\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{t18\_dirort (TMM7CxEQgwLr74HVMjorjT6QhVvUequ4G5r)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_dirort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_dirort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_dirort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_dirort : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_dirort : {{\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 $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dirort~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
((v6\_dirort~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\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~\\
X0)){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X3~X4){\unicdbdjdcd}(r2\_analoaf~X0~X3~X4~X1~X2)))))))\end{array}
\label{hyp:egidpfegjgchpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dirort~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
((v5\_dirort~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\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~\\
X0)){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X3~X4){\unicdbdjdcd}(r2\_analoaf~X0~X3~X4~X2~X1)))))))\end{array}
\label{hyp:eghdpfegjgchpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dirort~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
((v4\_dirort~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\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~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (r2\_analoaf~X0~X1~X2~X4~X5){\unicdcdcdhd}((r2\_analoaf~X0~X4~X5~X7~X8){\unicdcdcdhd}((r2\_analoaf~\\
X0~X1~X2~X3~X6){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((X4{\unicdcdgdad}X5){\unicdcdcdhd}(\preoh r2\_analoaf~X0~X3~X6~X7~X8)))))))))))))))\end{array}
\label{hyp:eggdpfegjgchpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dirort~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
((v3\_dirort~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\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~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (r2\_analoaf~X0~X1~X2~X4~X5){\unicdcdcdhd}((r2\_analoaf~X0~X4~X5~X7~X8){\unicdcdcdhd}((r2\_analoaf~\\
X0~X3~X6~X7~X8){\unicdcdcdhd}((X7{\unicdcdgdad}X8){\unicdcdcdhd}((X4{\unicdcdgdad}X5){\unicdcdcdhd}(\preoh r2\_analoaf~X0~X1~X2~X3~X6)))))))))))))))\end{array}
\label{hyp:egfdpfegjgchpgcheh}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfegjgchpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_dirort~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
((v3\_dirort~X0){\unicdbdjdcd}(((\preoh v5\_dirort~X0){\unicdcdcdhd}(\preoh v6\_dirort~X0)){\unicdcdcdid}(v4\_dirort~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
