\forall H4:\forall V:Univ.\forall W:Univ.\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H17:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b (inverse a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add x z) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply x z) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse multiplicative_identity) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H4:\forall V:Univ.\forall W:Univ.\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.\forall E:Univ.\forall F:Univ.\forall G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a b (inverse b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.\forall E:Univ.\forall F:Univ.\forall G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (inverse b) b a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\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.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y) (apply y (apply (apply x x) y))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
intros.
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
\forall H0:\forall X1:Univ.\forall X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall X1:Univ.\forall X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t b)) (apply (apply b b) t)) x) y) z) (apply y (apply x z))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t b)) b)) t) x) y) z) (apply y (apply x z))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) b)) x) y) z) (apply x (apply z y))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) b) x) y) z) (apply x (apply z y))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)) x) y) z) (apply (apply x z) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) t) x) y) z) (apply (apply x z) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z y) x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) (apply (apply b b) b))) t) x) y) z) (apply (apply z y) x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t t)) b)) b)) t) x) y) z) (apply (apply z y) x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) b))) t) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) b)) t) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b t) t))) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) t)) t)) x) y) z) (apply (apply z x) y)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
2:
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
2:
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
2:
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
2:
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
\forall H6:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply b a) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b a) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b c) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H4:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (multiply a b)) (multiply (inverse b) (inverse a))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H4:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (inverse a)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H4:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse identity) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a (multiply a a)) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply identity a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a identity) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ a b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ a b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) a) (greatest_lower_bound a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) b) b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) b) (greatest_lower_bound a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (least_upper_bound a b)) (least_upper_bound a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound a b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b c)) (multiply b c)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply c a) (multiply c b)) (multiply c a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a a) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a c) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a c) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply b c))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply a c))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ identity a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ identity a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H8:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply a b) (multiply b a)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join a (meet a b)) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join xx xx) xx
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet xx xx) xx
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H10:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet yy (join xx zz))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H10:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz))
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H11:\forall X:Univ.eq Univ (meet X X) X.eq Univ yy zz
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H13:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (not x)) x) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not (not x))) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (not x) y) (implies (not y) x)) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (not y) (not x))) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (implies a b)) (not b)) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x x) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H4:\forall X:Univ.eq Univ (implies truth X) X.eq Univ x y
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x truth) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (implies y x)) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not truth)) (not x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (not (not x)) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not x) (not y)) (implies y x)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (not x) (xor x truth)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (xor x falsehood) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (xor x x) falsehood
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x truth) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x falsehood) falsehood
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (and_star (xor truth x) x) falsehood
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H12:\forall X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies truth x) x
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H12:\forall X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (not x) (not y)) (implies y x)) truth
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f (f n3 n2) u) (f (f u u) u)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (add a a) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H15:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H20:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H21:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H14:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H21:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ a b
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add b a)))) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add (negate b) a)))) a
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.
2:
exists[
2:
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
|
skip]
\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) Z).eq Univ (f a (f b (f c d))) (f (f (f a b) c) d)
.
intros.
-autobatch paramodulation timeout=100.
+autobatch paramodulation timeout=100;
try assumption.
print proofterm.
qed.