\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{t1\_rat\_1 (TMQMhDKQSfFMFMfnX2uox4JUtMbd6H5Pxa7)}
\maketitle
Let $ k3\_numbers : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k7\_xcmplx\_0}~{k6\_numbers}}~{X0}}={k6\_numbers}})}}}\label{hyp:ehfdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k7\_xcmplx\_0}~{X0}}~{k6\_numbers}}={k6\_numbers}})}}}\label{hyp:ehedjdpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k4\_numbers}{\unicdcdgdad}{k3\_numbers}}\label{hyp:ehcdedpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v1\_int\_1}~{X0}}}\label{hyp:chdgcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k3\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k7\_xcmplx\_0~X1~X2)))\end{array}
\label{hyp:mggdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_numbers}})}}}\label{hyp:egcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (X0=k3\_numbers){\unicdbdjded}({\unicdcdadad} X1 .  (X1 \in X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(v1\_int\_1~X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (v1\_int\_1~X3){\unicdcdcdhd}(X1=k7\_xcmplx\_0~X2~X3))))\end{array}
\label{hyp:egbdpfchbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgddpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfchbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k3\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}(\preoh (X2{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(X0=k7\_xcmplx\_0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
