\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\_ndiff\_5 (TMRgknj8rm27AkhPnmfdL97FnxcSwD4D2wz)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_prvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k4\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_ndiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_ndiff\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k4\_finseq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgidpfchfgmgbgehpfbd}
\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 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v2\_prvect\_2~X0))))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(k4\_finseq\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
(k14\_prvect\_2~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k4\_ndiff\_5~X0~X1~X2)){\unicdcdcdhd}((\\
v1\_funct\_2~(k4\_ndiff\_5~X0~X1~X2)~(u1\_struct\_0~(k11\_prvect\_2~X0~\\
X1))~(u1\_struct\_0~(k14\_prvect\_2~X0))){\unicdcdcdhd}(m1\_subset\_1~(k4\_ndiff\_5~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k11\_prvect\_2~\\
X0~X1))~(u1\_struct\_0~(k14\_prvect\_2~X0)))))))\end{array}
\label{hyp:egehpflgedpfogegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_finseq\_1~X0)~(k1\_zfmisc\_1~k5\_numbers))\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1)))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X3))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_partfun1~X0~X1~X2~X3~X4~X5)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_partfun1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X3))))\end{array}
\label{hyp:egehpflgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v2\_prvect\_2~X0){\unicdcdcdhd}(v1\_ndiff\_5~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}\\
(l1\_normsp\_1~X1)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(\\
k14\_prvect\_2~X0))~(u1\_struct\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k14\_prvect\_2~X0))){\unicdbdjdcd}(k6\_ndiff\_5~X0~X1~X2~X3~X4=\\
k3\_ndiff\_1~(k11\_prvect\_2~X0~(k5\_ndiff\_5~X0~X2))~X1~(k1\_partfun1~\\
(u1\_struct\_0~(k11\_prvect\_2~X0~(k5\_ndiff\_5~X0~X2)))~(u1\_struct\_0~\\
(k14\_prvect\_2~X0))~(u1\_struct\_0~(k14\_prvect\_2~X0))~(u1\_struct\_0~\\
X1)~(k4\_ndiff\_5~X0~(k5\_ndiff\_5~X0~X2)~X4)~X3)~(k3\_funct\_2~(u1\_struct\_0~\\
(k14\_prvect\_2~X0))~(u1\_struct\_0~(k11\_prvect\_2~X0~(k5\_ndiff\_5~\\
X0~X2)))~(k3\_ndiff\_5~X0~(k5\_ndiff\_5~X0~X2))~X4)))))\end{array}
\label{hyp:eghdpfogegjgggggpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v2\_prvect\_2~X0){\unicdcdcdhd}(v1\_ndiff\_5~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (X1 \in k4\_finseq\_1~X0){\unicdbdjdcd}(k5\_ndiff\_5~X0~X1=X1))\end{array}
\label{hyp:egfdpfogegjgggggpffd}
\end{equation}
\begin{theorem}\label{thm:ehfdadpfogegjgggggpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v2\_prvect\_2~X0){\unicdcdcdhd}(v1\_ndiff\_5~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v7\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v5\_rlvect\_1~X1){\unicdcdcdhd}((v6\_rlvect\_1~X1){\unicdcdcdhd}((v7\_rlvect\_1~X1){\unicdcdcdhd}((v8\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_normsp\_0~X1){\unicdcdcdhd}((v4\_normsp\_0~X1){\unicdcdcdhd}((v2\_normsp\_1~X1){\unicdcdcdhd}\\
(l1\_normsp\_1~X1)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~\\
(k4\_finseq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k14\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k11\_prvect\_2~X0~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k14\_prvect\_2~X0))~\\
(u1\_struct\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}(m1\_subset\_1~\\
X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k11\_prvect\_2~X0~X2))~\\
(u1\_struct\_0~X1))))){\unicdbdjdcd}(((k3\_funct\_2~(u1\_struct\_0~(k14\_prvect\_2~\\
X0))~(u1\_struct\_0~(k11\_prvect\_2~X0~X2))~(k3\_ndiff\_5~X0~X2)~X3=X4){\unicdcdcdhd}\\
(r2\_relset\_1~(u1\_struct\_0~(k11\_prvect\_2~X0~X2))~(u1\_struct\_0~\\
X1)~X6~(k1\_partfun1~(u1\_struct\_0~(k11\_prvect\_2~X0~X2))~(u1\_struct\_0~\\
(k14\_prvect\_2~X0))~(u1\_struct\_0~(k14\_prvect\_2~X0))~(u1\_struct\_0~\\
X1)~(k4\_ndiff\_5~X0~X2~X3)~X5))){\unicdbdjdcd}(k3\_ndiff\_1~(k11\_prvect\_2~X0~X2)~\\
X1~X6~X4=k6\_ndiff\_5~X0~X1~X2~X5~X3))))))))\end{array}$$
\end{theorem}
\end{document}
