text:
Санчо I Ордоньес (; около 895 — 16 августа(?) ) — король Галисии с 926 года. Старший сын короля Леона Ордоньо II и Эльвиры Менендес, представитель династии Перес.

Биография
После смерти в 924 году Ордоньо II его королевство перешло не к его сыновьям: Санчо, Альфонсо и Рамиро, а было присоединено к владениям его младшего брата Фруэлы II, который, таким образом, объедининил в своих руках управление тремя королевствами — Леоном, Галисией и Астурией. Когда в 925 году Фруэла II умер, королём стал его сын Альфонсо Фройлас. Однако сыновья Ордоньо II в этом же году подняли мятеж против нового короля, мотивируя свои права на престол тем, что их отец был старшим братом Фруэлы II. Опираясь на поддержку галисийского дворянства, на представительницах знатных семейств которого были женаты Санчо и Рамиро, и духовенства (особенно епископа Сантьяго-де-Компостела Херменгильда), а также на помощь короля Наварры Санчо I Гарсеса, братьям удалось вытеснить Альфонсо Фройласа из Леона.

Санчо отказался от короны в пользу младшего брата Альфонсо, который взошёл на престол под именем Альфонсо IV. В 926 году братья изгнали Альфонсо Фройласа и из Галисии. Королём здесь был провозглашён Санчо I Ордоньес. Его брат Рамиро получил графство Визеу, подчинявшееся верховной власти короля Галисии. Альфонсо Фройлас до самой своей смерти предпринимал безуспешные попытки отвоевать у сыновей Ордоньо II владения своего отца.

Став королём, Санчо I продолжил политику своего отца Ордоньо II на укрепление связей с дворянством и Церковью. Сохранилось несколько хартий, подписанных Санчо и его супругой Готу, в которых королевская чета передавала представителям галисийской знати или получала от них в дар владения и ценности. Ещё больше документов сохранилось о дарениях, сделанных королём монастырям и церквям. Особенно щедрые пожертвования были произведены в пользу Сантьяго-де-Компостела и монастыря Санта-Мария-де-Леон. Хартия в пользу Санта-Мария-де-Леон была дана на генеральном сейме всех трёх королевств, состоявшемся в декабре 927 года в Сарриа, и была подписана также братьями Санчо, Альфонсо IV и Рамиро.

Санчо I Ордоньес был женат (ранее 927 года) на  (Гото Нуньес) (умерла не позднее 1 марта 963 года), дочери знатного галисийского аристократа Муниу Гутерреша и Эльвиры Ариаш, которая была дочерью графа Коимбры Ариаша Мендеша. Брак был бездетным.

Король Санчо I скончался летом 929 года. Новым королём стал его брат Альфонсо IV, который вновь объединил под своей властью Леон, Галисию и Астурию.

Примечания

Литература

Ссылки

Родившиеся в 895 году
Умершие 16 августа
Правители Галисии
Правители Европы X века


Flame Vines are sprawling plants with bright orange coloured flowers. They belong to the Bignoniaceae family.
The Flame vine is a common plant of Florida which grows with virtually no care but dazzles its surrounding with bright orange flowers. The Flame vine requires minimum care but certainly lives up to its name as far as its appearance is concerned.
These plants do not need a lot of maintenance. All it needs is a good spot with lots of light and it takes care of itself once it is established. The Flame vines are rampant growers and might prove to be a nuisance to other plants if not properly pruned and trained. These plants need a support to grow. They also are pest-free, therefore the only care they need is regular pruning.
The Flame vines grow well under full sunlight or partial shade. The optimum temperature for growth is 25 degrees Celsius.
These plants are drought resistant. Therefore they don't need too much water. They should be watered only when the soil is dry. During the hot and dry months, watering once in 2-3 days is enough.
The Flame vines grow well in well-drained soil. However, sandy soil is ideal for its growth.
The plant grows 30-40 ft in height. The leaves are 4 inches in length.
The Plant has a dark green foliage and bears clusters of bright orange or yellow flowers. The flowers are tubular in shape and about 3 inches long. They bloom from fall to spring.
This vine is fast growing and can spread over vast areas in a very short time if not properly pruned. As they are rampant growers, pruning must be done regularly and meticulously by the gardeners.
The plant tends to bear flowers at the top. Thus the stems must be cut back properly to encourage growth in the middle and lower portions.
Any organic fertilizer can be applied. It must be noted that the plant is pest-free.
The leaves of the Flame vine is used for medicinal purposes in Brazil. These leaves are also edible. But the Flame vine is mainly used for ornamental purposes.


Involuntarily leaving a job can be extremely traumatic. Most large employers who decide to downsize offer what we call an "outplacement packet". Financially, your employer may offer a severance package. Most of the time, the amount you receive is determined by how long you've been employed. We see severances given out in two ways; lump sum, or a steady stream of income. If yours comes in a lump sum, be diligent. Perhaps put it all in a savings account, and withdraw only the amount needed to replace your previous paycheck. Additionally, many employers offer assistance with finding a new job, training for potential new jobs and sometimes counseling. Help with resumes is often given. Seriously consider taking advantage of every benefit that is afforded to you. Take any job training classes offered. Take any outplacement assistance that you can.
We recommend transferring all retirement accounts to Qualified IRA's. We can assist with this, Click HERE to setup an appointment!
Most folks will want to re-establish health/disability/life insurance privately. We can assist with this, Click HERE to setup an appointment!
If you need it, your health insurance can usually continue. This is called Cobra. Normally, you'll keep the exact insurance you had, however you'll have to pay all of the premiums yourself. You usually have 60 days to enroll in Cobra. Cobra should last you at least 18 months. Again, Cobra can be expensive; consider switching to a spouse's plan.
Have a loan from your 401K? That's usually bad news for you. If you took out a loan at some point, and even if you're diligently paying it back each payday, the entire loan will "come due" when you cease employment. You usually have an option to write them a check and pay it back. For most employees who've just lost a job, that's pretty difficult.
The good news is you don't HAVE to pay it back immediately. The bad news is that you will receive a 1099R after January. You will have to claim the remaining balance as income on your tax return for this year. To make matters worse, if you're under 59 1⁄2, the 1099R will be coded in such a way that you'll probably have a 10% penalty assessed by the IRS. Had you just stayed employed, you had a loan, and hopefully worked long enough to pay it back. No taxes or penalty. But when you're no longer employed, it is treated as if you withdrew the money. We can deal with this at tax time next year.
ALWAYS file for unemployment as soon as you reasonably can. You will not be eligible for unemployment benefits (In Virginia) until all of your severance has been paid. If you're still receiving payments, you'll have to wait until the severance payments cease. Unemployment benefits are NOT taxable in the state of Virginia. That's great. But they are taxable on the federal side. Consider having the VEC withhold some federal taxes.
Use Technology to your Advantage. To aid you in being successful at searching for a new position, you'll need to be computer literate. We recommend saving your resumé in a "word" document. It's often best to edit your resumé by changing it for each position you apply for. You will want use some of the "key words" that are listed in the job description, to also show up on your resumé. If you're not on Facebook, you need to sign up ASAP. If you're already there, change your employment info immediately. Let folks know right there, what your skill sets are.
Where else do you look for a job? Local major employers have their own "careers" pages on their websites. Sign up for all of them. You could spend an entire day, just setting up accounts.
AEP, Allstate, Altec, Anthem/Blue Cross/Wellpoint (whatever they're called this week) Carillon, Cox, Comcast, Fed Ex, Food Lion, GE, Kroger, Lewis Gale, Macy's, Norfolk Southern, UPS, United Healthcare are just a very few. Think about all of the state and local government offices; cities and counties.
DON'T be ashamed! It's not your fault your company wasn't profitable. Your friends and family know your character. Use your contacts to promote you. Use social media such as Facebook, Twitter and Linkedin. Ask your friends to mention you to anyone they can, as well as listening out for job openings. Make sure your "network" knows what your skills are. Many times, your friends and family don't know exactly what you do. Or, you might have had one particular job, but you possess many different skill sets. Now, maybe, you'll put that degree in History to work.


text:
Q: CSS3 Style button: how can I make a button fades away while playing I have been trying to style a CSS3 button that currently activates on hover and each time it gets stopped/started it fades. I am trying to modify the current code in order for the play button to fade away only on click (play/pause action)
Here is the code:
 .play-button {
        background-color: rgb(80,80,80);
        border: 2px solid rgb(136,136,136);
        width: 60px;
        height: 60px;
        position: absolute;
        border-radius: 30px;
        top: 50%;
        left: 50%;
        margin: -30px;
        cursor: pointer;
        opacity: 0;
        transition: opacity 0.25s ease-in-out;
        -moz-transition: opacity 0.25s ease-in-out;
        -webkit-transition: opacity 0.25s ease-in-out;
        -o-transition: opacity 0.25s ease-in-out;
        transition: opacity 0.25s ease-in-out;

        &:hover {
            opacity: 3;
        }
    }

    .play-button:before {
        content: "";
        position: absolute;
        background: transparent;
        border: 14px solid transparent;
        top: 16px;
        left: 25px;
        height: 0;
        border-right-color: transparent;
        border-top-color: transparent;
        border-bottom-color: transparent;
        border-right: 0;
        -webkit-transition: all 250ms ease-in-out;
        -moz-transition: all 250ms ease-in-out;
        -ms-transition: all 250ms ease-in-out;
        -o-transition: all 250ms ease-in-out;
        transition: all 250ms ease-in-out;
    }

    .play-button:after {
        content: "";
        position: absolute;
        border: 14px solid white;
        top: 15px;
        left: 24px;
        height: 0;
        border-right-color: transparent;
        border-top-color: transparent;
        border-bottom-color: transparent;
        border-right: 0;
        -webkit-transition: all 250ms ease-in-out;
        -moz-transition: all 250ms ease-in-out;
        -ms-transition: all 250ms ease-in-out;
        -o-transition: all 250ms ease-in-out;
        transition: all 250ms ease-in-out;
    }

    .play-button.pause:before {
        border: 4px solid white;
        top: 18px;
        left: 18px;
        height: 16px;
    }

    .play-button.pause:after {
        content: "";
        position: absolute;
        border: 4px solid white;
        top: 18px;
        left: 33px;
        height: 16px;
    }

If I modify .play-button as follows, the button will be fixed, but then it does not fade away on click, meaning that it stays over the animated gif while it is playing:
.play-button {
            background-color: rgb(80,80,80);
            border: 2px solid rgb(136,136,136);
            width: 60px;
            height: 60px;
            position: absolute;
            border-radius: 30px;
            top: 50%;
            left: 50%;
            margin: -30px;
            cursor: pointer;
        }

How can I change my current to achieve what I want?
Thank you for your help

redpajama_set_name: RedPajamaStackExchange


>> US president, Donald Trump's effort to halt Iran's oil exports met with a swift threat, Thursday. The OPEC nation saying it will retaliate by blocking the Strait of Hormuz to all nations who pass through it, potentially closing one of the world's most important oil passages. Iran announcing the Strait will be, quote, for all or for no one, according to the country's Tasnim News Agency.
This comes after Trump on Wednesday, took a swipe at OPEC, tweeting, they are driving prices higher as the United States defends many of their members for very little money. This must be a two way street. Reduce pricing now. The Iranian OPEC governor hit back with this message for Trump.
Quote, your tweets have increased the prices by at least $10. Please stop this method. His retort quoted in the Iranian oil ministry's news agency, SHANA. Trump has been urging OPEC to stabilize prices with more supply, as higher prices at the pump could create a headache for him ahead of November's midterm elections.
Just days ago he called on Saudi Arabia to increase oil output. A move Iran claimed was meant to intensify tensions between it and OPEC's biggest member. Trump has also called on European allies to stop buying oil from Iran as it looks to impose sanctions on the country, having pulled the US out of the Iran nuclear deal in May.
On Friday, the remaining signatories of the Iran deal will meet in Vienna, to discuss how to keep the accord alive after the US withdrawal.


