Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: left


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(not_null, P:
{() -> not_null([cons(x, ll)])
(not_null([nil])) -> BOT}
)
}

properties:
{(not_null([l2])) -> not_null([l2])}


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

Clause system for inference is:

{
() -> not_null([cons(x, ll)]) -> 0
(not_null([l2])) -> not_null([l2]) -> 0
(not_null([nil])) -> BOT -> 0
}


Solving took 0.038606 seconds.
Proved
Model:
|_
{
not_null -> 
{{{
Q={q_gen_0, q_gen_1, q_gen_2},
Q_f={q_gen_0},
Delta=
{
<cons>(q_gen_2, q_gen_0) -> q_gen_0
<cons>(q_gen_2, q_gen_1) -> q_gen_0
<nil>() -> q_gen_1
<s>(q_gen_2) -> q_gen_2
<z>() -> q_gen_2
}

Datatype: <natlist>
Convolution form: left
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009247 s (model generation: 0.009161,  model checking: 0.000086):

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

}

Datatype: <natlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> not_null([cons(x, ll)]) -> 3
(not_null([l2])) -> not_null([l2]) -> 1
(not_null([nil])) -> BOT -> 1
}
Sat witness: Found: (() -> not_null([cons(x, ll)]), {
ll -> nil  ;  x -> z
})

-------------------------------------------
Step 1, which took 0.009181 s (model generation: 0.009167,  model checking: 0.000014):

Model:
|_
{
not_null -> 
{{{
Q={q_gen_0, q_gen_2},
Q_f={q_gen_0},
Delta=
{
<cons>(q_gen_2, q_gen_0) -> q_gen_0
<nil>() -> q_gen_0
<z>() -> q_gen_2
}

Datatype: <natlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> not_null([cons(x, ll)]) -> 3
(not_null([l2])) -> not_null([l2]) -> 1
(not_null([nil])) -> BOT -> 4
}
Sat witness: Found: ((not_null([nil])) -> BOT, {

})

-------------------------------------------
Step 2, which took 0.008858 s (model generation: 0.008495,  model checking: 0.000363):

Model:
|_
{
not_null -> 
{{{
Q={q_gen_0, q_gen_1, q_gen_2},
Q_f={q_gen_0},
Delta=
{
<cons>(q_gen_2, q_gen_1) -> q_gen_0
<nil>() -> q_gen_1
<z>() -> q_gen_2
}

Datatype: <natlist>
Convolution form: left
}}}

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

Teacher's answer:
New clause system:
{
() -> not_null([cons(x, ll)]) -> 6
(not_null([l2])) -> not_null([l2]) -> 2
(not_null([nil])) -> BOT -> 4
}
Sat witness: Found: (() -> not_null([cons(x, ll)]), {
ll -> cons(s(z), nil)  ;  x -> z
})

Total time: 0.038606
Reason for stopping: Proved