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% prove the commutative law of addition in PA.
% Both the basis case and the induction step themselves are proved by induction.
% Otter-lambda finds all three instances of induction automatically.


set(lambda).
set(binary_res).
set(induction).
set(demod_inf).
set(para_into).
set(para_from).
assign(max_distinct_vars,0).
assign(max_weight,24).
assign(pick_given_ratio,4).
assign(bsub_hint_wt,1).
weight_list(pick_and_purge).
weight(junk,50).
weight(g($(0)),1).   %every g-term counts like a constant
end_of_list.


list(demodulators).
x+0 = x.
end_of_list.

list(usable).
x = x.         
s(x) != s(y) | x = y.
s(x) != 0.
-ap(y,0) | ap(y,g(y)) | ap(y,z).
-ap(y,0) | -ap(y,s(g(y))) | ap(y,z).
x + s(y) = s(x+y).
end_of_list.

list(sos).
a  + n != n + a.
end_of_list.