\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{t22\_yellow18 (TMQMVeMxhFbzSddgLpExwD6h3WDhCaFmM4p)}
\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 $ 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 $ v1\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k8\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~\\
X1))){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjded}((u1\_struct\_0~X1=u1\_struct\_0~X0){\unicdcdcdhd}\\
({\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~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(((X5=X2){\unicdcdcdhd}((X6=X3){\unicdcdcdhd}(X7=X4))){\unicdbdjdcd}((k1\_altcat\_1~\\
X0~X2~X3=k1\_altcat\_1~X1~X6~X5){\unicdcdcdhd}(\preoh (k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((k1\_altcat\_1~X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~(k1\_altcat\_1~X0~X2~X3)){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(k1\_altcat\_1~\\
X0~X3~X4)){\unicdcdcdhd}({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~(k1\_altcat\_1~X1~X6~X5)){\unicdcdcdhd}\\
({\unicdcdaddd} X11 .  (m1\_subset\_1~X11~(k1\_altcat\_1~X1~X7~X6)){\unicdcdcdhd}((X10=X8){\unicdcdcdhd}\\
((X11=X9){\unicdcdcdhd}(k5\_altcat\_1~X1~X7~X6~X5~X11~X10{\unicdcdgdad}k5\_altcat\_1~X0~X2~X3~X4~\\
X8~X9))))))))))))))))))))\end{array}
\label{hyp:ehjdpfjhfgmgmgpghhbdid}
\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}(l2\_altcat\_1~X1)){\unicdbdjdcd}((r2\_yellow18~X0~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}(((X4=X2){\unicdcdcdhd}\\
(X5=X3)){\unicdbdjdcd}(k1\_altcat\_1~X0~X2~X3=k1\_altcat\_1~X1~X5~X4))))))))\end{array}
\label{hyp:ehhdpfjhfgmgmgpghhbdid}
\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 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~X0~X2~\\
X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_altcat\_1~X0~\\
X1~X2)){\unicdcdcdhd}((v1\_altcat\_3~X3~X0~X1~X2){\unicdcdcdhd}((v2\_altcat\_3~X3~X0~X1~X2){\unicdcdcdhd}(\preoh \\
(k5\_altcat\_1~X0~X1~X2~X1~X3~(k1\_altcat\_3~X0~X1~X2~X3)=k8\_altcat\_1~\\
X0~X1){\unicdcdcdhd}(k5\_altcat\_1~X0~X2~X1~X2~(k1\_altcat\_3~X0~X1~X2~X3)~X3=k8\_altcat\_1~\\
X0~X2)))))))))\end{array}
\label{hyp:ehcdpfbgmgehdgbgehpfdd}
\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}((r2\_yellow18~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k8\_altcat\_1~X0~X2=k8\_altcat\_1~X1~\\
X3))))))\end{array}
\label{hyp:ehbdadpfjhfgmgmgpghhbdid}
\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}((r2\_yellow18~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~\\
X0~X3~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((X4=X2){\unicdcdcdhd}\\
((X5=X3){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(k1\_altcat\_1~X0~X2~X3)){\unicdcdcdhd}\\
({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(k1\_altcat\_1~X1~X5~X4)){\unicdcdcdhd}((X7=X6){\unicdcdcdhd}\\
(\preoh ((v1\_altcat\_3~X6~X0~X2~X3){\unicdbdjdcd}(v2\_altcat\_3~X7~X1~X5~X4)){\unicdcdcdhd}((v2\_altcat\_3~\\
X6~X0~X2~X3){\unicdbdjdcd}(v1\_altcat\_3~X7~X1~X5~X4))))))))))))))))\end{array}
\label{hyp:mgcdfdpfjhfgmgmgpghhbdid}
\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}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_altcat\_1~X0~X1~X2))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_altcat\_3~X0~X1~X2~X3)~(k1\_altcat\_1~X0~X2~X1))\end{array}
\label{hyp:egehpflgbdpfbgmgehdgbgehpfdd}
\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 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~X0~X2~\\
X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_altcat\_1~X0~\\
X1~X2)){\unicdcdcdhd}((v1\_altcat\_3~X3~X0~X1~X2){\unicdcdcdhd}((v2\_altcat\_3~X3~X0~X1~X2){\unicdcdcdhd}(\preoh \\
{\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_altcat\_1~X0~X2~X1)){\unicdbdjdcd}((X4=k1\_altcat\_3~\\
X0~X1~X2~X3){\unicdbdjded}((r1\_altcat\_3~X0~X2~X1~X4~X3){\unicdcdcdhd}(r1\_altcat\_3~X0~X1~X2~X3~\\
X4)))))))))))\end{array}
\label{hyp:egedpfbgmgehdgbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_altcat\_1~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_altcat\_1~\\
X0~X2~X1)){\unicdbdjdcd}((r1\_altcat\_3~X0~X1~X2~X3~X4){\unicdbdjded}(k5\_altcat\_1~X0~X2~X1~X2~X4~\\
X3=k8\_altcat\_1~X0~X2))))))\end{array}
\label{hyp:egbdpfbgmgehdgbgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}((r2\_yellow18~X0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~\\
X0~X3~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((X4=X2){\unicdcdcdhd}\\
((X5=X3){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(k1\_altcat\_1~X0~X2~X3)){\unicdcdcdhd}\\
({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(k1\_altcat\_1~X1~X5~X4)){\unicdcdcdhd}((X7=X6){\unicdcdcdhd}\\
((v1\_altcat\_3~X6~X0~X2~X3){\unicdcdcdhd}((v2\_altcat\_3~X6~X0~X2~X3){\unicdcdcdhd}(k1\_altcat\_3~\\
X1~X5~X4~X7{\unicdcdgdad}k1\_altcat\_3~X0~X2~X3~X6))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
