Solving ../../benchmarks/false/timbuk_deleteBUG.smt2...

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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(delete, F:
{() -> delete([x, nil, nil])
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala])
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)])}
(delete([_cla, _dla, _ela]) /\ delete([_cla, _dla, _fla])) -> eq_eltlist([_ela, _fla])
)
(mem, P:
{() -> mem([h, cons(h, t)])
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)])
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t])
(mem([e, nil])) -> BOT}
)
}

properties:
{(delete([i, l, _gla])) -> mem([i, _gla])}


over-approximation: {delete}
under-approximation: {mem}

Clause system for inference is:

{
() -> delete([x, nil, nil]) -> 0
() -> mem([h, cons(h, t)]) -> 0
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 0
(delete([i, l, _gla])) -> mem([i, _gla]) -> 0
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 0
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 0
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 0
(mem([e, nil])) -> BOT -> 0
}


Solving took 0.090609 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010607 s (model generation: 0.009921,  model checking: 0.000686):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 1
(delete([i, l, _gla])) -> mem([i, _gla]) -> 1
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 1
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 1
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 1
(mem([e, nil])) -> BOT -> 1
}
Sat witness: Found: (() -> mem([h, cons(h, t)]), {
h -> b  ;  t -> nil
})

-------------------------------------------
Step 1, which took 0.010285 s (model generation: 0.010072,  model checking: 0.000213):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={q_gen_6803, q_gen_6804, q_gen_6805},
Q_f={q_gen_6803},
Delta=
{
<nil>() -> q_gen_6804
<b>() -> q_gen_6805
<b, cons>(q_gen_6805, q_gen_6804) -> q_gen_6803
}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 1
(delete([i, l, _gla])) -> mem([i, _gla]) -> 1
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 1
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 1
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 1
(mem([e, nil])) -> BOT -> 1
}
Sat witness: Found: (() -> delete([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 2, which took 0.011168 s (model generation: 0.010129,  model checking: 0.001039):

Model:
|_
{
delete -> 
{{{
Q={q_gen_6806},
Q_f={q_gen_6806},
Delta=
{
<b, nil, nil>() -> q_gen_6806
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={q_gen_6803, q_gen_6804, q_gen_6805},
Q_f={q_gen_6803},
Delta=
{
<nil>() -> q_gen_6804
<b>() -> q_gen_6805
<b, cons>(q_gen_6805, q_gen_6804) -> q_gen_6803
}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 1
(delete([i, l, _gla])) -> mem([i, _gla]) -> 1
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 1
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 4
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 2
(mem([e, nil])) -> BOT -> 2
}
Sat witness: Found: ((mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]), {
e -> b  ;  h -> a  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 3, which took 0.011165 s (model generation: 0.010827,  model checking: 0.000338):

Model:
|_
{
delete -> 
{{{
Q={q_gen_6806},
Q_f={q_gen_6806},
Delta=
{
<b, nil, nil>() -> q_gen_6806
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={q_gen_6803, q_gen_6804, q_gen_6805},
Q_f={q_gen_6803},
Delta=
{
<cons>(q_gen_6805, q_gen_6804) -> q_gen_6804
<nil>() -> q_gen_6804
<a>() -> q_gen_6805
<b>() -> q_gen_6805
<b, cons>(q_gen_6805, q_gen_6804) -> q_gen_6803
}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 1
(delete([i, l, _gla])) -> mem([i, _gla]) -> 1
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 4
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 4
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 2
(mem([e, nil])) -> BOT -> 2
}
Sat witness: Found: ((delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]), {
_bla -> nil  ;  h -> a  ;  t -> nil  ;  x -> b
})

-------------------------------------------
Step 4, which took 0.011202 s (model generation: 0.011050,  model checking: 0.000152):