text:
Education and Dramatic Art £29.99
by David Hornbrook
To this day, Education and Dramatic Art remains the only fully worked critique of drama education in schools. Provocative and iconoclastic, this new edition brings the argument up-to-date and locates the author's proposals for a curriculum based on the making, performing and appraisal of dramas securely in the evolving culture of schools.
The first section of the book traces the origins and fortunes of drama in schools in the context of changing political times and argues that by neglecting the customs and practices of the theatre, drama-in-education has often kept from the students it professes to empower, the very knowledge and understanding necessary for them to take command of their subject.
Part two examines the developmental and pedagogic claims of drama-in-education. Theories of knowledge and meaning and assumptions about schools drama's power to establish a moral and social agenda, are all called to account.
Finally, Education and Dramatic Art proposes a multiculturally-based, theoretical structure for the teaching of drama which pulls the theatre and the classroom together and offers teachers the foundation for a broad and balanced drama curriculum with its own distinctive body of knowledge and skills.
Acting (Re)Considered (£24.99)
by Phillip B. Zarilli
ISBN: 0-415-26300-X
Analysing Performance (£15.99)
by Patrick Gardner (Editor)
ISBN: 0-7190-4250-X
Teacher-in-Training Membership (£20.00)

redpajama_set_name: RedPajamaCommonCrawl


text:
Turn Left At The Bridge
A view from the Galloway hills
David Icke and the Robots' Rebellion
New Age Fascism
The Burning Times
The Atlantis Commune
Satan and the Little Green Men
The Renfrewshire Witches
Prophecies of the New Millennium
Designated Survivor review Pt 2
August 3, 2018 GeneralVal
Well, I've carried on watching and have now finished Ep 15 (of 22). I'm not really excited about it, but I've paid for the whole series so I'm determined to get my money's worth. Besides, I am mildly curious about how the story will pan out.
The US has turned out some excellent TV series – The Americans, The Wire, Mad Men, West Wing – but DS is nowhere near that standard, I'm afraid. The writing is pretty poor, with each eopisode settling into a formulaic action/family soap/drama/action pattern. And there's little attention paid to what should be running storylines. For instance, are Muslims and other minorities still being persecuted? What happened to the arrested Michigan governor? How is the country managing with the loss of its entire Government? These and other questions are never addressed at all.
And then there's the ongoing family soap. Kirkman's teenage son started out as a typical teenager, lying to his parents,going to raves, selling drugs to his friends, being a total brat at home. Plenty of material there for some interesting plotlines and character development. But no, just a week or so of living in the White House turned him into a squeaky-clean angel. Oh, there was that episode-and-a-half half of overworked histrionics about who his real dad was, but that ended in gallons of schmaltz. tears and "Love you guys…(sniffle)". And the cute young daughter? She could have been played by an animatronic dummy – and that's NOT being mean to the kid playing her, who did a perfectly good job with very poor material.
Thankfully, the kids have now been despatched to live somewhere else – Camp David, or their Granny's place, I've really not cared enough to pay attention. I suspect that the writers realised that the soapy family drama really wasn't working and so sent them off to a nice farm somewhere where they'll have a lovely life playing with the animals….
And the writing…! Oh dear, oh dear….. To give one example – the Prez is in the War Room with his generals, coping with the latest international-crisis-of-the-week; a Lords Army-type gang of murderous African rebels is headed towards a town where thousands of refugees have gathered; said refugees will get horribly genocided if US/UN forces don't stop the rebels; something or other (I wasn't paying attention) is stopping the Western forces from bombing the crap out of the rebels before they reach the town. So Kirkman grabs a map; crying "I used to be an urban planner!" he points to a couple of bridges. "The rebels have to cross these to get to the town, don't they?" he asks, and the generals nod. "So," he exclaims in triumph, "Why don't we BOMB THE BRIDGES?"
The generals don't quite step back and gasp in amazement at this civilian's uncanny grasp of military strategy, but they come close. And, kids, that's how thousands of African refugees owe their lives to a middle-aged US urban planner!
However, it's turning into a surprisingly good thriller, due in large part to actor Maggie Q, who plays FBI agent Hannah Wells. She is basically Jack Bauer in a well-fitting pantsuit. She may be mourning the death of a lover, but she keeps the tears firmly under control and works though her grief by going totally hard-bitch on the asses of any nearby bad guys. She is honestly just brilliant at the action stuff; and really, action stuff is pretty much all this series has going for it. Also, there are enough twists and turns in the conspiracy storyline to keep me watching, just to see how silly it gets.
So, watch this if you want a decent action thriller with a kickass female lead. Just don't expect 24 Hours: The West Wing.
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text:
\section{Introduction}
\label{sec:intro}

Propositional satisfiability (SAT) solvers based on \emph{conflict-driven
clause learning
(CDCL)}~\cite{DBLP:series/faia/SilvaLM09}
implement
a combination of the DPLL algorithm~\cite{DBLP:journals/cacm/DavisLL62} and
propositional \emph{resolution}~\cite{DBLP:journals/jacm/Robinson65} to derive
\emph{learned clauses} from a CNF to be solved.

CDCL has been extended to solve \emph{quantified Boolean formulas
(QBFs)}~\cite{DBLP:series/faia/BuningB09}, resulting in the \emph{QCDCL}
approach~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02}. The
logic of QBFs allows for explicit universal and existential quantification of
propositional variables. As a consequence, the satisfiability problem of QBFs
is PSPACE-complete.

In contrast to SAT solving, where CDCL is the dominant solving paradigm in
practice, QCDCL is complemented by \emph{variable
expansion}~\cite{DBLP:conf/fmcad/AyariB02,DBLP:conf/sat/Biere04a}. This
approach successively eliminates variables from a QBF until it reduces to
either true or false. Many modern solvers
(e.g.~\cite{Janota20161,DBLP:conf/ijcai/JanotaM15,DBLP:conf/fmcad/RabeT15})
implement expansion by \emph{counter-example guided abstraction refinement
(CEGAR)}~\cite{DBLP:journals/jacm/ClarkeGJLV03}.

The \emph{Q-resolution calculus
(QRES\xspace)}~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:journals/iandc/BuningKF95,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02}
is a QBF proof system that underlies QCDCL in a way that is analogous
to propositional resolution in CDCL. The empty clause is derivable
from a PCNF $\psi$ by QRES\xspace iff $\psi$ is
unsatisfiable. According to QBF proof complexity, there is an
exponential separation between the sizes of proofs that variable expansion
and Q-resolution can
produce for certain QBFs~\cite{beyersdorff_et_al:LIPIcs:2015:4905,DBLP:journals/tcs/JanotaM15}.
This
theoretical result suggests to combine such orthogonal proof systems in QBF
solvers to leverage their individual strengths.

As a first step towards a solver framework that allows for the combination of QBF
proof systems in a systematic way, we present the latest major release version~6.0 of the QCDCL solver
\textsf{DepQBF}\xspace.\footnote{\textsf{DepQBF}\xspace is licensed under GPLv3:
\url{http://lonsing.github.io/depqbf/}} In contrast to traditional
QCDCL based on
QRES\xspace~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:journals/iandc/BuningKF95,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02},
\textsf{DepQBF~6.0}\xspace implements a variant of QCDCL that relies on a generalization of
QRES\xspace. This generalization is due to a set of new axioms added to
QRES\xspace~\cite{DBLP:conf/sat/LonsingES16}. In practice, derivations made
by the added axioms in QCDCL are based on \emph{arbitrary} QBF proof
systems. As a consequence, when applying proof systems that are orthogonal to
Q-resolution, the generalization of QRES\xspace via the new axioms enables QCDCL as
implemented in \textsf{DepQBF~6.0}\xspace to potentially produce exponentially shorter
proofs than traditional QCDCL.

We report on experiments where we compare
\textsf{DepQBF~6.0}\xspace to state of the art QBF solvers. Experimental results
demonstrate the effectiveness of generalized QRES\xspace in QCDCL.
Additionally, we briefly summarize the evolution of \textsf{DepQBF}\xspace since the first
version~0.1~\cite{DBLP:journals/jsat/LonsingB10}. We relate the features that
were added to the different versions of \textsf{DepQBF}\xspace over time to the enhanced variant of QCDCL
implemented in \textsf{DepQBF~6.0}\xspace.

\section{Preliminaries}
\label{sec:prelims}

A QBF $\psi := \Pi.\phi$ in \emph{prenex conjunctive normal form (PCNF)}
consists of a \emph{quantifier prefix} $\Pi := Q_1X_1 \ldots Q_nX_n$ and a
CNF $\phi$ not containing tautological clauses.
The CNF $\phi$ is defined over the propositional variables $X_1 \cup \ldots \cup X_n$
that appear in $\Pi$. The variable sets $X_i$ are pairwise disjoint and $Q_i
\not= Q_{i+1}$ for
$Q_i \in \{\forall, \exists\}$.
QBFs $\psi := \Pi.\phi$ in \emph{prenex disjunctive normal
  form (PDNF)} are defined analogously to PCNFs, where $\phi$ is a DNF
consisting of \emph{cubes}. A cube is a conjunction of literals.
 The \emph{quantifier}
$\quant{\Pi}{l}$ of  a literal $l$ is  $Q_i$ if the variable $\lit{l}$ of $l$ appears in
$X_i$. If $\quant{\Pi}{l} = Q_i$
and $\quant{\Pi}{k} = Q_j$,
then \nolinebreak $l \leq_\Pi k$ \nolinebreak iff \nolinebreak $i \leq j$.

An \emph{assignment} $A$ maps variables
of a QBF $\Pi.\phi$ to truth values \emph{true} ($\top$) and
\emph{false} ($\bot$). We
represent $A = \{l_1,\ldots,l_n\}$
as a set of literals such that if a variable $x$ is
assigned \emph{true} (\emph{false}) then $l_i \in A$ with $l_i = x$ ($l_i =
\bar x$), where $\bar x$ is the negation of $x$.
Further, $\lit{l_i} \not= \lit{l_j}$ for any $l_i, l_j \in A$ with $i \not= j$.

The PCNF $\psi$ \emph{under assignment} $A$,
written as
$\psi[A]$, is the PCNF
obtained from $\psi$ in which
for all $l \in A$, all clauses containing $l$ are removed,
all occurrences of $\bar l$ are deleted, and $\lit{l}$ is
removed from the prefix.
If the CNF of $\psi[A]$ is empty (respectively, contains the empty clause $\emptyset$), then
it is satisfied (falsified) by $A$ and
$A$ is a \emph{satisfying} (\emph{falsifying}) assignment, written as $\psi[A] = \top$ ($\psi[A] = \bot$).
A \emph{PDNF $\psi$ under an assignment
$A$} and an \emph{empty cube} are defined in a way dual to PCNFs and empty clauses.
A QBF $\Pi.\phi$
with $Q_1 = \exists$ ($Q_1 = \forall$)
is satisfiable iff, for $x \in X_1$,
$\Pi.\phi[\{x\}]$ or (and)
$\Pi.\phi[\{\bar x\}]$ is satisfiable.
Two QBFs $\psi$ and $\psi'$ are \emph{satisfiability-equivalent}
($\psi \equiv_{\mathit{sat}} \psi'$), iff
$\psi$ is satisfiable whenever $\psi'$ is
satisfiable.

\section{QCDCL and the Generalized Q-Resolution Calculus}
\label{sec:qcdcl}

In the following, we present the variant of QCDCL implemented in
\textsf{DepQBF~6.0}\xspace that relies on a generalization of the Q-resolution calculus
(QRES\xspace). We
illustrate the workflow of that variant in Fig.~\ref{fig:qcdcl:enhanced}.

In general, QCDCL is based on the successive generation of assignments that
guide the application of the inference rules of QRES\xspace to derive
\emph{learned clauses} and \emph{cubes} from a
given input PCNF $\psi = \Pi. \phi$. Learned cubes are dual to
clauses. While learned clauses represent assignments that falsify the CNF
$\phi$ of $\psi$, learned cubes represent assignments that satisfy
$\phi$.
The empty cube is derivable
from a PCNF $\psi$ by QRES\xspace iff $\psi$ is
satisfiable.
Based on our presentation of the rules of QRES\xspace
we illustrate the differences between traditional
QCDCL and the variant implemented in
\textsf{DepQBF~6.0}\xspace.

