\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\_functor3 (TMSHUApX3xYgRRi1YkGneXD6DgQ9zKFRdcZ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k8\_functor3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k4\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ l2\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_functor0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_functor2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v3\_altcat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_functor2~\\
X0~X1~X2~X2~(k1\_functor2~X0~X1~X2)~X3=k8\_altcat\_1~X1~(k3\_functor0~\\
X0~X1~X2~X3)))))\end{array}
\label{hyp:ehedpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_functor0~X3~X0~X1){\unicdbdjdcd}((r1\_functor2~X0~X1~\\
X2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor2~X4~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_functor2~\\
X5~X0~X1~X2~X3){\unicdbdjdcd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k2\_functor2~X0~X1~X2~X3~X4~X6=k2\_functor2~X0~X1~X2~X3~X5~X6)){\unicdbdjdcd}(r8\_pboole~\\
(u1\_struct\_0~X0)~X4~X5))))))))\end{array}
\label{hyp:ehddpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X1~X0){\unicdcdcdhd}\\
(m2\_functor0~X2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X1~X0){\unicdcdcdhd}(\\
m2\_functor0~X3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor3~X4~X1~X0~X2~X3){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}((r1\_functor3~\\
X1~X0~X2~X3){\unicdbdjdcd}(k2\_functor2~X1~X0~X3~X2~(k8\_functor3~X1~X0~X2~X3~X4)~X5=\\
k1\_altcat\_3~X0~(k3\_functor0~X1~X0~X2~X5)~(k3\_functor0~X1~X0~X3~X5)~\\
(k2\_functor2~X1~X0~X2~X3~X4~X5))))))))\end{array}
\label{hyp:ehddidpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}\\
((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}((r1\_functor3~X0~X1~X2~X3){\unicdbdjdcd}\\
(r1\_functor3~X0~X1~X3~X2))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}((m2\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~\\
X1)))){\unicdbdjdcd}(r1\_functor2~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfggfhogdgehpgchcd}
\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 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdcdcdhd}\\
((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)))){\unicdbdjdcd}(k4\_functor2~\\
X0~X1~X2=k1\_functor2~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggfhogdgehpgchcd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~\\
X0~X1)){\unicdcdcdhd}((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_functor2~X4~X0~X1~X2~X3){\unicdbdjdcd}(m1\_functor2~X4~X0~X1~X2~X3))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}\\
((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}(l2\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}\\
((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor3~\\
X4~X0~X1~X2~X3){\unicdbdjdcd}(m2\_functor2~X4~X0~X1~X2~X3))\end{array}
\label{hyp:egehpfngbdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(\\
l2\_altcat\_1~X1)))){\unicdcdcdhd}((m2\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~\\
X1)))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor2~X4~X0~X1~X2~X3){\unicdbdjdcd}((v1\_relat\_1~X4){\unicdcdcdhd}\\
((v4\_relat\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_partfun1~\\
X4~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpfngbdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_altcat\_1~X0){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (l2\_functor0~X2~X0~X1){\unicdbdjdcd}(l1\_functor0~X2~X0~X1))\end{array}
\label{hyp:egehpfmgcdpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_altcat\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_altcat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}\\
((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdcdcdhd}\\
(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~X2~X0~X1)){\unicdcdcdhd}(((v15\_functor0~\\
X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1)){\unicdcdcdhd}(m1\_functor3~X4~X0~X1~X2~X3))))){\unicdbdjdcd}\\
(m1\_functor3~(k8\_functor3~X0~X1~X2~X3~X4)~X0~X1~X3~X2)\end{array}
\label{hyp:egehpflgidpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}\\
(l2\_altcat\_1~X1))))){\unicdcdcdhd}(((v15\_functor0~X2~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
X2~X0~X1)){\unicdcdcdhd}(((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(m2\_functor0~X3~X0~X1)){\unicdcdcdhd}((\\
(v15\_functor0~X4~X0~X1){\unicdcdcdhd}(m2\_functor0~X4~X0~X1)){\unicdcdcdhd}((m2\_functor2~\\
X5~X0~X1~X2~X3){\unicdcdcdhd}(m2\_functor2~X6~X0~X1~X3~X4))))))){\unicdbdjdcd}(m2\_functor2~(\\
k5\_functor2~X0~X1~X2~X3~X4~X5~X6)~X0~X1~X2~X4)\end{array}
\label{hyp:egehpflgfdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdcdcdhd}((m2\_functor0~X2~\\
X0~X1){\unicdcdcdhd}((m2\_functor0~X3~X0~X1){\unicdcdcdhd}((m2\_functor0~X4~X0~X1){\unicdcdcdhd}((m1\_functor2~\\
