Solving ../../benchmarks/smtlib/true/plus_succ_le_1.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(_pta)) <= plus(n, mm, _pta)
}
eq_nat(_sta, _tta) <= plus(_qta, _rta, _sta) /\ plus(_qta, _rta, _tta)
)
(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(m, _uta) <= plus(s(n), m, _uta)
}


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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 0
}


Solving took 0.124158 seconds.
Yes: |_
name: None

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


;
plus ->
[
plus : <nat * nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_1_0, x_2_0)
  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}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.008144 s (model generation: 0.008068,  model checking: 0.000076):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 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: ()

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

le(m, _uta) <= plus(s(n), m, _uta)  :
No: ()


-------------------------------------------
Step 1, which took 0.011688 s (model generation: 0.011486,  model checking: 0.000202):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 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(_qksba_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: ()

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

le(m, _uta) <= plus(s(n), m, _uta)  :
No: ()


-------------------------------------------
Step 2, which took 0.019976 s (model generation: 0.019812,  model checking: 0.000164):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 0
}

Accumulated learning constraints:
{
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>
{
  
}
]


;
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)  :
No: ()

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

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

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

plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta)  :
Yes: {
_pta -> s(_uksba_0)  ;  mm -> z  ;  n -> s(_wksba_0)
}

le(m, _uta) <= plus(s(n), m, _uta)  :
Yes: {
_uta -> s(_xksba_0)  ;  m -> z
}


-------------------------------------------
Step 3, which took 0.021446 s (model generation: 0.021317,  model checking: 0.000129):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 0
}

Accumulated learning constraints:
{
le(z, 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
}

Current best model:
|_
name: None

le ->
[
le : <nat * nat>
{
  le(z, s(x_1_0)) <= 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: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_alsba_0)
}

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

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

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

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

le(m, _uta) <= plus(s(n), m, _uta)  :
Yes: {
_uta -> s(_blsba_0)  ;  m -> s(_clsba_0)
}


-------------------------------------------
Step 4, which took 0.014112 s (model generation: 0.014028,  model checking: 0.000084):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 0
}

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

Current best model:
|_
name: None

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

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

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

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

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

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

le(m, _uta) <= plus(s(n), m, _uta)  :
No: ()


-------------------------------------------
Step 5, which took 0.011378 s (model generation: 0.011285,  model checking: 0.000093):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 0
}

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

Current best model:
|_
name: None

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

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

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_hlsba_0)  ;  nn2 -> z
}

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

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

}

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

le(m, _uta) <= plus(s(n), m, _uta)  :
No: ()


-------------------------------------------
Step 6, which took 0.022448 s (model generation: 0.022149,  model checking: 0.000299):

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
plus(n, s(mm), s(_pta)) <= plus(n, mm, _pta) -> 0
le(m, _uta) <= plus(s(n), m, _uta) -> 0
}

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

Current best model:
|_
name: None

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


;
plus ->
[
plus : <nat * nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(s(x_0_0), z) <= True
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_0_0, x_2_0)
  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)  :
No: ()

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

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

}

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

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

le(m, _uta) <= plus(s(n), m, _uta)  :
Yes: {
_uta -> s(z)  ;  m -> s(z)  ;  n -> s(_fmsba_0)
}


Total time: 0.124158
Learner time: 0.108145
Teacher time: 0.001047
Reasons for stopping: Yes: |_
name: None

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


;
plus ->
[
plus : <nat * nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= le(x_1_0, x_2_0)
  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}
_|