\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\_waybel15 (TMGwPks5efHQwKYoFLheWrRe1VcS4okZaZr)}
\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 $ v11\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_8 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r5\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_waybel\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_waybel15 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_waybel\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v24\_waybel\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_waybel\_8 : {{\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}(l1\_orders\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~\\
X1){\unicdcdcdhd}(l1\_orders\_2~X1))))){\unicdbdjdcd}(((r5\_waybel\_1~X0~X1){\unicdcdcdhd}(v3\_waybel\_3~\\
X0)){\unicdbdjdcd}(v3\_waybel\_3~X1)))\end{array}
\label{hyp:ehjdpfhhbgjhcgfgmgbdfd}
\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}((r5\_waybel\_1~X0~X1){\unicdbdjdcd}(\\
r5\_waybel\_1~X1~X0)))\end{array}
\label{hyp:ehgdpfhhbgjhcgfgmgpfbd}
\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}((v1\_waybel\_5~X0){\unicdbdjded}((v2\_waybel\_1~X0){\unicdcdcdhd}\\
((v3\_waybel\_3~X0){\unicdcdcdhd}(v3\_waybel\_3~(k7\_lattice3~X0)))))\end{array}
\label{hyp:ehddjdpfhhbgjhcgfgmgpfgd}
\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}((v11\_waybel\_1~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}(r5\_waybel\_1~X0~(k7\_lattice3~X0))\end{array}
\label{hyp:ehddidpfjhfgmgmgpghhpfhd}
\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}\\
(((r5\_waybel\_1~X0~X1){\unicdcdcdhd}((v1\_yellow\_0~X0){\unicdcdcdhd}(v3\_waybel\_8~X0))){\unicdbdjdcd}\\
(v3\_waybel\_8~X1)))\end{array}
\label{hyp:ehbdadpfhhbgjhcgfgmgbdfd}
\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}((v11\_waybel\_1~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}(\preoh (v3\_lattice3~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}((r1\_tarski~X2~(k1\_waybel15~X0)){\unicdcdcdhd}(X1=k1\_yellow\_0~\\
X0~X2)))){\unicdcdcdhd}({\unicdcdadad} X1 .  \preoh r5\_waybel\_1~X0~(k3\_yellow\_1~X1))))\end{array}
\label{hyp:mgddedpfhhbgjhcgfgmgbdfd}
\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}((v11\_waybel\_1~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}((v1\_waybel\_5~X0){\unicdbdjdcd}((v3\_lattice3~X0){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((r1\_tarski~X2~(k1\_waybel15~\\
X0)){\unicdcdcdhd}(X1=k1\_yellow\_0~X0~X2))))))\end{array}
\label{hyp:mgddddpfhhbgjhcgfgmgbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(v3\_lattice3~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:ggdgidpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k3\_yellow\_1~X0)){\unicdcdcdhd}((v1\_orders\_2~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}((v3\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}((v4\_orders\_2~(k3\_yellow\_1~\\
X0)){\unicdcdcdhd}(v5\_orders\_2~(k3\_yellow\_1~X0)))))\end{array}
\label{hyp:ggdghdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k7\_lattice3~X0)){\unicdcdcdhd}(v1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:ggdggdpfmgbgehehjgdgfgdd}
\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}(l1\_orders\_2~X0)))){\unicdbdjdcd}((v1\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}((\\
v3\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}((v4\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}\\
(v5\_orders\_2~(k7\_lattice3~X0)))))\end{array}
\label{hyp:ggdgfdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(v3\_waybel\_8~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:ggdgbdpfhhbgjhcgfgmgbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~(k7\_lattice3~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k7\_lattice3~X0)))\end{array}
\label{hyp:egehpflghdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k3\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k3\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgddpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v11\_waybel\_1~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_yellow\_0~\\
X0){\unicdcdcdhd}((v2\_waybel\_1~X0){\unicdcdcdhd}(v10\_waybel\_1~X0))))))))))\end{array}
\label{hyp:dgdgidpfhhbgjhcgfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v3\_yellow\_0~X0){\unicdbdjdcd}((v1\_yellow\_0~\\
X0){\unicdcdcdhd}(v2\_yellow\_0~X0)))\end{array}
\label{hyp:dgdgedpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}(v3\_waybel\_3~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}\\
((v24\_waybel\_0~X0){\unicdcdcdhd}(v2\_waybel\_3~X0)))))\end{array}
\label{hyp:dgdgedpfhhbgjhcgfgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_lattice3~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_yellow\_0~X0)))\end{array}
\label{hyp:dgdgddpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
(v3\_waybel\_8~X0)))))){\unicdbdjdcd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(v2\_waybel\_8~\\
X0)))))))\end{array}
\label{hyp:dgdgddpfhhbgjhcgfgmgpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_lattice3~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}(v2\_lattice3~X0))))\end{array}
\label{hyp:dgdgbdpfjhfgmgmgpghhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
(v2\_waybel\_8~X0)))))){\unicdbdjdcd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}(v3\_waybel\_3~\\
X0)))))))\end{array}
\label{hyp:dgdgbdpfhhbgjhcgfgmgpfid}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}\\
((v1\_yellow\_0~X0){\unicdcdcdhd}(v24\_waybel\_0~X0))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}\\
((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(v3\_lattice3~\\
X0))))))\end{array}
\label{hyp:dgdgbdddpfhhbgjhcgfgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfhhbgjhcgfgmgbdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v11\_waybel\_1~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}((v3\_waybel\_8~X0){\unicdbdjded}({\unicdcdaddd} X1 .  r5\_waybel\_1~\\
X0~(k3\_yellow\_1~X1)))\end{array}$$
\end{theorem}
\end{document}
