(RTL::DIVIDES
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(RTL::LEMMA0
 (13 2 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (12 3 (:REWRITE RATIONALP-X))
 (8 8 (:REWRITE THE-FLOOR-BELOW))
 (8 8 (:REWRITE THE-FLOOR-ABOVE))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-2))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-1))
 (7 7 (:REWRITE SIMPLIFY-SUMS-<))
 (7 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (7 7 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (7 7 (:REWRITE INTEGERP-<-CONSTANT))
 (7 7 (:REWRITE CONSTANT-<-INTEGERP))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (- x))|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (7 7 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) (/ y))|))
 (7 7 (:REWRITE |(< (- x) c)|))
 (7 7 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE DEFAULT-TIMES-2))
 (4 4 (:REWRITE DEFAULT-TIMES-1))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:META META-RATIONALP-CORRECT))
 (3 3 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(RTL::LEMMA1
 (39 15 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (18 18 (:REWRITE THE-FLOOR-BELOW))
 (18 18 (:REWRITE THE-FLOOR-ABOVE))
 (18 18 (:REWRITE DEFAULT-LESS-THAN-2))
 (18 18 (:REWRITE DEFAULT-LESS-THAN-1))
 (17 17 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE INTEGERP-<-CONSTANT))
 (16 16 (:REWRITE CONSTANT-<-INTEGERP))
 (16 16 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (16 16 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (16 16 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (16 16 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (16 16 (:REWRITE |(< c (- x))|))
 (16 16 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (16 16 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (16 16 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (16 16 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (16 16 (:REWRITE |(< (/ x) (/ y))|))
 (16 16 (:REWRITE |(< (- x) c)|))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (16 4 (:REWRITE RATIONALP-X))
 (15 15 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (15 15 (:REWRITE DEFAULT-TIMES-2))
 (15 15 (:REWRITE DEFAULT-TIMES-1))
 (15 14 (:REWRITE DEFAULT-PLUS-1))
 (14 14 (:REWRITE SIMPLIFY-SUMS-<))
 (14 14 (:REWRITE DEFAULT-PLUS-2))
 (14 3 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 8 (:REWRITE |(< 0 (/ x))|))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:META META-RATIONALP-CORRECT))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-MINUS))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(* x (- y))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(RTL::DIVIDES-LEQ
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (28 28 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (14 10 (:REWRITE DEFAULT-TIMES-2))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (10 10 (:REWRITE DEFAULT-TIMES-1))
 (5 5 (:REWRITE THE-FLOOR-BELOW))
 (5 5 (:REWRITE THE-FLOOR-ABOVE))
 (5 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-2))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) c)|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE DEFAULT-DIVIDE))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(RTL::DIVIDES-MINUS
 (18 2 (:REWRITE ACL2-NUMBERP-X))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (17 17 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (8 2 (:REWRITE RATIONALP-X))
 (5 5 (:REWRITE DEFAULT-TIMES-2))
 (5 5 (:REWRITE DEFAULT-TIMES-1))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE REDUCE-RATIONALP-+))
 (2 2 (:REWRITE REDUCE-RATIONALP-*))
 (2 2 (:REWRITE RATIONALP-MINUS-X))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE DEFAULT-DIVIDE))
 (2 2 (:META META-RATIONALP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(RTL::DIVIDES-SUM
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (27 3 (:REWRITE ACL2-NUMBERP-X))
 (12 3 (:REWRITE RATIONALP-X))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (8 8 (:REWRITE DEFAULT-TIMES-2))
 (8 8 (:REWRITE DEFAULT-TIMES-1))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (3 3 (:REWRITE DEFAULT-DIVIDE))
 (3 3 (:META META-RATIONALP-CORRECT))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(RTL::DIVIDES-PRODUCT
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (16 4 (:REWRITE RATIONALP-X))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 11 (:REWRITE DEFAULT-TIMES-2))
 (11 11 (:REWRITE DEFAULT-TIMES-1))
 (7 7 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (4 4 (:REWRITE DEFAULT-DIVIDE))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 1 (:REWRITE INTEGERP-/))
 (3 3 (:TYPE-PRESCRIPTION FIX))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(* c (* d x))|))
 )
(RTL::DIVIDES-TRANSITIVE
 (84 84 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (84 84 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (84 84 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (84 84 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (72 8 (:REWRITE ACL2-NUMBERP-X))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (32 8 (:REWRITE RATIONALP-X))
 (25 21 (:REWRITE DEFAULT-TIMES-2))
 (21 21 (:REWRITE DEFAULT-TIMES-1))
 (14 14 (:REWRITE REDUCE-INTEGERP-+))
 (14 14 (:REWRITE INTEGERP-MINUS-X))
 (14 14 (:META META-INTEGERP-CORRECT))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (10 10 (:REWRITE DEFAULT-DIVIDE))
 (8 8 (:REWRITE REDUCE-RATIONALP-+))
 (8 8 (:REWRITE REDUCE-RATIONALP-*))
 (8 8 (:REWRITE RATIONALP-MINUS-X))
 (8 8 (:META META-RATIONALP-CORRECT))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (5 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5 5 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 )
(RTL::DIVIDES-SELF
 (9 1 (:REWRITE ACL2-NUMBERP-X))
 (4 1 (:REWRITE RATIONALP-X))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-TIMES-2))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:META META-RATIONALP-CORRECT))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(RTL::DIVIDES-0
 (9 1 (:REWRITE ACL2-NUMBERP-X))
