Solving ../../benchmarks/true/isaplanner_prop65.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, _a])) -> plus([n, s(mm), s(_a)])}
(plus([_b, _c, _d]) /\ plus([_b, _c, _e])) -> eq_nat([_d, _e])
)
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
}

properties:
{(plus([m, i, _f])) -> le([i, s(_f)])}


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

Clause system for inference is:

{
() -> le([z, s(nn2)]) -> 0  ;  () -> plus([n, z, n]) -> 0  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0  ;  (le([s(nn1), z])) -> BOT -> 0  ;  (le([z, z])) -> BOT -> 0  ;  (plus([m, i, _f])) -> le([i, s(_f)]) -> 0  ;  (plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]) -> 0
}


Solving took 0.084878 seconds.
Proved
Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<s>(q_gen_2749) -> q_gen_2749
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751, q_gen_2758},
Q_f={q_gen_2747},
Delta=
{
<s>(q_gen_2758) -> q_gen_2758
<z>() -> q_gen_2758
<s, s>(q_gen_2751) -> q_gen_2751
<z, s>(q_gen_2758) -> q_gen_2751
<z, z>() -> q_gen_2751
<s, s, s>(q_gen_2747) -> q_gen_2747
<s, z, s>(q_gen_2751) -> q_gen_2747
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, s>(q_gen_2758) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.003924 s (model generation: 0.003769,  model checking: 0.000155):

Model:
|_
{
le -> 
{{{
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:
{
() -> le([z, s(nn2)]) -> 0  ;  () -> plus([n, z, n]) -> 3  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1  ;  (le([s(nn1), z])) -> BOT -> 1  ;  (le([z, z])) -> BOT -> 1  ;  (plus([m, i, _f])) -> le([i, s(_f)]) -> 1  ;  (plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]) -> 1
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.003468 s (model generation: 0.003431,  model checking: 0.000037):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747},
Q_f={q_gen_2747},
Delta=
{
<z, z, z>() -> q_gen_2747
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1  ;  (le([s(nn1), z])) -> BOT -> 1  ;  (le([z, z])) -> BOT -> 1  ;  (plus([m, i, _f])) -> le([i, s(_f)]) -> 1  ;  (plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]) -> 1
}
Sat witness: Yes: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.003607 s (model generation: 0.003538,  model checking: 0.000069):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<z>() -> q_gen_2749
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747},
Q_f={q_gen_2747},
Delta=
{
<z, z, z>() -> q_gen_2747
}

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

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

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

-------------------------------------------
Step 3, which took 0.004368 s (model generation: 0.004282,  model checking: 0.000086):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<z>() -> q_gen_2749
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751},
Q_f={q_gen_2747},
Delta=
{
<z, z>() -> q_gen_2751
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

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

-------------------------------------------
Step 4, which took 0.007517 s (model generation: 0.006858,  model checking: 0.000659):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751},
Q_f={q_gen_2747},
Delta=
{
<z, z>() -> q_gen_2751
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

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

-------------------------------------------
Step 5, which took 0.010046 s (model generation: 0.009901,  model checking: 0.000145):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751},
Q_f={q_gen_2747},
Delta=
{
<z, z>() -> q_gen_2751
<s, z, s>(q_gen_2751) -> q_gen_2747
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

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

-------------------------------------------
Step 6, which took 0.008683 s (model generation: 0.008058,  model checking: 0.000625):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<s>(q_gen_2749) -> q_gen_2749
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751},
Q_f={q_gen_2747},
Delta=
{
<z, z>() -> q_gen_2751
<s, z, s>(q_gen_2751) -> q_gen_2747
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

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

-------------------------------------------
Step 7, which took 0.007697 s (model generation: 0.007509,  model checking: 0.000188):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<s>(q_gen_2749) -> q_gen_2749
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751, q_gen_2758},
Q_f={q_gen_2747},
Delta=
{
<z>() -> q_gen_2758
<z, z>() -> q_gen_2751
<s, s, s>(q_gen_2747) -> q_gen_2747
<s, z, s>(q_gen_2751) -> q_gen_2747
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, s>(q_gen_2758) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

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

-------------------------------------------
Step 8, which took 0.007977 s (model generation: 0.007729,  model checking: 0.000248):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<s>(q_gen_2749) -> q_gen_2749
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751, q_gen_2758},
Q_f={q_gen_2747},
Delta=
{
<z>() -> q_gen_2758
<s, s>(q_gen_2751) -> q_gen_2751
<z, z>() -> q_gen_2751
<s, s, s>(q_gen_2747) -> q_gen_2747
<s, z, s>(q_gen_2751) -> q_gen_2747
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, s>(q_gen_2758) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7  ;  () -> plus([n, z, n]) -> 9  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6  ;  (le([s(nn1), z])) -> BOT -> 6  ;  (le([z, z])) -> BOT -> 6  ;  (plus([m, i, _f])) -> le([i, s(_f)]) -> 6  ;  (plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]) -> 10
}
Sat witness: Yes: ((plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]), {
_a -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 9, which took 0.010859 s (model generation: 0.009750,  model checking: 0.001109):

Model:
|_
{
le -> 
{{{
Q={q_gen_2748, q_gen_2749},
Q_f={q_gen_2748},
Delta=
{
<s>(q_gen_2749) -> q_gen_2749
<z>() -> q_gen_2749
<s, s>(q_gen_2748) -> q_gen_2748
<z, s>(q_gen_2749) -> q_gen_2748
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2747, q_gen_2751, q_gen_2758},
Q_f={q_gen_2747},
Delta=
{
<z>() -> q_gen_2758
<s, s>(q_gen_2751) -> q_gen_2751
<z, s>(q_gen_2758) -> q_gen_2751
<z, z>() -> q_gen_2751
<s, s, s>(q_gen_2747) -> q_gen_2747
<s, z, s>(q_gen_2751) -> q_gen_2747
<z, s, s>(q_gen_2751) -> q_gen_2747
<z, z, s>(q_gen_2758) -> q_gen_2747
<z, z, z>() -> q_gen_2747
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8  ;  () -> plus([n, z, n]) -> 10  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 7  ;  (le([s(nn1), z])) -> BOT -> 7  ;  (le([z, z])) -> BOT -> 7  ;  (plus([m, i, _f])) -> le([i, s(_f)]) -> 7  ;  (plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]) -> 13
}
Sat witness: Yes: ((plus([n, mm, _a])) -> plus([n, s(mm), s(_a)]), {
_a -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

Total time: 0.084878
Reason for stopping: Proved