\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{t18\_waybel15 (TMTdABdnHmFF4oB3V7aeoNFpxEoWZ4Logz5)}
\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 $ v1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k3\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_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 $ v22\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r5\_waybel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_waybel\_8 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v17\_waybel\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
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}((v1\_yellow\_0~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}((v3\_waybel\_3~X0){\unicdbdjded}({\unicdcdaddd} X1 .  ((v3\_orders\_2~\\
X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}\\
((v2\_lattice3~X1){\unicdcdcdhd}((v1\_yellow\_0~X1){\unicdcdcdhd}((v2\_waybel\_8~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1)))))))){\unicdcdcdhd}({\unicdcdaddd} 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)))))){\unicdcdcdhd}((v2\_funct\_2~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v17\_waybel\_0~X2~X1~X0){\unicdcdcdhd}(v22\_waybel\_0~X2~X1~X0))))))\end{array}
\label{hyp:ehbdhdpfhhbgjhcgfgmgbdfd}
\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}\\
(({\unicdcdaddd} X1 .  {\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1))){\unicdcdcdhd}((v6\_waybel\_1~\\
X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1)))))))){\unicdcdcdhd}\\
((v22\_waybel\_0~X2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~X1)){\unicdcdcdhd}(r5\_waybel\_1~\\
X0~(k1\_yellow\_2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~X1)~X2)))){\unicdbdjdcd}(v3\_waybel\_3~\\
X0))\end{array}
\label{hyp:mgbdjdpfhhbgjhcgfgmgbdfd}
\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}((v1\_yellow\_0~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~\\
X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~X1){\unicdcdcdhd}\\
((v1\_yellow\_0~X1){\unicdcdcdhd}((v2\_waybel\_8~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))))){\unicdcdcdhd}\\
({\unicdcdaddd} 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)))))){\unicdcdcdhd}((v2\_funct\_2~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v17\_waybel\_0~X2~X1~X0){\unicdcdcdhd}(v22\_waybel\_0~X2~X1~X0))))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1))){\unicdcdcdhd}\\
((v6\_waybel\_1~X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~\\
X1)))))))){\unicdbdjdcd}(\preoh (v22\_waybel\_0~X2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~\\
X1)){\unicdcdcdhd}(r5\_waybel\_1~X0~(k1\_yellow\_2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~\\
X1)~X2))))))\end{array}
\label{hyp:mgbdgdpfhhbgjhcgfgmgbdfd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfhhbgjhcgfgmgbdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v1\_yellow\_0~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}((\preoh (v3\_waybel\_3~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1))){\unicdcdcdhd}((v6\_waybel\_1~\\
X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1)))))))){\unicdbdjdcd}\\
(\preoh (v22\_waybel\_0~X2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~X1)){\unicdcdcdhd}(r5\_waybel\_1~\\
X0~(k1\_yellow\_2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~X1)~X2)))))){\unicdcdcdhd}((\\
{\unicdcdaddd} X1 .  {\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1))){\unicdcdcdhd}((v6\_waybel\_1~\\
X2~(k3\_yellow\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_yellow\_1~X1))~(u1\_struct\_0~(k3\_yellow\_1~X1)))))))){\unicdcdcdhd}\\
((v22\_waybel\_0~X2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~X1)){\unicdcdcdhd}(r5\_waybel\_1~\\
X0~(k1\_yellow\_2~(k3\_yellow\_1~X1)~(k3\_yellow\_1~X1)~X2)))){\unicdbdjdcd}(v3\_waybel\_3~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
