\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{t36\_yellow\_3 (TMGjwXvorsjTT4WMtd71nVNgRMN6fyWzkub)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_yellow\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(((r1\_lattice3~X0~X2~X4){\unicdcdcdhd}(r1\_lattice3~X1~X3~X5)){\unicdbdjdcd}(r1\_lattice3~\\
(k3\_yellow\_3~X0~X1)~(k6\_yellow\_3~X0~X1~X2~X3)~(k7\_yellow\_3~X0~X1~X4~\\
X5))))))))\end{array}
\label{hyp:ehddddpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\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~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}(((r1\_orders\_2~X0~X2~X3){\unicdcdcdhd}(r1\_orders\_2~\\
X1~X4~X5)){\unicdbdjded}(r1\_orders\_2~(k3\_yellow\_3~X0~X1)~(k7\_yellow\_3~X0~X1~X2~\\
X4)~(k7\_yellow\_3~X0~X1~X3~X5))))))))\end{array}
\label{hyp:ehbdbdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1)){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}(m1\_subset\_1~(k7\_yellow\_3~X0~X1~X2~X3)~(u1\_struct\_0~(k3\_yellow\_3~\\
X0~X1)))\end{array}
\label{hyp:egehpflghdpfjhfgmgmgpghhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r2\_yellow\_0~X0~X1){\unicdbdjded}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_lattice3~\\
X0~X1~X2){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice3~\\
X0~X1~X3){\unicdbdjdcd}(r1\_orders\_2~X0~X3~X2))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(((r1\_lattice3~X0~X1~X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice3~X0~X1~X4){\unicdbdjdcd}(r1\_orders\_2~X0~X4~\\
X3)))){\unicdbdjdcd}(X3=X2)))))))\end{array}
\label{hyp:egidpfjhfgmgmgpghhpfad}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfjhfgmgmgpghhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}(((r2\_yellow\_0~X0~X2){\unicdcdcdhd}((r2\_yellow\_0~\\
X1~X3){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~(k3\_yellow\_3~\\
X0~X1))){\unicdbdjdcd}((r1\_lattice3~(k3\_yellow\_3~X0~X1)~(k6\_yellow\_3~X0~X1~X2~\\
X3)~X6){\unicdbdjdcd}(r1\_orders\_2~(k3\_yellow\_3~X0~X1)~X6~(k7\_yellow\_3~X0~X1~X4~\\
X5)))))){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_lattice3~\\
X0~X2~X6){\unicdbdjdcd}(r1\_orders\_2~X0~X6~X4))){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_lattice3~X1~X3~X6){\unicdbdjdcd}(r1\_orders\_2~X1~X6~X5))))))))))\end{array}$$
\end{theorem}
\end{document}
