\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{t37\_yellow20 (TMJZuc7YAkpKSMuY6aUHXmKFus1ehM95Xv1)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_yellow20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v21\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_functor0 : {{\iota}{\unicdbdjdcd}{{\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}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (l2\_functor0~X2~X0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v2\_altcat\_1~X3){\unicdcdcdhd}((v11\_altcat\_1~\\
X3){\unicdcdcdhd}((v12\_altcat\_1~X3){\unicdcdcdhd}(l2\_altcat\_1~X3))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\\
\preoh v2\_struct\_0~X4){\unicdcdcdhd}((v2\_altcat\_1~X4){\unicdcdcdhd}((v11\_altcat\_1~X4){\unicdcdcdhd}((v12\_altcat\_1~\\
X4){\unicdcdcdhd}(l2\_altcat\_1~X4))))){\unicdbdjdcd}((r2\_yellow20~X0~X1~X2~X3~X4){\unicdbdjded}(((v2\_altcat\_1~\\
X3){\unicdcdcdhd}((v3\_altcat\_2~X3~X0){\unicdcdcdhd}(m1\_altcat\_2~X3~X0))){\unicdcdcdhd}(((v2\_altcat\_1~\\
X4){\unicdcdcdhd}((v3\_altcat\_2~X4~X1){\unicdcdcdhd}(m1\_altcat\_2~X4~X1))){\unicdcdcdhd}({\unicdcdaddd} X5 .  (\\
(v15\_functor0~X5~X3~X4){\unicdcdcdhd}(m2\_functor0~X5~X3~X4)){\unicdcdcdhd}((v21\_functor0~\\
X5~X3~X4){\unicdcdcdhd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}((X6=X7){\unicdbdjdcd}(k3\_functor0~X3~X4~\\
X5~X6=k3\_functor0~X0~X1~X2~X7)))){\unicdcdcdhd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(\\
u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X3)){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X6=X8){\unicdcdcdhd}(X7=X9)){\unicdbdjdcd}((k1\_altcat\_1~X3~X6~\\
X7=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(k1\_altcat\_1~\\
X3~X6~X7)){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~X11~(k1\_altcat\_1~X0~X8~X9)){\unicdbdjdcd}\\
((X10=X11){\unicdbdjdcd}(k6\_functor0~X3~X4~X5~X6~X7~X10=k1\_funct\_1~(k4\_functor0~\\
X0~X1~X2~X8~X9)~X11))))))))))))))))))))\end{array}
\label{hyp:egedpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}((r1\_functor0~X0~\\
X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_functor0~X2~X0~X1){\unicdcdcdhd}((v21\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(v15\_functor0~X2~X0~X1)))))\end{array}
\label{hyp:egddjdpfggfhogdgehpgchad}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfjhfgmgmgpghhcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\\
v2\_altcat\_1~X2){\unicdcdcdhd}((v11\_altcat\_1~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}(l2\_altcat\_1~\\
X2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((v2\_altcat\_1~X3){\unicdcdcdhd}(\\
(v11\_altcat\_1~X3){\unicdcdcdhd}((v12\_altcat\_1~X3){\unicdcdcdhd}(l2\_altcat\_1~X3))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (l2\_functor0~X4~X0~X1){\unicdbdjdcd}((r2\_yellow20~X0~X1~X4~X2~X3){\unicdbdjdcd}\\
(r1\_functor0~X2~X3))))))\end{array}$$
\end{theorem}
\end{document}
