\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{t43\_cat\_4 (TMdmsFusARKZEZKxf7zzxypMFUzhDCFX9qC)}
\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 $ v3\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_4 : {{\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 $ m1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k18\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k9\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_cat\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~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~(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~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_cat\_1~X6~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_cat\_1~X7~X0~X3~X4){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_cat\_1~X8~X0~X5~X1){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(m1\_cat\_1~X9~X0~X5~X3){\unicdbdjdcd}(\preoh (k2\_cat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~\\
X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~X0~X5~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~\\
X0~X5~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k5\_cat\_1~X0~X5~(k2\_cat\_4~X0~X1~X3)~(k2\_cat\_4~\\
X0~X2~X4)~(k9\_cat\_4~X0~X1~X3~X5~X8~X9)~(k18\_cat\_4~X0~X1~X2~X3~X4~X6~X7){\unicdcdgdad}\\
k9\_cat\_4~X0~X2~X4~X5~(k5\_cat\_1~X0~X5~X1~X2~X8~X6)~(k5\_cat\_1~X0~X5~X3~X4~\\
X9~X7)))))))))))))))\end{array}
\label{hyp:ehedbdpfdgbgehpfed}
\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 .  (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~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_cat\_1~X6~X0~X2~X3){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_cat\_1~X7~X0~X3~X4){\unicdbdjdcd}(\preoh (k2\_cat\_1~\\
X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~\\
X0~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k5\_cat\_1~X0~X1~X2~X4~X5~(k5\_cat\_1~X0~X2~X3~X4~\\
X6~X7){\unicdcdgdad}k5\_cat\_1~X0~X1~X3~X4~(k5\_cat\_1~X0~X1~X2~X3~X5~X6)~X7)))))))))))\end{array}
\label{hyp:ehcdfdpfdgbgehpfbd}
\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 .  (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~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k2\_cat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((k2\_cat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k2\_cat\_1~X0~X1~X3=k1\_xboole\_0))))))\end{array}
\label{hyp:ehcdedpfdgbgehpfbd}
\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}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k2\_cat\_1~X0~(k2\_cat\_4~X0~X1~X2)~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k2\_cat\_1~\\
X0~(k2\_cat\_4~X0~X1~X2)~X2{\unicdcdgdad}k1\_xboole\_0))))\end{array}
\label{hyp:ehbdjdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_cat\_4}~{X0}})}{\unicdbdjdcd}{({{l1\_cat\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgbgehpfed}
\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}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdcdcdhd}((\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_cat\_1~(k8\_cat\_4~X0~X1~X2)~X0~(k2\_cat\_4~X0~X1~X2)~X2)\end{array}
\label{hyp:egehpflgidpfdgbgehpfed}
\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}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdcdcdhd}((\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_cat\_1~(k7\_cat\_4~X0~X1~X2)~X0~(k2\_cat\_4~X0~X1~X2)~X1)\end{array}
\label{hyp:egehpflghdpfdgbgehpfed}
\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}((\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}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((m1\_cat\_1~\\
X4~X0~X1~X2){\unicdcdcdhd}(m1\_cat\_1~X5~X0~X2~X3)))))){\unicdbdjdcd}(m1\_cat\_1~(k5\_cat\_1~X0~X1~\\
X2~X3~X4~X5)~X0~X1~X3)\end{array}
\label{hyp:egehpflgfdpfdgbgehpfbd}
\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}(l1\_cat\_4~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_cat\_4~X0~X1~X2)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdgbgehpfed}
\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}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~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~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~\\
X1~X2){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_cat\_1~X6~X0~X3~X4){\unicdbdjdcd}(k18\_cat\_4~X0~X1~X2~X3~X4~\\
X5~X6=k9\_cat\_4~X0~X2~X4~(k2\_cat\_4~X0~X1~X3)~(k5\_cat\_1~X0~(k2\_cat\_4~\\
X0~X1~X3)~X1~X2~(k7\_cat\_4~X0~X1~X3)~X5)~(k5\_cat\_1~X0~(k2\_cat\_4~X0~X1~X3)~\\
X3~X4~(k8\_cat\_4~X0~X1~X3)~X6))))))))\end{array}
\label{hyp:egbdjdpfdgbgehpfed}
\end{equation}
\begin{theorem}\label{thm:ehedddpfdgbgehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_4~X0){\unicdcdcdhd}(l1\_cat\_4~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_cat\_1~X7~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_cat\_1~X8~X0~X3~\\
X4){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_cat\_1~X9~X0~X5~X1){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_cat\_1~\\
X10~X0~X6~X3){\unicdbdjdcd}(\preoh (k2\_cat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~X0~X3~\\
X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~X0~X5~X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k2\_cat\_1~\\
X0~X6~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k5\_cat\_1~X0~(k2\_cat\_4~X0~X5~X6)~(k2\_cat\_4~\\
X0~X1~X3)~(k2\_cat\_4~X0~X2~X4)~(k18\_cat\_4~X0~X5~X1~X6~X3~X9~X10)~(k18\_cat\_4~\\
X0~X1~X2~X3~X4~X7~X8){\unicdcdgdad}k18\_cat\_4~X0~X5~X2~X6~X4~(k5\_cat\_1~X0~X5~X1~X2~X9~X7)~\\
(k5\_cat\_1~X0~X6~X3~X4~X10~X8))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
