\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{t20\_scmfsa8c (TMWFtSR2zHEca7k7LhYwnXBKwyf5n4JTNiy)}
\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 $ r5\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r6\_scmfsa7b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}({\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\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
(k1\_funct\_1~X0~X2=k1\_funct\_1~X1~X2)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_scmfsa\_2~\\
X2){\unicdbdjdcd}(k18\_scmfsa\_2~X0~X2=k18\_scmfsa\_2~X1~X2))){\unicdbdjded}(k6\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~X0=k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X1)))\end{array}
\label{hyp:ehcdpfdhdgngggdhbgpfng}
\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}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\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}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X4~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v1\_finset\_1~X4){\unicdcdcdhd}(v1\_afinsq\_1~X4))))))){\unicdbdjdcd}(((k1\_funct\_1~X2~(\\
k4\_scmfsa\_2~k6\_numbers)=np\_\_1){\unicdcdcdhd}((r5\_scmfsa7b~X4~X2~X0){\unicdcdcdhd}((r6\_scmfsa7b~\\
X4~X2~X0){\unicdcdcdhd}(({\unicdcdadad} X5 .  ((v1\_ami\_2~X5){\unicdcdcdhd}((\preoh v1\_scmfsa\_m~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(u1\_struct\_0~k1\_scmfsa\_2)))){\unicdbdjdcd}(k1\_funct\_1~X2~X5=k1\_funct\_1~\\
X3~X5)){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_scmfsa\_2~X5){\unicdbdjdcd}(k18\_scmfsa\_2~X2~X5=k18\_scmfsa\_2~\\
X3~X5)))))){\unicdbdjdcd}(k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k1\_scmfsa6b~X4~X2~\\
X0)=k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k1\_scmfsa6b~X4~X3~X1)))))))\end{array}
\label{hyp:ehbdjdpfdhdgngggdhbgiddg}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdhdgngggdhbgiddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X4~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v1\_finset\_1~X4){\unicdcdcdhd}(v1\_afinsq\_1~X4))))))){\unicdbdjdcd}(((k1\_funct\_1~X2~(\\
k4\_scmfsa\_2~k6\_numbers)=np\_\_1){\unicdcdcdhd}((r5\_scmfsa7b~X4~X2~X0){\unicdcdcdhd}((r6\_scmfsa7b~\\
X4~X2~X0){\unicdcdcdhd}(k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X2=k6\_memstr\_0~np\_\_3~\\
k1\_scmfsa\_2~X3)))){\unicdbdjdcd}(k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k1\_scmfsa6b~\\
X4~X2~X0)=k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~(k1\_scmfsa6b~X4~X3~X1)))))))\end{array}$$
\end{theorem}
\end{document}