 (4 1 (:REWRITE RATIONALP-X))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-TIMES-2))
 (1 1 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:META META-RATIONALP-CORRECT))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(RTL::DIVIDES-MOD-EQUAL
 (1467 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1385 1385 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1385 1385 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1385 1385 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (936 24 (:REWRITE CANCEL-MOD-+))
 (935 187 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (934 32 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (840 24 (:REWRITE MOD-X-Y-=-X . 4))
 (840 24 (:REWRITE MOD-X-Y-=-X . 3))
 (767 187 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (762 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (735 187 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (735 187 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (651 24 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (624 24 (:REWRITE RTL::MOD-DOES-NOTHING))
 (609 24 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (504 24 (:REWRITE MOD-ZERO . 3))
 (448 20 (:LINEAR MOD-BOUNDS-1))
 (432 27 (:REWRITE |(integerp (- x))|))
 (432 24 (:REWRITE MOD-ZERO . 4))
 (374 187 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (310 10 (:LINEAR RTL::MOD-BND-2))
 (263 32 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (245 24 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (245 24 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (240 24 (:REWRITE DEFAULT-MOD-RATIO))
 (240 24 (:REWRITE |(* (- x) y)|))
 (229 31 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (210 10 (:LINEAR MOD-BOUNDS-3))
 (187 187 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (187 187 (:TYPE-PRESCRIPTION NATP))
 (187 187 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (187 187 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (187 187 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (187 187 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (187 187 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (187 187 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (187 187 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (184 10 (:LINEAR RTL::MOD-BND-1))
 (164 77 (:REWRITE REDUCE-INTEGERP-+))
 (162 162 (:REWRITE THE-FLOOR-BELOW))
 (162 162 (:REWRITE THE-FLOOR-ABOVE))
 (162 162 (:REWRITE SIMPLIFY-SUMS-<))
 (162 162 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (162 162 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (162 162 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (162 162 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (162 162 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (162 162 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (162 162 (:REWRITE INTEGERP-<-CONSTANT))
 (162 162 (:REWRITE DEFAULT-LESS-THAN-2))
 (162 162 (:REWRITE DEFAULT-LESS-THAN-1))
 (162 162 (:REWRITE CONSTANT-<-INTEGERP))
 (162 162 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (162 162 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (162 162 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (162 162 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (162 162 (:REWRITE |(< c (- x))|))
 (162 162 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (162 162 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (162 162 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (162 162 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (162 162 (:REWRITE |(< (/ x) (/ y))|))
 (162 162 (:REWRITE |(< (- x) c)|))
 (162 162 (:REWRITE |(< (- x) (- y))|))
 (162 38 (:REWRITE DEFAULT-MINUS))
 (150 150 (:REWRITE DEFAULT-TIMES-2))
 (150 150 (:REWRITE DEFAULT-TIMES-1))
 (120 24 (:REWRITE MOD-X-Y-=-X . 2))
 (120 24 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (120 24 (:REWRITE MOD-CANCEL-*-CONST))
 (120 24 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (120 24 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (120 24 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (120 24 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (102 102 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (93 77 (:REWRITE INTEGERP-MINUS-X))
 (90 90 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (90 90 (:REWRITE DEFAULT-DIVIDE))
 (82 21 (:REWRITE DEFAULT-PLUS-2))
 (77 77 (:META META-INTEGERP-CORRECT))
 (74 74 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (68 68 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (68 68 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (68 68 (:REWRITE |(< 0 (/ x))|))
 (68 68 (:REWRITE |(< 0 (* x y))|))
 (56 56 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (56 56 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (56 56 (:REWRITE |(< (/ x) 0)|))
 (56 56 (:REWRITE |(< (* x y) 0)|))
 (50 21 (:REWRITE DEFAULT-PLUS-1))
 (42 42 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (36 9 (:REWRITE RATIONALP-X))
 (32 32 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (32 32 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (32 32 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (32 32 (:REWRITE |(equal c (/ x))|))
 (32 32 (:REWRITE |(equal c (- x))|))
 (32 32 (:REWRITE |(equal (/ x) c)|))
 (32 32 (:REWRITE |(equal (/ x) (/ y))|))
 (32 32 (:REWRITE |(equal (- x) c)|))
 (32 32 (:REWRITE |(equal (- x) (- y))|))
 (31 31 (:REWRITE |(- (* c x))|))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 24 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (24 24 (:REWRITE DEFAULT-MOD-2))
 (24 24 (:REWRITE DEFAULT-MOD-1))
 (24 24 (:REWRITE |(mod x (- y))| . 3))
 (24 24 (:REWRITE |(mod x (- y))| . 2))
 (24 24 (:REWRITE |(mod x (- y))| . 1))
 (24 24 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (24 24 (:REWRITE |(mod (- x) y)| . 3))
 (24 24 (:REWRITE |(mod (- x) y)| . 2))
 (24 24 (:REWRITE |(mod (- x) y)| . 1))
 (24 24 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (23 17 (:REWRITE NORMALIZE-ADDENDS))
