Solving ../../benchmarks/smtlib/true/isaplanner_prop69.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(_as)) <= plus(n, mm, _as)
}
eq_nat(_ds, _es) <= plus(_bs, _cs, _ds) /\ plus(_bs, _cs, _es)
)
(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:
{
leq(n, _fs) <= plus(n, m, _fs)
}


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

Clause system for inference is:

{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}


Solving took 0.070801 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>
{
  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(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, 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}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006397 s (model generation: 0.006094,  model checking: 0.000303):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 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:

plus(n, z, n) <= True  :
Yes: {
n -> 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(n, _fs) <= plus(n, m, _fs)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.006427 s (model generation: 0.006363,  model checking: 0.000064):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

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

Current best model:
|_
name: None

leq ->
[
leq : <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(_nisk_0)
}

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

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


-------------------------------------------
Step 2, which took 0.006799 s (model generation: 0.006744,  model checking: 0.000055):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

Accumulated learning constraints:
{
leq(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

leq ->
[
leq : <nat * nat>
{
  leq(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: ()

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(n, _fs) <= plus(n, m, _fs)  :
Yes: {
_fs -> s(_zisk_0)  ;  m -> s(_ajsk_0)  ;  n -> z
}

plus(n, s(mm), s(_as)) <= plus(n, mm, _as)  :
Yes: {
_as -> s(_cjsk_0)  ;  mm -> z  ;  n -> s(_ejsk_0)
}


-------------------------------------------
Step 3, which took 0.008038 s (model generation: 0.007978,  model checking: 0.000060):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

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

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>
{
  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:

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

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_fjsk_0)  ;  nn2 -> z
}

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

leq(n, _fs) <= plus(n, m, _fs)  :
No: ()

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


-------------------------------------------
Step 4, which took 0.008717 s (model generation: 0.008671,  model checking: 0.000046):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

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

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

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

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

False <= leq(s(nn1), z)  :
Yes: {

}

leq(n, _fs) <= plus(n, m, _fs)  :
No: ()

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


-------------------------------------------
Step 5, which took 0.007829 s (model generation: 0.007720,  model checking: 0.000109):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

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


;
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:

plus(n, z, n) <= True  :
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(n, _fs) <= plus(n, m, _fs)  :
Yes: {
_fs -> s(z)  ;  m -> z  ;  n -> s(s(_zjsk_0))
}

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


-------------------------------------------
Step 6, which took 0.008245 s (model generation: 0.008131,  model checking: 0.000114):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

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


;
plus ->
[
plus : <nat * 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(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, 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:

plus(n, z, n) <= True  :
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(n, _fs) <= plus(n, m, _fs)  :
Yes: {
_fs -> s(z)  ;  m -> s(_nksk_0)  ;  n -> s(s(_vksk_0))
}

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


-------------------------------------------
Step 7, which took 0.008498 s (model generation: 0.008059,  model checking: 0.000439):

Clauses:
{
plus(n, z, n) <= True -> 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(n, _fs) <= plus(n, m, _fs) -> 0
plus(n, s(mm), s(_as)) <= plus(n, mm, _as) -> 0
}

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


;
plus ->
[
plus : <nat * 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(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, 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:

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

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


Total time: 0.070801
Learner time: 0.059760
Teacher time: 0.001190
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>
{
  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(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, 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}
_|