\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{t6\_algstr\_1 (TMRWmxnGztQAq6kjBGas6y8NFKiTJTKmQBC)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_algstr\_1 : {{\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 $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_algstr\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_algstr\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v6\_algstr\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v3\_algstr\_0~X1~X0)))\end{array}
\label{hyp:eghdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v5\_algstr\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v2\_algstr\_0~X1~X0)))\end{array}
\label{hyp:eggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}((v3\_algstr\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(k1\_algstr\_0~X0~X1~X3=X2)))))\end{array}
\label{hyp:egedpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v3\_algstr\_0~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_algstr\_0~\\
X0~X2~X1=k1\_algstr\_0~X0~X3~X1){\unicdbdjdcd}(X2=X3))))))\end{array}
\label{hyp:egedpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}((v2\_algstr\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(k1\_algstr\_0~X0~X3~X1=X2)))))\end{array}
\label{hyp:egddpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v2\_algstr\_0~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_algstr\_0~\\
X0~X1~X2=k1\_algstr\_0~X0~X1~X3){\unicdbdjdcd}(X2=X3))))))\end{array}
\label{hyp:egddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_algstr\_0~\\
X0){\unicdcdcdhd}((v6\_algstr\_0~X0){\unicdcdcdhd}((v2\_algstr\_1~X0){\unicdcdcdhd}(v3\_algstr\_1~X0))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v4\_algstr\_1~X0)))\end{array}
\label{hyp:dgdgcdpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v4\_algstr\_1~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v5\_algstr\_0~X0){\unicdcdcdhd}((v6\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_algstr\_1~X0){\unicdcdcdhd}(v3\_algstr\_1~X0))))))\end{array}
\label{hyp:dgdgbdpfbgmghgdhehchpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfbgmghgdhehchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}((v4\_algstr\_1~\\
X0){\unicdbdjded}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(k1\_algstr\_0~X0~X1~X3=X2)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(k1\_algstr\_0~X0~X3~X1=X2)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_algstr\_0~X0~X1~X2=k1\_algstr\_0~\\
X0~X1~X3){\unicdbdjdcd}(X2=X3))))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_algstr\_0~X0~X2~X1=k1\_algstr\_0~\\
X0~X3~X1){\unicdbdjdcd}(X2=X3)))))))))\end{array}$$
\end{theorem}
\end{document}
