\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{t17\_circuit2 (TMH6hNSvCj2MF77Qb8EuyDX7WjMNV93rH2c)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_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 $ v5\_msafree2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_funct\_6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_circuit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_circuit1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_msafree2~X0){\unicdcdcdhd}((v5\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k6\_circuit1~X0~X1~X2)~(k7\_circuit1~X0~X1))))\end{array}
\label{hyp:ehbdhdpfdgjgchdgfhjgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_msafree2~X0){\unicdcdcdhd}((v5\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_pboole~X2~(k2\_msafree2~X0)~(k7\_funcop\_1~\\
(k2\_msafree2~X0)~k5\_numbers)~(k5\_relat\_1~(u3\_msualg\_1~X0~X1)~(\\
k2\_msafree2~X0))){\unicdbdjdcd}((v3\_funct\_1~(k10\_funct\_6~X2)){\unicdbdjdcd}((v1\_xboole\_0~\\
(k2\_msafree2~X0)){\unicdcdcdid}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(u3\_msualg\_1~\\
X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_msafree2~X4~X0~X1){\unicdbdjdcd}((X4=k1\_funct\_1~(\\
k10\_funct\_6~X2)~k6\_numbers){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k6\_circuit1~X0~X1~X6)~X5){\unicdbdjdcd}(k1\_funct\_1~(k8\_nat\_1~(k4\_card\_3~(u3\_msualg\_1~\\
X0~X1))~(k9\_circuit2~X0~X1~X2~X3)~X5)~X6=k5\_circuit2~X0~X1~X6~X4)))))))))))\end{array}
\label{hyp:ehbdgdpfdgjgchdgfhjgehcd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfdgjgchdgfhjgehcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_msafree2~X0){\unicdcdcdhd}((v5\_msafree2~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v4\_msafree2~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_pboole~X2~(k2\_msafree2~X0)~(k7\_funcop\_1~\\
(k2\_msafree2~X0)~k5\_numbers)~(k5\_relat\_1~(u3\_msualg\_1~X0~X1)~(\\
k2\_msafree2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_msafree2~X3~X0~X1){\unicdbdjdcd}(((v3\_funct\_1~\\
(k10\_funct\_6~X2)){\unicdcdcdhd}(X3=k1\_funct\_1~(k10\_funct\_6~X2)~k6\_numbers)){\unicdbdjdcd}\\
((v1\_xboole\_0~(k2\_msafree2~X0)){\unicdcdcdid}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k4\_card\_3~(u3\_msualg\_1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k5\_numbers){\unicdbdjdcd}(\\
(X6=k7\_circuit1~X0~X1){\unicdbdjdcd}(k1\_funct\_1~(k8\_nat\_1~(k4\_card\_3~(u3\_msualg\_1~\\
X0~X1))~(k9\_circuit2~X0~X1~X2~X4)~X6)~X5=k5\_circuit2~X0~X1~X5~X3))))))))))\end{array}$$
\end{theorem}
\end{document}
