\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{t12\_random\_2 (TMdb9heSdXmYUpLVdRfPCekjRq9swxbnE1r)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ 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 $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_bhsp\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k33\_binop\_2 : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_bhsp\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~X0){\unicdcdcdhd}((v2\_funct\_1~\\
X3){\unicdcdcdhd}((k2\_relset\_1~X0~X3=X2){\unicdcdcdhd}(k5\_bhsp\_5~k1\_numbers~X0~k33\_binop\_2~\\
X2~X1=k18\_rvsum\_1~(k4\_bhsp\_5~k1\_numbers~X0~X1~X3)))))))\end{array}
\label{hyp:ehjdpfchbgogegpgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~\\
X1)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~X5){\unicdcdcdhd}((v1\_finset\_1~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_finseq\_1~\\
X6~X0){\unicdbdjdcd}(((v2\_funct\_1~X6){\unicdcdcdhd}(k2\_relset\_1~X0~X6=X5)){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m2\_finseq\_1~X7~X1){\unicdbdjdcd}({\unicdcdadad} X8 .  (m2\_finseq\_1~X8~(k2\_zfmisc\_1~\\
X0~X1)){\unicdbdjdcd}({\unicdcdadad} X9 .  ((\preoh v1\_xboole\_0~X9){\unicdcdcdhd}((v1\_finset\_1~X9){\unicdcdcdhd}(m1\_subset\_1~\\
X9~(k1\_zfmisc\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X10 .  ((v1\_finset\_1~X10){\unicdcdcdhd}(m1\_subset\_1~\\
X10~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(((v2\_funct\_1~X7){\unicdcdcdhd}((\\
k2\_relset\_1~X1~X7=X9){\unicdcdcdhd}((v2\_funct\_1~X8){\unicdcdcdhd}((r2\_relset\_1~X0~X1~(k2\_relset\_1~\\
(k2\_zfmisc\_1~X0~X1)~X8)~X10){\unicdcdcdhd}((X10=k2\_zfmisc\_1~X5~X9){\unicdcdcdhd}({\unicdcdadad} X11 .  \\
{\unicdcdadad} X12 .  ((X11 \in X5){\unicdcdcdhd}(X12 \in X9)){\unicdbdjdcd}(k1\_binop\_1~X4~X11~X12=k11\_binop\_2~\\
(k1\_seq\_1~X2~X11)~(k1\_seq\_1~X3~X12)))))))){\unicdbdjdcd}(k18\_rvsum\_1~(k4\_bhsp\_5~\\
k1\_numbers~(k2\_zfmisc\_1~X0~X1)~X4~X8)=k11\_binop\_2~(k18\_rvsum\_1~\\
(k4\_bhsp\_5~k1\_numbers~X0~X2~X6))~(k18\_rvsum\_1~(k4\_bhsp\_5~k1\_numbers~\\
X1~X3~X7)))))))))))))))\end{array}
\label{hyp:ehbdbdpfchbgogegpgngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
(\preoh v1\_xboole\_0~(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:ggdgbdadpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfchbgogegpgngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X1~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k1\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~\\
X1)~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~X5){\unicdcdcdhd}((v1\_finset\_1~\\
X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((\preoh v1\_xboole\_0~\\
X6){\unicdcdcdhd}((v1\_finset\_1~X6){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~X1)))){\unicdbdjdcd}(\\
{\unicdcdadad} X7 .  ((v1\_finset\_1~X7){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdbdjdcd}(((X7=k2\_zfmisc\_1~X5~X6){\unicdcdcdhd}({\unicdcdadad} X8 .  {\unicdcdadad} X9 .  ((\\
X8 \in X5){\unicdcdcdhd}(X9 \in X6)){\unicdbdjdcd}(k1\_binop\_1~X4~X8~X9=k11\_binop\_2~(k1\_seq\_1~X2~\\
X8)~(k1\_seq\_1~X3~X9)))){\unicdbdjdcd}(k5\_bhsp\_5~k1\_numbers~(k2\_zfmisc\_1~X0~\\
X1)~k33\_binop\_2~X7~X4=k11\_binop\_2~(k5\_bhsp\_5~k1\_numbers~X0~k33\_binop\_2~\\
X5~X2)~(k5\_bhsp\_5~k1\_numbers~X1~k33\_binop\_2~X6~X3))))))))))\end{array}$$
\end{theorem}
\end{document}
