\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{t7\_msafree3 (TMWjwo4v5j35yYYmTKbccqRPkXWi1rovitE)}
\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\_subset\_1 : {{\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 $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ k8\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_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))))){\unicdcdcdhd}(m2\_pboole~\\
X2~(u4\_struct\_0~X0)~(k3\_relat\_1~(u1\_msualg\_1~X0)~(k6\_finseq\_2~\\
(u1\_struct\_0~X0)~X1))~(k3\_relat\_1~(u2\_msualg\_1~X0)~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g3\_msualg\_1~X0~X1~X2=g3\_msualg\_1~X3~X4~X5){\unicdbdjdcd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgddpfngdhfhbgmghgpfbd}
\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}((v3\_msualg\_1~(k11\_msafree~X0~X1)~X0){\unicdcdcdhd}(v4\_msualg\_1~\\
(k11\_msafree~X0~X1)~X0))\end{array}
\label{hyp:ggdgjdpfngdhbgggchfgfg}
\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}((v1\_relat\_1~(k8\_msafree~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k8\_msafree~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(k8\_msafree~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(k8\_msafree~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpflgidpfngdhbgggchfgfg}
\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}(l3\_msualg\_1~(k11\_msafree~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdbdpfngdhbgggchfgfg}
\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}(m2\_pboole~(k10\_msafree~X0~X1)~(u4\_struct\_0~X0)~(k3\_relat\_1~\\
(u1\_msualg\_1~X0)~(k6\_finseq\_2~(u1\_struct\_0~X0)~(k8\_msafree~X0~\\
X1)))~(k3\_relat\_1~(u2\_msualg\_1~X0)~(k8\_msafree~X0~X1)))\end{array}
\label{hyp:egehpflgbdadpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((X3=k7\_msaterm~\\
X0~X1~X2){\unicdbdjded}(X2 \in k7\_msafree~X0~X1~X3)))))\end{array}
\label{hyp:egfdpfngdhbgehfgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~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}(k11\_msafree~X0~X1=g3\_msualg\_1~X0~(k8\_msafree~X0~X1)~\\
(k10\_msafree~X0~X1)))\end{array}
\label{hyp:egbdedpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~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 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
((X2=k8\_msafree~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k7\_msafree~X0~X1~X3)))))\end{array}
\label{hyp:egbdbdpfngdhbgggchfgfg}
\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 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdcdcdhd}\\
(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}((v3\_msualg\_1~X1~X0){\unicdbdjdcd}(X1=g3\_msualg\_1~X0~\\
(u3\_msualg\_1~X0~X1)~(u4\_msualg\_1~X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddpfngdhfhbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfngdhbgggchfgfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_dtconstr~X3~(u1\_struct\_0~(k5\_msafree~X0~X1))~(k5\_trees\_3~(\\
u1\_struct\_0~(k5\_msafree~X0~X1)))~(k1\_msaterm~X0~X1)){\unicdbdjdcd}((X3 \in k1\_funct\_1~\\
(u3\_msualg\_1~X0~(k11\_msafree~X0~X1))~X2){\unicdbdjded}(k7\_msaterm~X0~X1~X3=X2)))))\end{array}$$
\end{theorem}
\end{document}
