\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{t11\_filter\_2 (TMJPKieXKFes78YhSBFBS6xc522wKNoUSUr)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v13\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v14\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v13\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v10\_lattices~\\
X1){\unicdcdcdhd}((v13\_lattices~X1){\unicdcdcdhd}(l3\_lattices~X1)))){\unicdbdjdcd}((g3\_lattices~(\\
u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~X0)=g3\_lattices~\\
(u1\_struct\_0~X1)~(u2\_lattices~X1)~(u1\_lattices~X1)){\unicdbdjdcd}(k5\_lattices~\\
X0=k5\_lattices~X1)))\end{array}
\label{hyp:ehjdpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_lattices~X1)){\unicdbdjdcd}((g3\_lattices~(u1\_struct\_0~\\
X0)~(u2\_lattices~X0)~(u1\_lattices~X0)=g3\_lattices~(u1\_struct\_0~\\
X1)~(u2\_lattices~X1)~(u1\_lattices~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}(((X2=X4){\unicdcdcdhd}(X3=X5)){\unicdbdjdcd}((k1\_lattices~\\
X0~X2~X3=k1\_lattices~X1~X4~X5){\unicdcdcdhd}((k2\_lattices~X0~X2~X3=k2\_lattices~\\
X1~X4~X5){\unicdcdcdhd}(((r1\_lattices~X0~X2~X3){\unicdbdjdcd}(r1\_lattices~X1~X4~X5)){\unicdcdcdhd}((r1\_lattices~\\
X1~X4~X5){\unicdbdjdcd}(r1\_lattices~X0~X2~X3))))))))))))\end{array}
\label{hyp:ehbdpfbhfhbgogehbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v14\_lattices~\\
X0){\unicdcdcdhd}(l3\_lattices~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v10\_lattices~\\
X1){\unicdcdcdhd}((v14\_lattices~X1){\unicdcdcdhd}(l3\_lattices~X1)))){\unicdbdjdcd}((g3\_lattices~(\\
u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~X0)=g3\_lattices~\\
(u1\_struct\_0~X1)~(u2\_lattices~X1)~(u1\_lattices~X1)){\unicdbdjdcd}(k6\_lattices~\\
X0=k6\_lattices~X1)))\end{array}
\label{hyp:ehbdadpfggjgmgehfgchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_lattices~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_lattices~X0~X1~X2){\unicdbdjded}((k1\_lattices~X0~X1~\\
X2=k6\_lattices~X0){\unicdcdcdhd}((k1\_lattices~X0~X2~X1=k6\_lattices~X0){\unicdcdcdhd}((\\
k2\_lattices~X0~X1~X2=k5\_lattices~X0){\unicdcdcdhd}(k2\_lattices~X0~X2~X1=k5\_lattices~\\
X0)))))))\end{array}
\label{hyp:egbdidpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v15\_lattices~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_lattices~X0){\unicdcdcdhd}(v14\_lattices~X0))))\end{array}
\label{hyp:dgdgedpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfggjgmgehfgchpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}((v15\_lattices~\\
X0){\unicdcdcdhd}((v16\_lattices~X0){\unicdcdcdhd}(l3\_lattices~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v10\_lattices~X1){\unicdcdcdhd}((v15\_lattices~X1){\unicdcdcdhd}((v16\_lattices~\\
X1){\unicdcdcdhd}(l3\_lattices~X1))))){\unicdbdjdcd}((g3\_lattices~(u1\_struct\_0~X0)~(u2\_lattices~\\
X0)~(u1\_lattices~X0)=g3\_lattices~(u1\_struct\_0~X1)~(u2\_lattices~\\
X1)~(u1\_lattices~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(((X2=X4){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}(r2\_lattices~X0~X2~X3))){\unicdbdjdcd}\\
(r2\_lattices~X1~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
