\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{t11\_group\_6 (TMcJU8X5vSRPD2WThP9GMzSZTxUapAEP5kA)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_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 $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{k1\_card\_1}~{X0}}={np\_\_1}})}{\unicdbdjded}{({{\unicdcdaddd} X1 .  {{X0}={{k1\_tarski}~{X1}}}})}}}\label{hyp:ehedcdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_card\_1}~{({{k1\_tarski}~{X0}})}}={np\_\_1}}}\label{hyp:ehddadpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(k7\_group\_1~\\
X0=k7\_struct\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}((v7\_struct\_0~\\
X0){\unicdbdjded}({\unicdcdaddd} X1 .  u1\_struct\_0~X0=k1\_tarski~X1))\end{array}
\label{hyp:egcdpfhgchpgfhahpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}(k7\_struct\_0~X0=k1\_card\_1~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egbdgdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({{v7\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{v8\_struct\_0}~{X0}})}})}}}\label{hyp:dgdggdpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfhgchpgfhahpfgd}
$$\begin{array}{c}({\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v7\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}((k7\_group\_1~X0=\\
np\_\_1){\unicdcdcdhd}(v8\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(\\
(v8\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))))){\unicdbdjdcd}((k7\_group\_1~X0=np\_\_1){\unicdbdjdcd}(v7\_struct\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
