Solving ../../benchmarks/smtlib/true/plus_odd_odd_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))
}
)
(is_odd, P:
{
is_odd(s(z)) <= True
is_odd(s(s(n3))) <= is_odd(n3)
is_odd(n3) <= is_odd(s(s(n3)))
False <= is_odd(z)
}
)
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_uha)) <= plus(n, mm, _uha)
}
eq_nat(_xha, _yha) <= plus(_vha, _wha, _xha) /\ plus(_vha, _wha, _yha)
)
}

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


over-approximation: {is_odd, plus}
under-approximation: {is_even}

Clause system for inference is:

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


Solving took 0.127526 seconds.
Yes: |_
name: None

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


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


;
plus ->
[
plus : <nat * nat * nat>
{
  is_even(s(x_0_0)) <= is_odd(x_0_0)
  is_even(z) <= True
  is_odd(s(x_0_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_odd(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_2_0) /\ is_odd(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_odd(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.016029 s (model generation: 0.015875,  model checking: 0.000154):

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

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


;
is_odd ->
[
is_odd : <nat>
{
  
}
]


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



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




Answer of teacher:

is_odd(s(z)) <= True  :
Yes: {

}

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

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

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

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

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

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

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

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


-------------------------------------------
Step 1, which took 0.007633 s (model generation: 0.007502,  model checking: 0.000131):

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

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

Current best model:
|_
name: None

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


;
is_odd ->
[
is_odd : <nat>
{
  is_odd(s(x_0_0)) <= True
}
]


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



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




Answer of teacher:

is_odd(s(z)) <= True  :
No: ()

plus(n, z, n) <= True  :
Yes: {
n -> s(_qxrba_0)
}

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

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

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

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

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

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

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


-------------------------------------------
Step 2, which took 0.009988 s (model generation: 0.009905,  model checking: 0.000083):

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

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

Current best model:
|_
name: None

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


;
is_odd ->
[
is_odd : <nat>
{
  is_odd(s(x_0_0)) <= True
  is_odd(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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

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

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

plus(n, s(mm), s(_uha)) <= plus(n, mm, _uha)  :
Yes: {
_uha -> s(_eyrba_0)  ;  mm -> z  ;  n -> s(_gyrba_0)
}


-------------------------------------------
Step 3, which took 0.008716 s (model generation: 0.008648,  model checking: 0.000068):

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

Accumulated learning constraints:
{
is_odd(s(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
is_odd(z) <= is_odd(s(s(z)))
is_even(z) <= is_odd(z)
}

Current best model:
|_
name: None

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


;
is_odd ->
[
is_odd : <nat>
{
  is_odd(s(x_0_0)) <= True
  is_odd(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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

is_even(_zha) <= is_odd(x) /\ is_odd(y) /\ plus(x, y, _zha)  :
Yes: {
_zha -> s(_oyrba_0)  ;  x -> z  ;  y -> s(_qyrba_0)
}

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

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


-------------------------------------------
Step 4, which took 0.008355 s (model generation: 0.008304,  model checking: 0.000051):

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

Accumulated learning constraints:
{
is_odd(s(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
is_even(s(s(z))) <= is_even(z)
is_odd(z) <= is_odd(s(s(z)))
is_even(s(z)) <= is_odd(z)
is_even(z) <= is_odd(z)
}

Current best model:
|_
name: None

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


;
is_odd ->
[
is_odd : <nat>
{
  is_odd(s(x_0_0)) <= True
  is_odd(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_odd(s(z)) <= True  :
No: ()

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

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

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

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

}

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

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

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

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


-------------------------------------------
Step 5, which took 0.015286 s (model generation: 0.014855,  model checking: 0.000431):

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

Accumulated learning constraints:
{
is_odd(s(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))
is_even(s(s(z))) <= is_even(z)
False <= is_odd(s(s(z)))
False <= is_odd(z)
}

Current best model:
|_
name: None

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


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


;
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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

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

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

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


-------------------------------------------
Step 6, which took 0.014245 s (model generation: 0.013837,  model checking: 0.000408):

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

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

Current best model:
|_
name: None

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


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


;
plus ->
[
plus : <nat * nat * nat>
{
  is_even(s(x_0_0)) <= is_odd(x_0_0)
  is_even(z) <= True
  is_odd(s(x_0_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_2_0)
  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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

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

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

plus(n, s(mm), s(_uha)) <= plus(n, mm, _uha)  :
Yes: {
_uha -> s(s(z))  ;  mm -> z  ;  n -> s(_yzrba_0)
}


-------------------------------------------
Step 7, which took 0.009592 s (model generation: 0.009180,  model checking: 0.000412):

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

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

Current best model:
|_
name: None

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


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


;
plus ->
[
plus : <nat * nat * nat>
{
  is_even(s(x_0_0)) <= is_odd(x_0_0)
  is_even(z) <= True
  is_odd(s(x_0_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

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

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

plus(n, s(mm), s(_uha)) <= plus(n, mm, _uha)  :
Yes: {
_uha -> s(s(z))  ;  mm -> s(_zasba_0)  ;  n -> s(_absba_0)
}


-------------------------------------------
Step 8, which took 0.011222 s (model generation: 0.010686,  model checking: 0.000536):

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

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

Current best model:
|_
name: None

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


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


;
plus ->
[
plus : <nat * nat * nat>
{
  is_even(s(x_0_0)) <= is_odd(x_0_0)
  is_even(z) <= True
  is_odd(s(x_0_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_odd(x_0_0)
  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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

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

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

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


-------------------------------------------
Step 9, which took 0.011555 s (model generation: 0.011008,  model checking: 0.000547):

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

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

Current best model:
|_
name: None

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


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


;
plus ->
[
plus : <nat * nat * nat>
{
  is_even(s(x_0_0)) <= is_odd(x_0_0)
  is_even(z) <= True
  is_odd(s(x_0_0)) <= is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_odd(x_0_0)
  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_odd(s(z)) <= True  :
No: ()

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

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

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

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

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

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

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

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


Total time: 0.127526
Learner time: 0.109800
Teacher time: 0.002821
Reasons for stopping: Yes: |_
name: None

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


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


;
plus ->
[
plus : <nat * nat * nat>
{
  is_even(s(x_0_0)) <= is_odd(x_0_0)
  is_even(z) <= True
  is_odd(s(x_0_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_odd(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_even(x_2_0) /\ is_odd(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= is_odd(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_odd(x_0_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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