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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t93\_qc\_lang2 (TMN2aC6mMRRUnK51Xmm9EGxdw6iJTgLi4H9)}
\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 $ k15\_qc\_lang2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_qc\_lang2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ k13\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_qc\_lang2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ 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}(k15\_qc\_lang2~\\
X0~(k2\_qc\_lang2~X0~X1~X2)=k2\_xboole\_0~(k2\_xboole\_0~(k15\_qc\_lang2~\\
X0~X1)~(k15\_qc\_lang2~X0~X2))~(k1\_enumset1~(k13\_qc\_lang1~X0~X2)~(\\
k14\_qc\_lang1~X0~X1~(k13\_qc\_lang1~X0~X2))~(k2\_qc\_lang2~X0~X1~X2)))))\end{array}
\label{hyp:ehjdbdpfbhdgpfmgbgoghgcd}
\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}(k15\_qc\_lang2~\\
X0~(k14\_qc\_lang1~X0~X1~X2)=k2\_xboole\_0~(k2\_xboole\_0~(k15\_qc\_lang2~\\
X0~X1)~(k15\_qc\_lang2~X0~X2))~(k1\_tarski~(k14\_qc\_lang1~X0~X1~X2)))))\end{array}
\label{hyp:ehidjdpfbhdgpfmgbgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xboole\_0~(k2\_xboole\_0~X0~\\
X1)~X2=k2\_xboole\_0~X0~(k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:ehedpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  k5\_enumset1~X0~X1~X2~X3~X4~X5~X6=k2\_xboole\_0~(k4\_enumset1~\\
X0~X1~X2~X3~X4~X5)~(k1\_tarski~X6)\end{array}
\label{hyp:ehcdbdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
k4\_enumset1~X0~X1~X2~X3~X4~X5=k2\_xboole\_0~(k1\_enumset1~X0~X1~X2)~(\\
k1\_enumset1~X3~X4~X5)\end{array}
\label{hyp:ehbdddpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X0}}={X0}}}}\label{hyp:jgegfgngahpgehfgogdgfgpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(k9\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k9\_qc\_lang1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k2\_qc\_lang2~X0~X1~X2)~(k9\_qc\_lang1~X0))\end{array}
\label{hyp:egehpflgcdpfbhdgpfmgbgoghgcd}
\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}(k4\_qc\_lang2~\\
X0~X1~X2=k14\_qc\_lang1~X0~(k2\_qc\_lang2~X0~X1~X2)~(k2\_qc\_lang2~X0~X2~\\
X1))))\end{array}
\label{hyp:egedpfbhdgpfmgbgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehjdddpfbhdgpfmgbgoghgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k9\_qc\_lang1~X0)){\unicdbdjdcd}(k15\_qc\_lang2~\\
X0~(k4\_qc\_lang2~X0~X1~X2)=k2\_xboole\_0~(k2\_xboole\_0~(k15\_qc\_lang2~\\
X0~X1)~(k15\_qc\_lang2~X0~X2))~(k5\_enumset1~(k13\_qc\_lang1~X0~X2)~(\\
k14\_qc\_lang1~X0~X1~(k13\_qc\_lang1~X0~X2))~(k2\_qc\_lang2~X0~X1~X2)~(\\
k13\_qc\_lang1~X0~X1)~(k14\_qc\_lang1~X0~X2~(k13\_qc\_lang1~X0~X1))~(k2\_qc\_lang2~\\
X0~X2~X1)~(k4\_qc\_lang2~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
