\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{t26\_catalg\_1 (TMbFNnsdCHFAR158MeDeQRLnLuW13jRA61p)}
\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 $ k3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k13\_catalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_catalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ 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}((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 .  (l3\_msualg\_1~X1~(k3\_catalg\_1~\\
(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}(k1\_funct\_1~\\
(u3\_msualg\_1~(k3\_catalg\_1~(u1\_struct\_0~X0))~X1)~(k9\_catalg\_1~\\
(u1\_struct\_0~X0)~X2~X3)=k2\_cat\_1~X0~X2~X3))){\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}((k3\_msualg\_1~\\
(k3\_catalg\_1~(u1\_struct\_0~X0))~(k10\_catalg\_1~(u1\_struct\_0~X0)~\\
X2~X3~X4)~X1=k4\_card\_3~(k2\_finseq\_4~(k1\_zfmisc\_1~(u4\_struct\_0~\\
X0))~(k2\_cat\_1~X0~X3~X4)~(k2\_cat\_1~X0~X2~X3))){\unicdcdcdhd}(k4\_msualg\_1~(k3\_catalg\_1~\\
(u1\_struct\_0~X0))~(k10\_catalg\_1~(u1\_struct\_0~X0)~X2~X3~X4)~X1=k2\_cat\_1~\\
X0~X2~X4)))))))\end{array}
\label{hyp:mgddjdpfdgbgehbgmghgpfbd}
\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}((v3\_msualg\_1~(k13\_catalg\_1~X0)~(k3\_catalg\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}(l3\_msualg\_1~(k13\_catalg\_1~X0)~(k3\_catalg\_1~\\
(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgbdddpfdgbgehbgmghgpfbd}
\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 .  ((v3\_msualg\_1~X1~(k3\_catalg\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}(l3\_msualg\_1~X1~(k3\_catalg\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((X1=k13\_catalg\_1~X0){\unicdbdjded}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k1\_funct\_1~(u3\_msualg\_1~(k3\_catalg\_1~(u1\_struct\_0~X0))~X1)~(\\
k9\_catalg\_1~(u1\_struct\_0~X0)~X2~X3)=k2\_cat\_1~X0~X2~X3))){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~(k5\_msualg\_1~(\\
k3\_catalg\_1~(u1\_struct\_0~X0))~(k8\_catalg\_1~(u1\_struct\_0~X0)~X2)~\\
X1)~k1\_xboole\_0=k4\_cat\_1~X0~X2)){\unicdcdcdhd}({\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~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}(((k3\_graph\_1~X0~X5=X2){\unicdcdcdhd}((k4\_graph\_1~X0~X5=X3){\unicdcdcdhd}((k3\_graph\_1~\\
X0~X6=X3){\unicdcdcdhd}(k4\_graph\_1~X0~X6=X4)))){\unicdbdjdcd}(k1\_funct\_1~(k5\_msualg\_1~\\
(k3\_catalg\_1~(u1\_struct\_0~X0))~(k10\_catalg\_1~(u1\_struct\_0~X0)~\\
X2~X3~X4)~X1)~(k2\_finseq\_4~(u4\_struct\_0~X0)~X6~X5)=k1\_cat\_1~X0~X5~\\
X6)))))))))))\end{array}
\label{hyp:egbdddpfdgbgehbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfdgbgehbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k3\_msualg\_1~(k3\_catalg\_1~\\
(u1\_struct\_0~X0))~(k10\_catalg\_1~(u1\_struct\_0~X0)~X1~X2~X3)~(k13\_catalg\_1~\\
X0)=k4\_card\_3~(k2\_finseq\_4~(k1\_zfmisc\_1~(u4\_struct\_0~X0))~(k2\_cat\_1~\\
X0~X2~X3)~(k2\_cat\_1~X0~X1~X2))){\unicdcdcdhd}(k4\_msualg\_1~(k3\_catalg\_1~(u1\_struct\_0~\\
X0))~(k10\_catalg\_1~(u1\_struct\_0~X0)~X1~X2~X3)~(k13\_catalg\_1~X0)=\\
k2\_cat\_1~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
