\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{t20\_lattice6 (TMNybKGxUYAbqL352UMkGdR2kcvWsdUbaYC)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\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 $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_lattice6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_waybel\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_lattice6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_waybel\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}((v2\_lattice6~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}k5\_lattices~X0){\unicdbdjdcd}((v4\_lattice6~X1~X0){\unicdbdjded}\\
(v3\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~X0)))))\end{array}
\label{hyp:ehbdjdpfmgbgehehjgdgfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v4\_lattice3~\\
X0){\unicdcdcdhd}((v1\_lattice6~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}k6\_lattices~X0){\unicdbdjdcd}((v3\_lattice6~X1~X0){\unicdbdjded}\\
(v2\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~X0)))))\end{array}
\label{hyp:ehbdhdpfmgbgehehjgdgfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~\\
X0){\unicdcdcdhd}(v10\_lattices~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v2\_lattice6~X0))))\end{array}
\label{hyp:dgdgddpfmgbgehehjgdgfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~\\
X0){\unicdcdcdhd}(v10\_lattices~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v1\_lattice6~X0))))\end{array}
\label{hyp:dgdgcdpfmgbgehehjgdgfggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~\\
X0){\unicdcdcdhd}(v10\_lattices~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v4\_lattice3~X0))))\end{array}
\label{hyp:dgdgbdpfmgbgehehjgdgfggd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfmgbgehehjgdgfggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k5\_lattices~X0){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_lattices~X0){\unicdcdcdhd}(\preoh ((v3\_lattice6~\\
X1~X0){\unicdbdjdcd}(v2\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~X0))){\unicdcdcdhd}((\\
(v2\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~X0)){\unicdbdjdcd}(v3\_lattice6~\\
X1~X0)){\unicdcdcdhd}(((v4\_lattice6~X1~X0){\unicdbdjdcd}(v3\_waybel\_6~(k4\_lattice3~X0~X1)~\\
(k3\_lattice3~X0))){\unicdcdcdhd}((v3\_waybel\_6~(k4\_lattice3~X0~X1)~(k3\_lattice3~\\
X0)){\unicdbdjdcd}(v4\_lattice6~X1~X0))))))))\end{array}$$
\end{theorem}
\end{document}
