Sindbad~EG File Manager

% prove the commutative law of multiplication in PA.
%

set(lambda).
set(binary_res).
set(induction).
set(demod_inf).
set(para_into).
set(para_from).
assign(max_distinct_vars,0).
assign(max_weight,32).
assign(pick_given_ratio,4).
assign(bsub_hint_wt,1).
weight_list(pick_and_purge).
weight(junk,50).
weight(g($(0)),2).   %every g-term counts 2
end_of_list.
%set(very_verbose).


list(demodulators).
x+0 = x.
x*0 = 0.
0*x = 0.
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+0 = x.
x + s(y) = s(x)+y.
x + (y+z) = (x+y)+z.
x+y = y+x.
x * s(y) = x * y + x.
%s(x)*y = x*y + y.
%x + 0 = 0 + x.
x + s(y) = s(x) + y.
y != z | x + y = x + z.
end_of_list.

list(sos).
m * n != n * m.

% 0!=0*m.
end_of_list.