\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{t34\_altcat\_2 (TMJshFt4HbinxczCi4GMRYjNgRs9U4DHeTW)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_altcat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_altcat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_altcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}(((X2=X4){\unicdcdcdhd}(X3=X5)){\unicdbdjdcd}((k1\_altcat\_1~\\
X1~X4~X5=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_altcat\_1~\\
X1~X4~X5)){\unicdbdjdcd}(m1\_subset\_1~X6~(k1\_altcat\_1~X0~X2~X3))))))))))\end{array}
\label{hyp:ehddddpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(m1\_altcat\_2~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~X1)){\unicdbdjdcd}(\preoh (k1\_altcat\_1~X1~X2~X3{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((k1\_altcat\_1~\\
X1~X3~X4{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdcdcdhd}((X5=X2){\unicdcdcdhd}((X6=X3){\unicdcdcdhd}((X7=X4){\unicdcdcdhd}\\
({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~(k1\_altcat\_1~X0~X5~X6)){\unicdcdcdhd}({\unicdcdaddd} X9 .  \\
(m1\_subset\_1~X9~(k1\_altcat\_1~X0~X6~X7)){\unicdcdcdhd}({\unicdcdaddd} X10 .  (m1\_subset\_1~\\
X10~(k1\_altcat\_1~X1~X2~X3)){\unicdcdcdhd}({\unicdcdaddd} X11 .  (m1\_subset\_1~X11~(k1\_altcat\_1~\\
X1~X3~X4)){\unicdcdcdhd}((X8=X10){\unicdcdcdhd}((X9=X11){\unicdcdcdhd}(k5\_altcat\_1~X0~X5~X6~X7~X8~X9{\unicdcdgdad}k5\_altcat\_1~\\
X1~X2~X3~X4~X10~X11)))))))))))))))))))\end{array}
\label{hyp:ehddcdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_altcat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(m1\_altcat\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~X2~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ehcdjdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~X0~X1~X2{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_altcat\_1~X0~X1~X2)){\unicdbdjdcd}(k5\_altcat\_1~\\
X0~X1~X2~X2~X3~(k8\_altcat\_1~X0~X2)=X3)))))\end{array}
\label{hyp:ehcdadpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_altcat\_1~\\
X0~X1~X1{\unicdcdgdad}k1\_xboole\_0))\end{array}
\label{hyp:ehbdidpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_altcat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}\\
(l2\_altcat\_1~X1))\end{array}
\label{hyp:egehpfngbdpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}\\
(l2\_altcat\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k8\_altcat\_1~X0~X1)~(k1\_altcat\_1~X0~X1~X1))\end{array}
\label{hyp:egehpflgidpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_altcat\_1~X0~X1~X1)){\unicdbdjdcd}((X2=k8\_altcat\_1~X0~X1){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_altcat\_1~\\
X0~X1~X3{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_altcat\_1~\\
X0~X1~X3)){\unicdbdjdcd}(k5\_altcat\_1~X0~X1~X1~X3~X2~X4=X4)))))))\end{array}
\label{hyp:egbdhdpfbgmgehdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X1){\unicdbdjdcd}(\\
(v3\_altcat\_2~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}\\
(k8\_altcat\_1~X0~X3 \in k1\_altcat\_1~X1~X2~X2)))))){\unicdcdcdhd}((v2\_struct\_0~X1){\unicdbdjdcd}\\
(v3\_altcat\_2~X1~X0))))\end{array}
\label{hyp:egbdedpfbgmgehdgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v12\_altcat\_1~\\
X0){\unicdcdcdhd}(l2\_altcat\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_altcat\_2~X1~X0){\unicdbdjdcd}(((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}(v3\_altcat\_2~X1~X0))){\unicdbdjdcd}((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}(v12\_altcat\_1~X1))))\end{array}
\label{hyp:dgdgedpfbgmgehdgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfbgmgehdgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_altcat\_1~X0){\unicdcdcdhd}((v11\_altcat\_1~\\
X0){\unicdcdcdhd}((v12\_altcat\_1~X0){\unicdcdcdhd}(l2\_altcat\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_altcat\_1~X1){\unicdcdcdhd}((v3\_altcat\_2~X1~X0){\unicdcdcdhd}(m1\_altcat\_2~\\
X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}(k8\_altcat\_1~X1~X2=\\
k8\_altcat\_1~X0~X3)))))\end{array}$$
\end{theorem}
\end{document}
