\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{t10\_pdiff\_1 (TMZKNgXn2YHuvfUKGoSBrpk1ATVhj8tFsRA)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_fdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
np\_\_1)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}(((X0=k2\_pdiff\_1~X1){\unicdcdcdhd}((X2=k12\_finseq\_1~k1\_numbers~\\
X3){\unicdcdcdhd}(r1\_fdiff\_1~X1~X3))){\unicdbdjdcd}((r1\_ndiff\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~\\
np\_\_1)~X0~X2){\unicdcdcdhd}(k1\_funct\_1~(k3\_ndiff\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~\\
np\_\_1)~X0~X2)~(k12\_finseq\_1~k5\_numbers~np\_\_1)=k12\_finseq\_1~k1\_numbers~\\
(k1\_fdiff\_1~X1~X3)))))))\end{array}
\label{hyp:ehidpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
np\_\_1)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}(((X0=k2\_pdiff\_1~X1){\unicdcdcdhd}((X2=k12\_finseq\_1~k1\_numbers~\\
X3){\unicdcdcdhd}(r1\_ndiff\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~np\_\_1)~X0~X2))){\unicdbdjdcd}\\
((r1\_fdiff\_1~X1~X3){\unicdcdcdhd}(k1\_fdiff\_1~X1~X3=k1\_seq\_1~(k3\_relat\_1~(k2\_funct\_1~\\
(k1\_pdiff\_1~np\_\_1~np\_\_1))~(k3\_relat\_1~(k3\_ndiff\_1~(k4\_real\_ns1~\\
np\_\_1)~(k4\_real\_ns1~np\_\_1)~X0~X2)~(k1\_pdiff\_1~np\_\_1~np\_\_1)))~np\_\_1))))))\end{array}
\label{hyp:ehhdpfahegjgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfahegjgggggpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
np\_\_1)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}(((X0=k2\_pdiff\_1~X1){\unicdcdcdhd}((X2=k12\_finseq\_1~k1\_numbers~\\
X3){\unicdcdcdhd}(r1\_ndiff\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~np\_\_1)~X0~X2))){\unicdbdjdcd}\\
(k1\_funct\_1~(k3\_ndiff\_1~(k4\_real\_ns1~np\_\_1)~(k4\_real\_ns1~np\_\_1)~\\
X0~X2)~(k12\_finseq\_1~k5\_numbers~np\_\_1)=k12\_finseq\_1~k1\_numbers~\\
(k1\_fdiff\_1~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
