\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\_isocat\_2 (TMXG9Qru5SeRfc4y2A2nkEvEonuyEUV1NrU)}
\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 $ r1\_isocat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_nattra\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_cat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v12\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_isocat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_cat\_1 : {{\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 .  {\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}((\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}(v12\_cat\_1~(k7\_isocat\_2~X0~X1~X2)~(k11\_nattra\_1~\\
(k8\_cat\_2~X0~X1)~X2)~(k11\_nattra\_1~X0~(k11\_nattra\_1~X1~X2)))\end{array}
\label{hyp:ggdgbdpfjgdhpgdgbgehpfcd}
\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}((\preoh v2\_struct\_0~\\
(k8\_cat\_2~X0~X1)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k8\_cat\_2~X0~X1)){\unicdcdcdhd}((v2\_cat\_1~\\
(k8\_cat\_2~X0~X1)){\unicdcdcdhd}((v3\_cat\_1~(k8\_cat\_2~X0~X1)){\unicdcdcdhd}((v4\_cat\_1~(k8\_cat\_2~\\
X0~X1)){\unicdcdcdhd}((v5\_cat\_1~(k8\_cat\_2~X0~X1)){\unicdcdcdhd}((v6\_cat\_1~(k8\_cat\_2~X0~X1)){\unicdcdcdhd}\\
(l1\_cat\_1~(k8\_cat\_2~X0~X1)))))))))\end{array}
\label{hyp:egehpflgidpfdgbgehpfcd}
\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}((\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}(m2\_cat\_1~(k7\_isocat\_2~X0~X1~X2)~(k11\_nattra\_1~(\\
k8\_cat\_2~X0~X1)~X2)~(k11\_nattra\_1~X0~(k11\_nattra\_1~X1~X2)))\end{array}
\label{hyp:egehpflghdpfjgdhpgdgbgehpfcd}
\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}((\preoh v2\_struct\_0~\\
(k11\_nattra\_1~X0~X1)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k11\_nattra\_1~X0~X1)){\unicdcdcdhd}\\
((v1\_cat\_1~(k11\_nattra\_1~X0~X1)){\unicdcdcdhd}((v2\_cat\_1~(k11\_nattra\_1~X0~\\
X1)){\unicdcdcdhd}((v3\_cat\_1~(k11\_nattra\_1~X0~X1)){\unicdcdcdhd}((v4\_cat\_1~(k11\_nattra\_1~\\
X0~X1)){\unicdcdcdhd}((v5\_cat\_1~(k11\_nattra\_1~X0~X1)){\unicdcdcdhd}((v6\_cat\_1~(k11\_nattra\_1~\\
X0~X1)){\unicdcdcdhd}(l1\_cat\_1~(k11\_nattra\_1~X0~X1))))))))))\end{array}
\label{hyp:egehpflgbdbdpfogbgehehchbgpfbd}
\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 .  ((\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}((r1\_isocat\_1~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_cat\_1~X2~X0~X1){\unicdcdcdhd}(v12\_cat\_1~X2~X0~X1))))\end{array}
\label{hyp:egedpfjgdhpgdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfjgdhpgdgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\\
\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_cat\_1~X1){\unicdcdcdhd}((v3\_cat\_1~X1){\unicdcdcdhd}((v4\_cat\_1~\\
X1){\unicdcdcdhd}((v5\_cat\_1~X1){\unicdcdcdhd}((v6\_cat\_1~X1){\unicdcdcdhd}(l1\_cat\_1~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((v2\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_1~\\
X2){\unicdcdcdhd}((v4\_cat\_1~X2){\unicdcdcdhd}((v5\_cat\_1~X2){\unicdcdcdhd}((v6\_cat\_1~X2){\unicdcdcdhd}(l1\_cat\_1~\\
X2)))))))){\unicdbdjdcd}(r1\_isocat\_1~(k11\_nattra\_1~(k8\_cat\_2~X0~X1)~X2)~(k11\_nattra\_1~\\
X0~(k11\_nattra\_1~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
