\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{t3\_yellow18 (TMMbA3Hi1oQjGge9Y8QXMAn4xmcbocRUpn4)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ g2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\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 $ m1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ u1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v9\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r8\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}\\
((l1\_altcat\_1~X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1))))))){\unicdcdcdhd}(m1\_functor0~X3~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1))~X2~(u1\_altcat\_1~X0)~(u1\_altcat\_1~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (g2\_functor0~X0~\\
X1~X2~X3=g2\_functor0~X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}\\
(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}((l1\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_functor0~X2~X0~X1))){\unicdbdjdcd}(m1\_functor0~(u2\_functor0~X0~X1~X2)~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~(u1\_functor0~X0~X1~X2)~(u1\_altcat\_1~\\
X0)~(u1\_altcat\_1~X1))\end{array}
\label{hyp:egehpffhcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_struct\_0~X0){\unicdcdcdhd}((l1\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_functor0~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~(u1\_functor0~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_functor0~X0~X1~X2)~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))){\unicdcdcdhd}(m1\_subset\_1~(u1\_functor0~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X1)))))))\end{array}
\label{hyp:egehpffhbdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (l2\_functor0~X2~X0~X1){\unicdbdjdcd}(l1\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfmgcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmgehdgbgehpfbd}
\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}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}\\
(l1\_altcat\_1~X1))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(\\
l1\_altcat\_1~X2))){\unicdcdcdhd}(((v8\_functor0~X3~X0~X1){\unicdcdcdhd}(l2\_functor0~X3~X0~\\
X1)){\unicdcdcdhd}(l2\_functor0~X4~X1~X2))))){\unicdbdjdcd}((v9\_functor0~(k13\_functor0~\\
X0~X1~X2~X3~X4)~X0~X2){\unicdcdcdhd}(l2\_functor0~(k13\_functor0~X0~X1~X2~X3~X4)~X0~\\
X2))\end{array}
\label{hyp:egehpflgbdddpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l1\_altcat\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(l1\_altcat\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v8\_functor0~X3~X0~X1){\unicdcdcdhd}(l2\_functor0~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (l2\_functor0~\\
X4~X1~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v9\_functor0~X5~X0~X2){\unicdcdcdhd}(l2\_functor0~X5~X0~\\
X2)){\unicdbdjdcd}((X5=k13\_functor0~X0~X1~X2~X3~X4){\unicdbdjded}((r8\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X2)~(u1\_struct\_0~\\
X2))~(u1\_functor0~X0~X2~X5)~(k1\_partfun1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X2)~(u1\_struct\_0~X2))~(u1\_functor0~X0~X1~X3)~(u1\_functor0~\\
X1~X2~X4))){\unicdcdcdhd}(r8\_pboole~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))~(u2\_functor0~X0~X2~X5)~(k8\_pboole~(u2\_functor0~X0~X1~X3)~(k3\_relat\_1~\\
(u1\_functor0~X0~X1~X3)~(u2\_functor0~X1~X2~X4)))))))))))\end{array}
\label{hyp:egddgdpfggfhogdgehpgchad}
\end{equation}
\begin{theorem}\label{thm:ehddpfjhfgmgmgpghhbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_altcat\_2~X0){\unicdcdcdhd}(l1\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_altcat\_2~X1){\unicdcdcdhd}(l1\_altcat\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v1\_altcat\_2~X2){\unicdcdcdhd}(l1\_altcat\_1~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_functor0~X3~X0~X1){\unicdcdcdhd}(l2\_functor0~X3~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v8\_functor0~X4~X0~X1){\unicdcdcdhd}(l2\_functor0~X4~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(l2\_functor0~X5~X1~X2){\unicdbdjdcd}({\unicdcdadad} X6 .  (l2\_functor0~X6~X1~X2){\unicdbdjdcd}(((g2\_functor0~\\
X0~X1~(u1\_functor0~X0~X1~X3)~(u2\_functor0~X0~X1~X3)=g2\_functor0~X0~\\
X1~(u1\_functor0~X0~X1~X4)~(u2\_functor0~X0~X1~X4)){\unicdcdcdhd}(g2\_functor0~X1~\\
X2~(u1\_functor0~X1~X2~X5)~(u2\_functor0~X1~X2~X5)=g2\_functor0~X1~X2~\\
(u1\_functor0~X1~X2~X6)~(u2\_functor0~X1~X2~X6))){\unicdbdjdcd}(k13\_functor0~X0~\\
X1~X2~X3~X5=k13\_functor0~X0~X1~X2~X4~X6))))))))\end{array}$$
\end{theorem}
\end{document}