 (16 16 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (16 1 (:REWRITE |(+ y (+ x z))|))
 (10 10 (:LINEAR RTL::MOD-BND-3))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:META META-RATIONALP-CORRECT))
 (4 4 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (4 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (4 1 (:REWRITE |(+ y x)|))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (2 1 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ 0 x)|))
 )
(RTL::DIVIDES-MOD-0
 (305 37 (:REWRITE REDUCE-RATIONALP-*))
 (270 9 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (270 9 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (270 9 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (270 9 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (236 60 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (220 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (174 30 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (151 43 (:REWRITE RATIONALP-X))
 (148 16 (:DEFINITION RFIX))
 (136 136 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (136 136 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (136 136 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (136 136 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (124 4 (:REWRITE MOD-X-Y-=-X . 4))
 (124 4 (:REWRITE MOD-X-Y-=-X . 3))
 (104 4 (:REWRITE RTL::MOD-DOES-NOTHING))
 (102 56 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (100 60 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (100 60 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (76 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (74 9 (:REWRITE MOD-ZERO . 4))
 (64 4 (:REWRITE |(+ y (+ x z))|))
 (60 60 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (60 60 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (60 60 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (60 60 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (56 56 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (56 56 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (56 56 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (56 56 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (56 56 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (56 56 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (56 8 (:REWRITE ACL2-NUMBERP-X))
 (54 6 (:REWRITE RATIONALP-/))
 (48 48 (:REWRITE THE-FLOOR-BELOW))
 (48 48 (:REWRITE THE-FLOOR-ABOVE))
 (48 48 (:REWRITE SIMPLIFY-SUMS-<))
 (48 48 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (48 48 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (48 48 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (48 48 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (48 48 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (48 48 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (48 48 (:REWRITE INTEGERP-<-CONSTANT))
 (48 48 (:REWRITE DEFAULT-LESS-THAN-2))
 (48 48 (:REWRITE DEFAULT-LESS-THAN-1))
 (48 48 (:REWRITE CONSTANT-<-INTEGERP))
 (48 48 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (48 48 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (48 48 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (48 48 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (48 48 (:REWRITE |(< c (- x))|))
 (48 48 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (48 48 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (48 48 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (48 48 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (48 48 (:REWRITE |(< (/ x) (/ y))|))
 (48 48 (:REWRITE |(< (- x) c)|))
 (48 48 (:REWRITE |(< (- x) (- y))|))
 (46 46 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (46 46 (:TYPE-PRESCRIPTION NATP))
 (44 4 (:REWRITE CANCEL-MOD-+))
 (42 38 (:REWRITE DEFAULT-PLUS-1))
 (38 38 (:REWRITE REDUCE-INTEGERP-+))
 (38 38 (:REWRITE INTEGERP-MINUS-X))
 (38 38 (:REWRITE DEFAULT-PLUS-2))
 (38 38 (:META META-INTEGERP-CORRECT))
 (37 37 (:REWRITE REDUCE-RATIONALP-+))
 (37 37 (:REWRITE RATIONALP-MINUS-X))
 (37 37 (:META META-RATIONALP-CORRECT))
 (36 12 (:REWRITE NORMALIZE-ADDENDS))
 (30 30 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (30 30 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (30 30 (:REWRITE DEFAULT-TIMES-2))
 (30 30 (:REWRITE DEFAULT-TIMES-1))
 (30 30 (:REWRITE |(equal c (/ x))|))
 (30 30 (:REWRITE |(equal c (- x))|))
 (30 30 (:REWRITE |(equal (/ x) c)|))
 (30 30 (:REWRITE |(equal (/ x) (/ y))|))
 (30 30 (:REWRITE |(equal (- x) c)|))
 (30 30 (:REWRITE |(equal (- x) (- y))|))
 (26 26 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (26 26 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (26 26 (:REWRITE DEFAULT-DIVIDE))
 (24 4 (:REWRITE |(* (- x) y)|))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (22 22 (:REWRITE |(< 0 (/ x))|))
 (22 22 (:REWRITE |(< 0 (* x y))|))
 (22 22 (:REWRITE |(< (/ x) 0)|))
 (22 22 (:REWRITE |(< (* x y) 0)|))
 (13 13 (:REWRITE DEFAULT-MOD-2))
 (13 13 (:REWRITE DEFAULT-MOD-1))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:REWRITE DEFAULT-MINUS))
 (8 8 (:REWRITE |(equal (+ (- c) x) y)|))
 (8 8 (:DEFINITION FIX))
 (8 4 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (6 6 (:REWRITE INTEGERP-/))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE MOD-ZERO . 2))
 (4 4 (:REWRITE MOD-X-Y-=-X . 2))
 (4 4 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE MOD-CANCEL-*-CONST))
 (4 4 (:REWRITE |(mod x (- y))| . 3))
 (4 4 (:REWRITE |(mod x (- y))| . 2))
 (4 4 (:REWRITE |(mod x (- y))| . 1))
 (4 4 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (4 4 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(mod (- x) y)| . 3))
 (4 4 (:REWRITE |(mod (- x) y)| . 2))
 (4 4 (:REWRITE |(mod (- x) y)| . 1))
 (4 4 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (4 4 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (4 4 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (4 4 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(- (* c x))|))
 (4 4 (:REWRITE |(+ x (- x))|))
 )
