Solving ../../benchmarks/smtlib/false/plus_even_implies.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(_wza)) <= plus(n, mm, _wza)
}
eq_nat(_zza, _aab) <= plus(_xza, _yza, _aab) /\ plus(_xza, _yza, _zza)
)
}

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


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

Clause system for inference is:

{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(x) <= is_even(_bab) /\ plus(x, y, _bab) -> 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
plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza) -> 0
}


Solving took 0.051078 seconds.
No: Contradictory set of ground constraints:
{
False <= True
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(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(z), z, s(s(z)))
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006158 s (model generation: 0.006096,  model checking: 0.000062):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(x) <= is_even(_bab) /\ plus(x, y, _bab) -> 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
plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza) -> 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(x) <= is_even(_bab) /\ plus(x, y, _bab)  :
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: ()

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


-------------------------------------------
Step 1, which took 0.006376 s (model generation: 0.006312,  model checking: 0.000064):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(x) <= is_even(_bab) /\ plus(x, y, _bab) -> 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
plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza) -> 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(_vdpqw_0)
}

is_even(x) <= is_even(_bab) /\ plus(x, y, _bab)  :
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: ()

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


-------------------------------------------
Step 2, which took 0.008171 s (model generation: 0.007752,  model checking: 0.000419):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(x) <= is_even(_bab) /\ plus(x, y, _bab) -> 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
plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza) -> 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(x) <= is_even(_bab) /\ plus(x, y, _bab)  :
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: {

}

plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza)  :
Yes: {
_wza -> s(_aepqw_0)  ;  mm -> z  ;  n -> s(_cepqw_0)
}


-------------------------------------------
Step 3, which took 0.011508 s (model generation: 0.011395,  model checking: 0.000113):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(x) <= is_even(_bab) /\ plus(x, y, _bab) -> 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
plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza) -> 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(x) <= is_even(_bab) /\ plus(x, y, _bab)  :
Yes: {
_bab -> s(s(_mepqw_0))  ;  x -> s(z)  ;  y -> z
}

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

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

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

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


-------------------------------------------
Step 4, which took 0.011569 s (model generation: 0.011314,  model checking: 0.000255):

Clauses:
{
is_even(z) <= True -> 0
plus(n, z, n) <= True -> 0
is_even(x) <= is_even(_bab) /\ plus(x, y, _bab) -> 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
plus(n, s(mm), s(_wza)) <= plus(n, mm, _wza) -> 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(s(z), 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)) <= True
  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_even(z) <= True  :
No: ()

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

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

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


Total time: 0.051078
Learner time: 0.042869
Teacher time: 0.000913
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
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(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(z), z, s(s(z)))
}