\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{t31\_pcs\_0 (TMZR6AVqxbYPfaKFsRH2kfXpLj68f1jVUaY)}
\maketitle
Let $ v13\_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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v12\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\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~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
(((X2=X4){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}(r1\_pcs\_0~(k19\_pcs\_0~X0~X1)~X4~X5))){\unicdbdjdcd}((X2=\\
X1){\unicdcdcdid}((X3=X1){\unicdcdcdid}(r1\_pcs\_0~X0~X2~X3))))))))\end{array}
\label{hyp:ehcdjdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\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~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
(((X2=X4){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}(r1\_pcs\_0~X0~X2~X3))){\unicdbdjdcd}(r1\_pcs\_0~(k19\_pcs\_0~\\
X0~X1)~X4~X5))))))\end{array}
\label{hyp:ehcdidpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}((X2=X1){\unicdbdjdcd}((r1\_pcs\_0~(k19\_pcs\_0~\\
X0~X1)~X2~X3){\unicdcdcdhd}(r1\_pcs\_0~(k19\_pcs\_0~X0~X1)~X3~X2)))))\end{array}
\label{hyp:ehcdhdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\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~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}\\
(((X2=X4){\unicdcdcdhd}((X3=X5){\unicdcdcdhd}(r1\_orders\_2~(k19\_pcs\_0~X0~X1)~X4~X5))){\unicdbdjdcd}(\\
(X2=X1){\unicdcdcdid}(r1\_orders\_2~X0~X2~X3)))))))\end{array}
\label{hyp:ehcdgdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}((X2{\unicdcdgdad}X1){\unicdbdjdcd}(X2 \in u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:ehcdfdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k19\_pcs\_0~X0~X1))){\unicdbdjdcd}(((X2=X3){\unicdcdcdhd}(r1\_orders\_2~(k19\_pcs\_0~X0~X1)~\\
X3~X4)){\unicdbdjdcd}((X2=X1){\unicdcdcdid}((X1 \in u1\_struct\_0~X0){\unicdcdcdid}((X4 \in u1\_struct\_0~X0){\unicdcdcdhd}\\
(X4{\unicdcdgdad}X1))))))))\end{array}
\label{hyp:ehcdedpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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}((v13\_pcs\_0~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}(((r1\_pcs\_0~X0~X1~X3){\unicdcdcdhd}((r1\_orders\_2~\\
X0~X2~X1){\unicdcdcdhd}(r1\_orders\_2~X0~X4~X3))){\unicdbdjdcd}(r1\_pcs\_0~X0~X2~X4)))))))\end{array}
\label{hyp:egcdcdpfahdgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfahdgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v13\_pcs\_0~X0){\unicdcdcdhd}(l2\_pcs\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh X1 \in \\
u1\_struct\_0~X0){\unicdbdjdcd}(v13\_pcs\_0~(k19\_pcs\_0~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
