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

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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(delete, F:
{() -> delete([x, nil, nil])
(delete([h, t, _kka])) -> delete([h, cons(h, t), _kka])
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)])}
(delete([_mka, _nka, _oka]) /\ delete([_mka, _nka, _pka])) -> eq_eltlist([_oka, _pka])
)
(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, _qka])) -> mem([i, _qka])}


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, _kka])) -> delete([h, cons(h, t), _kka]) -> 0
(delete([i, l, _qka])) -> mem([i, _qka]) -> 0
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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 0.147486 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.017132 s (model generation: 0.016174,  model checking: 0.000958):

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

}

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

}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 1
(delete([i, l, _qka])) -> mem([i, _qka]) -> 1
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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 0.016663 s (model generation: 0.016353,  model checking: 0.000310):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  mem -> 
{{{
Q={q_gen_8976, q_gen_8977, q_gen_8978},
Q_f={q_gen_8976},
Delta=
{
<nil>() -> q_gen_8977
<b>() -> q_gen_8978
<b, cons>(q_gen_8978, q_gen_8977) -> q_gen_8976
}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 1
(delete([i, l, _qka])) -> mem([i, _qka]) -> 1
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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 0.017635 s (model generation: 0.016972,  model checking: 0.000663):

Model:
|_
{
delete -> 
{{{
Q={q_gen_8979},
Q_f={q_gen_8979},
Delta=
{
<b, nil, nil>() -> q_gen_8979
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  mem -> 
{{{
Q={q_gen_8976, q_gen_8977, q_gen_8978},
Q_f={q_gen_8976},
Delta=
{
<nil>() -> q_gen_8977
<b>() -> q_gen_8978
<b, cons>(q_gen_8978, q_gen_8977) -> q_gen_8976
}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 1
(delete([i, l, _qka])) -> mem([i, _qka]) -> 1
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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 0.017818 s (model generation: 0.017513,  model checking: 0.000305):

Model:
|_
{
delete -> 
{{{
Q={q_gen_8979},
Q_f={q_gen_8979},
Delta=
{
<b, nil, nil>() -> q_gen_8979
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  mem -> 
{{{
Q={q_gen_8976, q_gen_8977, q_gen_8978},
Q_f={q_gen_8976},
Delta=
{
<cons>(q_gen_8978, q_gen_8977) -> q_gen_8977
<nil>() -> q_gen_8977
<a>() -> q_gen_8978
<b>() -> q_gen_8978
<b, cons>(q_gen_8978, q_gen_8977) -> q_gen_8976
}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 1
(delete([i, l, _qka])) -> mem([i, _qka]) -> 1
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]), {
_lka -> nil  ;  h -> a  ;  t -> nil  ;  x -> b
})

-------------------------------------------
Step 4, which took 0.018789 s (model generation: 0.018621,  model checking: 0.000168):

Model:
|_
{
delete -> 
{{{
Q={q_gen_8979, q_gen_8984, q_gen_8985},
Q_f={q_gen_8979},
Delta=
{
<nil, nil>() -> q_gen_8984
<a, a>() -> q_gen_8985
<b, cons, cons>(q_gen_8985, q_gen_8984) -> q_gen_8979
<b, nil, nil>() -> q_gen_8979
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  mem -> 
{{{
Q={q_gen_8976, q_gen_8977, q_gen_8978},
Q_f={q_gen_8976},
Delta=
{
<cons>(q_gen_8978, q_gen_8977) -> q_gen_8977
<nil>() -> q_gen_8977
<a>() -> q_gen_8978
<b>() -> q_gen_8978
<b, cons>(q_gen_8978, q_gen_8977) -> q_gen_8976
}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 1
(delete([i, l, _qka])) -> mem([i, _qka]) -> 4
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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, _qka])) -> mem([i, _qka]), {
_qka -> nil  ;  i -> b  ;  l -> nil
})

-------------------------------------------
Step 5, which took 0.019479 s (model generation: 0.019022,  model checking: 0.000457):

Model:
|_
{
delete -> 
{{{
Q={q_gen_8979, q_gen_8984, q_gen_8985},
Q_f={q_gen_8979},
Delta=
{
<nil, nil>() -> q_gen_8984
<a, a>() -> q_gen_8985
<b, cons, cons>(q_gen_8985, q_gen_8984) -> q_gen_8979
<b, nil, nil>() -> q_gen_8979
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  mem -> 
{{{
Q={q_gen_8976, q_gen_8977, q_gen_8978},
Q_f={q_gen_8976},
Delta=
{
<cons>(q_gen_8978, q_gen_8977) -> q_gen_8977
<nil>() -> q_gen_8977
<a>() -> q_gen_8978
<b>() -> q_gen_8978
<b, cons>(q_gen_8978, q_gen_8977) -> q_gen_8976
<b, nil>() -> q_gen_8976
}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 4
(delete([i, l, _qka])) -> mem([i, _qka]) -> 4
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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, _kka])) -> delete([h, cons(h, t), _kka]), {
_kka -> nil  ;  h -> b  ;  t -> nil
})

-------------------------------------------
Step 6, which took 0.020037 s (model generation: 0.019993,  model checking: 0.000044):

Model:
|_
{
delete -> 
{{{
Q={q_gen_8979, q_gen_8984, q_gen_8985, q_gen_8988, q_gen_8989},
Q_f={q_gen_8979},
Delta=
{
<nil>() -> q_gen_8988
<b>() -> q_gen_8989
<nil, nil>() -> q_gen_8984
<a, a>() -> q_gen_8985
<b, cons, cons>(q_gen_8985, q_gen_8984) -> q_gen_8979
<b, cons, nil>(q_gen_8989, q_gen_8988) -> q_gen_8979
<b, nil, nil>() -> q_gen_8979
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  mem -> 
{{{
Q={q_gen_8976, q_gen_8977, q_gen_8978},
Q_f={q_gen_8976},
Delta=
{
<cons>(q_gen_8978, q_gen_8977) -> q_gen_8977
<nil>() -> q_gen_8977
<a>() -> q_gen_8978
<b>() -> q_gen_8978
<b, cons>(q_gen_8978, q_gen_8977) -> q_gen_8976
<b, nil>() -> q_gen_8976
}

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

}
--
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, _kka])) -> delete([h, cons(h, t), _kka]) -> 4
(delete([i, l, _qka])) -> mem([i, _qka]) -> 4
(delete([x, t, _lka]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _lka)]) -> 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: 0.147486
Reason for stopping: Disproved