(M
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 )
(RTL::MERSENNE-19)
(RTL::MERSENNE-23)
(RTL::LEAST-DIVISOR-2
 (54 54 (:REWRITE DEFAULT-PLUS-2))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (30 21 (:REWRITE DEFAULT-LESS-THAN-2))
 (23 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (21 21 (:REWRITE THE-FLOOR-BELOW))
 (21 21 (:REWRITE THE-FLOOR-ABOVE))
 (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))
 (9 9 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:REWRITE |(+ c (+ d x))|))
 (7 7 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE DEFAULT-EXPT-2))
 (5 5 (:REWRITE DEFAULT-EXPT-1))
 (5 5 (:REWRITE |(expt 1/c n)|))
 (5 5 (:REWRITE |(expt (- x) n)|))
 (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))|))
 (3 2 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DEFAULT-TIMES-2))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2 2 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (2 2 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (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))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1 1 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (1 1 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1 1 (:LINEAR EXPT->=-1-TWO))
 (1 1 (:LINEAR EXPT->-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-ONE))
 (1 1 (:LINEAR EXPT-<-1-TWO))
 (1 1 (:LINEAR EXPT-<-1-ONE))
 )
(RTL::HACK-1
 (15 11 (:REWRITE DEFAULT-TIMES-2))
 (11 11 (: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 DEFAULT-LESS-THAN-2))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (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 NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (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::HACK-2
 (15 11 (:REWRITE DEFAULT-TIMES-2))
 (11 11 (: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 DEFAULT-LESS-THAN-2))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (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 NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (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::HACK-3)
(RTL::HACK-4)
(RTL::LEAST-DIVISOR-REWRITE-LEMMA-1
 (843 843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (843 843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (843 843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (843 843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (843 843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (539 218 (:REWRITE DEFAULT-LESS-THAN-2))
 (468 160 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (468 160 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (459 160 (:REWRITE SIMPLIFY-SUMS-<))
 (281 29 (:REWRITE ACL2-NUMBERP-X))
 (264 218 (:REWRITE DEFAULT-LESS-THAN-1))
 (249 213 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (218 218 (:REWRITE THE-FLOOR-BELOW))
 (218 218 (:REWRITE THE-FLOOR-ABOVE))
 (213 213 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (213 213 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (213 213 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (213 213 (:REWRITE INTEGERP-<-CONSTANT))
 (213 213 (:REWRITE CONSTANT-<-INTEGERP))
 (213 213 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (213 213 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (213 213 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (213 213 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (213 213 (:REWRITE |(< c (- x))|))
 (213 213 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (213 213 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (213 213 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (213 213 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (213 213 (:REWRITE |(< (/ x) (/ y))|))
 (213 213 (:REWRITE |(< (- x) c)|))
 (213 213 (:REWRITE |(< (- x) (- y))|))
 (145 145 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (145 145 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (126 18 (:REWRITE RATIONALP-X))
 (104 69 (:REWRITE DEFAULT-TIMES-1))
 (83 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (74 74 (:REWRITE DEFAULT-EXPT-2))
 (74 74 (:REWRITE DEFAULT-EXPT-1))
 (74 74 (:REWRITE |(expt 1/c n)|))
 (74 74 (:REWRITE |(expt (- x) n)|))
 (60 12 (:REWRITE |(+ c (+ d x))|))
 (57 57 (:REWRITE DEFAULT-PLUS-2))
 (57 57 (:REWRITE DEFAULT-PLUS-1))
 (49 49 (:REWRITE REDUCE-INTEGERP-+))
 (49 49 (:REWRITE INTEGERP-MINUS-X))
 (49 49 (:META META-INTEGERP-CORRECT))
 (45 45 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (45 45 (:REWRITE NORMALIZE-ADDENDS))
 (34 34 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (27 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (27 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (26 26 (:REWRITE |(< y (+ (- c) x))|))
 (26 26 (:REWRITE |(< x (+ c/d y))|))
