\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t24\_qc\_lang4 (TMKTK3wujhqoCb6hqLECNgZFU1jm1ioPEsg)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_qc\_lang4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_qc\_lang2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_trees\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_trees\_1~X3~(k9\_xtuple\_0~(k2\_qc\_lang4~X0~X2))){\unicdbdjdcd}((r1\_qc\_lang2~\\
X0~X1~(k3\_trees\_2~(k9\_qc\_lang1~X0)~(k2\_qc\_lang4~X0~X2)~X3)){\unicdbdjded}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~k5\_numbers){\unicdcdcdhd}((k8\_finseq\_1~k5\_numbers~X3~(k12\_finseq\_1~\\
k5\_numbers~X4) \in k9\_xtuple\_0~(k2\_qc\_lang4~X0~X2)){\unicdcdcdhd}(X1=k1\_funct\_1~\\
(k2\_qc\_lang4~X0~X2)~(k8\_finseq\_1~k5\_numbers~X3~(k12\_finseq\_1~k5\_numbers~\\
X4)))))))))\end{array}
\label{hyp:ehhdpfbhdgpfmgbgoghged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}((v3\_qc\_lang1~\\
X1~X0){\unicdbdjdcd}((r1\_qc\_lang2~X0~X2~X1){\unicdbdjded}(X2=k18\_qc\_lang1~X0~X1)))))\end{array}
\label{hyp:ehedidpfbhdgpfmgbgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_trees\_1~\\
X3~(k9\_xtuple\_0~(k2\_qc\_lang4~X0~X2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_trees\_1~\\
X4~(k9\_xtuple\_0~(k2\_qc\_lang4~X0~X2))){\unicdbdjdcd}(((X3=k8\_finseq\_1~k5\_numbers~\\
X4~(k12\_finseq\_1~k5\_numbers~X1)){\unicdcdcdhd}(v3\_qc\_lang1~(k3\_trees\_2~(k9\_qc\_lang1~\\
X0)~(k2\_qc\_lang4~X0~X2)~X4)~X0)){\unicdbdjdcd}((k3\_trees\_2~(k9\_qc\_lang1~X0)~\\
(k2\_qc\_lang4~X0~X2)~X3=k18\_qc\_lang1~X0~(k3\_trees\_2~(k9\_qc\_lang1~\\
X0)~(k2\_qc\_lang4~X0~X2)~X4)){\unicdcdcdhd}(X1=k6\_numbers)))))))\end{array}
\label{hyp:ehcdbdpfbhdgpfmgbgoghged}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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 .  \\
(m1\_trees\_1~X1~X0){\unicdbdjded}(m1\_subset\_1~X1~X0))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngbdpfehchfgfgdhpfbd}
\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~\\
X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1)))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k9\_xtuple\_0~X1)))){\unicdbdjdcd}(k3\_trees\_2~X0~X1~X2=k1\_funct\_1~\\
X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfehchfgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_trees\_2~X0))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(v1\_trees\_1~(k9\_xtuple\_0~X0)))\end{array}
\label{hyp:ggdgcdpfehchfgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k9\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:egehpflgjdpfbhdgpfmgbgoghgbd}
\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~\\
X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1)))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k9\_xtuple\_0~X1)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_trees\_2~\\
X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgddpfehchfgfgdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k2\_qc\_lang4~X0~X1)){\unicdcdcdhd}((v5\_relat\_1~(k2\_qc\_lang4~\\
X0~X1)~(k9\_qc\_lang1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k2\_qc\_lang4~X0~X1)){\unicdcdcdhd}((\\
v1\_finset\_1~(k2\_qc\_lang4~X0~X1)){\unicdcdcdhd}(v3\_trees\_2~(k2\_qc\_lang4~X0~\\
X1))))))\end{array}
\label{hyp:egehpflgcdpfbhdgpfmgbgoghged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k18\_qc\_lang1~X0~X1)~(k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgbdidpfbhdgpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfbhdgpfmgbgoghged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_1~X2~(k9\_xtuple\_0~(k2\_qc\_lang4~X0~\\
X1))){\unicdbdjdcd}((v3\_qc\_lang1~(k3\_trees\_2~(k9\_qc\_lang1~X0)~(k2\_qc\_lang4~\\
X0~X1)~X2)~X0){\unicdbdjdcd}((k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~k5\_numbers~\\
k6\_numbers) \in k9\_xtuple\_0~(k2\_qc\_lang4~X0~X1)){\unicdcdcdhd}(k1\_funct\_1~(k2\_qc\_lang4~\\
X0~X1)~(k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~k5\_numbers~k6\_numbers))=\\
k18\_qc\_lang1~X0~(k3\_trees\_2~(k9\_qc\_lang1~X0)~(k2\_qc\_lang4~X0~X1)~\\
X2))))))\end{array}$$
\end{theorem}
\end{document}
