\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{t10\_ff\_siec (TMbF4QKcwyewZhC7wbMRwmdiRUAjc16JM5G)}
\maketitle
Let $ v1\_net\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_petri : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_net\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_petri : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_petri : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}((r1\_tarski~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)))~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
((r1\_tarski~(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u4\_struct\_0~X0)))~(u1\_struct\_0~X0)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)))~(u4\_struct\_0~X0)){\unicdcdcdhd}\\
((r1\_tarski~(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u1\_struct\_0~X0)))~(u4\_struct\_0~X0)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~\\
(k4\_relat\_1~(u4\_struct\_0~X0)))~(u4\_struct\_0~X0)){\unicdcdcdhd}((r1\_tarski~\\
(k9\_xtuple\_0~(k4\_relat\_1~(u4\_struct\_0~X0)))~(u4\_struct\_0~X0)){\unicdcdcdhd}\\
((r1\_tarski~(k10\_xtuple\_0~(k4\_relat\_1~(u1\_struct\_0~X0)))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(r1\_tarski~(k9\_xtuple\_0~(k4\_relat\_1~(u1\_struct\_0~X0)))~\\
(u1\_struct\_0~X0)))))))))\end{array}
\label{hyp:ehjdpfggggpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(r1\_tarski~(k9\_xtuple\_0~\\
(k5\_relat\_1~X1~X0))~X0)\end{array}
\label{hyp:ehfdidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_xboole\_0}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{r1\_xboole\_0}~{X1}}~{X0}})}}}}\label{hyp:dhjhngngfgehchjhpfchbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k10\_xtuple\_0}~{({{k4\_relat\_1}~{X0}})}}={X0}}}\label{hyp:chegcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_xtuple\_0}~{({{k4\_relat\_1}~{X0}})}}={X0}}}\label{hyp:chegbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((r1\_xboole\_0~X1~\\
X3){\unicdcdcdhd}((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~X2~X3))){\unicdbdjdcd}(r1\_xboole\_0~X0~X2)\end{array}
\label{hyp:mgbdgdpfggggpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_petri}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{({{k1\_net\_1}~{X0}})}})}}}\label{hyp:ggdgbdpfogfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_relat\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{({{k2\_relat\_1}~{X0}})}})}}}\label{hyp:egehpflgcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_petri~X0){\unicdbdjdcd}((v1\_net\_1~X0){\unicdbdjded}((r1\_xboole\_0~(u1\_struct\_0~\\
X0)~(u4\_struct\_0~X0)){\unicdcdcdhd}(r1\_tarski~(k1\_net\_1~X0)~(k2\_xboole\_0~(\\
k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u4\_struct\_0~X0))~(k2\_zfmisc\_1~(\\
u4\_struct\_0~X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egcdpfogfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_petri~X0){\unicdbdjdcd}(k1\_net\_1~X0=k2\_xboole\_0~(u1\_petri~\\
X0)~(u2\_petri~X0))\end{array}
\label{hyp:egbdpfogfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfggggpfdhjgfgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}((r1\_xboole\_0~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)))~(k9\_xtuple\_0~(k5\_relat\_1~\\
(k1\_net\_1~X0)~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)))~(k9\_xtuple\_0~(k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~\\
(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)))~(k9\_xtuple\_0~\\
(k4\_relat\_1~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0)))~(k9\_xtuple\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~\\
(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~\\
X0)))~(k9\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~\\
X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~\\
(k1\_net\_1~X0))~(u4\_struct\_0~X0)))~(k9\_xtuple\_0~(k4\_relat\_1~(u4\_struct\_0~\\
X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~\\
(u4\_struct\_0~X0)))~(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~\\
X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~\\
(u4\_struct\_0~X0)))~(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~\\
(k1\_net\_1~X0)~(u4\_struct\_0~X0)))~(k10\_xtuple\_0~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(\\
k1\_net\_1~X0))~(u4\_struct\_0~X0)))~(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~\\
X0)~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0)))~(k10\_xtuple\_0~(\\
k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0)))){\unicdcdcdhd}((\\
r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~\\
(u4\_struct\_0~X0)))~(k10\_xtuple\_0~(k4\_relat\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}\\
((r1\_xboole\_0~(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0)))~(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)))){\unicdcdcdhd}\\
((r1\_xboole\_0~(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0)))~(k9\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~\\
(u1\_struct\_0~X0)))~(k9\_xtuple\_0~(k4\_relat\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}\\
((r1\_xboole\_0~(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u1\_struct\_0~X0)))~(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~\\
(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~(k10\_xtuple\_0~(k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0)))~(k9\_xtuple\_0~(k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~\\
(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~\\
X0)))~(k9\_xtuple\_0~(k4\_relat\_1~(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~\\
(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)))~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~\\
(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)))~(k10\_xtuple\_0~\\
(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0)))){\unicdcdcdhd}(\\
(r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0)))~(k10\_xtuple\_0~(k4\_relat\_1~(u4\_struct\_0~X0)))){\unicdcdcdhd}((r1\_xboole\_0~\\
(k9\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~\\
X0)))~(k10\_xtuple\_0~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)))){\unicdcdcdhd}\\
((r1\_xboole\_0~(k9\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u1\_struct\_0~X0)))~(k10\_xtuple\_0~(k5\_relat\_1~(k2\_relat\_1~\\
(k1\_net\_1~X0))~(u1\_struct\_0~X0)))){\unicdcdcdhd}(r1\_xboole\_0~(k9\_xtuple\_0~\\
(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0)))~(k10\_xtuple\_0~\\
(k4\_relat\_1~(u4\_struct\_0~X0)))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
