\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{l100\_geomtrap (TMTnDSRMRagvSDtejJ3cKJfm3yAr93Zfcz7)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_geomtrap : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\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 $ k2\_diraf : {{\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}((v3\_geomtrap~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\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~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(\\
u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}(((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}((X3=X7){\unicdcdcdhd}(\\
X4=X8)))){\unicdbdjdcd}((r2\_analoaf~(k2\_diraf~X0)~X5~X6~X7~X8){\unicdbdjded}((r2\_analoaf~\\
X0~X1~X2~X3~X4){\unicdcdcdid}(r2\_analoaf~X0~X1~X2~X4~X3))))))))))))\end{array}
\label{hyp:ehedidpfhgfgpgngehchbgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_geomtrap~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjded}(m1\_subset\_1~\\
X1~(u1\_struct\_0~(k2\_diraf~X0))))\end{array}
\label{hyp:ehedhdpfhgfgpgngehchbgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analoaf~X0)){\unicdbdjdcd}((v3\_geomtrap~\\
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}({\unicdcdadad} X9 .  \\
(m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~\\
X10~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r2\_analoaf~X0~X1~X2~X2~X3){\unicdbdjdcd}((X1=X2){\unicdcdcdhd}(\\
X2=X3))){\unicdcdcdhd}((((r2\_analoaf~X0~X1~X2~X5~X6){\unicdcdcdhd}(r2\_analoaf~X0~X1~X2~X7~X8)){\unicdbdjdcd}\\
((X1=X2){\unicdcdcdid}(r2\_analoaf~X0~X5~X6~X7~X8))){\unicdcdcdhd}(((r2\_analoaf~X0~X1~X2~X3~\\
X4){\unicdbdjdcd}((r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}(r2\_analoaf~X0~X2~X1~X4~X3))){\unicdcdcdhd}((\\
\preoh {\unicdcdadad} X11 .  (m1\_subset\_1~X11~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh r2\_analoaf~\\
X0~X1~X2~X3~X11){\unicdcdcdhd}(\preoh r2\_analoaf~X0~X1~X2~X11~X3))){\unicdcdcdhd}(\preoh (r2\_analoaf~X0~\\
X1~X2~X3~X9){\unicdcdcdhd}((r2\_analoaf~X0~X1~X2~X3~X10){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(X9{\unicdcdgdad}X10)))))))))))))))))))\end{array}
\label{hyp:egbdddpfhgfgpgngehchbgah}
\end{equation}
\begin{theorem}\label{thm:mgbdadadpfhgfgpgngehchbgah}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_geomtrap~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(\\
u1\_struct\_0~(k2\_diraf~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
(k2\_diraf~X0))){\unicdbdjdcd}(((r2\_analoaf~(k2\_diraf~X0)~X1~X2~X3~X4){\unicdcdcdhd}(r2\_analoaf~\\
(k2\_diraf~X0)~X1~X2~X5~X6)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(r2\_analoaf~(k2\_diraf~X0)~\\
X3~X4~X5~X6)))))))))\end{array}$$
\end{theorem}
\end{document}
