Solving ../../benchmarks/smtlib/false/plus_le.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:
{
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_ikb)) <= plus(n, mm, _ikb)
}
eq_nat(_lkb, _mkb) <= plus(_jkb, _kkb, _lkb) /\ plus(_jkb, _kkb, _mkb)
)
(le, P:
{
le(z, s(nn2)) <= True
le(s(nn1), s(nn2)) <= le(nn1, nn2)
le(nn1, nn2) <= le(s(nn1), s(nn2))
False <= le(s(nn1), z)
False <= le(z, z)
}
)
}

properties:
{
le(n, _nkb) <= plus(n, m, _nkb)
}


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

Clause system for inference is:

{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(n, _nkb) <= plus(n, m, _nkb) -> 0
plus(n, s(mm), s(_ikb)) <= plus(n, mm, _ikb) -> 0
}


Solving took 0.038301 seconds.
No: Contradictory set of ground constraints:
{
le(z, s(z)) <= True
le(z, 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 <= le(z, z)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005614 s (model generation: 0.005558,  model checking: 0.000056):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(n, _nkb) <= plus(n, m, _nkb) -> 0
plus(n, s(mm), s(_ikb)) <= plus(n, mm, _ikb) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  
}
]


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



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




Answer of teacher:

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(n, _nkb) <= plus(n, m, _nkb)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.005986 s (model generation: 0.005904,  model checking: 0.000082):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(n, _nkb) <= plus(n, m, _nkb) -> 0
plus(n, s(mm), s(_ikb)) <= plus(n, mm, _ikb) -> 0
}

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

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  
}
]


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



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




Answer of teacher:

plus(n, z, n) <= True  :
Yes: {
n -> s(_mfpqw_0)
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

le(n, _nkb) <= plus(n, m, _nkb)  :
Yes: {
_nkb -> z  ;  m -> z  ;  n -> z
}

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


-------------------------------------------
Step 2, which took 0.007031 s (model generation: 0.006959,  model checking: 0.000072):

Clauses:
{
plus(n, z, n) <= True -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
le(n, _nkb) <= plus(n, m, _nkb) -> 0
plus(n, s(mm), s(_ikb)) <= plus(n, mm, _ikb) -> 0
}

Accumulated learning constraints:
{
le(z, 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

le ->
[
le : <nat * nat>
{
  le(z, 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:

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
Yes: {

}

le(n, _nkb) <= plus(n, m, _nkb)  :
Yes: {
_nkb -> s(_yfpqw_0)  ;  m -> s(_zfpqw_0)  ;  n -> z
}

plus(n, s(mm), s(_ikb)) <= plus(n, mm, _ikb)  :
Yes: {
_ikb -> s(_bgpqw_0)  ;  mm -> z  ;  n -> s(_dgpqw_0)
}


Total time: 0.038301
Learner time: 0.018421
Teacher time: 0.000210
Reasons for stopping: No: Contradictory set of ground constraints:
{
le(z, s(z)) <= True
le(z, 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 <= le(z, z)
}