\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{t25\_pencil\_2 (TMTbjMbgqaGbQWYopQCErUEQG5h2AkMrsrh)}
\maketitle
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 $ v15\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_pencil\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_pencil\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_t\_0topsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_struct\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X1))){\unicdbdjdcd}(((k2\_relset\_1~(u1\_struct\_0~X1)~X2=k2\_struct\_0~\\
X1){\unicdcdcdhd}(v2\_funct\_1~X2)){\unicdbdjdcd}(k8\_relset\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~X2~X3=k7\_relset\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X0)~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~X3)))))\end{array}
\label{hyp:ehfdfdpfehpgahdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v15\_pencil\_1~\\
X1))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(v10\_pencil\_1~(k2\_pencil\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pencil\_2~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~(k5\_pencil\_1~X0~X1))~(u1\_struct\_0~\\
(k5\_pencil\_1~X0~X1))){\unicdcdcdhd}((v1\_pencil\_2~X3~(k5\_pencil\_1~X0~X1)~(k5\_pencil\_1~\\
X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k5\_pencil\_1~X0~X1))~(u1\_struct\_0~(k5\_pencil\_1~X0~X1)))))))){\unicdbdjdcd}\\
(m1\_pencil\_2~(k7\_relset\_1~(u1\_struct\_0~(k5\_pencil\_1~X0~X1))~(\\
u1\_struct\_0~(k5\_pencil\_1~X0~X1))~X3~X2)~X0~X1)))))\end{array}
\label{hyp:ehcdedpfahfgogdgjgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_pencil\_2~X1~X0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))){\unicdbdjdcd}((v1\_funct\_1~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1)){\unicdcdcdhd}((v1\_funct\_2~(k2\_tops\_2~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_pencil\_2~(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X1)~X0~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0))))))))\end{array}
\label{hyp:ehbdddpfahfgogdgjgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\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}(v15\_pencil\_1~\\
X1)))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_pencil\_1~X0~X1)){\unicdcdcdhd}((\preoh v3\_pencil\_1~\\
(k5\_pencil\_1~X0~X1)){\unicdcdcdhd}((\preoh v4\_pencil\_1~(k5\_pencil\_1~X0~X1)){\unicdcdcdhd}((v5\_pencil\_1~\\
(k5\_pencil\_1~X0~X1)){\unicdcdcdhd}(v6\_pencil\_1~(k5\_pencil\_1~X0~X1))))))\end{array}
\label{hyp:ggdgfdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\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}((v11\_pencil\_1~\\
X1){\unicdcdcdhd}(v14\_pencil\_1~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pencil\_2~X2~X0~X1){\unicdbdjdcd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k5\_pencil\_1~X0~X1)))))\end{array}
\label{hyp:egehpfngbdpfahfgogdgjgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\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}((v4\_waybel\_3~\\
X1){\unicdcdcdhd}(v11\_pencil\_1~X1))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_pencil\_1~X0~\\
X1)){\unicdcdcdhd}(l1\_pre\_topc~(k5\_pencil\_1~X0~X1)))\end{array}
\label{hyp:egehpflgfdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k2\_tops\_2~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k2\_tops\_2~X0~\\
X1~X2)~X1~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_tops\_2~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0)))))\end{array}
\label{hyp:egehpflgcdpfehpgahdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_pre\_topc~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((v1\_pencil\_2~X2~X0~X1){\unicdbdjded}((v3\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_t\_0topsp~X2~X0~X1){\unicdcdcdhd}\\
((v3\_funct\_2~(k2\_tops\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}(v1\_t\_0topsp~(k2\_tops\_2~(\\
u1\_struct\_0~X0)~(u1\_struct\_0~X1)~X2)~X1~X0)))))))\end{array}
\label{hyp:egedpfahfgogdgjgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_struct\_0}~{X0}}={{u1\_struct\_0}~{X0}}})}}}\label{hyp:egddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
(v2\_funct\_2~X1~X0){\unicdbdjded}(k2\_relset\_1~X0~X1=X0))\end{array}
\label{hyp:egddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v11\_pencil\_1~\\
X0){\unicdcdcdhd}(v15\_pencil\_1~X0)))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((v11\_pencil\_1~X0){\unicdcdcdhd}(v14\_pencil\_1~X0))))\end{array}
\label{hyp:dgdgfdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(((v1\_funct\_1~X2){\unicdcdcdhd}(v3\_funct\_2~X2~X0~X1)){\unicdbdjdcd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}(v2\_funct\_2~X2~X1))))\end{array}
\label{hyp:dgdgfdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v15\_pencil\_1~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v4\_waybel\_3~X0){\unicdcdcdhd}\\
(v11\_pencil\_1~X0))))\end{array}
\label{hyp:dgdgddpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfahfgogdgjgmgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v15\_pencil\_1~\\
X1))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(v10\_pencil\_1~(k2\_pencil\_1~\\
X0~X1~X2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pencil\_2~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~(k5\_pencil\_1~X0~X1))~(u1\_struct\_0~\\
(k5\_pencil\_1~X0~X1))){\unicdcdcdhd}((v1\_pencil\_2~X3~(k5\_pencil\_1~X0~X1)~(k5\_pencil\_1~\\
X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k5\_pencil\_1~X0~X1))~(u1\_struct\_0~(k5\_pencil\_1~X0~X1)))))))){\unicdbdjdcd}\\
(m1\_pencil\_2~(k8\_relset\_1~(u1\_struct\_0~(k5\_pencil\_1~X0~X1))~(\\
u1\_struct\_0~(k5\_pencil\_1~X0~X1))~X3~X2)~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
