\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{t14\_bcialg\_3 (TMNn8PPDLLwMPXYfR2CLvzCFD9RdN28zgaP)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_bcialg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_bcialg\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_bcialg\_3 : {{\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 $ r1\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_bcialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}\\
(l2\_bcialg\_1~X0))))))){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}\\
((v4\_bcialg\_1~X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~\\
X0){\unicdcdcdhd}((v1\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_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}((r1\_bcialg\_1~X0~X1~X2){\unicdbdjdcd}(X1=k1\_bcialg\_1~X0~\\
X2~(k1\_bcialg\_1~X0~X2~X1))))))\end{array}
\label{hyp:ehfdpfcgdgjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_1~X0~\\
X1~(k4\_struct\_0~X0)=X1))\end{array}
\label{hyp:ehcdpfcgdgjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_bcialg\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_bcialg\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfcgdgjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_bcialg\_1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_bcialg\_1~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdpfcgdgjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)){\unicdbdjdcd}((v8\_bcialg\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_bcialg\_1~\\
X0~X1=k4\_struct\_0~X0)))\end{array}
\label{hyp:egidpfcgdgjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
((v5\_bcialg\_3~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_1~X0~\\
(k1\_bcialg\_1~X0~X1~(k1\_bcialg\_1~X0~X1~X2))~(k1\_bcialg\_1~X0~(k4\_struct\_0~\\
X0)~(k1\_bcialg\_1~X0~X1~X2))=k1\_bcialg\_1~X0~X2~(k1\_bcialg\_1~X0~X2~\\
X1)))))\end{array}
\label{hyp:egfdpfcgdgjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))){\unicdbdjdcd}\\
((v4\_bcialg\_3~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_bcialg\_1~\\
X0~X1~X2=k4\_struct\_0~X0){\unicdbdjdcd}(X1=k1\_bcialg\_1~X0~X2~(k1\_bcialg\_1~X0~\\
X2~X1))))))\end{array}
\label{hyp:egedpfcgdgjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_bcialg\_1~X0~X1=k1\_bcialg\_1~\\
X0~(k4\_struct\_0~X0)~X1))\end{array}
\label{hyp:egcdpfcgdgjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)){\unicdbdjdcd}((v1\_bcialg\_3~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_bcialg\_1~X0~X1~(k1\_bcialg\_1~\\
X0~X1~X2)=k1\_bcialg\_1~X0~X2~(k1\_bcialg\_1~X0~X2~X1)))))\end{array}
\label{hyp:egbdpfcgdgjgbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_bcialg\_1~X0~X1~X2){\unicdbdjded}(k1\_bcialg\_1~X0~X1~X2=\\
k4\_struct\_0~X0))))\end{array}
\label{hyp:egbdbdpfcgdgjgbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfcgdgjgbgmghgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~\\
X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v8\_bcialg\_1~X0){\unicdcdcdhd}\\
((v1\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0)))))))){\unicdbdjdcd}(((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~X0){\unicdcdcdhd}((v5\_bcialg\_1~X0){\unicdcdcdhd}\\
((v7\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0))))))){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_bcialg\_1~X0){\unicdcdcdhd}((v4\_bcialg\_1~X0){\unicdcdcdhd}((v5\_bcialg\_1~\\
X0){\unicdcdcdhd}((v7\_bcialg\_1~X0){\unicdcdcdhd}((v5\_bcialg\_3~X0){\unicdcdcdhd}(l2\_bcialg\_1~X0))))))))\end{array}$$
\end{theorem}
\end{document}
