Solving ../../benchmarks/true/isaplanner_prop22.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(max, F:
{() -> max([s(u), z, s(u)])
() -> max([z, y, y])
(max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)])}
(max([_lo, _mo, _no]) /\ max([_lo, _mo, _oo])) -> eq_nat([_no, _oo])
)
}

properties:
{(max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so])}


over-approximation: {max}
under-approximation: {}

Clause system for inference is:

{
() -> max([s(u), z, s(u)]) -> 0  ;  () -> max([z, y, y]) -> 0  ;  (max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 0  ;  (max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 0
}


Solving took 0.022646 seconds.
Proved
Model:
|_
{
max -> 
{{{
Q={q_gen_1582, q_gen_1584},
Q_f={q_gen_1582},
Delta=
{
<s, s>(q_gen_1584) -> q_gen_1584
<z, z>() -> q_gen_1584
<s, s, s>(q_gen_1582) -> q_gen_1582
<s, z, s>(q_gen_1584) -> q_gen_1582
<z, s, s>(q_gen_1584) -> q_gen_1582
<z, z, z>() -> q_gen_1582
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.003378 s (model generation: 0.003201,  model checking: 0.000177):

Model:
|_
{
max -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 0  ;  () -> max([z, y, y]) -> 3  ;  (max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 1  ;  (max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 1
}
Sat witness: Yes: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.003373 s (model generation: 0.003314,  model checking: 0.000059):

Model:
|_
{
max -> 
{{{
Q={q_gen_1582},
Q_f={q_gen_1582},
Delta=
{
<z, z, z>() -> q_gen_1582
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 3  ;  (max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 1  ;  (max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 1
}
Sat witness: Yes: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.003562 s (model generation: 0.003470,  model checking: 0.000092):

Model:
|_
{
max -> 
{{{
Q={q_gen_1582, q_gen_1584},
Q_f={q_gen_1582},
Delta=
{
<z, z>() -> q_gen_1584
<s, z, s>(q_gen_1584) -> q_gen_1582
<z, z, z>() -> q_gen_1582
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 3  ;  (max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 1  ;  (max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 4
}
Sat witness: Yes: ((max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]), {
_ko -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 3, which took 0.003766 s (model generation: 0.003514,  model checking: 0.000252):

Model:
|_
{
max -> 
{{{
Q={q_gen_1582, q_gen_1584},
Q_f={q_gen_1582},
Delta=
{
<z, z>() -> q_gen_1584
<s, s, s>(q_gen_1582) -> q_gen_1582
<s, z, s>(q_gen_1584) -> q_gen_1582
<z, z, z>() -> q_gen_1582
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 6  ;  (max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 2  ;  (max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 4
}
Sat witness: Yes: (() -> max([z, y, y]), {
y -> s(z)
})

-------------------------------------------
Step 4, which took 0.004001 s (model generation: 0.003398,  model checking: 0.000603):

Model:
|_
{
max -> 
{{{
Q={q_gen_1582, q_gen_1584},
Q_f={q_gen_1582},
Delta=
{
<z, z>() -> q_gen_1584
<s, s, s>(q_gen_1582) -> q_gen_1582
<s, z, s>(q_gen_1584) -> q_gen_1582
<z, s, s>(q_gen_1584) -> q_gen_1582
<z, z, z>() -> q_gen_1582
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 6  ;  () -> max([z, y, y]) -> 6  ;  (max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 3  ;  (max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 4
}
Sat witness: Yes: (() -> max([s(u), z, s(u)]), {
u -> s(z)
})

Total time: 0.022646
Reason for stopping: Proved