(RTL::LEAST-DIVISOR
 (54 54 (:REWRITE DEFAULT-PLUS-2))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (21 21 (:REWRITE THE-FLOOR-BELOW))
 (21 21 (:REWRITE THE-FLOOR-ABOVE))
 (21 21 (:REWRITE DEFAULT-LESS-THAN-2))
 (21 21 (:REWRITE DEFAULT-LESS-THAN-1))
 (17 17 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (- x))|))
 (17 17 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) (/ y))|))
 (17 17 (:REWRITE |(< (- x) (- y))|))
 (16 4 (:REWRITE RATIONALP-X))
 (15 15 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (15 15 (:REWRITE INTEGERP-<-CONSTANT))
 (15 15 (:REWRITE CONSTANT-<-INTEGERP))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-INTEGERP-CORRECT))
 (7 7 (:REWRITE |(+ c (+ d x))|))
 (5 5 (:REWRITE |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (+ c/d x) y)|))
 (5 5 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:META META-RATIONALP-CORRECT))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 )
(RTL::LEAST-DIVISOR-DIVIDES
 (92 92 (:REWRITE THE-FLOOR-BELOW))
 (92 92 (:REWRITE THE-FLOOR-ABOVE))
 (92 92 (:REWRITE DEFAULT-LESS-THAN-2))
 (91 91 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (91 91 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (91 91 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (86 86 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (86 86 (:REWRITE INTEGERP-<-CONSTANT))
 (86 86 (:REWRITE CONSTANT-<-INTEGERP))
 (86 86 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (86 86 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (86 86 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (86 86 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (86 86 (:REWRITE |(< c (- x))|))
 (86 86 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (86 86 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (86 86 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (86 86 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (86 86 (:REWRITE |(< (/ x) (/ y))|))
 (86 86 (:REWRITE |(< (- x) c)|))
 (86 86 (:REWRITE |(< (- x) (- y))|))
 (60 4 (:REWRITE ACL2-NUMBERP-X))
 (57 57 (:REWRITE SIMPLIFY-SUMS-<))
 (57 57 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (29 29 (:REWRITE REDUCE-INTEGERP-+))
 (29 29 (:REWRITE INTEGERP-MINUS-X))
 (29 29 (:META META-INTEGERP-CORRECT))
 (28 4 (:REWRITE RATIONALP-X))
 (20 20 (:REWRITE DEFAULT-TIMES-2))
 (20 20 (:REWRITE DEFAULT-TIMES-1))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 15 (:REWRITE NORMALIZE-ADDENDS))
 (15 15 (:REWRITE DEFAULT-PLUS-2))
 (15 15 (:REWRITE DEFAULT-PLUS-1))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 (5 5 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (5 5 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (5 5 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:META META-RATIONALP-CORRECT))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 )
(RTL::LEAST-DIVISOR-IS-LEAST
 (75 5 (:REWRITE ACL2-NUMBERP-X))
 (54 54 (:REWRITE THE-FLOOR-BELOW))
 (54 54 (:REWRITE THE-FLOOR-ABOVE))
 (52 52 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (52 52 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (52 52 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (52 52 (:REWRITE DEFAULT-LESS-THAN-1))
 (51 51 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (51 51 (:REWRITE INTEGERP-<-CONSTANT))
 (51 51 (:REWRITE CONSTANT-<-INTEGERP))
 (51 51 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (51 51 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (51 51 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (51 51 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (51 51 (:REWRITE |(< c (- x))|))
 (51 51 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (51 51 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (51 51 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (51 51 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (51 51 (:REWRITE |(< (/ x) (/ y))|))
 (51 51 (:REWRITE |(< (- x) c)|))
 (51 51 (:REWRITE |(< (- x) (- y))|))
 (38 38 (:REWRITE SIMPLIFY-SUMS-<))
 (38 38 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (35 5 (:REWRITE RATIONALP-X))
 (25 25 (:REWRITE REDUCE-INTEGERP-+))
 (25 25 (:REWRITE INTEGERP-MINUS-X))
 (25 25 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE REDUCE-RATIONALP-+))
 (5 5 (:REWRITE REDUCE-RATIONALP-*))
 (5 5 (:REWRITE RATIONALP-MINUS-X))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE NORMALIZE-ADDENDS))
 (5 5 (:REWRITE DEFAULT-PLUS-2))
 (5 5 (:REWRITE DEFAULT-PLUS-1))
 (5 5 (:META META-RATIONALP-CORRECT))
 (4 4 (:REWRITE DEFAULT-TIMES-2))
 (4 4 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(RTL::PRIMEP)
(RTL::PRIMEP-GT-1)
(RTL::PRIMEP-NO-DIVISOR
 (20 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (17 3 (:REWRITE ACL2-NUMBERP-X))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (10 10 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
 (7 7 (:REWRITE SIMPLIFY-SUMS-<))
 (7 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (7 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (7 1 (:REWRITE RATIONALP-X))
 (6 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(RTL::PRIMEP-LEAST-DIVISOR
 (858 33 (:DEFINITION RTL::LEAST-DIVISOR))
 (44 44 (:REWRITE THE-FLOOR-BELOW))
 (44 44 (:REWRITE THE-FLOOR-ABOVE))
 (44 44 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (44 44 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (44 44 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (44 44 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (44 44 (:REWRITE INTEGERP-<-CONSTANT))
 (44 44 (:REWRITE DEFAULT-LESS-THAN-2))
 (44 44 (:REWRITE DEFAULT-LESS-THAN-1))
 (44 44 (:REWRITE CONSTANT-<-INTEGERP))
 (44 44 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (44 44 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (44 44 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (44 44 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (44 44 (:REWRITE |(< c (- x))|))
