Solving ../../benchmarks/false/member_cons.smt2...

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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(memberl, P:
{() -> memberl([h1, cons(h1, t1)])
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)])
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1])
(memberl([e, nil])) -> BOT}
)
(not_null, P:
{() -> not_null([cons(x, ll)])
(not_null([nil])) -> BOT}
)
}

properties:
{(memberl([i, cons(i, l)])) -> memberl([i, l])}


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

Clause system for inference is:

{
() -> memberl([h1, cons(h1, t1)]) -> 0
() -> not_null([cons(x, ll)]) -> 0
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)]) -> 0
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1]) -> 0
(memberl([e, nil])) -> BOT -> 0
(memberl([i, cons(i, l)])) -> memberl([i, l]) -> 0
(not_null([nil])) -> BOT -> 0
}


Solving took 0.114911 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.016838 s (model generation: 0.016277,  model checking: 0.000561):

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

}

Datatype: <nat, natlist>
Convolution form: left
}}}
  ;  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:
{
() -> memberl([h1, cons(h1, t1)]) -> 0
() -> not_null([cons(x, ll)]) -> 3
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)]) -> 1
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1]) -> 1
(memberl([e, nil])) -> BOT -> 1
(memberl([i, cons(i, l)])) -> memberl([i, l]) -> 1
(not_null([nil])) -> BOT -> 1
}
Sat witness: Found: (() -> not_null([cons(x, ll)]), {
ll -> nil  ;  x -> z
})

-------------------------------------------
Step 1, which took 0.017903 s (model generation: 0.017671,  model checking: 0.000232):

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

}

Datatype: <nat, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8899, q_gen_8901},
Q_f={q_gen_8899},
Delta=
{
<cons>(q_gen_8901, q_gen_8899) -> q_gen_8899
<nil>() -> q_gen_8899
<z>() -> q_gen_8901
}

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

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

Teacher's answer:
New clause system:
{
() -> memberl([h1, cons(h1, t1)]) -> 3
() -> not_null([cons(x, ll)]) -> 3
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)]) -> 1
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1]) -> 1
(memberl([e, nil])) -> BOT -> 1
(memberl([i, cons(i, l)])) -> memberl([i, l]) -> 1
(not_null([nil])) -> BOT -> 1
}
Sat witness: Found: (() -> memberl([h1, cons(h1, t1)]), {
h1 -> z  ;  t1 -> nil
})

-------------------------------------------
Step 2, which took 0.019686 s (model generation: 0.019653,  model checking: 0.000033):

Model:
|_
{
memberl -> 
{{{
Q={q_gen_8902, q_gen_8903, q_gen_8904},
Q_f={q_gen_8902},
Delta=
{
<nil>() -> q_gen_8903
<z>() -> q_gen_8904
<z, cons>(q_gen_8904, q_gen_8903) -> q_gen_8902
}

Datatype: <nat, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8899, q_gen_8901},
Q_f={q_gen_8899},
Delta=
{
<cons>(q_gen_8901, q_gen_8899) -> q_gen_8899
<nil>() -> q_gen_8899
<z>() -> q_gen_8901
}

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

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

Teacher's answer:
New clause system:
{
() -> memberl([h1, cons(h1, t1)]) -> 3
() -> not_null([cons(x, ll)]) -> 3
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)]) -> 1
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1]) -> 1
(memberl([e, nil])) -> BOT -> 1
(memberl([i, cons(i, l)])) -> memberl([i, l]) -> 1
(not_null([nil])) -> BOT -> 4
}
Sat witness: Found: ((not_null([nil])) -> BOT, {

})

-------------------------------------------
Step 3, which took 0.024469 s (model generation: 0.018784,  model checking: 0.005685):

Model:
|_
{
memberl -> 
{{{
Q={q_gen_8902, q_gen_8903, q_gen_8904},
Q_f={q_gen_8902},
Delta=
{
<nil>() -> q_gen_8903
<z>() -> q_gen_8904
<z, cons>(q_gen_8904, q_gen_8903) -> q_gen_8902
}

Datatype: <nat, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8899, q_gen_8900, q_gen_8901},
Q_f={q_gen_8899},
Delta=
{
<cons>(q_gen_8901, q_gen_8900) -> q_gen_8899
<nil>() -> q_gen_8900
<z>() -> q_gen_8901
}

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

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

Teacher's answer:
New clause system:
{
() -> memberl([h1, cons(h1, t1)]) -> 3
() -> not_null([cons(x, ll)]) -> 3
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)]) -> 1
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1]) -> 1
(memberl([e, nil])) -> BOT -> 1
(memberl([i, cons(i, l)])) -> memberl([i, l]) -> 4
(not_null([nil])) -> BOT -> 4
}
Sat witness: Found: ((memberl([i, cons(i, l)])) -> memberl([i, l]), {
i -> z  ;  l -> nil
})

-------------------------------------------
Step 4, which took 0.018215 s (model generation: 0.018176,  model checking: 0.000039):

Model:
|_
{
memberl -> 
{{{
Q={q_gen_8902, q_gen_8903, q_gen_8904},
Q_f={q_gen_8902},
Delta=
{
<nil>() -> q_gen_8903
<z>() -> q_gen_8904
<z, cons>(q_gen_8904, q_gen_8903) -> q_gen_8902
<z, nil>() -> q_gen_8902
}

Datatype: <nat, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8899, q_gen_8900, q_gen_8901},
Q_f={q_gen_8899},
Delta=
{
<cons>(q_gen_8901, q_gen_8900) -> q_gen_8899
<nil>() -> q_gen_8900
<z>() -> q_gen_8901
}

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

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

Teacher's answer:
New clause system:
{
() -> memberl([h1, cons(h1, t1)]) -> 3
() -> not_null([cons(x, ll)]) -> 3
(memberl([e, t1]) /\ not eq_nat([e, h1])) -> memberl([e, cons(h1, t1)]) -> 1
(memberl([e, cons(h1, t1)]) /\ not eq_nat([e, h1])) -> memberl([e, t1]) -> 1
(memberl([e, nil])) -> BOT -> 4
(memberl([i, cons(i, l)])) -> memberl([i, l]) -> 4
(not_null([nil])) -> BOT -> 4
}
Sat witness: Found: ((memberl([e, nil])) -> BOT, {
e -> z
})

Total time: 0.114911
Reason for stopping: Disproved