\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{t17\_yellow18 (TMKifEFDsy8FS8CXUG6TNiTJVJEpWyY9FaZ)}
\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 $ r2\_yellow18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v21\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_yellow18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_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 $ v15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v16\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v9\_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}((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}((r2\_yellow18~X0~X1){\unicdbdjdcd}(v21\_functor0~\\
(k2\_yellow18~X0~X1)~X0~X1)))\end{array}
\label{hyp:ehbdfdpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l1\_altcat\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(l1\_altcat\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v8\_functor0~X3~X0~X1){\unicdcdcdhd}(l2\_functor0~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (l2\_functor0~\\
X4~X1~X2){\unicdbdjdcd}(((v21\_functor0~X3~X0~X1){\unicdcdcdhd}(v21\_functor0~X4~X1~X2)){\unicdbdjdcd}(v21\_functor0~\\
(k13\_functor0~X0~X1~X2~X3~X4)~X0~X2))))))\end{array}
\label{hyp:ehbdcdpfggfhogdgehpgchbd}
\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}\\
((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}\\
((r2\_functor0~X0~X1){\unicdbdjdcd}(r2\_functor0~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchcdpfggfhogdgehpgchad}
\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}\\
((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}\\
((r1\_functor0~X0~X1){\unicdbdjdcd}(r1\_functor0~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\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}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}\\
(l2\_altcat\_1~X2))){\unicdcdcdhd}(((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~\\
X0~X1)){\unicdcdcdhd}((v16\_functor0~X4~X1~X2){\unicdcdcdhd}(m2\_functor0~X4~X1~X2)))))){\unicdbdjdcd}(\\
k3\_functor3~X0~X1~X2~X3~X4=k13\_functor0~X0~X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\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}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}\\
(l2\_altcat\_1~X2))){\unicdcdcdhd}(((v16\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~\\
X0~X1)){\unicdcdcdhd}((v16\_functor0~X4~X1~X2){\unicdcdcdhd}(m2\_functor0~X4~X1~X2)))))){\unicdbdjdcd}(\\
k2\_functor3~X0~X1~X2~X3~X4=k13\_functor0~X0~X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggfhogdgehpgchdd}
\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}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\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}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}\\
(l2\_altcat\_1~X2))){\unicdcdcdhd}(((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~\\
X0~X1)){\unicdcdcdhd}((v16\_functor0~X4~X1~X2){\unicdcdcdhd}(m2\_functor0~X4~X1~X2)))))){\unicdbdjdcd}(\\
(v9\_functor0~(k3\_functor3~X0~X1~X2~X3~X4)~X0~X2){\unicdcdcdhd}((v16\_functor0~\\
(k3\_functor3~X0~X1~X2~X3~X4)~X0~X2){\unicdcdcdhd}(m2\_functor0~(k3\_functor3~X0~\\
X1~X2~X3~X4)~X0~X2)))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpgchdd}
\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}((v11\_altcat\_1~X1){\unicdcdcdhd}((\\
v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))))){\unicdbdjdcd}((v9\_functor0~(k2\_yellow18~\\
X0~X1)~X0~X1){\unicdcdcdhd}((v16\_functor0~(k2\_yellow18~X0~X1)~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
(k2\_yellow18~X0~X1)~X0~X1)))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\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}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}\\
(l2\_altcat\_1~X2))){\unicdcdcdhd}(((v16\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~\\
X0~X1)){\unicdcdcdhd}((v16\_functor0~X4~X1~X2){\unicdcdcdhd}(m2\_functor0~X4~X1~X2)))))){\unicdbdjdcd}(\\
(v9\_functor0~(k2\_functor3~X0~X1~X2~X3~X4)~X0~X2){\unicdcdcdhd}((v15\_functor0~\\
(k2\_functor3~X0~X1~X2~X3~X4)~X0~X2){\unicdcdcdhd}(m2\_functor0~(k2\_functor3~X0~\\
X1~X2~X3~X4)~X0~X2)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpgchdd}
\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}((r2\_functor0~X0~\\
X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_functor0~X2~X0~X1){\unicdcdcdhd}((v21\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(v16\_functor0~X2~X0~X1)))))\end{array}
\label{hyp:egedadpfggfhogdgehpgchad}
\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}
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:ehbdhdpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\\
v2\_altcat\_1~X2){\unicdcdcdhd}((v11\_altcat\_1~X2){\unicdcdcdhd}((v12\_altcat\_1~X2){\unicdcdcdhd}(l2\_altcat\_1~\\
X2))))){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjdcd}((r1\_functor0~X0~X2){\unicdbdjded}(r2\_functor0~\\
X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