Model:
|_
{
delete -> 
{{{
Q={q_gen_6806, q_gen_6811, q_gen_6812},
Q_f={q_gen_6806},
Delta=
{
<nil, nil>() -> q_gen_6811
<a, a>() -> q_gen_6812
<b, cons, cons>(q_gen_6812, q_gen_6811) -> q_gen_6806
<b, nil, nil>() -> q_gen_6806
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={q_gen_6803, q_gen_6804, q_gen_6805},
Q_f={q_gen_6803},
Delta=
{
<cons>(q_gen_6805, q_gen_6804) -> q_gen_6804
<nil>() -> q_gen_6804
<a>() -> q_gen_6805
<b>() -> q_gen_6805
<b, cons>(q_gen_6805, q_gen_6804) -> q_gen_6803
}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 1
(delete([i, l, _gla])) -> mem([i, _gla]) -> 4
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 4
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 4
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 2
(mem([e, nil])) -> BOT -> 2
}
Sat witness: Found: ((delete([i, l, _gla])) -> mem([i, _gla]), {
_gla -> nil  ;  i -> b  ;  l -> nil
})

-------------------------------------------
Step 5, which took 0.012153 s (model generation: 0.011389,  model checking: 0.000764):

Model:
|_
{
delete -> 
{{{
Q={q_gen_6806, q_gen_6811, q_gen_6812},
Q_f={q_gen_6806},
Delta=
{
<nil, nil>() -> q_gen_6811
<a, a>() -> q_gen_6812
<b, cons, cons>(q_gen_6812, q_gen_6811) -> q_gen_6806
<b, nil, nil>() -> q_gen_6806
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={q_gen_6803, q_gen_6804, q_gen_6805},
Q_f={q_gen_6803},
Delta=
{
<cons>(q_gen_6805, q_gen_6804) -> q_gen_6804
<nil>() -> q_gen_6804
<a>() -> q_gen_6805
<b>() -> q_gen_6805
<b, cons>(q_gen_6805, q_gen_6804) -> q_gen_6803
<b, nil>() -> q_gen_6803
}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 4
(delete([i, l, _gla])) -> mem([i, _gla]) -> 4
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 4
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 4
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 2
(mem([e, nil])) -> BOT -> 2
}
Sat witness: Found: ((delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]), {
_ala -> nil  ;  h -> b  ;  t -> nil
})

-------------------------------------------
Step 6, which took 0.012020 s (model generation: 0.011983,  model checking: 0.000037):

Model:
|_
{
delete -> 
{{{
Q={q_gen_6806, q_gen_6811, q_gen_6812, q_gen_6815, q_gen_6816},
Q_f={q_gen_6806},
Delta=
{
<nil>() -> q_gen_6815
<b>() -> q_gen_6816
<nil, nil>() -> q_gen_6811
<a, a>() -> q_gen_6812
<b, cons, cons>(q_gen_6812, q_gen_6811) -> q_gen_6806
<b, cons, nil>(q_gen_6816, q_gen_6815) -> q_gen_6806
<b, nil, nil>() -> q_gen_6806
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  mem -> 
{{{
Q={q_gen_6803, q_gen_6804, q_gen_6805},
Q_f={q_gen_6803},
Delta=
{
<cons>(q_gen_6805, q_gen_6804) -> q_gen_6804
<nil>() -> q_gen_6804
<a>() -> q_gen_6805
<b>() -> q_gen_6805
<b, cons>(q_gen_6805, q_gen_6804) -> q_gen_6803
<b, nil>() -> q_gen_6803
}

Datatype: <elt, eltlist>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_elt, eq_eltlist}
_|

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> mem([h, cons(h, t)]) -> 3
(delete([h, t, _ala])) -> delete([h, cons(h, t), _ala]) -> 4
(delete([i, l, _gla])) -> mem([i, _gla]) -> 4
(delete([x, t, _bla]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _bla)]) -> 4
(mem([e, t]) /\ not eq_elt([e, h])) -> mem([e, cons(h, t)]) -> 4
(mem([e, cons(h, t)]) /\ not eq_elt([e, h])) -> mem([e, t]) -> 2
(mem([e, nil])) -> BOT -> 5
}
Sat witness: Found: ((mem([e, nil])) -> BOT, {
e -> b
})

Total time: 0.090609
Reason for stopping: Disproved