(DM::FIND-ORDER
 (1456 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1448 2 (:LINEAR RTL::MOD-BND-2))
 (1104 69 (:REWRITE RATIONALP-X))
 (938 234 (:REWRITE DEFAULT-LESS-THAN-2))
 (790 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (730 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (684 4 (:LINEAR MOD-BOUNDS-2))
 (684 4 (:LINEAR MOD-BOUNDS-1))
 (661 218 (:REWRITE DEFAULT-LESS-THAN-1))
 (486 54 (:REWRITE ACL2-NUMBERP-X))
 (426 36 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (422 18 (:LINEAR EXPT-<=-1-ONE))
 (408 18 (:LINEAR EXPT->=-1-TWO))
 (408 18 (:LINEAR EXPT->-1-TWO))
 (408 18 (:LINEAR EXPT-<-1-ONE))
 (378 36 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (374 18 (:LINEAR EXPT-X->=-X))
 (374 18 (:LINEAR EXPT->=-1-ONE))
 (374 18 (:LINEAR EXPT-<=-1-TWO))
 (360 18 (:LINEAR EXPT-X->-X))
 (360 18 (:LINEAR EXPT->-1-ONE))
 (360 18 (:LINEAR EXPT-<-1-TWO))
 (279 45 (:REWRITE DEFAULT-TIMES-1))
 (274 45 (:REWRITE DEFAULT-TIMES-2))
 (265 265 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (265 265 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (254 189 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (234 234 (:REWRITE THE-FLOOR-BELOW))
 (234 234 (:REWRITE THE-FLOOR-ABOVE))
 (204 2 (:LINEAR MOD-BOUNDS-3))
 (196 196 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (196 196 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (196 196 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (196 196 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (196 196 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (196 196 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (196 196 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (196 196 (:REWRITE |(< c (- x))|))
 (196 196 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (196 196 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (196 196 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (196 196 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (196 196 (:REWRITE |(< (/ x) (/ y))|))
 (196 196 (:REWRITE |(< (- x) (- y))|))
 (189 189 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (189 189 (:REWRITE INTEGERP-<-CONSTANT))
 (189 189 (:REWRITE CONSTANT-<-INTEGERP))
 (182 182 (:REWRITE DEFAULT-PLUS-2))
 (160 32 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (152 32 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (88 88 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (86 86 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (86 86 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (86 86 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (80 2 (:LINEAR RTL::MOD-BND-1))
 (76 76 (:REWRITE REDUCE-INTEGERP-+))
 (76 76 (:REWRITE INTEGERP-MINUS-X))
 (76 76 (:META META-INTEGERP-CORRECT))
 (76 1 (:REWRITE MOD-ZERO . 4))
 (70 1 (:REWRITE MOD-X-Y-=-X . 4))
 (70 1 (:REWRITE MOD-X-Y-=-X . 3))
 (69 69 (:REWRITE RATIONALP-MINUS-X))
 (69 1 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (67 67 (:REWRITE REDUCE-RATIONALP-+))
 (67 67 (:META META-RATIONALP-CORRECT))
 (66 1 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (64 32 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (59 59 (:REWRITE |(< 0 (/ x))|))
 (59 59 (:REWRITE |(< 0 (* x y))|))
 (55 1 (:REWRITE CANCEL-MOD-+))
 (52 32 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (52 32 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (43 4 (:REWRITE DEFAULT-MOD-1))
 (37 37 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (37 1 (:REWRITE MOD-ZERO . 3))
 (36 36 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (36 36 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (32 32 (:TYPE-PRESCRIPTION NATP))
 (32 32 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (32 32 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (32 32 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (32 32 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (32 32 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (32 32 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (32 32 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (32 32 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (29 1 (:REWRITE |(integerp (- x))|))
 (28 28 (:REWRITE |(< (/ x) 0)|))
 (28 28 (:REWRITE |(< (* x y) 0)|))
 (27 27 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (26 26 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (23 23 (:REWRITE |(+ c (+ d x))|))
 (19 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (18 18 (:REWRITE DEFAULT-DIVIDE))
 (18 18 (:REWRITE |(< y (+ (- c) x))|))
 (18 18 (:REWRITE |(< x (+ c/d y))|))
 (18 18 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (18 18 (:LINEAR EXPT-LINEAR-UPPER-<))
 (18 18 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (18 18 (:LINEAR EXPT-LINEAR-LOWER-<))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (16 16 (:REWRITE |(< (+ c/d x) y)|))
 (16 16 (:REWRITE |(< (+ (- c) x) y)|))
 (13 1 (:REWRITE |(* (- x) y)|))
 (9 9 (:REWRITE FOLD-CONSTS-IN-+))
 (9 1 (:REWRITE |(equal (expt x n) 1)|))
 (8 2 (:REWRITE |(integerp (expt x n))|))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE |(equal c (/ x))|))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (/ x) c)|))
 (6 6 (:REWRITE |(equal (/ x) (/ y))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (5 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (5 1 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (5 1 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (5 1 (:REWRITE MOD-X-Y-=-X . 2))
 (5 1 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (5 1 (:REWRITE MOD-CANCEL-*-CONST))
 (5 1 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (5 1 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (5 1 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (5 1 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (4 4 (:REWRITE DEFAULT-MOD-2))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE DEFAULT-EXPT-2))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1 1 (:REWRITE |(mod x (- y))| . 3))
 (1 1 (:REWRITE |(mod x (- y))| . 2))
 (1 1 (:REWRITE |(mod x (- y))| . 1))
 (1 1 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(mod (- x) y)| . 3))
 (1 1 (:REWRITE |(mod (- x) y)| . 2))
 (1 1 (:REWRITE |(mod (- x) y)| . 1))
 (1 1 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(expt 1/c n)|))
 (1 1 (:REWRITE |(expt (- x) n)|))
 (1 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (1 1 (:REWRITE |(equal (expt x n) 0)|))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(DM::ORDER)
(DM::ROOTP-FIND-ORDER
 (15084 9 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (8288 16 (:REWRITE |(< (if a b c) x)|))
 (8219 69 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7560 9 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (6868 10 (:LINEAR RTL::MOD-BND-2))
 (5350 268 (:REWRITE RATIONALP-X))
 (4483 1978 (:REWRITE DEFAULT-LESS-THAN-2))
 (4382 1924 (:REWRITE DEFAULT-LESS-THAN-1))
 (4370 691 (:REWRITE DEFAULT-TIMES-1))
 (4247 691 (:REWRITE DEFAULT-TIMES-2))
 (4115 538 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (4115 538 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (3971 269 (:LINEAR EXPT-<=-1-ONE))
 (3846 269 (:LINEAR EXPT->=-1-TWO))
 (3846 269 (:LINEAR EXPT->-1-TWO))
 (3846 269 (:LINEAR EXPT-<-1-ONE))
 (3764 538 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (3639 538 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (3495 269 (:LINEAR EXPT-X->=-X))
 (3495 269 (:LINEAR EXPT->=-1-ONE))
 (3495 269 (:LINEAR EXPT-<=-1-TWO))
 (3370 269 (:LINEAR EXPT-X->-X))
 (3370 269 (:LINEAR EXPT->-1-ONE))
 (3370 269 (:LINEAR EXPT-<-1-TWO))
 (3280 3280 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3280 3280 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (3220 25 (:REWRITE MOD-ZERO . 4))
 (3070 25 (:REWRITE MOD-X-Y-=-X . 4))
 (3070 25 (:REWRITE MOD-X-Y-=-X . 3))
 (2931 1878 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2928 25 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (2853 25 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2814 1878 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2476 1878 (:REWRITE SIMPLIFY-SUMS-<))
 (2332 20 (:LINEAR MOD-BOUNDS-2))
 (2205 25 (:REWRITE CANCEL-MOD-+))
 (2109 388 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1978 1978 (:REWRITE THE-FLOOR-BELOW))
 (1978 1978 (:REWRITE THE-FLOOR-ABOVE))
 (1945 388 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1878 1878 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1878 1878 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1878 1878 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1878 1878 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1878 1878 (:REWRITE INTEGERP-<-CONSTANT))
 (1878 1878 (:REWRITE CONSTANT-<-INTEGERP))
 (1878 1878 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1878 1878 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1878 1878 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1878 1878 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1878 1878 (:REWRITE |(< c (- x))|))
 (1878 1878 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1878 1878 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1878 1878 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1878 1878 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1878 1878 (:REWRITE |(< (/ x) (/ y))|))
 (1878 1878 (:REWRITE |(< (- x) c)|))
 (1878 1878 (:REWRITE |(< (- x) (- y))|))
 (1656 184 (:REWRITE ACL2-NUMBERP-X))
 (1485 25 (:REWRITE MOD-ZERO . 3))
 (1410 1410 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1410 1410 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1410 1410 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (945 388 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (900 10 (:LINEAR MOD-BOUNDS-3))
 (869 388 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (869 388 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (743 25 (:REWRITE MOD-X-Y-=-X . 2))
 (743 25 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (743 25 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (729 729 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (714 25 (:REWRITE |(integerp (- x))|))
 (626 25 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (626 25 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (626 25 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (626 25 (:REWRITE MOD-CANCEL-*-CONST))
 (626 25 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (626 25 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (620 620 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (620 620 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (620 620 (:REWRITE |(< 0 (/ x))|))
 (620 620 (:REWRITE |(< 0 (* x y))|))
 (618 618 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (618 618 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (557 388 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (557 388 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (557 388 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (557 388 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (557 388 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (557 388 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (557 388 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (557 388 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (534 53 (:REWRITE DEFAULT-MOD-1))
 (495 25 (:REWRITE |(* (- x) y)|))
 (470 301 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (388 388 (:TYPE-PRESCRIPTION NATP))
 (346 346 (:REWRITE REDUCE-INTEGERP-+))
 (346 346 (:REWRITE INTEGERP-MINUS-X))
 (346 346 (:META META-INTEGERP-CORRECT))
 (300 300 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (300 300 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (300 300 (:REWRITE DEFAULT-DIVIDE))
 (290 69 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (269 269 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (269 269 (:LINEAR EXPT-LINEAR-UPPER-<))
 (269 269 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (269 269 (:LINEAR EXPT-LINEAR-LOWER-<))
 (268 268 (:REWRITE RATIONALP-MINUS-X))
 (250 250 (:REWRITE REDUCE-RATIONALP-+))
 (250 250 (:META META-RATIONALP-CORRECT))
 (179 179 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (179 179 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (179 179 (:REWRITE |(< (/ x) 0)|))
 (179 179 (:REWRITE |(< (* x y) 0)|))
 (135 27 (:REWRITE |(+ y x)|))
 (126 45 (:REWRITE NORMALIZE-ADDENDS))
 (99 90 (:REWRITE DEFAULT-PLUS-1))
 (90 90 (:REWRITE DEFAULT-PLUS-2))
 (72 18 (:REWRITE |(integerp (expt x n))|))
 (72 8 (:REWRITE |(equal (expt x n) 1)|))
 (70 34 (:REWRITE DEFAULT-MINUS))
 (69 69 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (69 69 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (69 69 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (69 69 (:REWRITE |(equal c (/ x))|))
 (69 69 (:REWRITE |(equal c (- x))|))
 (69 69 (:REWRITE |(equal (/ x) c)|))
 (69 69 (:REWRITE |(equal (/ x) (/ y))|))
 (69 69 (:REWRITE |(equal (- x) c)|))
 (69 69 (:REWRITE |(equal (- x) (- y))|))
 (60 60 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (53 53 (:REWRITE DEFAULT-MOD-2))
 (45 9 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (36 36 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (32 32 (:REWRITE ZP-OPEN))
 (27 27 (:REWRITE DEFAULT-EXPT-2))
 (27 27 (:REWRITE |(equal (+ (- c) x) y)|))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (25 25 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (25 25 (:REWRITE |(mod x (- y))| . 3))
 (25 25 (:REWRITE |(mod x (- y))| . 2))
 (25 25 (:REWRITE |(mod x (- y))| . 1))
 (25 25 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (25 25 (:REWRITE |(mod (- x) y)| . 3))
 (25 25 (:REWRITE |(mod (- x) y)| . 2))
 (25 25 (:REWRITE |(mod (- x) y)| . 1))
 (25 25 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (25 25 (:REWRITE |(equal (expt x n) 0)|))
 (25 25 (:REWRITE |(- (* c x))|))
 (16 16 (:REWRITE |(expt 1/c n)|))
 (16 16 (:REWRITE |(expt (- x) n)|))
 (10 10 (:LINEAR RTL::MOD-BND-3))
 (9 9 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (9 9 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (9 9 (:REWRITE |(+ x (- x))|))
 (9 9 (:REWRITE |(+ c (+ d x))|))
 (9 9 (:REWRITE |(+ 0 x)|))
 (6 6 (:REWRITE |(< y (+ (- c) x))|))
 (6 6 (:REWRITE |(< x (+ c/d y))|))
 )
(DM::ROOTP-ORDER
 (724 1 (:LINEAR RTL::MOD-BND-2))
 (377 25 (:REWRITE DEFAULT-LESS-THAN-2))
 (368 28 (:REWRITE RATIONALP-X))
 (342 2 (:LINEAR MOD-BOUNDS-2))
 (342 2 (:LINEAR MOD-BOUNDS-1))
 (308 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (216 24 (:REWRITE ACL2-NUMBERP-X))
 (206 17 (:REWRITE DEFAULT-LESS-THAN-1))
 (102 1 (:LINEAR MOD-BOUNDS-3))
 (85 5 (:REWRITE |(* y x)|))
 (83 83 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (75 15 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (75 15 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (75 10 (:REWRITE DEFAULT-TIMES-2))
 (75 10 (:REWRITE DEFAULT-TIMES-1))
 (53 1 (:LINEAR EXPT-<=-1-ONE))
 (52 2 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (51 1 (:LINEAR EXPT->=-1-TWO))
 (51 1 (:LINEAR EXPT->-1-TWO))
 (51 1 (:LINEAR EXPT-<-1-ONE))
 (49 1 (:LINEAR EXPT-X->=-X))
 (49 1 (:LINEAR EXPT->=-1-ONE))
 (49 1 (:LINEAR EXPT-<=-1-TWO))
 (48 2 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (47 1 (:LINEAR EXPT-X->-X))
 (47 1 (:LINEAR EXPT->-1-ONE))
 (47 1 (:LINEAR EXPT-<-1-TWO))
 (40 1 (:LINEAR RTL::MOD-BND-1))
 (30 15 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (29 29 (:REWRITE REDUCE-INTEGERP-+))
 (29 29 (:REWRITE INTEGERP-MINUS-X))
 (29 29 (:META META-INTEGERP-CORRECT))
 (28 28 (:REWRITE REDUCE-RATIONALP-+))
 (28 28 (:REWRITE REDUCE-RATIONALP-*))
 (28 28 (:REWRITE RATIONALP-MINUS-X))
 (28 28 (:META META-RATIONALP-CORRECT))
 (26 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (26 13 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (25 25 (:REWRITE THE-FLOOR-BELOW))
 (25 25 (:REWRITE THE-FLOOR-ABOVE))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (15 15 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (15 15 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (15 15 (:TYPE-PRESCRIPTION NATP))
 (15 15 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (15 15 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (15 15 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (15 15 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (15 15 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (15 15 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (15 15 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (15 15 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (15 15 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (15 15 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (15 15 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (13 13 (:REWRITE SIMPLIFY-SUMS-<))
 (13 13 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (13 13 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (13 13 (:REWRITE INTEGERP-<-CONSTANT))
 (13 13 (:REWRITE CONSTANT-<-INTEGERP))
 (13 13 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (13 13 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (13 13 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (13 13 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (13 13 (:REWRITE |(< c (- x))|))
 (13 13 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (13 13 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (13 13 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (13 13 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (13 13 (:REWRITE |(< (/ x) (/ y))|))
 (13 13 (:REWRITE |(< (- x) c)|))
 (13 13 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (5 5 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 5 (:REWRITE DEFAULT-DIVIDE))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (4 4 (:REWRITE |(< 0 (/ x))|))
 (4 4 (:REWRITE |(< 0 (* 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)|))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-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-LINEAR-LOWER-<))
 )
(DM::FIND-ORDER-1
 (13503 33 (:REWRITE |(< (if a b c) x)|))
 (8327 9 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (6234 9 (:LINEAR RTL::MOD-BND-2))
 (5712 324 (:REWRITE RATIONALP-X))
 (4648 52 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4570 1487 (:REWRITE DEFAULT-LESS-THAN-1))
 (4406 1550 (:REWRITE DEFAULT-LESS-THAN-2))
 (4183 9 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (4137 633 (:REWRITE DEFAULT-TIMES-1))
 (3658 633 (:REWRITE DEFAULT-TIMES-2))
 (3462 204 (:LINEAR EXPT-<=-1-ONE))
 (3351 204 (:LINEAR EXPT->=-1-TWO))
 (3351 204 (:LINEAR EXPT->-1-TWO))
 (3351 204 (:LINEAR EXPT-<-1-ONE))
 (3078 18 (:LINEAR MOD-BOUNDS-2))
 (3078 18 (:LINEAR MOD-BOUNDS-1))
 (3054 204 (:LINEAR EXPT-X->=-X))
 (3054 204 (:LINEAR EXPT->=-1-ONE))
 (3054 204 (:LINEAR EXPT-<=-1-TWO))
 (2943 204 (:LINEAR EXPT-X->-X))
 (2943 204 (:LINEAR EXPT->-1-ONE))
 (2943 204 (:LINEAR EXPT-<-1-TWO))
 (2829 2829 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2829 2829 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (2442 1415 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2364 1415 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2135 20 (:REWRITE MOD-ZERO . 4))
