\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{t20\_helly (TMMwVgNL3xU8qbhQqRXXZ3WHfmSfWWFgxor)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_glib\_001~X2~X0){\unicdbdjdcd}((k4\_glib\_001~X0~X1=k3\_glib\_001~\\
X0~X2){\unicdbdjdcd}((k3\_glib\_001~X0~(k7\_glib\_001~X0~X1~X2)=k3\_glib\_001~X0~X1){\unicdcdcdhd}\\
((k4\_glib\_001~X0~(k7\_glib\_001~X0~X1~X2)=k4\_glib\_001~X0~X2){\unicdcdcdhd}(r1\_glib\_001~\\
X0~(k3\_glib\_001~X0~X1)~(k4\_glib\_001~X0~X2)~(k7\_glib\_001~X0~X1~X2)))))))\end{array}
\label{hyp:ehddadpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X2)){\unicdbdjdcd}\\
(r1\_xxreal\_0~X0~X2))))\end{array}
\label{hyp:ehcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_glib\_001~X2~X0){\unicdbdjdcd}((k4\_glib\_001~X0~X1=k3\_glib\_001~\\
X0~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X1)~(k3\_finseq\_1~(k7\_glib\_001~\\
X0~X1~X2))){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_finseq\_1~X2)~(k3\_finseq\_1~(k7\_glib\_001~\\
X0~X1~X2)))))))\end{array}
\label{hyp:ehcdjdpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_glib\_001~\\
X1~X0){\unicdcdcdhd}(m3\_glib\_001~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_glib\_001~X2~X0){\unicdcdcdhd}\\
(m3\_glib\_001~X2~X0)){\unicdbdjdcd}(((k4\_glib\_001~X0~X1=k3\_glib\_001~X0~X2){\unicdcdcdhd}\\
((r1\_xboole\_0~(k14\_glib\_001~X0~X1)~(k14\_glib\_001~X0~X2)){\unicdcdcdhd}(r1\_tarski~\\
(k9\_subset\_1~(k6\_glib\_000~X0)~(k13\_glib\_001~X0~X1)~(k13\_glib\_001~\\
X0~X2))~(k2\_tarski~(k3\_glib\_001~X0~X1)~(k4\_glib\_001~X0~X1))))){\unicdbdjdcd}\\
((v1\_glib\_001~X1~X0){\unicdcdcdid}((v1\_glib\_001~X2~X0){\unicdcdcdid}(((k3\_glib\_001~X0~X1 \in \\
k13\_glib\_001~X0~X2){\unicdcdcdhd}(k3\_glib\_001~X0~X1{\unicdcdgdad}k4\_glib\_001~X0~X2)){\unicdcdcdid}(v5\_glib\_001~\\
(k7\_glib\_001~X0~X1~X2)~X0)))))))\end{array}
\label{hyp:ehbdidpfigfgmgmgjh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}(\preoh (k3\_glib\_001~X0~X1{\unicdcdgdad}k4\_glib\_001~X0~X1){\unicdcdcdhd}(v3\_glib\_001~X1~\\
X0)))\end{array}
\label{hyp:ehbdcdhdpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}((\preoh v3\_glib\_001~X1~X0){\unicdbdjded}(r1\_xxreal\_0~np\_\_3~(k3\_finseq\_1~\\
X1))))\end{array}
\label{hyp:ehbdcdfdpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k3\_finseq\_1~X0=k1\_card\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}((v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}(\\
v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}(m2\_finseq\_1~X1~(k2\_xboole\_0~(k6\_glib\_000~X0)~(k7\_glib\_000~\\
X0))))\end{array}
\label{hyp:egehpfngddpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~\\
X0))))){\unicdcdcdhd}((m3\_glib\_001~X1~X0){\unicdcdcdhd}(m3\_glib\_001~X2~X0))){\unicdbdjdcd}(m3\_glib\_001~\\
(k7\_glib\_001~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflghdpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}((v8\_glib\_001~X1~X0){\unicdbdjded}((v1\_glib\_001~X1~X0){\unicdcdcdhd}((v5\_glib\_001~\\
X1~X0){\unicdcdcdhd}(\preoh v3\_glib\_001~X1~X0)))))\end{array}
\label{hyp:egddbdpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m3\_glib\_001~\\
X1~X0){\unicdbdjdcd}((v1\_glib\_001~X1~X0){\unicdbdjded}(k3\_glib\_001~X0~X1=k4\_glib\_001~X0~\\
X1)))\end{array}
\label{hyp:egcdedpfhgmgjgcgpfadadbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({{v3\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v1\_finset\_1}~{X0}})}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0)))\end{array}
\label{hyp:dgdgcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfigfgmgmgjh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_glib\_001~\\
X1~X0){\unicdcdcdhd}(m3\_glib\_001~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_glib\_001~X2~X0){\unicdcdcdhd}\\
(m3\_glib\_001~X2~X0)){\unicdbdjdcd}(((k4\_glib\_001~X0~X1=k3\_glib\_001~X0~X2){\unicdcdcdhd}\\
((k4\_glib\_001~X0~X2=k3\_glib\_001~X0~X1){\unicdcdcdhd}((r1\_xboole\_0~(k14\_glib\_001~\\
X0~X1)~(k14\_glib\_001~X0~X2)){\unicdcdcdhd}(k9\_subset\_1~(k6\_glib\_000~X0)~(k13\_glib\_001~\\
X0~X1)~(k13\_glib\_001~X0~X2)=k2\_tarski~(k4\_glib\_001~X0~X1)~(k3\_glib\_001~\\
X0~X1))))){\unicdbdjdcd}((v1\_glib\_001~X1~X0){\unicdcdcdid}((v1\_glib\_001~X2~X0){\unicdcdcdid}(v8\_glib\_001~\\
(k7\_glib\_001~X0~X1~X2)~X0))))))\end{array}$$
\end{theorem}
\end{document}
