Solving ../../benchmarks/smtlib/false/mult_leq.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:
{
(leq, P:
{
leq(z, s(nn2)) <= True
leq(z, z) <= True
leq(s(nn1), s(nn2)) <= leq(nn1, nn2)
leq(nn1, nn2) <= leq(s(nn1), s(nn2))
False <= leq(s(nn1), z)
}
)
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb)
}
eq_nat(_ihb, _jhb) <= plus(_ghb, _hhb, _ihb) /\ plus(_ghb, _hhb, _jhb)
)
(mult, F:
{
mult(n, z, z) <= True
mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb)
}
eq_nat(_ohb, _phb) <= mult(_mhb, _nhb, _ohb) /\ mult(_mhb, _nhb, _phb)
)
}

properties:
{
leq(n, _qhb) <= mult(n, m, _qhb)
}


over-approximation: {mult, plus}
under-approximation: {leq}

Clause system for inference is:

{
mult(n, z, z) <= True -> 0
plus(n, z, n) <= True -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(n, _qhb) <= mult(n, m, _qhb) -> 0
mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb) -> 0
plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb) -> 0
}


Solving took 0.058887 seconds.
No: Contradictory set of ground constraints:
{
leq(s(z), s(z)) <= True
leq(s(z), z) <= True
leq(z, z) <= True
mult(s(z), s(z), s(z)) <= True
mult(s(z), z, z) <= True
mult(z, s(z), z) <= True
mult(z, z, z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
leq(z, s(z)) <= leq(s(z), s(s(z)))
False <= leq(s(z), z)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007838 s (model generation: 0.007571,  model checking: 0.000267):

Clauses:
{
mult(n, z, z) <= True -> 0
plus(n, z, n) <= True -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(n, _qhb) <= mult(n, m, _qhb) -> 0
mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb) -> 0
plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  
}
]


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


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



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




Answer of teacher:

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

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

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

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

False <= leq(s(nn1), z)  :
No: ()

leq(n, _qhb) <= mult(n, m, _qhb)  :
No: ()

mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.006424 s (model generation: 0.006343,  model checking: 0.000081):

Clauses:
{
mult(n, z, z) <= True -> 0
plus(n, z, n) <= True -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(n, _qhb) <= mult(n, m, _qhb) -> 0
mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb) -> 0
plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb) -> 0
}

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

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  
}
]


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


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



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




Answer of teacher:

mult(n, z, z) <= True  :
Yes: {
n -> s(_lcpqw_0)
}

plus(n, z, n) <= True  :
Yes: {
n -> s(_mcpqw_0)
}

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

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

False <= leq(s(nn1), z)  :
No: ()

leq(n, _qhb) <= mult(n, m, _qhb)  :
Yes: {
_qhb -> z  ;  m -> z  ;  n -> z
}

mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb)  :
Yes: {
_khb -> z  ;  _lhb -> z  ;  mm -> z  ;  n -> z
}

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


-------------------------------------------
Step 2, which took 0.007727 s (model generation: 0.007643,  model checking: 0.000084):

Clauses:
{
mult(n, z, z) <= True -> 0
plus(n, z, n) <= True -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(n, _qhb) <= mult(n, m, _qhb) -> 0
mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb) -> 0
plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb) -> 0
}

Accumulated learning constraints:
{
leq(z, z) <= True
mult(s(z), z, z) <= True
mult(z, s(z), z) <= True
mult(z, z, 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

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


;
mult ->
[
mult : <nat * nat * nat>
{
  mult(s(x_0_0), z, z) <= True
  mult(z, s(x_1_0), z) <= True
  mult(z, z, z) <= 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:

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

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

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

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

False <= leq(s(nn1), z)  :
No: ()

leq(n, _qhb) <= mult(n, m, _qhb)  :
Yes: {
_qhb -> z  ;  m -> z  ;  n -> s(_bdpqw_0)
}

mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb)  :
Yes: {
_khb -> z  ;  _lhb -> s(_ddpqw_0)  ;  mm -> z  ;  n -> s(_fdpqw_0)
}

plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb)  :
Yes: {
_fhb -> s(_gdpqw_0)  ;  mm -> z  ;  n -> s(_idpqw_0)
}


-------------------------------------------
Step 3, which took 0.008962 s (model generation: 0.008891,  model checking: 0.000071):

Clauses:
{
mult(n, z, z) <= True -> 0
plus(n, z, n) <= True -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(n, _qhb) <= mult(n, m, _qhb) -> 0
mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb) -> 0
plus(n, s(mm), s(_fhb)) <= plus(n, mm, _fhb) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(s(z), z) <= True
leq(z, z) <= True
mult(s(z), s(z), s(z)) <= True
mult(s(z), z, z) <= True
mult(z, s(z), z) <= True
mult(z, z, z) <= True
plus(s(z), s(z), s(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

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= True
  leq(s(x_0_0), z) <= True
  leq(z, z) <= True
}
]


;
mult ->
[
mult : <nat * nat * nat>
{
  mult(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  mult(s(x_0_0), z, z) <= True
  mult(z, s(x_1_0), z) <= True
  mult(z, z, z) <= 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}
_|




Answer of teacher:

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

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

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> z  ;  nn2 -> s(_kdpqw_0)
}

False <= leq(s(nn1), z)  :
Yes: {

}

leq(n, _qhb) <= mult(n, m, _qhb)  :
No: ()

mult(n, s(mm), _lhb) <= mult(n, mm, _khb) /\ plus(n, _khb, _lhb)  :
No: ()

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


Total time: 0.058887
Learner time: 0.030448
Teacher time: 0.000503
Reasons for stopping: No: Contradictory set of ground constraints:
{
leq(s(z), s(z)) <= True
leq(s(z), z) <= True
leq(z, z) <= True
mult(s(z), s(z), s(z)) <= True
mult(s(z), z, z) <= True
mult(z, s(z), z) <= True
mult(z, z, z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
leq(z, s(z)) <= leq(s(z), s(s(z)))
False <= leq(s(z), z)
}