\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{t30\_prob\_4 (TMK9bBGhDGSRjZbzJB9M1c8d9FjeGrm7NXR)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_prob\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_prob\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_prob\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(X1=k2\_xboole\_0~X0~(k4\_xboole\_0~\\
X1~X0))\end{array}
\label{hyp:ehedfdpfihcgpgpgmgfgpfbd}
\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 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  ((X3 \in X1){\unicdcdcdhd}(X4 \in X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_prob\_4~X5~X0~X1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_prob\_4~X6~X0~X1~X2){\unicdbdjdcd}((k2\_xboole\_0~X3~X5=k2\_xboole\_0~\\
X4~X6){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k1\_funct\_1~X2~X4)))))))\end{array}
\label{hyp:ehcdfdpfahchpgcgpfed}
\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){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k7\_subset\_1~X0~X1~X2=k4\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdhfhcgdhfgehpfbd}
\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){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((\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)))))){\unicdcdcdhd}((m2\_prob\_1~X2~X0~X1){\unicdcdcdhd}(\\
m1\_subset\_1~X3~(k4\_prob\_4~X0~X1~X2))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_prob\_4~\\
X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k6\_prob\_4~X0~X1~X2~X3)~(k1\_zfmisc\_1~(\\
k1\_zfmisc\_1~X0))))\end{array}
\label{hyp:egehpflggdpfahchpgcgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((\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)))))){\unicdcdcdhd}(m2\_prob\_1~X2~X0~X1))){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k4\_prob\_4~X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k4\_prob\_4~X0~X1~X2)~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0))))\end{array}
\label{hyp:egehpflgedpfahchpgcgpfed}
\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 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k1\_zfmisc\_1~X0)~(k4\_prob\_4~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))){\unicdbdjdcd}((X4=k6\_prob\_4~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (X5 \in X4){\unicdbdjded}((X5 \in \\
X1){\unicdcdcdhd}((r1\_tarski~X5~X3){\unicdcdcdhd}(m1\_prob\_4~(k7\_subset\_1~X0~X3~X5)~X0~X1~X2)))))))))\end{array}
\label{hyp:eghdpfahchpgcgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfahchpgcgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k1\_zfmisc\_1~X0)~(k4\_prob\_4~X0~X1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
{\unicdcdadad} X5 .  ((X4 \in k6\_prob\_4~X0~X1~X2~X3){\unicdcdcdhd}(X5 \in k6\_prob\_4~X0~X1~X2~X3)){\unicdbdjdcd}\\
(k1\_funct\_1~X2~X4=k1\_funct\_1~X2~X5)))))\end{array}$$
\end{theorem}
\end{document}
