\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{t47\_cc0sp2 (TMZYmuNaxhYBTWQKfsoeMkTZb619YsskYyQ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_cc0sp2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((v13\_algstr\_0~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v3\_normsp\_0~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v4\_normsp\_0~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v2\_clvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v3\_clvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v4\_clvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v5\_clvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}(v8\_clvect\_1~(k9\_cc0sp2~X0))))))))))))\end{array}
\label{hyp:ggdgbdfdpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_cc0sp2~X0)){\unicdcdcdhd}(v7\_clvect\_1~(k9\_cc0sp2~\\
X0)))\end{array}
\label{hyp:ggdgbdedpfdgdgaddhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}(l2\_clvect\_1~(k9\_cc0sp2~X0))\end{array}
\label{hyp:egehpflgjdpfdgdgaddhahcd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfdgdgaddhahcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v3\_normsp\_0~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v4\_normsp\_0~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v2\_clvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v3\_clvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v4\_clvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}((v5\_clvect\_1~(k9\_cc0sp2~X0)){\unicdcdcdhd}((v8\_clvect\_1~(k9\_cc0sp2~\\
X0)){\unicdcdcdhd}(l2\_clvect\_1~(k9\_cc0sp2~X0))))))))))))))\end{array}$$
\end{theorem}
\end{document}
