\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t96\_xcmplx\_1 (TMZjXENt5LsoZ4RtE9Vmij5AQGodn9D3eBW)}
\maketitle
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k3\_xcmplx\_0~X1~X2=k7\_xcmplx\_0~\\
(k3\_xcmplx\_0~X1~X0)~(k7\_xcmplx\_0~X0~X2)))))\end{array}
\label{hyp:ehjdddpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k7\_xcmplx\_0~X1~X2=k7\_xcmplx\_0~\\
(k7\_xcmplx\_0~X1~X0)~(k7\_xcmplx\_0~X2~X0)))))\end{array}
\label{hyp:ehfdfdpfihdgngahmgihpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdgdpfihdgngahmgihpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xcmplx\_0~X3){\unicdbdjdcd}((k3\_xcmplx\_0~\\
X2~X0=k7\_xcmplx\_0~X3~X1){\unicdbdjdcd}((X0=k6\_numbers){\unicdcdcdid}((X1=k6\_numbers){\unicdcdcdid}\\
(k3\_xcmplx\_0~X2~X1=k7\_xcmplx\_0~X3~X0)))))))\end{array}$$
\end{theorem}
\end{document}