 (18 18 (:REWRITE REDUCE-RATIONALP-+))
 (18 18 (:REWRITE REDUCE-RATIONALP-*))
 (18 18 (:REWRITE RATIONALP-MINUS-X))
 (18 18 (:META META-RATIONALP-CORRECT))
 (16 16 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (16 16 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (16 16 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (16 16 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<))
 (8 8 (:LINEAR EXPT->=-1-TWO))
 (8 8 (:LINEAR EXPT->-1-TWO))
 (8 8 (:LINEAR EXPT-<=-1-TWO))
 (8 8 (:LINEAR EXPT-<=-1-ONE))
 (8 8 (:LINEAR EXPT-<-1-TWO))
 (8 8 (:LINEAR EXPT-<-1-ONE))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (6 6 (:REWRITE |(< (/ x) 0)|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
 (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 |(* x (if a b c))|))
 (1 1 (:REWRITE |(* (if a b c) x)|))
 )
(RTL::HACK-5
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (5 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-TIMES-2))
 (2 2 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(< (* (/ x) y) 1) with (< x 0)|))
 )
(RTL::LEAST-DIVISOR-REWRITE-LEMMA-2
 (1395 31 (:DEFINITION RTL::LEAST-DIVISOR))
 (375 78 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B-EXPT))
 (229 229 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (229 229 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (229 229 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (229 229 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (229 229 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (185 47 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (142 49 (:REWRITE DEFAULT-LESS-THAN-1))
 (127 96 (:REWRITE DEFAULT-TIMES-2))
 (106 96 (:REWRITE DEFAULT-TIMES-1))
 (94 49 (:REWRITE DEFAULT-LESS-THAN-2))
 (92 47 (:REWRITE SIMPLIFY-SUMS-<))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (88 88 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (87 87 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (87 87 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (87 87 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (87 87 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (78 78 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B-EXPT))
 (78 78 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B-EXPT))
 (49 49 (:REWRITE THE-FLOOR-BELOW))
 (49 49 (:REWRITE THE-FLOOR-ABOVE))
 (49 49 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (49 49 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (49 49 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (48 48 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (48 48 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (48 48 (:REWRITE INTEGERP-<-CONSTANT))
 (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))|))
 (36 36 (:REWRITE REDUCE-INTEGERP-+))
 (36 36 (:REWRITE INTEGERP-MINUS-X))
 (36 36 (:META META-INTEGERP-CORRECT))
 (28 28 (:REWRITE DEFAULT-EXPT-2))
 (28 28 (:REWRITE DEFAULT-EXPT-1))
 (28 28 (:REWRITE |(expt 1/c n)|))
 (28 28 (:REWRITE |(expt (- x) n)|))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3H))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2H))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (13 13 (:REWRITE DEFAULT-DIVIDE))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (10 10 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (6 6 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (5 5 (:REWRITE |(expt c (* d n))|))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE |(equal c (/ x))|))
 (3 3 (:REWRITE |(equal c (- x))|))
 (3 3 (:REWRITE |(equal (/ x) c)|))
 (3 3 (:REWRITE |(equal (/ x) (/ y))|))
 (3 3 (:REWRITE |(equal (- x) c)|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (3 3 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (3 3 (:LINEAR EXPT-LINEAR-UPPER-<))
 (3 3 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (3 3 (:LINEAR EXPT-LINEAR-LOWER-<))
 (3 3 (:LINEAR EXPT->=-1-TWO))
 (3 3 (:LINEAR EXPT->-1-TWO))
 (3 3 (:LINEAR EXPT-<=-1-TWO))
 (3 3 (:LINEAR EXPT-<=-1-ONE))
 (3 3 (:LINEAR EXPT-<-1-TWO))
 (3 3 (:LINEAR EXPT-<-1-ONE))
 (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::LEAST-DIVISOR-REWRITE-LEMMA-3
 (411 24 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (393 65 (:REWRITE ACL2-NUMBERP-X))
 (297 162 (:REWRITE DEFAULT-LESS-THAN-2))
 (246 120 (:REWRITE SIMPLIFY-SUMS-<))
 (246 120 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (164 23 (:REWRITE RATIONALP-X))
 (162 162 (:REWRITE THE-FLOOR-BELOW))
 (162 162 (:REWRITE THE-FLOOR-ABOVE))
 (161 161 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (161 161 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (161 161 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (158 158 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (158 158 (:REWRITE INTEGERP-<-CONSTANT))
