\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{t40\_incsp\_1 (TMbkvAP1W8QcJe8CqpUQGefT9HVGq39shVN)}
\maketitle
Let $ v15\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r5\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_incsp\_1~X0))){\unicdbdjdcd}(((r5\_incsp\_1~\\
X0~X3~X2){\unicdcdcdhd}(r2\_incsp\_1~X0~X1~X2)){\unicdbdjded}(r5\_incsp\_1~X0~(k4\_subset\_1~(u1\_incsp\_1~\\
X0)~X3~(k6\_domain\_1~(u1\_incsp\_1~X0)~X1))~X2)))))\end{array}
\label{hyp:ehjdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k1\_enumset1~X0~X1~X2=k1\_enumset1~\\
X0~X2~X1\end{array}
\label{hyp:ehfdhdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u4\_incsp\_1~X0)){\unicdbdjdcd}((r5\_incsp\_1~X0~(k7\_domain\_1~\\
(u1\_incsp\_1~X0)~X1~X2)~X3){\unicdbdjded}((r2\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(r2\_incsp\_1~X0~\\
X2~X3))))))\end{array}
\label{hyp:ehddpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k1\_enumset1~X0~X1~X2=k2\_xboole\_0~\\
(k2\_tarski~X0~X1)~(k1\_tarski~X2)\end{array}
\label{hyp:ehddpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
((r1\_incsp\_1~X0~X3~(k1\_incsp\_1~X0~X1~X2)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(v3\_incsp\_1~\\
(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X0))))))\end{array}
\label{hyp:ehddfdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}((r4\_incsp\_1~X0~(k7\_domain\_1~\\
(u1\_incsp\_1~X0)~X2~X3)~X1){\unicdbdjded}((r1\_incsp\_1~X0~X2~X1){\unicdcdcdhd}(r1\_incsp\_1~X0~\\
X3~X1))))))\end{array}
\label{hyp:ehbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}(v3\_incsp\_1~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X1~\\
X2)~X0)))\end{array}
\label{hyp:ehbdfdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u4\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_incsp\_1~\\
X0))){\unicdbdjdcd}(((r4\_incsp\_1~X0~X3~X1){\unicdcdcdhd}(r3\_incsp\_1~X0~X1~X2)){\unicdbdjdcd}(r5\_incsp\_1~\\
X0~X3~X2)))))\end{array}
\label{hyp:ehbdedpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X1~X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X0)))){\unicdbdjdcd}\\
(k8\_domain\_1~X0~X1~X2~X3=k1\_enumset1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k7\_domain\_1~X0~X1~X2=k2\_tarski~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_incsp\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{u1\_incsp\_1}~{X0}})}}}})}}}\label{hyp:egehpffhbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_incsp\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_incsp\_1}~{X0}})}}}\label{hyp:egehpfmgcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(m1\_subset\_1~(k7\_domain\_1~X0~X1~X2)~\\
(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(k6\_domain\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u2\_incsp\_1~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k4\_incsp\_1~X0~X1~X2)~(u4\_incsp\_1~X0))\end{array}
\label{hyp:egehpflgedpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v15\_incsp\_1~X0){\unicdcdcdhd}\\
(l2\_incsp\_1~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_incsp\_1~X0))))){\unicdbdjdcd}(m1\_subset\_1~\\
(k2\_incsp\_1~X0~X1~X2~X3)~(u4\_incsp\_1~X0))\end{array}
\label{hyp:egehpflgcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_incsp\_1~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k1\_incsp\_1~X0~X1~X2)~(u2\_incsp\_1~X0))\end{array}
\label{hyp:egehpflgbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}(({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~\\
X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}(r1\_incsp\_1~X0~X3~X2))){\unicdcdcdhd}(\preoh {\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u4\_incsp\_1~X0)){\unicdbdjdcd}((X3=k4\_incsp\_1~X0~X1~X2){\unicdbdjded}((\\
r3\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(r3\_incsp\_1~X0~X2~X3))))))))\end{array}
\label{hyp:egcdcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
((\preoh v3\_incsp\_1~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u4\_incsp\_1~X0)){\unicdbdjdcd}((X4=k2\_incsp\_1~X0~X1~X2~X3){\unicdbdjded}\\
(r5\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X4)))))))\end{array}
\label{hyp:egcdadpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u2\_incsp\_1~\\
X0)){\unicdbdjdcd}((X3=k1\_incsp\_1~X0~X1~X2){\unicdbdjded}(r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~\\
X0)~X1~X2)~X3))))))\end{array}
\label{hyp:egbdjdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k7\_domain\_1~X0~X1~X2=k7\_domain\_1~\\
X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflghdpfegpgngbgjgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfjgogdgdhahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v15\_incsp\_1~X0){\unicdcdcdhd}(l2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
((\preoh v3\_incsp\_1~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X3)~X0){\unicdbdjdcd}(k2\_incsp\_1~\\
X0~X1~X2~X3=k4\_incsp\_1~X0~(k1\_incsp\_1~X0~X1~X2)~(k1\_incsp\_1~X0~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
