\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{t45\_int\_4 (TMTLoTzr9LiHmN14wqNna16edDmi9NJLsnk)}
\maketitle
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_int\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((\preoh r1\_int\_1~(k3\_int\_2~X0~X1)~(k6\_xcmplx\_0~X2~\\
X3)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (v1\_int\_1~X4){\unicdcdcdhd}((k6\_int\_1~(k6\_xcmplx\_0~X4~X2)~\\
X0=k6\_numbers){\unicdcdcdhd}(k6\_int\_1~(k6\_xcmplx\_0~X4~X3)~X1=k6\_numbers)))))))))\end{array}
\label{hyp:ehedbdpfjgogehpfed}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfjgogehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v1\_int\_1~X5){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((\preoh (r1\_int\_1~(k3\_int\_2~X0~X1)~(k6\_xcmplx\_0~\\
X3~X4)){\unicdcdcdhd}((r1\_int\_1~(k3\_int\_2~X0~X2)~(k6\_xcmplx\_0~X3~X5)){\unicdcdcdhd}(r1\_int\_1~\\
(k3\_int\_2~X1~X2)~(k6\_xcmplx\_0~X4~X5)))){\unicdcdcdhd}({\unicdcdaddd} X6 .  (v1\_int\_1~\\
X6){\unicdcdcdhd}((k6\_int\_1~(k6\_xcmplx\_0~X6~X3)~X0=k6\_numbers){\unicdcdcdhd}((k6\_int\_1~\\
(k6\_xcmplx\_0~X6~X4)~X1=k6\_numbers){\unicdcdcdhd}(k6\_int\_1~(k6\_xcmplx\_0~X6~\\
X5)~X2=k6\_numbers)))))))))))))\end{array}$$
\end{theorem}
\end{document}
