Solving ../../benchmarks/smtlib/true/mult_leq_succ.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(_naa)) <= plus(n, mm, _naa)
}
eq_nat(_qaa, _raa) <= plus(_oaa, _paa, _qaa) /\ plus(_oaa, _paa, _raa)
)
(mult, F:
{
mult(n, z, z) <= True
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)
}
eq_nat(_waa, _xaa) <= mult(_uaa, _vaa, _waa) /\ mult(_uaa, _vaa, _xaa)
)
(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)
}
)
}

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


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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}


Solving took 0.122067 seconds.
Yes: |_
name: None

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


;
mult ->
[
mult : <nat * nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  mult(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0)
  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>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, x_2_0)
  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 0.005778 s (model generation: 0.005723,  model checking: 0.000055):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 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: ()

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
No: ()

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.007386 s (model generation: 0.007316,  model checking: 0.000070):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 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(_ogpaa_0)
}

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

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

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.007298 s (model generation: 0.007212,  model checking: 0.000086):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

Accumulated learning constraints:
{
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>
{
  
}
]


;
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)  :
No: ()

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

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
Yes: {
_saa -> z  ;  _taa -> s(_ygpaa_0)  ;  mm -> z  ;  n -> s(_ahpaa_0)
}

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

plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa)  :
Yes: {
_naa -> s(_dhpaa_0)  ;  mm -> z  ;  n -> s(_fhpaa_0)
}


-------------------------------------------
Step 3, which took 0.015417 s (model generation: 0.015286,  model checking: 0.000131):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

Accumulated learning constraints:
{
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(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)  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

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

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
No: ()

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
Yes: {
_yaa -> s(_ihpaa_0)  ;  n -> s(_jhpaa_0)
}

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


-------------------------------------------
Step 4, which took 0.009105 s (model generation: 0.009034,  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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(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(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(_nhpaa_0)
}

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
No: ()

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
No: ()

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


-------------------------------------------
Step 5, which took 0.009210 s (model generation: 0.009143,  model checking: 0.000067):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(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)))
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= True
  leq(z, s(x_1_0)) <= 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 -> s(_ohpaa_0)  ;  nn2 -> z
}

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
No: ()

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
No: ()

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


-------------------------------------------
Step 6, which took 0.009416 s (model generation: 0.009354,  model checking: 0.000062):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

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

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, s(x_1_0)) <= 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))  :
No: ()

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

}

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
No: ()

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
No: ()

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


-------------------------------------------
Step 7, which took 0.015640 s (model generation: 0.015392,  model checking: 0.000248):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(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
False <= leq(s(s(z)), s(z))
leq(z, s(z)) <= leq(s(z), s(s(z)))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= 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))  :
No: ()

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
No: ()

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
Yes: {
_yaa -> s(z)  ;  n -> s(s(_eipaa_0))
}

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


-------------------------------------------
Step 8, which took 0.014684 s (model generation: 0.014457,  model checking: 0.000227):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

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

Current best model:
|_
name: None

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


;
mult ->
[
mult : <nat * nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  mult(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_1_0)
  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))  :
No: ()

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
Yes: {
_saa -> z  ;  _taa -> s(_vipaa_0)  ;  mm -> z  ;  n -> s(s(_ajpaa_0))
}

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

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


-------------------------------------------
Step 9, which took 0.013652 s (model generation: 0.013212,  model checking: 0.000440):

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
mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa) -> 0
leq(n, _yaa) <= mult(n, s(m), _yaa) -> 0
plus(n, s(mm), s(_naa)) <= plus(n, mm, _naa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(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
False <= leq(s(s(z)), s(z))
leq(z, s(z)) <= leq(s(z), s(s(z)))
False <= leq(s(z), z)
False <= mult(s(s(z)), s(s(z)), s(z))
False <= mult(s(s(z)), s(z), s(z))
False <= mult(s(s(z)), z, z) /\ plus(s(s(z)), z, s(z))
}

Current best model:
|_
name: None

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


;
mult ->
[
mult : <nat * nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  mult(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0)
  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>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, x_2_0)
  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))  :
No: ()

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

mult(n, s(mm), _taa) <= mult(n, mm, _saa) /\ plus(n, _saa, _taa)  :
Yes: {
_saa -> s(s(z))  ;  _taa -> s(z)  ;  mm -> s(_akpaa_0)  ;  n -> s(s(z))
}

leq(n, _yaa) <= mult(n, s(m), _yaa)  :
No: ()

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


Total time: 0.122067
Learner time: 0.106129
Teacher time: 0.001457
Reasons for stopping: Yes: |_
name: None

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


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



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