\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{t35\_yellow18 (TMYb6ZRP4hk3HHZk7d93QomjYD2F1HbZxKP)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_yellow18 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\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 $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_yellow18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}((v2\_yellow18~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_tarski~(k1\_altcat\_1~X0~\\
X1~X2)~(k1\_funct\_2~(k3\_yellow18~X0~X1)~(k3\_yellow18~X0~X2))))))\end{array}
\label{hyp:ehddddpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k1\_funct\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdcdcdhd}((X3=\\
X4){\unicdcdcdhd}((k9\_xtuple\_0~X4=X0){\unicdcdcdhd}(r1\_tarski~(k10\_xtuple\_0~X4)~X1)))))\end{array}
\label{hyp:egcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}\\
(X1 \in X0))){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1)))\end{array}
\label{hyp:egbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}((v2\_yellow18~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_altcat\_1~X0~X1~X2)){\unicdbdjdcd}((k9\_xtuple\_0~X3=k3\_yellow18~\\
X0~X1){\unicdcdcdhd}(r1\_tarski~(k10\_xtuple\_0~X3)~(k3\_yellow18~X0~X2)))))))\end{array}$$
\end{theorem}
\end{document}