A QCDCL solver maintains a PCNF $\theta = \Pi.\theta'$ (PDNF $\gamma =
\Pi.\gamma'$) consisting of a CNF $\theta'$ (DNF $\gamma'$) of learned clauses
(cubes).  The clauses in $\theta$ are added conjunctively to $\psi$ to
obtain $\psi_{\theta} = \Pi.(\phi \wedge (\bigwedge_{C
\in \theta'} C))$, and the cubes in $\gamma$ are added disjunctively to $\psi$
to obtain $\psi_{\gamma} = \Pi.(\phi \vee (\bigvee_{C \in \gamma'}
C))$.  It holds that $\psi \equiv_{\mathit{sat}} \psi_{\theta}$ and $\psi
\equiv_{\mathit{sat}} \psi_{\gamma}$.  Initially the current assignment $A$, the PCNF
$\theta$, and PDNF $\gamma$ are empty.  We use the notation $C$, $C'$, and $C_L$
for both clauses and cubes.

\begin{figure}[t]
\centering
\includegraphics{figure-qcdcl-enhanced.pdf}
\caption{Workflow of the variant of QCDCL implemented in \textsf{DepQBF~6.0}\xspace
that relies on a generalization of the Q-resolution calculus (QRES\xspace)
(figure adapted from~\cite{DBLP:conf/sat/LonsingES16}).}
\label{fig:qcdcl:enhanced}
\end{figure}

During \emph{propagation}, the formulas $\psi_{\theta}$ and
$\psi_{\gamma}$ are first simplified under the current assignment $A$ by
computing $\psi_{\theta}[A]$ and $\psi_{\gamma}[A]$.  Then
\emph{universal} and \emph{existential reduction} is applied to
$\psi_{\theta}[A]$ and to $\psi_{\gamma}[A]$ based on the following
inference rule.

\begin{definition}[Reduction~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:journals/iandc/BuningKF95,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02}]Let $\psi = \Pi.\phi$ be a PCNF.
\begin{align}\tag{$\mathit{red}$}
\AxiomC{$C \cup \{l\}$}
\UnaryInfC{C}
\label{rule_red}
\DisplayProof
\quad
\begin{minipage}{0.7625\textwidth}
(1) $C$ is a
clause, $\quant{\Pi}{l} = \forall$, \\
\hspace*{0.5cm}
$l' <_\Pi l$
for all $l' \in C$ with $\quant{\Pi}{l'} = \exists$
or \\
(2) $C$ is a
cube, $\quant{\Pi}{l} = \exists$, \\
\hspace*{0.5cm}
$l' <_\Pi l$
for all $l' \in C$ with $\quant{\Pi}{l'} = \forall$
\end{minipage}
\end{align}
\end{definition}

Universal (existential) reduction of clauses (cubes) by rule~\ref{rule_red}
eliminates trailing universal (existential) literals from a
clause (cube)  with respect to the linear quantifier ordering in the prefix of the PCNF $\psi$.  We
write $\mathit{UR}(C) = C'$ ($\mathit{ER}(C) = C'$) to denote the clause (cube) $C'$ resulting
from clause (cube) $C$ by fully reducing universal (existential) literals.

Let $\psi_{\theta}'$ and $\psi_{\gamma}'$ denote the formulas obtained
by applying universal (existential) reduction to all the clauses (cubes) in
$\psi_{\theta}[A]$ ($\psi_{\gamma}[A]$) until saturation.  New
assignments are generated by \emph{unit literal detection} with respect to
$\psi_{\theta}'$ and $\psi_{\gamma}'$.  If a PCNF
(PDNF) $\psi$ contains a \emph{unit clause (cube)} $C = (l)$, where
$\quant{\Pi}{l} = \exists$ ($\quant{\Pi}{l} = \forall$), then literal
$l$ is \emph{unit} and $\psi \equiv_{\mathit{sat}} \psi[A']$ where $A' = \{l\}$
($A' = \{\bar l\}$).
Assignment $A$ is extended by assignments $A'$ derived from unit clauses
(cubes) in $\psi_{\theta}'$ ($\psi_{\gamma}'$).
For every unit clause (cube)
$C' \in \psi_{\theta}'$ ($C' \in \psi_{\gamma}'$) with $C' = (l)$,
the corresponding assignment $A' := \{l\}$ ($A' := \{\bar l\}$) is recorded.

After propagation, in \emph{conflict/solution detection} it is checked whether
$\psi_{\theta}'$ is unsatisfiable or whether $\psi_{\gamma}'$ is
satisfiable (only one of the two cases can occur). To this end, \emph{incomplete} methods are applied. In traditional
QCDCL, for example, it is \emph{syntactically} checked if the current
assignment $A$ is falsifying or satisfying, i.e., whether $\psi_{\theta}'$ contains the empty clause (i.e., $\psi_{\theta}' =
\bot$) or whether $\psi_{\gamma}'$ contains the empty cube (i.e., $\psi_{\gamma}' = \top$).  In \textsf{DepQBF~6.0}\xspace, we extend these
incomplete syntactic checks to incomplete \emph{semantic} checks based on \emph{arbitrary} QBF decision procedures
(proof systems)
that are applied to $\psi_{\theta}'$ and $\psi_{\gamma}'$ in a resource bounded \nolinebreak way.

 If neither $\psi_{\theta}'$ is found unsatisfiable nor $\psi_{\gamma}'$
 is found satisfiable by the incomplete satisfiability checks, then in \emph{decision
  making} $A$ is extended by heuristically assigning some \emph{decision variable} $x$ from the leftmost
quantifier block of $\psi[A]$ ($A := A \cup \{l\}$ where
$\lit{l} = x$),
and propagation continues. Assignments by decision
making must follow the prefix ordering of $\psi$, in contrast to assignments by
propagation (unit literals), which results in assignments of the following kind.
\begin{definition}[QCDCL assignment~\cite{DBLP:conf/lpar/LonsingBBES15}]\label{def:qcdcl:assignment}
Assignments generated by decision making and
propagation in QCDCL are called \emph{QCDCL assignments}.
\end{definition}

If $\psi_{\theta}'$ ($\psi_{\gamma}'$) is found unsatisfiable
(satisfiable) in conflict/solution detection then a
learned clause
(cube) is derived using QRES\xspace depending on the incomplete
satisfiability checks.
In traditional QCDCL, conflict/solution detection relies only on
falsifying or satisfying assignments. If $\psi_{\theta}' = \bot$ then
$\psi_{\theta}'$ contains an empty clause $C' = \emptyset$ such that there
is a clause $C \in \psi_{\theta}$ with $C' = \mathit{UR}(C[A])$.  Clause $C$ is the
\emph{falsified clause} with respect to assignment $A$. If $C$
appears in the given PCNF $\psi$ then in traditional QRES\xspace it is
derived trivially by the following axiom.

\begin{definition}[Clause Axiom~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:journals/iandc/BuningKF95,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02}] \label{def_trad_clause_axiom}
Let $\psi = \Pi.\phi$ be a PCNF.
\begin{align}\tag{$\operatorname{\emph{cl-init}}$}
\AxiomC{\phantom{A}}
\UnaryInfC{C}
\label{rule_cl_init}
\DisplayProof
\quad
\begin{minipage}{0.79\textwidth}
$C$ is a clause and $C \in \phi$
\end{minipage}
\end{align}
\end{definition}

If $\psi_{\theta}' \not = \bot$ but $\psi_{\gamma}' = \top$ then either
(1) $\psi_{\gamma}'$ contains an empty learned cube $C' = \emptyset$
such that there is a cube $C \in \psi_{\gamma}$ with
$C' = \mathit{ER}(C[A])$, or (2) $A$ is a satisfying assignment that satisfies all clauses in
$\psi_{\gamma}'$. For case (2), a cube $C$ is derived by the
following axiom of traditional QRES\xspace
(in either case (1) or (2) cube $C$ is the \emph{satisfied
cube} with respect to $A$).

\begin{definition}[Cube Axiom~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:journals/iandc/BuningKF95,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02}] \label{def_trad_cube_axiom}
Let $\psi = \Pi.\phi$ be a PCNF.
\begin{align}\tag{$\operatorname{\emph{cu-init}}$}
\AxiomC{\phantom{A}}
\UnaryInfC{C}
\label{rule_cu_init}
\DisplayProof
\quad
\begin{minipage}{0.79\textwidth}
$A$ is an assignment,
$\psi[A] = \top$,
and $C = (\bigwedge_{l \in A} l)$ is a cube
\end{minipage}
\end{align}
\end{definition}

\textsf{DepQBF~6.0}\xspace supports the application of \emph{arbitrary} (incomplete)
QBF decision procedures (proof systems) in conflict/solution detection and thus generalizes
the syntactic checks for falsifying and satisfying assignments  in
traditional QCDCL.

To check the satisfiability of $\psi_{\gamma}'$, in \textsf{DepQBF~6.0}\xspace we apply a
dynamic variant of \emph{blocked clause elimination
(QBCE)}~\cite{DBLP:conf/lpar/LonsingBBES15}. This approach was
introduced in version~5.0 of \textsf{DepQBF}\xspace.
QBCE has been presented as a
preprocessing technique to eliminate redundant \emph{blocked clauses}
\cite{DBLP:journals/jair/HeuleJLSB15,DBLP:journals/dam/Kullmann99} from a
PCNF. If all clauses in $\psi_{\gamma}'$ are satisfied under $A$ or
identified as blocked, then $\psi_{\gamma}'$ is determined
satisfiable. In our implementation applications of QBCE are tightly integrated in the propagation
phase via efficient data structures. Clauses that are blocked are
temporarily considered as removed from the formula. Hence such clauses
cannot be used to detect unit clauses or empty clauses during
propagation.

In addition to dynamic QBCE, we implemented incomplete QBF satisfiability
checks based on propositional abstractions of $\psi_{\theta}'$ and
$\psi_{\gamma}'$~\cite{DBLP:conf/sat/LonsingES16}, which are solved using
an integrated SAT solver. These abstractions are constructed by treating
universally quantified literals in the given PCNF $\psi$ in a special
way. Propositional abstractions and SAT solving leverage the benefits of
techniques like \emph{trivial truth} and \emph{trivial
falsity} presented already in early search-based QBF
solvers~\cite{DBLP:conf/aaai/CadoliGS98}. Additionally, the power of
\emph{QU-resolution}~\cite{DBLP:conf/cp/Gelder12}, which is exponentially
stronger than Q-resolution~\cite{DBLP:journals/iandc/BuningKF95} but has not
been applied systematically in QCDCL, is harnessed to a certain extent (cf.~Example~3 in~\cite{DBLP:conf/sat/LonsingES16}).

As a simple way of applying a QBF decision procedure that is incomplete by its
nature we integrated the preprocessor
\textsf{Bloqqer}\xspace~\cite{DBLP:journals/jair/HeuleJLSB15} in \textsf{DepQBF~6.0}\xspace.
Preprocessing aims at simplifying a formula within a restricted
amount of time but might already solve certain formulas
(cf.~\cite{Lonsing201692}). Among several techniques, \textsf{Bloqqer}\xspace applies bounded
expansion of universally quantified
variables~\cite{DBLP:conf/sat/Biere04a,DBLP:conf/sat/BubeckB07}. Hence by
integrating \textsf{Bloqqer}\xspace in QCDCL we in fact integrate expansion, a QBF proof
system that is orthogonal to Q-resolution~\cite{beyersdorff_et_al:LIPIcs:2015:4905,DBLP:journals/tcs/JanotaM15}.
Due to usability issues, in the follow-up release version 6.02 of \textsf{DepQBF}\xspace we replaced \textsf{Bloqqer}\xspace by the
expansion based QBF solver
\textsf{Nenofex}\xspace,\footnote{\url{https://github.com/lonsing/nenofex}} which is applied
in a resource bounded way.

