\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{t16\_algstr\_1 (TMGwNN8wTkw2ydHdCMUsuCCFAjteHZnGDKV)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_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 $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_algstr\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v31\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v17\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v30\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v32\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l3\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}((v6\_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}(\preoh (X1{\unicdcdgdad}k4\_struct\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~X1~X3{\unicdcdgdad}X2))))){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k4\_struct\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~X3~X1{\unicdcdgdad}X2)))))))\end{array}
\label{hyp:egjdpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l5\_algstr\_0~X0){\unicdbdjdcd}((v31\_algstr\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}k4\_struct\_0~X0){\unicdbdjdcd}(v17\_algstr\_0~\\
X1~X0))))\end{array}
\label{hyp:egddhdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l5\_algstr\_0~X0){\unicdbdjdcd}((v30\_algstr\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}k4\_struct\_0~X0){\unicdbdjdcd}(v16\_algstr\_0~\\
X1~X0))))\end{array}
\label{hyp:egddgdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v17\_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}((k6\_algstr\_0~\\
X0~X2~X1=k6\_algstr\_0~X0~X3~X1){\unicdbdjdcd}(X2=X3))))))\end{array}
\label{hyp:egcdbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v16\_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}((k6\_algstr\_0~\\
X0~X1~X2=k6\_algstr\_0~X0~X1~X3){\unicdbdjdcd}(X2=X3))))))\end{array}
\label{hyp:egcdadpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}((v7\_algstr\_1~\\
X0){\unicdbdjded}((v6\_algstr\_1~X0){\unicdcdcdhd}((v32\_algstr\_0~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~X1~(k4\_struct\_0~X0)=k4\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~\\
X0~(k4\_struct\_0~X0)~X1=k4\_struct\_0~X0))))))\end{array}
\label{hyp:egbdadpfbgmghgdhehchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l5\_algstr\_0~X0){\unicdbdjdcd}((v32\_algstr\_0~X0){\unicdbdjdcd}((v30\_algstr\_0~\\
X0){\unicdcdcdhd}(v31\_algstr\_0~X0)))\end{array}
\label{hyp:dgdgcdgdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l5\_algstr\_0~X0){\unicdbdjdcd}(((v30\_algstr\_0~X0){\unicdcdcdhd}(v31\_algstr\_0~\\
X0)){\unicdbdjdcd}(v32\_algstr\_0~X0))\end{array}
\label{hyp:dgdgcdfdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfbgmghgdhehchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}((v7\_algstr\_1~\\
X0){\unicdbdjded}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k4\_struct\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~X1~X3{\unicdcdgdad}X2))))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k4\_struct\_0~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~X3~X1{\unicdcdgdad}X2))))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~X0~X1~X2=k6\_algstr\_0~X0~X1~X3){\unicdbdjdcd}\\
((X1=k4\_struct\_0~X0){\unicdcdcdid}(X2=X3)))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~\\
X0~X2~X1=k6\_algstr\_0~X0~X3~X1){\unicdbdjdcd}((X1=k4\_struct\_0~X0){\unicdcdcdid}(X2=X3)))))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~\\
X0~X1~(k4\_struct\_0~X0)=k4\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~(k4\_struct\_0~X0)~X1=k4\_struct\_0~\\
X0))))))))\end{array}$$
\end{theorem}
\end{document}
