Solving ../../benchmarks/smtlib/true/isaplanner_prop33.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:
{
(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)
}
)
(min, F:
{
min(s(u), z, z) <= True
min(z, y, z) <= True
min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju)
}
eq_nat(_mu, _nu) <= min(_ku, _lu, _mu) /\ min(_ku, _lu, _nu)
)
}

properties:
{
eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu)
leq(i, j) <= min(i, j, i)
}


over-approximation: {min}
under-approximation: {}

Clause system for inference is:

{
leq(z, n2) <= True -> 0
min(s(u), z, z) <= True -> 0
min(z, y, z) <= True -> 0
eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, j) <= min(i, j, i) -> 0
min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju) -> 0
}


Solving took 0.042135 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
}
]


;
min ->
[
min : <nat * nat * nat>
{
  min(s(x_0_0), s(x_1_0), s(x_2_0)) <= min(x_0_0, x_1_0, x_2_0)
  min(s(x_0_0), z, z) <= True
  min(z, s(x_1_0), z) <= True
  min(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006588 s (model generation: 0.006508,  model checking: 0.000080):

Clauses:
{
leq(z, n2) <= True -> 0
min(s(u), z, z) <= True -> 0
min(z, y, z) <= True -> 0
eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, j) <= min(i, j, i) -> 0
min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

min(s(u), z, z) <= True  :
Yes: {

}

min(z, y, z) <= True  :
Yes: {
y -> z
}

eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu)  :
No: ()

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

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

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

leq(i, j) <= min(i, j, i)  :
No: ()

min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju)  :
No: ()


-------------------------------------------
Step 1, which took 0.006923 s (model generation: 0.006837,  model checking: 0.000086):

Clauses:
{
leq(z, n2) <= True -> 0
min(s(u), z, z) <= True -> 0
min(z, y, z) <= True -> 0
eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, j) <= min(i, j, i) -> 0
min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(z, n2) <= True  :
Yes: {
n2 -> s(_vihh_0)
}

min(s(u), z, z) <= True  :
No: ()

min(z, y, z) <= True  :
Yes: {
y -> s(_wihh_0)
}

eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu)  :
No: ()

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

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

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

leq(i, j) <= min(i, j, i)  :
No: ()

min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju)  :
Yes: {
_ju -> z  ;  u -> z  ;  y1 -> z
}


-------------------------------------------
Step 2, which took 0.008726 s (model generation: 0.008386,  model checking: 0.000340):

Clauses:
{
leq(z, n2) <= True -> 0
min(s(u), z, z) <= True -> 0
min(z, y, z) <= True -> 0
eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, j) <= min(i, j, i) -> 0
min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju) -> 0
}

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


;
min ->
[
min : <nat * nat * nat>
{
  min(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  min(s(x_0_0), z, z) <= True
  min(z, s(x_1_0), z) <= True
  min(z, z, z) <= True
}
]



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




Answer of teacher:

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

min(s(u), z, z) <= True  :
No: ()

min(z, y, z) <= True  :
No: ()

eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu)  :
Yes: {
_pu -> s(z)  ;  i -> s(s(_pjhh_0))  ;  j -> s(_hjhh_0)
}

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_ijhh_0)  ;  nn2 -> z
}

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

leq(i, j) <= min(i, j, i)  :
No: ()

min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju)  :
No: ()


-------------------------------------------
Step 3, which took 0.009654 s (model generation: 0.009430,  model checking: 0.000224):

Clauses:
{
leq(z, n2) <= True -> 0
min(s(u), z, z) <= True -> 0
min(z, y, z) <= True -> 0
eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, j) <= min(i, j, i) -> 0
min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
min(s(z), s(z), s(z)) <= True
min(s(z), z, z) <= True
min(z, s(z), z) <= True
min(z, z, z) <= True
leq(s(z), z) <= leq(s(s(z)), s(z))
False <= leq(s(s(z)), s(z)) /\ min(s(s(z)), s(z), s(z))
}

Current best model:
|_
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
}
]


;
min ->
[
min : <nat * nat * nat>
{
  min(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  min(s(x_0_0), z, z) <= True
  min(z, s(x_1_0), z) <= True
  min(z, z, z) <= True
}
]



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




Answer of teacher:

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

min(s(u), z, z) <= True  :
No: ()

min(z, y, z) <= True  :
No: ()

eq_nat(_pu, i) <= leq(i, j) /\ min(i, j, _pu)  :
Yes: {
_pu -> s(s(_qkhh_0))  ;  i -> s(z)  ;  j -> s(z)
}

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

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

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

leq(i, j) <= min(i, j, i)  :
Yes: {
i -> s(s(_tkhh_0))  ;  j -> s(z)
}

min(s(u), s(y1), s(_ju)) <= min(u, y1, _ju)  :
No: ()


Total time: 0.042135
Learner time: 0.031161
Teacher time: 0.000730
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
}
]


;
min ->
[
min : <nat * nat * nat>
{
  min(s(x_0_0), s(x_1_0), s(x_2_0)) <= min(x_0_0, x_1_0, x_2_0)
  min(s(x_0_0), z, z) <= True
  min(z, s(x_1_0), z) <= True
  min(z, z, z) <= True
}
]



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