if(Prover9).

assign(order, kbo).

assign(eq_defs,fold).

end_if.

 

formulas(assumptions).

 

% identity element

0 * x = x.

x * 0 = x.

 

% quasigroup

x * (x \ y) = y.

x \ (x * y) = y.

(x * y) / y = x.

(x / y) * y = x.

 

% left Bol (universally LIP, universally LAP)

(x * (y * x)) * z = x * (y * (x * z)).

 

% C a Moufang element

C * ((x * y) * C) = (C * x) * (y * C).

 

% C in commutant

C * x = x * C.

 

end_of_list.

 

formulas(goals).

 

(C * C) * (x * y) = (C * x) * (C * y).

 

end_of_list.

 

 

if(Prover9).

assign(order, kbo).

assign(eq_defs,fold).

end_if.

 

formulas(assumptions).

 

% identity element

0 * x = x.

x * 0 = x.

 

% quasigroup

x * (x \ y) = y.

x \ (x * y) = y.

(x * y) / y = x.

(x / y) * y = x.

 

% left Bol (universally LIP, universally LAP)

(x * (y * x)) * z = x * (y * (x * z)).

 

% C a Moufang element

C * ((x * y) * C) = (C * x) * (y * C).

 

% assumption

(C * C) * (x * y) = (C * x) * (C * y).

 

end_of_list.

 

formulas(goals).

 

 (x * x) * (C * y) = (x * C) * (x * y).

 

end_of_list.

 

 

if(Prover9).

assign(order, kbo).

assign(eq_defs,fold).

end_if.

 

formulas(assumptions).

 

% identity element

0 * x = x.

x * 0 = x.

 

% quasigroup

x * (x \ y) = y.

x \ (x * y) = y.

(x * y) / y = x.

(x / y) * y = x.

 

% left Bol (universally LIP, universally LAP)

(x * (y * x)) * z = x * (y * (x * z)).

 

% C a Moufang element

C * ((x * y) * C) = (C * x) * (y * C).

 

% assumption

 (x * x) * (C * y) = (x * C) * (x * y).

 

end_of_list.

 

formulas(goals).

 

% C in commutant

C * x = x * C.

 

end_of_list.