\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{t25\_mod\_2 (TMX6eE5RkncTRpDaeBhxWuEVgLWBGoCyWUa)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k11\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_mod\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (m1\_subset\_1~X0~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdcdcdhd}\\
(X0=np\_\_2)\end{array}
\label{hyp:mgddgdpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh v1\_xboole\_0~(k1\_enumset1~X0~\\
X1~X2)\end{array}
\label{hyp:ggdgcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X3=k1\_enumset1~\\
X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}(\preoh (X4{\unicdcdgdad}X0){\unicdcdcdhd}((X4{\unicdcdgdad}X1){\unicdcdcdhd}(X4{\unicdcdgdad}X2))))\end{array}
\label{hyp:egbdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
(((X1=k6\_numbers){\unicdbdjdcd}(k12\_mod\_2~X0~X1=k6\_numbers)){\unicdcdcdhd}(((X0=k6\_numbers){\unicdbdjdcd}\\
(k12\_mod\_2~X0~X1=k6\_numbers)){\unicdcdcdhd}(((X1=np\_\_1){\unicdbdjdcd}(k12\_mod\_2~X0~X1=\\
X0)){\unicdcdcdhd}(((X0=np\_\_1){\unicdbdjdcd}(k12\_mod\_2~X0~X1=X1)){\unicdcdcdhd}(((X0=np\_\_2){\unicdcdcdhd}(X1=\\
np\_\_2)){\unicdbdjdcd}(k12\_mod\_2~X0~X1=np\_\_1)))))))\end{array}
\label{hyp:egbdedpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
(((X0=k6\_numbers){\unicdbdjdcd}(k11\_mod\_2~X0~X1=X1)){\unicdcdcdhd}(((X1=k6\_numbers){\unicdbdjdcd}\\
(k11\_mod\_2~X0~X1=X0)){\unicdcdcdhd}((((X0=np\_\_1){\unicdcdcdhd}(X1=np\_\_1)){\unicdbdjdcd}(k11\_mod\_2~\\
X0~X1=np\_\_2)){\unicdcdcdhd}((((X0=np\_\_1){\unicdcdcdhd}(X1=np\_\_2)){\unicdbdjdcd}(k11\_mod\_2~X0~X1=k6\_numbers)){\unicdcdcdhd}\\
((((X0=np\_\_2){\unicdcdcdhd}(X1=np\_\_1)){\unicdbdjdcd}(k11\_mod\_2~X0~X1=k6\_numbers)){\unicdcdcdhd}(\\
((X0=np\_\_2){\unicdcdcdhd}(X1=np\_\_2)){\unicdbdjdcd}(k11\_mod\_2~X0~X1=np\_\_1))))))))\end{array}
\label{hyp:egbdddpfngpgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
(((X0=k6\_numbers){\unicdbdjdcd}(k10\_mod\_2~X0=k6\_numbers)){\unicdcdcdhd}(((X0=np\_\_1){\unicdbdjdcd}\\
(k10\_mod\_2~X0=np\_\_2)){\unicdcdcdhd}((X0=np\_\_2){\unicdbdjdcd}(k10\_mod\_2~X0=np\_\_1))))\end{array}
\label{hyp:egbdcdpfngpgegpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfngpgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_enumset1~k6\_numbers~np\_\_1~np\_\_2)){\unicdbdjdcd}\\
(((X3=k6\_numbers){\unicdcdcdhd}(X4=np\_\_1)){\unicdbdjdcd}((k11\_mod\_2~X0~X1=k11\_mod\_2~\\
X1~X0){\unicdcdcdhd}((k11\_mod\_2~(k11\_mod\_2~X0~X1)~X2=k11\_mod\_2~X0~(k11\_mod\_2~\\
X1~X2)){\unicdcdcdhd}((k11\_mod\_2~X0~X3=X0){\unicdcdcdhd}((k11\_mod\_2~X0~(k10\_mod\_2~X0)=X3){\unicdcdcdhd}\\
((k12\_mod\_2~X0~X1=k12\_mod\_2~X1~X0){\unicdcdcdhd}((k12\_mod\_2~(k12\_mod\_2~X0~X1)~\\
X2=k12\_mod\_2~X0~(k12\_mod\_2~X1~X2)){\unicdcdcdhd}((k12\_mod\_2~X4~X0=X0){\unicdcdcdhd}((\preoh (\\
X0{\unicdcdgdad}X3){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_enumset1~k6\_numbers~np\_\_1~\\
np\_\_2)){\unicdbdjdcd}(k12\_mod\_2~X0~X5{\unicdcdgdad}X4))){\unicdcdcdhd}((X3{\unicdcdgdad}X4){\unicdcdcdhd}(k12\_mod\_2~X0~(k11\_mod\_2~\\
X1~X2)=k11\_mod\_2~(k12\_mod\_2~X0~X1)~(k12\_mod\_2~X0~X2))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
