(HACK2)
(PRODUCT-LESS-THAN-ZERO-1
 (30 6 (:REWRITE HACK2))
 (26 26 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (26 26 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (26 26 (:REWRITE DEFAULT-<-2))
 (26 26 (:REWRITE DEFAULT-<-1))
 (10 10 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (10 10 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (6 6 (:REWRITE DEFAULT-*-2))
 (6 6 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(PRODUCT-LESS-THAN-ZERO-2
 (20 16 (:REWRITE DEFAULT-<-1))
 (18 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (16 16 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (13 13 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 4 (:REWRITE DEFAULT-*-1))
 (8 3 (:REWRITE HACK2))
 (6 4 (:REWRITE DEFAULT-*-2))
 (3 3 (:REWRITE EQUAL-OF-PREDS-REWRITE))
 (3 3 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (3 3 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 )
(PRODUCT-LESS-THAN-ZERO
 (26 19 (:REWRITE DEFAULT-<-1))
 (24 19 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (19 19 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (19 19 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (5 5 (:REWRITE EQUAL-OF-PREDS-REWRITE))
 (5 5 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (5 5 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (4 2 (:REWRITE DEFAULT-*-2))
 (4 2 (:REWRITE DEFAULT-*-1))
 )
(PRODUCT-GREATER-THAN-ZERO
 (116 94 (:REWRITE DEFAULT-*-1))
 (114 94 (:REWRITE DEFAULT-*-2))
 (82 56 (:REWRITE DEFAULT-<-1))
 (72 72 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (64 56 (:REWRITE DEFAULT-<-2))
 (56 56 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (56 56 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (36 4 (:REWRITE PRODUCT-LESS-THAN-ZERO))
 (6 6 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (6 6 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (6 6 (:REWRITE A5))
 )
(PRODUCT-GREATER-THAN-ZERO-2
 (21 17 (:REWRITE DEFAULT-<-1))
 (19 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (17 17 (:REWRITE LESS-THAN-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (12 12 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 4 (:REWRITE DEFAULT-*-2))
 (6 4 (:REWRITE DEFAULT-*-1))
 (1 1 (:REWRITE EQUAL-OF-PREDS-REWRITE))
 (1 1 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (1 1 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 )
(PRODUCT-EQUAL-ZERO
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:REWRITE EQUAL-OF-PREDS-REWRITE))
 (6 6 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-RIGHT-HAND-SIDE))
 (6 6 (:REWRITE EQUAL-MULTIPLY-THROUGH-BY-INVERTED-FACTOR-FROM-LEFT-HAND-SIDE))
 (4 2 (:REWRITE DEFAULT-*-2))
 (4 2 (:REWRITE DEFAULT-*-1))
 )
