Solving ../../benchmarks/smtlib/false/plus_odd_odd.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_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(_qza)) <= plus(n, mm, _qza)
}
eq_nat(_tza, _uza) <= plus(_rza, _sza, _tza) /\ plus(_rza, _sza, _uza)
)
}

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


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

Clause system for inference is:

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


Solving took 0.038173 seconds.
No: Contradictory set of ground constraints:
{
False <= True
is_odd(s(s(s(z)))) <= True
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_odd(s(s(z)))
False <= is_odd(z)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006130 s (model generation: 0.006067,  model checking: 0.000063):

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

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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

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

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

False <= is_odd(z)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.006122 s (model generation: 0.006058,  model checking: 0.000064):

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

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

Current best model:
|_
name: None

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(_ggpqw_0)
}

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

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

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

False <= is_odd(z)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.007082 s (model generation: 0.007022,  model checking: 0.000060):

Clauses:
{
is_odd(s(z)) <= True -> 0
plus(n, z, n) <= True -> 0
is_odd(s(s(n3))) <= is_odd(n3) -> 0
is_odd(_vza) <= is_odd(x) /\ is_odd(y) /\ plus(x, y, _vza) -> 0
is_odd(n3) <= is_odd(s(s(n3))) -> 0
False <= is_odd(z) -> 0
plus(n, s(mm), s(_qza)) <= plus(n, mm, _qza) -> 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_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_odd(s(s(n3))) <= is_odd(n3)  :
No: ()

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

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

False <= is_odd(z)  :
Yes: {

}

plus(n, s(mm), s(_qza)) <= plus(n, mm, _qza)  :
Yes: {
_qza -> s(_lgpqw_0)  ;  mm -> z  ;  n -> s(_ngpqw_0)
}


-------------------------------------------
Step 3, which took 0.011158 s (model generation: 0.010975,  model checking: 0.000183):

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

Current best model:
|_
name: None

is_odd ->
[
is_odd : <nat>
{
  _r_1(z) <= True
  is_odd(s(x_0_0)) <= _r_1(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_odd(s(s(n3))) <= is_odd(n3)  :
Yes: {
n3 -> s(z)
}

is_odd(_vza) <= is_odd(x) /\ is_odd(y) /\ plus(x, y, _vza)  :
Yes: {
_vza -> s(s(_vgpqw_0))  ;  x -> s(z)  ;  y -> s(z)
}

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

False <= is_odd(z)  :
No: ()

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


Total time: 0.038173
Learner time: 0.030122
Teacher time: 0.000370
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
is_odd(s(s(s(z)))) <= True
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_odd(s(s(z)))
False <= is_odd(z)
}