\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{t5\_afproj (TMVahYzmUB729sgS1B9omHq2VqEzqdbAmR7)}
\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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~(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)){\unicdbdjdcd}((r1\_aff\_4~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X6 .  \\
(m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((\preoh r5\_aff\_1~\\
X0~X3~X4){\unicdcdcdhd}((r1\_tarski~X3~X1){\unicdcdcdhd}((r1\_tarski~X4~X1){\unicdcdcdhd}((r1\_tarski~X5~\\
X2){\unicdcdcdhd}((r1\_tarski~X6~X2){\unicdcdcdhd}(((r5\_aff\_1~X0~X3~X5){\unicdcdcdid}(r5\_aff\_1~X0~X5~X3)){\unicdcdcdhd}\\
((r5\_aff\_1~X0~X4~X6){\unicdcdcdid}(r5\_aff\_1~X0~X6~X4))))))))))))))))\end{array}
\label{hyp:ehfdfdpfbgggggpfed}
\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}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((\preoh (\preoh (r5\_aff\_1~X0~X1~X2){\unicdcdcdhd}(r5\_aff\_1~X0~X2~X3)){\unicdcdcdhd}((\preoh (r5\_aff\_1~X0~X1~\\
X2){\unicdcdcdhd}(r5\_aff\_1~X0~X3~X2)){\unicdcdcdhd}((\preoh (r5\_aff\_1~X0~X2~X1){\unicdcdcdhd}(r5\_aff\_1~X0~X2~\\
X3)){\unicdcdcdhd}(\preoh (r5\_aff\_1~X0~X2~X1){\unicdcdcdhd}(r5\_aff\_1~X0~X3~X2))))){\unicdbdjdcd}(r5\_aff\_1~X0~\\
X1~X3)))))\end{array}
\label{hyp:ehededpfbgggggpfbd}
\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\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_4~X2~X0)){\unicdbdjdcd}((r1\_aff\_4~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((r1\_tarski~\\
X3~X2){\unicdcdcdhd}((r5\_aff\_1~X0~X1~X3){\unicdcdcdid}(r5\_aff\_1~X0~X3~X1))))))))\end{array}
\label{hyp:ehedbdpfbgggggpfed}
\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){\unicdbdjdcd}(r5\_aff\_1~X0~X2~X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchfdpfbgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((r1\_aff\_4~X0~X1~X3){\unicdcdcdhd}((r1\_aff\_4~X0~X1~X4){\unicdcdcdhd}((r1\_aff\_4~X0~X2~X3){\unicdcdcdhd}\\
((r1\_aff\_4~X0~X2~X4){\unicdcdcdhd}((v1\_aff\_1~X1~X0){\unicdcdcdhd}((v1\_aff\_1~X2~X0){\unicdcdcdhd}((v1\_aff\_4~\\
X3~X0){\unicdcdcdhd}(v1\_aff\_4~X4~X0)))))))){\unicdbdjdcd}((r5\_aff\_1~X0~X1~X2){\unicdcdcdid}(r1\_aff\_4~\\
X0~X3~X4)))))))\end{array}$$
\end{theorem}
\end{document}