 (158 158 (:REWRITE CONSTANT-<-INTEGERP))
 (158 158 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (158 158 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (158 158 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (158 158 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (158 158 (:REWRITE |(< c (- x))|))
 (158 158 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (158 158 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (158 158 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (158 158 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (158 158 (:REWRITE |(< (/ x) (/ y))|))
 (158 158 (:REWRITE |(< (- x) c)|))
 (158 158 (:REWRITE |(< (- x) (- y))|))
 (155 155 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (155 155 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (155 155 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (155 155 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (155 155 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (155 155 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (111 24 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (111 24 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (63 46 (:REWRITE DEFAULT-TIMES-1))
 (48 48 (:REWRITE REDUCE-INTEGERP-+))
 (48 48 (:REWRITE INTEGERP-MINUS-X))
 (48 48 (:META META-INTEGERP-CORRECT))
 (46 46 (:REWRITE DEFAULT-TIMES-2))
 (36 36 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (36 36 (:REWRITE NORMALIZE-ADDENDS))
 (36 36 (:REWRITE DEFAULT-PLUS-2))
 (36 36 (:REWRITE DEFAULT-PLUS-1))
 (24 24 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (24 24 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (24 24 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (24 24 (:REWRITE |(equal c (/ x))|))
 (24 24 (:REWRITE |(equal c (- x))|))
 (24 24 (:REWRITE |(equal (/ x) c)|))
 (24 24 (:REWRITE |(equal (/ x) (/ y))|))
 (24 24 (:REWRITE |(equal (- x) c)|))
 (24 24 (:REWRITE |(equal (- x) (- y))|))
 (23 23 (:REWRITE REDUCE-RATIONALP-+))
 (23 23 (:REWRITE REDUCE-RATIONALP-*))
 (23 23 (:REWRITE RATIONALP-MINUS-X))
 (23 23 (:META META-RATIONALP-CORRECT))
 (21 21 (:REWRITE DEFAULT-EXPT-2))
 (21 21 (:REWRITE DEFAULT-EXPT-1))
 (21 21 (:REWRITE |(expt 1/c n)|))
 (21 21 (:REWRITE |(expt (- x) n)|))
 (17 17 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (3 3 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (3 3 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2 2 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (2 2 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (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 |(equal x (if a b c))|))
 (1 1 (:REWRITE |(equal (if a b c) x)|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1 1 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (1 1 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1 1 (:LINEAR EXPT->=-1-TWO))
 (1 1 (:LINEAR EXPT->-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-ONE))
 (1 1 (:LINEAR EXPT-<-1-TWO))
 (1 1 (:LINEAR EXPT-<-1-ONE))
 )
(RTL::LEAST-DIVISOR-REWRITE
 (120 54 (:REWRITE DEFAULT-LESS-THAN-2))
 (92 92 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (92 92 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (92 92 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (92 92 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (92 92 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (87 51 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (87 51 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (78 51 (:REWRITE SIMPLIFY-SUMS-<))
 (68 10 (:REWRITE ACL2-NUMBERP-X))
 (54 54 (:REWRITE THE-FLOOR-BELOW))
 (54 54 (:REWRITE THE-FLOOR-ABOVE))
 (51 51 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (51 51 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (51 51 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (51 51 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (51 51 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (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))|))
 (39 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (31 31 (:REWRITE REDUCE-INTEGERP-+))
 (31 31 (:REWRITE INTEGERP-MINUS-X))
 (31 31 (:META META-INTEGERP-CORRECT))
 (29 29 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (29 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (29 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (29 5 (:REWRITE RATIONALP-X))
 (11 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 6 (:REWRITE DEFAULT-TIMES-1))
 (5 5 (:REWRITE REDUCE-RATIONALP-+))
 (5 5 (:REWRITE REDUCE-RATIONALP-*))
 (5 5 (:REWRITE RATIONALP-MINUS-X))
 (5 5 (:META META-RATIONALP-CORRECT))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE DEFAULT-EXPT-1))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (3 3 (:REWRITE |(equal c (/ x))|))
