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

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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)])}
(append([_jha, _kha, _lha]) /\ append([_jha, _kha, _mha])) -> eq_natlist([_lha, _mha])
)
(reverse, F:
{() -> reverse([nil, nil])
(append([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha])}
(reverse([_pha, _qha]) /\ reverse([_pha, _rha])) -> eq_natlist([_qha, _rha])
)
(not_null, P:
{() -> not_null([cons(x, ll)])
(not_null([nil])) -> BOT}
)
}

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


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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 0
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 0
(not_null([nil])) -> BOT -> 0
(reverse([l1, _sha])) -> not_null([_sha]) -> 0
}


Solving took 0.076639 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010222 s (model generation: 0.009785,  model checking: 0.000437):

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

}

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

}

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

}

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

}
--
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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 1
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 1
(not_null([nil])) -> BOT -> 1
(reverse([l1, _sha])) -> not_null([_sha]) -> 1
}
Sat witness: Found: (() -> reverse([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.010322 s (model generation: 0.010152,  model checking: 0.000170):

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

}

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

}

Datatype: <natlist>
Convolution form: right
}}}
  ;  reverse -> 
{{{
Q={q_gen_6544},
Q_f={q_gen_6544},
Delta=
{
<nil, nil>() -> q_gen_6544
}

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

}
--
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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 1
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 1
(not_null([nil])) -> BOT -> 1
(reverse([l1, _sha])) -> not_null([_sha]) -> 1
}
Sat witness: Found: (() -> not_null([cons(x, ll)]), {
ll -> nil  ;  x -> z
})

-------------------------------------------
Step 2, which took 0.011274 s (model generation: 0.010717,  model checking: 0.000557):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  not_null -> 
{{{
Q={q_gen_6545, q_gen_6547},
Q_f={q_gen_6545},
Delta=
{
<cons>(q_gen_6547, q_gen_6545) -> q_gen_6545
<nil>() -> q_gen_6545
<z>() -> q_gen_6547
}

Datatype: <natlist>
Convolution form: right
}}}
  ;  reverse -> 
{{{
Q={q_gen_6544},
Q_f={q_gen_6544},
Delta=
{
<nil, nil>() -> q_gen_6544
}

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

}
--
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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 1
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 1
(not_null([nil])) -> BOT -> 1
(reverse([l1, _sha])) -> not_null([_sha]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.011105 s (model generation: 0.011004,  model checking: 0.000101):

Model:
|_
{
append -> 
{{{
Q={q_gen_6548},
Q_f={q_gen_6548},
Delta=
{
<nil, nil, nil>() -> q_gen_6548
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  not_null -> 
{{{
Q={q_gen_6545, q_gen_6547},
Q_f={q_gen_6545},
Delta=
{
<cons>(q_gen_6547, q_gen_6545) -> q_gen_6545
<nil>() -> q_gen_6545
<z>() -> q_gen_6547
}

Datatype: <natlist>
Convolution form: right
}}}
  ;  reverse -> 
{{{
Q={q_gen_6544},
Q_f={q_gen_6544},
Delta=
{
<nil, nil>() -> q_gen_6544
}

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

}
--
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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 1
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 1
(not_null([nil])) -> BOT -> 4
(reverse([l1, _sha])) -> not_null([_sha]) -> 2
}
Sat witness: Found: ((not_null([nil])) -> BOT, {

})

-------------------------------------------
Step 4, which took 0.011359 s (model generation: 0.010818,  model checking: 0.000541):

Model:
|_
{
append -> 
{{{
Q={q_gen_6548},
Q_f={q_gen_6548},
Delta=
{
<nil, nil, nil>() -> q_gen_6548
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  not_null -> 
{{{
Q={q_gen_6545, q_gen_6546, q_gen_6547},
Q_f={q_gen_6545},
Delta=
{
<cons>(q_gen_6547, q_gen_6546) -> q_gen_6545
<nil>() -> q_gen_6546
<z>() -> q_gen_6547
}

Datatype: <natlist>
Convolution form: right
}}}
  ;  reverse -> 
{{{
Q={q_gen_6544},
Q_f={q_gen_6544},
Delta=
{
<nil, nil>() -> q_gen_6544
}

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

}
--
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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 1
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 4
(not_null([nil])) -> BOT -> 4
(reverse([l1, _sha])) -> not_null([_sha]) -> 2
}
Sat witness: Found: ((append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]), {
_iha -> nil  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 5, which took 0.011350 s (model generation: 0.011120,  model checking: 0.000230):

Model:
|_
{
append -> 
{{{
Q={q_gen_6548, q_gen_6550, q_gen_6551},
Q_f={q_gen_6548},
Delta=
{
<nil, nil>() -> q_gen_6550
<z, z>() -> q_gen_6551
<cons, nil, cons>(q_gen_6551, q_gen_6550) -> q_gen_6548
<nil, nil, nil>() -> q_gen_6548
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  not_null -> 
{{{
Q={q_gen_6545, q_gen_6546, q_gen_6547},
Q_f={q_gen_6545},
Delta=
{
<cons>(q_gen_6547, q_gen_6546) -> q_gen_6545
<nil>() -> q_gen_6546
<z>() -> q_gen_6547
}

Datatype: <natlist>
Convolution form: right
}}}
  ;  reverse -> 
{{{
Q={q_gen_6544},
Q_f={q_gen_6544},
Delta=
{
<nil, nil>() -> q_gen_6544
}

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

}
--
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([_nha, cons(h1, nil), _oha]) /\ reverse([t1, _nha])) -> reverse([cons(h1, t1), _oha]) -> 2
(append([t1, l2, _iha])) -> append([cons(h1, t1), l2, cons(h1, _iha)]) -> 4
(not_null([nil])) -> BOT -> 4
(reverse([l1, _sha])) -> not_null([_sha]) -> 5
}
Sat witness: Found: ((reverse([l1, _sha])) -> not_null([_sha]), {
_sha -> nil  ;  l1 -> nil
})

Total time: 0.076639
Reason for stopping: Disproved