 (2108 20 (:REWRITE MOD-X-Y-=-X . 3))
 (2091 1415 (:REWRITE SIMPLIFY-SUMS-<))
 (2088 232 (:REWRITE ACL2-NUMBERP-X))
 (2033 20 (:REWRITE MOD-X-Y-=-X . 4))
 (1975 395 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1965 20 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1938 20 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1921 408 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1921 408 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1799 395 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1774 408 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1721 408 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1550 1550 (:REWRITE THE-FLOOR-BELOW))
 (1550 1550 (:REWRITE THE-FLOOR-ABOVE))
 (1509 20 (:REWRITE CANCEL-MOD-+))
 (1415 1415 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1415 1415 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1415 1415 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1415 1415 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1415 1415 (:REWRITE INTEGERP-<-CONSTANT))
 (1415 1415 (:REWRITE CONSTANT-<-INTEGERP))
 (1415 1415 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1415 1415 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1415 1415 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1415 1415 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1415 1415 (:REWRITE |(< c (- x))|))
 (1415 1415 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1415 1415 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1415 1415 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1415 1415 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1415 1415 (:REWRITE |(< (/ x) (/ y))|))
 (1415 1415 (:REWRITE |(< (- x) c)|))
 (1415 1415 (:REWRITE |(< (- x) (- y))|))
 (1281 1281 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1281 1281 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1281 1281 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (939 20 (:REWRITE MOD-ZERO . 3))
 (918 9 (:LINEAR MOD-BOUNDS-3))
 (774 387 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (664 61 (:REWRITE DEFAULT-MOD-1))
 (611 395 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (611 395 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (598 598 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (598 598 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (598 598 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (565 565 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (525 20 (:REWRITE |(integerp (- x))|))
 (460 20 (:REWRITE MOD-X-Y-=-X . 2))
 (460 20 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (460 20 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (427 395 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (423 423 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (423 423 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (423 423 (:REWRITE |(< 0 (/ x))|))
 (423 423 (:REWRITE |(< 0 (* x y))|))
 (395 395 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (395 395 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (395 395 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (395 395 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (388 388 (:REWRITE REDUCE-INTEGERP-+))
 (388 388 (:REWRITE INTEGERP-MINUS-X))
 (388 388 (:META META-INTEGERP-CORRECT))
 (387 387 (:TYPE-PRESCRIPTION NATP))
 (387 387 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (387 387 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (387 387 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (382 20 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (382 20 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (382 20 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (382 20 (:REWRITE MOD-CANCEL-*-CONST))
 (382 20 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (370 20 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (360 9 (:LINEAR RTL::MOD-BND-1))
 (336 20 (:REWRITE |(* (- x) y)|))
 (324 324 (:REWRITE RATIONALP-MINUS-X))
 (323 323 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (312 312 (:REWRITE REDUCE-RATIONALP-+))
 (312 312 (:META META-RATIONALP-CORRECT))
 (260 260 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (260 260 (:REWRITE DEFAULT-DIVIDE))
 (250 250 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (234 52 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (204 204 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (204 204 (:LINEAR EXPT-LINEAR-UPPER-<))
 (204 204 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (204 204 (:LINEAR EXPT-LINEAR-LOWER-<))
 (145 145 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (145 145 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (145 145 (:REWRITE |(< (/ x) 0)|))
 (145 145 (:REWRITE |(< (* x y) 0)|))
 (90 18 (:REWRITE |(+ y x)|))
 (84 30 (:REWRITE NORMALIZE-ADDENDS))
 (78 3 (:REWRITE |(mod (+ 1 x) y)|))
 (72 8 (:REWRITE |(equal (expt x n) 1)|))
 (66 60 (:REWRITE DEFAULT-PLUS-1))
 (61 61 (:REWRITE DEFAULT-MOD-2))
 (60 60 (:REWRITE DEFAULT-PLUS-2))
 (52 52 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (52 52 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (52 52 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (52 52 (:REWRITE |(equal c (/ x))|))
 (52 52 (:REWRITE |(equal c (- x))|))
 (52 52 (:REWRITE |(equal (/ x) c)|))
 (52 52 (:REWRITE |(equal (/ x) (/ y))|))
 (52 52 (:REWRITE |(equal (- x) c)|))
 (52 52 (:REWRITE |(equal (- x) (- y))|))
 (50 26 (:REWRITE DEFAULT-MINUS))
 (48 12 (:REWRITE |(integerp (expt x n))|))
 (46 46 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (42 6 (:REWRITE INTEGERP-/))
 (31 31 (:REWRITE ZP-OPEN))
 (30 6 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (24 24 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (23 23 (:REWRITE |(expt 1/c n)|))
 (23 23 (:REWRITE |(expt (- x) n)|))
 (20 20 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (20 20 (:REWRITE |(mod x (- y))| . 3))
 (20 20 (:REWRITE |(mod x (- y))| . 2))
 (20 20 (:REWRITE |(mod x (- y))| . 1))
 (20 20 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(mod (- x) y)| . 3))
 (20 20 (:REWRITE |(mod (- x) y)| . 2))
 (20 20 (:REWRITE |(mod (- x) y)| . 1))
 (20 20 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (18 18 (:REWRITE |(equal (+ (- c) x) y)|))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (17 17 (:REWRITE |(equal (expt x n) 0)|))
 (17 17 (:REWRITE |(- (* c x))|))
 (9 9 (:LINEAR RTL::MOD-BND-3))
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (6 6 (:REWRITE |(+ x (- x))|))
 (6 6 (:REWRITE |(+ c (+ d x))|))
 (6 6 (:REWRITE |(+ 0 x)|))
 (6 3 (:REWRITE |(* -1 x)|))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 )
(DM::ORDER-1
 (1256 2 (:LINEAR RTL::MOD-BND-2))
 (704 48 (:REWRITE RATIONALP-X))
 (684 4 (:LINEAR MOD-BOUNDS-2))
 (684 4 (:LINEAR MOD-BOUNDS-1))
 (616 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (570 42 (:REWRITE DEFAULT-LESS-THAN-2))
 (408 30 (:REWRITE DEFAULT-LESS-THAN-1))
 (360 40 (:REWRITE ACL2-NUMBERP-X))
 (204 2 (:LINEAR MOD-BOUNDS-3))
 (170 10 (:REWRITE |(* y x)|))
 (150 150 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (150 150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (150 20 (:REWRITE DEFAULT-TIMES-2))
 (150 20 (:REWRITE DEFAULT-TIMES-1))
 (130 26 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (130 26 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (106 2 (:LINEAR EXPT-<=-1-ONE))
 (102 2 (:LINEAR EXPT->=-1-TWO))
 (102 2 (:LINEAR EXPT->-1-TWO))
 (102 2 (:LINEAR EXPT-<-1-ONE))
 (98 2 (:LINEAR EXPT-X->=-X))
 (98 2 (:LINEAR EXPT->=-1-ONE))
 (98 2 (:LINEAR EXPT-<=-1-TWO))
 (94 2 (:LINEAR EXPT-X->-X))
 (94 2 (:LINEAR EXPT->-1-ONE))
 (94 2 (:LINEAR EXPT-<-1-TWO))
 (80 2 (:LINEAR RTL::MOD-BND-1))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (52 26 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (50 50 (:REWRITE REDUCE-INTEGERP-+))
 (50 50 (:REWRITE INTEGERP-MINUS-X))
 (50 50 (:META META-INTEGERP-CORRECT))
 (48 48 (:REWRITE REDUCE-RATIONALP-+))
 (48 48 (:REWRITE REDUCE-RATIONALP-*))
 (48 48 (:REWRITE RATIONALP-MINUS-X))
 (48 48 (:META META-RATIONALP-CORRECT))
 (48 22 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (48 22 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (42 42 (:REWRITE THE-FLOOR-BELOW))
 (42 42 (:REWRITE THE-FLOOR-ABOVE))
 (26 26 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (26 26 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (26 26 (:TYPE-PRESCRIPTION NATP))
 (26 26 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (26 26 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (26 26 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (26 26 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (26 26 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (26 26 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (26 26 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (26 26 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (26 26 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (26 26 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (26 26 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (22 22 (:REWRITE SIMPLIFY-SUMS-<))
 (22 22 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (22 22 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (22 22 (:REWRITE INTEGERP-<-CONSTANT))
 (22 22 (:REWRITE CONSTANT-<-INTEGERP))
 (22 22 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (22 22 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (22 22 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (22 22 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (22 22 (:REWRITE |(< c (- x))|))
 (22 22 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (22 22 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (22 22 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (22 22 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (22 22 (:REWRITE |(< (/ x) (/ y))|))
 (22 22 (:REWRITE |(< (- x) c)|))
 (22 22 (:REWRITE |(< (- x) (- y))|))
 (10 10 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (10 10 (:REWRITE DEFAULT-DIVIDE))
 (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))|))
 (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 |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (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-INCREASING-FOR-BASE->-1))
 (4 4 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<))
 )
(DM::FIND-ORDER-BOUNDS
 (7408 16 (:REWRITE |(< (if a b c) x)|))
 (2912 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (2240 329 (:REWRITE DEFAULT-TIMES-1))
 (2172 3 (:LINEAR RTL::MOD-BND-2))
 (1970 329 (:REWRITE DEFAULT-TIMES-2))
 (1948 679 (:REWRITE DEFAULT-LESS-THAN-1))
 (1904 126 (:REWRITE RATIONALP-X))
 (1811 703 (:REWRITE DEFAULT-LESS-THAN-2))
 (1639 19 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1597 200 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1546 100 (:LINEAR EXPT-<=-1-ONE))
 (1497 100 (:LINEAR EXPT->=-1-TWO))
 (1497 100 (:LINEAR EXPT->-1-TWO))
 (1497 100 (:LINEAR EXPT-<-1-ONE))
 (1460 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1413 200 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1362 100 (:LINEAR EXPT-X->=-X))
 (1362 100 (:LINEAR EXPT->=-1-ONE))
 (1362 100 (:LINEAR EXPT-<=-1-TWO))
 (1313 100 (:LINEAR EXPT-X->-X))
 (1313 100 (:LINEAR EXPT->-1-ONE))
 (1313 100 (:LINEAR EXPT-<-1-TWO))
 (1236 651 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1236 9 (:REWRITE MOD-ZERO . 4))
 (1222 1222 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1222 1222 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (1184 651 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1182 9 (:REWRITE MOD-X-Y-=-X . 4))
 (1182 9 (:REWRITE MOD-X-Y-=-X . 3))
 (1121 9 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1094 9 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1041 651 (:REWRITE SIMPLIFY-SUMS-<))
 (1026 6 (:LINEAR MOD-BOUNDS-2))
 (1026 6 (:LINEAR MOD-BOUNDS-1))
 (831 9 (:REWRITE CANCEL-MOD-+))
 (828 92 (:REWRITE ACL2-NUMBERP-X))
 (703 703 (:REWRITE THE-FLOOR-BELOW))
 (703 703 (:REWRITE THE-FLOOR-ABOVE))
 (651 651 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (651 651 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (651 651 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (651 651 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (651 651 (:REWRITE INTEGERP-<-CONSTANT))
 (651 651 (:REWRITE CONSTANT-<-INTEGERP))
 (651 651 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (651 651 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (651 651 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (651 651 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (651 651 (:REWRITE |(< c (- x))|))
 (651 651 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (651 651 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (651 651 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (651 651 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (651 651 (:REWRITE |(< (/ x) (/ y))|))
 (651 651 (:REWRITE |(< (- x) c)|))
 (651 651 (:REWRITE |(< (- x) (- y))|))
 (513 9 (:REWRITE MOD-ZERO . 3))
 (369 31 (:REWRITE DEFAULT-MOD-1))
 (365 73 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (331 331 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (331 331 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (331 331 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (306 3 (:LINEAR MOD-BOUNDS-3))
 (301 73 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (285 9 (:REWRITE MOD-X-Y-=-X . 2))
 (285 9 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (285 9 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (257 9 (:REWRITE |(integerp (- x))|))
 (243 243 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (233 9 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (233 9 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (233 9 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (233 9 (:REWRITE MOD-CANCEL-*-CONST))
 (233 9 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (233 9 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (200 200 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (200 200 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (196 196 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (196 196 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (196 196 (:REWRITE |(< 0 (/ x))|))
 (196 196 (:REWRITE |(< 0 (* x y))|))
 (193 9 (:REWRITE |(* (- x) y)|))
 (190 190 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (190 190 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (190 190 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (157 157 (:REWRITE REDUCE-INTEGERP-+))
 (157 157 (:REWRITE INTEGERP-MINUS-X))
 (157 157 (:META META-INTEGERP-CORRECT))
 (146 73 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (136 136 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (136 136 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (136 136 (:REWRITE DEFAULT-DIVIDE))
 (126 126 (:REWRITE RATIONALP-MINUS-X))
 (125 73 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (125 73 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (122 122 (:REWRITE REDUCE-RATIONALP-+))
 (122 122 (:META META-RATIONALP-CORRECT))
 (120 3 (:LINEAR RTL::MOD-BND-1))
 (100 100 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (100 100 (:LINEAR EXPT-LINEAR-UPPER-<))
 (100 100 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (100 100 (:LINEAR EXPT-LINEAR-LOWER-<))
 (97 19 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (73 73 (:TYPE-PRESCRIPTION NATP))
 (73 73 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (73 73 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (73 73 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (73 73 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (73 73 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (73 73 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (73 73 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (73 73 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (67 67 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (67 67 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (67 67 (:REWRITE |(< (/ x) 0)|))
 (67 67 (:REWRITE |(< (* x y) 0)|))
 (55 55 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (31 31 (:REWRITE DEFAULT-MOD-2))
 (30 6 (:REWRITE |(+ y x)|))
 (29 11 (:REWRITE NORMALIZE-ADDENDS))
 (27 27 (:REWRITE DEFAULT-EXPT-2))
 (23 21 (:REWRITE DEFAULT-PLUS-1))
 (21 21 (:REWRITE DEFAULT-PLUS-2))
 (19 19 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (19 19 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (19 19 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (19 19 (:REWRITE |(equal c (/ x))|))
 (19 19 (:REWRITE |(equal c (- x))|))
 (19 19 (:REWRITE |(equal (/ x) c)|))
 (19 19 (:REWRITE |(equal (/ x) (/ y))|))
 (19 19 (:REWRITE |(equal (- x) c)|))
 (19 19 (:REWRITE |(equal (- x) (- y))|))
 (19 11 (:REWRITE DEFAULT-MINUS))
 (18 2 (:REWRITE |(equal (expt x n) 1)|))
 (17 17 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (16 4 (:REWRITE |(integerp (expt x n))|))
 (13 13 (:REWRITE |(expt 1/c n)|))
 (13 13 (:REWRITE |(expt (- x) n)|))
 (10 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (9 9 (:REWRITE |(mod x (- y))| . 3))
 (9 9 (:REWRITE |(mod x (- y))| . 2))
 (9 9 (:REWRITE |(mod x (- y))| . 1))
 (9 9 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (9 9 (:REWRITE |(mod (- x) y)| . 3))
 (9 9 (:REWRITE |(mod (- x) y)| . 2))
 (9 9 (:REWRITE |(mod (- x) y)| . 1))
 (9 9 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (9 9 (:REWRITE |(equal (expt x n) 0)|))
 (9 9 (:REWRITE |(- (* c x))|))
 (6 6 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 3 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE |(+ 0 x)|))
 )
(DM::ORDER-BOUNDS)
(DM::FIND-ORDER-MINIMAL
 (25140 15 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (13679 126 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (13050 21 (:LINEAR RTL::MOD-BND-2))
 (12600 15 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (10360 20 (:REWRITE |(< (if a b c) x)|))
 (8224 412 (:REWRITE RATIONALP-X))
 (7371 1092 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (7371 1092 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (7315 1244 (:REWRITE DEFAULT-TIMES-1))
 (7227 1244 (:REWRITE DEFAULT-TIMES-2))
 (7160 3421 (:REWRITE DEFAULT-LESS-THAN-1))
 (7044 546 (:LINEAR EXPT-<=-1-ONE))
 (6825 546 (:LINEAR EXPT->=-1-TWO))
 (6825 546 (:LINEAR EXPT->-1-TWO))
 (6825 546 (:LINEAR EXPT-<-1-ONE))
 (6750 1092 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (6620 56 (:REWRITE MOD-ZERO . 4))
 (6531 1092 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (6284 56 (:REWRITE MOD-X-Y-=-X . 4))
 (6284 56 (:REWRITE MOD-X-Y-=-X . 3))
 (6204 546 (:LINEAR EXPT-X->=-X))
 (6204 546 (:LINEAR EXPT->=-1-ONE))
 (6204 546 (:LINEAR EXPT-<=-1-TWO))
 (6020 56 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (5985 546 (:LINEAR EXPT-X->-X))
 (5985 546 (:LINEAR EXPT->-1-ONE))
 (5985 546 (:LINEAR EXPT-<-1-TWO))
