\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{t27\_pencil\_1 (TMXYpcUC3UMQSePJHdqZafxvphfv2eqzcJg)}
\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 $ v13\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v16\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
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)))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_zfmisc\_1~X3){\unicdbdjdcd}\\
(\preoh v13\_pencil\_1~(k2\_funct\_7~X1~X2~X3)))))\end{array}
\label{hyp:ehjdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (X2{\unicdcdgdad}X3){\unicdbdjdcd}(k1\_funct\_1~(k2\_funct\_7~X0~X2~X1)~X3=k1\_funct\_1~\\
X0~X3))\end{array}
\label{hyp:ehddcdpfggfhogdgehpfhd}
\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}((\preoh \\
v13\_pencil\_1~X1){\unicdcdcdhd}(v16\_pencil\_1~X1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X0){\unicdbdjdcd}((X2{\unicdcdgdad}k3\_pencil\_1~X0~X1){\unicdbdjdcd}(v3\_card\_1~(k1\_funct\_1~X1~X2)~np\_\_1))))\end{array}
\label{hyp:ehbdcdpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X1){\unicdcdcdhd}\\
((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k2\_funct\_7~X1~X2~X3)){\unicdcdcdhd}((v4\_relat\_1~(k2\_funct\_7~\\
X1~X2~X3)~X0){\unicdcdcdhd}((v1\_funct\_1~(k2\_funct\_7~X1~X2~X3)){\unicdcdcdhd}(v1\_partfun1~\\
(k2\_funct\_7~X1~X2~X3)~X0))))\end{array}
\label{hyp:ggdgddpfahchfgpfahpgmgjh}
\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}((\preoh \\
v13\_pencil\_1~X1){\unicdcdcdhd}(v16\_pencil\_1~X1~X0))))))){\unicdbdjdcd}(m1\_subset\_1~(k3\_pencil\_1~\\
X0~X1)~X0)\end{array}
\label{hyp:egehpflgddpfahfgogdgjgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~\\
X0)){\unicdbdjdcd}((v1\_relat\_1~(k2\_funct\_7~X0~X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(k2\_funct\_7~\\
X0~X1~X2)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpfhd}
\end{equation}
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}((v16\_pencil\_1~X1~X0){\unicdbdjded}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
((X2{\unicdcdgdad}X3){\unicdbdjdcd}(v3\_card\_1~(k1\_funct\_1~X1~X3)~np\_\_1)))))\end{array}
\label{hyp:egcdadpfahfgogdgjgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfahfgogdgjgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((\preoh \\
v13\_pencil\_1~X1){\unicdcdcdhd}(v16\_pencil\_1~X1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_zfmisc\_1~\\
X2){\unicdbdjdcd}((v16\_pencil\_1~(k2\_funct\_7~X1~(k3\_pencil\_1~X0~X1)~X2)~X0){\unicdcdcdhd}\\
(\preoh v13\_pencil\_1~(k2\_funct\_7~X1~(k3\_pencil\_1~X0~X1)~X2)))))\end{array}$$
\end{theorem}
\end{document}
