\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\_scmisort (TMds92sm2xUVxQZ9GWLYM6gnJeVNtBfGBEv)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_scmfsa6a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_scmfsa6a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~\\
(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}(k5\_card\_1~(k5\_scmfsa6a~\\
X1~X0)=k2\_nat\_1~(k5\_card\_1~X1)~np\_\_2))\end{array}
\label{hyp:ehddedpfdhdgngggdhbggdbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}(k5\_card\_1~(k5\_scmfsa6a~(k6\_scmfsa6a~\\
X0~X1)~X2)=np\_\_6)))\end{array}
\label{hyp:ehcdddpfdhdgngcgdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_6){\unicdcdcdhd}(m2\_subset\_1~np\_\_6~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_6~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_6~k1\_numbers))\end{array}
\label{hyp:dhahdggdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_6}}~{np\_\_2}}={np\_\_8}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchgdpfchcdpfchid}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(k2\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2))){\unicdbdjdcd}((v1\_relat\_1~(k6\_scmfsa6a~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k6\_scmfsa6a~X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k6\_scmfsa6a~X0~X1)~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
(k6\_scmfsa6a~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k6\_scmfsa6a~X0~X1)){\unicdcdcdhd}((v1\_finset\_1~\\
(k6\_scmfsa6a~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~(k6\_scmfsa6a~X0~X1))))))))\end{array}
\label{hyp:egehpflggdpfdhdgngggdhbggdbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))))){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2))){\unicdbdjdcd}((v1\_relat\_1~(k5\_scmfsa6a~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k5\_scmfsa6a~X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k5\_scmfsa6a~X0~X1)~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
(k5\_scmfsa6a~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k5\_scmfsa6a~X0~X1)){\unicdcdcdhd}((v1\_finset\_1~\\
(k5\_scmfsa6a~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~(k5\_scmfsa6a~X0~X1))))))))\end{array}
\label{hyp:egehpflgfdpfdhdgngggdhbggdbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfdhdgngjgdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdbdjdcd}(k5\_card\_1~(k5\_scmfsa6a~(k5\_scmfsa6a~(k6\_scmfsa6a~\\
X0~X1)~X2)~X3)=np\_\_8))))\end{array}$$
\end{theorem}
\end{document}