 (5852 56 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (5790 5790 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5790 5790 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (5071 3355 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4863 3355 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4564 56 (:REWRITE CANCEL-MOD-+))
 (4523 837 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (4283 837 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (4278 3355 (:REWRITE SIMPLIFY-SUMS-<))
 (3678 42 (:LINEAR MOD-BOUNDS-2))
 (3511 3511 (:REWRITE THE-FLOOR-BELOW))
 (3511 3511 (:REWRITE THE-FLOOR-ABOVE))
 (3356 3356 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3356 3356 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3356 3356 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3356 3356 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (3356 3356 (:REWRITE INTEGERP-<-CONSTANT))
 (3356 3356 (:REWRITE CONSTANT-<-INTEGERP))
 (3356 3356 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3356 3356 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3356 3356 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3356 3356 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3356 3356 (:REWRITE |(< c (- x))|))
 (3356 3356 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3356 3356 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3356 3356 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3356 3356 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3356 3356 (:REWRITE |(< (/ x) (/ y))|))
 (3356 3356 (:REWRITE |(< (- x) c)|))
 (3356 3356 (:REWRITE |(< (- x) (- y))|))
 (3256 56 (:REWRITE MOD-ZERO . 3))
 (3131 3131 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3131 3131 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3131 3131 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2658 286 (:REWRITE ACL2-NUMBERP-X))
 (2012 837 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1907 837 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1907 837 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1694 21 (:LINEAR MOD-BOUNDS-3))
 (1600 56 (:REWRITE |(integerp (- x))|))
 (1396 56 (:REWRITE MOD-X-Y-=-X . 2))
 (1396 56 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1396 56 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1188 56 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1188 56 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1188 56 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1188 56 (:REWRITE MOD-CANCEL-*-CONST))
 (1188 56 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1188 56 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1175 837 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1175 837 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1175 837 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1175 837 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1175 837 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1175 837 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1175 837 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (1175 837 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (1106 1106 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1106 1106 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1106 1106 (:REWRITE |(< 0 (/ x))|))
 (1106 1106 (:REWRITE |(< 0 (* x y))|))
 (1092 1092 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1092 1092 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1028 56 (:REWRITE |(* (- x) y)|))
 (982 644 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (837 837 (:TYPE-PRESCRIPTION NATP))
 (810 95 (:REWRITE DEFAULT-MOD-1))
 (575 575 (:REWRITE REDUCE-INTEGERP-+))
 (575 575 (:REWRITE INTEGERP-MINUS-X))
 (575 575 (:META META-INTEGERP-CORRECT))
 (549 549 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (549 549 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (549 549 (:REWRITE DEFAULT-DIVIDE))
 (546 546 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (546 546 (:LINEAR EXPT-LINEAR-UPPER-<))
 (546 546 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (546 546 (:LINEAR EXPT-LINEAR-LOWER-<))
 (464 126 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (412 412 (:REWRITE RATIONALP-MINUS-X))
 (382 382 (:REWRITE REDUCE-RATIONALP-+))
 (382 382 (:META META-RATIONALP-CORRECT))
 (352 352 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (352 352 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (352 352 (:REWRITE |(< (/ x) 0)|))
 (352 352 (:REWRITE |(< (* x y) 0)|))
 (225 45 (:REWRITE |(+ y x)|))
 (204 69 (:REWRITE NORMALIZE-ADDENDS))
 (179 71 (:REWRITE DEFAULT-MINUS))
 (159 144 (:REWRITE DEFAULT-PLUS-1))
 (144 144 (:REWRITE DEFAULT-PLUS-2))
 (126 126 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (126 126 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (126 126 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (126 126 (:REWRITE |(equal c (/ x))|))
 (126 126 (:REWRITE |(equal c (- x))|))
 (126 126 (:REWRITE |(equal (/ x) c)|))
 (126 126 (:REWRITE |(equal (/ x) (/ y))|))
 (126 126 (:REWRITE |(equal (- x) c)|))
 (126 126 (:REWRITE |(equal (- x) (- y))|))
 (120 30 (:REWRITE |(integerp (expt x n))|))
 (111 111 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (95 95 (:REWRITE DEFAULT-MOD-2))
 (90 10 (:REWRITE |(equal (expt x n) 1)|))
 (75 15 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (56 56 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (56 56 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (56 56 (:REWRITE |(mod x (- y))| . 3))
 (56 56 (:REWRITE |(mod x (- y))| . 2))
 (56 56 (:REWRITE |(mod x (- y))| . 1))
 (56 56 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (56 56 (:REWRITE |(mod (- x) y)| . 3))
 (56 56 (:REWRITE |(mod (- x) y)| . 2))
 (56 56 (:REWRITE |(mod (- x) y)| . 1))
 (56 56 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (56 56 (:REWRITE |(equal (expt x n) 0)|))
 (56 56 (:REWRITE |(- (* c x))|))
 (54 54 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (51 51 (:REWRITE ZP-OPEN))
 (45 45 (:REWRITE |(equal (+ (- c) x) y)|))
 (38 38 (:REWRITE DEFAULT-EXPT-2))
 (24 24 (:REWRITE |(expt 1/c n)|))
 (24 24 (:REWRITE |(expt (- x) n)|))
 (21 21 (:LINEAR RTL::MOD-BND-3))
 (15 15 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (15 15 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (15 15 (:REWRITE |(+ x (- x))|))
 (15 15 (:REWRITE |(+ c (+ d x))|))
 (15 15 (:REWRITE |(+ 0 x)|))
 (6 6 (:REWRITE |(< y (+ (- c) x))|))
 (6 6 (:REWRITE |(< x (+ c/d y))|))
 )
(DM::ORDER-MINIMAL
 (1967 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1294 12 (:REWRITE |(< (if a b c) x)|))
 (1258 36 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1120 77 (:REWRITE RATIONALP-X))
 (963 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (724 1 (:LINEAR RTL::MOD-BND-2))
 (664 34 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (583 231 (:REWRITE DEFAULT-LESS-THAN-2))
 (580 34 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (477 223 (:REWRITE DEFAULT-LESS-THAN-1))
 (369 17 (:LINEAR EXPT-<=-1-ONE))
 (364 160 (:REWRITE DEFAULT-TIMES-2))
 (357 17 (:LINEAR EXPT->=-1-TWO))
 (357 17 (:LINEAR EXPT->-1-TWO))
 (357 17 (:LINEAR EXPT-<-1-ONE))
 (355 355 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (355 355 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (355 355 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (350 70 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (350 70 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (342 2 (:LINEAR MOD-BOUNDS-2))
 (342 2 (:LINEAR MOD-BOUNDS-1))
 (329 160 (:REWRITE DEFAULT-TIMES-1))
 (325 17 (:LINEAR EXPT-X->=-X))
 (325 17 (:LINEAR EXPT->=-1-ONE))
 (325 17 (:LINEAR EXPT-<=-1-TWO))
 (324 36 (:REWRITE ACL2-NUMBERP-X))
 (313 17 (:LINEAR EXPT-X->-X))
 (313 17 (:LINEAR EXPT->-1-ONE))
 (313 17 (:LINEAR EXPT-<-1-TWO))
 (265 6 (:REWRITE CANCEL-MOD-+))
 (259 207 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (259 207 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (246 207 (:REWRITE SIMPLIFY-SUMS-<))
 (245 6 (:REWRITE MOD-X-Y-=-X . 4))
 (245 6 (:REWRITE MOD-X-Y-=-X . 3))
 (239 6 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (231 231 (:REWRITE THE-FLOOR-BELOW))
 (231 231 (:REWRITE THE-FLOOR-ABOVE))
 (228 228 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (228 228 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (223 223 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (223 223 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (223 223 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (221 6 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (214 70 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (214 70 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (207 207 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (207 207 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (207 207 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (207 207 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (207 207 (:REWRITE INTEGERP-<-CONSTANT))
 (207 207 (:REWRITE CONSTANT-<-INTEGERP))
 (207 207 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (207 207 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (207 207 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (207 207 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (207 207 (:REWRITE |(< c (- x))|))
 (207 207 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (207 207 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (207 207 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (207 207 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (207 207 (:REWRITE |(< (/ x) (/ y))|))
 (207 207 (:REWRITE |(< (- x) c)|))
 (207 207 (:REWRITE |(< (- x) (- y))|))
 (166 6 (:REWRITE MOD-ZERO . 4))
 (157 6 (:REWRITE MOD-ZERO . 3))
 (140 70 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (109 6 (:REWRITE |(integerp (- x))|))
 (102 102 (:REWRITE REDUCE-INTEGERP-+))
 (102 102 (:REWRITE INTEGERP-MINUS-X))
 (102 102 (:META META-INTEGERP-CORRECT))
 (102 1 (:LINEAR MOD-BOUNDS-3))
 (90 18 (:REWRITE |(+ y x)|))
 (78 24 (:REWRITE NORMALIZE-ADDENDS))
 (78 6 (:REWRITE |(* (- x) y)|))
 (77 77 (:REWRITE RATIONALP-MINUS-X))
 (70 70 (:TYPE-PRESCRIPTION NATP))
 (70 70 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (70 70 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (70 70 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (70 70 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (70 70 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (70 70 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (70 70 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (70 70 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (69 69 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (65 65 (:REWRITE REDUCE-RATIONALP-+))
 (65 65 (:META META-RATIONALP-CORRECT))
 (63 24 (:REWRITE DEFAULT-MOD-1))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (60 60 (:REWRITE |(< 0 (/ x))|))
 (60 60 (:REWRITE |(< 0 (* x y))|))
 (60 54 (:REWRITE DEFAULT-PLUS-1))
 (54 54 (:REWRITE DEFAULT-PLUS-2))
 (53 53 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (53 53 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (53 53 (:REWRITE DEFAULT-DIVIDE))
 (49 36 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (40 10 (:REWRITE DM::FIRST-POWER))
 (40 1 (:LINEAR RTL::MOD-BND-1))
 (36 36 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (36 36 (:REWRITE |(equal c (/ x))|))
 (36 36 (:REWRITE |(equal c (- x))|))
 (36 36 (:REWRITE |(equal (/ x) c)|))
 (36 36 (:REWRITE |(equal (/ x) (/ y))|))
 (36 36 (:REWRITE |(equal (- x) c)|))
 (36 36 (:REWRITE |(equal (- x) (- y))|))
 (36 12 (:REWRITE DEFAULT-MINUS))
 (34 34 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (34 34 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (33 33 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (30 30 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (30 6 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (30 6 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (30 6 (:REWRITE MOD-X-Y-=-X . 2))
 (30 6 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (30 6 (:REWRITE MOD-CANCEL-*-CONST))
 (30 6 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (30 6 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (30 6 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (30 6 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (30 6 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE DEFAULT-MOD-2))
 (24 24 (:REWRITE |(< (/ x) 0)|))
 (24 24 (:REWRITE |(< (* x y) 0)|))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (18 18 (:REWRITE |(equal (+ (- c) x) y)|))
 (17 17 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (17 17 (:LINEAR EXPT-LINEAR-UPPER-<))
 (17 17 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (17 17 (:LINEAR EXPT-LINEAR-LOWER-<))
 (12 12 (:REWRITE DEFAULT-EXPT-2))
 (9 1 (:REWRITE |(equal (expt x n) 1)|))
 (8 2 (:REWRITE |(integerp (expt x n))|))
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (6 6 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (6 6 (:REWRITE |(mod x (- y))| . 3))
 (6 6 (:REWRITE |(mod x (- y))| . 2))
 (6 6 (:REWRITE |(mod x (- y))| . 1))
 (6 6 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (6 6 (:REWRITE |(mod (- x) y)| . 3))
 (6 6 (:REWRITE |(mod (- x) y)| . 2))
 (6 6 (:REWRITE |(mod (- x) y)| . 1))
 (6 6 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (6 6 (:REWRITE |(- (* c x))|))
 (6 6 (:REWRITE |(+ x (- x))|))
 (6 6 (:REWRITE |(+ c (+ d x))|))
 (6 6 (:REWRITE |(+ 0 x)|))
 (1 1 (:REWRITE |(equal (expt x n) 0)|))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::MOD-POWER-INDUCT)
(DM::MOD-POWER-1
 (66290 21 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (35236 213 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (32330 21 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (31574 475 (:REWRITE |(* (* x y) z)|))
 (28047 131 (:REWRITE CANCEL-MOD-+))
 (20444 3040 (:REWRITE DEFAULT-TIMES-2))
 (17471 131 (:REWRITE MOD-ZERO . 3))
 (15810 1969 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (15501 3040 (:REWRITE DEFAULT-TIMES-1))
 (14692 131 (:REWRITE MOD-X-Y-=-X . 3))
 (14638 131 (:REWRITE MOD-X-Y-=-X . 4))
 (14031 131 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (13859 131 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (13736 135 (:REWRITE DEFAULT-MOD-RATIO))
 (13282 131 (:REWRITE |(* (- x) y)|))
 (12579 131 (:REWRITE MOD-ZERO . 4))
 (11312 10560 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (11093 11093 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (11093 11093 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (11093 11093 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (11019 2319 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (10731 2331 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (10731 2331 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (10560 10560 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (10560 10560 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (10560 10560 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (10560 10560 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (8026 131 (:REWRITE |(integerp (- x))|))
 (7005 652 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6475 36 (:LINEAR RTL::MOD-BND-2))
 (5955 660 (:REWRITE DEFAULT-LESS-THAN-1))
 (5892 652 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5449 36 (:LINEAR MOD-BOUNDS-3))
 (4623 524 (:META META-INTEGERP-CORRECT))
 (3173 131 (:REWRITE MOD-X-Y-=-X . 2))
 (3173 131 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (3173 131 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (3166 652 (:REWRITE SIMPLIFY-SUMS-<))
 (2363 2331 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (2331 2331 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (2331 2331 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (2331 2331 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (2331 213 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2319 2319 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1969 1969 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1969 1969 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1969 1969 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1944 144 (:REWRITE DEFAULT-MINUS))
 (1914 131 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1914 131 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1819 660 (:REWRITE DEFAULT-LESS-THAN-2))
 (1762 131 (:REWRITE MOD-CANCEL-*-CONST))
 (1449 135 (:REWRITE DEFAULT-MOD-1))
 (1096 72 (:LINEAR MOD-BOUNDS-2))
 (1076 131 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (969 131 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (969 131 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (969 131 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (924 137 (:REWRITE DEFAULT-PLUS-2))
 (894 6 (:REWRITE MOD-ZERO . 1))
 (831 200 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (821 269 (:REWRITE INTEGERP-/))
 (660 660 (:REWRITE THE-FLOOR-BELOW))
 (660 660 (:REWRITE THE-FLOOR-ABOVE))
 (656 656 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (656 656 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (656 656 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (656 656 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (656 656 (:REWRITE INTEGERP-<-CONSTANT))
 (656 656 (:REWRITE CONSTANT-<-INTEGERP))
 (656 656 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (656 656 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (656 656 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (656 656 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (656 656 (:REWRITE |(< c (- x))|))
 (656 656 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (656 656 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (656 656 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (656 656 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (656 656 (:REWRITE |(< (/ x) (/ y))|))
 (656 656 (:REWRITE |(< (- x) c)|))
 (656 656 (:REWRITE |(< (- x) (- y))|))
 (585 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (541 524 (:REWRITE INTEGERP-MINUS-X))
 (537 537 (:REWRITE |(* c (* d x))|))
 (537 57 (:REWRITE NORMALIZE-ADDENDS))
 (524 524 (:REWRITE REDUCE-INTEGERP-+))
 (468 234 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (430 430 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (430 430 (:REWRITE DEFAULT-DIVIDE))
 (416 131 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (416 131 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (406 137 (:REWRITE DEFAULT-PLUS-1))
 (333 4 (:REWRITE |(< (if a b c) x)|))
 (307 13 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (280 280 (:REWRITE |(< (/ x) 0)|))
 (280 280 (:REWRITE |(< (* x y) 0)|))
 (276 276 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (276 276 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (259 259 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (234 234 (:TYPE-PRESCRIPTION NATP))
 (234 234 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (232 232 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (232 232 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (213 213 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (213 213 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (213 213 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (213 213 (:REWRITE |(equal c (/ x))|))
