\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t16\_modal\_1 (TMGz5Zo1yUrcmrYndgbGde1oxaKrRhbxNSD)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_trees\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}(X0=k5\_trees\_1~X0~X1~(k4\_trees\_1~\\
X0~X1))))\end{array}
\label{hyp:ehgdpfehchfgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v1\_trees\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~\\
X2~k5\_numbers){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_trees\_1~X3~(k5\_trees\_1~\\
X0~X2~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_trees\_1~X4~X1){\unicdbdjdcd}((X3=k8\_finseq\_1~k5\_numbers~\\
X2~X4){\unicdbdjdcd}(r2\_wellord2~(k1\_trees\_2~(k5\_trees\_1~X0~X2~X1)~X3)~(k1\_trees\_2~\\
X1~X4))))))))\end{array}
\label{hyp:ehbdfdpfngpgegbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k4\_trees\_1~X0~X1)){\unicdcdcdhd}\\
(v1\_trees\_1~(k4\_trees\_1~X0~X1)))\end{array}
\label{hyp:egehpflgedpfehchfgfgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfngpgegbgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_trees\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_trees\_1~X3~(k4\_trees\_1~X0~X1)){\unicdbdjdcd}((X2=k8\_finseq\_1~\\
k5\_numbers~X1~X3){\unicdbdjdcd}(r2\_wellord2~(k1\_trees\_2~X0~X2)~(k1\_trees\_2~\\
(k4\_trees\_1~X0~X1)~X3)))))))\end{array}$$
\end{theorem}
\end{document}
