\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a
.
intros.
-auto paramodulation timeout=600.
+autobatch paramodulation timeout=600;
try assumption.
print proofterm.
qed.
\forall H:(\forall x,y:A. x = y).
\forall H:(\forall x,y,z:A. f x = y).
\forall x,y:A. x=y.
-intros.auto paramodulation.
+intros.autobatch paramodulation.
qed.
theorem GRP049_simple:
\forall mult: A \to A \to A.
\forall H: (\forall x,y,z:A.mult z (inv (mult (inv (mult (inv (mult z y)) x)) (inv (mult y (mult (inv y) y))))) = x).
\forall a,b:A. mult (inv a) a = mult (inv b) b.
-intros.auto paramodulation;
+intros.autobatch paramodulation;
qed.
theorem GRP049 :
\forall mult: A \to A \to A.
\forall H: (\forall x,y,z:A.mult z (inv (mult (inv (mult (inv (mult z y)) x)) (inv (mult y (mult (inv y) y))))) = x).
\forall a,b:A. mult a (inv a)= mult b (inv b).
-intros.auto paramodulation timeout = 600;exact a.
+intros.autobatch paramodulation timeout = 600;exact a.
qed.