 (44 44 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (44 44 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (44 44 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (44 44 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (44 44 (:REWRITE |(< (/ x) (/ y))|))
 (44 44 (:REWRITE |(< (- x) c)|))
 (44 44 (:REWRITE |(< (- x) (- y))|))
 (20 20 (:REWRITE SIMPLIFY-SUMS-<))
 (20 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (20 20 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(RTL::FACT)
(RTL::GREATER-PRIME)
(RTL::GREATER-PRIME-DIVIDES)
(RTL::DIVIDES-FACT
 (102 3 (:REWRITE ZP-OPEN))
 (54 3 (:REWRITE |(* (+ x y) z)|))
 (37 21 (:REWRITE DEFAULT-TIMES-2))
 (30 25 (:REWRITE DEFAULT-PLUS-1))
 (28 25 (:REWRITE DEFAULT-PLUS-2))
 (22 21 (:REWRITE DEFAULT-TIMES-1))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 3 (:REWRITE |(+ c (+ d x))|))
 (14 14 (:REWRITE THE-FLOOR-BELOW))
 (14 14 (:REWRITE THE-FLOOR-ABOVE))
 (14 14 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (14 14 (:REWRITE DEFAULT-LESS-THAN-2))
 (14 14 (:REWRITE DEFAULT-LESS-THAN-1))
 (13 13 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (12 12 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (12 12 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (12 12 (:REWRITE INTEGERP-<-CONSTANT))
 (12 12 (:REWRITE CONSTANT-<-INTEGERP))
 (12 12 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (12 12 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (12 12 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (12 12 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (12 12 (:REWRITE |(< c (- x))|))
 (12 12 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (12 12 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (12 12 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (12 12 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (12 12 (:REWRITE |(< (/ x) (/ y))|))
 (12 12 (:REWRITE |(< (- x) c)|))
 (12 12 (:REWRITE |(< (- x) (- y))|))
 (11 11 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (9 3 (:REWRITE |(* -1 x)|))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 3 (:REWRITE DEFAULT-MINUS))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(* (- x) y)|))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (1 1 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 )
(RTL::NOT-DIVIDES-FACT-PLUS1
 (63 7 (:DEFINITION RTL::FACT))
 (19 13 (:REWRITE DEFAULT-PLUS-2))
 (18 13 (:REWRITE DEFAULT-PLUS-1))
 (17 9 (:REWRITE DEFAULT-TIMES-2))
 (10 9 (:REWRITE DEFAULT-TIMES-1))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (6 3 (:REWRITE DEFAULT-MINUS))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE SIMPLIFY-SUMS-<))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(* x (- y))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(RTL::INFINITUDE-OF-PRIMES
 (110 11 (:DEFINITION RTL::FACT))
 (33 22 (:REWRITE DEFAULT-PLUS-2))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (22 22 (:REWRITE NORMALIZE-ADDENDS))
 (22 22 (:REWRITE DEFAULT-PLUS-1))
 (22 11 (:REWRITE DEFAULT-TIMES-2))
 (18 10 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (18 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (17 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (11 11 (:REWRITE ZP-OPEN))
 (11 11 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (11 11 (:REWRITE DEFAULT-TIMES-1))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE SIMPLIFY-SUMS-<))
 (10 10 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
 (8 8 (:REWRITE |(< (+ c/d x) y)|))
 (8 8 (:REWRITE |(< (+ (- c) x) y)|))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:META META-INTEGERP-CORRECT))
 )
(RTL::G-C-D-NAT
 (103 3 (:REWRITE |(< (if a b c) x)|))
 (45 5 (:REWRITE ACL2-NUMBERP-X))
 (26 26 (:REWRITE THE-FLOOR-BELOW))
 (26 26 (:REWRITE THE-FLOOR-ABOVE))
 (26 26 (:REWRITE DEFAULT-LESS-THAN-2))
 (26 26 (:REWRITE DEFAULT-LESS-THAN-1))
 (23 23 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (23 23 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (23 23 (:REWRITE INTEGERP-<-CONSTANT))
 (23 23 (:REWRITE CONSTANT-<-INTEGERP))
 (23 23 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (23 23 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (23 23 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (23 23 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (23 23 (:REWRITE |(< c (- x))|))
 (23 23 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (23 23 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (23 23 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (23 23 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (23 23 (:REWRITE |(< (/ x) (/ y))|))
 (23 23 (:REWRITE |(< (- x) c)|))
 (23 23 (:REWRITE |(< (- x) (- y))|))
 (22 22 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (20 5 (:REWRITE RATIONALP-X))
 (13 13 (:REWRITE |(< (/ x) 0)|))
 (13 13 (:REWRITE |(< (* x y) 0)|))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 8 (:REWRITE ZP-OPEN))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE REDUCE-RATIONALP-+))
 (5 5 (:REWRITE REDUCE-RATIONALP-*))
 (5 5 (:REWRITE RATIONALP-MINUS-X))
 (5 5 (:REWRITE |(< (+ c/d x) y)|))
 (5 5 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:META META-RATIONALP-CORRECT))
 (4 4 (:REWRITE DEFAULT-MINUS))
 (3 3 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 )
(RTL::G-C-D
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 )
(RTL::G-C-D-NAT-POS
 (55 46 (:REWRITE DEFAULT-LESS-THAN-2))
 (50 41 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (46 46 (:REWRITE THE-FLOOR-BELOW))
 (46 46 (:REWRITE THE-FLOOR-ABOVE))
 (46 46 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (46 46 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (46 46 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (46 46 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (46 46 (:REWRITE INTEGERP-<-CONSTANT))
 (46 46 (:REWRITE DEFAULT-LESS-THAN-1))
 (46 46 (:REWRITE CONSTANT-<-INTEGERP))
 (46 46 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (46 46 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (46 46 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (46 46 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (46 46 (:REWRITE |(< c (- x))|))