 (213 213 (:REWRITE |(equal c (- x))|))
 (213 213 (:REWRITE |(equal (/ x) c)|))
 (213 213 (:REWRITE |(equal (/ x) (/ y))|))
 (213 213 (:REWRITE |(equal (- x) c)|))
 (213 213 (:REWRITE |(equal (- x) (- y))|))
 (211 21 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (189 189 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (135 135 (:REWRITE DEFAULT-MOD-2))
 (134 134 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (133 133 (:REWRITE |(- (* c x))|))
 (131 131 (:REWRITE |(mod x (- y))| . 3))
 (131 131 (:REWRITE |(mod x (- y))| . 2))
 (131 131 (:REWRITE |(mod x (- y))| . 1))
 (131 131 (:REWRITE |(mod (- x) y)| . 3))
 (131 131 (:REWRITE |(mod (- x) y)| . 2))
 (131 131 (:REWRITE |(mod (- x) y)| . 1))
 (122 6 (:REWRITE MOD-ZERO . 2))
 (119 119 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (119 119 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (119 119 (:REWRITE |(< 0 (/ x))|))
 (119 119 (:REWRITE |(< 0 (* x y))|))
 (110 110 (:REWRITE |(equal (* x y) 0)|))
 (110 110 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (99 21 (:REWRITE DEFAULT-EXPT-1))
 (97 97 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (44 44 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (44 18 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (36 36 (:LINEAR RTL::MOD-BND-3))
 (32 32 (:REWRITE |(equal (+ (- c) x) y)|))
 (21 21 (:REWRITE DEFAULT-EXPT-2))
 (21 21 (:REWRITE |(expt 1/c n)|))
 (21 21 (:REWRITE |(expt (- x) n)|))
 (13 13 (:REWRITE |(+ x (- x))|))
 (6 6 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE |(* c (expt d n))|))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 )
(DM::MOD-POWER
 (298484 320 (:REWRITE RTL::MOD-DOES-NOTHING))
 (44020 310 (:REWRITE CANCEL-MOD-+))
 (40246 310 (:REWRITE MOD-X-Y-=-X . 4))
 (39246 980 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (39082 490 (:LINEAR EXPT->=-1-TWO))
 (39082 490 (:LINEAR EXPT->-1-TWO))
 (39082 490 (:LINEAR EXPT-<-1-ONE))
 (38621 310 (:REWRITE MOD-X-Y-=-X . 3))
 (38286 980 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (38092 490 (:LINEAR EXPT-X->=-X))
 (38092 490 (:LINEAR EXPT->=-1-ONE))
 (38092 490 (:LINEAR EXPT-<=-1-TWO))
 (37942 490 (:LINEAR EXPT-X->-X))
 (37942 490 (:LINEAR EXPT->-1-ONE))
 (37942 490 (:LINEAR EXPT-<-1-TWO))
 (35994 310 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (35614 490 (:LINEAR EXPT-<=-1-ONE))
 (34634 310 (:REWRITE MOD-ZERO . 4))
 (29580 2676 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (24980 24980 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (22794 310 (:REWRITE MOD-ZERO . 3))
 (18268 3146 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (15890 2382 (:REWRITE DEFAULT-TIMES-1))
 (14260 310 (:REWRITE |(integerp (- x))|))
 (13460 3146 (:REWRITE DEFAULT-LESS-THAN-1))
 (13330 310 (:REWRITE DEFAULT-MOD-RATIO))
 (13330 310 (:REWRITE |(* (- x) y)|))
 (12790 2382 (:REWRITE DEFAULT-TIMES-2))
 (12664 308 (:REWRITE |(equal (expt x n) 0)|))
 (12596 3146 (:REWRITE SIMPLIFY-SUMS-<))
 (12358 3146 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (10354 10354 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (10354 10354 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (10354 10354 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (7954 3146 (:REWRITE DEFAULT-LESS-THAN-2))
 (7750 310 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (7750 310 (:REWRITE MOD-X-Y-=-X . 2))
 (7750 310 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (7750 310 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (6225 1245 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (6225 1245 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (6177 1245 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6177 1245 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (5984 76 (:LINEAR MOD-BOUNDS-3))
 (4650 310 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (4650 310 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (4650 310 (:REWRITE DEFAULT-MINUS))
 (4342 310 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4342 310 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (4342 310 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (4272 310 (:REWRITE MOD-CANCEL-*-CONST))
 (3410 310 (:REWRITE DEFAULT-MOD-1))
 (3146 3146 (:REWRITE THE-FLOOR-BELOW))
 (3146 3146 (:REWRITE THE-FLOOR-ABOVE))
 (3146 3146 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3146 3146 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3146 3146 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3146 3146 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (3146 3146 (:REWRITE INTEGERP-<-CONSTANT))
 (3146 3146 (:REWRITE CONSTANT-<-INTEGERP))
 (3146 3146 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3146 3146 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3146 3146 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3146 3146 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3146 3146 (:REWRITE |(< c (- x))|))
 (3146 3146 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3146 3146 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3146 3146 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3146 3146 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3146 3146 (:REWRITE |(< (/ x) (/ y))|))
 (3146 3146 (:REWRITE |(< (- x) c)|))
 (3146 3146 (:REWRITE |(< (- x) (- y))|))
 (2676 2676 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2676 2676 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2676 2676 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2424 152 (:LINEAR MOD-BOUNDS-2))
 (2112 24 (:REWRITE MOD-POSITIVE . 3))
 (1421 1421 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1245 1245 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1245 1245 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1245 1245 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1245 1245 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1245 1245 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1232 1232 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1232 1232 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1232 1232 (:REWRITE |(equal c (/ x))|))
 (1232 1232 (:REWRITE |(equal c (- x))|))
 (1232 1232 (:REWRITE |(equal (/ x) c)|))
 (1232 1232 (:REWRITE |(equal (/ x) (/ y))|))
 (1232 1232 (:REWRITE |(equal (- x) c)|))
 (1232 1232 (:REWRITE |(equal (- x) (- y))|))
 (1040 1040 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1028 1028 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1028 1028 (:REWRITE DEFAULT-DIVIDE))
 (980 980 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (980 980 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (946 946 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (946 946 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (946 946 (:REWRITE |(< 0 (/ x))|))
 (946 946 (:REWRITE |(< 0 (* x y))|))
 (924 924 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (924 924 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (924 924 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (924 924 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (924 924 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (722 722 (:REWRITE REDUCE-INTEGERP-+))
 (722 722 (:REWRITE INTEGERP-MINUS-X))
 (722 722 (:META META-INTEGERP-CORRECT))
 (618 310 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (618 310 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (618 310 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (490 490 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (490 490 (:LINEAR EXPT-LINEAR-UPPER-<))
 (490 490 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (490 490 (:LINEAR EXPT-LINEAR-LOWER-<))
 (310 310 (:REWRITE DEFAULT-MOD-2))
 (310 310 (:REWRITE |(mod x (- y))| . 3))
 (310 310 (:REWRITE |(mod x (- y))| . 2))
 (310 310 (:REWRITE |(mod x (- y))| . 1))
 (310 310 (:REWRITE |(mod (- x) y)| . 3))
 (310 310 (:REWRITE |(mod (- x) y)| . 2))
 (310 310 (:REWRITE |(mod (- x) y)| . 1))
 (310 310 (:REWRITE |(- (* c x))|))
 (211 29 (:REWRITE DEFAULT-EXPT-1))
 (76 76 (:LINEAR RTL::MOD-BND-3))
 (36 36 (:REWRITE |(equal (* x y) 0)|))
 (29 29 (:REWRITE DEFAULT-EXPT-2))
 (26 26 (:TYPE-PRESCRIPTION NATP))
 (26 26 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (26 26 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (26 26 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (24 24 (:REWRITE MOD-POSITIVE . 2))
 (24 24 (:REWRITE MOD-POSITIVE . 1))
 (18 18 (:REWRITE |(expt 1/c n)|))
 (18 18 (:REWRITE |(expt (- x) n)|))
 (12 12 (:REWRITE |(expt c (* d n))|))
 (11 11 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (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 |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 )
(DM::ORDER-DIVIDES-1
 (2976 28 (:REWRITE CANCEL-MOD-+))
 (2732 28 (:REWRITE MOD-X-Y-=-X . 4))
 (2440 28 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2230 28 (:REWRITE MOD-ZERO . 4))
 (2021 11 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1998 28 (:REWRITE MOD-X-Y-=-X . 3))
 (1752 232 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1572 28 (:REWRITE MOD-ZERO . 3))
 (1498 1498 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1498 1498 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1498 1498 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1498 1498 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1498 1498 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1496 1496 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1461 96 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1081 1081 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1081 1081 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1081 1081 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (988 28 (:REWRITE |(integerp (- x))|))
 (971 211 (:REWRITE DEFAULT-TIMES-1))
 (936 276 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (904 28 (:REWRITE DEFAULT-MOD-RATIO))
 (904 28 (:REWRITE |(* (- x) y)|))
 (791 211 (:REWRITE DEFAULT-TIMES-2))
 (756 276 (:REWRITE SIMPLIFY-SUMS-<))
 (756 276 (:REWRITE DEFAULT-LESS-THAN-1))
 (724 18 (:REWRITE |(equal (expt x n) 0)|))
 (665 133 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (657 133 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (641 133 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (641 133 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (636 276 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (500 28 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (500 28 (:REWRITE MOD-X-Y-=-X . 2))
 (500 28 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (500 28 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (456 276 (:REWRITE DEFAULT-LESS-THAN-2))
 (444 38 (:LINEAR EXPT->=-1-TWO))
 (444 38 (:LINEAR EXPT->-1-TWO))
 (444 38 (:LINEAR EXPT-<-1-ONE))
 (402 38 (:LINEAR EXPT-X->=-X))
 (402 38 (:LINEAR EXPT->=-1-ONE))
 (402 38 (:LINEAR EXPT-<=-1-TWO))
 (402 38 (:LINEAR EXPT-<=-1-ONE))
 (388 38 (:LINEAR EXPT-X->-X))
 (388 38 (:LINEAR EXPT->-1-ONE))
 (388 38 (:LINEAR EXPT-<-1-TWO))
 (337 76 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (331 39 (:REWRITE DEFAULT-MINUS))
 (320 28 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (320 28 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (320 28 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (320 28 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (320 28 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (310 76 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (296 4 (:LINEAR MOD-BOUNDS-3))
 (276 276 (:REWRITE THE-FLOOR-BELOW))
 (276 276 (:REWRITE THE-FLOOR-ABOVE))
 (276 276 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (276 276 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (276 276 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (276 276 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (276 276 (:REWRITE INTEGERP-<-CONSTANT))
 (276 276 (:REWRITE CONSTANT-<-INTEGERP))
 (276 276 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (276 276 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (276 276 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (276 276 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (276 276 (:REWRITE |(< c (- x))|))
 (276 276 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (276 276 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (276 276 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (276 276 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (276 276 (:REWRITE |(< (/ x) (/ y))|))
 (276 276 (:REWRITE |(< (- x) c)|))
 (276 276 (:REWRITE |(< (- x) (- y))|))
 (236 28 (:REWRITE MOD-CANCEL-*-CONST))
 (232 232 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
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 (232 232 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (208 28 (:REWRITE DEFAULT-MOD-1))
 (162 33 (:REWRITE NORMALIZE-ADDENDS))
 (141 133 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (133 133 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (133 133 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (133 133 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
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 (133 133 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (120 22 (:REWRITE |(+ y x)|))
 (120 8 (:LINEAR MOD-BOUNDS-2))
 (117 77 (:REWRITE DEFAULT-PLUS-2))
 (116 96 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (114 114 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (114 114 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (114 114 (:REWRITE |(equal c (/ x))|))
 (114 114 (:REWRITE |(equal c (- x))|))
 (114 114 (:REWRITE |(equal (/ x) c)|))
 (114 114 (:REWRITE |(equal (/ x) (/ y))|))
 (114 114 (:REWRITE |(equal (- x) c)|))
 (114 114 (:REWRITE |(equal (- x) (- y))|))
 (98 77 (:REWRITE DEFAULT-PLUS-1))
 (96 96 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (95 85 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (91 91 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (91 91 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (91 91 (:REWRITE DEFAULT-DIVIDE))
 (79 79 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (79 79 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (79 79 (:REWRITE |(< 0 (/ x))|))
 (79 79 (:REWRITE |(< 0 (* x y))|))
 (76 76 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (76 76 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (75 11 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (63 63 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (60 60 (:REWRITE REDUCE-INTEGERP-+))
 (60 60 (:REWRITE INTEGERP-MINUS-X))
 (60 60 (:META META-INTEGERP-CORRECT))
 (38 38 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (38 38 (:LINEAR EXPT-LINEAR-UPPER-<))
 (38 38 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (38 38 (:LINEAR EXPT-LINEAR-LOWER-<))
 (28 28 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (28 28 (:REWRITE DEFAULT-MOD-2))
 (28 28 (:REWRITE |(mod x (- y))| . 3))
 (28 28 (:REWRITE |(mod x (- y))| . 2))
 (28 28 (:REWRITE |(mod x (- y))| . 1))
 (28 28 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (28 28 (:REWRITE |(mod (- x) y)| . 3))
 (28 28 (:REWRITE |(mod (- x) y)| . 2))
 (28 28 (:REWRITE |(mod (- x) y)| . 1))
 (28 28 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (28 28 (:REWRITE |(- (* c x))|))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (22 22 (:REWRITE |(equal (+ (- c) x) y)|))
 (22 22 (:DEFINITION FIX))
 (21 11 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (21 11 (:REWRITE |(+ 0 x)|))
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 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (12 6 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (11 11 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (11 11 (:REWRITE |(+ x (- x))|))
 (11 11 (:REWRITE |(+ c (+ d x))|))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (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))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:REWRITE DEFAULT-EXPT-2))
 (2 2 (:REWRITE DEFAULT-EXPT-1))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 )
(DM::ORDER-DIVIDES-2
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 (54982 49 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (46699 137 (:LINEAR EXPT-X->=-X))
 (41062 388 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (40775 388 (:REWRITE CANCEL-MOD-+))
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 (34924 34924 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (32150 6430 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (31866 6430 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (31658 6430 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (31658 6430 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (22506 1164 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (20202 388 (:REWRITE MOD-ZERO . 3))
 (16777 388 (:REWRITE MOD-X-Y-=-X . 4))
 (13781 388 (:REWRITE |(integerp (- x))|))
 (13006 2208 (:REWRITE DEFAULT-TIMES-1))
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 (11866 388 (:REWRITE |(* (- x) y)|))
 (10822 1835 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (10501 2208 (:REWRITE DEFAULT-TIMES-2))
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 (9092 1835 (:REWRITE DEFAULT-LESS-THAN-1))
 (9085 1835 (:REWRITE SIMPLIFY-SUMS-<))
 (8470 6430 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (7318 7318 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (7318 7318 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (7318 7318 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (7318 7318 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (7318 7318 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6982 388 (:REWRITE MOD-X-Y-=-X+Y . 2))
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 (6982 388 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (6982 388 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (6430 6430 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (6082 1835 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
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 (3136 388 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (3136 388 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (1835 1835 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (1835 1835 (:REWRITE INTEGERP-<-CONSTANT))
 (1835 1835 (:REWRITE CONSTANT-<-INTEGERP))
 (1835 1835 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (1835 1835 (:REWRITE |(< c (- x))|))
 (1835 1835 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (1835 1835 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1835 1835 (:REWRITE |(< (/ x) (/ y))|))
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 (1713 388 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1713 388 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (1315 1315 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
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 (1164 1164 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
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 (928 928 (:REWRITE REDUCE-INTEGERP-+))
