\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t47\_valuat\_1 (TMb7FZQ75VJjQceLgo48Mzwn87FqcxwmAdn)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k24\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k8\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~\\
X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k9\_qc\_lang1~\\
X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((\preoh X1 \in k24\_qc\_lang1~X0~X3){\unicdcdcdhd}(X1 \in k24\_qc\_lang1~\\
X0~(k13\_cqc\_lang~X0~X3~X2)))))))\end{array}
\label{hyp:ehddbdpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_subset\_1~X5~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_valuat\_1~X6~X0~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(k9\_qc\_lang1~X0)){\unicdbdjdcd}(((X4=k13\_cqc\_lang~X0~X7~X2){\unicdcdcdhd}(X5=k13\_cqc\_lang~\\
X0~X7~X3)){\unicdbdjdcd}((X2=X3){\unicdcdcdid}({\unicdcdadad} X8 .  (m2\_funct\_2~X8~(k3\_qc\_lang1~X0)~\\
X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}((k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X8~X2=\\
k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X8~X3){\unicdbdjdcd}(k3\_funct\_2~(k2\_valuat\_1~\\
X0~X1)~k6\_margrel1~(k8\_valuat\_1~X0~X1~X6~X4)~X8=k3\_funct\_2~(k2\_valuat\_1~\\
X0~X1)~k6\_margrel1~(k8\_valuat\_1~X0~X1~X6~X5)~X8))))))))))))\end{array}
\label{hyp:ehddadpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_valuat\_1~X4~X0~X1){\unicdbdjdcd}((\preoh X2 \in k24\_qc\_lang1~X0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_funct\_2~X5~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m2\_funct\_2~X6~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~\\
X0~X1)){\unicdbdjdcd}(({\unicdcdadad} X7 .  (m2\_subset\_1~X7~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)){\unicdbdjdcd}((X2{\unicdcdgdad}X7){\unicdbdjdcd}(k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X6~X7=k3\_funct\_2~\\
(k3\_qc\_lang1~X0)~X1~X5~X7))){\unicdbdjdcd}(k3\_funct\_2~(k2\_valuat\_1~X0~X1)~k6\_margrel1~\\
(k8\_valuat\_1~X0~X1~X4~X3)~X5=k3\_funct\_2~(k2\_valuat\_1~X0~X1)~k6\_margrel1~\\
(k8\_valuat\_1~X0~X1~X4~X3)~X6)))))))))\end{array}
\label{hyp:ehcdhdpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_funct\_2~X4~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_funct\_2~X5~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~\\
X0~X1)){\unicdbdjdcd}({\unicdcdaddd} X6 .  (m2\_funct\_2~X6~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~\\
X0~X1)){\unicdcdcdhd}(({\unicdcdadad} X7 .  (m2\_subset\_1~X7~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)){\unicdbdjdcd}((X7{\unicdcdgdad}X2){\unicdbdjdcd}(k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X6~X7=k3\_funct\_2~\\
(k3\_qc\_lang1~X0)~X1~X4~X7))){\unicdcdcdhd}(k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X6~\\
X2=k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X5~X3))))))))\end{array}
\label{hyp:mgddgdpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_valuat\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~\\
(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}((r2\_valuat\_1~X0~X1~X2~X3){\unicdbdjded}\\
({\unicdcdadad} X4 .  (m2\_funct\_2~X4~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~\\
X1)){\unicdbdjdcd}(r1\_valuat\_1~X0~X1~X3~X2~X4))))))\end{array}
\label{hyp:egidpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_valuat\_1~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~\\
(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}((r1\_valuat\_1~X0~X1~X2~\\
X3~X4){\unicdbdjded}(k3\_funct\_2~(k2\_valuat\_1~X0~X1)~k6\_margrel1~(k8\_valuat\_1~\\
X0~X1~X3~X2)~X4=k8\_margrel1))))))\end{array}
\label{hyp:eghdpfghbgmgfhbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfghbgmgfhbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m2\_subset\_1~X5~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_valuat\_1~X6~X0~X1){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(k9\_qc\_lang1~X0)){\unicdbdjdcd}(((X4=k13\_cqc\_lang~X0~X7~X2){\unicdcdcdhd}((X5=k13\_cqc\_lang~\\
X0~X7~X3){\unicdcdcdhd}(r2\_valuat\_1~X0~X1~X6~X4))){\unicdbdjdcd}((X2 \in k24\_qc\_lang1~X0~X7){\unicdcdcdid}\\
(r2\_valuat\_1~X0~X1~X6~X5))))))))))\end{array}$$
\end{theorem}
\end{document}
