\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{t15\_msafree3 (TMREd8QxvE2ud6Qr9mFSWAipjWZN2p4of6H)}
\maketitle
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_dtconstr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r6\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_trees\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
((r2\_pboole~X0~X1~X2){\unicdbdjdcd}(r6\_pboole~X0~(k3\_pboole~X0~X1~X2)~X1)))\end{array}
\label{hyp:ehcdddpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_dtconstr~X2~(u1\_struct\_0~(k5\_msafree~\\
X0~X1))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~X1)))~(k1\_msaterm~\\
X0~X1)){\unicdbdjdcd}(r2\_pboole~(u1\_struct\_0~X0)~(k2\_msafree3~X0~X2)~X1)))\end{array}
\label{hyp:ehbdedpfngdhbgggchfgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~\\
X2~X0)))))){\unicdbdjdcd}((r8\_pboole~X0~X1~X2){\unicdbdjded}(X1=X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchidpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
((r6\_pboole~X0~X1~X2){\unicdbdjded}(X1=X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchgdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k5\_msafree~X0~X1)){\unicdcdcdhd}(v1\_lang1~(k5\_msafree~X0~X1)))\end{array}
\label{hyp:ggdgfdpfngdhbgggchfgfg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0))))))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_msaterm~X0~X1))\end{array}
\label{hyp:ggdgbdpfngdhbgehfgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_trees\_3~X1~X0){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~X1))\end{array}
\label{hyp:egehpfngbdpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_trees\_3~X1~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_dtconstr~X3~X0~X1~X2){\unicdbdjdcd}(m1\_subset\_1~\\
X3~X1))\end{array}
\label{hyp:egehpfngbdpfegehdgpgogdhehch}
\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\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_lang1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({{{m1\_trees\_3}~{({{k5\_trees\_3}~{X0}})}}~{X0}})}}}\label{hyp:egehpflgfdpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
(l1\_lang1~(k5\_msafree~X0~X1))\end{array}
\label{hyp:egehpflgfdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k3\_pboole~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k3\_pboole~X0~\\
X1~X2)~X0){\unicdcdcdhd}((v1\_funct\_1~(k3\_pboole~X0~X1~X2)){\unicdcdcdhd}(v1\_partfun1~(k3\_pboole~\\
X0~X1~X2)~X0))))\end{array}
\label{hyp:egehpflgddpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_msualg\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(v1\_relat\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k2\_msafree3~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~\\
(k2\_msafree3~X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(k2\_msafree3~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k2\_msafree3~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpflgcdpfngdhbgggchfgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_msaterm~X0~X1)~(k1\_zfmisc\_1~(k5\_trees\_3~(u1\_struct\_0~\\
(k5\_msafree~X0~X1)))))\end{array}
\label{hyp:egehpflgbdpfngdhbgehfgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_dtconstr~X2~(u1\_struct\_0~(k5\_msafree~\\
X0~X1))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~X1)))~(k1\_msaterm~\\
X0~X1)){\unicdbdjdcd}(k4\_msafree3~X0~X1~X2=k2\_msafree3~X0~X2)))\end{array}
\label{hyp:egedpfngdhbgggchfgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~\\
X1~(u1\_struct\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(v1\_relat\_1~\\
X2)){\unicdbdjdcd}(k3\_msafree3~X0~X1~X2=k3\_pboole~(u1\_struct\_0~X0)~X1~(k2\_msafree3~\\
X0~X2))))\end{array}
\label{hyp:egddpfngdhbgggchfgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
(k3\_pboole~X0~X1~X2=k3\_pboole~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v3\_trees\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdbdjdcd}(v3\_trees\_2~X1))\end{array}
\label{hyp:dgdgjdpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_trees\_3}~{X0}})}{\unicdbdjdcd}{({{v4\_funct\_1}~{X0}})}}}\label{hyp:dgdgidpfehchfgfgdhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)))\end{array}
\label{hyp:dgdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~\\
X0))))\end{array}
\label{hyp:dgdgedpfngdhbgggchfgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}(((v2\_struct\_0~X0){\unicdcdcdhd}(v1\_instalg1~\\
X0)){\unicdbdjdcd}(v11\_struct\_0~X0))\end{array}
\label{hyp:dgdgedpfjgogdhehbgmghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{X0}})}}}\label{hyp:dgdgbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_funct\_1}~{X0}})}}}\label{hyp:dgdgbdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_trees\_3~X1~X0){\unicdbdjdcd}\\
(v3\_trees\_3~X1))\end{array}
\label{hyp:dgdgbdadpfehchfgfgdhpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfngdhbgggchfgfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_dtconstr~X2~(u1\_struct\_0~(k5\_msafree~\\
X0~X1))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X0~X1)))~(k1\_msaterm~\\
X0~X1)){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~X0)~(k4\_msafree3~X0~X1~X2)~(k3\_msafree3~\\
X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