 (928 928 (:META META-INTEGERP-CORRECT))
 (892 892 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (875 418 (:REWRITE DEFAULT-PLUS-2))
 (846 274 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (825 33 (:REWRITE MOD-POSITIVE . 3))
 (802 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (788 53 (:REWRITE RTL::INTEGERP-FL))
 (702 418 (:REWRITE DEFAULT-PLUS-1))
 (392 392 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (392 392 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (392 392 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (392 392 (:REWRITE |(equal c (/ x))|))
 (392 392 (:REWRITE |(equal c (- x))|))
 (392 392 (:REWRITE |(equal (/ x) c)|))
 (392 392 (:REWRITE |(equal (/ x) (/ y))|))
 (392 392 (:REWRITE |(equal (- x) c)|))
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 (324 274 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
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 (317 166 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
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 (307 307 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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 (274 274 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (250 245 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (236 236 (:REWRITE DEFAULT-EXPT-1))
 (236 236 (:REWRITE |(expt 1/c n)|))
 (236 236 (:REWRITE |(expt (- x) n)|))
 (226 49 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (170 62 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (166 166 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
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 (165 33 (:REWRITE MOD-NONPOSITIVE))
 (151 151 (:TYPE-PRESCRIPTION NATP))
 (138 138 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (138 138 (:LINEAR EXPT-LINEAR-UPPER-<))
 (138 138 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (138 138 (:LINEAR EXPT-LINEAR-LOWER-<))
 (137 137 (:LINEAR EXPT->-1-TWO))
 (137 137 (:LINEAR EXPT-<-1-ONE))
 (126 4 (:LINEAR RTL::FL-DEF))
 (121 121 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (104 104 (:REWRITE |(equal (+ (- c) x) y)|))
 (98 98 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (86 86 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (84 84 (:LINEAR RTL::MOD-BND-3))
 (79 79 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (79 79 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (55 55 (:REWRITE |(+ c (+ d x))|))
 (53 2 (:REWRITE |(integerp (expt x n))|))
 (33 33 (:REWRITE MOD-POSITIVE . 2))
 (33 33 (:REWRITE MOD-POSITIVE . 1))
 (14 1 (:REWRITE |(* y (* x z))|))
 (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 |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (8 8 (:REWRITE |(expt c (* d n))|))
 (7 7 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (7 7 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:LINEAR RTL::FL-MONOTONE-LINEAR))
 (3 3 (:REWRITE |(* (expt c m) (expt d n))|))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:LINEAR RTL::N<=FL-LINEAR))
 (1 1 (:REWRITE |(* a (/ a))|))
 )
(DM::ORDER-DIVIDES-3
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 (8876 124 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7656 14 (:LINEAR EXPT-X->=-X))
 (7346 14 (:LINEAR EXPT-<=-1-TWO))
 (6640 80 (:REWRITE RTL::MOD-DOES-NOTHING))
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 (2968 640 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2548 640 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2108 79 (:REWRITE MOD-X-Y-=-X . 4))
 (1591 76 (:REWRITE |(integerp (- x))|))
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 (1304 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1258 80 (:REWRITE DEFAULT-MOD-RATIO))
 (1252 79 (:REWRITE |(* (- x) y)|))
 (1232 80 (:REWRITE MOD-ZERO . 4))
 (1043 1043 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1043 1043 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1043 1043 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1043 1043 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1043 1043 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
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 (640 640 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
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 (633 79 (:REWRITE MOD-X-Y-=-X . 2))
 (633 79 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (633 79 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (616 356 (:REWRITE DEFAULT-LESS-THAN-2))
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 (534 105 (:REWRITE DEFAULT-MINUS))
 (509 80 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (509 80 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (467 77 (:REWRITE NORMALIZE-ADDENDS))
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 (395 183 (:REWRITE DEFAULT-PLUS-2))
 (357 357 (:REWRITE THE-FLOOR-BELOW))
 (357 357 (:REWRITE THE-FLOOR-ABOVE))
 (356 356 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (356 356 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (356 356 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (356 356 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
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 (348 79 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
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 (348 12 (:LINEAR MOD-BOUNDS-3))
 (311 52 (:REWRITE |(+ y x)|))
 (295 124 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (268 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (268 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (268 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (262 183 (:REWRITE DEFAULT-PLUS-1))
 (259 259 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (259 259 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (259 259 (:REWRITE DEFAULT-DIVIDE))
 (252 126 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (239 79 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (239 79 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (239 79 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (231 25 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (222 14 (:LINEAR EXPT->=-1-TWO))
 (222 14 (:LINEAR EXPT-<=-1-ONE))
 (214 14 (:LINEAR EXPT-X->-X))
 (214 14 (:LINEAR EXPT->-1-ONE))
 (214 14 (:LINEAR EXPT-<-1-TWO))
 (205 80 (:REWRITE DEFAULT-MOD-1))
 (181 181 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (177 177 (:REWRITE REDUCE-INTEGERP-+))
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 (177 177 (:META META-INTEGERP-CORRECT))
 (156 24 (:LINEAR MOD-BOUNDS-2))
 (151 98 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (126 126 (:TYPE-PRESCRIPTION NATP))
 (126 126 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (126 6 (:REWRITE MOD-POSITIVE . 3))
 (124 124 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (124 124 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (124 124 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (124 124 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (124 124 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (124 124 (:REWRITE |(equal c (/ x))|))
 (124 124 (:REWRITE |(equal c (- x))|))
 (124 124 (:REWRITE |(equal (/ x) c)|))
 (124 124 (:REWRITE |(equal (/ x) (/ y))|))
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 (124 124 (:REWRITE |(equal (- x) (- y))|))
 (106 28 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (99 99 (:TYPE-PRESCRIPTION RATIONALP-MOD))
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 (79 79 (:REWRITE |(mod x (- y))| . 3))
 (79 79 (:REWRITE |(mod x (- y))| . 2))
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 (79 26 (:REWRITE |(equal (mod (+ x y) z) x)|))
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 (54 54 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (54 54 (:REWRITE |(< 0 (/ x))|))
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 (52 52 (:DEFINITION FIX))
 (51 51 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (51 51 (:REWRITE |(equal (+ (- c) x) y)|))
 (47 47 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (37 37 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (37 37 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (37 37 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (31 31 (:REWRITE DEFAULT-EXPT-1))
 (31 31 (:REWRITE |(expt 1/c n)|))
 (31 31 (:REWRITE |(expt (- x) n)|))
 (28 28 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (28 28 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (26 26 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (26 26 (:REWRITE |(+ x (- x))|))
 (25 25 (:REWRITE |(+ c (+ d x))|))
 (25 5 (:REWRITE MOD-NONPOSITIVE))
 (25 1 (:REWRITE MOD-ZERO . 1))
 (16 1 (:REWRITE |(+ y (+ x z))|))
 (14 14 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (14 14 (:LINEAR EXPT-LINEAR-UPPER-<))
 (14 14 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (14 14 (:LINEAR EXPT-LINEAR-LOWER-<))
 (14 14 (:LINEAR EXPT->-1-TWO))
 (14 14 (:LINEAR EXPT-<-1-ONE))
 (13 13 (:LINEAR RTL::MOD-BND-3))
 (6 6 (:REWRITE MOD-POSITIVE . 2))
 (5 1 (:REWRITE MOD-ZERO . 2))
 (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)|))
 (2 1 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 )
(DM::ORDER-DIVIDES
 (3137 845 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (3137 845 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2518 1278 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2302 16 (:REWRITE CANCEL-MOD-+))
 (2005 7 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1965 16 (:REWRITE MOD-X-Y-=-X . 4))
 (1931 16 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1381 16 (:REWRITE MOD-ZERO . 4))
 (1293 46 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1278 1278 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1278 1278 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1278 1278 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1199 16 (:REWRITE MOD-ZERO . 3))
 (987 16 (:REWRITE MOD-X-Y-=-X . 3))
 (845 845 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (845 845 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (845 845 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (845 845 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (804 116 (:REWRITE DEFAULT-TIMES-1))
 (770 770 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (745 16 (:REWRITE |(integerp (- x))|))
 (725 50 (:REWRITE |(* y x)|))
 (697 16 (:REWRITE DEFAULT-MOD-RATIO))
 (697 16 (:REWRITE |(* (- x) y)|))
 (688 153 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (641 116 (:REWRITE DEFAULT-TIMES-2))
 (623 623 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (623 623 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (623 623 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (534 153 (:REWRITE SIMPLIFY-SUMS-<))
 (534 153 (:REWRITE DEFAULT-LESS-THAN-1))
 (470 153 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (410 82 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (406 16 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (406 16 (:REWRITE MOD-X-Y-=-X . 2))
 (406 16 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (406 16 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (362 82 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (338 82 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (338 82 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (307 153 (:REWRITE DEFAULT-LESS-THAN-2))
 (265 9 (:REWRITE |(equal (expt x n) 0)|))
 (250 23 (:REWRITE DEFAULT-MINUS))
 (243 16 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (243 16 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (243 16 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (243 16 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (243 16 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (232 48 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (228 2 (:LINEAR MOD-BOUNDS-3))
 (219 48 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (195 24 (:LINEAR EXPT->=-1-TWO))
 (193 24 (:LINEAR EXPT->=-1-ONE))
 (184 24 (:LINEAR EXPT-<=-1-TWO))
 (179 24 (:LINEAR EXPT-X->=-X))
 (179 16 (:REWRITE DEFAULT-MOD-1))
 (174 24 (:LINEAR EXPT-X->-X))
 (174 24 (:LINEAR EXPT->-1-ONE))
 (174 24 (:LINEAR EXPT-<-1-TWO))
 (169 24 (:LINEAR EXPT->-1-TWO))
 (169 24 (:LINEAR EXPT-<-1-ONE))
 (153 153 (:REWRITE THE-FLOOR-BELOW))
 (153 153 (:REWRITE THE-FLOOR-ABOVE))
 (153 153 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (153 153 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (153 153 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (153 153 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (153 153 (:REWRITE INTEGERP-<-CONSTANT))
 (153 153 (:REWRITE CONSTANT-<-INTEGERP))
 (153 153 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (153 153 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (153 153 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (153 153 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (153 153 (:REWRITE |(< c (- x))|))
 (153 153 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (153 153 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (153 153 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (153 153 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (153 153 (:REWRITE |(< (/ x) (/ y))|))
 (153 153 (:REWRITE |(< (- x) c)|))
 (153 153 (:REWRITE |(< (- x) (- y))|))
 (126 82 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (114 21 (:REWRITE NORMALIZE-ADDENDS))
 (111 16 (:REWRITE MOD-CANCEL-*-CONST))
 (92 4 (:LINEAR MOD-BOUNDS-2))
 (89 49 (:REWRITE DEFAULT-PLUS-2))
 (88 88 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (82 82 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (82 82 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (82 82 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (82 82 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (80 14 (:REWRITE |(+ y x)|))
 (66 49 (:REWRITE DEFAULT-PLUS-1))
 (66 46 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (55 55 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (55 55 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (55 55 (:REWRITE |(equal c (/ x))|))
 (55 55 (:REWRITE |(equal c (- x))|))
 (55 55 (:REWRITE |(equal (/ x) c)|))
 (55 55 (:REWRITE |(equal (/ x) (/ y))|))
 (55 55 (:REWRITE |(equal (- x) c)|))
 (55 55 (:REWRITE |(equal (- x) (- y))|))
 (55 7 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (55 7 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (50 50 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (50 50 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (50 50 (:REWRITE DEFAULT-DIVIDE))
 (49 39 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (48 48 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (48 48 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (46 46 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (43 43 (:REWRITE REDUCE-INTEGERP-+))
 (43 43 (:REWRITE INTEGERP-MINUS-X))
 (43 43 (:META META-INTEGERP-CORRECT))
 (34 34 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (34 34 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (34 34 (:REWRITE |(< 0 (/ x))|))
 (34 34 (:REWRITE |(< 0 (* x y))|))
 (25 25 (:REWRITE DEFAULT-EXPT-2))
 (25 25 (:REWRITE DEFAULT-EXPT-1))
 (25 25 (:REWRITE |(expt 1/c n)|))
 (25 25 (:REWRITE |(expt (- x) n)|))
 (24 24 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (24 24 (:LINEAR EXPT-LINEAR-UPPER-<))
 (24 24 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (24 24 (:LINEAR EXPT-LINEAR-LOWER-<))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (21 21 (:TYPE-PRESCRIPTION NATP))
 (21 21 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (21 21 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (21 21 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (17 7 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (17 7 (:REWRITE |(+ 0 x)|))
 (16 16 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (16 16 (:REWRITE DEFAULT-MOD-2))
 (16 16 (:REWRITE |(mod x (- y))| . 3))
 (16 16 (:REWRITE |(mod x (- y))| . 2))
 (16 16 (:REWRITE |(mod x (- y))| . 1))
 (16 16 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (16 16 (:REWRITE |(mod (- x) y)| . 3))
 (16 16 (:REWRITE |(mod (- x) y)| . 2))
 (16 16 (:REWRITE |(mod (- x) y)| . 1))
 (16 16 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (16 16 (:REWRITE |(- (* c x))|))
 (14 14 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (14 14 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (14 14 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (14 14 (:REWRITE ZIP-OPEN))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (14 14 (:REWRITE |(equal (+ (- c) x) y)|))
 (14 14 (:DEFINITION FIX))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:REWRITE |(< (/ x) 0)|))
 (8 8 (:REWRITE |(< (* x y) 0)|))
 (7 7 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (7 7 (:REWRITE |(+ x (- x))|))
 (7 7 (:REWRITE |(+ c (+ d x))|))
 (4 4 (:REWRITE EXPT-X->-X))
 (3 3 (:REWRITE |(expt x 0)|))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |(equal x (if a b c))|))
 (2 2 (:REWRITE |(equal (if a b c) x)|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 )
(DM::MAX-ORDER-P)
(DM::MOD-POWERS
 (5 1 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (2 1 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1 1 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1 1 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1 1 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1 1 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1 1 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1 1 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (1 1 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 )
(DM::POWERS-DISTINCT-1
 (23427 25 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (10657 83 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (9474 79 (:REWRITE CANCEL-MOD-+))
 (9403 5723 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (8415 79 (:REWRITE MOD-X-Y-=-X . 3))
 (8076 25 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (7694 2530 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5723 5723 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (5723 5723 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (5723 5723 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (5723 5723 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5628 5628 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (5628 5628 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (5628 5628 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4785 79 (:REWRITE MOD-ZERO . 3))
 (4545 909 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (4545 909 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (4197 909 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (4197 909 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (3895 606 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3299 643 (:REWRITE DEFAULT-TIMES-1))
 (3262 79 (:REWRITE |(integerp (- x))|))
 (3077 83 (:REWRITE DEFAULT-MOD-RATIO))
 (2953 909 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (2810 80 (:REWRITE |(* (- x) y)|))
 (2761 79 (:REWRITE MOD-X-Y-=-X . 4))
 (2713 643 (:REWRITE DEFAULT-TIMES-2))
