\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{l113\_scmfsa\_2 (TMKFkuCWBnpRWvtpHQpPVvyX2WavS88Gk97)}
\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 $ v2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k11\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k16\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjded}(\preoh (X0{\unicdcdgdad}\\
k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(X0{\unicdcdgdad}k6\_scmfsa\_2~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k7\_scmfsa\_2~\\
X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k8\_scmfsa\_2~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(X0{\unicdcdgdad}k9\_scmfsa\_2~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}(X0{\unicdcdgdad}k10\_scmfsa\_2~\\
X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}(X0{\unicdcdgdad}k11\_scmfsa\_2~\\
X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}(\\
X0{\unicdcdgdad}k12\_scmfsa\_2~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(X0{\unicdcdgdad}k13\_scmfsa\_2~X1~X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_scmfsa\_2~\\
X3){\unicdbdjdcd}(X0{\unicdcdgdad}k14\_scmfsa\_2~X2~X1~X3)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_scmfsa\_2~X3){\unicdbdjdcd}(X0{\unicdcdgdad}k15\_scmfsa\_2~X2~X1~X3)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_scmfsa\_2~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k16\_scmfsa\_2~X1~X2))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_scmfsa\_2~X2){\unicdbdjdcd}(X0{\unicdcdgdad}k17\_scmfsa\_2~X1~X2)))))))))))))))\end{array}
\label{hyp:ehjdddpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k9\_scmfsa\_2~X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgjdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k8\_scmfsa\_2~X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgidpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k7\_scmfsa\_2~X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdghdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k6\_scmfsa\_2~X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdggdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}(m1\_scmfsa\_2~X1)){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k17\_scmfsa\_2~\\
X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdhdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}(m1\_scmfsa\_2~X1)){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k16\_scmfsa\_2~\\
X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdgdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdcdcdhd}((m1\_scmfsa\_2~X1){\unicdcdcdhd}((v1\_ami\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))))){\unicdbdjdcd}(\preoh v2\_extpro\_1~\\
(k15\_scmfsa\_2~X0~X2~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdfdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdcdcdhd}((m1\_scmfsa\_2~X1){\unicdcdcdhd}((v1\_ami\_2~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))))){\unicdbdjdcd}(\preoh v2\_extpro\_1~\\
(k14\_scmfsa\_2~X0~X2~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdedpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}(\preoh v2\_extpro\_1~\\
(k13\_scmfsa\_2~X1~X0)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdddpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}(\preoh v2\_extpro\_1~\\
(k12\_scmfsa\_2~X1~X0)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k11\_scmfsa\_2~\\
X0)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2))){\unicdcdcdhd}((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(\preoh v2\_extpro\_1~(k10\_scmfsa\_2~X0~X1)~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgbdadpfdhdgngggdhbgpfcd}
\end{equation}
\begin{theorem}\label{thm:mgbdbdddpfdhdgngggdhbgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}((v2\_extpro\_1~\\
X0~np\_\_3~k1\_scmfsa\_2){\unicdbdjdcd}(X0=k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~\\
k1\_xboole\_0))\end{array}$$
\end{theorem}
\end{document}
