\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{t32\_pcs\_0 (TMQsF8LpgET9Ze5JY9VF7yKTy3Q84Eeqi2A)}
\maketitle
Let $ v14\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v13\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v13\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh X1 \in \\
u1\_struct\_0~X0){\unicdbdjdcd}(v13\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:ehddbdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_orders\_2~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh X1 \in \\
u1\_struct\_0~X0){\unicdbdjdcd}(v4\_orders\_2~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:ehddadpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v6\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}((v6\_pcs\_0~\\
(k19\_pcs\_0~X0~X1)){\unicdcdcdhd}(v12\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:ggdggdadpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v4\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}((v4\_pcs\_0~\\
(k19\_pcs\_0~X0~X1)){\unicdcdcdhd}(v12\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:ggdgfdjdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_orders\_2~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}((v3\_orders\_2~\\
(k19\_pcs\_0~X0~X1)){\unicdcdcdhd}(v12\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:ggdgfdidpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l2\_pcs\_0~X0){\unicdbdjdcd}((v12\_pcs\_0~(k19\_pcs\_0~X0~\\
X1)){\unicdcdcdhd}(l2\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}
\label{hyp:egehpflgbdjdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}(((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}\\
((v4\_pcs\_0~X0){\unicdcdcdhd}((v6\_pcs\_0~X0){\unicdcdcdhd}(v13\_pcs\_0~X0))))){\unicdbdjdcd}(v14\_pcs\_0~\\
X0))\end{array}
\label{hyp:dgdgidpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}((v14\_pcs\_0~X0){\unicdbdjdcd}((v3\_orders\_2~X0){\unicdcdcdhd}\\
((v4\_orders\_2~X0){\unicdcdcdhd}((v4\_pcs\_0~X0){\unicdcdcdhd}((v6\_pcs\_0~X0){\unicdcdcdhd}(v13\_pcs\_0~\\
X0))))))\end{array}
\label{hyp:dgdghdpfahdgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfahdgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v14\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh X1 \in \\
u1\_struct\_0~X0){\unicdbdjdcd}((v14\_pcs\_0~(k19\_pcs\_0~X0~X1)){\unicdcdcdhd}(l2\_pcs\_0~(k19\_pcs\_0~\\
X0~X1))))\end{array}$$
\end{theorem}
\end{document}
