\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{t31\_scmfsa8c (TMW3ABnwK7cY6Y4czkacXA753JGF5fQadQt)}
\maketitle
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 $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_scmfsa8a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_scmfsa6a : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_scmfsa6b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_scmfsa6a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_scmfsa8a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_amistd\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_scmfsa7b : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}((r1\_scmfsa8a~X1~X0~(k2\_scmfsa6a~X2)){\unicdbdjdcd}(k6\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~(k6\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~\\
X0~(k3\_scmfsa6a~X2~(k4\_compos\_1~k1\_scmfsa\_2)))~(k8\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~X1))=k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k1\_funct\_4~X0~X2)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X1)~(k2\_scmfsa8a~X1~X0~(k2\_scmfsa6a~X2)))))))\end{array}
\label{hyp:ehddadpfdhdgngggdhbgiddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((k1\_funct\_1~\\
X0~(k4\_scmfsa\_2~k6\_numbers)=np\_\_1){\unicdbdjdcd}(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X0=k1\_scmfsa\_m~X0))\end{array}
\label{hyp:ehbdidpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_relat\_1~(k4\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v4\_relat\_1~(k4\_compos\_1~\\
k1\_scmfsa\_2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k4\_compos\_1~k1\_scmfsa\_2)~\\
(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~(k4\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_finset\_1~(k4\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v7\_amistd\_1~(k4\_compos\_1~\\
k1\_scmfsa\_2)~np\_\_3~k1\_scmfsa\_2){\unicdcdcdhd}(v1\_scmfsa7b~(k4\_compos\_1~k1\_scmfsa\_2)))))))\end{array}
\label{hyp:ggdgfdpfdhdgngggdhbghdcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k4\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_zfmisc\_1~(k4\_compos\_1~X0)){\unicdcdcdhd}((v1\_relat\_1~(k4\_compos\_1~X0)){\unicdcdcdhd}\\
((v4\_relat\_1~(k4\_compos\_1~X0)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k4\_compos\_1~\\
X0)~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_compos\_1~X0)){\unicdcdcdhd}((v1\_finset\_1~\\
(k4\_compos\_1~X0)){\unicdcdcdhd}(v1\_afinsq\_1~(k4\_compos\_1~X0)))))))))\end{array}
\label{hyp:ggdgcdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\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}\\
((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}((v1\_relat\_1~\\
(k3\_scmfsa6a~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k3\_scmfsa6a~X0~X1)~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~(k3\_scmfsa6a~X0~X1)~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~(k3\_scmfsa6a~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k3\_scmfsa6a~\\
X0~X1)){\unicdcdcdhd}((v1\_finset\_1~(k3\_scmfsa6a~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~(k3\_scmfsa6a~\\
X0~X1))))))))\end{array}
\label{hyp:egehpflgddpfdhdgngggdhbggdbg}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}}\label{hyp:egehpflgbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((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))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
(v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~\\
(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~\\
k5\_numbers))))){\unicdbdjdcd}(k1\_scmfsa6b~X0~X1~X2=k6\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X2~X0)~(k1\_scmfsa\_m~X1))))\end{array}
\label{hyp:egbdpfdhdgngggdhbggdcg}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfdhdgngggdhbgiddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}(((k1\_funct\_1~X1~(k4\_scmfsa\_2~k6\_numbers)=np\_\_1){\unicdcdcdhd}\\
(r1\_scmfsa8a~X1~X0~(k2\_scmfsa6a~X2))){\unicdbdjdcd}(k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
(k1\_scmfsa6b~(k3\_scmfsa6a~X2~(k4\_compos\_1~k1\_scmfsa\_2))~X1~X0)=\\
k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k5\_extpro\_1~np\_\_3~k1\_scmfsa\_2~\\
(k1\_funct\_4~X0~X2)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X1)~(k2\_scmfsa8a~\\
X1~X0~(k2\_scmfsa6a~X2)))))))\end{array}$$
\end{theorem}
\end{document}