 (2530 2530 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2530 2530 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2530 2530 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2487 606 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2419 90 (:LINEAR EXPT-X->=-X))
 (2415 606 (:REWRITE DEFAULT-LESS-THAN-1))
 (2367 558 (:REWRITE SIMPLIFY-SUMS-<))
 (2333 96 (:LINEAR EXPT-<=-1-TWO))
 (1747 83 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1583 79 (:REWRITE MOD-X-Y-=-X . 2))
 (1583 79 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1583 79 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1388 17 (:LINEAR MOD-BOUNDS-3))
 (1081 83 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1081 83 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1078 90 (:LINEAR EXPT->=-1-TWO))
 (1046 96 (:LINEAR EXPT-<-1-TWO))
 (1045 109 (:REWRITE DEFAULT-MINUS))
 (1040 90 (:LINEAR EXPT-X->-X))
 (1040 90 (:LINEAR EXPT->-1-ONE))
 (976 79 (:REWRITE MOD-CANCEL-*-CONST))
 (909 909 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (909 909 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (909 909 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (909 909 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (793 556 (:REWRITE DEFAULT-PLUS-2))
 (749 83 (:REWRITE DEFAULT-MOD-1))
 (704 556 (:REWRITE DEFAULT-PLUS-1))
 (678 606 (:REWRITE DEFAULT-LESS-THAN-2))
 (651 79 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (651 79 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (651 79 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (624 312 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (606 606 (:REWRITE THE-FLOOR-BELOW))
 (606 606 (:REWRITE THE-FLOOR-ABOVE))
 (606 606 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (606 606 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (606 606 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (606 606 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (606 606 (:REWRITE INTEGERP-<-CONSTANT))
 (606 606 (:REWRITE CONSTANT-<-INTEGERP))
 (606 606 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (606 606 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (606 606 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (606 606 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (606 606 (:REWRITE |(< c (- x))|))
 (606 606 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (606 606 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (606 606 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (606 606 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (606 606 (:REWRITE |(< (/ x) (/ y))|))
 (606 606 (:REWRITE |(< (- x) c)|))
 (606 606 (:REWRITE |(< (- x) (- y))|))
 (591 94 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (566 34 (:LINEAR MOD-BOUNDS-2))
 (450 65 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (417 79 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (417 79 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (417 79 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (395 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (330 180 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (312 312 (:TYPE-PRESCRIPTION NATP))
 (312 312 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (312 312 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (312 312 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (284 180 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (284 46 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (270 270 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (259 259 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (259 259 (:REWRITE DEFAULT-DIVIDE))
 (202 176 (:REWRITE INTEGERP-MINUS-X))
 (180 180 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (176 176 (:REWRITE REDUCE-INTEGERP-+))
 (176 176 (:META META-INTEGERP-CORRECT))
 (106 106 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (102 102 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (102 102 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (102 102 (:REWRITE |(equal c (/ x))|))
 (102 102 (:REWRITE |(equal c (- x))|))
 (102 102 (:REWRITE |(equal (/ x) c)|))
 (102 102 (:REWRITE |(equal (/ x) (/ y))|))
 (102 102 (:REWRITE |(equal (- x) c)|))
 (102 102 (:REWRITE |(equal (- x) (- y))|))
 (101 101 (:REWRITE DEFAULT-EXPT-2))
 (101 101 (:REWRITE DEFAULT-EXPT-1))
 (101 101 (:REWRITE |(expt 1/c n)|))
 (101 101 (:REWRITE |(expt (- x) n)|))
 (96 96 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (96 96 (:LINEAR EXPT-LINEAR-UPPER-<))
 (96 96 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (96 96 (:LINEAR EXPT-LINEAR-LOWER-<))
 (94 94 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (90 90 (:LINEAR EXPT->-1-TWO))
 (90 90 (:LINEAR EXPT-<-1-ONE))
 (88 25 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (87 78 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (84 84 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (83 83 (:REWRITE DEFAULT-MOD-2))
 (81 81 (:REWRITE |(- (* c x))|))
 (79 79 (:REWRITE |(mod x (- y))| . 3))
 (79 79 (:REWRITE |(mod x (- y))| . 2))
 (79 79 (:REWRITE |(mod x (- y))| . 1))
 (79 79 (:REWRITE |(mod (- x) y)| . 3))
 (79 79 (:REWRITE |(mod (- x) y)| . 2))
 (79 79 (:REWRITE |(mod (- x) y)| . 1))
 (78 78 (:REWRITE |(< y (+ (- c) x))|))
 (78 78 (:REWRITE |(< x (+ c/d y))|))
 (62 62 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (51 51 (:REWRITE |(equal (+ (- c) x) y)|))
 (48 48 (:REWRITE |(+ c (+ d x))|))
 (38 38 (:REWRITE |(< 0 (/ x))|))
 (38 38 (:REWRITE |(< 0 (* x y))|))
 (24 24 (:REWRITE |(< (+ c/d x) y)|))
 (24 24 (:REWRITE |(< (+ (- c) x) y)|))
 (18 18 (:LINEAR RTL::MOD-BND-3))
 (15 15 (:REWRITE |(expt c (* d n))|))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (6 6 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (5 5 (:REWRITE |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE EXPT-X->-X))
 (3 3 (:REWRITE |(equal (* x y) 0)|))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE |(equal x (if a b c))|))
 (1 1 (:REWRITE |(* x (- y))|))
 (1 1 (:REWRITE |(* (expt c m) (expt d n))|))
 )
(DM::POWERS-DISTINCT-2
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 )
(DM::POWERS-DISTINCT-3
 (10394 46 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4788 36 (:REWRITE CANCEL-MOD-+))
 (4625 36 (:REWRITE MOD-X-Y-=-X . 3))
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 (36 36 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
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(DM::POWERS-DISTINCT-4
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(DM::POWERS-DISTINCT-5
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 (252 18 (:LINEAR MOD-BOUNDS-2))
 (205 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (202 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (165 165 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (160 160 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (160 160 (:REWRITE DEFAULT-DIVIDE))
 (126 126 (:TYPE-PRESCRIPTION NATP))
 (126 126 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (126 126 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (126 126 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
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 (116 116 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (116 116 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
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 (109 109 (:META META-INTEGERP-CORRECT))
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 (66 66 (:REWRITE |(expt 1/c n)|))
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 (58 58 (:LINEAR EXPT-LINEAR-LOWER-<))
 (58 58 (:LINEAR EXPT->-1-TWO))
 (58 58 (:LINEAR EXPT-<-1-ONE))
 (55 37 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (52 52 (:REWRITE |(- (* c x))|))
 (51 51 (:REWRITE DEFAULT-MOD-2))
 (51 51 (:REWRITE |(mod x (- y))| . 3))
 (51 51 (:REWRITE |(mod x (- y))| . 2))
 (51 51 (:REWRITE |(mod x (- y))| . 1))
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 (35 35 (:REWRITE |(+ x (- x))|))
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 (30 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (26 1 (:REWRITE |(integerp (expt x n))|))
 (24 24 (:REWRITE |(< 0 (/ x))|))
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 (19 19 (:REWRITE |(+ c (+ d x))|))
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 (10 10 (:REWRITE |(< (+ (- c) x) y)|))
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 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
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 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (4 4 (:REWRITE |(equal c (/ x))|))
 (4 4 (:REWRITE |(equal c (- x))|))
 (4 4 (:REWRITE |(equal (/ x) c)|))
 (4 4 (:REWRITE |(equal (/ x) (/ y))|))
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 (2 2 (:REWRITE |(* (expt c m) (expt d n))|))
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 )
(DM::POWERS-DISTINCT-6
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 (680 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
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 (663 663 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (663 663 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (663 663 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (663 663 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (663 663 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
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 (375 75 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (366 60 (:REWRITE DEFAULT-TIMES-1))
 (359 75 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (359 75 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (338 26 (:REWRITE |(* y x)|))
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 (320 8 (:REWRITE |(* (- x) y)|))
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 (273 57 (:REWRITE DEFAULT-LESS-THAN-1))
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 (184 8 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (2 2 (:REWRITE |(< x (+ c/d y))|))
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 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(DM::POWERS-DISTINCT-7
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 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
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 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(DM::POWERS-DISTINCT-8
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 )
(DM::POWERS-DISTINCT-11
 (1014 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (823 1 (:LINEAR RTL::MOD-BND-1))
 (671 5 (:REWRITE MOD-X-Y-=-X . 3))
 (660 5 (:REWRITE CANCEL-MOD-+))
 (586 5 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (578 514 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (571 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (514 514 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (514 514 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (514 514 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (514 514 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (452 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (403 403 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (403 403 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (403 403 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (345 5 (:REWRITE MOD-ZERO . 3))
 (250 50 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (250 50 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (246 50 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (246 50 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (242 53 (:REWRITE DEFAULT-TIMES-1))
 (215 5 (:REWRITE |(integerp (- x))|))
 (200 5 (:REWRITE DEFAULT-MOD-RATIO))
 (200 5 (:REWRITE |(* (- x) y)|))
 (197 53 (:REWRITE DEFAULT-TIMES-2))
 (195 60 (:REWRITE SIMPLIFY-SUMS-<))
 (195 60 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (195 60 (:REWRITE DEFAULT-LESS-THAN-1))
 (193 11 (:LINEAR EXPT->=-1-TWO))
 (193 11 (:LINEAR EXPT-<=-1-ONE))
 (191 11 (:LINEAR EXPT-X->=-X))
 (186 11 (:LINEAR EXPT-X->-X))
 (186 11 (:LINEAR EXPT->-1-ONE))
 (186 11 (:LINEAR EXPT-<-1-TWO))
 (160 5 (:REWRITE MOD-X-Y-=-X . 4))
 (150 50 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (115 5 (:REWRITE MOD-ZERO . 4))
 (115 5 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (115 5 (:REWRITE MOD-X-Y-=-X . 2))
 (115 5 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (115 5 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (105 60 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (71 6 (:REWRITE DEFAULT-MINUS))
 (70 5 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (70 5 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (70 5 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (70 5 (:REWRITE MOD-CANCEL-*-CONST))
 (70 5 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (70 5 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (69 1 (:LINEAR MOD-BOUNDS-3))
 (60 60 (:REWRITE THE-FLOOR-BELOW))
 (60 60 (:REWRITE THE-FLOOR-ABOVE))
 (60 60 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (60 60 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (60 60 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (60 60 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (60 60 (:REWRITE INTEGERP-<-CONSTANT))
 (60 60 (:REWRITE DEFAULT-LESS-THAN-2))
 (60 60 (:REWRITE CONSTANT-<-INTEGERP))
 (60 60 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (60 60 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (60 60 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (60 60 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (60 60 (:REWRITE |(< c (- x))|))
 (60 60 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (60 60 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (60 60 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (60 60 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (60 60 (:REWRITE |(< (/ x) (/ y))|))
 (60 60 (:REWRITE |(< (- x) c)|))
 (60 60 (:REWRITE |(< (- x) (- y))|))
 (50 50 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (50 50 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (50 50 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (50 50 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (50 5 (:REWRITE DEFAULT-MOD-1))
 (46 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (43 7 (:REWRITE DEFAULT-PLUS-2))
 (39 3 (:REWRITE NORMALIZE-ADDENDS))
 (37 37 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (28 2 (:LINEAR MOD-BOUNDS-2))
 (23 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (22 22 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (22 22 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (22 22 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (22 22 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (22 22 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (22 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (20 20 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (19 2 (:REWRITE |(+ y x)|))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (18 18 (:REWRITE DEFAULT-DIVIDE))
 (17 7 (:REWRITE DEFAULT-PLUS-1))
 (13 13 (:REWRITE DEFAULT-EXPT-2))
 (13 13 (:REWRITE DEFAULT-EXPT-1))
 (13 13 (:REWRITE |(expt 1/c n)|))
 (13 13 (:REWRITE |(expt (- x) n)|))
 (12 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:META META-INTEGERP-CORRECT))
 (11 11 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (11 11 (:LINEAR EXPT-LINEAR-UPPER-<))
 (11 11 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (11 11 (:LINEAR EXPT-LINEAR-LOWER-<))
 (11 11 (:LINEAR EXPT->-1-TWO))
 (11 11 (:LINEAR EXPT-<=-1-TWO))
 (11 11 (:LINEAR EXPT-<-1-ONE))
 (11 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (10 1 (:REWRITE |(+ 0 x)|))
 (8 8 (:REWRITE |(expt c (* d n))|))
 (5 5 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE |(mod x (- y))| . 3))
 (5 5 (:REWRITE |(mod x (- y))| . 2))
 (5 5 (:REWRITE |(mod x (- y))| . 1))
 (5 5 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(mod (- x) y)| . 3))
 (5 5 (:REWRITE |(mod (- x) y)| . 2))
 (5 5 (:REWRITE |(mod (- x) y)| . 1))
 (5 5 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(- (* c x))|))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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))|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (2 1 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1 1 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (1 1 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (1 1 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::POWERS-DISTINCT
 (3432 26 (:REWRITE CANCEL-MOD-+))
 (2884 26 (:REWRITE MOD-X-Y-=-X . 3))
 (2544 26 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2020 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1839 1839 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1839 1839 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1839 1839 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1839 1839 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1839 1839 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1839 1839 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1493 10 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1386 26 (:REWRITE MOD-ZERO . 3))
 (1118 26 (:REWRITE |(integerp (- x))|))
 (1085 176 (:REWRITE DEFAULT-TIMES-1))
 (1040 26 (:REWRITE DEFAULT-MOD-RATIO))
 (1040 26 (:REWRITE |(* (- x) y)|))
 (975 75 (:REWRITE |(* y x)|))
 (870 276 (:REWRITE DEFAULT-LESS-THAN-1))
 (868 274 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (851 176 (:REWRITE DEFAULT-TIMES-2))
 (832 26 (:REWRITE MOD-X-Y-=-X . 4))
 (821 821 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (821 821 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (821 821 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (713 36 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (598 26 (:REWRITE MOD-ZERO . 4))
 (598 26 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (598 26 (:REWRITE MOD-X-Y-=-X . 2))
 (598 26 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (598 26 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (568 48 (:LINEAR EXPT->=-1-TWO))
 (568 48 (:LINEAR EXPT-<=-1-ONE))
 (555 111 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (548 48 (:LINEAR EXPT-X->-X))
 (548 48 (:LINEAR EXPT->-1-ONE))
 (548 48 (:LINEAR EXPT-<-1-TWO))
 (546 96 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (508 274 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (498 48 (:LINEAR EXPT-X->=-X))
 (419 111 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (383 111 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (383 111 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (383 111 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (368 30 (:REWRITE DEFAULT-MINUS))
 (364 26 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (364 26 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (325 85 (:REWRITE ACL2-NUMBERP-X))
 (304 36 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (296 10 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (286 26 (:REWRITE MOD-CANCEL-*-CONST))
 (276 276 (:REWRITE THE-FLOOR-BELOW))
 (276 276 (:REWRITE THE-FLOOR-ABOVE))
