\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{t50\_scmfsa8c (TMcV3xUKoKxbEbcZRERXrNMJJmf33QAoq46)}
\maketitle
Let $ v1\_ami\_2 : {{\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 $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ r1\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ k15\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ k14\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ k10\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ k9\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k8\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_amistd\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\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 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
((k7\_scmfsa\_2~X0~X1=k7\_scmfsa\_2~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))))))\end{array}
\label{hyp:ehcdpfdhggpfngbgdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_scmfsa\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~\\
(k17\_scmfsa\_2~X1~X0)=np\_\_12))\end{array}
\label{hyp:ehcdjdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_scmfsa\_2~X0){\unicdbdjdcd}({\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}(k2\_compos\_0~(u1\_compos\_1~\\
k1\_scmfsa\_2)~(k15\_scmfsa\_2~X2~X1~X0)=np\_\_10)))\end{array}
\label{hyp:ehcdhdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_scmfsa\_2~X0){\unicdbdjdcd}({\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}(k2\_compos\_0~(u1\_compos\_1~\\
k1\_scmfsa\_2)~(k14\_scmfsa\_2~X1~X2~X0)=np\_\_9)))\end{array}
\label{hyp:ehcdgdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~(k10\_scmfsa\_2~X0~X1)=\\
np\_\_5))\end{array}
\label{hyp:ehcdcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~(k9\_scmfsa\_2~X0~X1)=np\_\_4))\end{array}
\label{hyp:ehcdbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~(k8\_scmfsa\_2~X0~X1)=np\_\_3))\end{array}
\label{hyp:ehcdadpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~(k7\_scmfsa\_2~X0~X1)=np\_\_2))\end{array}
\label{hyp:ehbdjdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(k2\_compos\_0~(u1\_compos\_1~k1\_scmfsa\_2)~(k6\_scmfsa\_2~X0~X1)=np\_\_1))\end{array}
\label{hyp:ehbdidpfdhdgngggdhbgpfcd}
\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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\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 v1\_amistd\_1~(k4\_xtuple\_0~(k7\_scmfsa\_2~X0~\\
X1))~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgddddpfdhdgngggdhbgbdad}
\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}(v1\_amistd\_1~(\\
k4\_xtuple\_0~(k13\_scmfsa\_2~X1~X0))~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgcdjdpfdhdgngggdhbgbdad}
\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}(v1\_amistd\_1~(\\
k4\_xtuple\_0~(k12\_scmfsa\_2~X1~X0))~np\_\_3~k1\_scmfsa\_2)\end{array}
\label{hyp:ggdgcdidpfdhdgngggdhbgbdad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\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}(m1\_subset\_1~(k7\_scmfsa\_2~X0~X1)~(u1\_compos\_1~\\
k1\_scmfsa\_2))\end{array}
\label{hyp:egehpflghdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\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 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
((r1\_scmfsa7b~X0~X1){\unicdbdjded}(\preoh {\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_scmfsa\_2~X4){\unicdbdjdcd}((k6\_scmfsa\_2~X2~X1{\unicdcdgdad}\\
X0){\unicdcdcdhd}((k7\_scmfsa\_2~X2~X1{\unicdcdgdad}X0){\unicdcdcdhd}((k8\_scmfsa\_2~X2~X1{\unicdcdgdad}X0){\unicdcdcdhd}((k9\_scmfsa\_2~\\
X2~X1{\unicdcdgdad}X0){\unicdcdcdhd}((k10\_scmfsa\_2~X2~X1{\unicdcdgdad}X0){\unicdcdcdhd}((k10\_scmfsa\_2~X1~X2{\unicdcdgdad}X0){\unicdcdcdhd}\\
((k12\_scmfsa\_2~X3~X1{\unicdcdgdad}X0){\unicdcdcdhd}((k13\_scmfsa\_2~X3~X1{\unicdcdgdad}X0){\unicdcdcdhd}((k14\_scmfsa\_2~\\
X2~X1~X4{\unicdcdgdad}X0){\unicdcdcdhd}((k15\_scmfsa\_2~X1~X2~X4{\unicdcdgdad}X0){\unicdcdcdhd}((k15\_scmfsa\_2~X2~X1~X4{\unicdcdgdad}\\
X0){\unicdcdcdhd}(k17\_scmfsa\_2~X1~X4{\unicdcdgdad}X0)))))))))))))))))\end{array}
\label{hyp:egbdpfdhdgngggdhbghdcg}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfdhdgngggdhbgiddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(\preoh (X0{\unicdcdgdad}X1){\unicdcdcdhd}(r1\_scmfsa7b~(k7\_scmfsa\_2~X2~X1)~X0))))\end{array}$$
\end{theorem}
\end{document}
