\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{t29\_index\_1 (TMSLLXsXDnWd15gzBCseWadVxdYD2Q3kXBF)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m5\_index\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_graph\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_cat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_isocat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m4\_index\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ v3\_cat\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k15\_index\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ m3\_cat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_cat\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_index\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_subset\_1 : {{\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 $ m3\_index\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_cat\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m3\_cat\_2~X2~X1){\unicdbdjdcd}(m3\_cat\_2~X2~X0)))\end{array}
\label{hyp:ehedpfdgbgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m5\_index\_1~X1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~\\
X0)~(k7\_isocat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_index\_1~X2~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((\preoh v11\_struct\_0~X3){\unicdcdcdhd}((v2\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_1~\\
X3){\unicdcdcdhd}((v4\_cat\_1~X3){\unicdcdcdhd}((v5\_cat\_1~X3){\unicdcdcdhd}((v6\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_5~\\
X3){\unicdcdcdhd}(l1\_cat\_1~X3))))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_cat\_1~X4~X2~X3){\unicdbdjdcd}(m4\_index\_1~\\
(k4\_cat\_5~X2~X3~X4)~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~\\
X0)~(u2\_graph\_1~X0)~(k15\_index\_1~X0~X1~X2~X3~X4))))))\end{array}
\label{hyp:ehcdidpfjgogegfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m5\_index\_1~X1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~\\
X0)~(k7\_isocat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_1~X2){\unicdcdcdhd}((v4\_cat\_1~X2){\unicdcdcdhd}((v5\_cat\_1~\\
X2){\unicdcdcdhd}((v6\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_5~X2){\unicdcdcdhd}(l1\_cat\_1~X2))))))))){\unicdbdjdcd}((\\
m3\_cat\_2~(k10\_index\_1~X0~X1)~X2){\unicdbdjded}(m4\_index\_1~X2~(u1\_struct\_0~X0)~\\
(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~X1))))\end{array}
\label{hyp:ehbdedpfjgogegfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l5\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u4\_struct\_0~X0))\end{array}
\label{hyp:ggdgbdedpfdhehchfhdgehpfad}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_1~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_cat\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(u1\_cat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u4\_struct\_0~\\
X0)~(u4\_struct\_0~X0))~(u4\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(((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)))){\unicdcdcdhd}((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m5\_index\_1~X6~X0~X1~X2~X3~X4~X5){\unicdbdjdcd}(m3\_index\_1~\\
X6~X0~X1~X2~X3))\end{array}
\label{hyp:egehpfngfdpfjgogegfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(((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}(m3\_index\_1~X4~X0~X1~X2~X3))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m4\_index\_1~X5~X0~X1~X2~X3~X4){\unicdbdjdcd}((\preoh v2\_struct\_0~X5){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X5){\unicdcdcdhd}((v2\_cat\_1~X5){\unicdcdcdhd}((v3\_cat\_1~X5){\unicdcdcdhd}((v4\_cat\_1~X5){\unicdcdcdhd}((v5\_cat\_1~\\
X5){\unicdcdcdhd}((v6\_cat\_1~X5){\unicdcdcdhd}((v3\_cat\_5~X5){\unicdcdcdhd}(l1\_cat\_1~X5))))))))))\end{array}
\label{hyp:egehpfngedpfjgogegfgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_graph\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfhgchbgahigpfbd}
\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 v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}((v1\_funct\_1~(k7\_isocat\_1~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(k7\_isocat\_1~X0)~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k7\_isocat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflghdpfjgdhpgdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_cat\_1~X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~\\
X0){\unicdcdcdhd}((v6\_cat\_1~X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_cat\_1~X1){\unicdcdcdhd}((v3\_cat\_1~X1){\unicdcdcdhd}((v4\_cat\_1~\\
X1){\unicdcdcdhd}((v5\_cat\_1~X1){\unicdcdcdhd}((v6\_cat\_1~X1){\unicdcdcdhd}(l1\_cat\_1~X1)))))))){\unicdcdcdhd}(m2\_cat\_1~\\
X2~X0~X1))){\unicdbdjdcd}((v1\_cat\_1~(k4\_cat\_5~X0~X1~X2)){\unicdcdcdhd}(m3\_cat\_2~(k4\_cat\_5~\\
X0~X1~X2)~X1))\end{array}
\label{hyp:egehpflgedpfdgbgehpffd}
\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}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~\\
X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdcdcdhd}((m5\_index\_1~\\
X1~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~\\
X0)~(u1\_cat\_1~X0)~(k7\_isocat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X2){\unicdcdcdhd}((v2\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_1~X2){\unicdcdcdhd}((v4\_cat\_1~X2){\unicdcdcdhd}((v5\_cat\_1~\\
X2){\unicdcdcdhd}((v6\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_5~X2){\unicdcdcdhd}(l1\_cat\_1~X2))))))))){\unicdcdcdhd}((\\
(\preoh v2\_struct\_0~X3){\unicdcdcdhd}((\preoh v11\_struct\_0~X3){\unicdcdcdhd}((v2\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_1~\\
X3){\unicdcdcdhd}((v4\_cat\_1~X3){\unicdcdcdhd}((v5\_cat\_1~X3){\unicdcdcdhd}((v6\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_5~\\
X3){\unicdcdcdhd}(l1\_cat\_1~X3))))))))){\unicdcdcdhd}(m2\_cat\_1~X4~X2~X3))))){\unicdbdjdcd}(m5\_index\_1~\\
(k15\_index\_1~X0~X1~X2~X3~X4)~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~\\
X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~X0)~(k7\_isocat\_1~X0))\end{array}
\label{hyp:egehpflgbdfdpfjgogegfgihpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfjgogegfgihpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m5\_index\_1~X1~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~(u1\_cat\_1~\\
X0)~(k7\_isocat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_index\_1~X2~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~X0)~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((\preoh v11\_struct\_0~X3){\unicdcdcdhd}((v2\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_1~\\
X3){\unicdcdcdhd}((v4\_cat\_1~X3){\unicdcdcdhd}((v5\_cat\_1~X3){\unicdcdcdhd}((v6\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_5~\\
X3){\unicdcdcdhd}(l1\_cat\_1~X3))))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_cat\_1~X4~X2~X3){\unicdbdjdcd}(m4\_index\_1~\\
X3~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_graph\_1~X0)~(u2\_graph\_1~\\
X0)~(k15\_index\_1~X0~X1~X2~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
