Solving ../../benchmarks/smtlib/true/plus_not_zero_implication.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(_ge)) <= plus(n, mm, _ge)
}
eq_nat(_je, _ke) <= plus(_he, _ie, _je) /\ plus(_he, _ie, _ke)
)
(not_zero, P:
{
not_zero(s(nn)) <= True
False <= not_zero(z)
}
)
}

properties:
{
not_zero(_le) <= not_zero(n) /\ plus(n, m, _le)
}


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

Clause system for inference is:

{
not_zero(s(nn)) <= True -> 0
plus(n, z, n) <= True -> 0
not_zero(_le) <= not_zero(n) /\ plus(n, m, _le) -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_ge)) <= plus(n, mm, _ge) -> 0
}


Solving took 0.038783 seconds.
Yes: |_
name: None

not_zero ->
[
not_zero : <nat>
{
  not_zero(s(x_0_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}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005687 s (model generation: 0.005648,  model checking: 0.000039):

Clauses:
{
not_zero(s(nn)) <= True -> 0
plus(n, z, n) <= True -> 0
not_zero(_le) <= not_zero(n) /\ plus(n, m, _le) -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_ge)) <= plus(n, mm, _ge) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

not_zero ->
[
not_zero : <nat>
{
  
}
]


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



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




Answer of teacher:

not_zero(s(nn)) <= True  :
Yes: {

}

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

not_zero(_le) <= not_zero(n) /\ plus(n, m, _le)  :
No: ()

False <= not_zero(z)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.007272 s (model generation: 0.007223,  model checking: 0.000049):

Clauses:
{
not_zero(s(nn)) <= True -> 0
plus(n, z, n) <= True -> 0
not_zero(_le) <= not_zero(n) /\ plus(n, m, _le) -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_ge)) <= plus(n, mm, _ge) -> 0
}

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

Current best model:
|_
name: None

not_zero ->
[
not_zero : <nat>
{
  not_zero(s(x_0_0)) <= True
}
]


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



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




Answer of teacher:

not_zero(s(nn)) <= True  :
No: ()

plus(n, z, n) <= True  :
Yes: {
n -> s(_hxrba_0)
}

not_zero(_le) <= not_zero(n) /\ plus(n, m, _le)  :
No: ()

False <= not_zero(z)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.007693 s (model generation: 0.007636,  model checking: 0.000057):

Clauses:
{
not_zero(s(nn)) <= True -> 0
plus(n, z, n) <= True -> 0
not_zero(_le) <= not_zero(n) /\ plus(n, m, _le) -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_ge)) <= plus(n, mm, _ge) -> 0
}

Accumulated learning constraints:
{
not_zero(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

not_zero ->
[
not_zero : <nat>
{
  not_zero(s(x_0_0)) <= 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:

not_zero(s(nn)) <= True  :
No: ()

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

not_zero(_le) <= not_zero(n) /\ plus(n, m, _le)  :
No: ()

False <= not_zero(z)  :
No: ()

plus(n, s(mm), s(_ge)) <= plus(n, mm, _ge)  :
Yes: {
_ge -> s(_lxrba_0)  ;  mm -> z  ;  n -> s(_nxrba_0)
}


Total time: 0.038783
Learner time: 0.020507
Teacher time: 0.000145
Reasons for stopping: Yes: |_
name: None

not_zero ->
[
not_zero : <nat>
{
  not_zero(s(x_0_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}
_|