Solving ../../benchmarks/smtlib/true/append_not_null_nat.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}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{
append(nil, l2, l2) <= True
append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua)
}
eq_natlist(_qua, _rua) <= append(_oua, _pua, _qua) /\ append(_oua, _pua, _rua)
)
(not_null, P:
{
not_null(cons(x, ll)) <= True
False <= not_null(nil)
}
)
}

properties:
{
not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1)
not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2)
}


over-approximation: {append}
under-approximation: {}

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1) -> 0
not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2) -> 0
append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua) -> 0
False <= not_null(nil) -> 0
}


Solving took 0.055992 seconds.
Yes: |_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
not_null ->
[
not_null : <natlist>
{
  not_null(cons(x_0_0, x_0_1)) <= True
}
]



--
Equality automata are defined for: {nat, natlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009664 s (model generation: 0.009602,  model checking: 0.000062):

Clauses:
{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1) -> 0
not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2) -> 0
append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua) -> 0
False <= not_null(nil) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  
}
]


;
not_null ->
[
not_null : <natlist>
{
  
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> nil
}

not_null(cons(x, ll)) <= True  :
Yes: {

}

not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1)  :
No: ()

not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua)  :
No: ()

False <= not_null(nil)  :
No: ()


-------------------------------------------
Step 1, which took 0.010942 s (model generation: 0.010805,  model checking: 0.000137):

Clauses:
{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1) -> 0
not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2) -> 0
append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua) -> 0
False <= not_null(nil) -> 0
}

Accumulated learning constraints:
{
append(nil, nil, nil) <= True
not_null(cons(z, nil)) <= True
}

Current best model:
|_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  append(nil, nil, nil) <= True
}
]


;
not_null ->
[
not_null : <natlist>
{
  not_null(cons(x_0_0, x_0_1)) <= True
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_ocud_0, _ocud_1)
}

not_null(cons(x, ll)) <= True  :
No: ()

not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1)  :
No: ()

not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua)  :
Yes: {
_nua -> nil  ;  l2 -> nil  ;  t1 -> nil
}

False <= not_null(nil)  :
No: ()


-------------------------------------------
Step 2, which took 0.018281 s (model generation: 0.018205,  model checking: 0.000076):

Clauses:
{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1) -> 0
not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2) -> 0
append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua) -> 0
False <= not_null(nil) -> 0
}

Accumulated learning constraints:
{
append(cons(z, nil), nil, cons(z, nil)) <= True
append(nil, cons(z, nil), cons(z, nil)) <= True
append(nil, nil, nil) <= True
not_null(cons(z, nil)) <= True
}

Current best model:
|_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
not_null ->
[
not_null : <natlist>
{
  not_null(cons(x_0_0, x_0_1)) <= True
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

not_null(cons(x, ll)) <= True  :
No: ()

not_null(_sua) <= append(l1, l2, _sua) /\ not_null(l1)  :
No: ()

not_null(_tua) <= append(l1, l2, _tua) /\ not_null(l2)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _nua)) <= append(t1, l2, _nua)  :
Yes: {
_nua -> cons(_scud_0, _scud_1)  ;  l2 -> cons(_tcud_0, _tcud_1)  ;  t1 -> nil
}

False <= not_null(nil)  :
No: ()


Total time: 0.055992
Learner time: 0.038612
Teacher time: 0.000275
Reasons for stopping: Yes: |_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
not_null ->
[
not_null : <natlist>
{
  not_null(cons(x_0_0, x_0_1)) <= True
}
]



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