\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t118\_pboole (TMa7MqfiKo2N5tjNpACUMnLf25W2w4edJjG)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  r1\_xboole\_0~(k4\_xboole\_0~X0~X1)~(k4\_xboole\_0~\\
X1~X0)\end{array}
\label{hyp:ehidcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k4\_pboole~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k4\_pboole~X0~\\
X1~X2)~X0){\unicdcdcdhd}((v1\_funct\_1~(k4\_pboole~X0~X1~X2)){\unicdcdcdhd}(v1\_partfun1~(k4\_pboole~\\
X0~X1~X2)~X0))))\end{array}
\label{hyp:egehpflgedpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
((r5\_pboole~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}(r1\_xboole\_0~(k1\_funct\_1~\\
X1~X3)~(k1\_funct\_1~X2~X3)))))\end{array}
\label{hyp:egidpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_partfun1~X3~X0)))){\unicdbdjdcd}((X3=k4\_pboole~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
(X4 \in X0){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k6\_subset\_1~(k1\_funct\_1~X1~X4)~(k1\_funct\_1~\\
X2~X4))))))\end{array}
\label{hyp:eggdpfahcgpgpgmgfg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdidpfahcgpgpgmgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
(r5\_pboole~X0~(k4\_pboole~X0~X1~X2)~(k4\_pboole~X0~X2~X1)))\end{array}$$
\end{theorem}
\end{document}
