\documentclass{article}
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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\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t110\_sincos10 (TMc4K5jPSyFJMM8wFBV39g85jXBp2fGrbPL)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k10\_sincos10 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_fdiff\_9 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_sin\_cos9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sin\_cos9 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k30\_sin\_cos : {\iota}$ be given.
Let $ k2\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_sin\_cos : {\iota}$ be given.
Let $ k6\_sincos10 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k2\_sincos10 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~\\
(k7\_square\_1~np\_\_2))~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1))){\unicdbdjdcd}\\
(k1\_seq\_1~k1\_fdiff\_9~(k10\_sincos10~X0)=X0))\end{array}
\label{hyp:ehjdadpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k6\_sin\_cos9~(k1\_real\_1~np\_\_1)=k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~\\
k32\_sin\_cos){\unicdcdcdhd}(k1\_seq\_1~k2\_sin\_cos9~(k1\_real\_1~np\_\_1)=k8\_real\_1~\\
(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)\end{array}
\label{hyp:ehddidpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_seq\_1~k1\_fdiff\_9~k6\_numbers=np\_\_1){\unicdcdcdhd}((k1\_seq\_1~k1\_fdiff\_9~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_4)=k7\_square\_1~np\_\_2){\unicdcdcdhd}((k1\_seq\_1~\\
k1\_fdiff\_9~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)=\\
k1\_real\_1~(k7\_square\_1~np\_\_2)){\unicdcdcdhd}(k1\_seq\_1~k1\_fdiff\_9~k32\_sin\_cos=\\
k1\_real\_1~np\_\_1)))\end{array}
\label{hyp:ehddbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_seq\_1~k30\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_4)=np\_\_1){\unicdcdcdhd}\\
((k2\_sin\_cos4~(k10\_real\_1~k32\_sin\_cos~np\_\_4)=np\_\_1){\unicdcdcdhd}((k1\_seq\_1~\\
k30\_sin\_cos~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)=\\
k1\_real\_1~np\_\_1){\unicdcdcdhd}(k2\_sin\_cos4~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~\\
k32\_sin\_cos)=k1\_real\_1~np\_\_1)))\end{array}
\label{hyp:ehbdidpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~\\
(k7\_square\_1~np\_\_2))~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1))){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)~\\
(k10\_sincos10~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k10\_sincos10~X0)~k32\_sin\_cos)))\end{array}
\label{hyp:ehbdadgdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k32\_sin\_cos}={k31\_sin\_cos}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddcdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k10\_sincos10~X0=k6\_sincos10~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdcdcdhd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:chdgedpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k6\_sin\_cos9~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflggdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xreal\_0}~{k31\_sin\_cos}}\label{hyp:egehpflgddbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k30\_sin\_cos){\unicdcdcdhd}(m1\_subset\_1~k30\_sin\_cos~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgddadpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_sincos10){\unicdcdcdhd}(m1\_subset\_1~k2\_sincos10~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgcdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k1\_seq\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_fdiff\_9){\unicdcdcdhd}(m1\_subset\_1~k1\_fdiff\_9~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdpfggegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k6\_sincos10~X0=k1\_seq\_1~\\
k2\_sincos10~X0)\end{array}
\label{hyp:eggdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v3\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdidpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xxreal\_0~X1))\end{array}
\label{hyp:dgdgbdddpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdadpfdhjgogdgpgdhbdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~(k1\_real\_1~\\
(k7\_square\_1~np\_\_2))){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~X0){\unicdcdcdhd}\\
(\preoh (\preoh r1\_xxreal\_0~(k10\_sincos10~X0)~(k8\_real\_1~(k10\_real\_1~np\_\_3~\\
np\_\_4)~k32\_sin\_cos)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~k32\_sin\_cos~(k10\_sincos10~\\
X0)))))\end{array}$$
\end{theorem}
\end{document}
