Solving ../../benchmarks/smtlib/false/insert_length_eq.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: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{
leq(a, y) <= True
leq(b, b) <= True
False <= leq(b, a)
}
)
(insert, F:
{
insert(x, nil, cons(x, nil)) <= True
insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb)
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)
}
eq_eltlist(_tcb, _ucb) <= insert(_rcb, _scb, _tcb) /\ insert(_rcb, _scb, _ucb)
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_vcb)) <= length(ll, _vcb)
}
eq_nat(_xcb, _ycb) <= length(_wcb, _xcb) /\ length(_wcb, _ycb)
)
(leqnat, P:
{
leqnat(z, s(nn2)) <= True
leqnat(z, z) <= True
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2)
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2))
False <= leqnat(s(nn1), z)
}
)
}

properties:
{
eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb)
}


over-approximation: {insert, length, leqnat}
under-approximation: {leqnat}

Clause system for inference is:

{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb) -> 0
insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb) -> 0
length(cons(x, ll), s(_vcb)) <= length(ll, _vcb) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 0
}


Solving took 0.030725 seconds.
No: Contradictory set of ground constraints:
{
False <= True
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005876 s (model generation: 0.005786,  model checking: 0.000090):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb) -> 0
insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb) -> 0
length(cons(x, ll), s(_vcb)) <= length(ll, _vcb) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  
}
]


;
length ->
[
length : <eltlist * nat>
{
  
}
]


;
leq ->
[
leq : <elt * elt>
{
  
}
]


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



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




Answer of teacher:

insert(x, nil, cons(x, nil)) <= True  :
Yes: {
x -> b
}

length(nil, z) <= True  :
Yes: {

}

leq(a, y) <= True  :
Yes: {
y -> b
}

leq(b, b) <= True  :
Yes: {

}

eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb)  :
No: ()

insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb)  :
No: ()

length(cons(x, ll), s(_vcb)) <= length(ll, _vcb)  :
No: ()

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()

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

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


-------------------------------------------
Step 1, which took 0.006883 s (model generation: 0.006784,  model checking: 0.000099):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb) -> 0
insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb) -> 0
length(cons(x, ll), s(_vcb)) <= length(ll, _vcb) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 0
}

Accumulated learning constraints:
{
insert(b, nil, cons(b, nil)) <= True
length(nil, z) <= True
leq(a, b) <= True
leq(b, b) <= True
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, b) <= True
  leq(b, b) <= True
}
]


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



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




Answer of teacher:

insert(x, nil, cons(x, nil)) <= True  :
Yes: {
x -> a
}

length(nil, z) <= True  :
No: ()

leq(a, y) <= True  :
Yes: {
y -> a
}

leq(b, b) <= True  :
No: ()

eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb)  :
No: ()

insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb)  :
Yes: {
_qcb -> cons(_otoqw_0, _otoqw_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

length(cons(x, ll), s(_vcb)) <= length(ll, _vcb)  :
Yes: {
_vcb -> z  ;  ll -> nil
}

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> b  ;  y -> b
}

False <= leq(b, a)  :
No: ()

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

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


-------------------------------------------
Step 2, which took 0.009327 s (model generation: 0.009121,  model checking: 0.000206):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb) -> 0
insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb) -> 0
length(cons(x, ll), s(_vcb)) <= length(ll, _vcb) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 0
}

Accumulated learning constraints:
{
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
insert(b, cons(a, nil), cons(a, cons(a, nil))) \/ leq(b, a) <= insert(b, nil, cons(a, nil))
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
length ->
[
length : <eltlist * nat>
{
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= True
  length(nil, z) <= True
}
]


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, a) <= True
  leq(b, b) <= True
}
]


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



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




Answer of teacher:

insert(x, nil, cons(x, nil)) <= True  :
No: ()

length(nil, z) <= True  :
No: ()

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(_zcb, _bdb) <= insert(x, l, _adb) /\ length(_adb, _bdb) /\ length(l, _zcb)  :
Yes: {
_adb -> cons(_ytoqw_0, _ytoqw_1)  ;  _bdb -> s(_ztoqw_0)  ;  _zcb -> z  ;  l -> nil  ;  x -> a
}

insert(x, cons(y, z), cons(y, _qcb)) \/ leq(x, y) <= insert(x, z, _qcb)  :
No: ()

length(cons(x, ll), s(_vcb)) <= length(ll, _vcb)  :
No: ()

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> a  ;  y -> b
}

False <= leq(b, a)  :
Yes: {

}

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

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


Total time: 0.030725
Learner time: 0.021691
Teacher time: 0.000395
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
}