\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{t60\_arytm\_3 (TMdADxJSgrpuY4ZXQkqv5sbt2A7JHxVqGHb)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k9\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k12\_arytm\_3 : {\iota}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_arytm\_3 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~k5\_arytm\_3)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v3\_ordinal1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_arytm\_3)){\unicdbdjdcd}(\\
k9\_arytm\_3~X0~X1=k8\_ordinal3~X0~X1))\end{array}
\label{hyp:ehfdidpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}(k10\_arytm\_3~\\
X0~(k9\_arytm\_3~X1~X2)=k9\_arytm\_3~(k10\_arytm\_3~X0~X1)~(k10\_arytm\_3~\\
X0~X2))))\end{array}
\label{hyp:ehfdhdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}(k10\_arytm\_3~X0~X1{\unicdcdgdad}np\_\_1)))\end{array}
\label{hyp:ehfdedpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(k10\_arytm\_3~X0~k12\_arytm\_3=\\
X0)\end{array}
\label{hyp:ehfdddpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
k10\_ordinal2~X0~X1=k1\_xboole\_0){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdhd}(X1=k1\_xboole\_0))))\end{array}
\label{hyp:ehcdgdpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1))){\unicdbdjdcd}(k8\_ordinal3~X0~X1=k10\_ordinal2~\\
X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
{{k12\_arytm\_3}={k1\_arytm\_3}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_arytm\_3)){\unicdbdjdcd}(m1\_subset\_1~(k9\_arytm\_3~X0~X1)~k5\_arytm\_3)\end{array}
\label{hyp:egehpflgjdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~k12\_arytm\_3){\unicdcdcdhd}((v3\_ordinal1~k12\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
k12\_arytm\_3~k5\_arytm\_3))\end{array}
\label{hyp:egehpflgbdcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_arytm\_3)){\unicdbdjdcd}(m1\_subset\_1~(k10\_arytm\_3~X0~X1)~k5\_arytm\_3)\end{array}
\label{hyp:egehpflgbdadpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_arytm\_3}={np\_\_1}}\label{hyp:egbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_arytm\_3)){\unicdbdjdcd}(k10\_arytm\_3~X0~X1=k10\_arytm\_3~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdadpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}((v3\_ordinal1~X0){\unicdbdjdcd}((\\
v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)))\end{array}
\label{hyp:dgdgbdpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehgdadpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdcdcdhd}(X0=k9\_arytm\_3~X1~X1))\end{array}$$
\end{theorem}
\end{document}
