3\_waybel\_1~\\
X0~X0~X1))~(k2\_waybel\_1~X0~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
