Solving ../../benchmarks/true/isaplanner_prop17.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)])}
(plus([_xx, _yx, _ay]) /\ plus([_xx, _yx, _zx])) -> eq_nat([_zx, _ay])
)
(leq, P:
{() -> leq([z, n2])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
}

properties:
{(leq([i, z])) -> eq_nat([i, z])}


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

Clause system for inference is:

{
() -> leq([z, n2]) -> 0  ;  () -> plus([n, z, n]) -> 0  ;  (leq([i, z])) -> eq_nat([i, z]) -> 0  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0  ;  (leq([s(nn1), z])) -> BOT -> 0  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 0
}


Solving took 0.062135 seconds.
Proved
Model:
|_
{
leq -> 
{{{
Q={q_gen_1308, q_gen_1314},
Q_f={q_gen_1308},
Delta=
{
<s>(q_gen_1314) -> q_gen_1314
<z>() -> q_gen_1314
<s, s>(q_gen_1308) -> q_gen_1308
<z, s>(q_gen_1314) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310, q_gen_1317},
Q_f={q_gen_1307},
Delta=
{
<s>(q_gen_1317) -> q_gen_1317
<z>() -> q_gen_1317
<s, s>(q_gen_1310) -> q_gen_1310
<z, s>(q_gen_1317) -> q_gen_1310
<z, z>() -> q_gen_1310
<s, s, s>(q_gen_1307) -> q_gen_1307
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, s>(q_gen_1317) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005078 s (model generation: 0.004811,  model checking: 0.000267):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0  ;  () -> plus([n, z, n]) -> 3  ;  (leq([i, z])) -> eq_nat([i, z]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 1
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.004798 s (model generation: 0.004745,  model checking: 0.000053):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307},
Q_f={q_gen_1307},
Delta=
{
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([i, z])) -> eq_nat([i, z]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 1
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 2, which took 0.004120 s (model generation: 0.004040,  model checking: 0.000080):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308},
Q_f={q_gen_1308},
Delta=
{
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307},
Q_f={q_gen_1307},
Delta=
{
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([i, z])) -> eq_nat([i, z]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 4
}
Sat witness: Yes: ((plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]), {
_wx -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.004475 s (model generation: 0.004125,  model checking: 0.000350):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308},
Q_f={q_gen_1308},
Delta=
{
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310},
Q_f={q_gen_1307},
Delta=
{
<z, z>() -> q_gen_1310
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([i, z])) -> eq_nat([i, z]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 4
}
Sat witness: Yes: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 4, which took 0.005094 s (model generation: 0.004847,  model checking: 0.000247):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308},
Q_f={q_gen_1308},
Delta=
{
<s, s>(q_gen_1308) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310},
Q_f={q_gen_1307},
Delta=
{
<z, z>() -> q_gen_1310
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 6  ;  (leq([i, z])) -> eq_nat([i, z]) -> 2  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3  ;  (leq([s(nn1), z])) -> BOT -> 3  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 4
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(z)
})

-------------------------------------------
Step 5, which took 0.005056 s (model generation: 0.004890,  model checking: 0.000166):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308},
Q_f={q_gen_1308},
Delta=
{
<s, s>(q_gen_1308) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310},
Q_f={q_gen_1307},
Delta=
{
<z, z>() -> q_gen_1310
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (leq([i, z])) -> eq_nat([i, z]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 4
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> s(z)
})