 (3 3 (:REWRITE |(equal c (- x))|))
 (3 3 (:REWRITE |(equal (/ x) c)|))
 (3 3 (:REWRITE |(equal (/ x) (/ y))|))
 (3 3 (:REWRITE |(equal (- x) c)|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (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 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))|))
 )
(RTL::MERSENNE-31-REVISITED)
(RTL::THEOREM-103
 (8831 15 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (6074 72 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5806 99 (:REWRITE CANCEL-MOD-+))
 (4695 4695 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4695 4695 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3776 49 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3575 99 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (3565 713 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (3565 713 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (3523 99 (:REWRITE MOD-X-Y-=-X . 3))
 (3009 713 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2894 690 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2374 258 (:REWRITE INTEGERP-MINUS-X))
 (2131 1427 (:REWRITE DEFAULT-TIMES-2))
 (2054 99 (:REWRITE MOD-ZERO . 3))
 (1913 99 (:REWRITE DEFAULT-MOD-RATIO))
 (1679 1427 (:REWRITE DEFAULT-TIMES-1))
 (1636 1636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1636 1636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1636 1636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1636 1636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1636 1636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1621 387 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1512 126 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1449 63 (:LINEAR EXPT->-1-ONE))
 (1141 63 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (1094 554 (:REWRITE DEFAULT-PLUS-2))
 (1092 198 (:REWRITE |(* (- x) y)|))
 (945 126 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (903 903 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (903 903 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (903 903 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (903 903 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (882 63 (:LINEAR EXPT-X->=-X))
 (882 63 (:LINEAR EXPT-X->-X))
 (882 63 (:LINEAR EXPT->=-1-ONE))
 (868 49 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (829 554 (:REWRITE DEFAULT-PLUS-1))
 (807 160 (:REWRITE DEFAULT-MINUS))
 (772 772 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (713 713 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (713 713 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (690 690 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (690 690 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (690 291 (:REWRITE NORMALIZE-ADDENDS))
 (684 99 (:REWRITE MOD-X-Y-=-X . 4))
 (645 153 (:REWRITE |(- (* c x))|))
 (621 99 (:REWRITE MOD-ZERO . 4))
 (621 99 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (621 99 (:REWRITE MOD-X-Y-=-X . 2))
 (621 99 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (621 99 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (620 314 (:REWRITE INTEGERP-<-CONSTANT))
 (576 387 (:REWRITE DEFAULT-LESS-THAN-1))
 (558 99 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (558 99 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (505 115 (:REWRITE |(* c (* d x))|))
 (504 252 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (497 308 (:REWRITE SIMPLIFY-SUMS-<))
 (497 308 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (497 308 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (452 452 (:REWRITE DEFAULT-EXPT-2))
 (452 452 (:REWRITE DEFAULT-EXPT-1))
 (452 452 (:REWRITE |(expt 1/c n)|))
 (452 452 (:REWRITE |(expt (- x) n)|))
 (450 18 (:REWRITE |(* x (+ y z))|))
 (442 364 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (387 387 (:REWRITE THE-FLOOR-BELOW))
 (387 387 (:REWRITE THE-FLOOR-ABOVE))
 (387 387 (:REWRITE DEFAULT-LESS-THAN-2))
 (383 64 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (383 64 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (329 15 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (314 314 (:REWRITE CONSTANT-<-INTEGERP))
 (314 314 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (314 314 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (314 314 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (314 314 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (314 314 (:REWRITE |(< c (- x))|))
 (314 314 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (314 314 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (314 314 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (314 314 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (314 314 (:REWRITE |(< (/ x) (/ y))|))