 (46 46 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (46 46 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (46 46 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (46 46 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (46 46 (:REWRITE |(< (/ x) (/ y))|))
 (46 46 (:REWRITE |(< (- x) c)|))
 (46 46 (:REWRITE |(< (- x) (- y))|))
 (44 41 (:REWRITE DEFAULT-PLUS-1))
 (41 41 (:REWRITE DEFAULT-PLUS-2))
 (39 39 (:REWRITE SIMPLIFY-SUMS-<))
 (20 20 (:REWRITE |(< (/ x) 0)|))
 (20 20 (:REWRITE |(< (* x y) 0)|))
 (15 15 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (15 15 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:REWRITE DEFAULT-MINUS))
 (15 15 (:META META-INTEGERP-CORRECT))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (13 13 (:REWRITE |(< 0 (/ x))|))
 (13 13 (:REWRITE |(< 0 (* x y))|))
 (10 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (9 9 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 8 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(RTL::G-C-D-POS
 (1099 17 (:DEFINITION RTL::G-C-D-NAT))
 (285 4 (:REWRITE |(< x (if a b c))|))
 (223 78 (:REWRITE |(< (- x) (- y))|))
 (186 10 (:REWRITE ZP-OPEN))
 (135 73 (:REWRITE |(< c (- x))|))
 (128 1 (:REWRITE |(< (if a b c) x)|))
 (100 20 (:REWRITE |(+ y x)|))
 (84 83 (:REWRITE DEFAULT-LESS-THAN-2))
 (83 83 (:REWRITE THE-FLOOR-BELOW))
 (83 83 (:REWRITE THE-FLOOR-ABOVE))
 (83 83 (:REWRITE DEFAULT-LESS-THAN-1))
 (78 78 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (78 78 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (78 78 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (78 78 (:REWRITE |(< (/ x) (/ y))|))
 (73 73 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (73 73 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (73 73 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (73 73 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (73 73 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (73 73 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (73 73 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (73 73 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (72 72 (:REWRITE DEFAULT-MINUS))
 (72 71 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (72 71 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (71 71 (:REWRITE SIMPLIFY-SUMS-<))
 (71 71 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (71 71 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (71 71 (:REWRITE INTEGERP-<-CONSTANT))
 (71 71 (:REWRITE CONSTANT-<-INTEGERP))
 (71 71 (:REWRITE |(< (- x) c)|))
 (66 66 (:REWRITE DEFAULT-PLUS-2))
 (66 66 (:REWRITE DEFAULT-PLUS-1))
 (58 2 (:REWRITE |(+ x (if a b c))|))
 (48 4 (:REWRITE |(+ (if a b c) x)|))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (40 40 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (40 40 (:REWRITE NORMALIZE-ADDENDS))
 (40 40 (:REWRITE |(< (/ x) 0)|))
 (40 40 (:REWRITE |(< (* x y) 0)|))
 (30 30 (:REWRITE |(- (- x))|))
 (13 13 (:REWRITE |(< 0 (/ x))|))
 (13 13 (:REWRITE |(< 0 (* x y))|))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-INTEGERP-CORRECT))
 (8 2 (:REWRITE |(- (if a b c))|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (5 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5 5 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 )
(RTL::DIVIDES-G-C-D-NAT
 (141 120 (:REWRITE DEFAULT-PLUS-1))
 (120 120 (:REWRITE DEFAULT-PLUS-2))
 (64 64 (:REWRITE THE-FLOOR-BELOW))
 (64 64 (:REWRITE THE-FLOOR-ABOVE))
 (64 64 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (64 64 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (64 64 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (64 64 (:REWRITE DEFAULT-LESS-THAN-2))
 (64 64 (:REWRITE DEFAULT-LESS-THAN-1))
 (56 56 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (56 56 (:REWRITE INTEGERP-<-CONSTANT))
 (56 56 (:REWRITE CONSTANT-<-INTEGERP))
 (56 56 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (56 56 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (56 56 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (56 56 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (56 56 (:REWRITE |(< c (- x))|))
 (56 56 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (56 56 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (56 56 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (56 56 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (56 56 (:REWRITE |(< (/ x) (/ y))|))
 (56 56 (:REWRITE |(< (- x) c)|))
 (56 56 (:REWRITE |(< (- x) (- y))|))
 (32 32 (:REWRITE DEFAULT-TIMES-2))
 (32 32 (:REWRITE DEFAULT-TIMES-1))
 (28 28 (:REWRITE DEFAULT-MINUS))
 (26 26 (:REWRITE SIMPLIFY-SUMS-<))
 (26 26 (:REWRITE |(< (/ x) 0)|))
 (26 26 (:REWRITE |(< (* x y) 0)|))
 (21 21 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (20 20 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (14 14 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (14 14 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (14 14 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (14 14 (:REWRITE |(equal c (/ x))|))
 (14 14 (:REWRITE |(equal c (- x))|))
 (14 14 (:REWRITE |(equal (/ x) c)|))
 (14 14 (:REWRITE |(equal (/ x) (/ y))|))
 (14 14 (:REWRITE |(equal (- x) c)|))
 (14 14 (:REWRITE |(equal (- x) (- y))|))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (9 9 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 8 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (8 8 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (8 8 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (8 8 (:REWRITE |(< 0 (* x y))|))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE ZP-OPEN))
 (6 6 (:REWRITE |(< (+ c/d x) y)|))
 (6 6 (:REWRITE |(< (+ (- c) x) y)|))
 (6 6 (:REWRITE |(+ c (+ d x))|))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 3 (:TYPE-PRESCRIPTION RTL::G-C-D-NAT))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(RTL::G-C-D-DIVIDES