If $\psi_{\theta}'$ ($\psi_{\gamma}'$) is found unsatisfiable
(satisfiable) by an incomplete decision procedure but, unlike above, $A$ is neither falsifying nor satisfying, then a clause
(cube) is derived by the following \emph{generalized} axioms of
QRES\xspace. These axioms are added to QRES\xspace and applied in addition to the traditional
axioms~\ref{rule_cl_init} and~\ref{rule_cu_init}.

\begin{definition}[Generalized Axioms~\cite{DBLP:conf/sat/LonsingES16}] \label{def_gen_axioms}
Let $\psi = \Pi.\phi$ be a PCNF.
\begin{align}\tag{$\operatorname{\emph{gen-cl-init}}$}
\AxiomC{\phantom{A}}
\UnaryInfC{C}
\label{rule_gen_cl_init}
\DisplayProof
\quad
\begin{minipage}{0.7\textwidth}
$A$ is a QCDCL assignment,
$\psi[A]$ is unsatisfiable, \\
and $C = (\bigvee_{l \in A} \bar l)$ is a clause
\end{minipage}
\end{align}

\begin{align}\tag{$\operatorname{\emph{gen-cu-init}}$}
\AxiomC{\phantom{A}}
\UnaryInfC{C}
\label{rule_gen_cu_init}
\DisplayProof
\quad
\begin{minipage}{0.7\textwidth}
$A$ is a QCDCL assignment,
$\psi[A]$ is satisfiable, \\
and $C = (\bigwedge_{l \in A} l)$ is a cube
\end{minipage}
\end{align}
\end{definition}
Note that the generalized axioms allow to derive clauses and cubes that cannot be
derived by the traditional axioms~\ref{rule_cl_init}
and~\ref{rule_cu_init} in general. This is due to the application of
arbitrary QBF decision procedures (proof systems) for satisfiability checking
in conflict/solution detection or in the side conditions of the axioms, respectively. In the side conditions the satisfiability of the PCNF $\psi[A]$ is checked, in contrast to formulas $\psi_{\theta}'$ and $\psi_{\gamma}'$ as in conflict/solution detection. This is possible since $\psi_{\theta}' \equiv_{\mathit{sat}} \psi[A]$ and $\psi_{\gamma}' \equiv_{\mathit{sat}} \psi[A]$.
The clause (cube) $C$ derived by applying the generalized clause
axiom~\ref{rule_gen_cl_init} (\ref{rule_gen_cu_init}) is the \emph{falsified
clause (satisfied cube)} with respect to $A$.

During \emph{clause (cube) learning}, a new \emph{learned clause (cube)}
$C_{L}$ is derived by QRES\xspace. The falsified clause (satisfied cube) $C$ is
the start clause (cube) of a derivation of $C_{L}$. Given $A$,
clauses (cubes) which became unit during propagation are systematically resolved
based on the following \emph{Q-resolution} rule.
\begin{definition}[Q-Resolution~\cite{DBLP:journals/iandc/BuningKF95}] Let $\psi = \Pi.\phi$ be a PCNF.
\begin{align}\tag{$\mathit{res}$}
\AxiomC{$C_1 \cup \{p\}$}
\AxiomC{$C_2 \cup \{\bar p\}$}
\BinaryInfC{$C_1 \cup C_2$}
\label{rule_res}
\DisplayProof
\quad
\begin{minipage}{0.57\textwidth}
For all $x \in \Pi \colon \{x, \bar x\} \not \subseteq (C_1 \cup C_2)$,
\\
$\bar p \not \in C_1$, $p
\not \in C_2$, and \emph{either} \\\hspace*{0.25cm} (1) $C_1$, $C_2$ are
clauses and $\quant{\Pi}{p} = \exists$ \emph{or} \\\hspace*{0.25cm}  (2) $C_1$, $C_2$ are cubes and $\quant{\Pi}{p} = \forall$
\end{minipage}
\end{align}
\end{definition}
Rule~\ref{rule_res} does not allow the resolvent $(C_1 \cup C_2)$ to be a tautological clause (contradictory cube) and requires existential (universal) variables as pivots $p$.  In
general, learning produces a nonempty clause (cube) $C_{L} \not = \emptyset$,
which is added to the PCNF $\theta$ (PDNF $\gamma$) of learned clauses (cubes),
and hence  also  to  $\psi_{\theta}$ ($\psi_{\gamma}$).

In \emph{backtracking}, a certain subassignment $A' \subset A$ is
retracted such that $C_{L}$ becomes unit in propagation. $C_{L}$ is called an
\emph{asserting} clause (cube)~\cite{DBLP:journals/jair/GiunchigliaNT06}.
Clauses (cubes) derived by rules~\ref{rule_cl_init}
and~\ref{rule_gen_cl_init} (\ref{rule_cu_init}
and~\ref{rule_gen_cu_init}) are used in exactly the same way in
learning to produce asserting clauses (cubes).

QCDCL terminates (``UNSAT'' or ``SAT'' in
Fig.~\ref{fig:qcdcl:enhanced}) by deriving the empty learned clause (cube)
$C_{L} = \emptyset$. A \emph{clause (cube) resolution proof} of the
unsatisfiability (satisfiability) of $\psi$ can be
obtained from the derivations of the learned clauses (cubes) up to
the empty clause (cube).

By applying the generalized axioms using a complete QBF decision
procedure, the empty assignment $A$, and an unlimited amount of time,
the empty clause (cube) can
be derived right away from any given unsatisfiable (satisfiable) PCNF
$\psi$.
\emph{In practice} it is crucial to apply incomplete polynomial time procedures
to limit the time spent on the satisfiability checks.
However,
the costs of frequent checks may outweigh the benefits. Hence
in \textsf{DepQBF~6.0}\xspace, satisfiability checks for applications of
the generalized axioms are dynamically disabled if they turn out to be too
costly, and the traditional axioms are used instead. We refer to
related work for implementation details~\cite{DBLP:conf/lpar/LonsingBBES15,DBLP:conf/sat/LonsingES16}.

\section{Features of \textsf{DepQBF}\xspace} \label{sec_features}

We briefly summarize the general features of \textsf{DepQBF}\xspace that have been
incorporated since its initial version~0.1~\cite{DBLP:journals/jsat/LonsingB10,DBLP:conf/sat/LonsingB10}. Most features were described
in related publications. Additionally, we comment on the
compatibility of the features with the implementation of QRES\xspace
with generalized axioms (Fig.~\ref{fig:qcdcl:enhanced}) in
\textsf{DepQBF~6.0}\xspace.

\paragraph{\textbf{Dependency Schemes.}}
Since the initial version~0.1, \textsf{DepQBF}\xspace has been equipped with the
\emph{standard dependency scheme}~\cite{DBLP:journals/jar/SamerS09} to
relax the linear quantifier ordering in the prefix of a given PCNF
$\psi$. In general, \emph{dependency
  schemes} are used to compute
\emph{dependency relations} $D$, which are binary relations over the
set of variables in $\psi$. If $(x,y) \not \in D$ for two
variables $x$ and $y$ then the ordering of $x$ and $y$ in $\psi$
can safely be swapped. Otherwise, if $(x,y) \in D$ then $y$ is
considered to depend on $x$. The integration of dependency schemes in
QCDCL results in the following reduction rule, which is added to
QRES\xspace and implemented in \textsf{DepQBF}\xspace.

\begin{definition}[Dependency-Aware Reduction~\cite{DBLP:conf/sat/LonsingB10}] Let $\psi = \Pi.\phi$ be a PCNF and $D$ be a dependency relation computed using a dependency scheme.
\begin{align}\tag{$\operatorname{\emph{dep-red}}$}
\AxiomC{$C \cup \{l\}$}
\UnaryInfC{C}
\label{rule_dep_red}
\DisplayProof
\quad
\begin{minipage}{0.70\textwidth}
(1) $C$ is a
clause, $\quant{\Pi}{l} = \forall$, \\
\hspace*{0.5cm}
$(l,l') \not \in D$
for all $l' \in C$ with $\quant{\Pi}{l'} = \exists$
or \\
(2) $C$ is a
cube, $\quant{\Pi}{l} = \exists$, \\
\hspace*{0.5cm}
$(l,l') \not \in D$
for all $l' \in C$ with $\quant{\Pi}{l'} = \forall$
\end{minipage}
\end{align}
\end{definition}
Rule~\ref{rule_dep_red} generalizes the traditional reduction
rule~\ref{rule_red} by the use of dependency relation instead of the
linear ordering of variables ($\leq_\Pi$) in the prefix of PCNF
$\psi$. This way, it might be possible to reduce literals by
rule~\ref{rule_dep_red} which cannot be reduced by
rule~\ref{rule_red}. The soundness of QRES\xspace with
rule~\ref{rule_dep_red} has been proved for a dependency relation that
is even more general (and thus allows for additional reductions) than
the one implemented in
\textsf{DepQBF}\xspace~\cite{DBLP:conf/sat/SlivovskyS12,DBLP:journals/tcs/SlivovskyS16,DBLP:conf/cp/Gelder11}. The
generalized axioms~\ref{rule_gen_cl_init} and~\ref{rule_gen_cu_init}
of QRES\xspace implemented in \textsf{DepQBF~6.0}\xspace are naturally compatible
with rule~\ref{rule_dep_red}. Additionally, dependency schemes enable a
relaxed variant of QCDCL assignments (Definition~\ref{def:qcdcl:assignment})
based on the respective dependency relation rather than the prefix ordering of
a PCNF $\psi$.

\paragraph{\textbf{Long-Distance Resolution.}}
The Q-resolution
rule~\ref{rule_res}~\cite{DBLP:journals/iandc/BuningKF95} explicitly
disallows to generate clauses (cubes) that are tautological
(contradictory). This restriction is relaxed under certain
side conditions in \emph{long-distance (LD)
  Q-resolution}~\cite{DBLP:journals/fmsd/BalabanovJ12,DBLP:conf/iccad/ZhangM02,DBLP:conf/cp/ZhangM02}. LDQ-resolution
was first implemented in the QCDCL solver
\textsf{Quaffle}\xspace~\cite{DBLP:conf/iccad/ZhangM02} and was incorporated in
version~3.0 of \textsf{DepQBF}\xspace. Compared to QRES\xspace with traditional
Q-resolution~\ref{rule_res}~\cite{DBLP:journals/iandc/BuningKF95},
QRES\xspace with LDQ-resolution is exponentially more powerful in terms
of proof sizes~\cite{DBLP:conf/lpar/EglyLW13}. The generalized
axioms~\ref{rule_gen_cl_init} and~\ref{rule_gen_cu_init} implemented
in \textsf{DepQBF~6.0}\xspace are not only compatible with the LDQ-resolution
rule, but with \emph{any} variants of Q-resolution
(cf.~\cite{DBLP:conf/sat/BalabanovWJ14}). Recently, the soundness of
the combination of LDQ-resolution of clauses and dependency schemes in
QRES\xspace has been
proved~\cite{DBLP:conf/cp/BeyersdorffB16,DBLP:conf/sat/PeitlSS16},
leaving the soundness of cube resolutions as an open
problem. Therefore, the combination of LDQ-resolution and dependency
schemes is not supported in \textsf{DepQBF~6.0}\xspace.

\paragraph{\textbf{Incremental Solving.}}
Since version~3.0, \textsf{DepQBF}\xspace has been equipped with an API in C and Java
for incremental solving of sequences $S := \langle \psi_0,
\ldots, \psi_n \rangle$ of syntactically related PCNFs
$\psi_i$~\cite{DBLP:conf/cp/LonsingE14,DBLP:conf/date/MarinMLB12}.
Incremental solving aims at reusing the clauses and cubes that were
learned when solving PCNF $\psi_i$ when it comes to solve the
PCNFs $\psi_j$ with $i < j$.  The API of \textsf{DepQBF}\xspace allows to modify
the PCNFs in $S$ by manipulating the quantifier prefix and adding or
removing sets of clauses in a stack-based way. Since version 4.0, it
is possible to add or remove sets of clauses
arbitrarily~\cite{DBLP:conf/sat/LonsingE15}
and to extract \emph{unsatisfiable cores},
i.e., unsatisfiable subformulas of the PCNF $\psi_i$.
At any time
when solving $\psi_i \in S$, the soundness property of QCDCL
(Section~\ref{sec:qcdcl}) that $\psi \equiv_{\mathit{sat}} \psi_{\theta}$
and $\psi \equiv_{\mathit{sat}} \psi_{\gamma}$, where $\psi =
\psi_i$, must hold. To guarantee that property
when using the generalized axioms for incremental solving,
\textsf{DepQBF~6.0}\xspace currently only applies the generalized cube
axiom~\ref{rule_gen_cu_init} with dynamic QBCE used to check
satisfiability of $\psi_{\gamma}'$ in conflict/solution detection
(Fig.~\ref{fig:qcdcl:enhanced}). Although this configuration restricts the power of the
generalized axioms, it has improved incremental solving in the context
of QBF-based conformant planning~\cite{DBLP:journals/amai/EglyKLP17}. As it is unclear
how to use dependency schemes effectively in incremental solving,
their application is disabled in \textsf{DepQBF~6.0}\xspace.

