\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{t20\_int\_7 (TMZBNEnnwqFZqT8FR52ZT4yXk2X6EnkGRYE)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_int\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ g3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_int\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_int\_7 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k8\_group\_1~X0~X1~X2=k6\_algstr\_0~\\
X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(g3\_algstr\_0~(k1\_int\_7~X0)~(k2\_int\_7~X0)))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(g3\_algstr\_0~(k1\_int\_7~\\
X0)~(k2\_int\_7~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k9\_int\_3~\\
X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X4=X2)){\unicdbdjdcd}(k8\_group\_1~(k9\_int\_3~X0)~X3~X4=k6\_algstr\_0~\\
(g3\_algstr\_0~(k1\_int\_7~X0)~(k2\_int\_7~X0))~X1~X2))))))\end{array}
\label{hyp:mgddddpfjgogehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k3\_int\_7~X0)){\unicdcdcdhd}((v2\_group\_1~(k3\_int\_7~X0)){\unicdcdcdhd}((v3\_group\_1~(k3\_int\_7~\\
X0)){\unicdcdcdhd}((v5\_group\_1~(k3\_int\_7~X0)){\unicdcdcdhd}(l3\_algstr\_0~(k3\_int\_7~X0))))))\end{array}
\label{hyp:egehpflgddpfjgogehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}(k3\_int\_7~X0=g3\_algstr\_0~\\
(k1\_int\_7~X0)~(k2\_int\_7~X0))\end{array}
\label{hyp:egedpfjgogehpfhd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfjgogehpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k3\_int\_7~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k3\_int\_7~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k9\_int\_3~\\
X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}(k8\_group\_1~(k3\_int\_7~X0)~X1~X2=k8\_group\_1~\\
(k9\_int\_3~X0)~X3~X4))))))\end{array}$$
\end{theorem}
\end{document}
