Solving ../../benchmarks/smtlib/true/mult_leq_not_null.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(_kh)) <= plus(n, mm, _kh)
}
eq_nat(_nh, _oh) <= plus(_lh, _mh, _nh) /\ plus(_lh, _mh, _oh)
)
(mult, F:
{
mult(n, z, z) <= True
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)
}
eq_nat(_th, _uh) <= mult(_rh, _sh, _th) /\ mult(_rh, _sh, _uh)
)
(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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)
}


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

Clause system for inference is:

{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}


Solving took 0.090947 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 0.006204 s (model generation: 0.006106,  model checking: 0.000098):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 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:

leq(z, s(nn2)) <= True  :
Yes: {

}

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

}

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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
No: ()

mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.006439 s (model generation: 0.006361,  model checking: 0.000078):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

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

Current best model:
|_
name: None

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


;
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:

leq(z, s(nn2)) <= True  :
No: ()

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

mult(n, z, z) <= True  :
Yes: {
n -> s(_jyoaa_0)
}

plus(n, z, n) <= True  :
Yes: {
n -> s(_kyoaa_0)
}

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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
No: ()

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

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


-------------------------------------------
Step 2, which took 0.007794 s (model generation: 0.007717,  model checking: 0.000077):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

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

leq(z, s(nn2)) <= True  :
No: ()

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

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(_wyoaa_0)  ;  nn2 -> z
}

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

leq(n, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
No: ()

mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)  :
Yes: {
_ph -> z  ;  _qh -> s(_zyoaa_0)  ;  mm -> z  ;  n -> s(_bzoaa_0)
}

plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh)  :
Yes: {
_kh -> s(_czoaa_0)  ;  mm -> z  ;  n -> s(_ezoaa_0)
}


-------------------------------------------
Step 3, which took 0.009005 s (model generation: 0.008931,  model checking: 0.000074):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

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

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:

leq(z, s(nn2)) <= True  :
No: ()

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

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: {

}

leq(n, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
No: ()

mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)  :
No: ()

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


-------------------------------------------
Step 4, which took 0.010352 s (model generation: 0.010144,  model checking: 0.000208):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

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

leq(z, s(nn2)) <= True  :
No: ()

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

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: ()

leq(n, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
Yes: {
_vh -> s(z)  ;  m -> s(z)  ;  n -> s(s(_uzoaa_0))
}

mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)  :
No: ()

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


-------------------------------------------
Step 5, which took 0.014804 s (model generation: 0.014591,  model checking: 0.000213):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

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

leq(z, s(nn2)) <= True  :
No: ()

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

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: ()

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

mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)  :
Yes: {
_ph -> z  ;  _qh -> s(_qapaa_0)  ;  mm -> z  ;  n -> s(s(_zapaa_0))
}

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


-------------------------------------------
Step 6, which took 0.010911 s (model generation: 0.010600,  model checking: 0.000311):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

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

leq(z, s(nn2)) <= True  :
No: ()

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

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: ()

leq(n, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
No: ()

mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh)  :
Yes: {
_ph -> s(s(z))  ;  _qh -> s(z)  ;  mm -> s(_wbpaa_0)  ;  n -> s(s(z))
}

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


-------------------------------------------
Step 7, which took 0.014209 s (model generation: 0.013916,  model checking: 0.000293):

Clauses:
{
leq(z, s(nn2)) <= True -> 0
leq(z, z) <= True -> 0
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, _vh) <= leq(s(z), m) /\ mult(n, m, _vh) -> 0
mult(n, s(mm), _qh) <= mult(n, mm, _ph) /\ plus(n, _ph, _qh) -> 0
plus(n, s(mm), s(_kh)) <= plus(n, mm, _kh) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(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))
False <= leq(s(z), s(s(z))) /\ mult(s(s(z)), s(s(z)), s(z))
False <= leq(s(z), z)
mult(s(s(z)), s(s(z)), s(z)) <= mult(s(s(z)), s(z), s(s(z))) /\ plus(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_1_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:

leq(z, s(nn2)) <= True  :
No: ()

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

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: ()

leq(n, _vh) <= leq(s(z), m) /\ mult(n, m, _vh)  :
No: ()

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

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


Total time: 0.090947
Learner time: 0.078366
Teacher time: 0.001352
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}
_|