Solving ../../benchmarks/false/reverse_not_null.smt2...

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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)])}
(append([_sia, _tia, _uia]) /\ append([_sia, _tia, _via])) -> eq_natlist([_uia, _via])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia])}
(reverse([_yia, _aja]) /\ reverse([_yia, _zia])) -> eq_natlist([_zia, _aja])
)
(not_null, P:
{() -> not_null([cons(x, ll)])
(not_null([nil])) -> BOT}
)
}

properties:
{(reverse([l1, _bja])) -> not_null([_bja])}


over-approximation: {append, reverse}
under-approximation: {not_null}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> not_null([cons(x, ll)]) -> 0
() -> reverse([nil, nil]) -> 0
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 0
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 0
(not_null([nil])) -> BOT -> 0
(reverse([l1, _bja])) -> not_null([_bja]) -> 0
}


Solving took 0.129427 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.017231 s (model generation: 0.016653,  model checking: 0.000578):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <natlist>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={},
Q_f={},
Delta=
{

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> not_null([cons(x, ll)]) -> 0
() -> reverse([nil, nil]) -> 3
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 1
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 1
(not_null([nil])) -> BOT -> 1
(reverse([l1, _bja])) -> not_null([_bja]) -> 1
}
Sat witness: Found: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.017151 s (model generation: 0.016993,  model checking: 0.000158):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <natlist>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8906},
Q_f={q_gen_8906},
Delta=
{
<nil, nil>() -> q_gen_8906
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> not_null([cons(x, ll)]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 1
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 1
(not_null([nil])) -> BOT -> 1
(reverse([l1, _bja])) -> not_null([_bja]) -> 1
}
Sat witness: Found: (() -> not_null([cons(x, ll)]), {
ll -> nil  ;  x -> z
})

-------------------------------------------
Step 2, which took 0.017531 s (model generation: 0.017214,  model checking: 0.000317):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8907, q_gen_8909},
Q_f={q_gen_8907},
Delta=
{
<cons>(q_gen_8909, q_gen_8907) -> q_gen_8907
<nil>() -> q_gen_8907
<z>() -> q_gen_8909
}

Datatype: <natlist>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8906},
Q_f={q_gen_8906},
Delta=
{
<nil, nil>() -> q_gen_8906
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> not_null([cons(x, ll)]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 1
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 1
(not_null([nil])) -> BOT -> 1
(reverse([l1, _bja])) -> not_null([_bja]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.022336 s (model generation: 0.017805,  model checking: 0.004531):

Model:
|_
{
append -> 
{{{
Q={q_gen_8910},
Q_f={q_gen_8910},
Delta=
{
<nil, nil, nil>() -> q_gen_8910
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8907, q_gen_8909},
Q_f={q_gen_8907},
Delta=
{
<cons>(q_gen_8909, q_gen_8907) -> q_gen_8907
<nil>() -> q_gen_8907
<z>() -> q_gen_8909
}

Datatype: <natlist>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8906},
Q_f={q_gen_8906},
Delta=
{
<nil, nil>() -> q_gen_8906
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> not_null([cons(x, ll)]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 1
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 1
(not_null([nil])) -> BOT -> 4
(reverse([l1, _bja])) -> not_null([_bja]) -> 2
}
Sat witness: Found: ((not_null([nil])) -> BOT, {

})

-------------------------------------------
Step 4, which took 0.018109 s (model generation: 0.017640,  model checking: 0.000469):

Model:
|_
{
append -> 
{{{
Q={q_gen_8910},
Q_f={q_gen_8910},
Delta=
{
<nil, nil, nil>() -> q_gen_8910
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8907, q_gen_8908, q_gen_8909},
Q_f={q_gen_8907},
Delta=
{
<cons>(q_gen_8909, q_gen_8908) -> q_gen_8907
<nil>() -> q_gen_8908
<z>() -> q_gen_8909
}

Datatype: <natlist>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8906},
Q_f={q_gen_8906},
Delta=
{
<nil, nil>() -> q_gen_8906
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> not_null([cons(x, ll)]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 1
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 4
(not_null([nil])) -> BOT -> 4
(reverse([l1, _bja])) -> not_null([_bja]) -> 2
}
Sat witness: Found: ((append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]), {
_ria -> nil  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 5, which took 0.018694 s (model generation: 0.018406,  model checking: 0.000288):

Model:
|_
{
append -> 
{{{
Q={q_gen_8910, q_gen_8912, q_gen_8913},
Q_f={q_gen_8910},
Delta=
{
<nil, nil>() -> q_gen_8912
<z, z>() -> q_gen_8913
<cons, nil, cons>(q_gen_8913, q_gen_8912) -> q_gen_8910
<nil, nil, nil>() -> q_gen_8910
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  not_null -> 
{{{
Q={q_gen_8907, q_gen_8908, q_gen_8909},
Q_f={q_gen_8907},
Delta=
{
<cons>(q_gen_8909, q_gen_8908) -> q_gen_8907
<nil>() -> q_gen_8908
<z>() -> q_gen_8909
}

Datatype: <natlist>
Convolution form: left
}}}
  ;  reverse -> 
{{{
Q={q_gen_8906},
Q_f={q_gen_8906},
Delta=
{
<nil, nil>() -> q_gen_8906
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> not_null([cons(x, ll)]) -> 3
() -> reverse([nil, nil]) -> 3
(append([_wia, cons(h1, nil), _xia]) /\ reverse([t1, _wia])) -> reverse([cons(h1, t1), _xia]) -> 2
(append([t1, l2, _ria])) -> append([cons(h1, t1), l2, cons(h1, _ria)]) -> 4
(not_null([nil])) -> BOT -> 4
(reverse([l1, _bja])) -> not_null([_bja]) -> 5
}
Sat witness: Found: ((reverse([l1, _bja])) -> not_null([_bja]), {
_bja -> nil  ;  l1 -> nil
})

Total time: 0.129427
Reason for stopping: Disproved