beta eta contract the Sledgehammer conjecture (and also the axioms, although this might not be needed), just like Metis does (implicitly);
another consequence of the transition to FOF
BoolNat = Arith +
types bool,nat 0
arities bool,nat :: arith
consts Suc :: "nat=>nat"
rules add0 "0 + n = n::nat"
addS "Suc(m)+n = Suc(m+n)"
nat1 "1 = Suc(0)"
or0l "0 + x = x::bool"
or0r "x + 0 = x::bool"
or1l "1 + x = 1::bool"
or1r "x + 1 = 1::bool"
end