\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t20\_sin\_cos4 (TMW5MArmji5FbnMur8QTMvsMUG1w69713Dj)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k17\_sin\_cos~\\
(k6\_xcmplx\_0~X0~X1)=k6\_xcmplx\_0~(k3\_xcmplx\_0~(k17\_sin\_cos~X0)~\\
(k20\_sin\_cos~X1))~(k3\_xcmplx\_0~(k20\_sin\_cos~X0)~(k17\_sin\_cos~\\
X1))))\end{array}
\label{hyp:ehidcdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xcmplx\_0~X3){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(k6\_xcmplx\_0~(k7\_xcmplx\_0~X2~X0)~(k7\_xcmplx\_0~\\
X3~X1){\unicdcdgdad}k7\_xcmplx\_0~(k6\_xcmplx\_0~(k3\_xcmplx\_0~X2~X1)~(k3\_xcmplx\_0~\\
X3~X0))~(k3\_xcmplx\_0~X0~X1)))))))\end{array}
\label{hyp:ehbdddadpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k20\_sin\_cos}~{X0}})}})}}}\label{hyp:ggdgedpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k17\_sin\_cos}~{X0}})}})}}}\label{hyp:ggdgddpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k1\_sin\_cos4~X0=k7\_xcmplx\_0~(k17\_sin\_cos~\\
X0)~(k20\_sin\_cos~X0))\end{array}
\label{hyp:egbdpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k3\_xcmplx\_0~X0~X1=k3\_xcmplx\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdhjgogpfdgpgdhed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (k20\_sin\_cos~\\
X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k20\_sin\_cos~X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(k6\_xcmplx\_0~\\
(k1\_sin\_cos4~X0)~(k1\_sin\_cos4~X1){\unicdcdgdad}k7\_xcmplx\_0~(k17\_sin\_cos~(\\
k6\_xcmplx\_0~X0~X1))~(k3\_xcmplx\_0~(k20\_sin\_cos~X0)~(k20\_sin\_cos~\\
X1))))))\end{array}$$
\end{theorem}
\end{document}