\paragraph{\textbf{Generation of Proofs and Certificates.}}
QCDCL solvers can produce \emph{clause (cube) resolution proofs} of
the unsatisfiability (satisfiability) of PCNFs as a byproduct of
clause (cube) learning. Since
version~1.0~\cite{DBLP:conf/sat/NiemetzPLSB12}, \textsf{DepQBF}\xspace is capable of
producing proofs without employing dependency schemes by
rule~\ref{rule_dep_red}. Given a proof $P$ of a PCNF $\psi$, a
\emph{certificate} of $\psi$ can be extracted from $P$ by
inspecting the reduction steps by rule~\ref{rule_red} in
$P$~\cite{DBLP:journals/fmsd/BalabanovJ12}. A certificate of an
unsatisfiable (satisfiable) PCNF $\psi$ is given by a set of
Herbrand (Skolem) functions which represent the universal
(existential) variables in $\psi$. Applications of the
generalized axioms in QCDCL in general impose considerable
restrictions on the certificate extraction process. The
workflow~\cite{DBLP:journals/fmsd/BalabanovJ12} to extract a
certificate from $P$ was originally presented for traditional
QRES\xspace proofs. If proof $P$ contains clauses (cubes) derived by
rule~\ref{rule_gen_cl_init} (rule~\ref{rule_gen_cu_init}), then $P$
may lack information needed to extract correct certificates. As a
result, \textsf{DepQBF~6.0}\xspace does not support cube resolution proof
generation combined with the generalized cube
axiom~\ref{rule_gen_cu_init}. However, it supports clause resolution
proof generation with the generalized clause
axiom~\ref{rule_gen_cl_init} provided that only propositional
abstractions and SAT solving are used for satisfiability checking in
the side condition of this axiom.

\paragraph{\textbf{Advanced Generation of Learned Clauses and Cubes.}}
The derivation of a single asserting clause (cube) starting from a falsified
clause (satisfied cube) as implemented in traditional
QCDCL~\cite{DBLP:journals/jair/GiunchigliaNT06,DBLP:conf/tableaux/Letz02,DBLP:conf/iccad/ZhangM02}
has an exponential worst case~\cite{DBLP:conf/cp/Gelder12}. Since version 2.0
\textsf{DepQBF}\xspace comes with an approach that avoids this exponential
case~\cite{DBLP:conf/sat/LonsingEG13} by a revised selection of clauses
(cubes) to be resolved in learning. This advanced approach is compatible with
all the techniques presented above.

\section{Experiments} \label{sec_experiments}

We compare variants of \textsf{DepQBF~6.02}\xspace, which is the latest
follow-up release of
\textsf{DepQBF~6.0}\xspace, to top performing solvers of
QBFEVAL'16~\cite{DBLP:conf/sat/Pulina16}. As benchmarks we consider
all 825 instances from the PCNF track, both in original form
(Table~\ref{fig:exp:825:instances:noprepro}) and preprocessed by
\textsf{Bloqqer}\xspace version 37
(Table~\ref{fig:exp:825:instances:prepro}).
We take preprocessing into account as it might have a positive impact
on certain solvers while a negative on
others (cf.~\cite{Lonsing201692,DBLP:journals/fuin/MarinNPTG16}).
Experiments were run on an AMD Opteron
6238 processor (2.6 GHz) under 64-bit Ubuntu Linux 12.04 with time and
memory limits of 1800 seconds and seven GB. Exceeding the memory limit
is counted as a time out.\footnote{We refer to the appendix of this paper with
  additional experimental results.}

\begin{table}[t]
\caption{Solved instances (\emph{S}), solved unsatisfiable
  (\emph{$\bot$}) and satisfiable ones (\emph{$\top$}), uniquely
  solved ones among all solvers (\emph{U}), and total wall clock time including time
  outs on 825 PCNFs from QBFEVAL'16 without
  (\ref{fig:exp:825:instances:noprepro}) and with preprocessing by \textsf{Bloqqer}\xspace (\ref{fig:exp:825:instances:prepro}).}
\addtocounter{table}{-1}
\begin{minipage}[b]{0.48\textwidth}
\begin{center}
\subfloat[Original instances.]{
{\setlength\tabcolsep{0.15cm}
\begin{tabular}{l@{\quad}c@{\quad}c@{\quad}c@{\quad}r@{\quad}c}
\hline
\emph{Solver} & \emph{S} & \emph{$\bot$} & \emph{$\top$} & \emph{U} & \emph{Time} \\
\hline
\textsf{AIGSolve}\xspace & 603 & 301 & 302 & 34 & 440K \\
\textsf{GhostQ}\xspace & 593 & 292 & 301 & 7 & 457K \\
\textsf{QSTS}\xspace & 578 & 294 & 284 & 3 & 469K \\
\textsf{DQ}\xspace & 458 & 255 & 203 & 0 & 682K \\
\textsf{DQ-linldq}\xspace & 458 & 257 & 201 & 2 & 686K \\
\textsf{DQ-lin}\xspace & 456 & 255 & 201 & 0 & 686K \\
\textsf{DQ-ncl}\xspace & 448 & 246 & 202 & 0 & 703K \\
\textsf{DQ-nq}\xspace & 397 & 228 & 169 & 0 & 788K \\
\textsf{DQ-ncu}\xspace & 393 & 229 & 164 & 0 & 796K \\
\textsf{DQ-n}\xspace & 383 & 221 & 162 & 0 & 814K \\
\textsf{CAQE}\xspace & 378 & 202 & 176 & 9 & 831K \\
\textsf{QESTO}\xspace & 369 & 210 & 159 & 0 & 864K \\
\textsf{RAReQS}\xspace & 341 & 211 & 130 & 2 & 891K \\
\hline
\end{tabular}

\label{fig:exp:825:instances:noprepro}

\end{center}
\end{minipage}
\hfill
\begin{minipage}[b]{0.48\textwidth}
\begin{center}
\subfloat[Preprocessed by \textsf{Bloqqer}\xspace.]{
{\setlength\tabcolsep{0.15cm}
\begin{tabular}{l@{\quad}c@{\quad}c@{\quad}c@{\quad}r@{\quad}r}
\hline
\emph{Solver} & \emph{S} & \emph{$\bot$} & \emph{$\top$} & \emph{U} & \emph{Time} \\
\hline
\textsf{QSTS}\xspace & 633 & 330 & 303 & 11 & 365K \\
\textsf{RAReQS}\xspace & 633 & 334 & 299 & 8 & 375K \\
\textsf{QESTO}\xspace & 620 & 321 & 299 & 0 & 395K \\
\textsf{DQ-ncl}\xspace & 601 & 303 & 298 & 0 & 428K \\
\textsf{DQ}\xspace & 601 & 301 & 300 & 0 & 429K \\
\textsf{DQ-linldq}\xspace & 598 & 300 & 298 & 2 & 437K \\
\textsf{DQ-lin}\xspace & 597 & 299 & 298 & 0 & 436K \\
\textsf{CAQE}\xspace & 596 & 301 & 295 & 4 & 451K \\
\textsf{DQ-n}\xspace & 593 & 296 & 297 & 0 & 444K \\
\textsf{DQ-ncu}\xspace & 591 & 297 & 294 & 0 & 455K \\
\textsf{DQ-nq}\xspace & 587 & 293 & 294 & 0 & 455K \\
\textsf{GhostQ}\xspace & 570 & 282 & 288 & 0 & 485K \\
\textsf{AIGSolve}\xspace & 567 & 286 & 281 & 14 & 481K \\
\hline
\end{tabular}

\label{fig:exp:825:instances:prepro}

\end{center}
\end{minipage}
\label{fig:exp:825:instances}
\refstepcounter{table}
\end{table}

\begin{table}[t]
\caption{Related to Table~\ref{fig:exp:825:instances:noprepro}: solver
performance on 402 filtered original (\emph{not preprocessed}) instances partitioned into
261 instances with at most two (\ref{fig:exp:bloqqer37:classes:few:noprepro})
and 141 with three or more quantifier alternations
(\ref{fig:exp:bloqqer37:classes:many:noprepro}).}
\addtocounter{table}{-1}
\begin{minipage}[b]{0.48\textwidth}
\begin{center}
\subfloat[At most two quantifier alternations.]{
{\setlength\tabcolsep{0.15cm}
\begin{tabular}{l@{\quad}r@{\quad}r@{\quad}r@{\quad}r@{\quad}c}
\hline
\emph{Solver} & \multicolumn{1}{l}{\emph{S}} & \emph{$\bot$} & \multicolumn{1}{l}{\emph{$\top$}} & \emph{U} & \emph{Time} \\
\hline
\textsf{GhostQ}\xspace & 176 & 75 & 101 & 5 & 171K \\
\textsf{AIGSolve}\xspace & 138 & 66 & 72 & 14 & 250K \\
\textsf{QSTS}\xspace & 136 & 58 & 78 & 0 & 232K \\
\textsf{RAReQS}\xspace & 76 & 43 & 33 & 1 & 340K \\
\textsf{DQ-lin}\xspace & 69 & 35 & 34 & 0 & 351K \\
\textsf{DQ}\xspace & 69 & 35 & 34 & 0 & 351K \\
\textsf{DQ-ncl}\xspace & 68 & 35 & 33 & 0 & 354K \\
\textsf{DQ-linldq}\xspace & 67 & 34 & 33 & 0 & 354K \\
\textsf{QESTO}\xspace & 66 & 37 & 29 & 0 & 359K \\
\textsf{DQ-ncu}\xspace & 53 & 24 & 29 & 0 & 378K \\
\textsf{DQ-n}\xspace & 52 & 24 & 28 & 0 & 378K \\
\textsf{DQ-nq}\xspace & 52 & 23 & 29 & 0 & 379K \\
\textsf{CAQE}\xspace & 43 & 17 & 26 & 3 & 397K \\
\hline
\end{tabular}

\label{fig:exp:bloqqer37:classes:few:noprepro}

\end{center}
\end{minipage}
\hfill
\begin{minipage}[b]{0.48\textwidth}
\begin{center}
\subfloat[Three or more quantifier alternations.]{
{\setlength\tabcolsep{0.15cm}
\begin{tabular}{l@{\quad}c@{\quad}c@{\quad}c@{\quad}r@{\quad}c}
\hline
\emph{Solver} & \emph{S} & \emph{$\bot$} & \emph{$\top$} & \emph{U} & \emph{Time} \\
\hline
\textsf{DQ-linldq}\xspace & 81 & 50 & 31 & 2 & 120K \\
\textsf{DQ}\xspace & 79 & 47 & 32 & 0 & 119K \\
\textsf{DQ-ncl}\xspace & 79 & 47 & 32 & 0 & 120K \\
\textsf{DQ-lin}\xspace & 78 & 47 & 31 & 0 & 123K \\
\textsf{QSTS}\xspace & 72 & 44 & 28 & 3 & 132K \\
\textsf{DQ-nq}\xspace & 56 & 37 & 19 & 0 & 159K \\
\textsf{GhostQ}\xspace & 56 & 31 & 25 & 2 & 160K \\
\textsf{DQ-n}\xspace & 55 & 36 & 19 & 0 & 159K \\
\textsf{DQ-ncu}\xspace & 55 & 36 & 19 & 0 & 159K \\
\textsf{AIGSolve}\xspace & 54 & 25 & 29 & 9 & 161K \\
\textsf{QESTO}\xspace & 49 & 33 & 16 & 0 & 179K \\
\textsf{CAQE}\xspace & 46 & 29 & 17 & 2 & 182K \\
\textsf{RAReQS}\xspace & 43 & 33 & 10 & 0 & 180K \\
\hline
\end{tabular}

