\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t56\_bvfunc26 (TMQjkGgfLuNA5cCizhvHUhJCFcWyXZwnDr2)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_bvfunc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_bvfunc26 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_bvfunc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_bvfunc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_bvfunc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}(r2\_funct\_2~X0~k6\_margrel1~(\\
k5\_bvfunc\_1~X0~X1~(k11\_bvfunc\_1~X0))~X1))\end{array}
\label{hyp:ehjdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}(r2\_funct\_2~X0~k6\_margrel1~(\\
k2\_bvfunc\_1~X0~X1~(k1\_bvfunc\_1~X0~X1))~(k11\_bvfunc\_1~X0)))\end{array}
\label{hyp:ehfdpfcgghggfhogdgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}(r2\_funct\_2~X0~k6\_margrel1~\\
(k2\_bvfunc\_1~X0~X1~(k5\_bvfunc26~X0~X2~X3))~(k5\_bvfunc\_1~X0~(k2\_bvfunc\_1~\\
X0~X1~(k1\_bvfunc\_1~X0~X2))~(k2\_bvfunc\_1~X0~X1~(k1\_bvfunc\_1~X0~X3)))))))\end{array}
\label{hyp:ehfdadpfcgghggfhogdgcdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k6\_margrel1))))))){\unicdbdjdcd}(k2\_bvfunc\_1~X0~X1~X2=k14\_margrel1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k6\_margrel1)))))){\unicdbdjdcd}(k1\_bvfunc\_1~X0~X1=k13\_margrel1~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k11\_bvfunc\_1~X0)){\unicdcdcdhd}\\
((v3\_funct\_1~(k11\_bvfunc\_1~X0)){\unicdcdcdhd}(v1\_funct\_2~(k11\_bvfunc\_1~X0)~\\
X0~k6\_margrel1)))\end{array}
\label{hyp:ggdgedpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k6\_margrel1))))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_bvfunc\_1~X0~X1~X2)){\unicdcdcdhd}(\\
(v1\_funct\_2~(k5\_bvfunc\_1~X0~X1~X2)~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
(k5\_bvfunc\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k6\_margrel1)))))\end{array}
\label{hyp:egehpflgfdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k6\_margrel1))))))){\unicdbdjdcd}((v1\_funct\_1~(k2\_bvfunc\_1~X0~X1~X2)){\unicdcdcdhd}(\\
(v1\_funct\_2~(k2\_bvfunc\_1~X0~X1~X2)~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
(k2\_bvfunc\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k6\_margrel1)))))\end{array}
\label{hyp:egehpflgcdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k6\_margrel1)))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_bvfunc\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_bvfunc\_1~X0~X1)~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_bvfunc\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k6\_margrel1)))))\end{array}
\label{hyp:egehpflgbdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k11\_bvfunc\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k11\_bvfunc\_1~X0)~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
(k11\_bvfunc\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k6\_margrel1)))))\end{array}
\label{hyp:egehpflgbdbdpfcgghggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k6\_margrel1))))))){\unicdbdjdcd}(k5\_bvfunc26~X0~X1~X2=k5\_bvfunc26~X0~X2~\\
X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgfdpfcgghggfhogdgcdgd}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfcgghggfhogdgcdgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k6\_margrel1))))){\unicdbdjdcd}(r2\_funct\_2~X0~k6\_margrel1~\\
(k2\_bvfunc\_1~X0~X1~(k5\_bvfunc26~X0~X1~X2))~(k2\_bvfunc\_1~X0~X1~(k1\_bvfunc\_1~\\
X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