 (276 276 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (276 276 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (276 276 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (276 276 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (276 276 (:REWRITE INTEGERP-<-CONSTANT))
 (276 276 (:REWRITE DEFAULT-LESS-THAN-2))
 (276 276 (:REWRITE CONSTANT-<-INTEGERP))
 (276 276 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (276 276 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (276 276 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (276 276 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (276 276 (:REWRITE |(< c (- x))|))
 (276 276 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (276 276 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (276 276 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (276 276 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (276 276 (:REWRITE |(< (/ x) (/ y))|))
 (276 276 (:REWRITE |(< (- x) c)|))
 (276 276 (:REWRITE |(< (- x) (- y))|))
 (260 26 (:REWRITE DEFAULT-MOD-1))
 (234 26 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (234 26 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (234 26 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (202 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (202 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (202 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (193 103 (:REWRITE DEFAULT-PLUS-2))
 (169 103 (:REWRITE DEFAULT-PLUS-1))
 (156 26 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (156 26 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (156 26 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (138 2 (:LINEAR MOD-BOUNDS-3))
 (120 27 (:REWRITE RATIONALP-X))
 (111 111 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (111 111 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (111 111 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (111 111 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (110 35 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (101 83 (:REWRITE DEFAULT-CAR))
 (100 10 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (96 96 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (96 96 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (96 96 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (95 95 (:REWRITE REDUCE-INTEGERP-+))
 (95 95 (:REWRITE INTEGERP-MINUS-X))
 (95 95 (:META META-INTEGERP-CORRECT))
 (91 1 (:REWRITE MOD-ZERO . 1))
 (86 43 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (83 11 (:REWRITE |(equal (+ (- c) x) y)|))
 (75 75 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (75 75 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (75 75 (:REWRITE DEFAULT-DIVIDE))
 (75 63 (:REWRITE DEFAULT-CDR))
 (56 4 (:LINEAR MOD-BOUNDS-2))
 (54 54 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (51 51 (:REWRITE DM::PERM-MEMBER))
 (50 50 (:REWRITE DEFAULT-EXPT-2))
 (50 50 (:REWRITE DEFAULT-EXPT-1))
 (50 50 (:REWRITE |(expt 1/c n)|))
 (50 50 (:REWRITE |(expt (- x) n)|))
 (48 48 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (48 48 (:LINEAR EXPT-LINEAR-UPPER-<))
 (48 48 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (48 48 (:LINEAR EXPT-LINEAR-LOWER-<))
 (48 48 (:LINEAR EXPT->-1-TWO))
 (48 48 (:LINEAR EXPT-<=-1-TWO))
 (48 48 (:LINEAR EXPT-<-1-ONE))
 (43 43 (:TYPE-PRESCRIPTION NATP))
 (43 43 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (43 43 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (43 43 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (43 43 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (37 37 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (37 37 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (37 37 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (37 37 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (36 36 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (36 36 (:REWRITE |(equal c (/ x))|))
 (36 36 (:REWRITE |(equal c (- x))|))
 (36 36 (:REWRITE |(equal (/ x) c)|))
 (36 36 (:REWRITE |(equal (/ x) (/ y))|))
 (36 36 (:REWRITE |(equal (- x) c)|))
 (36 36 (:REWRITE |(equal (- x) (- y))|))
 (31 31 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (31 31 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (31 31 (:REWRITE |(< 0 (/ x))|))
 (31 31 (:REWRITE |(< 0 (* x y))|))
 (27 27 (:REWRITE REDUCE-RATIONALP-+))
 (27 27 (:REWRITE REDUCE-RATIONALP-*))
 (27 27 (:REWRITE RATIONALP-MINUS-X))
 (27 27 (:META META-RATIONALP-CORRECT))
 (26 26 (:REWRITE DEFAULT-MOD-2))
 (26 26 (:REWRITE |(mod x (- y))| . 3))
 (26 26 (:REWRITE |(mod x (- y))| . 2))
 (26 26 (:REWRITE |(mod x (- y))| . 1))
 (26 26 (:REWRITE |(mod (- x) y)| . 3))
 (26 26 (:REWRITE |(mod (- x) y)| . 2))
 (26 26 (:REWRITE |(mod (- x) y)| . 1))
 (26 26 (:REWRITE |(- (* c x))|))
 (23 1 (:REWRITE MOD-ZERO . 2))
 (23 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (14 14 (:REWRITE |(< (+ c/d x) y)|))
 (14 14 (:REWRITE |(< (+ (- c) x) y)|))
 (8 8 (:LINEAR RTL::MOD-BND-3))
 (7 7 (:REWRITE |(< (/ x) 0)|))
 (7 7 (:REWRITE |(< (* x y) 0)|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(DM::LEN-MOD-POWERS
 (9168 18 (:REWRITE RTL::MOD-DOES-NOTHING))
 (5582 12 (:REWRITE |(< (if a b c) x)|))
 (3272 270 (:REWRITE DEFAULT-LESS-THAN-2))
 (1236 51 (:REWRITE RATIONALP-X))
 (1080 144 (:REWRITE DEFAULT-TIMES-1))
 (1065 45 (:REWRITE REDUCE-RATIONALP-*))
 (963 144 (:REWRITE DEFAULT-TIMES-2))
 (696 267 (:REWRITE DEFAULT-LESS-THAN-1))
 (681 3 (:REWRITE MOD-ZERO . 4))
 (663 3 (:REWRITE MOD-X-Y-=-X . 4))
 (663 3 (:REWRITE MOD-X-Y-=-X . 3))
 (636 636 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (636 636 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (630 45 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (570 30 (:LINEAR EXPT-<=-1-ONE))
 (566 254 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (558 12 (:DEFINITION RFIX))
 (552 30 (:LINEAR EXPT->=-1-TWO))
 (552 30 (:LINEAR EXPT->-1-TWO))
 (552 30 (:LINEAR EXPT-<-1-ONE))
 (527 254 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (498 30 (:LINEAR EXPT-X->=-X))
 (498 30 (:LINEAR EXPT->=-1-ONE))
 (498 30 (:LINEAR EXPT-<=-1-TWO))
 (480 30 (:LINEAR EXPT-X->-X))
 (480 30 (:LINEAR EXPT->-1-ONE))
 (480 30 (:LINEAR EXPT-<-1-TWO))
 (449 254 (:REWRITE SIMPLIFY-SUMS-<))
 (408 60 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (372 60 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (312 12 (:REWRITE |(equal (if a b c) x)|))
 (294 3 (:REWRITE MOD-ZERO . 3))
 (282 3 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (282 3 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (282 3 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (282 3 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (273 3 (:REWRITE MOD-X-Y-=-X . 2))
 (273 3 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (273 3 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (270 270 (:REWRITE THE-FLOOR-BELOW))
 (270 270 (:REWRITE THE-FLOOR-ABOVE))
 (255 255 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (255 255 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (255 255 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (255 255 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (255 255 (:REWRITE INTEGERP-<-CONSTANT))
 (255 255 (:REWRITE CONSTANT-<-INTEGERP))
 (255 255 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (255 255 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (255 255 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (255 255 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (255 255 (:REWRITE |(< c (- x))|))
 (255 255 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (255 255 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (255 255 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (255 255 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (255 255 (:REWRITE |(< (/ x) (/ y))|))
 (255 255 (:REWRITE |(< (- x) c)|))
 (255 255 (:REWRITE |(< (- x) (- y))|))
 (195 3 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (195 3 (:REWRITE MOD-CANCEL-*-CONST))
 (195 3 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (195 3 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (168 12 (:REWRITE DEFAULT-MOD-1))
 (138 18 (:REWRITE ACL2-NUMBERP-X))
 (87 87 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (87 87 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (87 87 (:REWRITE |(< 0 (/ x))|))
 (87 87 (:REWRITE |(< 0 (* x y))|))
 (81 3 (:REWRITE CANCEL-MOD-+))
 (72 30 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (72 30 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (63 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (63 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (63 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (63 63 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (63 63 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (63 63 (:REWRITE DEFAULT-DIVIDE))
 (62 62 (:REWRITE REDUCE-INTEGERP-+))
 (62 62 (:REWRITE INTEGERP-MINUS-X))
 (62 62 (:META META-INTEGERP-CORRECT))
 (60 60 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (60 60 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (57 9 (:REWRITE |(equal (expt x n) 0)|))
 (54 6 (:REWRITE RATIONALP-/))
 (45 45 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (45 45 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (45 45 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (45 45 (:REWRITE REDUCE-RATIONALP-+))
 (45 45 (:REWRITE RATIONALP-MINUS-X))
 (45 45 (:META META-RATIONALP-CORRECT))
 (33 33 (:REWRITE |(< (/ x) 0)|))
 (33 33 (:REWRITE |(< (* x y) 0)|))
 (33 30 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (31 31 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (31 31 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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))|))
 (30 30 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (30 30 (:LINEAR EXPT-LINEAR-UPPER-<))
 (30 30 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (30 30 (:LINEAR EXPT-LINEAR-LOWER-<))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 6 (:REWRITE |(integerp (expt x n))|))
 (13 8 (:REWRITE DEFAULT-PLUS-2))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:REWRITE NORMALIZE-ADDENDS))
 (8 8 (:REWRITE DEFAULT-PLUS-1))
 (6 6 (:REWRITE INTEGERP-/))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE |(not (equal x (/ y)))|))
 (6 6 (:REWRITE |(equal x (/ y))|))
 (5 4 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (3 3 (:REWRITE |(mod x (- y))| . 3))
 (3 3 (:REWRITE |(mod x (- y))| . 2))
 (3 3 (:REWRITE |(mod x (- y))| . 1))
 (3 3 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (3 3 (:REWRITE |(mod (- x) y)| . 3))
 (3 3 (:REWRITE |(mod (- x) y)| . 2))
 (3 3 (:REWRITE |(mod (- x) y)| . 1))
 (3 3 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 )
(DM::PERM-POWERS
 (5480 5 (:DEFINITION DM::MOD-POWERS))
 (1495 5 (:REWRITE RTL::MOD-DOES-NOTHING))
 (800 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (775 5 (:REWRITE MOD-X-Y-=-X . 3))
 (690 5 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (660 5 (:REWRITE CANCEL-MOD-+))
 (656 18 (:REWRITE DM::PIGEONHOLE-PRINCIPLE-LEMMA-1))
 (400 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (345 5 (:REWRITE MOD-ZERO . 3))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (335 335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (219 69 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (215 35 (:REWRITE DEFAULT-TIMES-1))
 (215 5 (:REWRITE |(integerp (- x))|))
 (210 15 (:LINEAR EXPT-X->=-X))
 (210 15 (:LINEAR EXPT->=-1-ONE))
 (207 7 (:DEFINITION MEMBER-EQUAL))
 (204 69 (:REWRITE DEFAULT-LESS-THAN-1))
 (200 5 (:REWRITE DEFAULT-MOD-RATIO))
 (200 5 (:REWRITE |(* (- x) y)|))
 (199 64 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (195 15 (:REWRITE |(* y x)|))
 (170 35 (:REWRITE DEFAULT-TIMES-2))
 (160 5 (:REWRITE MOD-X-Y-=-X . 4))
 (145 15 (:LINEAR EXPT->=-1-TWO))
 (145 15 (:LINEAR EXPT-<=-1-ONE))
 (140 15 (:LINEAR EXPT-X->-X))
 (140 15 (:LINEAR EXPT->-1-ONE))
 (140 15 (:LINEAR EXPT-<-1-TWO))
 (115 5 (:REWRITE MOD-ZERO . 4))
 (115 5 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (115 5 (:REWRITE MOD-X-Y-=-X . 2))
 (115 5 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (115 5 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (109 64 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (88 24 (:REWRITE ACL2-NUMBERP-X))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (80 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (70 5 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (70 5 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (70 5 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (70 5 (:REWRITE MOD-CANCEL-*-CONST))
 (70 5 (:REWRITE DEFAULT-MINUS))
 (70 5 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (70 5 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (69 69 (:REWRITE THE-FLOOR-BELOW))
 (69 69 (:REWRITE THE-FLOOR-ABOVE))
 (69 69 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (69 69 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (69 69 (:REWRITE DEFAULT-LESS-THAN-2))
 (66 15 (:REWRITE |(+ c (+ d x))|))
 (64 64 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (64 64 (:REWRITE INTEGERP-<-CONSTANT))
 (64 64 (:REWRITE CONSTANT-<-INTEGERP))
 (64 64 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (64 64 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (64 64 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (64 64 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (64 64 (:REWRITE |(< c (- x))|))
 (64 64 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (64 64 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (64 64 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (64 64 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (64 64 (:REWRITE |(< (/ x) (/ y))|))
 (64 64 (:REWRITE |(< (- x) c)|))
 (64 64 (:REWRITE |(< (- x) (- y))|))
 (54 52 (:REWRITE DEFAULT-PLUS-1))
 (52 52 (:REWRITE DEFAULT-PLUS-2))
 (50 5 (:REWRITE DEFAULT-MOD-1))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (32 8 (:REWRITE RATIONALP-X))
 (30 30 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (30 30 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (30 1 (:DEFINITION REMOVE1-EQUAL))
 (29 29 (:REWRITE DEFAULT-CAR))
 (24 24 (:REWRITE REDUCE-INTEGERP-+))
 (24 24 (:REWRITE INTEGERP-MINUS-X))
 (24 24 (:META META-INTEGERP-CORRECT))
 (22 22 (:REWRITE DEFAULT-CDR))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (20 20 (:REWRITE DEFAULT-EXPT-2))
 (20 20 (:REWRITE DEFAULT-EXPT-1))
 (20 20 (:REWRITE |(expt 1/c n)|))
 (20 20 (:REWRITE |(expt (- x) n)|))
 (16 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (16 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (15 15 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (15 15 (:REWRITE DEFAULT-DIVIDE))
 (15 15 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (15 15 (:LINEAR EXPT-LINEAR-UPPER-<))
 (15 15 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (15 15 (:LINEAR EXPT-LINEAR-LOWER-<))
 (15 15 (:LINEAR EXPT->-1-TWO))
 (15 15 (:LINEAR EXPT-<=-1-TWO))
 (15 15 (:LINEAR EXPT-<-1-ONE))
 (14 14 (:REWRITE DM::PERM-MEMBER))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (10 10 (:REWRITE |(< 0 (/ x))|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (9 9 (:REWRITE |(+ 0 x)|))
 (8 8 (:REWRITE REDUCE-RATIONALP-+))
 (8 8 (:REWRITE REDUCE-RATIONALP-*))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE RATIONALP-MINUS-X))
 (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 (:META META-RATIONALP-CORRECT))
 (8 1 (:DEFINITION DM::POSITIVES))
 (5 5 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE |(mod x (- y))| . 3))
 (5 5 (:REWRITE |(mod x (- y))| . 2))
 (5 5 (:REWRITE |(mod x (- y))| . 1))
 (5 5 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(mod (- x) y)| . 3))
 (5 5 (:REWRITE |(mod (- x) y)| . 2))
 (5 5 (:REWRITE |(mod (- x) y)| . 1))
 (5 5 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(< x (+ c/d y))|))
 (5 5 (:REWRITE |(< (+ c/d x) y)|))
 (5 5 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:REWRITE |(- (* c x))|))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 )
(DM::DIVIDES-MOD-PROD
 (2115 1575 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (1773 19 (:REWRITE MOD-ZERO . 3))
 (1625 325 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1575 1575 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1575 1575 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1575 1575 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1397 325 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1333 325 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1333 325 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1292 5 (:REWRITE |(* y x)|))
 (1279 19 (:REWRITE DEFAULT-MOD-RATIO))
 (1164 5 (:REWRITE |(* x (+ y z))|))
 (1149 19 (:REWRITE MOD-X-Y-=-X . 4))
 (1149 19 (:REWRITE MOD-X-Y-=-X . 3))
 (1124 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (929 97 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (909 19 (:REWRITE RTL::MOD-DOES-NOTHING))
 (899 31 (:REWRITE RTL::INTEGERP-FL))
 (867 100 (:REWRITE DEFAULT-PLUS-1))
 (745 224 (:REWRITE DEFAULT-TIMES-2))
 (744 4 (:REWRITE |(+ x (if a b c))|))
 (719 19 (:REWRITE MOD-ZERO . 4))
 (717 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (650 325 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (640 89 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (547 19 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (547 19 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (547 19 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (547 19 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (491 100 (:REWRITE DEFAULT-PLUS-2))
 (460 8 (:LINEAR RTL::FL-DEF))
 (376 103 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (348 224 (:REWRITE DEFAULT-TIMES-1))
 (325 325 (:TYPE-PRESCRIPTION NATP))
 (325 325 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (325 325 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (325 325 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (325 325 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (325 325 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (325 325 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (308 122 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (308 122 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (291 19 (:REWRITE MOD-X-Y-=-X . 2))
 (291 19 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (291 19 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (286 101 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (246 122 (:REWRITE DEFAULT-LESS-THAN-1))
 (240 108 (:META META-INTEGERP-CORRECT))
 (228 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (227 19 (:REWRITE CANCEL-MOD-+))
 (184 122 (:REWRITE SIMPLIFY-SUMS-<))
 (184 122 (:REWRITE DEFAULT-LESS-THAN-2))
 (176 176 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (157 19 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (157 19 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (157 19 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (153 153 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (153 153 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (153 153 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (153 153 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (153 19 (:REWRITE MOD-CANCEL-*-CONST))
