\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{t27\_prob\_1 (TMVFAZrW7f6YbryiEw1ipTAZ1GVm1P28VCH)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}o .  \\
{\unicdcdadad} X3 .  {\unicdcdaddd} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdcdcdhd}((k9\_xtuple\_0~\\
X4=X3){\unicdcdcdhd}({\unicdcdadad} X5 .  (X5 \in X3){\unicdbdjdcd}(((X2~X5){\unicdbdjdcd}(k1\_funct\_1~X4~X5=X1~X5)){\unicdcdcdhd}\\
((\preoh X2~X5){\unicdbdjdcd}(k1\_funct\_1~X4~X5=X0~X5)))))\end{array}
\label{hyp:dhbdpfahbgchehggfhogbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfahchpgcgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_prob\_1~\\
X2~X0){\unicdcdcdhd}((v4\_prob\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdcdcdhd}((k9\_xtuple\_0~\\
X3=X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}((X4 \in X2){\unicdbdjdcd}\\
(((X1 \in X4){\unicdbdjdcd}(k1\_funct\_1~X3~X4=np\_\_1)){\unicdcdcdhd}((\preoh X1 \in X4){\unicdbdjdcd}(k1\_funct\_1~\\
X3~X4=k6\_numbers)))))))\end{array}$$
\end{theorem}
\end{document}
