\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{t5\_yellow18 (TMXhiQkwPbKv2hPy8inCY1ZDx3PCwvfdaek)}
\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 $ r1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_yellow18 : {{\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 $ k15\_functor0 : {{\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 $ 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 $ k12\_functor0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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}((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}({\unicdcdadad} X2 .  ((v15\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}(\preoh (v21\_functor0~X2~X0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m2\_functor0~X3~X1~X0){\unicdbdjdcd}(\preoh (X3=k15\_functor0~X0~X1~X2){\unicdcdcdhd}((v21\_functor0~\\
X3~X1~X0){\unicdcdcdhd}(v15\_functor0~X3~X1~X0)))))))\end{array}
\label{hyp:ehedidpfggfhogdgehpgchad}
\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}((v1\_altcat\_2~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}((v1\_altcat\_2~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}((v21\_functor0~X2~X0~X1){\unicdbdjdcd}(k13\_functor0~\\
X0~X1~X0~X2~(k15\_functor0~X0~X1~X2)=k12\_functor0~X0))))\end{array}
\label{hyp:ehbdjdpfggfhogdgehpgchbd}
\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}((v1\_altcat\_2~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}((v1\_altcat\_2~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}((v21\_functor0~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
(v8\_functor0~X3~X1~X0){\unicdcdcdhd}(l2\_functor0~X3~X1~X0)){\unicdbdjdcd}((g2\_functor0~X1~\\
X0~(u1\_functor0~X1~X0~X3)~(u2\_functor0~X1~X0~X3)=k15\_functor0~X0~\\
X1~X2){\unicdbdjdcd}(k13\_functor0~X1~X0~X1~X3~X2=k12\_functor0~X1))))))\end{array}
\label{hyp:ehbdidpfggfhogdgehpgchbd}
\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}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}(r1\_functor3~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfggfhogdgehpgchdd}
\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}((v15\_functor0~X4~X1~X2){\unicdcdcdhd}(m2\_functor0~X4~X1~X2)))))){\unicdbdjdcd}(\\
k1\_functor3~X0~X1~X2~X3~X4=k13\_functor0~X0~X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfggfhogdgehpgchdd}
\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 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}(l2\_functor0~X2~\\
X0~X1))){\unicdbdjdcd}((v9\_functor0~(k15\_functor0~X0~X1~X2)~X1~X0){\unicdcdcdhd}(l2\_functor0~\\
(k15\_functor0~X0~X1~X2)~X1~X0))\end{array}
\label{hyp:egehpflgbdfdpfggfhogdgehpgchad}
\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}((v9\_functor0~(k12\_functor0~X0)~X0~X0){\unicdcdcdhd}\\
((v15\_functor0~(k12\_functor0~X0)~X0~X0){\unicdcdcdhd}(m2\_functor0~(k12\_functor0~\\
X0)~X0~X0)))\end{array}
\label{hyp:egehpflgbdcdpfggfhogdgehpgchad}
\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 .  ((\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}((r1\_yellow18~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (\\
(v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((\\
v15\_functor0~X3~X1~X0){\unicdcdcdhd}(m2\_functor0~X3~X1~X0)){\unicdcdcdhd}((r1\_functor3~X0~\\
X0~(k1\_functor3~X0~X1~X0~X2~X3)~(k12\_functor0~X0)){\unicdcdcdhd}(r1\_functor3~\\
X1~X1~(k1\_functor3~X1~X0~X1~X3~X2)~(k12\_functor0~X1)))))))\end{array}
\label{hyp:egcdpfjhfgmgmgpghhbdid}
\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}
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:dgdgbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}((l1\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1))){\unicdbdjdcd}((v9\_functor0~X2~X0~X1){\unicdbdjdcd}(X2=g2\_functor0~\\
X0~X1~(u1\_functor0~X0~X1~X2)~(u2\_functor0~X0~X1~X2)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghjdpfggfhogdgehpgchad}
\end{equation}
\begin{theorem}\label{thm:ehfdpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}((r1\_functor0~X0~X1){\unicdbdjdcd}(r1\_yellow18~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