 (314 314 (:REWRITE |(< (- x) c)|))
 (314 314 (:REWRITE |(< (- x) (- y))|))
 (308 308 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (301 7 (:REWRITE |(integerp (- x))|))
 (294 7 (:REWRITE BUBBLE-DOWN-+-BUBBLE-DOWN))
 (284 284 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (252 252 (:TYPE-PRESCRIPTION NATP))
 (252 252 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (252 252 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (252 252 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (194 194 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (179 179 (:TYPE-PRESCRIPTION ABS))
 (166 166 (:REWRITE REDUCE-INTEGERP-+))
 (166 166 (:META META-INTEGERP-CORRECT))
 (162 99 (:REWRITE DEFAULT-MOD-1))
 (155 64 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (155 42 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (145 15 (:REWRITE ACL2-NUMBERP-X))
 (126 126 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (126 126 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (99 99 (:REWRITE DEFAULT-MOD-2))
 (95 95 (:REWRITE |(< (+ c/d x) y)|))
 (78 15 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (77 7 (:REWRITE |(- (+ x y))|))
 (72 72 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (65 5 (:REWRITE RATIONALP-X))
 (64 64 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (64 64 (:REWRITE |(mod x (- y))| . 3))
 (64 64 (:REWRITE |(mod x (- y))| . 2))
 (64 64 (:REWRITE |(mod x (- y))| . 1))
 (64 64 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (64 64 (:REWRITE |(mod (- x) y)| . 3))
 (64 64 (:REWRITE |(mod (- x) y)| . 2))
 (64 64 (:REWRITE |(mod (- x) y)| . 1))
 (64 64 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (63 63 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (63 63 (:LINEAR EXPT-LINEAR-UPPER-<))
 (63 63 (:LINEAR EXPT-LINEAR-LOWER-<))
 (63 63 (:LINEAR EXPT->=-1-TWO))
 (63 63 (:LINEAR EXPT->-1-TWO))
 (63 63 (:LINEAR EXPT-<=-1-TWO))
 (63 63 (:LINEAR EXPT-<=-1-ONE))
 (63 63 (:LINEAR EXPT-<-1-TWO))
 (63 63 (:LINEAR EXPT-<-1-ONE))
 (49 49 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (49 49 (:REWRITE |(equal c (/ x))|))
 (49 49 (:REWRITE |(equal c (- x))|))
 (49 49 (:REWRITE |(equal (/ x) c)|))
 (49 49 (:REWRITE |(equal (/ x) (/ y))|))
 (49 49 (:REWRITE |(equal (- x) c)|))
 (49 49 (:REWRITE |(equal (- x) (- y))|))
 (45 45 (:REWRITE |(< (+ (- c) x) y)|))
 (42 14 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (33 33 (:REWRITE |(< y (+ (- c) x))|))
 (33 33 (:REWRITE |(< x (+ c/d y))|))
 (28 7 (:REWRITE |(+ (* c x) (* d x))|))
 (23 23 (:REWRITE RTL::NO-INTEGER-7-8))
 (22 1 (:LINEAR MOD-BOUNDS-3))
 (21 21 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (21 21 (:REWRITE DEFAULT-DIVIDE))
 (18 18 (:REWRITE |(equal (+ (- c) x) y)|))
 (14 14 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (14 14 (:DEFINITION FIX))
 (10 2 (:LINEAR MOD-BOUNDS-2))
 (8 8 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (7 7 (:REWRITE FOLD-CONSTS-IN-+))
 (7 7 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (7 7 (:REWRITE |(equal (expt 2 n) c)|))
 (7 7 (:REWRITE |(* 0 x)|))
 (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 |(< 0 (/ x))|))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 (5 5 (:REWRITE REDUCE-RATIONALP-+))
 (5 5 (:REWRITE REDUCE-RATIONALP-*))
 (5 5 (:REWRITE RATIONALP-MINUS-X))
 (5 5 (:REWRITE |(equal x (if a b c))|))
 (5 5 (:META META-RATIONALP-CORRECT))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(RTL::HACK-6)
(RTL::HACK-7
 (190 190 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (190 190 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (190 190 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (190 190 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (190 190 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (85 23 (:REWRITE DEFAULT-TIMES-2))
 (74 11 (:REWRITE DEFAULT-LESS-THAN-1))
 (53 8 (:REWRITE SIMPLIFY-SUMS-<))
 (53 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (43 2 (:LINEAR EXPT-<=-1-TWO))
 (42 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (26 23 (:REWRITE DEFAULT-TIMES-1))
 (19 19 (:REWRITE DEFAULT-EXPT-2))
 (19 19 (:REWRITE DEFAULT-EXPT-1))
 (19 19 (:REWRITE |(expt 1/c n)|))
 (19 19 (:REWRITE |(expt (- x) n)|))
 (17 17 (:REWRITE DEFAULT-PLUS-2))
 (17 17 (:REWRITE DEFAULT-PLUS-1))
 (13 13 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (13 13 (:REWRITE NORMALIZE-ADDENDS))
 (11 11 (:REWRITE THE-FLOOR-BELOW))
 (11 11 (:REWRITE THE-FLOOR-ABOVE))
 (11 11 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (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))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (4 4 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (4 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<))
