\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{t9\_neckla\_3 (TMXCRM7KoMqvX3CtupJvnN4Bs9AZNhh8mXi)}
\maketitle
Let $ v3\_necklace : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_neckla\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_neckla\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}(\\
(v1\_orders\_2~(k2\_neckla\_2~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k2\_neckla\_2~\\
X0~X1)))\end{array}
\label{hyp:egehpflgcdpfogfgdglgmgbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}(\\
(v1\_orders\_2~(k1\_neckla\_2~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(k1\_neckla\_2~\\
X0~X1)))\end{array}
\label{hyp:egehpflgbdpfogfgdglgmgbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v3\_necklace~X0){\unicdbdjded}({\unicdcdadad} X1 .  \preoh \\
(X1 \in u1\_struct\_0~X0){\unicdcdcdhd}(k4\_tarski~X1~X1 \in u1\_orders\_2~X0)))\end{array}
\label{hyp:egfdpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}((X2=k2\_neckla\_2~X0~X1){\unicdbdjded}\\
((u1\_struct\_0~X2=k2\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
(u1\_orders\_2~X2=k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(u1\_orders\_2~\\
X0)~(u1\_orders\_2~X1))~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)))~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)))))))\end{array}
\label{hyp:egddpfogfgdglgmgbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_orders\_2~X2){\unicdcdcdhd}(l1\_orders\_2~X2)){\unicdbdjdcd}((X2=k1\_neckla\_2~X0~X1){\unicdbdjded}\\
((u1\_struct\_0~X2=k2\_xboole\_0~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
(u1\_orders\_2~X2=k2\_xboole\_0~(u1\_orders\_2~X0)~(u1\_orders\_2~X1))))))\end{array}
\label{hyp:egcdpfogfgdglgmgbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehjdpfogfgdglgmgbgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_necklace~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l1\_orders\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (l1\_orders\_2~X2){\unicdbdjdcd}(((X0=k1\_neckla\_2~\\
X1~X2){\unicdcdcdid}(X0=k2\_neckla\_2~X1~X2)){\unicdbdjdcd}((v3\_necklace~X1){\unicdcdcdhd}(v3\_necklace~\\
X2)))))\end{array}$$
\end{theorem}
\end{document}
