\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{t1\_conmetr1 (TMdi4mzMxuQDLexwqpyaTdTJHkYeygdGpnr)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_conmetr1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_conmetr1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_conmetr1 : {{\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 $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_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}(\preoh (v1\_aff\_1~X1~X0){\unicdcdcdhd}((v1\_aff\_1~X2~X0){\unicdcdcdhd}((\preoh r5\_aff\_1~\\
X0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X3 \in \\
X1){\unicdcdcdhd}(X3 \in X2))))))))\end{array}
\label{hyp:ehfdidpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\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}\\
((r3\_aff\_1~X0~X1~X2){\unicdbdjdcd}((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_1~X2~X0)))))\end{array}
\label{hyp:ehddgdpfbgggggpfbd}
\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}
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 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}((v6\_conmetr1~X0){\unicdbdjded}({\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~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~X11~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(((v1\_aff\_1~X10~X0){\unicdcdcdhd}((v1\_aff\_1~X11~X0){\unicdcdcdhd}((X1 \in X10){\unicdcdcdhd}((X1 \in \\
X11){\unicdcdcdhd}((X2 \in X10){\unicdcdcdhd}((X4 \in X10){\unicdcdcdhd}((X7 \in X10){\unicdcdcdhd}((X9 \in X10){\unicdcdcdhd}((X3 \in X11){\unicdcdcdhd}\\
((X5 \in X11){\unicdcdcdhd}((X6 \in X11){\unicdcdcdhd}((X8 \in X11){\unicdcdcdhd}((r2\_analoaf~X0~X4~X3~X8~X7){\unicdcdcdhd}(\\
(r2\_analoaf~X0~X3~X2~X7~X6){\unicdcdcdhd}(r2\_analoaf~X0~X2~X5~X6~X9))))))))))))))){\unicdbdjdcd}\\
((X5 \in X10){\unicdcdcdid}((X3 \in X10){\unicdcdcdid}((X6 \in X10){\unicdcdcdid}((X8 \in X10){\unicdcdcdid}((X2 \in X11){\unicdcdcdid}((X4 \in \\
X11){\unicdcdcdid}((X7 \in X11){\unicdcdcdid}((X9 \in X11){\unicdcdcdid}(r2\_analoaf~X0~X4~X5~X8~X9))))))))))))))))))))))\end{array}
\label{hyp:eggdpfdgpgogngfgehchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}((v5\_conmetr1~X0){\unicdbdjded}({\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~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((r5\_aff\_1~X0~X9~X10){\unicdcdcdhd}((X1 \in X9){\unicdcdcdhd}((X3 \in X9){\unicdcdcdhd}\\
((X6 \in X9){\unicdcdcdhd}((X8 \in X9){\unicdcdcdhd}((X2 \in X10){\unicdcdcdhd}((X4 \in X10){\unicdcdcdhd}((X5 \in X10){\unicdcdcdhd}((X7 \in X10){\unicdcdcdhd}\\
((r2\_analoaf~X0~X3~X2~X7~X6){\unicdcdcdhd}((r2\_analoaf~X0~X2~X1~X6~X5){\unicdcdcdhd}(r2\_analoaf~\\
X0~X1~X4~X5~X8)))))))))))){\unicdbdjdcd}((X4 \in X9){\unicdcdcdid}((X2 \in X9){\unicdcdcdid}((X5 \in X9){\unicdcdcdid}((X7 \in \\
X9){\unicdcdcdid}((X1 \in X10){\unicdcdcdid}((X3 \in X10){\unicdcdcdid}((X6 \in X10){\unicdcdcdid}((X8 \in X10){\unicdcdcdid}(r2\_analoaf~\\
X0~X3~X4~X7~X8)))))))))))))))))))))\end{array}
\label{hyp:egfdpfdgpgogngfgehchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}((v4\_conmetr1~X0){\unicdbdjded}({\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~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_aff\_1~X9~X0){\unicdcdcdhd}((v1\_aff\_1~X10~X0){\unicdcdcdhd}((X1 \in \\
X9){\unicdcdcdhd}((X3 \in X9){\unicdcdcdhd}((X6 \in X9){\unicdcdcdhd}((X8 \in X9){\unicdcdcdhd}((X2 \in X10){\unicdcdcdhd}((X4 \in X10){\unicdcdcdhd}((X5 \in \\
X10){\unicdcdcdhd}((X7 \in X10){\unicdcdcdhd}((r2\_analoaf~X0~X3~X2~X7~X6){\unicdcdcdhd}((r2\_analoaf~X0~X2~\\
X1~X6~X5){\unicdcdcdhd}(r2\_analoaf~X0~X1~X4~X5~X8))))))))))))){\unicdbdjdcd}((X4 \in X9){\unicdcdcdid}((X2 \in \\
X9){\unicdcdcdid}((X5 \in X9){\unicdcdcdid}((X7 \in X9){\unicdcdcdid}((X1 \in X10){\unicdcdcdid}((X3 \in X10){\unicdcdcdid}((X6 \in X10){\unicdcdcdid}((X8 \in \\
X10){\unicdcdcdid}(r2\_analoaf~X0~X3~X4~X7~X8)))))))))))))))))))))\end{array}
\label{hyp:egedpfdgpgogngfgehchbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfdgpgogngfgehchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}((v2\_diraf~X0){\unicdcdcdhd}\\
(l1\_analoaf~X0)))){\unicdbdjdcd}((v4\_conmetr1~X0){\unicdbdjded}((v5\_conmetr1~X0){\unicdcdcdhd}(v6\_conmetr1~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
