\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{t12\_ens\_1 (TMXTGZ5BwQkWBJ6aLXD62rKDxfPQ1xzuXQd)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_ens\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_ens\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(k1\_domain\_1~X0~X1~X2~X3=k4\_tarski~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k2\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X1}}}}\label{hyp:chegcdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k1\_xtuple\_0}~{({{{k4\_tarski}~{X0}}~{X1}})}}={X0}}}}\label{hyp:chegbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k2\_ens\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k2\_ens\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k6\_ens\_1~X0~X1~X2)~(k2\_ens\_1~X0))\end{array}
\label{hyp:egehpflggdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_ens\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k4\_ens\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgedpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k2\_ens\_1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k3\_ens\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgddpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_ens\_1~X0)){\unicdbdjdcd}((k4\_ens\_1~X0~\\
X1=k3\_ens\_1~X0~X2){\unicdbdjdcd}(k6\_ens\_1~X0~X1~X2=k4\_tarski~(k1\_domain\_1~X0~\\
X0~(k3\_ens\_1~X0~X1)~(k4\_ens\_1~X0~X2))~(k3\_relat\_1~(k2\_xtuple\_0~X1)~\\
(k2\_xtuple\_0~X2))))))\end{array}
\label{hyp:eggdpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}(k4\_ens\_1~X0~X1=k2\_xtuple\_0~(k1\_xtuple\_0~X1)))\end{array}
\label{hyp:egedpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}(k3\_ens\_1~X0~X1=k1\_xtuple\_0~(k1\_xtuple\_0~X1)))\end{array}
\label{hyp:egddpffgogdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpffgogdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k2\_ens\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_ens\_1~X0)){\unicdbdjdcd}((k3\_ens\_1~X0~\\
X1=k4\_ens\_1~X0~X2){\unicdbdjdcd}((k2\_xtuple\_0~(k6\_ens\_1~X0~X2~X1)=k3\_relat\_1~\\
(k2\_xtuple\_0~X2)~(k2\_xtuple\_0~X1)){\unicdcdcdhd}((k3\_ens\_1~X0~(k6\_ens\_1~X0~\\
X2~X1)=k3\_ens\_1~X0~X2){\unicdcdcdhd}(k4\_ens\_1~X0~(k6\_ens\_1~X0~X2~X1)=k4\_ens\_1~\\
X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
