\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{t39\_osafree (TMbPszTGqtNVYnLXVKAwmZrGdekgrVL26ZM)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_osalg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_osalg\_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 $ v2\_osafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_osafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_osafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k24\_osafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_osafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v12\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v13\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\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}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_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}(v1\_osafree~(k24\_osafree~X0~X1)~X0~(k16\_osafree~X0~X1)))\end{array}
\label{hyp:ehddidpfpgdhbgggchfgfg}
\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}\\
((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_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}(m1\_osafree~(k24\_osafree~X0~X1)~X0~(k16\_osafree~X0~X1))\end{array}
\label{hyp:egehpflgcdedpfpgdhbgggchfgfg}
\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}\\
((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_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}((v3\_msualg\_1~(k16\_osafree~X0~X1)~X0){\unicdcdcdhd}((v4\_msualg\_1~\\
(k16\_osafree~X0~X1)~X0){\unicdcdcdhd}((v12\_osalg\_1~(k16\_osafree~X0~X1)~X0){\unicdcdcdhd}\\
((v13\_osalg\_1~(k16\_osafree~X0~X1)~X0){\unicdcdcdhd}(l3\_msualg\_1~(k16\_osafree~\\
X0~X1)~X0)))))\end{array}
\label{hyp:egehpflgbdgdpfpgdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}((v13\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}((v2\_osafree~\\
X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_osafree~X2~X0~X1){\unicdcdcdhd}(v1\_osafree~X2~X0~X1))))\end{array}
\label{hyp:egddpfpgdhbgggchfgfg}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfpgdhbgggchfgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}(v2\_osafree~(k16\_osafree~X0~X1)~X0))\end{array}$$
\end{theorem}
\end{document}
