\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{t48\_cgames\_1 (TMc2BEpPxMuvvzoQKcJgy8pZjF59QDbbkQ1)}
\maketitle
Let $ v2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v8\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}(((v5\_cgames\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in k7\_cgames\_1~X0){\unicdcdcdhd}((\preoh v8\_cgames\_1~X1){\unicdcdcdhd}\\
(\preoh v9\_cgames\_1~X1))))){\unicdcdcdhd}((({\unicdcdadad} X1 .  (v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in \\
k7\_cgames\_1~X0){\unicdcdcdhd}((\preoh v8\_cgames\_1~X1){\unicdcdcdhd}(\preoh v9\_cgames\_1~X1)))){\unicdbdjdcd}(v5\_cgames\_1~\\
X0)){\unicdcdcdhd}(((v6\_cgames\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in \\
k6\_cgames\_1~X0){\unicdcdcdhd}((\preoh v8\_cgames\_1~X1){\unicdcdcdhd}(\preoh v10\_cgames\_1~X1))))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in k6\_cgames\_1~X0){\unicdcdcdhd}((\preoh v8\_cgames\_1~\\
X1){\unicdcdcdhd}(\preoh v10\_cgames\_1~X1)))){\unicdbdjdcd}(v6\_cgames\_1~X0)))))\end{array}
\label{hyp:ehedfdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}(\preoh (\preoh v7\_cgames\_1~X0){\unicdcdcdhd}((\preoh v9\_cgames\_1~\\
X0){\unicdcdcdhd}((\preoh v10\_cgames\_1~X0){\unicdcdcdhd}(\preoh v8\_cgames\_1~X0))))\end{array}
\label{hyp:ehedcdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_cgames\_1~X0){\unicdcdcdhd}(v9\_cgames\_1~X0)){\unicdbdjdcd}((v2\_cgames\_1~\\
X0){\unicdcdcdhd}((v5\_cgames\_1~X0){\unicdcdcdhd}(\preoh v7\_cgames\_1~X0)))\end{array}
\label{hyp:dgdgjdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_cgames\_1~X0){\unicdcdcdhd}(v10\_cgames\_1~X0)){\unicdbdjdcd}((v2\_cgames\_1~\\
X0){\unicdcdcdhd}((v6\_cgames\_1~X0){\unicdcdcdhd}(\preoh v7\_cgames\_1~X0)))\end{array}
\label{hyp:dgdghdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_cgames\_1~X0){\unicdcdcdhd}((v5\_cgames\_1~X0){\unicdcdcdhd}(v6\_cgames\_1~\\
X0))){\unicdbdjdcd}((v2\_cgames\_1~X0){\unicdcdcdhd}(v7\_cgames\_1~X0))\end{array}
\label{hyp:dgdggdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_cgames\_1~X0){\unicdcdcdhd}(v7\_cgames\_1~X0)){\unicdbdjdcd}((v2\_cgames\_1~\\
X0){\unicdcdcdhd}((v5\_cgames\_1~X0){\unicdcdcdhd}(v6\_cgames\_1~X0)))\end{array}
\label{hyp:dgdgfdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_cgames\_1~X0){\unicdcdcdhd}(v8\_cgames\_1~X0)){\unicdbdjdcd}((v2\_cgames\_1~\\
X0){\unicdcdcdhd}((\preoh v5\_cgames\_1~X0){\unicdcdcdhd}(\preoh v6\_cgames\_1~X0)))\end{array}
\label{hyp:dgdgbdbdpfdghgbgngfgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedidpfdghgbgngfgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}((v9\_cgames\_1~X0){\unicdbdjded}(({\unicdcdadad} X1 .  \\
(v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in k7\_cgames\_1~X0){\unicdcdcdhd}((\preoh v8\_cgames\_1~X1){\unicdcdcdhd}\\
(\preoh v9\_cgames\_1~X1)))){\unicdcdcdhd}({\unicdcdaddd} X1 .  (v2\_cgames\_1~X1){\unicdcdcdhd}((X1 \in k6\_cgames\_1~\\
X0){\unicdcdcdhd}(v5\_cgames\_1~X1)))))\end{array}$$
\end{theorem}
\end{document}
