\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{t220\_member\_1 (TMSbpeuuoF4J6sEA8UUvTFSgz3bvPvcHB3N)}
\maketitle
Let $ v1\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k25\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_member\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k15\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}(k7\_member\_1~\\
(k5\_xboole\_0~X0~X1)=k5\_xboole\_0~(k7\_member\_1~X0)~(k7\_member\_1~\\
X1)))\end{array}
\label{hyp:ehddfdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}((X2{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k23\_member\_1~(k5\_xboole\_0~\\
X0~X1)~X2=k5\_xboole\_0~(k23\_member\_1~X0~X2)~(k23\_member\_1~X1~X2)))))\end{array}
\label{hyp:ehcdadadpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_membered}~{({{k1\_tarski}~{X0}})}})}}}\label{hyp:ggdghdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_membered~X0){\unicdcdcdhd}(v1\_membered~X1)){\unicdbdjdcd}(\\
v1\_membered~(k5\_xboole\_0~X0~X1))\end{array}
\label{hyp:ggdgedjdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_membered~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k7\_member\_1~X0)){\unicdcdcdhd}(v1\_membered~(k7\_member\_1~X0)))\end{array}
\label{hyp:ggdgbdddpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_xboole\_0~(k7\_member\_1~X0)){\unicdcdcdhd}\\
(v1\_membered~(k7\_member\_1~X0)))\end{array}
\label{hyp:ggdgbdcdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}(k25\_member\_1~\\
X0~X1=k15\_member\_1~(k1\_tarski~X1)~X0))\end{array}
\label{hyp:egcdcdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}(k23\_member\_1~\\
X0~X1=k13\_member\_1~(k1\_tarski~X1)~X0))\end{array}
\label{hyp:egcdadpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}(k15\_member\_1~\\
X0~X1=k13\_member\_1~X0~(k7\_member\_1~X1)))\end{array}
\label{hyp:egbdcdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k5\_xboole\_0}~{X0}}~{X1}}={{{k5\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgfdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdcdadpfngfgngcgfgchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}((X2{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k25\_member\_1~(k5\_xboole\_0~\\
X0~X1)~X2=k5\_xboole\_0~(k25\_member\_1~X0~X2)~(k25\_member\_1~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
