\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{t49\_stacks\_1 (TMayHjSmxhZh2oCTMGUrWv1ZK7wvVJe5bcm)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_stacks\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_stacks\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_stacks\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}((v7\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0))))))))){\unicdbdjdcd}\\
({\unicdcdaddd} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k9\_stacks\_1~\\
X0~X2)){\unicdcdcdhd}(r3\_stacks\_1~X0~(k8\_stacks\_1~(u1\_struct\_0~X0))~(k6\_partfun1~\\
(u1\_struct\_0~X0))~X1)))\end{array}
\label{hyp:ehedidpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_partfun1}~{X0}}={{k4\_relat\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}((v1\_stacks\_1~(k8\_stacks\_1~\\
X0)){\unicdcdcdhd}(v6\_stacks\_1~(k8\_stacks\_1~X0)))))\end{array}
\label{hyp:ggdgidpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}((v1\_stacks\_1~(k8\_stacks\_1~\\
X0)){\unicdcdcdhd}(v5\_stacks\_1~(k8\_stacks\_1~X0)))))\end{array}
\label{hyp:ggdghdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}((v1\_stacks\_1~(k8\_stacks\_1~\\
X0)){\unicdcdcdhd}(v4\_stacks\_1~(k8\_stacks\_1~X0)))))\end{array}
\label{hyp:ggdggdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}((v1\_stacks\_1~(k8\_stacks\_1~\\
X0)){\unicdcdcdhd}(v3\_stacks\_1~(k8\_stacks\_1~X0)))))\end{array}
\label{hyp:ggdgfdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}((v1\_stacks\_1~(k8\_stacks\_1~\\
X0)){\unicdcdcdhd}(v2\_stacks\_1~(k8\_stacks\_1~X0)))))\end{array}
\label{hyp:ggdgedpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}})}{\unicdcdcdhd}{({{v1\_funct\_1}~{({{k4\_relat\_1}~{X0}})}})}}}\label{hyp:ggdgddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_stacks\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~(k8\_stacks\_1~X0)){\unicdcdcdhd}((v1\_stacks\_1~(k8\_stacks\_1~\\
X0)){\unicdcdcdhd}(l1\_stacks\_1~(k8\_stacks\_1~X0)))))\end{array}
\label{hyp:egehpflgidpfdhehbgdglgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_stacks\_1~X1){\unicdcdcdhd}((v3\_stacks\_1~X1){\unicdcdcdhd}\\
((v4\_stacks\_1~X1){\unicdcdcdhd}((v5\_stacks\_1~X1){\unicdcdcdhd}((v6\_stacks\_1~X1){\unicdcdcdhd}(l1\_stacks\_1~\\
X1)))))))){\unicdbdjdcd}((r4\_stacks\_1~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}\\
(v1\_funct\_1~X2)){\unicdcdcdhd}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}(v1\_funct\_1~X3)){\unicdcdcdhd}\\
(r3\_stacks\_1~X0~X1~X2~X3)))))\end{array}
\label{hyp:egcdcdpfdhehbgdglgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfdhehbgdglgdhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_stacks\_1~\\
X0){\unicdcdcdhd}((v3\_stacks\_1~X0){\unicdcdcdhd}((v4\_stacks\_1~X0){\unicdcdcdhd}((v5\_stacks\_1~X0){\unicdcdcdhd}\\
((v6\_stacks\_1~X0){\unicdcdcdhd}((v7\_stacks\_1~X0){\unicdcdcdhd}(l1\_stacks\_1~X0))))))))){\unicdbdjdcd}\\
(r4\_stacks\_1~X0~(k8\_stacks\_1~(u1\_struct\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
