\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{t38\_cat\_1 (TMXRoWmZoxqMPFXRbpGwBerqDXi1LJHYLBH)}
\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 $ 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 $ v8\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_cat\_1 : {{\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}(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\_cat\_1~X3~X0~\\
X1~X2){\unicdbdjdcd}((k2\_cat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k3\_graph\_1~X0~X3=X1){\unicdcdcdhd}\\
(k4\_graph\_1~X0~X3=X2))))))\end{array}
\label{hyp:ehfdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_cat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}(k2\_cat\_1~\\
X0~(k3\_graph\_1~X0~X1)~(k4\_graph\_1~X0~X1){\unicdcdgdad}k1\_xboole\_0))\end{array}
\label{hyp:ehcdpfdgbgehpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_cat\_1~X3~X0~X1~X2){\unicdbdjdcd}(m1\_subset\_1~\\
X3~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpfngbdpfdgbgehpfbd}
\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 .  ((\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\_cat\_1~X3~X0~X1~X2){\unicdbdjdcd}((v8\_cat\_1~X3~X0~X1~X2){\unicdbdjded}((k2\_cat\_1~X0~X1~X2{\unicdcdgdad}\\
k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((k2\_cat\_1~X0~X2~X4{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~X2~\\
X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_cat\_1~X6~X0~X2~X4){\unicdbdjdcd}((k5\_cat\_1~X0~X1~X2~X4~X3~X5=\\
k5\_cat\_1~X0~X1~X2~X4~X3~X6){\unicdbdjdcd}(X5=X6)))))))))))\end{array}
\label{hyp:egbdfdpfdgbgehpfbd}
\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\_cat\_1~X4~X0~\\
X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~X2~X3){\unicdbdjdcd}(\preoh (k2\_cat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
((k2\_cat\_1~X0~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k5\_cat\_1~X0~X1~X2~X3~X4~X5{\unicdcdgdad}k1\_cat\_1~\\
X0~X4~X5))))))))\end{array}
\label{hyp:egbdddpfdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_cat\_1~X4~X0~\\
X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_cat\_1~X5~X0~X2~X3){\unicdbdjdcd}((v8\_cat\_1~(k5\_cat\_1~\\
X0~X1~X2~X3~X4~X5)~X0~X1~X3){\unicdbdjdcd}((k2\_cat\_1~X0~X1~X2=k1\_xboole\_0){\unicdcdcdid}((k2\_cat\_1~\\
X0~X2~X3=k1\_xboole\_0){\unicdcdcdid}(v8\_cat\_1~X5~X0~X2~X3)))))))))\end{array}$$
\end{theorem}
\end{document}
