Solving ../../benchmarks/smtlib/true/plus_succ_not_zero.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(_me)) <= plus(n, mm, _me)
}
eq_nat(_pe, _qe) <= plus(_ne, _oe, _pe) /\ plus(_ne, _oe, _qe)
)
(not_zero, P:
{
not_zero(s(nn)) <= True
False <= not_zero(z)
}
)
}

properties:
{
not_zero(_re) <= plus(s(n), m, _re)
}


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

Clause system for inference is:

{
plus(n, z, n) <= True -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_me)) <= plus(n, mm, _me) -> 0
not_zero(_re) <= plus(s(n), m, _re) -> 0
}


Solving took 0.049796 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 0.005800 s (model generation: 0.005771,  model checking: 0.000029):

Clauses:
{
plus(n, z, n) <= True -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_me)) <= plus(n, mm, _me) -> 0
not_zero(_re) <= plus(s(n), m, _re) -> 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:

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

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

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

not_zero(_re) <= plus(s(n), m, _re)  :
No: ()


-------------------------------------------
Step 1, which took 0.007113 s (model generation: 0.007060,  model checking: 0.000053):

Clauses:
{
plus(n, z, n) <= True -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_me)) <= plus(n, mm, _me) -> 0
not_zero(_re) <= plus(s(n), m, _re) -> 0
}

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

Current best model:
|_
name: None

not_zero ->
[
not_zero : <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(_dxsba_0)
}

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

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

not_zero(_re) <= plus(s(n), m, _re)  :
No: ()


-------------------------------------------
Step 2, which took 0.015884 s (model generation: 0.015766,  model checking: 0.000118):

Clauses:
{
plus(n, z, n) <= True -> 0
False <= not_zero(z) -> 0
plus(n, s(mm), s(_me)) <= plus(n, mm, _me) -> 0
not_zero(_re) <= plus(s(n), m, _re) -> 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

not_zero ->
[
not_zero : <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: ()

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

plus(n, s(mm), s(_me)) <= plus(n, mm, _me)  :
Yes: {
_me -> s(_hxsba_0)  ;  mm -> z  ;  n -> s(_jxsba_0)
}

not_zero(_re) <= plus(s(n), m, _re)  :
Yes: {
_re -> s(_kxsba_0)  ;  m -> z
}


Total time: 0.049796
Learner time: 0.028597
Teacher time: 0.000200
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}
_|