\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{t30\_yellow20 (TMHnnxz8cWAXc2VdpzsNp2xJu33djYhKjVb)}
\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 $ v3\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v16\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_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 $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_yellow20 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v10\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v11\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k13\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k10\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v14\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v12\_functor0 : {{\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}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(l2\_altcat\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v8\_functor0~X3~X0~X1){\unicdcdcdhd}((v10\_functor0~X3~X0~X1){\unicdcdcdhd}(l2\_functor0~\\
X3~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v8\_functor0~X4~X1~X2){\unicdcdcdhd}((v11\_functor0~\\
X4~X1~X2){\unicdcdcdhd}(l2\_functor0~X4~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k1\_altcat\_1~X0~X5~X6)){\unicdbdjdcd}((k1\_altcat\_1~\\
X0~X5~X6{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}(k8\_functor0~X0~X2~(k13\_functor0~X0~X1~X2~\\
X3~X4)~X5~X6~X7=k8\_functor0~X1~X2~X4~(k3\_functor0~X0~X1~X3~X5)~(k3\_functor0~\\
X0~X1~X3~X6)~(k6\_functor0~X0~X1~X3~X5~X6~X7))))))))))\end{array}
\label{hyp:ehidpfggfhogdgehpgchdd}
\end{equation}
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}((v3\_altcat\_2~X1~X0){\unicdcdcdhd}(m1\_altcat\_2~\\
X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}((k1\_altcat\_1~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_altcat\_1~X1~X2~X3)){\unicdbdjdcd}(k6\_functor0~\\
X1~X0~(k10\_functor0~X0~X1)~X2~X3~X4=X4))))))\end{array}
\label{hyp:ehcdhdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(k3\_functor0~X1~X0~(k10\_functor0~X0~X1)~X2=\\
X2)))\end{array}
\label{hyp:ehcdhdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\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))))){\unicdcdcdhd}(((\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))))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_altcat\_1~X2){\unicdcdcdhd}((v3\_altcat\_2~X2~X0){\unicdcdcdhd}\\
(m1\_altcat\_2~X2~X0)))){\unicdcdcdhd}((v16\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
X3~X0~X1))))){\unicdbdjdcd}(k5\_yellow20~X0~X1~X2~X3=k14\_functor0~X0~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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))))){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v3\_altcat\_2~X1~X0){\unicdcdcdhd}(\\
m1\_altcat\_2~X1~X0))))){\unicdbdjdcd}((v9\_functor0~(k10\_functor0~X0~X1)~X1~X0){\unicdcdcdhd}\\
(v10\_functor0~(k10\_functor0~X0~X1)~X1~X0))\end{array}
\label{hyp:ggdgddpfjhfgmgmgpghhcdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0))){\unicdbdjdcd}((v8\_functor0~(k10\_functor0~\\
X0~X1)~X1~X0){\unicdcdcdhd}(v9\_functor0~(k10\_functor0~X0~X1)~X1~X0))\end{array}
\label{hyp:ggdgbdcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}(l2\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}\\
(l2\_altcat\_1~X1))\end{array}
\label{hyp:egehpfngbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l2\_altcat\_1~X0){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}\\
((v9\_functor0~(k10\_functor0~X0~X1)~X1~X0){\unicdcdcdhd}(l2\_functor0~(k10\_functor0~\\
X0~X1)~X1~X0))\end{array}
\label{hyp:egehpflgbdadpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_altcat\_2~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}(m1\_altcat\_2~X2~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  (l2\_functor0~X3~X0~X1){\unicdbdjdcd}(k14\_functor0~X0~X1~X2~X3=k13\_functor0~\\
X2~X0~X1~(k10\_functor0~X0~X2)~X3))))\end{array}
\label{hyp:egddhdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}((v16\_functor0~X2~X0~X1){\unicdbdjdcd}((v11\_functor0~X2~X0~X1){\unicdcdcdhd}(v14\_functor0~\\
X2~X0~X1))))\end{array}
\label{hyp:dgdgedpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v12\_altcat\_1~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_altcat\_2~X0)))\end{array}
\label{hyp:dgdgcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}((v8\_functor0~X2~X0~X1){\unicdcdcdhd}(v12\_functor0~X2~X0~X1)))\end{array}
\label{hyp:dgdgbdpfggfhogdgehpgchcd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfjhfgmgmgpghhcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\\
v2\_altcat\_1~X2){\unicdcdcdhd}((v3\_altcat\_2~X2~X0){\unicdcdcdhd}(m1\_altcat\_2~X2~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v16\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X2)){\unicdbdjdcd}(((X6=X4){\unicdcdcdhd}\\
(X7=X5)){\unicdbdjdcd}((k1\_altcat\_1~X2~X6~X7=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(k1\_altcat\_1~X0~X4~X5)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k1\_altcat\_1~\\
X2~X6~X7)){\unicdbdjdcd}((X9=X8){\unicdbdjdcd}(k8\_functor0~X2~X1~(k5\_yellow20~X0~X1~X2~X3)~\\
X6~X7~X9=k8\_functor0~X0~X1~X3~X4~X5~X8)))))))))))))\end{array}$$
\end{theorem}
\end{document}
