\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\_cat\_5 (TMZFMQ5sVjizScPFnkarVEzrCLqAjsVYQPr)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_cat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_cat\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_cat\_1 : {{\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 $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_graph\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cat\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_cat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_graph\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_cat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_graph\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfhgchbgahigpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_cat\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_graph\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}(l1\_cat\_1~X0)))))))){\unicdbdjdcd}((v3\_cat\_5~X0){\unicdbdjded}((v2\_cat\_5~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((v2\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_1~\\
X2){\unicdcdcdhd}((v4\_cat\_1~X2){\unicdcdcdhd}((v5\_cat\_1~X2){\unicdcdcdhd}((v6\_cat\_1~X2){\unicdcdcdhd}(l1\_cat\_1~\\
X2)))))))){\unicdbdjdcd}((X1=X2){\unicdbdjdcd}(k4\_cat\_1~X0~X1=k4\_tarski~(k4\_tarski~X2~\\
X2)~(k10\_cat\_1~X2))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((\\
v2\_cat\_1~X2){\unicdcdcdhd}((v3\_cat\_1~X2){\unicdcdcdhd}((v4\_cat\_1~X2){\unicdcdcdhd}((v5\_cat\_1~X2){\unicdcdcdhd}(\\
(v6\_cat\_1~X2){\unicdcdcdhd}(l1\_cat\_1~X2)))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~\\
X3){\unicdcdcdhd}((\preoh v11\_struct\_0~X3){\unicdcdcdhd}((v2\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_1~X3){\unicdcdcdhd}((v4\_cat\_1~\\
X3){\unicdcdcdhd}((v5\_cat\_1~X3){\unicdcdcdhd}((v6\_cat\_1~X3){\unicdcdcdhd}(l1\_cat\_1~X3)))))))){\unicdbdjdcd}(\preoh (\\
X2=k3\_graph\_1~X0~X1){\unicdcdcdhd}((X3=k4\_graph\_1~X0~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_cat\_1~\\
X4~X2~X3){\unicdbdjdcd}(X1{\unicdcdgdad}k4\_tarski~(k4\_tarski~X2~X3)~X4))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X3){\unicdcdcdhd}((v2\_cat\_1~X3){\unicdcdcdhd}((v3\_cat\_1~X3){\unicdcdcdhd}((v4\_cat\_1~X3){\unicdcdcdhd}((v5\_cat\_1~\\
X3){\unicdcdcdhd}((v6\_cat\_1~X3){\unicdcdcdhd}(l1\_cat\_1~X3)))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh v2\_struct\_0~\\
X4){\unicdcdcdhd}((\preoh v11\_struct\_0~X4){\unicdcdcdhd}((v2\_cat\_1~X4){\unicdcdcdhd}((v3\_cat\_1~X4){\unicdcdcdhd}((v4\_cat\_1~\\
X4){\unicdcdcdhd}((v5\_cat\_1~X4){\unicdcdcdhd}((v6\_cat\_1~X4){\unicdcdcdhd}(l1\_cat\_1~X4)))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((\preoh v2\_struct\_0~X5){\unicdcdcdhd}((\preoh v11\_struct\_0~X5){\unicdcdcdhd}((v2\_cat\_1~X5){\unicdcdcdhd}((v3\_cat\_1~\\
X5){\unicdcdcdhd}((v4\_cat\_1~X5){\unicdcdcdhd}((v5\_cat\_1~X5){\unicdcdcdhd}((v6\_cat\_1~X5){\unicdcdcdhd}(l1\_cat\_1~\\
X5)))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_cat\_1~X6~X3~X4){\unicdbdjdcd}({\unicdcdadad} X7 .  (m2\_cat\_1~\\
X7~X4~X5){\unicdbdjdcd}(((X1=k4\_tarski~(k4\_tarski~X3~X4)~X6){\unicdcdcdhd}(X2=k4\_tarski~\\
(k4\_tarski~X4~X5)~X7)){\unicdbdjdcd}(k1\_cat\_1~X0~X1~X2=k4\_tarski~(k4\_tarski~\\
X3~X5)~(k9\_cat\_1~X3~X4~X5~X6~X7))))))))))))))\end{array}
\label{hyp:eggdpfdgbgehpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v2\_cat\_5~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v2\_cat\_1~X1){\unicdcdcdhd}\\
((v3\_cat\_1~X1){\unicdcdcdhd}((v4\_cat\_1~X1){\unicdcdcdhd}((v5\_cat\_1~X1){\unicdcdcdhd}((v6\_cat\_1~X1){\unicdcdcdhd}\\
(l1\_cat\_1~X1))))))))))\end{array}
\label{hyp:egfdpfdgbgehpffd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfdgbgehpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_1~X0){\unicdcdcdhd}((v4\_cat\_1~X0){\unicdcdcdhd}((v5\_cat\_1~X0){\unicdcdcdhd}((v6\_cat\_1~\\
X0){\unicdcdcdhd}((v3\_cat\_5~X0){\unicdcdcdhd}(l1\_cat\_1~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_cat\_1~X1){\unicdcdcdhd}((v3\_cat\_1~X1){\unicdcdcdhd}((v4\_cat\_1~X1){\unicdcdcdhd}((v5\_cat\_1~X1){\unicdcdcdhd}\\
((v6\_cat\_1~X1){\unicdcdcdhd}(l1\_cat\_1~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
