\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{t15\_grcat\_1 (TMQWPx43enJ7whRfBVRWDSDrqmgFqFuUAnY)}
\maketitle
Let $ v1\_grcat\_1 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ g1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v13\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_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 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 .  (m1\_grcat\_1~X2~X0~X1){\unicdbdjdcd}(\\
{\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdcdcdhd}((g1\_grcat\_1~(u1\_grcat\_1~\\
X2)~(u2\_grcat\_1~X2)~(u3\_grcat\_1~X2)=g1\_grcat\_1~X0~X1~X3){\unicdcdcdhd}(v13\_vectsp\_1~\\
X3~X0~X1)))))\end{array}
\label{hyp:ehbdcdpfhgchdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_grcat\_1~X0){\unicdbdjdcd}((v1\_grcat\_1~X0){\unicdbdjdcd}(X0=g1\_grcat\_1~\\
(u1\_grcat\_1~X0)~(u2\_grcat\_1~X0)~(u3\_grcat\_1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfhgchdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfhgchdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_grcat\_1~X0){\unicdcdcdhd}((v2\_grcat\_1~X0){\unicdcdcdhd}(l1\_grcat\_1~X0))){\unicdbdjdcd}\\
({\unicdcdaddd} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}(l2\_algstr\_0~X1))))){\unicdcdcdhd}({\unicdcdaddd} X2 .  ((\preoh \\
v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~\\
X2){\unicdcdcdhd}(l2\_algstr\_0~X2))))){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)))))){\unicdcdcdhd}((m1\_grcat\_1~\\
X0~X1~X2){\unicdcdcdhd}((X0=g1\_grcat\_1~X1~X2~X3){\unicdcdcdhd}(v13\_vectsp\_1~X3~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
