\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{t10\_poset\_1 (TMc6cQD1F2ceQitsKHW31yGY8gcPDGK8uan)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_poset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_poset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_orders\_3 : {{\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}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~X1~X0~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}(k3\_poset\_1~X0~X1=k1\_yellow\_0~X0~(k2\_poset\_1~X0~X1)))\end{array}
\label{hyp:ehjdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_orders\_3~X1~X0~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v5\_orders\_3~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
((r1\_yellow\_2~(u1\_struct\_0~X0)~X0~X1~X2){\unicdbdjdcd}(r3\_orders\_2~X0~(k1\_yellow\_0~\\
X0~(k2\_poset\_1~X0~X1))~(k1\_yellow\_0~X0~(k2\_poset\_1~X0~X2))))))\end{array}
\label{hyp:ehfdpfahpgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}\\
((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))))))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_orders\_2~\\
X1){\unicdcdcdhd}((v3\_orders\_2~X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}\\
((v1\_poset\_1~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))){\unicdbdjdcd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(v2\_poset\_1~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(v5\_orders\_3~X2~X0~X1)))))\end{array}
\label{hyp:dgdgcdpfahpgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfahpgdhfgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_orders\_2~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_poset\_1~X0){\unicdcdcdhd}(\\
l1\_orders\_2~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~X1~X0~X0){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_poset\_1~X2~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
((r1\_yellow\_2~(u1\_struct\_0~X0)~X0~X1~X2){\unicdbdjdcd}(r3\_orders\_2~X0~(k3\_poset\_1~\\
X0~X1)~(k3\_poset\_1~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