 (2 2 (:LINEAR EXPT->=-1-TWO))
 (2 2 (:LINEAR EXPT->-1-TWO))
 (2 2 (:LINEAR EXPT-<=-1-ONE))
 (2 2 (:LINEAR EXPT-<-1-TWO))
 (2 2 (:LINEAR EXPT-<-1-ONE))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(RTL::HACK-8
 (315 315 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (315 315 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (315 315 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (315 315 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (315 315 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (122 34 (:REWRITE DEFAULT-TIMES-2))
 (122 23 (:REWRITE DEFAULT-LESS-THAN-1))
 (115 23 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (85 3 (:LINEAR EXPT-<=-1-TWO))
 (79 16 (:REWRITE SIMPLIFY-SUMS-<))
 (79 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (43 3 (:LINEAR EXPT-<-1-TWO))
 (38 34 (:REWRITE DEFAULT-TIMES-1))
 (26 26 (:REWRITE DEFAULT-EXPT-2))
 (26 26 (:REWRITE DEFAULT-EXPT-1))
 (26 26 (:REWRITE |(expt 1/c n)|))
 (26 26 (:REWRITE |(expt (- x) n)|))
 (23 23 (:REWRITE THE-FLOOR-BELOW))
 (23 23 (:REWRITE THE-FLOOR-ABOVE))
 (23 23 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE DEFAULT-PLUS-2))
 (23 23 (:REWRITE DEFAULT-PLUS-1))
 (23 23 (:REWRITE DEFAULT-LESS-THAN-2))
 (20 20 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (20 20 (:REWRITE INTEGERP-<-CONSTANT))
 (20 20 (:REWRITE CONSTANT-<-INTEGERP))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (- x))|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) (/ y))|))
 (20 20 (:REWRITE |(< (- x) c)|))
 (20 20 (:REWRITE |(< (- x) (- y))|))
 (19 19 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (17 17 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (17 17 (:REWRITE NORMALIZE-ADDENDS))
 (12 3 (:REWRITE |(+ c (+ d x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (6 6 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (5 5 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:REWRITE |(+ 0 x)|))
 (3 3 (:META META-INTEGERP-CORRECT))
 (3 3 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (3 3 (:LINEAR EXPT-LINEAR-UPPER-<))
 (3 3 (:LINEAR EXPT-LINEAR-LOWER-<))
 (3 3 (:LINEAR EXPT->=-1-TWO))
 (3 3 (:LINEAR EXPT->-1-TWO))
 (3 3 (:LINEAR EXPT-<=-1-ONE))
 (3 3 (:LINEAR EXPT-<-1-ONE))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(RTL::HACK-9)
(RTL::EXPT-2-P-BND)
(RTL::THEOREM-103-COROLLARY
 (20953 20953 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (20953 20953 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (20953 20953 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (19025 3805 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (19025 3805 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (19001 3805 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (16606 3326 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (15176 15176 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (15176 15176 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (15176 15176 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (15176 15176 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (15176 15176 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (15176 15176 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (7420 140 (:REWRITE CANCEL-MOD-+))
 (7300 3574 (:REWRITE DEFAULT-PLUS-2))
 (6000 407 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4908 407 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4352 136 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (4200 140 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4200 140 (:REWRITE MOD-X-Y-=-X . 3))
 (3943 679 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3805 3805 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (3805 3805 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (3756 3027 (:REWRITE DEFAULT-LESS-THAN-1))
 (3683 463 (:REWRITE INTEGERP-MINUS-X))
 (3574 3574 (:REWRITE DEFAULT-PLUS-1))
 (3326 3326 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (3326 3326 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (3293 3027 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3293 3027 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3228 2463 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3228 2463 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3198 3027 (:REWRITE DEFAULT-LESS-THAN-2))
 (3080 140 (:REWRITE MOD-ZERO . 3))
 (3027 3027 (:REWRITE THE-FLOOR-BELOW))
 (3027 3027 (:REWRITE THE-FLOOR-ABOVE))
 (2856 136 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (2665 2665 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2665 2665 (:REWRITE INTEGERP-<-CONSTANT))
 (2665 2665 (:REWRITE CONSTANT-<-INTEGERP))
