Solving ../../benchmarks/false/mult_leq.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)])}
(plus([_pka, _qka, _rka]) /\ plus([_pka, _qka, _ska])) -> eq_nat([_rka, _ska])
)
(mult, F:
{() -> mult([n, z, z])
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka])}
(mult([_vka, _wka, _xka]) /\ mult([_vka, _wka, _yka])) -> eq_nat([_xka, _yka])
)
}

properties:
{(mult([n, m, _zka])) -> leq([n, _zka])}


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

Clause system for inference is:

{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> mult([n, z, z]) -> 0
() -> plus([n, z, n]) -> 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
(mult([n, m, _zka])) -> leq([n, _zka]) -> 0
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 0
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 0
}


Solving took 0.194796 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010223 s (model generation: 0.009793,  model checking: 0.000430):

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

}

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

}

Datatype: <nat, nat, 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:
{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> mult([n, z, z]) -> 0
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(mult([n, m, _zka])) -> leq([n, _zka]) -> 1
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 1
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.010707 s (model generation: 0.010543,  model checking: 0.000164):

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

}

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

}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779},
Q_f={q_gen_6779},
Delta=
{
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(mult([n, m, _zka])) -> leq([n, _zka]) -> 1
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 1
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 1
}
Sat witness: Found: (() -> mult([n, z, z]), {
n -> z
})

-------------------------------------------
Step 2, which took 0.010242 s (model generation: 0.010157,  model checking: 0.000085):

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780},
Q_f={q_gen_6780},
Delta=
{
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779},
Q_f={q_gen_6779},
Delta=
{
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(mult([n, m, _zka])) -> leq([n, _zka]) -> 1
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 1
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 3, which took 0.010299 s (model generation: 0.010175,  model checking: 0.000124):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781},
Q_f={q_gen_6781},
Delta=
{
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780},
Q_f={q_gen_6780},
Delta=
{
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779},
Q_f={q_gen_6779},
Delta=
{
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(mult([n, m, _zka])) -> leq([n, _zka]) -> 1
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 1
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 4, which took 0.010815 s (model generation: 0.010605,  model checking: 0.000210):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<z>() -> q_gen_6783
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780},
Q_f={q_gen_6780},
Delta=
{
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779},
Q_f={q_gen_6779},
Delta=
{
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(mult([n, m, _zka])) -> leq([n, _zka]) -> 1
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 1
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]), {
_oka -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 5, which took 0.010975 s (model generation: 0.010772,  model checking: 0.000203):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<z>() -> q_gen_6783
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780},
Q_f={q_gen_6780},
Delta=
{
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785},
Q_f={q_gen_6779},
Delta=
{
<z, z>() -> q_gen_6785
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(mult([n, m, _zka])) -> leq([n, _zka]) -> 1
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 4
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 4
}
Sat witness: Found: ((mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]), {
_tka -> z  ;  _uka -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 6, which took 0.011365 s (model generation: 0.011074,  model checking: 0.000291):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<z>() -> q_gen_6783
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787},
Q_f={q_gen_6780},
Delta=
{
<z>() -> q_gen_6787
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785},
Q_f={q_gen_6779},
Delta=
{
<z, z>() -> q_gen_6785
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 3
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(mult([n, m, _zka])) -> leq([n, _zka]) -> 2
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 4
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 4
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 7, which took 0.011714 s (model generation: 0.011246,  model checking: 0.000468):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787},
Q_f={q_gen_6780},
Delta=
{
<z>() -> q_gen_6787
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785},
Q_f={q_gen_6779},
Delta=
{
<z, z>() -> q_gen_6785
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 3
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
(mult([n, m, _zka])) -> leq([n, _zka]) -> 3
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 4
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 8, which took 0.012383 s (model generation: 0.011815,  model checking: 0.000568):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787},
Q_f={q_gen_6780},
Delta=
{
<z>() -> q_gen_6787
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785},
Q_f={q_gen_6779},
Delta=
{
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 6
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(mult([n, m, _zka])) -> leq([n, _zka]) -> 4
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 4
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 4
}
Sat witness: Found: (() -> mult([n, z, z]), {
n -> s(s(z))
})

