\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{t33\_circcomb (TMR52bNHKeBdJMVgQdK1hM1K5txTXrnSB8k)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_card\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}((r1\_circcomb~X0~X1){\unicdbdjdcd}(\\
k2\_circcomb~X0~X1=k2\_circcomb~X1~X0)))\end{array}
\label{hyp:ehfdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh \\
v11\_struct\_0~X1){\unicdcdcdhd}((v2\_msafree2~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((v2\_msafree2~X2){\unicdcdcdhd}(\\
l1\_msualg\_1~X2)))){\unicdbdjdcd}(((r1\_xboole\_0~(k3\_msafree2~X0)~(k2\_msafree2~\\
X1)){\unicdcdcdhd}(X2=k2\_circcomb~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msualg\_1~X3~X0){\unicdcdcdhd}\\
((v4\_msafree2~X3~X0){\unicdcdcdhd}(l3\_msualg\_1~X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~\\
X4~X1){\unicdcdcdhd}((v4\_msafree2~X4~X1){\unicdcdcdhd}(l3\_msualg\_1~X4~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v4\_msualg\_1~X5~X2){\unicdcdcdhd}((v4\_msafree2~X5~X2){\unicdcdcdhd}(l3\_msualg\_1~X5~X2))){\unicdbdjdcd}\\
(((r2\_circcomb~X0~X1~X3~X4){\unicdcdcdhd}(X5=k3\_circcomb~X0~X1~X3~X4)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k4\_card\_3~(u3\_msualg\_1~X2~X5))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k4\_card\_3~(u3\_msualg\_1~X0~X3))){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(k4\_card\_3~(u3\_msualg\_1~X1~X4))){\unicdbdjdcd}(((X7=k11\_card\_3~\\
(u3\_msualg\_1~X2~X5)~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}(X8=k11\_card\_3~(u3\_msualg\_1~\\
X2~X5)~X6~(u1\_struct\_0~X1))){\unicdbdjdcd}(k6\_circuit2~X2~X5~X6=k1\_funct\_4~(\\
k6\_circuit2~X0~X3~X7)~(k6\_circuit2~X1~X4~X8)))))))))))))\end{array}
\label{hyp:ehddcdpfdgjgchdgdgpgngcg}
\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 .  ((v4\_msualg\_1~\\
X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msualg\_1~X3~X1){\unicdcdcdhd}\\
(l3\_msualg\_1~X3~X1)){\unicdbdjdcd}((r2\_circcomb~X0~X1~X2~X3){\unicdbdjdcd}(k3\_circcomb~X0~\\
X1~X2~X3=k3\_circcomb~X1~X0~X3~X2)))))\end{array}
\label{hyp:ehcdcdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_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){\unicdbdjdcd}(r2\_circcomb~X1~\\
X0~X3~X2)))))\end{array}
\label{hyp:ehbdjdpfdgjgchdgdgpgngcg}
\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}
\begin{theorem}\label{thm:ehddddpfdgjgchdgdgpgngcg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v2\_msafree2~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh \\
v11\_struct\_0~X1){\unicdcdcdhd}((v2\_msafree2~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v11\_struct\_0~X2){\unicdcdcdhd}((v2\_msafree2~X2){\unicdcdcdhd}(\\
l1\_msualg\_1~X2)))){\unicdbdjdcd}(((r1\_xboole\_0~(k3\_msafree2~X1)~(k2\_msafree2~\\
X0)){\unicdcdcdhd}(X2=k2\_circcomb~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_msualg\_1~X3~X0){\unicdcdcdhd}\\
((v4\_msafree2~X3~X0){\unicdcdcdhd}(l3\_msualg\_1~X3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v4\_msualg\_1~\\
X4~X1){\unicdcdcdhd}((v4\_msafree2~X4~X1){\unicdcdcdhd}(l3\_msualg\_1~X4~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v4\_msualg\_1~X5~X2){\unicdcdcdhd}((v4\_msafree2~X5~X2){\unicdcdcdhd}(l3\_msualg\_1~X5~X2))){\unicdbdjdcd}\\
(((r2\_circcomb~X0~X1~X3~X4){\unicdcdcdhd}(X5=k3\_circcomb~X0~X1~X3~X4)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(k4\_card\_3~(u3\_msualg\_1~X2~X5))){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~(k4\_card\_3~(u3\_msualg\_1~X0~X3))){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(k4\_card\_3~(u3\_msualg\_1~X1~X4))){\unicdbdjdcd}(((X7=k11\_card\_3~\\
(u3\_msualg\_1~X2~X5)~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}(X8=k11\_card\_3~(u3\_msualg\_1~\\
X2~X5)~X6~(u1\_struct\_0~X1))){\unicdbdjdcd}(k6\_circuit2~X2~X5~X6=k1\_funct\_4~(\\
k6\_circuit2~X1~X4~X8)~(k6\_circuit2~X0~X3~X7)))))))))))))\end{array}$$
\end{theorem}
\end{document}
