\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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
print proofterm.
qed.
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
intros.
exists[
2:
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
print proofterm.
qed.
2:
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
2:
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
2:
exists[
2:
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
|
skip]
2:
exists[
2:
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
print proofterm.
qed.
(* -------------------------------------------------------------------------- *)
(* File : GRP168-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
(* Domain : Group Theory (Lattice Ordered) *)
-(* Problem : Inner group automorphisms are order preserving *)
+(* Problem : Inner group autobatchmorphisms are order preserving *)
(* Version : [Fuc94] (equality) axioms. *)
(* English : *)
(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
\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.
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
print proofterm.
qed.
(* -------------------------------------------------------------------------- *)
(* File : GRP168-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
(* Domain : Group Theory (Lattice Ordered) *)
-(* Problem : Inner group automorphisms are order preserving *)
+(* Problem : Inner group autobatchmorphisms are order preserving *)
(* Version : [Fuc94] (equality) axioms. *)
(* Theorem formulation : Dual. *)
(* English : *)
\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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto 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.
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
print proofterm.
qed.
2:
exists[
2:
-auto 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.
-auto paramodulation timeout=100.
+autobatch paramodulation timeout=100.
try assumption.
print proofterm.
qed.