Solving ../../benchmarks/smtlib/true/fst_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: {
elist -> {econs, enil}  ;  elt -> {a, b}  ;  nat -> {s, z}  ;  npair -> {npair}
}
definition:
{
(fst_nat, F:
{
fst_nat(npair(n1, n2), n1) <= True
}
eq_nat(_xba, _yba) <= fst_nat(_wba, _xba) /\ fst_nat(_wba, _yba)
)
}

properties:
{
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba)
}


over-approximation: {fst_nat}
under-approximation: {}

Clause system for inference is:

{
fst_nat(npair(n1, n2), n1) <= True -> 0
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba) -> 0
}


Solving took 0.065176 seconds.
Yes: |_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  _r_1(s(x_0_0), z) <= _r_2(x_0_0)
  _r_2(z) <= True
  fst_nat(npair(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  fst_nat(npair(x_0_0, x_0_1), z) <= _r_2(x_0_0)
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005680 s (model generation: 0.005656,  model checking: 0.000024):

Clauses:
{
fst_nat(npair(n1, n2), n1) <= True -> 0
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|




Answer of teacher:

fst_nat(npair(n1, n2), n1) <= True  :
Yes: {
n1 -> z
}

eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba)  :
No: ()


-------------------------------------------
Step 1, which took 0.008243 s (model generation: 0.008216,  model checking: 0.000027):

Clauses:
{
fst_nat(npair(n1, n2), n1) <= True -> 0
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba) -> 0
}

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

Current best model:
|_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  fst_nat(npair(x_0_0, x_0_1), z) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|




Answer of teacher:

fst_nat(npair(n1, n2), n1) <= True  :
Yes: {
n1 -> s(_owle_0)
}

eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba)  :
Yes: {
_zba -> z  ;  n1 -> s(_qwle_0)
}


-------------------------------------------
Step 2, which took 0.008656 s (model generation: 0.008529,  model checking: 0.000127):

Clauses:
{
fst_nat(npair(n1, n2), n1) <= True -> 0
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba) -> 0
}

Accumulated learning constraints:
{
fst_nat(npair(s(z), z), s(z)) <= True
fst_nat(npair(z, z), z) <= True
False <= fst_nat(npair(s(z), z), z)
}

Current best model:
|_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  _r_1(z) <= True
  fst_nat(npair(x_0_0, x_0_1), s(x_1_0)) <= True
  fst_nat(npair(x_0_0, x_0_1), z) <= _r_1(x_0_0)
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|




Answer of teacher:

fst_nat(npair(n1, n2), n1) <= True  :
No: ()

eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba)  :
Yes: {
_zba -> s(_uwle_0)  ;  n1 -> z
}


-------------------------------------------
Step 3, which took 0.013176 s (model generation: 0.013096,  model checking: 0.000080):

Clauses:
{
fst_nat(npair(n1, n2), n1) <= True -> 0
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba) -> 0
}

Accumulated learning constraints:
{
fst_nat(npair(s(z), z), s(z)) <= True
fst_nat(npair(z, z), z) <= True
False <= fst_nat(npair(s(z), z), z)
False <= fst_nat(npair(z, z), s(z))
}

Current best model:
|_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  fst_nat(npair(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0)
  fst_nat(npair(x_0_0, x_0_1), z) <= _r_2(x_0_0)
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|




Answer of teacher:

fst_nat(npair(n1, n2), n1) <= True  :
No: ()

eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba)  :
Yes: {
_zba -> s(s(_jxle_0))  ;  n1 -> s(z)
}


-------------------------------------------
Step 4, which took 0.012409 s (model generation: 0.012283,  model checking: 0.000126):

Clauses:
{
fst_nat(npair(n1, n2), n1) <= True -> 0
eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba) -> 0
}

Accumulated learning constraints:
{
fst_nat(npair(s(z), z), s(z)) <= True
fst_nat(npair(z, z), z) <= True
False <= fst_nat(npair(s(z), z), s(s(z)))
False <= fst_nat(npair(s(z), z), z)
False <= fst_nat(npair(z, z), s(z))
}

Current best model:
|_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  _r_1(s(x_0_0), z) <= True
  _r_2(z) <= True
  fst_nat(npair(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  fst_nat(npair(x_0_0, x_0_1), z) <= _r_2(x_0_0)
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|




Answer of teacher:

fst_nat(npair(n1, n2), n1) <= True  :
Yes: {
n1 -> s(s(_uxle_0))
}

eq_nat(_zba, n1) <= fst_nat(npair(n1, n2), _zba)  :
Yes: {
_zba -> s(z)  ;  n1 -> s(s(_vxle_0))
}


Total time: 0.065176
Learner time: 0.047780
Teacher time: 0.000384
Reasons for stopping: Yes: |_
name: None

fst_nat ->
[
fst_nat : <npair * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  _r_1(s(x_0_0), z) <= _r_2(x_0_0)
  _r_2(z) <= True
  fst_nat(npair(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  fst_nat(npair(x_0_0, x_0_1), z) <= _r_2(x_0_0)
}
]



--
Equality automata are defined for: {elist, elt, nat, npair}
_|