\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{t6\_random\_1 (TMYNMKuGtdsNQUV3ZYMizVSLR7tarsD9sXx)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k1\_numbers : {\iota}$ be given.
Let $ r2\_mesfunc6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_random\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_prob\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}((r2\_mesfunc6~\\
X0~X1~X2){\unicdbdjdcd}(m2\_subset\_1~(k1\_relset\_1~X0~X2)~(k1\_zfmisc\_1~X0)~X1))))\end{array}
\label{hyp:ehhdbdpfngfgdhggfhogdggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdaddd} X2 .  ((v1\_prob\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~\\
(k1\_random\_1~X0))){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(k1\_relset\_1~\\
X0~X1)){\unicdcdcdhd}((k1\_relset\_1~X0~X1=k3\_tarski~(k2\_relset\_1~(k1\_random\_1~\\
X0)~X2)){\unicdcdcdhd}((k4\_finseq\_1~X2=k4\_finseq\_1~X3){\unicdcdcdhd}((v2\_funct\_1~X3){\unicdcdcdhd}\\
((k2\_relset\_1~(k1\_relset\_1~X0~X1)~X3=k1\_relset\_1~X0~X1){\unicdcdcdhd}((k3\_finseq\_1~\\
X3=k5\_card\_1~(k1\_relset\_1~X0~X1)){\unicdcdcdhd}(({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}((X4 \in k4\_finseq\_1~X2){\unicdbdjdcd}(k1\_funct\_1~X2~X4=k1\_tarski~(k1\_funct\_1~\\
X3~X4)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}(((X4 \in k4\_finseq\_1~X2){\unicdcdcdhd}\\
((X5 \in k1\_funct\_1~X2~X4){\unicdcdcdhd}(X6 \in k1\_funct\_1~X2~X4))){\unicdbdjdcd}(k1\_seq\_1~X1~X5=\\
k1\_seq\_1~X1~X6))))))))))))))\end{array}
\label{hyp:ehfdpfchbgogegpgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_random\_1~X0)){\unicdcdcdhd}\\
((v1\_prob\_1~(k1\_random\_1~X0)~X0){\unicdcdcdhd}((v4\_prob\_1~(k1\_random\_1~X0)~\\
X0){\unicdcdcdhd}(m1\_subset\_1~(k1\_random\_1~X0)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))))))\end{array}
\label{hyp:egehpflgbdpfchbgogegpgngpfbd}
\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){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}((r2\_mesfunc6~\\
X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_prob\_2~X3){\unicdcdcdhd}(m2\_finseq\_1~X3~X1)){\unicdcdcdhd}((\\
k1\_relset\_1~X0~X2=k3\_tarski~(k2\_relset\_1~X1~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~X0){\unicdbdjdcd}(((X4 \in k4\_finseq\_1~X3){\unicdcdcdhd}((X5 \in k1\_funct\_1~X3~\\
X4){\unicdcdcdhd}(X6 \in k1\_funct\_1~X3~X4))){\unicdbdjdcd}(k1\_seq\_1~X2~X5=k1\_seq\_1~X2~X6))))))))))\end{array}
\label{hyp:egcdpfngfgdhggfhogdggd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfchbgogegpgngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~\\
k1\_numbers)))){\unicdbdjdcd}((r2\_mesfunc6~X0~(k1\_random\_1~X0)~X1){\unicdcdcdhd}(m2\_subset\_1~\\
(k1\_relset\_1~X0~X1)~(k1\_zfmisc\_1~X0)~(k1\_random\_1~X0))))\end{array}$$
\end{theorem}
\end{document}
