\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{t32\_grcat\_1 (TMWX3RQpnb688CkrNbiyXTiFzt1npDXRuDT)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ v4\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_grcat\_1~X1~(k18\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(\\
k18\_grcat\_1~X0)){\unicdbdjdcd}(\preoh (k19\_grcat\_1~X0~X1=k20\_grcat\_1~X0~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((v8\_algstr\_0~X3){\unicdcdcdhd}(m2\_grcat\_1~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v8\_algstr\_0~\\
X4){\unicdcdcdhd}(m2\_grcat\_1~X4~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v8\_algstr\_0~X5){\unicdcdcdhd}(m2\_grcat\_1~\\
X5~X0)){\unicdbdjdcd}(\preoh (m1\_grcat\_1~X1~X4~X5){\unicdcdcdhd}(m1\_grcat\_1~X2~X3~X4))))))))\end{array}
\label{hyp:ehddbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
(l2\_algstr\_0~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}\\
((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))){\unicdcdcdhd}(\\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((\\
v4\_rlvect\_1~X2){\unicdcdcdhd}(l2\_algstr\_0~X2))))){\unicdcdcdhd}((m1\_grcat\_1~X3~X1~X2){\unicdcdcdhd}\\
(m1\_grcat\_1~X4~X0~X1))))){\unicdbdjdcd}(k14\_grcat\_1~X0~X1~X2~X3~X4=k13\_grcat\_1~\\
X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_grcat\_1~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))))\end{array}
\label{hyp:egehpfngcdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k18\_grcat\_1~X0)){\unicdcdcdhd}(v4\_grcat\_1~(k18\_grcat\_1~X0)))\end{array}
\label{hyp:egehpflgbdidpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
(l2\_algstr\_0~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}\\
((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))){\unicdcdcdhd}(\\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((\\
v4\_rlvect\_1~X2){\unicdcdcdhd}(l2\_algstr\_0~X2))))){\unicdcdcdhd}((m1\_grcat\_1~X3~X1~X2){\unicdcdcdhd}\\
(m1\_grcat\_1~X4~X0~X1))))){\unicdbdjdcd}((v1\_grcat\_1~(k14\_grcat\_1~X0~X1~X2~X3~\\
X4)){\unicdcdcdhd}(m1\_grcat\_1~(k14\_grcat\_1~X0~X1~X2~X3~X4)~X0~X2))\end{array}
\label{hyp:egehpflgbdedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v4\_grcat\_1~X1)){\unicdbdjdcd}((X1=k18\_grcat\_1~X0){\unicdbdjded}(\\
{\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v8\_algstr\_0~X3){\unicdcdcdhd}(m2\_grcat\_1~\\
X3~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  ((v8\_algstr\_0~X4){\unicdcdcdhd}(m2\_grcat\_1~X4~X0)){\unicdcdcdhd}((\\
v1\_grcat\_1~X2){\unicdcdcdhd}(m1\_grcat\_1~X2~X3~X4)))))))\end{array}
\label{hyp:egcdfdpfhgchdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_grcat\_1~X1~(k18\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(\\
k18\_grcat\_1~X0)){\unicdbdjdcd}((k19\_grcat\_1~X0~X1=k20\_grcat\_1~X0~X2){\unicdbdjdcd}(k13\_grcat\_1~\\
X1~X2 \in k18\_grcat\_1~X0))))\end{array}$$
\end{theorem}
\end{document}
