\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{t118\_group\_9 (TMM4wKMR8iZNdvuyq6WgmCy53YjzyPjcBDX)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r4\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r5\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ np\_\_1 : {\iota}$ be given.
Let $ k21\_group\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\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 $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~(k3\_finseq\_1~X2)~np\_\_1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X3)~np\_\_1){\unicdcdcdhd}(\preoh r5\_group\_9~X0~X1~X1~(k21\_group\_9~X0~X1~\\
X2~X3)~(k21\_group\_9~X0~X1~X3~X2))))))\end{array}
\label{hyp:ehbdbdhdpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~(k3\_finseq\_1~X2)~np\_\_1){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k3\_finseq\_1~X3)~np\_\_1){\unicdcdcdhd}(\preoh r4\_group\_9~X0~X1~(k21\_group\_9~X0~X1~X2~\\
X3)~X2)))))\end{array}
\label{hyp:ehbdbdgdpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X2)~(k3\_finseq\_1~X3)){\unicdbdjdcd}((\\
(\preoh r1\_xxreal\_0~(k3\_finseq\_1~X2)~np\_\_1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k3\_finseq\_1~\\
X3)~np\_\_1)){\unicdcdcdid}(r4\_group\_9~X0~X1~X3~X2)))))\end{array}
\label{hyp:ehbdbdedpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}(r5\_group\_9~X0~X1~X1~X2~X2))\end{array}
\label{hyp:ehbdbdddpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(\\
l1\_group\_9~X1~X0))))){\unicdcdcdhd}(((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m1\_finseq\_1~X2~\\
(k6\_group\_9~X0~X1))){\unicdcdcdhd}((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m1\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))))){\unicdbdjdcd}(r4\_group\_9~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchedpfhgchpgfhahpfjd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\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}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\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}\\
(m2\_subset\_1~(k3\_finseq\_1~X0)~k1\_numbers~k5\_numbers)\end{array}
\label{hyp:egehpflgddpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(\\
l1\_group\_9~X1~X0))))){\unicdcdcdhd}(((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m1\_finseq\_1~X2~\\
(k6\_group\_9~X0~X1))){\unicdcdcdhd}((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m1\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))))){\unicdbdjdcd}((v8\_group\_9~(k21\_group\_9~X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
(k21\_group\_9~X0~X1~X2~X3)~(k6\_group\_9~X0~X1)))\end{array}
\label{hyp:egehpflgcdbdpfhgchpgfhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\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 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdidpfhgchpgfhahpfjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v3\_group\_9~X1~X0){\unicdcdcdhd}(l1\_group\_9~X1~X0))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((v8\_group\_9~X2~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X2~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v8\_group\_9~X3~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X3~(k6\_group\_9~\\
X0~X1))){\unicdbdjdcd}({\unicdcdaddd} X4 .  ((v8\_group\_9~X4~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X4~(k6\_group\_9~\\
X0~X1))){\unicdcdcdhd}({\unicdcdaddd} X5 .  ((v8\_group\_9~X5~X0~X1){\unicdcdcdhd}(m2\_finseq\_1~X5~(k6\_group\_9~\\
X0~X1))){\unicdcdcdhd}((r4\_group\_9~X0~X1~X4~X2){\unicdcdcdhd}((r4\_group\_9~X0~X1~X5~X3){\unicdcdcdhd}(r5\_group\_9~\\
X0~X1~X1~X4~X5)))))))\end{array}$$
\end{theorem}
\end{document}
