\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{t53\_filter\_2 (TMUToobtoQKiDYJzY77DR6P88HFSn5njx8D)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_lattice2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v15\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\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}(l3\_lattices~\\
X0))){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v15\_lattices~\\
X0){\unicdcdcdhd}((v16\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjded}((\preoh v2\_struct\_0~\\
(k1\_lattice2~X0)){\unicdcdcdhd}((v10\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}((v15\_lattices~\\
(k1\_lattice2~X0)){\unicdcdcdhd}((v16\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}(l3\_lattices~\\
(k1\_lattice2~X0)))))))\end{array}
\label{hyp:ehfdcdpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v11\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjded}((\preoh v2\_struct\_0~(k1\_lattice2~X0)){\unicdcdcdhd}(\\
(v10\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}((v11\_lattices~(k1\_lattice2~\\
X0)){\unicdcdcdhd}(l3\_lattices~(k1\_lattice2~X0))))))\end{array}
\label{hyp:ehfdadpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((v3\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}(v10\_lattices~(k1\_lattice2~\\
X0)))\end{array}
\label{hyp:ggdgidpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k1\_lattice2~X0)){\unicdcdcdhd}(v3\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:ggdgbdpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}((v3\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}\\
(l3\_lattices~(k1\_lattice2~X0)))\end{array}
\label{hyp:egehpflgbdpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v11\_lattices~\\
X0){\unicdcdcdhd}((v15\_lattices~X0){\unicdcdcdhd}(v16\_lattices~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(v17\_lattices~X0)))\end{array}
\label{hyp:dgdggdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v17\_lattices~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v11\_lattices~X0){\unicdcdcdhd}((v15\_lattices~\\
X0){\unicdcdcdhd}(v16\_lattices~X0)))))\end{array}
\label{hyp:dgdgfdpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehfdddpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v17\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjded}((\preoh v2\_struct\_0~(k1\_lattice2~X0)){\unicdcdcdhd}(\\
(v10\_lattices~(k1\_lattice2~X0)){\unicdcdcdhd}((v17\_lattices~(k1\_lattice2~\\
X0)){\unicdcdcdhd}(l3\_lattices~(k1\_lattice2~X0))))))\end{array}$$
\end{theorem}
\end{document}
