Solving ../../benchmarks/smtlib/true/isaplanner_prop17.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(_bka)) <= plus(n, mm, _bka)
}
eq_nat(_eka, _fka) <= plus(_cka, _dka, _eka) /\ plus(_cka, _dka, _fka)
)
(leq, P:
{
leq(z, n2) <= True
leq(s(nn1), s(nn2)) <= leq(nn1, nn2)
leq(nn1, nn2) <= leq(s(nn1), s(nn2))
False <= leq(s(nn1), z)
}
)
}

properties:
{
eq_nat(i, z) <= leq(i, z)
}


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

Clause system for inference is:

{
leq(z, n2) <= True -> 0
eq_nat(i, z) <= leq(i, z) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
plus(n, s(mm), s(_bka)) <= plus(n, mm, _bka) -> 0
}


Solving took 0.036450 seconds.
Yes: |_
name: None

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


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



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006525 s (model generation: 0.006469,  model checking: 0.000056):

Clauses:
{
leq(z, n2) <= True -> 0
eq_nat(i, z) <= leq(i, z) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
plus(n, s(mm), s(_bka)) <= plus(n, mm, _bka) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(z, n2) <= True  :
Yes: {
n2 -> z
}

eq_nat(i, z) <= leq(i, z)  :
No: ()

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

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

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


-------------------------------------------
Step 1, which took 0.007302 s (model generation: 0.007238,  model checking: 0.000064):

Clauses:
{
leq(z, n2) <= True -> 0
eq_nat(i, z) <= leq(i, z) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
plus(n, s(mm), s(_bka)) <= plus(n, mm, _bka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(z, n2) <= True  :
Yes: {
n2 -> s(_vise_0)
}

eq_nat(i, z) <= leq(i, z)  :
No: ()

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

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

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


-------------------------------------------
Step 2, which took 0.007278 s (model generation: 0.006729,  model checking: 0.000549):

Clauses:
{
leq(z, n2) <= True -> 0
eq_nat(i, z) <= leq(i, z) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
plus(n, s(mm), s(_bka)) <= plus(n, mm, _bka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(z, n2) <= True  :
No: ()

eq_nat(i, z) <= leq(i, z)  :
No: ()

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_yise_0)  ;  nn2 -> z
}

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


-------------------------------------------
Step 3, which took 0.007107 s (model generation: 0.007052,  model checking: 0.000055):

Clauses:
{
leq(z, n2) <= True -> 0
eq_nat(i, z) <= leq(i, z) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
plus(n, s(mm), s(_bka)) <= plus(n, mm, _bka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(z, n2) <= True  :
No: ()

eq_nat(i, z) <= leq(i, z)  :
Yes: {
i -> s(_ajse_0)
}

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

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

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


Total time: 0.036450
Learner time: 0.027488
Teacher time: 0.000724
Reasons for stopping: Yes: |_
name: None

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


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



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