\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{t27\_circcmb3 (TMR9pBgtPeD8Gjxdr8vCxhNSxdZLxRrgSjL)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (r1\_partfun1~(k7\_funcop\_1~\\
X0~X2)~(k7\_funcop\_1~X1~X3)){\unicdbdjded}((X2=X3){\unicdcdcdid}(r1\_xboole\_0~X0~X1))\end{array}
\label{hyp:ehidhdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_funct\_1~X0))){\unicdbdjdcd}\\
(X0=k7\_funcop\_1~(k9\_xtuple\_0~X0)~(k3\_funct\_1~X0))\end{array}
\label{hyp:ehidadpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~X1){\unicdbdjdcd}(((v4\_circcomb~X2~X0){\unicdcdcdhd}\\
(v4\_circcomb~X3~X1)){\unicdbdjdcd}(r1\_partfun1~(u4\_msualg\_1~X0~X2)~(u4\_msualg\_1~\\
X1~X3))))))\end{array}
\label{hyp:ehedidpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}((v2\_circcomb~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}(r1\_circcomb~X0~X1))\end{array}
\label{hyp:ehedhdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l2\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdcdcdhd}\\
(m1\_circcmb3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_circcmb3~X2~X0~X1){\unicdbdjdcd}((v4\_msafree2~\\
X2~X1){\unicdcdcdhd}(l3\_msualg\_1~X2~X1)))\end{array}
\label{hyp:egehpfngcdpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_circcmb3~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}\\
((v1\_circcomb~X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}((v5\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~\\
X1)))))))\end{array}
\label{hyp:egehpfngbdpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}(l2\_msualg\_1~X1~X0))\end{array}
\label{hyp:egehpfmgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (l3\_msualg\_1~X3~X1){\unicdbdjdcd}((r2\_circcomb~X0~X1~X2~X3){\unicdbdjded}\\
((r1\_circcomb~X0~X1){\unicdcdcdhd}((r1\_partfun1~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~\\
X1~X3)){\unicdcdcdhd}(r1\_partfun1~(u4\_msualg\_1~X0~X2)~(u4\_msualg\_1~X1~X3))))))))\end{array}
\label{hyp:egddpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_circcmb3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msafree2~X2~X1){\unicdcdcdhd}(l3\_msualg\_1~\\
X2~X1)){\unicdbdjdcd}((m2\_circcmb3~X2~X0~X1){\unicdbdjded}((v4\_circcomb~X2~X1){\unicdcdcdhd}((v3\_funct\_1~\\
(u3\_msualg\_1~X1~X2)){\unicdcdcdhd}(k3\_funct\_1~(u3\_msualg\_1~X1~X2)=X0))))))\end{array}
\label{hyp:egbdadpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdcdcdhd}\\
(m1\_circcmb3~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_circcmb3~X2~X0~X1){\unicdbdjdcd}((v4\_msualg\_1~\\
X2~X1){\unicdcdcdhd}(v4\_circcomb~X2~X1)))\end{array}
\label{hyp:dgdggdpfdgjgchdgdgngcgdd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfdgjgchdgdgngcgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_circcmb3~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_circcmb3~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_circcmb3~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_circcmb3~X4~X0~X2){\unicdbdjdcd}(r2\_circcomb~\\
X1~X2~X3~X4)))))\end{array}$$
\end{theorem}
\end{document}
