Solving ../../benchmarks/false/plus_odd_odd.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(is_odd, P:
{() -> is_odd([s(z)])
(is_odd([n3])) -> is_odd([s(s(n3))])
(is_odd([s(s(n3))])) -> is_odd([n3])
(is_odd([z])) -> BOT}
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)])}
(plus([_rla, _sla, _tla]) /\ plus([_rla, _sla, _ula])) -> eq_nat([_tla, _ula])
)
}

properties:
{(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla])}


over-approximation: {plus}
under-approximation: {}

Clause system for inference is:

{
() -> is_odd([s(z)]) -> 0
() -> plus([n, z, n]) -> 0
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 0
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 0
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 0
(is_odd([z])) -> BOT -> 0
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 0
}


Solving took 0.218514 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.016168 s (model generation: 0.015848,  model checking: 0.000320):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 0
() -> plus([n, z, n]) -> 3
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 1
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 1
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.016238 s (model generation: 0.016171,  model checking: 0.000067):

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

}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027},
Q_f={q_gen_9027},
Delta=
{
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 3
() -> plus([n, z, n]) -> 3
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 1
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 1
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 1
}
Sat witness: Found: (() -> is_odd([s(z)]), {

})

-------------------------------------------
Step 2, which took 0.017306 s (model generation: 0.017098,  model checking: 0.000208):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9028) -> q_gen_9028
<z>() -> q_gen_9028
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027},
Q_f={q_gen_9027},
Delta=
{
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 3
() -> plus([n, z, n]) -> 3
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 1
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 1
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]), {
_qla -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.017580 s (model generation: 0.017546,  model checking: 0.000034):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9028) -> q_gen_9028
<z>() -> q_gen_9028
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031},
Q_f={q_gen_9027},
Delta=
{
<z, z>() -> q_gen_9031
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 3
() -> plus([n, z, n]) -> 3
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 1
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 4
}
Sat witness: Found: ((is_odd([z])) -> BOT, {

})

-------------------------------------------
Step 4, which took 0.019382 s (model generation: 0.019056,  model checking: 0.000326):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028, q_gen_9029},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9029) -> q_gen_9028
<z>() -> q_gen_9029
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031},
Q_f={q_gen_9027},
Delta=
{
<z, z>() -> q_gen_9031
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 3
() -> plus([n, z, n]) -> 3
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 4
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 2
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 2
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 4
}
Sat witness: Found: ((is_odd([n3])) -> is_odd([s(s(n3))]), {
n3 -> s(z)
})

-------------------------------------------
Step 5, which took 0.021411 s (model generation: 0.020674,  model checking: 0.000737):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028, q_gen_9029},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9029) -> q_gen_9028
<s>(q_gen_9028) -> q_gen_9029
<z>() -> q_gen_9029
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031},
Q_f={q_gen_9027},
Delta=
{
<z, z>() -> q_gen_9031
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 3
() -> plus([n, z, n]) -> 6
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 4
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 3
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 3
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 6, which took 0.021997 s (model generation: 0.021504,  model checking: 0.000493):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028, q_gen_9029},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9029) -> q_gen_9028
<s>(q_gen_9028) -> q_gen_9029
<z>() -> q_gen_9029
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031},
Q_f={q_gen_9027},
Delta=
{
<s, s>(q_gen_9031) -> q_gen_9031
<z, z>() -> q_gen_9031
<s, z, s>(q_gen_9031) -> q_gen_9027
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 4
() -> plus([n, z, n]) -> 6
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 4
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 4
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 4
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]), {
_qla -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 7, which took 0.024018 s (model generation: 0.023704,  model checking: 0.000314):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028, q_gen_9029},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9029) -> q_gen_9028
<s>(q_gen_9028) -> q_gen_9029
<z>() -> q_gen_9029
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031, q_gen_9039},
Q_f={q_gen_9027},
Delta=
{
<z>() -> q_gen_9039
<s, s>(q_gen_9031) -> q_gen_9031
<z, z>() -> q_gen_9031
<s, s, s>(q_gen_9027) -> q_gen_9027
<s, z, s>(q_gen_9031) -> q_gen_9027
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, s>(q_gen_9039) -> q_gen_9027
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 4
() -> plus([n, z, n]) -> 6
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 4
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 7
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 5
(is_odd([z])) -> BOT -> 5
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 7
}
Sat witness: Found: ((is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]), {
_vla -> s(s(z))  ;  x -> s(z)  ;  y -> s(z)
})

-------------------------------------------
Step 8, which took 0.022102 s (model generation: 0.021945,  model checking: 0.000157):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028, q_gen_9029},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9028) -> q_gen_9028
<s>(q_gen_9029) -> q_gen_9028
<z>() -> q_gen_9029
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031, q_gen_9039},
Q_f={q_gen_9027},
Delta=
{
<z>() -> q_gen_9039
<s, s>(q_gen_9031) -> q_gen_9031
<z, z>() -> q_gen_9031
<s, s, s>(q_gen_9027) -> q_gen_9027
<s, z, s>(q_gen_9031) -> q_gen_9027
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, s>(q_gen_9039) -> q_gen_9027
<z, z, z>() -> q_gen_9027
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 5
() -> plus([n, z, n]) -> 6
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 5
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 7
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 8
(is_odd([z])) -> BOT -> 6
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 7
}
Sat witness: Found: ((is_odd([s(s(n3))])) -> is_odd([n3]), {
n3 -> z
})

-------------------------------------------
Step 9, which took 0.021765 s (model generation: 0.021373,  model checking: 0.000392):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_9028, q_gen_9029},
Q_f={q_gen_9028},
Delta=
{
<s>(q_gen_9029) -> q_gen_9028
<s>(q_gen_9028) -> q_gen_9029
<z>() -> q_gen_9029
}

Datatype: <nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_9027, q_gen_9031, q_gen_9035, q_gen_9036, q_gen_9039},
Q_f={q_gen_9027},
Delta=
{
<z>() -> q_gen_9039
<z, z>() -> q_gen_9031
<s, s>(q_gen_9031) -> q_gen_9035
<s, z, s>(q_gen_9035) -> q_gen_9027
<z, s, s>(q_gen_9031) -> q_gen_9027
<z, z, z>() -> q_gen_9027
<s, s, s>(q_gen_9036) -> q_gen_9036
<s, z, s>(q_gen_9031) -> q_gen_9036
<z, z, s>(q_gen_9039) -> q_gen_9036
}

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

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

Teacher's answer:
New clause system:
{
() -> is_odd([s(z)]) -> 6
() -> plus([n, z, n]) -> 9
(is_odd([n3])) -> is_odd([s(s(n3))]) -> 6
(is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _vla])) -> is_odd([_vla]) -> 7
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 8
(is_odd([z])) -> BOT -> 7
(plus([n, mm, _qla])) -> plus([n, s(mm), s(_qla)]) -> 7
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(z)
})

Total time: 0.218514
Reason for stopping: Disproved