\label{fig:exp:bloqqer37:classes:many:noprepro}

\end{center}
\end{minipage}
\label{fig:exp:bloqqer37:classes:noprepro}
\refstepcounter{table}
\end{table}

\begin{table}[t]
\caption{ Related to Table~\ref{fig:exp:825:instances:prepro}: solver
performance on 402 filtered and \emph{preprocessed} instances partitioned into 270
instances with at most two (\ref{fig:exp:bloqqer37:classes:few:prepro}) and
132 with three or more quantifier alternations
(\ref{fig:exp:bloqqer37:classes:many:prepro}).}
\addtocounter{table}{-1}
\begin{minipage}[b]{0.48\textwidth}
\begin{center}
\subfloat[At most two quantifier alternations.]{
{\setlength\tabcolsep{0.15cm}
\begin{tabular}{l@{\quad}c@{\quad}r@{\quad}r@{\quad}r@{\quad}c}
\hline
\emph{Solver} & \emph{S} & \emph{$\bot$} & \emph{$\top$} & \emph{U} & \emph{Time} \\
\hline
\textsf{RAReQS}\xspace & 157 & 79 & 78 & 8 & 227K \\
\textsf{QESTO}\xspace & 138 & 66 & 72 & 0 & 255K \\
\textsf{QSTS}\xspace & 136 & 62 & 74 & 2 & 255K \\
\textsf{CAQE}\xspace & 118 & 49 & 69 & 2 & 298K \\
\textsf{GhostQ}\xspace & 111 & 46 & 65 & 1 & 304K \\
\textsf{DQ}\xspace & 107 & 43 & 64 & 1 & 311K \\
\textsf{DQ-lin}\xspace & 106 & 42 & 64 & 0 & 311K \\
\textsf{DQ-ncl}\xspace & 105 & 43 & 62 & 0 & 312K \\
\textsf{DQ-n}\xspace & 105 & 41 & 64 & 0 & 313K \\
\textsf{DQ-linldq}\xspace & 104 & 40 & 64 & 0 & 315K \\
\textsf{AIGSolve}\xspace & 102 & 49 & 53 & 7 & 313K \\
\textsf{DQ-nq}\xspace & 102 & 39 & 63 & 0 & 322K \\
\textsf{DQ-ncu}\xspace & 102 & 40 & 62 & 0 & 323K \\
\hline
\end{tabular}

\label{fig:exp:bloqqer37:classes:few:prepro}

\end{center}
\end{minipage}
\hfill
\begin{minipage}[b]{0.48\textwidth}
\begin{center}
\subfloat[Three or more quantifier alternations.]{
{\setlength\tabcolsep{0.15cm}
\begin{tabular}{l@{\quad}c@{\quad}c@{\quad}c@{\quad}r@{\quad}r}
\hline
\emph{Solver} & \emph{S} & \emph{$\bot$} & \emph{$\top$} & \emph{U} & \emph{Time} \\
\hline
\textsf{DQ-ncl}\xspace & 83 & 51 & 32 & 0 & 96K \\
\textsf{DQ}\xspace & 81 & 49 & 32 & 0 & 98K \\
\textsf{DQ-linldq}\xspace & 81 & 51 & 30 & 2 & 102K \\
\textsf{DQ-lin}\xspace & 78 & 48 & 30 & 0 & 105K \\
\textsf{DQ-ncu}\xspace & 76 & 48 & 28 & 0 & 112K \\
\textsf{QSTS}\xspace & 75 & 50 & 25 & 1 & 107K \\
\textsf{DQ-n}\xspace & 75 & 46 & 29 & 0 & 112K \\
\textsf{DQ-nq}\xspace & 72 & 45 & 27 & 0 & 113K \\
\textsf{QESTO}\xspace & 69 & 45 & 24 & 0 & 120K \\
\textsf{CAQE}\xspace & 64 & 42 & 22 & 0 & 136K \\
\textsf{RAReQS}\xspace & 62 & 45 & 17 & 1 & 131K \\
\textsf{AIGSolve}\xspace & 51 & 27 & 24 & 6 & 151K \\
\textsf{GhostQ}\xspace & 46 & 26 & 20 & 0 & 162K \\
\hline
\end{tabular}

\label{fig:exp:bloqqer37:classes:many:prepro}

\end{center}
\end{minipage}
\label{fig:exp:bloqqer37:classes:prepro}
\refstepcounter{table}
\end{table}

To assess the impact of
the generalized axioms \ref{rule_gen_cl_init} and \ref{rule_gen_cu_init} on the performance, we consider \textsf{DepQBF~6.02}\xspace using
both \ref{rule_gen_cl_init} and \ref{rule_gen_cu_init} (variant \textsf{DQ}\xspace in the
tables), without \ref{rule_gen_cl_init} (\textsf{DQ-ncl}\xspace), without
\ref{rule_gen_cu_init} (\textsf{DQ-ncu}\xspace), and using no generalized
axioms at all (\mbox{\textsf{DQ-n}\xspace}).

On original instances (Table~\ref{fig:exp:825:instances:noprepro}),
\textsf{DQ}\xspace outperforms variants \textsf{DQ-ncl}\xspace,
\textsf{DQ-ncu}\xspace, and \textsf{DQ-n}\xspace with restricted or without
generalized axioms, respectively. Variant
\textsf{DQ-ncl}\xspace without axiom \ref{rule_gen_cl_init} outperforms
variant \textsf{DQ-ncu}\xspace without \ref{rule_gen_cu_init}. We
attribute this effect to the use of dynamic
QBCE (among other techniques) for applications of the cube axiom
\ref{rule_gen_cu_init} in \textsf{DQ-ncl}\xspace.
Compared to \textsf{DQ}\xspace, disabling
only dynamic QBCE in variant \textsf{DQ-nq}\xspace severely impacts performance.

On preprocessed instances (Table~\ref{fig:exp:825:instances:prepro}),
we make similar observations regarding the impact of the generalized
axioms like in Table~\ref{fig:exp:825:instances:noprepro}.  However,
variant \textsf{DQ-ncl}\xspace without the clause axiom
\ref{rule_gen_cl_init} is on par with
\textsf{DQ}\xspace. Preprocessing may blur the structure of an instance. We
conjecture that this blurring
hinders the success of the QBF decision procedures in
\textsf{DepQBF}\xspace, on which applications of the generalized axioms are based.
In general the performance
difference between the variants of
\textsf{DepQBF}\xspace is smaller than on original instances. The rankings of the
solvers \textsf{RAReQS}\xspace~\cite{Janota20161}, \textsf{QESTO}\xspace~\cite{DBLP:conf/ijcai/JanotaM15}, and \textsf{CAQE}\xspace~\cite{DBLP:conf/fmcad/RabeT15} are
improved substantially by preprocessing, whereas those of \textsf{AIGSolve}\xspace~\cite{DBLP:conf/sat/SchollP16}
and \textsf{GhostQ}\xspace~\cite{Janota20161,DBLP:conf/sat/KlieberSGC10} become worse. The best variant \textsf{DQ-ncl}\xspace
in Table~\ref{fig:exp:825:instances:prepro} ranks fourth behind \textsf{QSTS}\xspace~\cite{DBLP:conf/sat/0001JT16},
\textsf{RAReQS}\xspace, and
\textsf{QESTO}\xspace. However, the lag to the
solver ranked third is 19 instances compared to 120 instances
for the best variant \textsf{DQ}\xspace in
Table~\ref{fig:exp:825:instances:noprepro} that also ranks fourth.

To analyze the effects of preprocessing in more detail, we filtered the 825
PCNFs from QBFEVAL'16 by discarding 354 PCNFs that are already solved by
\textsf{Bloqqer}\xspace and 69 PCNFs where \textsf{Bloqqer}\xspace eliminated all universally quantified
variables, resulting in a set of 402 PCNFs. Further, we considered the 402
PCNFs in their original form and preprocessed by \textsf{Bloqqer}\xspace and partitioned them
into subsets containing PCNFs with at most two and with three or more
quantifier alternations. Such partitioning is motivated by a related
experimental study~\cite{DBLP:journals/corr/LonsingE17} where a large
diversity of solver performance was observed on instance classes defined by
alternations. Tables~\ref{fig:exp:bloqqer37:classes:noprepro}
and~\ref{fig:exp:bloqqer37:classes:prepro} show solver performance on these
subsets without and with preprocessing, respectively. Notably, variants of
\textsf{DepQBF}\xspace outperform the other solvers on the subsets with three or more
alternations, both without and with preprocessing
(Tables~\ref{fig:exp:bloqqer37:classes:many:noprepro}
and~\ref{fig:exp:bloqqer37:classes:many:prepro}).

All variants of \textsf{DepQBF}\xspace reported above apply dependency-aware reduction by
rule \ref{rule_dep_red}.  Variant \textsf{DQ-lin}\xspace is the same as
\textsf{DQ}\xspace (including generalized axioms) but uses the traditional reduction
rule~\ref{rule_red} based on the linear quantifier ordering of PCNFs.  Variant
\textsf{DQ}\xspace outperforms \textsf{DQ-lin}\xspace in all tables
except Table~\ref{fig:exp:bloqqer37:classes:few:noprepro}, where \textsf{DQ-lin}\xspace
is on par, which illustrates the benefits of dependency schemes in
QCDCL. Variant \textsf{DQ-linldq}\xspace differs from \textsf{DQ-lin}\xspace in the
use of LDQ-resolution in learning instead of traditional Q-resolution by
rule~\ref{rule_res}. The results with LDQ-resolution are mixed, despite being
a stronger proof system than Q-resolution. Variant
\textsf{DQ-linldq}\xspace outperforms \textsf{DQ-lin}\xspace in all tables
except Tables~\ref{fig:exp:bloqqer37:classes:few:noprepro}
and~\ref{fig:exp:bloqqer37:classes:few:prepro}, i.e., on instances with at
most two quantifier alternations.

\section{Conclusion}

We presented the latest major release
version~6.0 of the QCDCL solver \textsf{DepQBF}\xspace. \textsf{DepQBF~6.0}\xspace implements a
variant of QCDCL that is based on a generalization of the Q-resolution
calculus (QRES\xspace). The generalization is achieved by equipping
QRES\xspace with generalized clause and cube axioms to be used in
clause and cube learning~\cite{DBLP:conf/sat/LonsingES16}. The generalized
axioms provide an extensible framework of
interfaces for the integration of arbitrary QBF proof systems in
QRES\xspace, and hence in QCDCL. The integration of proof systems
orthogonal to Q-resolution, such as variable expansion, enables QCDCL
to potentially produce proofs that are exponentially shorter than
proofs produced by traditional QCDCL. This way, the state of the art
of QCDCL solving can be further advanced. A related open
problem is the inability of plain QCDCL to exploit the full power of
Q-resolution~\cite{DBLP:conf/sat/Janota16}.

The workflow of QCDCL with generalized axioms is not tailored towards
\textsf{DepQBF~6.0}\xspace but can be implemented in any QCDCL
solver. Furthermore, it is compatible with dependency
schemes~\cite{DBLP:journals/jar/SamerS09,DBLP:journals/tcs/SlivovskyS16}
and any Q-resolution variant~\cite{DBLP:conf/sat/BalabanovWJ14},
which offers potential for further improvements.

Experiments with variants of \textsf{DepQBF~6.0}\xspace showed considerable
performance gains due to the application of generalized axioms. However,
frequent applications are hindered by computationally expensive QBF
satisfiability checks in the side conditions of the axioms. To limit the
checking overhead, axiom applications must be carefully scheduled.
In this respect, there is room for improvements in fine tuning
\textsf{DepQBF~6.0}\xspace. Further, it may be beneficial
to integrate the QBF decision procedures that are
applied to satisfiability checking more tightly in the QCDCL workflow, like
with dynamic blocked clause elimination (QBCE)~\cite{DBLP:conf/lpar/LonsingBBES15}.

redpajama_set_name: RedPajamaArXiv


Westbrook: "The basketball stuff comes and goes. For me, it's always been about giving back..."
Russell Westbrook took the car that he won as the 2016 NBA All-Star Game MVP and gave it to a family in need in Los Angeles. The Thunder shared a video of the wonderful moment.
The clip shows the entire family, as well as the president/CEOs of two nonprofits ( United Way of L.A. and St. Joseph Center) that helped with the car giveaway. One of them explains that the family has four children with another on the way. Plus, they only recently moved into housing until their car broke down.
"The basketball stuff comes and goes. For me, it's always been about giving back and finding ways to impact the community where you come from and impact the community all across the world. Me being on a stage that I'm on, obviously basketball is something I love to do, but giving back is something I love doing more."
When the Thunder star won the All-Star Game MVP in 2015, he gave that car to a single mom in Oklahoma City.