-------------------------------------------
Step 9, which took 0.012057 s (model generation: 0.011863,  model checking: 0.000194):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787},
Q_f={q_gen_6780},
Delta=
{
<s>(q_gen_6787) -> q_gen_6787
<z>() -> q_gen_6787
<s, z, z>(q_gen_6787) -> q_gen_6780
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785},
Q_f={q_gen_6779},
Delta=
{
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 6
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(mult([n, m, _zka])) -> leq([n, _zka]) -> 4
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 4
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 4
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 10, which took 0.012938 s (model generation: 0.012624,  model checking: 0.000314):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<s>(q_gen_6783) -> q_gen_6783
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787},
Q_f={q_gen_6780},
Delta=
{
<s>(q_gen_6787) -> q_gen_6787
<z>() -> q_gen_6787
<s, z, z>(q_gen_6787) -> q_gen_6780
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785},
Q_f={q_gen_6779},
Delta=
{
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 6
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(mult([n, m, _zka])) -> leq([n, _zka]) -> 4
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 4
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]), {
_oka -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 11, which took 0.013605 s (model generation: 0.013303,  model checking: 0.000302):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<s>(q_gen_6783) -> q_gen_6783
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787},
Q_f={q_gen_6780},
Delta=
{
<s>(q_gen_6787) -> q_gen_6787
<z>() -> q_gen_6787
<s, z, z>(q_gen_6787) -> q_gen_6780
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785, q_gen_6798},
Q_f={q_gen_6779},
Delta=
{
<z>() -> q_gen_6798
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, s, s>(q_gen_6779) -> q_gen_6779
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, s>(q_gen_6798) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 6
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(mult([n, m, _zka])) -> leq([n, _zka]) -> 4
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 7
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 7
}
Sat witness: Found: ((mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]), {
_tka -> z  ;  _uka -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 12, which took 0.014271 s (model generation: 0.013679,  model checking: 0.000592):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<s>(q_gen_6783) -> q_gen_6783
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787, q_gen_6800},
Q_f={q_gen_6780},
Delta=
{
<s>(q_gen_6787) -> q_gen_6787
<z>() -> q_gen_6787
<z, z>() -> q_gen_6800
<s, z, z>(q_gen_6787) -> q_gen_6780
<z, s, s>(q_gen_6800) -> q_gen_6780
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785, q_gen_6798},
Q_f={q_gen_6779},
Delta=
{
<z>() -> q_gen_6798
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, s, s>(q_gen_6779) -> q_gen_6779
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, s>(q_gen_6798) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 6
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
(mult([n, m, _zka])) -> leq([n, _zka]) -> 7
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 7
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 7
}
Sat witness: Found: ((mult([n, m, _zka])) -> leq([n, _zka]), {
_zka -> z  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 13, which took 0.014483 s (model generation: 0.014416,  model checking: 0.000067):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783},
Q_f={q_gen_6781},
Delta=
{
<s>(q_gen_6783) -> q_gen_6783
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<s, z>(q_gen_6783) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787, q_gen_6800},
Q_f={q_gen_6780},
Delta=
{
<s>(q_gen_6787) -> q_gen_6787
<z>() -> q_gen_6787
<z, z>() -> q_gen_6800
<s, z, z>(q_gen_6787) -> q_gen_6780
<z, s, s>(q_gen_6800) -> q_gen_6780
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785, q_gen_6798},
Q_f={q_gen_6779},
Delta=
{
<z>() -> q_gen_6798
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, s, s>(q_gen_6779) -> q_gen_6779
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, s>(q_gen_6798) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 6
() -> plus([n, z, n]) -> 6
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 7
(mult([n, m, _zka])) -> leq([n, _zka]) -> 7
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 7
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 7
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 14, which took 0.015391 s (model generation: 0.014332,  model checking: 0.001059):

Model:
|_
{
leq -> 
{{{
Q={q_gen_6781, q_gen_6783, q_gen_6802},
Q_f={q_gen_6781},
Delta=
{
<s>(q_gen_6783) -> q_gen_6783
<z>() -> q_gen_6783
<s, s>(q_gen_6781) -> q_gen_6781
<z, s>(q_gen_6783) -> q_gen_6781
<z, z>() -> q_gen_6781
<s, z>(q_gen_6783) -> q_gen_6802
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  mult -> 
{{{
Q={q_gen_6780, q_gen_6787, q_gen_6792, q_gen_6800, q_gen_6801},
Q_f={q_gen_6780},
Delta=
{
<z>() -> q_gen_6787
<s>(q_gen_6787) -> q_gen_6792
<z, z>() -> q_gen_6800
<s, z, z>(q_gen_6792) -> q_gen_6780
<z, s, s>(q_gen_6800) -> q_gen_6780
<z, s, z>(q_gen_6787) -> q_gen_6780
<z, z, z>() -> q_gen_6780
<s, z, z>(q_gen_6787) -> q_gen_6801
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6779, q_gen_6785, q_gen_6798},
Q_f={q_gen_6779},
Delta=
{
<z>() -> q_gen_6798
<s, s>(q_gen_6785) -> q_gen_6785
<z, z>() -> q_gen_6785
<s, s, s>(q_gen_6779) -> q_gen_6779
<s, z, s>(q_gen_6785) -> q_gen_6779
<z, s, s>(q_gen_6785) -> q_gen_6779
<z, z, s>(q_gen_6798) -> q_gen_6779
<z, z, z>() -> q_gen_6779
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 5
() -> mult([n, z, z]) -> 9
() -> plus([n, z, n]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 7
(mult([n, m, _zka])) -> leq([n, _zka]) -> 7
(mult([n, mm, _tka]) /\ plus([n, _tka, _uka])) -> mult([n, s(mm), _uka]) -> 7
(plus([n, mm, _oka])) -> plus([n, s(mm), s(_oka)]) -> 7
}
Sat witness: Found: (() -> mult([n, z, z]), {
n -> s(z)
})

Total time: 0.194796
Reason for stopping: Disproved