(app (app (app S x) y) z) = (app (app x z) (app y z))).
\forall x:A.
(app (app (app S K) K) x) = x.
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool1:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
(inv zero) = one.
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool2:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x:A. (mult x zero) = zero.
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool3:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x:A. (inv (inv x)) = x.
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool266:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A. (mult x (add (inv x) y)) = (mult x y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
*)
theorem bool507:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A. zero = (mult x (mult (inv x) y)).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
(*
theorem bool515:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A. zero = mult (inv x) (mult x y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool304:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A. x = (mult (add y x) x).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool531:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A. zero = (mult (inv (add x y)) y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool253:
\forall inv1: (\forall x:A. (add x (inv x)) = one).
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A. (add (inv x) (mult y x)) = (add (inv x) y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool557:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A.
inv x = (add (inv x) (inv (add y x))).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool609:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A.
inv x = (add (inv (add y x)) (inv x)).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
(*
theorem bool260:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z:A.
add x (mult x y) = mult x (add x y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool276:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z,u:A.
(mult (add x y) (add z (add x u))) = (add (mult (add x y) z) (add x (mult y u))).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool250:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z:A.
add x (mult y z) = mult (add y x) (add x z).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool756minimal:
\forall x,y,z:A.
add x (add y (mult y z)) = add x (add y (mult x z)).
intros;
-auto paramodulation.
+autobatch paramodulation.
qed.
theorem bool756simplified:
\forall x,y,z:A.
add x (add y (mult y z)) = add x (add y (mult x z)).
intros;
-auto paramodulation.
+autobatch paramodulation.
qed.
theorem bool756:
add x y = add x (add y (mult x z)).
intros;
cut (mult (add y x) (add x (add y z)) = add x (add y (mult x z)));
-[auto paramodulation
-|auto paramodulation]
+[autobatch paramodulation
+|autobatch paramodulation]
qed.
theorem bool756full:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z:A.
add x y = add x (add y (mult x z)).
-intros;auto paramodulation.
+intros;autobatch paramodulation.
qed.
theorem bool1164:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z:A.
(add x y) = (add (add x (mult y z)) y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool1230:
\forall x,y,z:A.
\forall c1z: (\forall x:A.(add x z) = (add z x)).
add (add x y) z = add (add x y) (add z y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool1230:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z:A.
add (add x y) z = add (add x y) (add z y).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool1372:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y,z:A.
add x (add y z) = add (add x z) y.
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool381:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A.
add (inv x) y = add (mult x y) (inv x).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool5hint1:
\forall hint623:(\forall x,y:A. inv (mult x y) = add (inv x) (inv (mult x y))).
\forall x,y:A.
(inv (mult x y)) = (add (inv x) (inv y)).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool5hint2:
\forall hint623:(\forall x,y:A. inv (mult x y) = add (inv x) (inv (mult x y))).
\forall x,y:A.
(inv (mult x y)) = (add (inv x) (inv y)).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool5hint3:
\forall hint609:(\forall x,y:A. inv x = add (inv (add y x)) (inv x)).
\forall x,y:A.
(inv (mult x y)) = (add (inv x) (inv y)).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem bool5:
\forall inv2: (\forall x:A. (mult x (inv x)) = zero).
\forall x,y:A.
(inv (mult x y)) = (add (inv x) (inv y)).
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
*)*)