\documentclass{article}
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\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t5\_scm\_inst (TMWSMbvVjygCk2rBsETSW9e7aRWrrAh4pnb)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_scm\_inst : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_scm\_inst : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_scm\_inst : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}((k7\_partfun1~X0~(k2\_finseq\_4~\\
X0~X1~X2)~np\_\_1=X1){\unicdcdcdhd}(k7\_partfun1~X0~(k2\_finseq\_4~X0~X1~X2)~np\_\_2=\\
X2))))\end{array}
\label{hyp:ehbdhdpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xtuple\_0~(k3\_xtuple\_0~X0~\\
X1~X2)=X2\end{array}
\label{hyp:cheggdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_scm\_inst}}}}\label{hyp:ggdgbdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m2\_finseq\_1~(k2\_finseq\_4~X0~X1~X2)~\\
X0)\end{array}
\label{hyp:egehpflgcdpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k3\_scm\_inst){\unicdbdjdcd}(({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~k2\_scm\_inst){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k2\_scm\_inst){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(k7\_card\_1~np\_\_9)){\unicdcdcdhd}(X0=k3\_xtuple\_0~X3~k1\_xboole\_0~\\
(k2\_finseq\_4~k2\_scm\_inst~X1~X2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_scm\_inst){\unicdbdjdcd}((X1=k5\_scm\_inst~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_finseq\_1~\\
X2~k2\_scm\_inst){\unicdcdcdhd}((X2=k2\_xtuple\_0~X0){\unicdcdcdhd}(X1=k7\_partfun1~k2\_scm\_inst~\\
X2~np\_\_2))))))\end{array}
\label{hyp:egedpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k3\_scm\_inst){\unicdbdjdcd}(({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~k2\_scm\_inst){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k2\_scm\_inst){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(k7\_card\_1~np\_\_9)){\unicdcdcdhd}(X0=k3\_xtuple\_0~X3~k1\_xboole\_0~\\
(k2\_finseq\_4~k2\_scm\_inst~X1~X2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_scm\_inst){\unicdbdjdcd}((X1=k4\_scm\_inst~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m2\_finseq\_1~\\
X2~k2\_scm\_inst){\unicdcdcdhd}((X2=k2\_xtuple\_0~X0){\unicdcdcdhd}(X1=k7\_partfun1~k2\_scm\_inst~\\
X2~np\_\_1))))))\end{array}
\label{hyp:egddpfdhdgngpfjgogdheh}
\end{equation}
\begin{theorem}\label{thm:ehfdpfdhdgngpfjgogdheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k3\_scm\_inst){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_scm\_inst){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_scm\_inst){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k7\_card\_1~np\_\_9)){\unicdbdjdcd}((X0=k3\_xtuple\_0~X3~k1\_xboole\_0~\\
(k2\_finseq\_4~k2\_scm\_inst~X1~X2)){\unicdbdjdcd}((k4\_scm\_inst~X0=X1){\unicdcdcdhd}(k5\_scm\_inst~\\
X0=X2))))))\end{array}$$
\end{theorem}
\end{document}