text:
Gillingham boss addresses interest in Portsmouth target Brandon Hanlan
Gillingham boss Steve Evans admitted clubs have made enquiries about Brandon Hanlan amid Pompey's interest.
By Will Rooney
Sunday, 30th August 2020, 10:00 am
Updated Sunday, 30th August 2020, 10:03 am
Brandon Hanlan. Picture: Jack Thomas/Getty Images
Kenny Jackett has identified Hanlan as the pacy forward who can add an extra dimension to the Blues' attacking options.
The former Charlton man has spent the past two seasons at Priestfield, scoring 16 goals in 84 appearances.
Despite being out of contract, Hanlan's continued to train with the Gills during pre-season.
The 23-year-old came off the bench in their 1-0 friendly defeat to Leyton Orient on Saturday and has been offered a new deal to stay at the Gills.
Evans revealed 'two or three clubs' have asked about Hanlan – but a compensation fee will first need to be settled before he departs.
The Gillingham boss told his club's website: 'Brandon Hanlan, two or three clubs have asked about him.
'We turned good money down for Brandon back in January.
'Brandon said he'd perhaps like the opportunity to go and talk to these people.
'They need to agree a fee first otherwise he's not going anywhere.'
Pompey have also been linked with Gillingham's Connor Ogilvie.


text:
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Tesla, former Microsoft executives to attend NGA meeting in R.I.
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PROVIDENCE – Elon Musk, CEO of Tesla Inc. and SpaceX, and former Microsoft Corp. CEO Steve Ballmer are among the business and political leaders...
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Advice June 2, 2017 12:45 am
Two hikers were camped out overnight in the mountains. A thunderous voice roused them from their sleep. The voice said, "This will be the...
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Discussion in 'Looking For A Clan' started by sardaukar666, February 21, 2018.
Team Burning [BRN] is now actively recruiting people over the age of 16 for Planetary Annihilation primarily from the GMT+8 through GMT+12 time zones. At present most of our players are based in Australia, New Zealand and the US. The community was originally formed by players who played Planetary Annihilation competitively and socially.
Team Burning aims to create a social network for people interested in playing RTS games competitively and socially. We host social tournaments and challenge other clans to epic inter-clan wars. Players of any skill level who are interested in playing RTS games and improving their skills in a friendly environment are welcome.
Alongside playing Planetary Annihilation we have a community of members who play other games casually.
Furballman and NikolaMX like this.


text:
Canon considers the R6 a pro camera; adds big video updates to it and the 1D X Mark III
By James Artaius
New firmware for the Canon EOS R6 and 1D X Mark III brings significant updates for video shooters – including C-Log 3
(Image credit: Canon)
Canon has introduced some big video oriented updates to its "professional cameras", the EOS R6 and 1D X Mark III. The key additions for both cameras are the much-requested ability to shoot in Canon Log 3, as well as to simultaneously record to two memory cards.
It's also interesting that the manufacturer refers to both bodies as "professional cameras". When it comes to EOS stills cameras, the flagship Canon EOS-1D X Mark III (opens in new tab) has previously been the only body that the company considers a pro model. Even the Canon EOS 5D Mark IV (opens in new tab) isn't officially regarded as a professional camera, despite the overwhelming number of pros who use it as such.
So for the Canon EOS R6 (opens in new tab) to be classed as a professional body – if only in the context of its video capabilities – is noteworthy, with Canon stating in its firmware announcement that it "supports filmmakers with the release of new firmware for its professional cameras."
• Read more: Best Canon cameras (opens in new tab)
Both cameras inherit the headline feature of Canon Log 3, which was introduced to the Canon EOS R5 (opens in new tab) earlier this year. "Canon's renowned Log 3 expands the dynamic range and offers more color space options to achieve rich, high-quality video that mirrors that of Hollywood standard cinema cameras," says Canon.
"This logarithmic gamma curve also increases the compatibility of these models with cinema production workflows, making it easier to color match footage captured with Canon's Cinema EOS Series cameras."
Also new to each camera is the addition of dual card recording, enabling simultaneous recording of the same video file (in terms of resolution, frame-rate and codec) to both memory cards. In addition, the 1D X Mark III receives support for the new CFexpress VPG400 industry standard (guaranteeing minimum write speeds of 400MB/s).
Firmware 1.4.0 for the Canon EOS R6 can be downloaded here (opens in new tab), while Firmware 1.5.0 for the Canon EOS-1D X Mark III can be downloaded here (opens in new tab).
Today's best Canon EOS-1D X Mark III, Canon EOS R6 and Canon EOS R5 deals
Canon EOS-1D X Mark III
Best professional cameras (opens in new tab)
Canon EOS-1D X Mark III review (opens in new tab)
Canon EOS R6 review (opens in new tab)
Canon EOS 5D Mark IV review (opens in new tab)
James Artaius
The editor of Digital Camera World, James has 21 years experience as a magazine and web journalist and started working in the photographic industry in 2014 (as an assistant to Damian McGillicuddy, who succeeded David Bailey as Principal Photographer for Olympus). In this time he shot for clients as diverse as Aston Martin Racing, Elinchrom and L'Oréal, in addition to shooting campaigns and product testing for Olympus, and providing training for professionals. This has led him to being a go-to expert for camera and lens reviews, photographic and lighting tutorials, as well as industry analysis, news and rumors for publications such as Digital Camera Magazine (opens in new tab), PhotoPlus: The Canon Magazine (opens in new tab), N-Photo: The Nikon Magazine (opens in new tab), Digital Photographer (opens in new tab) and Professional Imagemaker, as well as hosting workshops and demonstrations at The Photography Show (opens in new tab). An Olympus and Canon shooter, he has a wealth of knowledge on cameras of all makes – and a fondness for vintage lenses and instant cameras.
Save $50 on an Instax Link Wide printer with double pack of film


Anyone can reserve today or you can walk-in and get a turkey.
Each reservation requires a 20.00 deposit.
Our family takes personal pride in each and every turkey we sell. We raise them with TLC from day old babies.; Our turkeys are processed humanely right on our farm in a State Inspected facility by the farmers who raised and cared for them, treating them with kindness and respect throughout the process.
We raise our turkeys as naturally as possible. This means they are raised with no growth stimulants or hormones. They are raised on open green pasture with free access to feed and shelter and full access to green grass, sunshine and fresh air.
No additives or preservatives are added during processing. Our turkeys come to you exactly as mother nature intended.
We invite you to make a TLV Tree Farm Turkey the centerpiece of your locally grown holiday tradition.


text:
JAES Mission Statement
KCS Mission & Vision
Adams Library Catalog
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Student Keyboarding
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Edulastic
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Website Admin.
Adams #1 - Best Public Elementary School Teachers in TN! Adams is PROUD to be a Reward School for 2017-18!
John Adams Elementary School Awarded Inaugural Governor's Award for Excellence in Early Foundations
Adams Elementary was awarded the inaugural Governor's Award for Excellence in Early Foundations – Excellence in Promoting Physical Activity Award.
Published: March 3, 2016 at 11:53 a.m.
KINGSPORT, Tenn. – John Adams Elementary School was awarded the inaugural Governor's Award for Excellence in Early Foundations – Excellence in Promoting Physical Activity Award by the Governor's Children's Cabinet, in recognition of their Morning Mile Program. Adams Elementary is the first school to ever receive this award.
"As I travel across the state, I'm always impressed with the commitment and creativity of so many Tennesseans working tirelessly to help get our children prepared for success in school and in life," said Tennessee Governor Bill Haslam. "These awards are a small but important way we can highlight and honor their good work."
More than 40 nominations were submitted for the awards, and winners were selected by teams of state employees and community partners based on criteria including family involvement, engagement of community leaders, and collaboration across partners and systems.
"To give our children the best chance for success, families, schools and communities must work together to create a nurturing environment for child development, beginning at birth," First Lady Crissy Haslam said. "These winners are wonderful examples of that collaborative spirit, and they have shown a true passion for serving Tennessee's children."
The first recipients of the Governor's Award for Excellence in Early Foundations include:
Community Excellence Award: Shelby County Early Success Coalition, Memphis
School Excellence Award: Knox County Schools, Parents as Teachers Program, Knoxville
Excellence in Supporting Children and Families Award: Children's Reading Foundation of the Upper Cumberland, Cookeville
Excellence in Promoting Physical Activity Award: John Adams Elementary School, Morning Mile Program, Kingsport
Excellence in Building Resiliency Award: Bradley County Family Resource Agency, Cleveland
Excellence in Promoting Early Literacy Award: Vaiden Taylor, Knoxville (nominated by Telamon Corporation Tennessee Head Start Programs)
Excellence in Keeping Kids Safe, Healthy, and On Track Awards:
Organizational winner: BlueCare Tennessee, Healthcare Continuum, Chattanooga
Individual winner: Jenny Williams, Trenton (nominated by Prevent Child Abuse Tennessee)
Excellence in Promoting Wellness Award: East Tennessee Children's Hospital, Obesity Coalition, Knoxville
Excellence in Promoting High Quality Early Care and Education Programs Award: Wilson County Schools, Early Childhood and Extended School Programs, Lebanon
"We are honored to receive another award recognizing the work done by Mr. Hincke, his Morning Mile participants, and the parent volunteers who assist with this program," said John Adams Elementary School Principal Dr. Stephanie Potter. "It is such a welcome sight each morning to see the dedication and commitment each of these students exhibits as they 'run their own race.' They are preparing themselves mentally and physically for a successful day and successful life as they demonstrate the stamina and perseverance needed to be 'world class' citizens."
The Morning Mile Program, coordinated by Physical Education teacher Jason Hincke, is a voluntary running program open to all students at Adams Elementary. With the assistance of nearly 30 parent volunteers over the course of a week, students in grades K-5 meet weekday mornings to run before school begins. Between 50 and 70 students in grades 3-5 run an average of one and one-half to two miles each day, and between 30 and 50 students in grades K-2 run an average of one mile each day. Studies show that students who participate in physical activities such as the Morning Mile program are better prepared to learn since blood flow to the brain is stimulated.
The Governor's Award for Excellence in Early Foundations will be presented on Tuesday, March 18 at 1 p.m. during the Tennessee Commission on Children Youth's (TCCY) Children's Advocacy Days at the War Memorial Auditorium in Nashville, TN.
In December 2015, Adams Elementary was also awarded the inaugural School Bell Award for Fitness Program Excellence by the Tennessee Principals Association (TPA), in recognition of the Morning Mile Program. They were the first school to ever receive that award. Read the full news release here.
For more information on the Morning Mile Program, visit morningmile.com.
Kingsport City Schools (KCS) is a public school district located in Kingsport, Tenn., serving students in Sullivan and Hawkins county. The district is comprised of 13 schools, including a Pre-K, eight elementary schools, two middle schools, one high school and a non-traditional school; with total enrollment over 7,100 students. The vision of Kingsport City Schools is to be, Student Focused … World Class.
KCS has been named the top school district in Tennessee as winner of the 2014 SCORE Prize District Award by the State Collaborative on Reforming Education (SCORE) and has earned the 2014 Achievement Award in the annual Excellence in Tennessee Recognition Program by the Tennessee Center for Performance Excellence (TNPCE).
For more information on KCS, visit k12k.com, listen live on WCSK 90.3 FM, The Voice of KCS, read our blog, We Are KCS, or call (423) 378.2100. We're social too; follow us on Facebook (Kingsport City Schools), Twitter (@KCS_District) and check out our YouTube Channel (KPTSchools).
John Adams Elementary™ 2727 Edinburgh Channel Rd.


text:
Q: How to replace a small matrix in a larger matrix with different rows and columns Suppose we have a large A(n*n) and a small B(m*m) matrices (m<n). Also, there is a set J  with the size of m which are values from {1,2,3,...,n}. I want to replace the matrix B in rows and columns of matrix A such that the first row (column) of matrix B is replaced in the first element of set J. For example,
   [[1 1 1 1 1],
    [1 1 1 1 1],
A = [1 1 1 1 1],
    [1 1 1 1 1],
    [1 1 1 1 1]]

and
J = [1, 3, 5]
B =[[2 3 4],
    [5 6 7],
    [8 9 10]]

Then, the result will be:
   [[2 1 3 1 4],
    [1 1 1 1 1],
A = [5 1 6 1 7],
    [1 1 1 1 1],
    [8 1 9 1 10]]

A: Try this:
tmp = A[J-1]
tmp[:, J-1] = B
A[J-1] = tmp

>>> A
array([[ 2,  1,  3,  1,  4],
       [ 1,  1,  1,  1,  1],
       [ 5,  1,  6,  1,  7],
       [ 1,  1,  1,  1,  1],
       [ 8,  1,  9,  1, 10]])

Why the roundtrip using a tmp variable, where the more intuitive way would be A[J-1][:, J-1] = B?  That is because A[J-1][:, J-1] cannot be a view of A (there is no simple striding of A that will give you that sub-array), and thus it is instead a view of a copy of A[J-1] (which you can use as lvalue but will be lost).  So, instead, we explicitly "put back into A" the value of tmp.