X5~X0~X1~X2~X3){\unicdcdcdhd}(m1\_functor2~X6~X0~X1~X3~X4))))))){\unicdbdjdcd}(m1\_functor2~(\\
k3\_functor2~X0~X1~X2~X3~X4~X5~X6)~X0~X1~X2~X4)\end{array}
\label{hyp:egehpflgddpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_altcat\_1~X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_altcat\_1~X1)){\unicdcdcdhd}\\
((l1\_functor0~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k3\_functor0~X0~X1~X2~X3)~(u1\_struct\_0~X1))\end{array}
\label{hyp:egehpflgddpfggfhogdgehpgchad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(\\
l2\_altcat\_1~X0)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(\\
(v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdcdcdhd}((m2\_functor0~X2~X0~X1){\unicdcdcdhd}\\
((m2\_functor0~X3~X0~X1){\unicdcdcdhd}((m1\_functor2~X4~X0~X1~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(u1\_struct\_0~X0))))))){\unicdbdjdcd}(m1\_subset\_1~(k2\_functor2~X0~X1~X2~X3~\\
X4~X5)~(k1\_altcat\_1~X1~(k3\_functor0~X0~X1~X2~X5)~(k3\_functor0~X0~X1~\\
X3~X5)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1))){\unicdbdjdcd}(m1\_functor2~(k1\_functor2~X0~X1~X2)~X0~\\
X1~X2~X2)\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(\\
m2\_functor0~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v15\_functor0~X4~X0~X1){\unicdcdcdhd}(m2\_functor0~\\
X4~X0~X1)){\unicdbdjdcd}(((r2\_functor2~X0~X1~X2~X3){\unicdcdcdhd}(r2\_functor2~X0~X1~X3~X4)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_functor2~X5~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_functor2~\\
X6~X0~X1~X3~X4){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_functor2~X7~X0~X1~X2~X4){\unicdbdjdcd}((X7=k5\_functor2~\\
X0~X1~X2~X3~X4~X5~X6){\unicdbdjded}(r8\_pboole~(u1\_struct\_0~X0)~X7~(k3\_functor2~\\
X0~X1~X2~X3~X4~X5~X6)))))))))))\end{array}
\label{hyp:egidpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(\\
m2\_functor0~X3~X0~X1)){\unicdbdjdcd}((r1\_functor3~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
m2\_functor2~X4~X0~X1~X2~X3){\unicdbdjdcd}((m1\_functor3~X4~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(v3\_altcat\_3~(k2\_functor2~\\
X0~X1~X2~X3~X4~X5)~X1~(k3\_functor0~X0~X1~X2~X5)~(k3\_functor0~X0~X1~X3~X5)))))))))\end{array}
\label{hyp:egfdpfggfhogdgehpgchdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~\\
X1){\unicdcdcdhd}((v12\_altcat\_1~X1){\unicdcdcdhd}(l2\_altcat\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_functor0~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_functor0~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_functor0~\\
X4~X0~X1){\unicdbdjdcd}(((r1\_functor2~X0~X1~X2~X3){\unicdcdcdhd}(r1\_functor2~X0~X1~X3~X4)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_functor2~X5~X0~X1~X2~X3){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_functor2~\\
X6~X0~X1~X3~X4){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_functor2~X7~X0~X1~X2~X4){\unicdbdjdcd}((X7=k3\_functor2~\\
X0~X1~X2~X3~X4~X5~X6){\unicdbdjded}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k2\_functor2~X0~X1~X2~X4~X7~X8=k5\_altcat\_1~X1~(k3\_functor0~X0~X1~X2~\\
X8)~(k3\_functor0~X0~X1~X3~X8)~(k3\_functor0~X0~X1~X4~X8)~(k2\_functor2~\\
X0~X1~X2~X3~X5~X8)~(k2\_functor2~X0~X1~X3~X4~X6~X8))))))))))))\end{array}
\label{hyp:egfdpfggfhogdgehpgchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_altcat\_1~X0~X1~X2)){\unicdbdjdcd}((v3\_altcat\_3~\\
X3~X0~X1~X2){\unicdbdjded}((k5\_altcat\_1~X0~X2~X1~X2~(k1\_altcat\_3~X0~X1~X2~X3)~X3=\\
k8\_altcat\_1~X0~X2){\unicdcdcdhd}(k5\_altcat\_1~X0~X1~X2~X1~X3~(k1\_altcat\_3~X0~X1~\\
X2~X3)=k8\_altcat\_1~X0~X1))))))\end{array}
\label{hyp:egfdpfbgmgehdgbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(\\
m2\_functor0~X3~X0~X1)){\unicdbdjdcd}((r1\_functor3~X0~X1~X2~X3){\unicdbdjded}((r2\_functor2~\\
X0~X1~X2~X3){\unicdcdcdhd}((r1\_functor2~X0~X1~X3~X2){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_functor2~\\
X4~X0~X1~X2~X3){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(\\
v3\_altcat\_3~(k2\_functor2~X0~X1~X2~X3~X4~X5)~X1~(k3\_functor0~X0~X1~X2~\\
X5)~(k3\_functor0~X0~X1~X3~X5))))))))))\end{array}
\label{hyp:egedpfggfhogdgehpgchdd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfggfhogdgehpgchdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v11\_altcat\_1~X1){\unicdcdcdhd}((v12\_altcat\_1~\\
X1){\unicdcdcdhd}(l2\_altcat\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v15\_functor0~X2~X0~X1){\unicdcdcdhd}\\
(m2\_functor0~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v15\_functor0~X3~X0~X1){\unicdcdcdhd}(\\
m2\_functor0~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_functor3~X4~X0~X1~X2~X3){\unicdbdjdcd}\\
((r1\_functor3~X0~X1~X2~X3){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~X0)~(k5\_functor2~\\
X0~X1~X3~X2~X3~(k8\_functor3~X0~X1~X2~X3~X4)~X4)~(k4\_functor2~X0~X1~X3)))))))\end{array}$$
\end{theorem}
\end{document}
