\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{t60\_filter\_0 (TMJwiqFJzwWbtvXdnTksRyuxZp1m97Bwz88)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v17\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_filter\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v15\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v19\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v20\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v11\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_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}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v15\_lattices~X0){\unicdcdcdhd}((v16\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))))){\unicdcdcdhd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
((v12\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k6\_filter\_0~\\
X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}((v10\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~\\
X0~X1))){\unicdcdcdhd}((v15\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}\\
((v16\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}(l3\_lattices~\\
(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1)))))))))\end{array}
\label{hyp:ehfdjdpfggjgmgehfgchpfad}
\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}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v19\_lattices~X1~X0){\unicdcdcdhd}\\
((v20\_lattices~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}((v11\_lattices~X0){\unicdbdjdcd}(v11\_lattices~(k6\_filter\_0~X0~X1))))\end{array}
\label{hyp:ehfdedpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}((v10\_lattices~(k6\_filter\_0~\\
X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}(v13\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~\\
X0~X1)))))\end{array}
\label{hyp:ggdgedpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}\\
(l3\_lattices~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k2\_filter\_0~X0~X1)){\unicdcdcdhd}((v19\_lattices~(k2\_filter\_0~X0~X1)~X0){\unicdcdcdhd}(\\
(v20\_lattices~(k2\_filter\_0~X0~X1)~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_filter\_0~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgcdpfggjgmgehfgchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v11\_lattices~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~\\
X0){\unicdcdcdhd}(v12\_lattices~X0))))\end{array}
\label{hyp:dgdghdpfmgbgehehjgdgfgdh}
\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:ehgdadpfggjgmgehfgchpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v17\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}((v10\_lattices~\\
(k6\_filter\_0~X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}((v17\_lattices~(k6\_filter\_0~\\
X0~(k2\_filter\_0~X0~X1))){\unicdcdcdhd}(l3\_lattices~(k6\_filter\_0~X0~(k2\_filter\_0~\\
X0~X1))))))))\end{array}$$
\end{theorem}
\end{document}
