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

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


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, _wga])) -> plus([n, s(mm), s(_wga)])}
(plus([_xga, _yga, _aha]) /\ plus([_xga, _yga, _zga])) -> eq_nat([_zga, _aha])
)
}

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


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, _bha])) -> is_odd([_bha]) -> 0
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 0
(is_odd([z])) -> BOT -> 0
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 0
}


Solving took 0.069036 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005335 s (model generation: 0.004767,  model checking: 0.000568):

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

}

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

}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.004889 s (model generation: 0.004813,  model checking: 0.000076):

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

}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508},
Q_f={q_gen_6508},
Delta=
{
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 1
}
Sat witness: Found: (() -> is_odd([s(z)]), {

})

-------------------------------------------
Step 2, which took 0.004920 s (model generation: 0.004653,  model checking: 0.000267):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6509) -> q_gen_6509
<z>() -> q_gen_6509
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508},
Q_f={q_gen_6508},
Delta=
{
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]), {
_wga -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.004465 s (model generation: 0.004456,  model checking: 0.000009):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6509) -> q_gen_6509
<z>() -> q_gen_6509
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512},
Q_f={q_gen_6508},
Delta=
{
<z, z>() -> q_gen_6512
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 1
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 1
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: ((is_odd([z])) -> BOT, {

})

-------------------------------------------
Step 4, which took 0.004079 s (model generation: 0.003958,  model checking: 0.000121):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509, q_gen_6510},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6510) -> q_gen_6509
<z>() -> q_gen_6510
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512},
Q_f={q_gen_6508},
Delta=
{
<z, z>() -> q_gen_6512
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 2
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 2
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: ((is_odd([n3])) -> is_odd([s(s(n3))]), {
n3 -> s(z)
})

-------------------------------------------
Step 5, which took 0.005438 s (model generation: 0.005261,  model checking: 0.000177):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509, q_gen_6510},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6510) -> q_gen_6509
<s>(q_gen_6509) -> q_gen_6510
<z>() -> q_gen_6510
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512},
Q_f={q_gen_6508},
Delta=
{
<z, z>() -> q_gen_6512
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 3
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 3
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 6, which took 0.006944 s (model generation: 0.006685,  model checking: 0.000259):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509, q_gen_6510},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6510) -> q_gen_6509
<s>(q_gen_6509) -> q_gen_6510
<z>() -> q_gen_6510
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512},
Q_f={q_gen_6508},
Delta=
{
<s, s>(q_gen_6512) -> q_gen_6512
<z, z>() -> q_gen_6512
<s, z, s>(q_gen_6512) -> q_gen_6508
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 4
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 4
(is_odd([z])) -> BOT -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]), {
_wga -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 7, which took 0.009344 s (model generation: 0.009043,  model checking: 0.000301):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509, q_gen_6510},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6510) -> q_gen_6509
<s>(q_gen_6509) -> q_gen_6510
<z>() -> q_gen_6510
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512, q_gen_6520},
Q_f={q_gen_6508},
Delta=
{
<z>() -> q_gen_6520
<s, s>(q_gen_6512) -> q_gen_6512
<z, z>() -> q_gen_6512
<s, s, s>(q_gen_6508) -> q_gen_6508
<s, z, s>(q_gen_6512) -> q_gen_6508
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, s>(q_gen_6520) -> q_gen_6508
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 7
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 5
(is_odd([z])) -> BOT -> 5
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((is_odd([x]) /\ is_odd([y]) /\ plus([x, y, _bha])) -> is_odd([_bha]), {
_bha -> s(s(z))  ;  x -> s(z)  ;  y -> s(z)
})

-------------------------------------------
Step 8, which took 0.008541 s (model generation: 0.008485,  model checking: 0.000056):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509, q_gen_6510},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6509) -> q_gen_6509
<s>(q_gen_6510) -> q_gen_6509
<z>() -> q_gen_6510
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512, q_gen_6520},
Q_f={q_gen_6508},
Delta=
{
<z>() -> q_gen_6520
<s, s>(q_gen_6512) -> q_gen_6512
<z, z>() -> q_gen_6512
<s, s, s>(q_gen_6508) -> q_gen_6508
<s, z, s>(q_gen_6512) -> q_gen_6508
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, s>(q_gen_6520) -> q_gen_6508
<z, z, z>() -> q_gen_6508
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 7
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 8
(is_odd([z])) -> BOT -> 6
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((is_odd([s(s(n3))])) -> is_odd([n3]), {
n3 -> z
})

-------------------------------------------
Step 9, which took 0.009492 s (model generation: 0.009379,  model checking: 0.000113):

Model:
|_
{
is_odd -> 
{{{
Q={q_gen_6509, q_gen_6510},
Q_f={q_gen_6509},
Delta=
{
<s>(q_gen_6510) -> q_gen_6509
<s>(q_gen_6509) -> q_gen_6510
<z>() -> q_gen_6510
}

Datatype: <nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6508, q_gen_6512, q_gen_6516, q_gen_6517, q_gen_6520},
Q_f={q_gen_6508},
Delta=
{
<z>() -> q_gen_6520
<z, z>() -> q_gen_6512
<s, s>(q_gen_6512) -> q_gen_6516
<s, z, s>(q_gen_6516) -> q_gen_6508
<z, s, s>(q_gen_6512) -> q_gen_6508
<z, z, z>() -> q_gen_6508
<s, s, s>(q_gen_6517) -> q_gen_6517
<s, z, s>(q_gen_6512) -> q_gen_6517
<z, z, s>(q_gen_6520) -> q_gen_6517
}

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

}
--
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, _bha])) -> is_odd([_bha]) -> 7
(is_odd([s(s(n3))])) -> is_odd([n3]) -> 8
(is_odd([z])) -> BOT -> 7
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(z)
})

Total time: 0.069036
Reason for stopping: Disproved