\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{t3\_yellow20 (TMUHNgiL39srxo9FB23H53WPdKnVGCc4X9w)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_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 $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v11\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_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 $ 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 $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k13\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k11\_functor0 : {{\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 $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_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}((v11\_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}(k6\_functor0~X0~X2~(k13\_functor0~X0~X1~X2~\\
X3~X4)~X5~X6~X7=k8\_functor0~X1~X2~X4~(k3\_functor0~X0~X1~X3~X6)~(k3\_functor0~\\
X0~X1~X3~X5)~(k8\_functor0~X0~X1~X3~X5~X6~X7))))))))))\end{array}
\label{hyp:ehhdpfggfhogdgehpgchdd}
\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 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v8\_functor0~X3~X0~X0){\unicdcdcdhd}((v10\_functor0~X3~X0~X0){\unicdcdcdhd}(l2\_functor0~\\
X3~X0~X0))){\unicdbdjdcd}((X3=k11\_functor0~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k1\_altcat\_1~X0~X1~X2)){\unicdbdjdcd}(k6\_functor0~X0~X0~X3~X1~X2~X4=X4)))))))\end{array}
\label{hyp:ehddbdpfggfhogdgehpgchad}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}(k12\_functor0~X0=k11\_functor0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}((v8\_functor0~\\
(k11\_functor0~X0)~X0~X0){\unicdcdcdhd}((v9\_functor0~(k11\_functor0~X0)~X0~X0){\unicdcdcdhd}\\
(v10\_functor0~(k11\_functor0~X0)~X0~X0)))\end{array}
\label{hyp:ggdgbdddpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (l2\_functor0~X2~X0~X1){\unicdbdjdcd}(l1\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfmgcdpfggfhogdgehpgchad}
\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 .  {\unicdcdadad} X5 .  \\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_altcat\_1~X1)){\unicdcdcdhd}(((v11\_functor0~X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~\\
X1)){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_altcat\_1~X0~X3~X4))))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k8\_functor0~X0~X1~X2~X3~X4~X5)~(k1\_altcat\_1~X1~(k3\_functor0~X0~X1~\\
X2~X4)~(k3\_functor0~X0~X1~X2~X3)))\end{array}
\label{hyp:egehpflgidpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}\\
((l1\_functor0~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k3\_functor0~X0~X1~X2~X3)~(u1\_struct\_0~X1))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpgchad}
\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 .  (l1\_altcat\_1~X0){\unicdbdjdcd}((v9\_functor0~(k11\_functor0~X0)~\\
X0~X0){\unicdcdcdhd}(l2\_functor0~(k11\_functor0~X0)~X0~X0))\end{array}
\label{hyp:egehpflgbdbdpfggfhogdgehpgchad}
\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}(l1\_altcat\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v11\_functor0~\\
X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1)){\unicdbdjdcd}((v8\_functor0~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k1\_altcat\_1~\\
X1~(k3\_functor0~X0~X1~X2~X4)~(k3\_functor0~X0~X1~X2~X3)=k1\_xboole\_0)))))))\end{array}
\label{hyp:egbdjdpfggfhogdgehpgchad}
\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:ehddpfjhfgmgmgpghhcdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v8\_functor0~\\
X2~X0~X1){\unicdcdcdhd}((v11\_functor0~X2~X0~X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v8\_functor0~X3~X1~X0){\unicdcdcdhd}((v11\_functor0~X3~X1~X0){\unicdcdcdhd}(l2\_functor0~\\
X3~X1~X0))){\unicdbdjdcd}(((v21\_functor0~X2~X0~X1){\unicdcdcdhd}(X3=k15\_functor0~X0~X1~X2)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X4~X5{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k1\_altcat\_1~X0~X4~X5)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(k1\_altcat\_1~X1~(k3\_functor0~X0~X1~X2~X5)~(k3\_functor0~X0~X1~X2~\\
X4))){\unicdbdjdcd}((k8\_functor0~X0~X1~X2~X4~X5~X6=X7){\unicdbdjded}(k8\_functor0~X1~X0~X3~(\\
k3\_functor0~X0~X1~X2~X5)~(k3\_functor0~X0~X1~X2~X4)~X7=X6)))))))))))\end{array}$$
\end{theorem}
\end{document}
