Solving ../../benchmarks/smtlib/true/plus_even_even.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: Some(60.) (sec)
Teacher_type: Checks all clauses every time
Approximation method: remove every clause that can be safely removed



Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(is_even, P:
{
is_even(z) <= True
is_even(s(s(n3))) <= is_even(n3)
is_even(n3) <= is_even(s(s(n3)))
False <= is_even(s(z))
}
)
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)
}
eq_nat(_ima, _jma) <= plus(_gma, _hma, _ima) /\ plus(_gma, _hma, _jma)
)
}

properties:
{
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)
}


over-approximation: {plus}
under-approximation: {}

Clause system for inference is:

{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}


Solving took 0.262431 seconds.
Yes: |_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006046 s (model generation: 0.005988,  model checking: 0.000058):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
Yes: {

}

plus(n, z, n) <= True  :
Yes: {
n -> z
}

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
No: ()


-------------------------------------------
Step 1, which took 0.005784 s (model generation: 0.005728,  model checking: 0.000056):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(z) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
Yes: {
n -> s(_azpba_0)
}

is_even(s(s(n3))) <= is_even(n3)  :
Yes: {
n3 -> z
}

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> z  ;  mm -> z  ;  n -> z
}


-------------------------------------------
Step 2, which took 0.008707 s (model generation: 0.008666,  model checking: 0.000041):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  is_even(s(x_0_0)) <= True
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
Yes: {

}

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(_fzpba_0)  ;  mm -> z  ;  n -> s(_hzpba_0)
}


-------------------------------------------
Step 3, which took 0.013172 s (model generation: 0.013048,  model checking: 0.000124):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(z))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= True
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
Yes: {
_kma -> s(z)  ;  x -> z  ;  y -> s(s(_uzpba_0))
}

is_even(n3) <= is_even(s(s(n3)))  :
Yes: {
n3 -> s(z)
}

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
No: ()


-------------------------------------------
Step 4, which took 0.013996 s (model generation: 0.013603,  model checking: 0.000393):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
Yes: {
_kma -> s(z)  ;  x -> s(s(z))  ;  y -> z
}

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(_jaqba_0)  ;  mm -> s(z)  ;  n -> z
}


-------------------------------------------
Step 5, which took 0.026688 s (model generation: 0.026170,  model checking: 0.000518):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), z, s(z))
False <= plus(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
Yes: {
n -> s(s(z))
}

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
Yes: {
_kma -> s(z)  ;  x -> s(s(z))  ;  y -> s(s(z))
}

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(s(z))  ;  mm -> s(z)  ;  n -> z
}


-------------------------------------------
Step 6, which took 0.022636 s (model generation: 0.021935,  model checking: 0.000701):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
False <= plus(s(s(z)), z, s(z))
False <= plus(z, s(s(z)), s(z))
plus(z, s(s(z)), s(s(s(z)))) <= plus(z, s(z), s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(s(z))  ;  mm -> z  ;  n -> s(_kdqba_0)
}


-------------------------------------------
Step 7, which took 0.022375 s (model generation: 0.021618,  model checking: 0.000757):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
False <= plus(s(s(z)), z, s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
False <= plus(z, s(s(z)), s(z))
plus(z, s(s(z)), s(s(s(z)))) <= plus(z, s(z), s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
}


-------------------------------------------
Step 8, which took 0.024370 s (model generation: 0.023778,  model checking: 0.000592):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
False <= plus(s(s(z)), z, s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
False <= plus(z, s(s(z)), s(z))
plus(z, s(s(z)), s(s(s(z)))) <= plus(z, s(z), s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(_kkqba_0)  ;  mm -> s(z)  ;  n -> s(_mkqba_0)
}


-------------------------------------------
Step 9, which took 0.024138 s (model generation: 0.023450,  model checking: 0.000688):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
False <= plus(s(s(z)), z, s(z))
plus(s(z), s(s(z)), s(s(z))) <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
False <= plus(z, s(s(z)), s(z))
plus(z, s(s(z)), s(s(s(z)))) <= plus(z, s(z), s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(_boqba_0)  ;  mm -> s(z)  ;  n -> s(s(z))
}


-------------------------------------------
Step 10, which took 0.026983 s (model generation: 0.026254,  model checking: 0.000729):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
plus(s(s(z)), s(s(z)), s(s(z))) <= plus(s(s(z)), s(z), s(z))
False <= plus(s(s(z)), z, s(z))
plus(s(z), s(s(z)), s(s(z))) <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
False <= plus(z, s(s(z)), s(z))
plus(z, s(s(z)), s(s(s(z)))) <= plus(z, s(z), s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(s(z))  ;  mm -> s(z)  ;  n -> s(_zrqba_0)
}


-------------------------------------------
Step 11, which took 0.031024 s (model generation: 0.030228,  model checking: 0.000796):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(s(z)), s(s(s(z)))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(s(z)), s(s(z))) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
plus(s(s(z)), s(s(z)), s(s(z))) <= plus(s(s(z)), s(z), s(z))
False <= plus(s(s(z)), z, s(z))
plus(s(z), s(s(z)), s(s(z))) <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
False <= plus(z, s(s(z)), s(z))
plus(z, s(s(z)), s(s(s(z)))) <= plus(z, s(z), s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

is_even(z) <= True  :
No: ()

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(_kma) <= is_even(x) /\ is_even(y) /\ plus(x, y, _kma)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fma)) <= plus(n, mm, _fma)  :
Yes: {
_fma -> s(s(z))  ;  mm -> s(z)  ;  n -> s(s(z))
}


Total time: 0.262431
Learner time: 0.220466
Teacher time: 0.005453
Reasons for stopping: Yes: |_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= is_even(x_1_0) /\ is_even(x_2_0)
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|