 (2665 2665 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2665 2665 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2665 2665 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2665 2665 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2665 2665 (:REWRITE |(< c (- x))|))
 (2665 2665 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2665 2665 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2665 2665 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2665 2665 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2665 2665 (:REWRITE |(< (/ x) (/ y))|))
 (2665 2665 (:REWRITE |(< (- x) c)|))
 (2665 2665 (:REWRITE |(< (- x) (- y))|))
 (2634 2463 (:REWRITE SIMPLIFY-SUMS-<))
 (2380 280 (:REWRITE |(* (- x) y)|))
 (2026 2026 (:REWRITE DEFAULT-TIMES-2))
 (2026 2026 (:REWRITE DEFAULT-TIMES-1))
 (1904 1904 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1904 1904 (:REWRITE NORMALIZE-ADDENDS))
 (1684 421 (:REWRITE |(* y x)|))
 (1540 140 (:REWRITE DEFAULT-MOD-RATIO))
 (1465 1465 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1400 280 (:REWRITE DEFAULT-MINUS))
 (1360 272 (:REWRITE |(+ y x)|))
 (1262 1262 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1262 1262 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1262 1262 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1262 1262 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1260 280 (:REWRITE |(- (* c x))|))
 (1218 126 (:REWRITE ACL2-NUMBERP-X))
 (972 972 (:REWRITE |(< (+ c/d x) y)|))
 (828 407 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (700 140 (:REWRITE MOD-ZERO . 4))
 (700 140 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (700 140 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (700 140 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (700 140 (:REWRITE MOD-X-Y-=-X . 4))
 (700 140 (:REWRITE MOD-X-Y-=-X . 2))
 (700 140 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (700 140 (:REWRITE MOD-CANCEL-*-CONST))
 (700 140 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (700 140 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (700 140 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (679 679 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (610 610 (:REWRITE |(< (+ (- c) x) y)|))
 (546 42 (:REWRITE RATIONALP-X))
 (532 532 (:TYPE-PRESCRIPTION ABS))
 (432 432 (:REWRITE DEFAULT-EXPT-2))
 (432 432 (:REWRITE DEFAULT-EXPT-1))
 (432 432 (:REWRITE |(expt 1/c n)|))
 (432 432 (:REWRITE |(expt (- x) n)|))
 (407 407 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (407 407 (:REWRITE |(equal c (/ x))|))
 (407 407 (:REWRITE |(equal c (- x))|))
 (407 407 (:REWRITE |(equal (/ x) c)|))
 (407 407 (:REWRITE |(equal (/ x) (/ y))|))
 (407 407 (:REWRITE |(equal (- x) c)|))
 (407 407 (:REWRITE |(equal (- x) (- y))|))
 (323 323 (:REWRITE REDUCE-INTEGERP-+))
 (323 323 (:META META-INTEGERP-CORRECT))
 (240 1 (:LINEAR RTL::MOD-BND-2))
 (140 140 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (140 140 (:REWRITE DEFAULT-MOD-2))
 (140 140 (:REWRITE DEFAULT-MOD-1))
 (140 140 (:REWRITE |(mod x (- y))| . 3))
 (140 140 (:REWRITE |(mod x (- y))| . 2))
 (140 140 (:REWRITE |(mod x (- y))| . 1))
 (140 140 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (140 140 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (140 140 (:REWRITE |(mod (- x) y)| . 3))
 (140 140 (:REWRITE |(mod (- x) y)| . 2))
 (140 140 (:REWRITE |(mod (- x) y)| . 1))
 (140 140 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (136 136 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (43 43 (:REWRITE |(equal x (if a b c))|))
 (43 43 (:REWRITE |(equal (+ (- c) x) y)|))
 (42 42 (:REWRITE REDUCE-RATIONALP-+))
 (42 42 (:REWRITE REDUCE-RATIONALP-*))
 (42 42 (:REWRITE RATIONALP-MINUS-X))
 (42 42 (:META META-RATIONALP-CORRECT))
 (22 1 (:LINEAR MOD-BOUNDS-3))
 (19 19 (:REWRITE ODD-EXPT-THM))
 (17 17 (:REWRITE |(< y (+ (- c) x))|))
 (17 17 (:REWRITE |(< x (+ c/d y))|))
 (12 6 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (10 2 (:LINEAR MOD-BOUNDS-2))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (6 6 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (6 6 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (6 6 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2 2 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1 1 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1 1 (:LINEAR EXPT->=-1-TWO))
 (1 1 (:LINEAR EXPT->-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-ONE))
 (1 1 (:LINEAR EXPT-<-1-TWO))
 (1 1 (:LINEAR EXPT-<-1-ONE))
 )
(RTL::MERSENNE-23-REVISITED)
(RTL::MERSENNE-999671-REVISITED
 (2 2 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2 2 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2 2 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (2 2 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2 2 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 )
