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


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 0.042254 seconds.
Proved
Model:
|_
{
not_null -> 
{{{
Q={q_gen_5633, q_gen_5634, q_gen_5635},
Q_f={q_gen_5633},
Delta=
{
<cons>(q_gen_5635, q_gen_5633) -> q_gen_5633
<cons>(q_gen_5635, q_gen_5634) -> q_gen_5633
<nil>() -> q_gen_5634
<s>(q_gen_5635) -> q_gen_5635
<z>() -> q_gen_5635
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009835 s (model generation: 0.009685,  model checking: 0.000150):

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

}

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

}
--
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 0.010259 s (model generation: 0.010236,  model checking: 0.000023):

Model:
|_
{
not_null -> 
{{{
Q={q_gen_5633, q_gen_5635},
Q_f={q_gen_5633},
Delta=
{
<cons>(q_gen_5635, q_gen_5633) -> q_gen_5633
<nil>() -> q_gen_5633
<z>() -> q_gen_5635
}

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

}
--
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 0.010845 s (model generation: 0.010407,  model checking: 0.000438):

Model:
|_
{
not_null -> 
{{{
Q={q_gen_5633, q_gen_5634, q_gen_5635},
Q_f={q_gen_5633},
Delta=
{
<cons>(q_gen_5635, q_gen_5634) -> q_gen_5633
<nil>() -> q_gen_5634
<z>() -> q_gen_5635
}

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

}
--
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: 0.042254
Reason for stopping: Proved