\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{t44\_cgames\_1 (TMSkcVGSdDpBWXX349qYqsWAqZTdhnXV2T3)}
\maketitle
Let $ v2\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_cgames\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k13\_cgames\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}((v5\_cgames\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in k7\_cgames\_1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v2\_cgames\_1~\\
X2){\unicdbdjdcd}(\preoh (X2 \in k6\_cgames\_1~X1){\unicdcdcdhd}(v5\_cgames\_1~X2))))))\end{array}
\label{hyp:ehedddpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_cgames\_1}~{X0}})}{\unicdbdjdcd}{({{{k13\_cgames\_1}~{({{k13\_cgames\_1}~{X0}})}}={X0}})}}}\label{hyp:ehedadpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}(({\unicdcdadad} X1 .  (X1 \in k6\_cgames\_1~(k13\_cgames\_1~\\
X0)){\unicdbdjded}({\unicdcdaddd} X2 .  (v2\_cgames\_1~X2){\unicdcdcdhd}((X2 \in k7\_cgames\_1~X0){\unicdcdcdhd}(X1=\\
k13\_cgames\_1~X2)))){\unicdcdcdhd}({\unicdcdadad} X1 .  (X1 \in k7\_cgames\_1~(k13\_cgames\_1~\\
X0)){\unicdbdjded}({\unicdcdaddd} X2 .  (v2\_cgames\_1~X2){\unicdcdcdhd}((X2 \in k6\_cgames\_1~X0){\unicdcdcdhd}(X1=\\
k13\_cgames\_1~X2)))))\end{array}
\label{hyp:ehddjdpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_cgames\_1}~{X0}})}{\unicdbdjdcd}{({{v2\_cgames\_1}~{({{k13\_cgames\_1}~{X0}})}})}}}\label{hyp:ggdgbdadpfdghgbgngfgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}((v6\_cgames\_1~X0){\unicdbdjded}(v5\_cgames\_1~\\
(k13\_cgames\_1~X0)))\end{array}
\label{hyp:egbdgdpfdghgbgngfgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehededpfdghgbgngfgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v2\_cgames\_1~X0){\unicdbdjdcd}((v6\_cgames\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
v2\_cgames\_1~X1){\unicdbdjdcd}(\preoh (X1 \in k6\_cgames\_1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v2\_cgames\_1~\\
X2){\unicdbdjdcd}(\preoh (X2 \in k7\_cgames\_1~X1){\unicdcdcdhd}(v6\_cgames\_1~X2))))))\end{array}$$
\end{theorem}
\end{document}
