\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{t36\_grcat\_1 (TMbnrS43GiTDJzKW2pf24gmd2ggxiuqdD3k)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k25\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_cat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k23\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u4\_struct\_0~(k25\_grcat\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~(k25\_grcat\_1~X0))){\unicdbdjdcd}((k4\_tarski~\\
X2~X1 \in k9\_xtuple\_0~(u1\_cat\_1~(k25\_grcat\_1~X0))){\unicdbdjded}(k3\_graph\_1~(\\
k25\_grcat\_1~X0)~X2=k4\_graph\_1~(k25\_grcat\_1~X0)~X1))))\end{array}
\label{hyp:ehddddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_grcat\_1~X1~X0){\unicdbdjded}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k18\_grcat\_1~X0))){\unicdbdjdcd}(k20\_grcat\_1~X0~X1=k8\_grcat\_1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdadpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k18\_grcat\_1~X0))){\unicdbdjdcd}(k19\_grcat\_1~X0~X1=k7\_grcat\_1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_cat\_1~X0~X1~X2~\\
X3~X4=g1\_cat\_1~X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=X7){\unicdcdcdhd}((X3=\\
X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(v3\_grcat\_1~\\
(k17\_grcat\_1~X0))\end{array}
\label{hyp:ggdgbdcdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k17\_grcat\_1~X0))\end{array}
\label{hyp:ggdgbdbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_graph\_1~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(u2\_graph\_1~X0)~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(u2\_graph\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_graph\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_graph\_1~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(u1\_graph\_1~X0)~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(u1\_graph\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_cat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_graph\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k25\_grcat\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k25\_grcat\_1~X0)){\unicdcdcdhd}((v1\_cat\_1~\\
(k25\_grcat\_1~X0)){\unicdcdcdhd}(l1\_cat\_1~(k25\_grcat\_1~X0)))))\end{array}
\label{hyp:egehpflgcdfdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k24\_grcat\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k24\_grcat\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k18\_grcat\_1~X0)~(k18\_grcat\_1~X0))~\\
(k18\_grcat\_1~X0)))))\end{array}
\label{hyp:egehpflgcdedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k23\_grcat\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k23\_grcat\_1~X0)~(k18\_grcat\_1~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k23\_grcat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k18\_grcat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflgcdddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k22\_grcat\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k22\_grcat\_1~X0)~(k18\_grcat\_1~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k22\_grcat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k18\_grcat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflgcdcdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k18\_grcat\_1~X0)){\unicdcdcdhd}(v4\_grcat\_1~(k18\_grcat\_1~X0)))\end{array}
\label{hyp:egehpflgbdidpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k4\_graph\_1~\\
X0~X1=k3\_funct\_2~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)~(u2\_graph\_1~\\
X0)~X1))\end{array}
\label{hyp:egedpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_graph\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k3\_graph\_1~\\
X0~X1=k3\_funct\_2~(u4\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_graph\_1~\\
X0)~X1))\end{array}
\label{hyp:egddpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}(k25\_grcat\_1~\\
X0=g1\_cat\_1~(k17\_grcat\_1~X0)~(k18\_grcat\_1~(k17\_grcat\_1~X0))~(\\
k22\_grcat\_1~(k17\_grcat\_1~X0))~(k23\_grcat\_1~(k17\_grcat\_1~X0))~\\