 (570 8 (:REWRITE |(< x (if a b c))|))
 (386 154 (:REWRITE |(< (- x) (- y))|))
 (376 24 (:REWRITE ZP-OPEN))
 (270 146 (:REWRITE |(< c (- x))|))
 (256 2 (:REWRITE |(< (if a b c) x)|))
 (164 164 (:REWRITE THE-FLOOR-BELOW))
 (164 164 (:REWRITE THE-FLOOR-ABOVE))
 (164 164 (:REWRITE DEFAULT-LESS-THAN-2))
 (164 164 (:REWRITE DEFAULT-LESS-THAN-1))
 (160 32 (:REWRITE |(+ y x)|))
 (154 154 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (154 154 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (154 154 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (154 154 (:REWRITE DEFAULT-MINUS))
 (154 154 (:REWRITE |(< (/ x) (/ y))|))
 (146 146 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (146 146 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (146 146 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (146 146 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (146 146 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (146 146 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (146 146 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (146 146 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (142 142 (:REWRITE SIMPLIFY-SUMS-<))
 (142 142 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (142 142 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (142 142 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (142 142 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (142 142 (:REWRITE INTEGERP-<-CONSTANT))
 (142 142 (:REWRITE CONSTANT-<-INTEGERP))
 (142 142 (:REWRITE |(< (- x) c)|))
 (116 4 (:REWRITE |(+ x (if a b c))|))
 (108 108 (:REWRITE DEFAULT-PLUS-2))
 (108 108 (:REWRITE DEFAULT-PLUS-1))
 (106 106 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (106 106 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (106 106 (:REWRITE |(< (/ x) 0)|))
 (106 106 (:REWRITE |(< (* x y) 0)|))
 (96 8 (:REWRITE |(+ (if a b c) x)|))
 (64 64 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (64 64 (:REWRITE NORMALIZE-ADDENDS))
 (30 30 (:REWRITE DEFAULT-TIMES-2))
 (30 30 (:REWRITE DEFAULT-TIMES-1))
 (16 4 (:REWRITE |(- (if a b c))|))
 (12 12 (:REWRITE REDUCE-INTEGERP-+))
 (12 12 (:REWRITE INTEGERP-MINUS-X))
 (12 12 (:REWRITE |(* x (- y))|))
 (12 12 (:META META-INTEGERP-CORRECT))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (8 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 8 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (8 8 (:REWRITE |(equal c (/ x))|))
 (8 8 (:REWRITE |(equal c (- x))|))
 (8 8 (:REWRITE |(equal (/ x) c)|))
 (8 8 (:REWRITE |(equal (/ x) (/ y))|))
 (8 8 (:REWRITE |(equal (- x) c)|))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:REWRITE |(< 0 (/ x))|))
 (8 8 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 )
(RTL::R-NAT
 (103 3 (:REWRITE |(< (if a b c) x)|))
 (45 5 (:REWRITE ACL2-NUMBERP-X))
 (26 26 (:REWRITE THE-FLOOR-BELOW))
 (26 26 (:REWRITE THE-FLOOR-ABOVE))
 (26 26 (:REWRITE DEFAULT-LESS-THAN-2))
 (26 26 (:REWRITE DEFAULT-LESS-THAN-1))
 (23 23 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (23 23 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (23 23 (:REWRITE INTEGERP-<-CONSTANT))
 (23 23 (:REWRITE CONSTANT-<-INTEGERP))
 (23 23 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (23 23 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (23 23 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (23 23 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (23 23 (:REWRITE |(< c (- x))|))
 (23 23 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (23 23 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (23 23 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (23 23 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (23 23 (:REWRITE |(< (/ x) (/ y))|))
 (23 23 (:REWRITE |(< (- x) c)|))
 (23 23 (:REWRITE |(< (- x) (- y))|))
 (22 22 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (20 5 (:REWRITE RATIONALP-X))
 (13 13 (:REWRITE |(< (/ x) 0)|))
 (13 13 (:REWRITE |(< (* x y) 0)|))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 8 (:REWRITE ZP-OPEN))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE REDUCE-RATIONALP-+))
 (5 5 (:REWRITE REDUCE-RATIONALP-*))
 (5 5 (:REWRITE RATIONALP-MINUS-X))
 (5 5 (:REWRITE |(< (+ c/d x) y)|))
 (5 5 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:META META-RATIONALP-CORRECT))
 (4 4 (:REWRITE DEFAULT-MINUS))
 (3 3 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 )
(RTL::R-S-NAT
 (1575 85 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1197 37 (:REWRITE ZP-OPEN))
 (732 561 (:REWRITE DEFAULT-PLUS-1))
 (662 561 (:REWRITE DEFAULT-PLUS-2))
 (412 58 (:REWRITE |(+ x x)|))
 (233 40 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (215 187 (:REWRITE DEFAULT-MINUS))
 (184 23 (:REWRITE |(- (+ x y))|))
 (177 177 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (168 135 (:REWRITE DEFAULT-TIMES-2))
 (137 135 (:REWRITE DEFAULT-TIMES-1))
 (105 105 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (104 24 (:REWRITE |(- (* c x))|))
 (96 92 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (93 93 (:REWRITE THE-FLOOR-BELOW))
 (93 93 (:REWRITE THE-FLOOR-ABOVE))
 (93 93 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (93 93 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (93 93 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (93 93 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (93 93 (:REWRITE INTEGERP-<-CONSTANT))
 (93 93 (:REWRITE DEFAULT-LESS-THAN-2))
 (93 93 (:REWRITE DEFAULT-LESS-THAN-1))
 (93 93 (:REWRITE CONSTANT-<-INTEGERP))
 (93 93 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (93 93 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (93 93 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (93 93 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (93 93 (:REWRITE |(< c (- x))|))
 (93 93 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (93 93 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (93 93 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (93 93 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (93 93 (:REWRITE |(< (/ x) (/ y))|))
