<s>
Prover9	B-Application
is	O
an	O
automated	B-Application
theorem	I-Application
prover	I-Application
for	O
first-order	O
and	O
equational	O
logic	O
developed	O
by	O
William	O
McCune	O
.	O
</s>
<s>
Prover9	B-Application
is	O
the	O
successor	O
of	O
the	O
Otter	B-Application
theorem	I-Application
prover	I-Application
also	O
developed	O
by	O
William	O
McCune	O
.	O
</s>
<s>
Prover9	B-Application
is	O
noted	O
for	O
producing	O
relatively	O
readable	O
proofs	O
and	O
having	O
a	O
powerful	O
hints	O
strategy	O
.	O
</s>
<s>
Prover9	B-Application
is	O
intentionally	O
paired	O
with	O
Mace4	B-Application
,	O
which	O
searches	O
for	O
finite	O
models	O
and	O
counterexamples	O
.	O
</s>
<s>
Both	O
can	O
be	O
run	O
simultaneously	O
from	O
the	O
same	O
input	O
,	O
with	O
Prover9	B-Application
attempting	O
to	O
find	O
a	O
proof	O
,	O
while	O
Mace4	B-Application
attempts	O
to	O
find	O
a	O
(	O
disproving	O
)	O
counter-example	O
.	O
</s>
<s>
Prover9	B-Application
,	O
Mace4	B-Application
,	O
and	O
many	O
other	O
tools	O
are	O
built	O
on	O
an	O
underlying	O
library	O
named	O
LADR	O
(	O
"	O
Library	O
for	O
Automated	B-Application
Deduction	I-Application
Research	O
"	O
)	O
to	O
simplify	O
implementation	O
.	O
</s>
<s>
Resulting	O
proofs	O
can	O
be	O
double-checked	O
by	O
Ivy	O
,	O
a	O
proof-checking	O
tool	O
that	O
has	O
been	O
separately	O
verified	O
using	O
ACL2	B-Application
.	O
</s>
<s>
In	O
July	O
2006	O
the	O
LADR/Prover9/Mace4	O
input	O
language	O
made	O
a	O
major	O
change	O
(	O
which	O
also	O
differentiates	O
it	O
from	O
Otter	B-Application
)	O
.	O
</s>
<s>
Prover9/Mace4	O
also	O
supports	O
a	O
"	O
goal	O
"	O
type	O
of	O
formula	O
,	O
which	O
is	O
automatically	O
negated	O
for	O
proof	O
.	O
</s>
<s>
Prover9	B-Application
attempts	O
to	O
automatically	O
generate	O
a	O
proof	O
by	O
default	O
;	O
in	O
contrast	O
,	O
Otter	B-Application
's	O
automatic	O
mode	O
must	O
be	O
explicitly	O
set	O
.	O
</s>
<s>
Prover9	B-Application
was	O
under	O
active	O
development	O
,	O
with	O
new	O
releases	O
every	O
month	O
or	O
every	O
other	O
month	O
,	O
until	O
2009	O
.	O
</s>
<s>
Prover9	B-Application
is	O
free	B-Application
software	I-Application
,	O
and	O
therefore	O
,	O
open	B-Application
source	I-Application
software	I-Application
;	O
it	O
is	O
released	O
under	O
GPL	B-License
version	O
2	O
or	O
later	O
.	O
</s>
<s>
The	O
traditional	O
"	O
all	O
men	O
are	O
mortal	O
"	O
,	O
"	O
Socrates	O
is	O
a	O
man	O
"	O
,	O
prove	O
"	O
Socrates	O
is	O
mortal	O
"	O
can	O
be	O
expressed	O
this	O
way	O
in	O
Prover9	B-Application
:	O
</s>
<s>
This	O
will	O
be	O
automatically	O
converted	O
into	O
clausal	O
form	O
(	O
which	O
Prover9	B-Application
also	O
accepts	O
)	O
:	O
</s>
