\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{t64\_aff\_4 (TMMVB4dyLEiFHEjcmqZe276ZscVoGvRJVsF)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r5\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~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\_subset\_1~X5~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_aff\_4~\\
X5~X0){\unicdcdcdhd}((v1\_aff\_4~X6~X0){\unicdcdcdhd}((v1\_aff\_4~X7~X0){\unicdcdcdhd}((r1\_aff\_4~X0~X5~X6){\unicdcdcdhd}\\
((X1 \in k9\_subset\_1~(u1\_struct\_0~X0)~X5~X7){\unicdcdcdhd}((X2 \in k9\_subset\_1~(u1\_struct\_0~\\
X0)~X5~X7){\unicdcdcdhd}((X3 \in k9\_subset\_1~(u1\_struct\_0~X0)~X6~X7){\unicdcdcdhd}(X4 \in k9\_subset\_1~\\
(u1\_struct\_0~X0)~X6~X7)))))))){\unicdbdjdcd}((X5=X6){\unicdcdcdid}(r2\_analoaf~X0~X1~X2~X3~\\
X4))))))))))\end{array}
\label{hyp:ehgdddpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~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 .  \\
((v1\_aff\_1~X5~X0){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((v1\_aff\_1~X6~X0){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(((X1 \in X5){\unicdcdcdhd}((X2 \in X5){\unicdcdcdhd}((X3 \in X6){\unicdcdcdhd}(X4 \in X6)))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}\\
((X3=X4){\unicdcdcdid}((r3\_aff\_1~X0~X5~X6){\unicdbdjded}(r2\_analoaf~X0~X1~X2~X3~X4)))))))))))\end{array}
\label{hyp:ehddidpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~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~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_aff\_4~X3~X0){\unicdcdcdhd}((v1\_aff\_4~X4~X0){\unicdcdcdhd}((X1 \in \\
X3){\unicdcdcdhd}((X2 \in X3){\unicdcdcdhd}((X1 \in X4){\unicdcdcdhd}(X2 \in X4)))))){\unicdbdjdcd}((X3=X4){\unicdcdcdid}((X1=X2){\unicdcdcdid}(v1\_aff\_1~\\
(k9\_subset\_1~(u1\_struct\_0~X0)~X3~X4)~X0))))))))\end{array}
\label{hyp:ehcdedpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~\\
X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}((r5\_aff\_1~\\
X0~X1~X2){\unicdbdjded}(r3\_aff\_1~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchfdpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v1\_aff\_4~X1~X0){\unicdcdcdhd}((v1\_aff\_4~X2~X0){\unicdcdcdhd}(r1\_aff\_4~X0~X1~X2))){\unicdbdjdcd}((X1=\\
X2){\unicdcdcdid}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X3 \in X1){\unicdcdcdhd}\\
(X3 \in X2)))))))\end{array}
\label{hyp:mghdjdpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(m1\_subset\_1~(k9\_subset\_1~X0~X1~X2)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k9\_subset\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdedpfbgggggpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_aff\_4~\\
X5~X0){\unicdcdcdhd}((v1\_aff\_4~X6~X0){\unicdcdcdhd}((v1\_aff\_4~X7~X0){\unicdcdcdhd}((r1\_aff\_4~X0~X5~X6){\unicdcdcdhd}\\
((X1 \in k9\_subset\_1~(u1\_struct\_0~X0)~X5~X7){\unicdcdcdhd}((X2 \in k9\_subset\_1~(u1\_struct\_0~\\
X0)~X5~X7){\unicdcdcdhd}((X3 \in k9\_subset\_1~(u1\_struct\_0~X0)~X6~X7){\unicdcdcdhd}(X4 \in k9\_subset\_1~\\
(u1\_struct\_0~X0)~X6~X7)))))))){\unicdbdjdcd}((X5=X6){\unicdcdcdid}((X1=X2){\unicdcdcdid}((X3=X4){\unicdcdcdid}\\
(r5\_aff\_1~X0~(k9\_subset\_1~(u1\_struct\_0~X0)~X5~X7)~(k9\_subset\_1~\\
(u1\_struct\_0~X0)~X6~X7)))))))))))))\end{array}$$
\end{theorem}
\end{document}
