\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{t44\_isocat\_1 (TMYYEj8xVd4ea4cAfWFHJ2xLmDEmojwPaLi)}
\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 $ m2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_nattra\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k10\_cat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ 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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ u4\_struct\_0 : {{\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}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\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)))))))){\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}(l1\_cat\_1~\\
X2)))))))){\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}(l1\_cat\_1~X3)))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_cat\_1~\\
X4~X0~X1){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_cat\_1~X5~X2~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_cat\_1~\\
X6~X1~X2){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_cat\_1~X7~X1~X2){\unicdbdjdcd}((r3\_nattra\_1~X1~X2~X6~\\
X7){\unicdbdjdcd}((r3\_nattra\_1~X1~X3~(k9\_cat\_1~X1~X2~X3~X6~X5)~(k9\_cat\_1~X1~X2~X3~\\
X7~X5)){\unicdcdcdhd}(r3\_nattra\_1~X0~X2~(k9\_cat\_1~X0~X1~X2~X4~X6)~(k9\_cat\_1~X0~X1~\\
X2~X4~X7)))))))))))\end{array}
\label{hyp:ehedddpfjgdhpgdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~(k4\_relset\_1~X0~X0~X0~\\
X1~(k6\_partfun1~X0)~X2)~X2){\unicdcdcdhd}(r2\_relset\_1~X0~X1~(k4\_relset\_1~X0~X1~\\
X1~X1~X2~(k6\_partfun1~X1))~X2))\end{array}
\label{hyp:ehbdhdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\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}(((\\
\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}(((\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}(l1\_cat\_1~X2)))))))){\unicdcdcdhd}((m2\_cat\_1~X3~X0~X1){\unicdcdcdhd}(m2\_cat\_1~X4~X1~\\
X2))))){\unicdbdjdcd}(k9\_cat\_1~X0~X1~X2~X3~X4=k3\_relat\_1~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))){\unicdbdjdcd}(k4\_relset\_1~X0~X1~X2~X3~\\
X4~X5=k3\_relat\_1~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfchfgmgdhfgehpfbd}
\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}\\
((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))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_cat\_1~X2~X0~X1){\unicdbdjdcd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u4\_struct\_0~\\
X0)~(u4\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u4\_struct\_0~X0)~(u4\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpfngcdpfdgbgehpfbd}
\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}(((\\
\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}(((\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}(l1\_cat\_1~X2)))))))){\unicdcdcdhd}((m2\_cat\_1~X3~X0~X1){\unicdcdcdhd}(m2\_cat\_1~X4~X1~\\
X2))))){\unicdbdjdcd}(m2\_cat\_1~(k9\_cat\_1~X0~X1~X2~X3~X4)~X0~X2)\end{array}
\label{hyp:egehpflgjdpfdgbgehpfbd}
\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}(m2\_cat\_1~(k10\_cat\_1~X0)~X0~X0)\end{array}
\label{hyp:egehpflgbdadpfdgbgehpfbd}
\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}(k10\_cat\_1~X0=k6\_partfun1~(u4\_struct\_0~\\
X0))\end{array}
\label{hyp:egcdedpfdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehededpfjgdhpgdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\\
\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_cat\_1~X1){\unicdcdcdhd}((v3\_cat\_1~X1){\unicdcdcdhd}((v4\_cat\_1~\\
X1){\unicdcdcdhd}((v5\_cat\_1~X1){\unicdcdcdhd}((v6\_cat\_1~X1){\unicdcdcdhd}(l1\_cat\_1~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_cat\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_cat\_1~X3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_cat\_1~X4~X0~X0){\unicdbdjdcd}((r3\_nattra\_1~X0~X0~X4~(k10\_cat\_1~X0)){\unicdbdjdcd}((r3\_nattra\_1~\\
X0~X1~(k9\_cat\_1~X0~X0~X1~X4~X2)~X2){\unicdcdcdhd}(r3\_nattra\_1~X1~X0~(k9\_cat\_1~X1~\\
X0~X0~X3~X4)~X3)))))))\end{array}$$
\end{theorem}
\end{document}