-------------------------------------------
Step 6, which took 0.004668 s (model generation: 0.004521,  model checking: 0.000147):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308, q_gen_1314},
Q_f={q_gen_1308},
Delta=
{
<z>() -> q_gen_1314
<s, s>(q_gen_1308) -> q_gen_1308
<z, s>(q_gen_1314) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310},
Q_f={q_gen_1307},
Delta=
{
<z, z>() -> q_gen_1310
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (leq([i, z])) -> eq_nat([i, z]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 7
}
Sat witness: Yes: ((plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]), {
_wx -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 7, which took 0.005598 s (model generation: 0.005303,  model checking: 0.000295):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308, q_gen_1314},
Q_f={q_gen_1308},
Delta=
{
<z>() -> q_gen_1314
<s, s>(q_gen_1308) -> q_gen_1308
<z, s>(q_gen_1314) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310, q_gen_1317},
Q_f={q_gen_1307},
Delta=
{
<z>() -> q_gen_1317
<z, z>() -> q_gen_1310
<s, s, s>(q_gen_1307) -> q_gen_1307
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, s>(q_gen_1317) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> plus([n, z, n]) -> 9  ;  (leq([i, z])) -> eq_nat([i, z]) -> 5  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5  ;  (leq([s(nn1), z])) -> BOT -> 5  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 7
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 8, which took 0.005519 s (model generation: 0.005330,  model checking: 0.000189):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308, q_gen_1314},
Q_f={q_gen_1308},
Delta=
{
<z>() -> q_gen_1314
<s, s>(q_gen_1308) -> q_gen_1308
<z, s>(q_gen_1314) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310, q_gen_1317},
Q_f={q_gen_1307},
Delta=
{
<z>() -> q_gen_1317
<s, s>(q_gen_1310) -> q_gen_1310
<z, z>() -> q_gen_1310
<s, s, s>(q_gen_1307) -> q_gen_1307
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, s>(q_gen_1317) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 9  ;  () -> plus([n, z, n]) -> 9  ;  (leq([i, z])) -> eq_nat([i, z]) -> 6  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6  ;  (leq([s(nn1), z])) -> BOT -> 6  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 7
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> s(s(z))
})

-------------------------------------------
Step 9, which took 0.004997 s (model generation: 0.004753,  model checking: 0.000244):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308, q_gen_1314},
Q_f={q_gen_1308},
Delta=
{
<s>(q_gen_1314) -> q_gen_1314
<z>() -> q_gen_1314
<s, s>(q_gen_1308) -> q_gen_1308
<z, s>(q_gen_1314) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310, q_gen_1317},
Q_f={q_gen_1307},
Delta=
{
<z>() -> q_gen_1317
<s, s>(q_gen_1310) -> q_gen_1310
<z, z>() -> q_gen_1310
<s, s, s>(q_gen_1307) -> q_gen_1307
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, s>(q_gen_1317) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 9  ;  () -> plus([n, z, n]) -> 9  ;  (leq([i, z])) -> eq_nat([i, z]) -> 7  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7  ;  (leq([s(nn1), z])) -> BOT -> 7  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 10
}
Sat witness: Yes: ((plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]), {
_wx -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 10, which took 0.006093 s (model generation: 0.005430,  model checking: 0.000663):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1308, q_gen_1314},
Q_f={q_gen_1308},
Delta=
{
<s>(q_gen_1314) -> q_gen_1314
<z>() -> q_gen_1314
<s, s>(q_gen_1308) -> q_gen_1308
<z, s>(q_gen_1314) -> q_gen_1308
<z, z>() -> q_gen_1308
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1307, q_gen_1310, q_gen_1317},
Q_f={q_gen_1307},
Delta=
{
<z>() -> q_gen_1317
<s, s>(q_gen_1310) -> q_gen_1310
<z, s>(q_gen_1317) -> q_gen_1310
<z, z>() -> q_gen_1310
<s, s, s>(q_gen_1307) -> q_gen_1307
<s, z, s>(q_gen_1310) -> q_gen_1307
<z, s, s>(q_gen_1310) -> q_gen_1307
<z, z, s>(q_gen_1317) -> q_gen_1307
<z, z, z>() -> q_gen_1307
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 10  ;  () -> plus([n, z, n]) -> 10  ;  (leq([i, z])) -> eq_nat([i, z]) -> 8  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8  ;  (leq([s(nn1), z])) -> BOT -> 8  ;  (plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]) -> 13
}
Sat witness: Yes: ((plus([n, mm, _wx])) -> plus([n, s(mm), s(_wx)]), {
_wx -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

Total time: 0.062135
Reason for stopping: Proved