(k24\_grcat\_1~(k17\_grcat\_1~X0)))\end{array}
\label{hyp:egddadpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k18\_grcat\_1~X0)~(k18\_grcat\_1~X0))~(k18\_grcat\_1~X0))))){\unicdbdjdcd}\\
((X1=k24\_grcat\_1~X0){\unicdbdjded}(({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(k18\_grcat\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m3\_grcat\_1~X3~(k18\_grcat\_1~X0)){\unicdbdjdcd}((k4\_tarski~\\
X2~X3 \in k9\_xtuple\_0~X1){\unicdbdjded}(k19\_grcat\_1~X0~X2=k20\_grcat\_1~X0~X3)))){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(k18\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m3\_grcat\_1~\\
X3~(k18\_grcat\_1~X0)){\unicdbdjdcd}((k4\_tarski~X2~X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_binop\_1~\\
X1~X2~X3=k13\_grcat\_1~X2~X3)))))))\end{array}
\label{hyp:egcdjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k18\_grcat\_1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k18\_grcat\_1~X0)~X0))))){\unicdbdjdcd}((X1=k23\_grcat\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(k18\_grcat\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(k18\_grcat\_1~X0)~X0~X1~X2=k20\_grcat\_1~X0~X2))))\end{array}
\label{hyp:egcdidpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k18\_grcat\_1~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k18\_grcat\_1~X0)~X0))))){\unicdbdjdcd}((X1=k22\_grcat\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(k18\_grcat\_1~X0)){\unicdbdjdcd}(k3\_funct\_2~\\
(k18\_grcat\_1~X0)~X0~X1~X2=k19\_grcat\_1~X0~X2))))\end{array}
\label{hyp:egcdhdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}((k4\_tarski~\\
X2~X1 \in k9\_xtuple\_0~(u1\_cat\_1~X0)){\unicdbdjdcd}(k1\_cat\_1~X0~X1~X2=k1\_binop\_1~\\
(u1\_cat\_1~X0)~X2~X1))))\end{array}
\label{hyp:egbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_1~X0){\unicdbdjdcd}((v1\_cat\_1~X0){\unicdbdjdcd}(X0=g1\_cat\_1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u4\_struct\_0~(k25\_grcat\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~(k25\_grcat\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m3\_grcat\_1~X3~(k18\_grcat\_1~(k17\_grcat\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
m3\_grcat\_1~X4~(k18\_grcat\_1~(k17\_grcat\_1~X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=\\
X4)){\unicdbdjdcd}(((k3\_graph\_1~(k25\_grcat\_1~X0)~X2=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X1){\unicdbdjdcd}(k19\_grcat\_1~(k17\_grcat\_1~X0)~X4=k20\_grcat\_1~(k17\_grcat\_1~\\
X0)~X3)){\unicdcdcdhd}(((k19\_grcat\_1~(k17\_grcat\_1~X0)~X4=k20\_grcat\_1~(k17\_grcat\_1~\\
X0)~X3){\unicdbdjdcd}(k3\_graph\_1~(k25\_grcat\_1~X0)~X2=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X1)){\unicdcdcdhd}(((k3\_graph\_1~(k25\_grcat\_1~X0)~X2=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X1){\unicdbdjdcd}(k4\_tarski~X4~X3 \in k9\_xtuple\_0~(k24\_grcat\_1~(k17\_grcat\_1~\\
X0)))){\unicdcdcdhd}(((k4\_tarski~X4~X3 \in k9\_xtuple\_0~(k24\_grcat\_1~(k17\_grcat\_1~\\
X0))){\unicdbdjdcd}(k3\_graph\_1~(k25\_grcat\_1~X0)~X2=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X1)){\unicdcdcdhd}(((k3\_graph\_1~(k25\_grcat\_1~X0)~X2=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X1){\unicdbdjdcd}(k1\_cat\_1~(k25\_grcat\_1~X0)~X1~X2=k13\_grcat\_1~X4~X3)){\unicdcdcdhd}(\\
((k3\_graph\_1~(k25\_grcat\_1~X0)~X1=k3\_graph\_1~(k25\_grcat\_1~X0)~\\
X2){\unicdbdjdcd}(k19\_grcat\_1~(k17\_grcat\_1~X0)~X3=k19\_grcat\_1~(k17\_grcat\_1~\\
X0)~X4)){\unicdcdcdhd}(((k19\_grcat\_1~(k17\_grcat\_1~X0)~X3=k19\_grcat\_1~(k17\_grcat\_1~\\
X0)~X4){\unicdbdjdcd}(k3\_graph\_1~(k25\_grcat\_1~X0)~X1=k3\_graph\_1~(k25\_grcat\_1~\\
X0)~X2)){\unicdcdcdhd}(((k4\_graph\_1~(k25\_grcat\_1~X0)~X1=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X2){\unicdbdjdcd}(k20\_grcat\_1~(k17\_grcat\_1~X0)~X3=k20\_grcat\_1~(k17\_grcat\_1~\\
X0)~X4)){\unicdcdcdhd}((k20\_grcat\_1~(k17\_grcat\_1~X0)~X3=k20\_grcat\_1~(k17\_grcat\_1~\\
X0)~X4){\unicdbdjdcd}(k4\_graph\_1~(k25\_grcat\_1~X0)~X1=k4\_graph\_1~(k25\_grcat\_1~\\
X0)~X2)))))))))))))))\end{array}$$
\end{theorem}
\end{document}
