\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{t19\_ringcat1 (TMJmrrE7jQioHTXDDzHMmEuteCXqBH8NwC7)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ringcat1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_ringcat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_ringcat1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_ringcat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_ringcat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_ringcat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_ringcat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_ringcat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_ringcat1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ringcat1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_ringcat1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ringcat1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ringcat1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_ringcat1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_ringcat1~X0){\unicdcdcdhd}((v3\_ringcat1~X0){\unicdcdcdhd}(l1\_ringcat1~\\
X0))){\unicdbdjdcd}((m1\_ringcat1~X0~(k1\_ringcat1~X0)~(k2\_ringcat1~X0)){\unicdcdcdhd}(r1\_ringcat1~\\
(k1\_ringcat1~X0)~(k2\_ringcat1~X0)))\end{array}
\label{hyp:ehddpfchjgoghgdgbgehbd}
\end{equation}
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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v5\_ringcat1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_ringcat1~X1~X0){\unicdbdjded}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngddpfchjgoghgdgbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_ringcat1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k10\_ringcat1~X0))){\unicdbdjdcd}(k12\_ringcat1~X0~X1=k2\_ringcat1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfchjgoghgdgbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_ringcat1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k10\_ringcat1~X0))){\unicdbdjdcd}(k11\_ringcat1~X0~X1=k1\_ringcat1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfchjgoghgdgbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_ringcat1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k10\_ringcat1~X0))){\unicdbdjdcd}(m2\_ringcat1~(k12\_ringcat1~\\
X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdcdpfchjgoghgdgbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_ringcat1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k10\_ringcat1~X0))){\unicdbdjdcd}(m2\_ringcat1~(k11\_ringcat1~\\
X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdbdpfchjgoghgdgbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_ringcat1~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k10\_ringcat1~X0)){\unicdcdcdhd}(v5\_ringcat1~(k10\_ringcat1~X0)))\end{array}
\label{hyp:egehpflgbdadpfchjgoghgdgbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v5\_ringcat1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (X1 \in X0){\unicdbdjdcd}((v2\_ringcat1~\\
X1){\unicdcdcdhd}((v3\_ringcat1~X1){\unicdcdcdhd}(l1\_ringcat1~X1))))\end{array}
\label{hyp:egbdcdpfchjgoghgdgbgehbd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfchjgoghgdgbgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_ringcat1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_ringcat1~X1~(k10\_ringcat1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_ringcat1~\\
X2~(k10\_ringcat1~X0)){\unicdbdjdcd}(\preoh (k11\_ringcat1~X0~X1=k12\_ringcat1~X0~X2){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m2\_ringcat1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_ringcat1~X4~X0){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_ringcat1~X5~X0){\unicdbdjdcd}(\preoh (r1\_ringcat1~X3~X4){\unicdcdcdhd}((r1\_ringcat1~\\
X4~X5){\unicdcdcdhd}((m1\_ringcat1~X1~X4~X5){\unicdcdcdhd}(m1\_ringcat1~X2~X3~X4))))))))))\end{array}$$
\end{theorem}
\end{document}
