\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{t31\_grcat\_1 (TMKJfuqRogHsTTe3JYPqipK6rLFJjMePWDx)}
\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 $ 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\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_grcat\_1 : {{\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 $ v4\_grcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_grcat\_1~X0){\unicdcdcdhd}(l1\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X1 .  ((\\
\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}({\unicdcdaddd} X2 .  ((\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~X0~X1~X2)))\end{array}
\label{hyp:ehbdedpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_grcat\_1~X1~X0){\unicdbdjded}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k18\_grcat\_1~X0))){\unicdbdjdcd}(k20\_grcat\_1~X0~X1=k8\_grcat\_1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdadpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k18\_grcat\_1~X0))){\unicdbdjdcd}(k19\_grcat\_1~X0~X1=k7\_grcat\_1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdjdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_grcat\_1~X1~X0){\unicdbdjdcd}((v2\_grcat\_1~X1){\unicdcdcdhd}(l1\_grcat\_1~X1)))\end{array}
\label{hyp:egehpfngddpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_grcat\_1~X2~X0~X1){\unicdbdjdcd}\\
((v2\_grcat\_1~X2){\unicdcdcdhd}(l1\_grcat\_1~X2)))\end{array}
\label{hyp:egehpfngbdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k18\_grcat\_1~X0))){\unicdbdjdcd}((v8\_algstr\_0~(k20\_grcat\_1~\\
X0~X1)){\unicdcdcdhd}(m2\_grcat\_1~(k20\_grcat\_1~X0~X1)~X0))\end{array}
\label{hyp:egehpflgcdadpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k18\_grcat\_1~X0))){\unicdbdjdcd}((v8\_algstr\_0~(k19\_grcat\_1~\\
X0~X1)){\unicdcdcdhd}(m2\_grcat\_1~(k19\_grcat\_1~X0~X1)~X0))\end{array}
\label{hyp:egehpflgbdjdpfhgchdgbgehpfbd}
\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 .  ((\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))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\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))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_grcat\_1~X2){\unicdcdcdhd}(l1\_grcat\_1~\\
X2)){\unicdbdjdcd}((m1\_grcat\_1~X2~X0~X1){\unicdbdjded}((k7\_grcat\_1~X2=X0){\unicdcdcdhd}(k8\_grcat\_1~\\
X2=X1)))))\end{array}
\label{hyp:egbdedpfhgchdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m3\_grcat\_1~X1~(k18\_grcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_grcat\_1~X2~(\\
k18\_grcat\_1~X0)){\unicdbdjdcd}(\preoh (k19\_grcat\_1~X0~X1=k20\_grcat\_1~X0~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((v8\_algstr\_0~X3){\unicdcdcdhd}(m2\_grcat\_1~X3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v8\_algstr\_0~\\
X4){\unicdcdcdhd}(m2\_grcat\_1~X4~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v8\_algstr\_0~X5){\unicdcdcdhd}(m2\_grcat\_1~\\
X5~X0)){\unicdbdjdcd}(\preoh (m1\_grcat\_1~X1~X4~X5){\unicdcdcdhd}(m1\_grcat\_1~X2~X3~X4))))))))\end{array}$$
\end{theorem}
\end{document}
