\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}
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\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{t19\_ff\_siec (TMMxHR7tfsK5vvYgvyoD9MnUEs2YmVqAHgH)}
\maketitle
Let $ v1\_net\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_petri : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_ff\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_ff\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_relat\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}(k3\_relat\_1~(k2\_xboole\_0~X0~X1)~X2=k2\_xboole\_0~\\
(k3\_relat\_1~X0~X2)~(k3\_relat\_1~X1~X2))))\end{array}
\label{hyp:ehgdpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}(k3\_relat\_1~X0~(k2\_xboole\_0~X1~X2)=k2\_xboole\_0~\\
(k3\_relat\_1~X0~X1)~(k3\_relat\_1~X0~X2))))\end{array}
\label{hyp:ehddcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={X0}}}\label{hyp:ehbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k3\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}~{({{k4\_relat\_1}~{X0}})}}={{k4\_relat\_1}~{X0}}}}\label{hyp:ehbdcdpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}((k3\_relat\_1~(k5\_relat\_1~\\
(k1\_net\_1~X0)~(u4\_struct\_0~X0))~(k4\_relat\_1~(u1\_struct\_0~X0))=\\
k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0))~(k4\_relat\_1~(u1\_struct\_0~\\
X0))=k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0)){\unicdcdcdhd}\\
((k3\_relat\_1~(k4\_relat\_1~(u4\_struct\_0~X0))~(k5\_relat\_1~(k1\_net\_1~\\
X0)~(u4\_struct\_0~X0))=k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0)){\unicdcdcdhd}\\
((k3\_relat\_1~(k4\_relat\_1~(u4\_struct\_0~X0))~(k5\_relat\_1~(k2\_relat\_1~\\
(k1\_net\_1~X0))~(u4\_struct\_0~X0))=k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u4\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k1\_net\_1~X0)~\\
(u1\_struct\_0~X0))~(k4\_relat\_1~(u4\_struct\_0~X0))=k5\_relat\_1~(\\
k1\_net\_1~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~\\
(k1\_net\_1~X0))~(u1\_struct\_0~X0))~(k4\_relat\_1~(u4\_struct\_0~X0))=\\
k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~\\
(k4\_relat\_1~(u1\_struct\_0~X0))~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0))=k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~\\
(k4\_relat\_1~(u1\_struct\_0~X0))~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u1\_struct\_0~X0))=k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0))~(k4\_relat\_1~(u4\_struct\_0~X0))=k5\_relat\_1~(k1\_net\_1~X0)~(\\
u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u1\_struct\_0~X0))~(k4\_relat\_1~(u4\_struct\_0~X0))=k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}((k3\_relat\_1~(k4\_relat\_1~\\
(u4\_struct\_0~X0))~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0))=\\
k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k4\_relat\_1~(u4\_struct\_0~X0))~(k5\_relat\_1~\\
(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}(\\
(k3\_relat\_1~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0))~(k4\_relat\_1~\\
(u1\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~\\
(k1\_net\_1~X0))~(u1\_struct\_0~X0))~(k4\_relat\_1~(u1\_struct\_0~X0))=\\
k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k4\_relat\_1~(u1\_struct\_0~X0))~(k5\_relat\_1~\\
(k1\_net\_1~X0)~(u4\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(\\
k4\_relat\_1~(u1\_struct\_0~X0))~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u4\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~\\
(k1\_net\_1~X0)~(u4\_struct\_0~X0))~(k4\_relat\_1~(u4\_struct\_0~X0))=\\
k1\_xboole\_0){\unicdcdcdhd}(k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u4\_struct\_0~X0))~(k4\_relat\_1~(u4\_struct\_0~X0))=k1\_xboole\_0))))))))))))))))))\end{array}
\label{hyp:ehbdcdpfggggpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}((k3\_relat\_1~(k5\_relat\_1~\\
(k1\_net\_1~X0)~(u4\_struct\_0~X0))~(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~\\
X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u4\_struct\_0~X0))~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~\\
(u4\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k1\_net\_1~\\
X0)~(u4\_struct\_0~X0))~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(\\
u4\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~\\
(k1\_net\_1~X0))~(u4\_struct\_0~X0))~(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~\\
X0))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0))~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~X0))=k1\_xboole\_0){\unicdcdcdhd}\\
((k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~\\
X0))~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0))=\\
k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0))~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u1\_struct\_0~X0))=\\
k1\_xboole\_0){\unicdcdcdhd}(k3\_relat\_1~(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~\\
X0))~(u1\_struct\_0~X0))~(k5\_relat\_1~(k1\_net\_1~X0)~(u1\_struct\_0~\\
X0))=k1\_xboole\_0))))))))\end{array}
\label{hyp:ehbdbdpfggggpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_relat\_1~X1)){\unicdbdjdcd}(v1\_relat\_1~\\
(k2\_xboole\_0~X0~X1))\end{array}
\label{hyp:ggdgddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k3\_relat\_1}~{X0}}~{X1}})}}}}\label{hyp:egehpflgddpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}(k8\_ff\_siec~X0=k2\_xboole\_0~\\
(k5\_relat\_1~(k1\_net\_1~X0)~(u4\_struct\_0~X0))~(k4\_relat\_1~(u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:egidpfggggpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}(k7\_ff\_siec~X0=k2\_xboole\_0~\\
(k5\_relat\_1~(k2\_relat\_1~(k1\_net\_1~X0))~(u4\_struct\_0~X0))~(k4\_relat\_1~\\
(u1\_struct\_0~X0)))\end{array}
\label{hyp:eghdpfggggpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfggggpfdhjgfgdg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_net\_1~X0){\unicdcdcdhd}(l1\_petri~X0)){\unicdbdjdcd}((k3\_relat\_1~(k8\_ff\_siec~\\
X0)~(k8\_ff\_siec~X0)=k8\_ff\_siec~X0){\unicdcdcdhd}((k3\_relat\_1~(k8\_ff\_siec~\\
X0)~(k7\_ff\_siec~X0)=k8\_ff\_siec~X0){\unicdcdcdhd}((k3\_relat\_1~(k7\_ff\_siec~\\
X0)~(k7\_ff\_siec~X0)=k7\_ff\_siec~X0){\unicdcdcdhd}(k3\_relat\_1~(k7\_ff\_siec~X0)~\\
(k8\_ff\_siec~X0)=k7\_ff\_siec~X0))))\end{array}$$
\end{theorem}
\end{document}
