\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{t10\_cat\_4 (TMLVtU1JnHH7HBNF4cE4CExBjjXohmpMuPm)}
\maketitle
Let $ v3\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_cat\_4 : {{\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 $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_cat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v10\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_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 $ v2\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u4\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_cat\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~(\\
k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u4\_struct\_0~(k5\_cat\_4~\\
X0~X1))){\unicdbdjdcd}(r2\_cat\_3~(k5\_cat\_4~X0~X1)~X2~X3~X4)))\end{array}
\label{hyp:ehjdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}(v10\_cat\_1~X2~(k5\_cat\_4~X0~X1))\end{array}
\label{hyp:ehidpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k5\_cat\_4~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k5\_cat\_4~X0~X1))){\unicdbdjdcd}(X2=X3))\end{array}
\label{hyp:ehddpfdgbgehpfed}
\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 .  {\unicdcdadad} X1 .  (\preoh v2\_struct\_0~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((v2\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((v3\_cat\_1~(k5\_cat\_4~\\
X0~X1)){\unicdcdcdhd}((v4\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}((v5\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}\\
((v6\_cat\_1~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}(v2\_cat\_4~(k5\_cat\_4~X0~X1))))))))\end{array}
\label{hyp:ggdgcdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_4~X0){\unicdbdjdcd}((v1\_funct\_1~(u4\_cat\_4~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(u4\_cat\_4~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(u4\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u4\_cat\_4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u4\_struct\_0~\\
X0))))))\end{array}
\label{hyp:egehpffhedpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_4~X0){\unicdbdjdcd}((v1\_funct\_1~(u3\_cat\_4~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(u3\_cat\_4~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(u4\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u3\_cat\_4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u4\_struct\_0~\\
X0))))))\end{array}
\label{hyp:egehpffhddpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_cat\_4~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_cat\_4~X0)){\unicdcdcdhd}((v1\_funct\_2~\\
(u2\_cat\_4~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u2\_cat\_4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0))))))\end{array}
\label{hyp:egehpffhcdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_cat\_4}~{X0}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{({{u1\_cat\_4}~{X0}})}}~{({{u1\_struct\_0}~{X0}})}})}}}\label{hyp:egehpffhbdpfdgbgehpfed}
\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\_4}~{X0}})}{\unicdbdjdcd}{({{l1\_cat\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgbgehpfed}
\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 .  {\unicdcdadad} X1 .  (v2\_cat\_4~(k5\_cat\_4~X0~X1)){\unicdcdcdhd}(l1\_cat\_4~(\\
k5\_cat\_4~X0~X1))\end{array}
\label{hyp:egehpflgfdpfdgbgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(m1\_subset\_1~(k5\_binop\_1~X0~X1~X2~X3)~X0)\end{array}
\label{hyp:egehpflgfdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_graph\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_graph\_1~X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgedpfhgchbgahigpfbd}
\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~X3){\unicdcdcdhd}((\\
v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X1)~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~X2))))){\unicdcdcdhd}((m1\_subset\_1~X4~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X5~X1))))){\unicdbdjdcd}(m1\_subset\_1~(k2\_binop\_1~X0~X1~X2~X3~X4~\\
X5)~X2)\end{array}
\label{hyp:egehpflgcdpfcgjgogpgahpfbd}
\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\_4~X0)))))))){\unicdbdjdcd}((v3\_cat\_4~X0){\unicdbdjded}((v10\_cat\_1~(u1\_cat\_4~\\
X0)~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k4\_graph\_1~X0~(k2\_binop\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u3\_cat\_4~X0)~\\
X1~X2)=X1){\unicdcdcdhd}((k4\_graph\_1~X0~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)~(u4\_cat\_4~X0)~X1~X2)=X2){\unicdcdcdhd}(r2\_cat\_3~X0~(k5\_binop\_1~\\
(u1\_struct\_0~X0)~(u2\_cat\_4~X0)~X1~X2)~(k2\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u3\_cat\_4~X0)~X1~X2)~(k2\_binop\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u4\_cat\_4~X0)~\\
X1~X2))))))))\end{array}
\label{hyp:egidpfdgbgehpfed}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfdgbgehpfed}
${{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v3\_cat\_4}~{({{{k5\_cat\_4}~{X0}}~{X1}})}}}}$.
\end{theorem}
\end{document}