 (93 93 (:REWRITE |(< (- x) c)|))
 (93 93 (:REWRITE |(< (- x) (- y))|))
 (85 85 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (56 56 (:REWRITE |(+ c (+ d x))|))
 (55 55 (:REWRITE SIMPLIFY-SUMS-<))
 (51 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (31 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (23 23 (:REWRITE |(- (- x))|))
 (20 20 (:REWRITE |(< y (+ (- c) x))|))
 (20 20 (:REWRITE |(< x (+ c/d y))|))
 (15 15 (:REWRITE |(< 0 (/ x))|))
 (15 15 (:REWRITE |(< 0 (* x y))|))
 (15 11 (:REWRITE |(equal (- x) (- y))|))
 (13 13 (:REWRITE |(< (/ x) 0)|))
 (13 13 (:REWRITE |(< (* x y) 0)|))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (11 11 (:REWRITE |(equal c (/ x))|))
 (11 11 (:REWRITE |(equal c (- x))|))
 (11 11 (:REWRITE |(equal (/ x) c)|))
 (11 11 (:REWRITE |(equal (/ x) (/ y))|))
 (11 11 (:REWRITE |(equal (- x) c)|))
 (11 11 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (10 10 (:REWRITE REDUCE-INTEGERP-+))
 (10 10 (:REWRITE INTEGERP-MINUS-X))
 (10 10 (:REWRITE |(< (+ c/d x) y)|))
 (10 10 (:REWRITE |(< (+ (- c) x) y)|))
 (10 10 (:META META-INTEGERP-CORRECT))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 )
(RTL::R-INT
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 )
(RTL::S-INT
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 )
(RTL::G-C-D-LINEAR-COMBINATION
 (855 12 (:REWRITE |(< x (if a b c))|))
 (681 5 (:DEFINITION RTL::S-NAT))
 (680 5 (:DEFINITION RTL::R-NAT))
 (564 5 (:DEFINITION RTL::G-C-D-NAT))
 (546 18 (:REWRITE ZP-OPEN))
 (384 3 (:REWRITE |(< (if a b c) x)|))
 (277 192 (:REWRITE DEFAULT-PLUS-2))
 (270 84 (:REWRITE |(< c (- x))|))
 (269 192 (:REWRITE DEFAULT-PLUS-1))
 (264 90 (:REWRITE |(< (- x) (- y))|))
 (136 116 (:REWRITE DEFAULT-MINUS))
 (105 105 (:REWRITE THE-FLOOR-BELOW))
 (105 105 (:REWRITE THE-FLOOR-ABOVE))
 (105 105 (:REWRITE DEFAULT-LESS-THAN-2))
 (105 105 (:REWRITE DEFAULT-LESS-THAN-1))
 (92 92 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (90 90 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (90 90 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (90 90 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (90 90 (:REWRITE |(< (/ x) (/ y))|))
 (84 84 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (84 84 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (84 84 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (84 84 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (84 84 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (84 84 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (84 84 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (84 84 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (78 78 (:REWRITE SIMPLIFY-SUMS-<))
 (78 78 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (78 78 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (78 78 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (78 78 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (78 78 (:REWRITE INTEGERP-<-CONSTANT))
 (78 78 (:REWRITE CONSTANT-<-INTEGERP))
 (78 78 (:REWRITE |(< (- x) c)|))
 (52 32 (:REWRITE DEFAULT-TIMES-1))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (48 48 (:REWRITE |(< (/ x) 0)|))
 (48 48 (:REWRITE |(< (* x y) 0)|))
 (48 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (44 32 (:REWRITE DEFAULT-TIMES-2))
 (42 42 (:REWRITE |(- (- x))|))
 (32 8 (:REWRITE |(- (if a b c))|))
 (22 12 (:REWRITE |(equal (- x) (- y))|))
 (16 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (13 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 12 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (12 12 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (12 12 (:REWRITE |(equal c (/ x))|))
 (12 12 (:REWRITE |(equal c (- x))|))
 (12 12 (:REWRITE |(equal (/ x) c)|))
 (12 12 (:REWRITE |(equal (/ x) (/ y))|))
 (12 12 (:REWRITE |(equal (- x) c)|))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (12 12 (:REWRITE |(< 0 (/ x))|))
 (12 12 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (6 6 (:REWRITE |(- (* c x))|))
 (6 6 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(RTL::DIVIDES-G-C-D
 (21 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 12 (:REWRITE DEFAULT-TIMES-2))
 (18 12 (:REWRITE DEFAULT-TIMES-1))
 (17 3 (:REWRITE ACL2-NUMBERP-X))
 (7 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 1 (:REWRITE RATIONALP-X))
 (7 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 6 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 2 (:REWRITE DEFAULT-PLUS-2))
 (4 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:META META-RATIONALP-CORRECT))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(RTL::G-C-D-PRIME
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(equal c (/ x))|))
 (4 4 (:REWRITE |(equal c (- x))|))
 (4 4 (:REWRITE |(equal (/ x) c)|))
 (4 4 (:REWRITE |(equal (/ x) (/ y))|))
 (4 4 (:REWRITE |(equal (- x) c)|))
 (4 4 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(RTL::HACK
 (45 20 (:REWRITE DEFAULT-TIMES-2))
 (20 20 (:REWRITE DEFAULT-TIMES-1))
 (11 6 (:REWRITE DEFAULT-PLUS-2))
 (11 6 (:REWRITE DEFAULT-PLUS-1))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (7 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (4 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE NORMALIZE-ADDENDS))
 (3 3 (:REWRITE |(* c (* d x))|))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 )
(RTL::EUCLID
 (51 34 (:REWRITE DEFAULT-TIMES-2))
 (44 34 (:REWRITE DEFAULT-TIMES-1))
 (22 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (21 21 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (16 2 (:REWRITE ACL2-NUMBERP-X))
 (8 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 1 (:REWRITE RATIONALP-X))
 (6 6 (:REWRITE |(* c (* d x))|))
 (6 3 (:REWRITE DEFAULT-PLUS-2))
 (6 3 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE NORMALIZE-ADDENDS))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:META META-RATIONALP-CORRECT))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
