\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{t45\_abcmiz\_0 (TMQ4wr37W6fA2bsJHCG75YVJ7pqjWDq24Zz)}
\maketitle
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\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_abcmiz\_0 : {{\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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}\\
((v9\_abcmiz\_0~X0){\unicdcdcdhd}(l2\_abcmiz\_0~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_abcmiz\_0~\\
X0)){\unicdbdjdcd}((r3\_abcmiz\_0~X0~X1~X2){\unicdbdjdcd}(r1\_tarski~(k2\_relset\_1~(u1\_abcmiz\_0~\\
X0)~X2)~(k2\_abcmiz\_0~X0~(k8\_abcmiz\_0~X0~X1~X2))))))\end{array}
\label{hyp:ehededpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}\\
((v9\_abcmiz\_0~X0){\unicdcdcdhd}(l2\_abcmiz\_0~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_abcmiz\_0~\\
X0)){\unicdbdjdcd}((r3\_abcmiz\_0~X0~X1~X2){\unicdbdjdcd}(r3\_orders\_2~X0~(k8\_abcmiz\_0~X0~X1~\\
X2)~X1))))\end{array}
\label{hyp:ehedddpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r3\_orders\_2~X0~X1~X2){\unicdbdjded}(r1\_orders\_2~\\
X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchddpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_abcmiz\_0}~{X0}})}{\unicdbdjdcd}{({{({{l1\_orders\_2}~{X0}})}{\unicdcdcdhd}{({{l1\_abcmiz\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}(l2\_abcmiz\_0~X0))))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_finseq\_1~X2~(u1\_abcmiz\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k8\_abcmiz\_0~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgidpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_abcmiz\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_abcmiz\_0~X0))){\unicdbdjdcd}\\
((r2\_abcmiz\_0~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((r1\_tarski~X2~(k2\_abcmiz\_0~X0~X3)){\unicdcdcdhd}(r1\_orders\_2~X0~X3~X1))))))\end{array}
\label{hyp:egbdgdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v1\_lattice3}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgbdpfmgbgehehjgdgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfbgcgdgngjgkhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}\\
((v9\_abcmiz\_0~X0){\unicdcdcdhd}(l2\_abcmiz\_0~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_abcmiz\_0~\\
X0)){\unicdbdjdcd}((r3\_abcmiz\_0~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_abcmiz\_0~X0))){\unicdbdjdcd}((X3=k2\_relset\_1~(u1\_abcmiz\_0~X0)~X2){\unicdbdjdcd}(r2\_abcmiz\_0~\\
X0~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