A: will the obvious way of doing things cut it?
A = [[1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1],
     [1, 1, 1, 1, 1]]
J = [1, 3, 5]
B = [[2, 3, 4],
     [5, 6, 7],
     [8, 9, 10]]

print(A)
for rB,rA in enumerate(J):
    for cB,cA in enumerate(J):
        A[rA-1][cA-1] = B[rB][cB]   #list indices are 0-based
print(A)
exit(-1)

#ok, let`s do it functional way
J = list(map(lambda x:x-1, J))  # convert inex array 0-based indices
lira = lambda l,i,r,a: r if type(l) is not list else lira(l[:i[0]] + [lira(l[i[0]], a, r[0], a)] + l[i[0] + 1:], i[1:], r[1:], a) if i else l
A = lira(A,J,B,J)
print(A)

A: You can use built-in np.ix_ for this purpose:
A[np.ix_(J-1,J-1)] = B

output:
array([[ 2.,  1.,  3.,  1.,  4.],
       [ 1.,  1.,  1.,  1.,  1.],
       [ 5.,  1.,  6.,  1.,  7.],
       [ 1.,  1.,  1.,  1.,  1.],
       [ 8.,  1.,  9.,  1., 10.]])


text:
Rage Against The Cowell
I often wonder just exactly what Simon Cowell asks for when he goes for a haircut. His hair is sort of square with an attempt at a centre parting that fails miserably.
A bad haircut isn't all Mr Cowell has to worry about because his usual march to the Christmas number one is under threat by an Internet campaign to get Rage Against the Machine to the Chrimbo top spot instead of the atrocious Hannah Montana song Simon has chosen for the X Factor winner to sing this year.
I'm all for it, i hate the way the whole show is geared towards claiming the Christmas top slot when it should be songs about snowmen and reindeer.
Not that 'Killing in the name of' is particularly festive, I've just read the lyrics and i have no idea what the songs about but it has a killer riff and the singer gets all shouty and that's always a winning combination at any time of the year.
Cowell is hitching his trousers even higher and hitting back. With an apparently straight face he branded the campaign stupid, cynical and dismissive of the shows viewers.
'It's incredibly dismissive of the people who watch and enjoy the show" he said, 'to treat our audiences as if they're stupid and I don't like that.' Indeed, he likes to treat the audience as if they are stupid. We all remember the Jedward incident when he went from hating them to loving over the length of an ad-break.
The Facebook group currently has 548,000 members and the page says to start buying the song as a download from this Sunday, the day the X Factor winner is announced.
Mind you, there is a certain irony to buying a song all about not being told what to do because someone told you to.
I think i'll just buy Merry Xmas Everybody by Slade instead.
Psychic Predictions: 2010
Psychic Predictions 2009: The Review
The Noughties: Palestine & Israel
The Noughties: Climate Change
The Noughties: Religion
The Noughties: 9/11
So Here It Is, Merry Christmas
Christmas Number 1
Climate No Change
Another Headache Mary?
2009 Person Of The Year
Come Back Soon Tzipi
Evil Chavez At It Again
Bliar
Meanwhile In Iraq...
The Lost Copenhagen Post
Amanda Knox Guilty
Tiger Woods Is Fair Game
Where's The Change Obama?


▶Title Videos : Fruits and Vegetables On The Farm For Kids | Nursery Rhymes and More By HooplaKidz .
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Description : Hey Kids! Wanna join the fun trio Annie, Ben and Mango while they tell you all about the nutritious veggies! Let's learn the different fruits and vegetable names.


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text:
Bill Madden: Kevin Cash is just another symbol of baseball's destruction
Bill Madden, New York Daily News
November 1, 2020, 5:30 AM ·5 min read
Three years ago, I was sitting in the visitors dugout at Tropicana Field along with another veteran baseball scribe, Hal Bodley, of MLB.com and formerly USA Today. We were talking to a prominent baseball person who shall remain nameless here about the state of the game. "You know what's really sad," this third person said, nodding at Cash in the opposite dugout. "We will never know how good a manager that guy really is."
In all likelihood, Cash will be a runaway winner of the American League manager of the year award. He guided the Rays (payroll $74.8 million) to an AL East title over the Yankees (payroll $165.7 million). But throughout the course of the season, during the playoffs and most especially in Game 6 of the World Series, Cash made no bones about the fact that he manages strictly by the plan set up by the Rays' analytics department.
With one out in the sixth of that fateful game, Cash came to get his ace Blake Snell, who was pitching the game of his life. Snell had just given up his second hit of the game, to the Dodgers' No. 9 hitter, Austin Barnes, and it was evident just how thoroughly the soul of the game has been destroyed.
As Cash explained, he didn't want Snell facing the Dodger lineup the third time around, the prime tenet of modern analytics for starting pitchers. It didn't matter if Snell had thrown only 73 pitches to that point, or that the first three batters in the Dodgers lineup, Mookie Betts, Corey Seager and Justin Turner had been a combined 0 for 6 with six strikeouts against him. The stats say over the last five years opposing batters' slash lines jump from .252/.317/.422 the first two times around the order against a starting pitcher to .269/.333/.463 the third time.
Those are the hard, cold facts — which have absolutely nothing to do with how the starting pitcher is pitching to that point, how stressful his pitch count, or perhaps most importantly his heart and his makeup. "I am definitely disappointed and upset," Snell said after the game. "I just want the ball. I felt good. I did everything I could to prove my case to stay out there and then for us to lose, it just sucks."
So the baseball audience was deprived once again from potentially seeing the kind of great postseason pitching performance which has been all but obliterated. Somewhere up in Baseball Heaven, Tom Seaver and Bob Gibson were looking down and throwing up.
Meanwhile, a direct contrast to the Snell pulling was Dusty Baker, one of the few remaining old-school managers in the game. In the sixth inning of Game 5 of the ALCS, the red-hot Randy Arozarena was coming up with two men on, one out. Baker strode to the mound, had a brief conference with his ace, Zack Greinke, and elected to leave him in.
After Greinke struck out Arozarena, the Rays were able to load the bases with an infield single by Ji-Man Choi and still Baker, managing with his gut and trusting Greinke's heart, didn't make a move. His confidence was rewarded when Greinke struck out Mike Brosseau to end the inning.
If you ask me, you could make just as strong a case for Baker for AL Manager of the Year — for very different reasons than Cash. Baker took on one of the most unenviable jobs imaginable this year, the cheating Astros being the most hated team in baseball. He had to create an "us-against-the-world" mentality while also convincing his players to put all the outside noise out of their heads and just play their game — which they did all the way to one game from the World Series.
This is more than just the analytics' emasculation of starting pitchers. It's also the neutering of managers, who are no longer allowed to come on the field to argue plays. And beyond that, it's another example of salary repression in baseball. For the longest time, owners have been trying to drive down the salaries of managers and they've slowly been able to do that by hiring analytics-driven GMs who, in turn, hire inexperienced managers on the cheap who are perfectly willing to allow the front office to run the games for them.
It is no coincidence the five highest paid managers in baseball — Terry Francona ($4M), Joe Maddon ($4M), Bob Melvin ($3.25M), Joe Girardi ($3.25M) and Baker ($3M) — are all what you call their own men, mostly old school, who are able to manage as much with their gut as by the numbers. Joe Torre was the first old-school manager to sound the alarm when Yankee GM Brian Cashman began intruding on his turf. "You can't remove the human element from the game," he said.
But more and more they have, turning players into numbers. It got far worse for Girardi, Torre's successor, and in particular his pitching coach Larry Rothschild, as they found themselves regularly second-guessed by the analytics people for their pitching moves. As for Aaron Boone, like was said about Cash, we will never know how good a manager he can be.
©2020 New York Daily News
Visit New York Daily News at www.nydailynews.com


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text:
Volume 2, Issue 7-11, Dead Space
Manapul, Francis
Batman, Superman and Wonder Woman-the superheroes known as the Trinity-have gone through a lot in the aftermath of the DC Rebirth epic event. But now the bonds of their friendship are tested like never before, as they must let their closest allies die in order to save the world! An emergency summons to the Justice League Watchtower puts the icons face-to-face with an unexpected crisis: The other members of the League have been infected with a fatal alien virus that will destroy all humankind…unless the Trinity destroys the Watchtower, and the Justice League along with it! Plus, the revelations of "Superman Reborn" require Batman and Wonder Woman to give their all to save Superman from his doubts about his very existence; and a trinity of villains-Lex Luthor, Ra's al Ghul and Circe-concoct a scheme to use the mysterious Pandora Pits to put an end to the World's Greatest Heroes. Best-selling writer-artist Francis Manapul (THE FLASH) is joined by writer Cullen Bunn and artists Clay Mann and Emanuela Lupacchino in TRINITY VOL. 2: DEAD SPACE.
Publisher: [United States] : DC Comics, 2017.
Branch Call Number: eComic hoopla
Additional Contributors: Bunn, Cullen - Author
Hanna, Scott - Illustrator
Quintana, Wil - Colorist
Wands, Steve
Napolitano, Tom
Alternative Title: Trinity (DC Comics, Inc.)
Read more reviews of Trinity at iDreamBooks.com
Superman (Fictitious Character) — Comic Books, Strips, Etc.
Batman (Fictitious Character) — Comic Books, Strips, Etc.
Wonder Woman (Fictitious Character) — Comic Books, Strips, Etc.
Superheroes — Comic Books, Strips, Etc.


text:
Home Chevron icon It indicates an expandable section or menu, or sometimes previous / next navigation options. Politics
Biden says he's in talks with Sen. Joe Manchin and believes they'll 'bridge our differences and advance the Build Back Better plan'
Kelsey Vlamis
President Joe Biden; Sen. Joe Manchin
Nina Riggio/San Francisco Chronicle via Getty Images; Tom Williams/CQ-Roll Call, Inc via Getty Images
President Joe Biden said he believes Democrats will pass the Build Back Better Act.
Biden said he is working with Sen. Joe Manchin and believes they will come to an agreement.
The $2 trillion social-spending plan needs the support of every Democratic senator to pass.
President Joe Biden said Thursday the White House is in ongoing talks with Sen. Joe Manchin and that he believes the Build Back Better Act will pass.
"Senator Manchin has reiterated his support for the Build Back Better funding at the level of the framework plan I announced in September," Biden said in a statement. "I believe that we will bridge our differences and advance the Build Back Better plan, even in the face of fierce Republican opposition."
The fate of the $2 trillion social- and climate- spending bill, which Democrats hoped to approve by the end of the year, has been up in the air.
On Wednesday, reports said Manchin raised last-minute concerns over the child tax credit, further delaying the timeline of the bill's passage, Insider's Joseph Zeballos-Roig reported. But a person familiar with Manchin's thinking told Insider "he has always been supportive of the child tax credit" but has stipulations on how much it should cost.
In his statement, Biden said he and Senate Majority Leader Chuck Schumer are trying to get the bill to a vote on the Senate floor "as early as possible."
Biden said he is also working with Senators on getting voting rights legislation passed.
More: Joe Biden Joe Manchin Build Back Better Congress


text:
Gippsland Times (Vic. : 1861 - 1954)
Mon 2 Jul 1877
In: Morning.
(1877, July 2). Gippsland Times (Vic. : 1861 - 1954), p. 1 (Morning.). Retrieved January 16, 2021, from http://nla.gov.au/nla.news-page6156285
Gippsland Times (Vic. : 1861 - 1954) 2 July 1877: 1 (Morning.). Web. 16 Jan 2021 <http://nla.gov.au/nla.news-page6156285>.
1877, Gippsland Times (Vic. : 1861 - 1954), 2 July, p. 1. (Morning.), viewed 16 Jan 2021, http://nla.gov.au/nla.news-page6156285
{{cite news |url=http://nla.gov.au/nla.news-page6156285 |newspaper=[[Gippsland Times]] |issue=1915 |location=Victoria, Australia |date=2 July 1877 |accessdate=16 January 2021 |page=1 (Morning.) |via=National Library of Australia}}
State Library of Victoria
Gippsland Times (Vic. : 1861 - 1954), Mon 2 Jul 1877, Page 1