\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{t27\_waybel27 (TMSKBXHtXbgaHKgQEEc5PANSn1ZZboFxLoL)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_waybel27 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_yellow\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_orders\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v22\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_monoid\_0 : {{\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}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~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}(m1\_yellow\_0~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}((k1\_yellow\_0~X0~X2 \in u1\_struct\_0~X1){\unicdbdjdcd}(k1\_yellow\_0~X1~X2=\\
k1\_yellow\_0~X0~X2))))\end{array}
\label{hyp:ehgdidpfjhfgmgmgpghhpfad}
\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}((v8\_yellow\_0~(k2\_waybel27~\\
X0~X1)~(k6\_yellow\_1~(u1\_struct\_0~X0)~X1)){\unicdcdcdhd}(m1\_yellow\_0~(k2\_waybel27~\\
X0~X1)~(k6\_yellow\_1~(u1\_struct\_0~X0)~X1))))\end{array}
\label{hyp:ehcdgdpfhhbgjhcgfgmgcdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v3\_lattice3~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_yellow\_0~X0~X1){\unicdcdcdhd}(r2\_yellow\_0~\\
X0~X1))\end{array}
\label{hyp:ehbdhdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~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}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_partfun1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
(v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v5\_orders\_3~\\
X2~X0~X1){\unicdcdcdhd}(v22\_waybel\_0~X2~X0~X1))))))))))\end{array}
\label{hyp:chdgbdpfjhfgmgmgpghhbdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~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}((\preoh v2\_struct\_0~(k2\_waybel27~X0~X1)){\unicdcdcdhd}((v1\_monoid\_0~(\\
k2\_waybel27~X0~X1)){\unicdcdcdhd}((v1\_orders\_2~(k2\_waybel27~X0~X1)){\unicdcdcdhd}((v3\_orders\_2~\\
(k2\_waybel27~X0~X1)){\unicdcdcdhd}(v5\_orders\_2~(k2\_waybel27~X0~X1))))))\end{array}
\label{hyp:ggdgedpfhhbgjhcgfgmgcdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~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)))))))){\unicdbdjdcd}((v1\_orders\_2~\\
(k6\_yellow\_1~X0~X1)){\unicdcdcdhd}(v3\_lattice3~(k6\_yellow\_1~X0~X1)))\end{array}
\label{hyp:ggdgcdpfhhbgjhcgfgmgbdhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
(l1\_orders\_2~X1))){\unicdbdjdcd}((v1\_orders\_2~(k6\_yellow\_1~X0~X1)){\unicdcdcdhd}(v5\_orders\_2~\\
(k6\_yellow\_1~X0~X1)))\end{array}
\label{hyp:ggdgbdgdpfjhfgmgmgpghhpfbd}
\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 .  {\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 .  (((\preoh v2\_struct\_0~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}((v1\_orders\_2~(k2\_waybel27~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k2\_waybel27~\\
X0~X1)))\end{array}
\label{hyp:egehpflgcdpfhhbgjhcgfgmgcdhd}
\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}((v3\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}((X2=\\
k2\_waybel27~X0~X1){\unicdbdjded}(((v4\_yellow\_0~X2~(k6\_yellow\_1~(u1\_struct\_0~\\
X0)~X1)){\unicdcdcdhd}(m1\_yellow\_0~X2~(k6\_yellow\_1~(u1\_struct\_0~X0)~X1))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (X3 \in u1\_struct\_0~X2){\unicdbdjded}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v22\_waybel\_0~X3~X0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))))))))))))\end{array}
\label{hyp:egedpfhhbgjhcgfgmgcdhd}
\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 .  \\
(m1\_yellow\_0~X1~X0){\unicdbdjdcd}((v8\_yellow\_0~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}((r1\_yellow\_0~X0~X2){\unicdbdjdcd}(k1\_yellow\_0~\\
X0~X2 \in u1\_struct\_0~X1)))))\end{array}
\label{hyp:egbdjdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0))))\end{array}
\label{hyp:dgdghdpfchfgmgbgehpfbd}
\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:ehcdhdpfhhbgjhcgfgmgcdhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v3\_lattice3~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k2\_waybel27~X0~X1)))){\unicdbdjdcd}(k1\_yellow\_0~\\
(k2\_waybel27~X0~X1)~X2=k1\_yellow\_0~(k6\_yellow\_1~(u1\_struct\_0~\\
X0)~X1)~X2)))\end{array}$$
\end{theorem}
\end{document}