 (140 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (140 2 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 1))
 (122 122 (:REWRITE THE-FLOOR-BELOW))
 (122 122 (:REWRITE THE-FLOOR-ABOVE))
 (122 122 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (122 122 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (122 122 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (122 122 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (122 122 (:REWRITE INTEGERP-<-CONSTANT))
 (122 122 (:REWRITE CONSTANT-<-INTEGERP))
 (122 122 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (122 122 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (122 122 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (122 122 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (122 122 (:REWRITE |(< c (- x))|))
 (122 122 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (122 122 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (122 122 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (122 122 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (122 122 (:REWRITE |(< (/ x) (/ y))|))
 (122 122 (:REWRITE |(< (- x) c)|))
 (122 122 (:REWRITE |(< (- x) (- y))|))
 (116 102 (:REWRITE |(equal (/ x) c)|))
 (108 108 (:REWRITE REDUCE-INTEGERP-+))
 (108 108 (:REWRITE INTEGERP-MINUS-X))
 (108 4 (:REWRITE |(* y (* x z))|))
 (103 103 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (102 102 (:REWRITE |(equal c (/ x))|))
 (102 102 (:REWRITE |(equal (/ x) (/ y))|))
 (102 102 (:REWRITE |(equal (- x) (- y))|))
 (101 101 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (101 101 (:REWRITE |(equal c (- x))|))
 (101 101 (:REWRITE |(equal (- x) c)|))
 (81 19 (:REWRITE DEFAULT-MOD-1))
 (73 73 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (73 73 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (65 65 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (61 61 (:REWRITE DEFAULT-DIVIDE))
 (60 60 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (60 4 (:REWRITE |(* a (/ a) b)|))
 (56 56 (:REWRITE |(* c (* d x))|))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (52 52 (:REWRITE |(< 0 (/ x))|))
 (52 52 (:REWRITE |(< 0 (* x y))|))
 (52 52 (:REWRITE |(< (/ x) 0)|))
 (52 52 (:REWRITE |(< (* x y) 0)|))
 (44 44 (:REWRITE INTEGERP-/))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (40 40 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (34 34 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (29 15 (:REWRITE DEFAULT-MINUS))
 (19 19 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (19 19 (:REWRITE DEFAULT-MOD-2))
 (19 19 (:REWRITE |(mod x (- y))| . 3))
 (19 19 (:REWRITE |(mod x (- y))| . 2))
 (19 19 (:REWRITE |(mod x (- y))| . 1))
 (19 19 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (19 19 (:REWRITE |(mod (- x) y)| . 3))
 (19 19 (:REWRITE |(mod (- x) y)| . 2))
 (19 19 (:REWRITE |(mod (- x) y)| . 1))
 (19 19 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (19 3 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (16 16 (:REWRITE |(equal (* x y) 0)|))
 (16 16 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (16 16 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (13 13 (:REWRITE |(equal (+ (- c) x) y)|))
 (13 9 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (12 12 (:REWRITE |(- (* c x))|))
 (11 6 (:REWRITE |(+ c (+ d x))|))
 (8 8 (:LINEAR RTL::FL-MONOTONE-LINEAR))
 (6 6 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 (4 4 (:LINEAR RTL::N<=FL-LINEAR))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 3))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 2))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (1 1 (:REWRITE |(/ (/ x))|))
 (1 1 (:REWRITE |(* 1 x)|))
 )
(DM::DIVIDES-MOD-POWER
 (966 8 (:REWRITE CANCEL-MOD-+))
 (807 8 (:REWRITE MOD-X-Y-=-X . 3))
 (528 60 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (455 455 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (455 455 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (455 455 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (455 455 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (455 455 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (371 8 (:REWRITE MOD-ZERO . 3))
 (356 73 (:REWRITE DEFAULT-TIMES-1))
 (317 8 (:REWRITE |(integerp (- x))|))
 (301 73 (:REWRITE DEFAULT-TIMES-2))
 (299 9 (:REWRITE DEFAULT-MOD-RATIO))
 (293 8 (:REWRITE |(* (- x) y)|))
 (268 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (268 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (268 268 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (242 68 (:REWRITE DEFAULT-LESS-THAN-1))
 (234 60 (:REWRITE SIMPLIFY-SUMS-<))
 (229 8 (:REWRITE MOD-X-Y-=-X . 4))
 (210 15 (:LINEAR EXPT->=-1-ONE))
 (190 68 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (168 15 (:LINEAR EXPT-X->=-X))
 (166 8 (:REWRITE MOD-ZERO . 4))
 (166 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (166 8 (:REWRITE MOD-X-Y-=-X . 2))
 (166 8 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (166 8 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (145 15 (:LINEAR EXPT->=-1-TWO))
 (145 15 (:LINEAR EXPT-<=-1-ONE))
 (144 60 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (140 15 (:LINEAR EXPT-X->-X))
 (140 15 (:LINEAR EXPT->-1-ONE))
 (140 15 (:LINEAR EXPT-<-1-TWO))
 (135 27 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (135 27 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (125 29 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (125 29 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (108 9 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (106 11 (:REWRITE DEFAULT-MINUS))
 (103 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (103 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (103 8 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (103 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (97 15 (:LINEAR EXPT-<=-1-TWO))
 (77 29 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (77 8 (:REWRITE MOD-CANCEL-*-CONST))
 (72 9 (:REWRITE DEFAULT-MOD-1))
 (68 68 (:REWRITE THE-FLOOR-BELOW))
 (68 68 (:REWRITE THE-FLOOR-ABOVE))
 (68 68 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (68 68 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (68 68 (:REWRITE DEFAULT-LESS-THAN-2))
 (62 62 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (62 62 (:REWRITE INTEGERP-<-CONSTANT))
 (62 62 (:REWRITE CONSTANT-<-INTEGERP))
 (62 62 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (62 62 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (62 62 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (62 62 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (62 62 (:REWRITE |(< c (- x))|))
 (62 62 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (62 62 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (62 62 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (62 62 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (62 62 (:REWRITE |(< (/ x) (/ y))|))
 (62 62 (:REWRITE |(< (- x) c)|))
 (62 62 (:REWRITE |(< (- x) (- y))|))
 (60 60 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (60 60 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (60 60 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (30 30 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (29 29 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (29 29 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (29 29 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (29 26 (:REWRITE DEFAULT-PLUS-1))
 (28 28 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (27 27 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (26 26 (:REWRITE DEFAULT-PLUS-2))
 (25 25 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (25 25 (:REWRITE DEFAULT-DIVIDE))
 (22 22 (:REWRITE DEFAULT-EXPT-2))
 (22 22 (:REWRITE DEFAULT-EXPT-1))
 (22 22 (:REWRITE |(expt 1/c n)|))
 (22 22 (:REWRITE |(expt (- x) n)|))
 (15 15 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (15 15 (:LINEAR EXPT-LINEAR-UPPER-<))
 (15 15 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (15 15 (:LINEAR EXPT-LINEAR-LOWER-<))
 (15 15 (:LINEAR EXPT->-1-TWO))
 (15 15 (:LINEAR EXPT-<-1-ONE))
 (14 14 (:REWRITE REDUCE-INTEGERP-+))
 (14 14 (:REWRITE INTEGERP-MINUS-X))
 (14 14 (:META META-INTEGERP-CORRECT))
 (11 11 (:REWRITE |(< 0 (* x y))|))
 (10 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (9 9 (:REWRITE DEFAULT-MOD-2))
 (8 8 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (8 8 (:REWRITE |(mod x (- y))| . 3))
 (8 8 (:REWRITE |(mod x (- y))| . 2))
 (8 8 (:REWRITE |(mod x (- y))| . 1))
 (8 8 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(mod (- x) y)| . 3))
 (8 8 (:REWRITE |(mod (- x) y)| . 2))
 (8 8 (:REWRITE |(mod (- x) y)| . 1))
 (8 8 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(- (* c x))|))
 (7 7 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (7 7 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (7 7 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:REWRITE |(< 0 (/ x))|))
 (5 5 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (3 3 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (3 3 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (3 3 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (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))|))
 (2 2 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (2 2 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (2 2 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(DM::MUST-BE-1-1
 (24619 31 (:REWRITE RTL::MOD-DOES-NOTHING))
 (9924 12 (:LINEAR MOD-BOUNDS-1))
 (6642 6 (:LINEAR RTL::MOD-BND-2))
 (4938 6 (:LINEAR RTL::MOD-BND-1))
 (4410 38 (:LINEAR EXPT->=-1-TWO))
 (4410 38 (:LINEAR EXPT-<=-1-ONE))
 (4392 38 (:LINEAR EXPT-X->-X))
 (4392 38 (:LINEAR EXPT->-1-ONE))
 (4392 38 (:LINEAR EXPT-<-1-TWO))
 (4001 76 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (3960 30 (:REWRITE CANCEL-MOD-+))
 (3559 30 (:REWRITE MOD-X-Y-=-X . 3))
 (3100 30 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2480 248 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2247 2247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2247 2247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2247 2247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2247 2247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2247 2247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1866 30 (:REWRITE MOD-ZERO . 3))
 (1335 219 (:REWRITE DEFAULT-TIMES-1))
 (1290 30 (:REWRITE |(integerp (- x))|))
 (1222 94 (:REWRITE |(* y x)|))
 (1200 30 (:REWRITE DEFAULT-MOD-RATIO))
 (1200 30 (:REWRITE |(* (- x) y)|))
 (1065 219 (:REWRITE DEFAULT-TIMES-2))
 (1003 1003 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1003 1003 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1003 1003 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1003 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (960 30 (:REWRITE MOD-X-Y-=-X . 4))
 (943 205 (:REWRITE SIMPLIFY-SUMS-<))
 (943 205 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (943 205 (:REWRITE DEFAULT-LESS-THAN-1))
 (690 30 (:REWRITE MOD-ZERO . 4))
 (690 30 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (690 30 (:REWRITE MOD-X-Y-=-X . 2))
 (690 30 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (690 30 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (564 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (540 38 (:LINEAR EXPT-X->=-X))
 (535 38 (:LINEAR EXPT->=-1-ONE))
 (457 205 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (421 31 (:REWRITE DEFAULT-MINUS))
 (420 30 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (420 30 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (414 6 (:LINEAR MOD-BOUNDS-3))
 (381 30 (:REWRITE MOD-CANCEL-*-CONST))
 (365 73 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (365 73 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (342 30 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (342 30 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (342 30 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (329 73 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (329 73 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (300 30 (:REWRITE DEFAULT-MOD-1))
 (248 248 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (248 248 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (248 248 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (241 73 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (205 205 (:REWRITE THE-FLOOR-BELOW))
 (205 205 (:REWRITE THE-FLOOR-ABOVE))
 (205 205 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (205 205 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (205 205 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (205 205 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (205 205 (:REWRITE INTEGERP-<-CONSTANT))
 (205 205 (:REWRITE DEFAULT-LESS-THAN-2))
 (205 205 (:REWRITE CONSTANT-<-INTEGERP))
 (205 205 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (205 205 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (205 205 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (205 205 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (205 205 (:REWRITE |(< c (- x))|))
 (205 205 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (205 205 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (205 205 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (205 205 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (205 205 (:REWRITE |(< (/ x) (/ y))|))
 (205 205 (:REWRITE |(< (- x) c)|))
 (205 205 (:REWRITE |(< (- x) (- y))|))
 (168 12 (:LINEAR MOD-BOUNDS-2))
 (108 30 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (108 30 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (108 30 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (95 95 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (94 94 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (94 94 (:REWRITE DEFAULT-DIVIDE))
 (91 1 (:REWRITE MOD-ZERO . 1))
 (76 76 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (76 76 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (76 76 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (73 73 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (73 73 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (73 73 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (73 73 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (69 69 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (64 64 (:REWRITE REDUCE-INTEGERP-+))
 (64 64 (:REWRITE INTEGERP-MINUS-X))
 (64 64 (:META META-INTEGERP-CORRECT))
 (55 46 (:REWRITE DEFAULT-EXPT-1))
 (46 46 (:REWRITE DEFAULT-EXPT-2))
 (45 45 (:REWRITE |(expt 1/c n)|))
 (45 45 (:REWRITE |(expt (- x) n)|))
 (43 7 (:REWRITE DEFAULT-PLUS-2))
 (38 38 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (38 38 (:LINEAR EXPT-LINEAR-UPPER-<))
 (38 38 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (38 38 (:LINEAR EXPT-LINEAR-LOWER-<))
 (38 38 (:LINEAR EXPT->-1-TWO))
 (38 38 (:LINEAR EXPT-<=-1-TWO))
 (38 38 (:LINEAR EXPT-<-1-ONE))
 (38 2 (:REWRITE NORMALIZE-ADDENDS))
 (30 30 (:REWRITE DEFAULT-MOD-2))
 (30 30 (:REWRITE |(mod x (- y))| . 3))
 (30 30 (:REWRITE |(mod x (- y))| . 2))
 (30 30 (:REWRITE |(mod x (- y))| . 1))
 (30 30 (:REWRITE |(mod (- x) y)| . 3))
 (30 30 (:REWRITE |(mod (- x) y)| . 2))
 (30 30 (:REWRITE |(mod (- x) y)| . 1))
 (30 30 (:REWRITE |(- (* c x))|))
 (23 1 (:REWRITE MOD-ZERO . 2))
 (23 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (23 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (21 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 9 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (18 2 (:REWRITE |(+ y x)|))
 (17 7 (:REWRITE DEFAULT-PLUS-1))
 (11 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 2 (:REWRITE |(+ 0 x)|))
 (10 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (9 9 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (9 9 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (9 9 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (9 9 (:TYPE-PRESCRIPTION NATP))
 (9 9 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (9 9 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (9 9 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (9 9 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:REWRITE |(expt c (* d n))|))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-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))|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(DM::MUST-BE-1-2
 (1439 10 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1251 10 (:REWRITE CANCEL-MOD-+))
 (1188 10 (:REWRITE MOD-X-Y-=-X . 3))
 (1035 10 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1014 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (920 920 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (920 920 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (920 920 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (920 920 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (920 920 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (730 730 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (730 730 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (730 730 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (593 10 (:REWRITE MOD-ZERO . 3))
 (571 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (505 101 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (497 89 (:REWRITE DEFAULT-TIMES-1))
 (417 101 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (407 89 (:REWRITE DEFAULT-TIMES-2))
 (387 10 (:REWRITE DEFAULT-MOD-RATIO))
 (387 10 (:REWRITE |(* (- x) y)|))
 (387 9 (:REWRITE |(integerp (- x))|))
 (377 101 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (377 101 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (349 101 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (323 80 (:REWRITE SIMPLIFY-SUMS-<))
 (323 80 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (323 80 (:REWRITE DEFAULT-LESS-THAN-1))
 (320 10 (:REWRITE MOD-X-Y-=-X . 4))
 (230 10 (:REWRITE MOD-ZERO . 4))
 (230 10 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (230 10 (:REWRITE MOD-X-Y-=-X . 2))
 (230 10 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (230 10 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (222 14 (:LINEAR EXPT->=-1-TWO))
 (222 14 (:LINEAR EXPT-<=-1-ONE))
 (220 14 (:LINEAR EXPT-X->=-X))
 (214 14 (:LINEAR EXPT-X->-X))
 (214 14 (:LINEAR EXPT->-1-ONE))
 (214 14 (:LINEAR EXPT-<-1-TWO))
 (152 80 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (140 10 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (140 10 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (140 10 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (140 10 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (140 10 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (128 11 (:REWRITE DEFAULT-MINUS))
 (114 10 (:REWRITE MOD-CANCEL-*-CONST))
 (101 101 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (101 101 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (101 101 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (101 101 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (100 10 (:REWRITE DEFAULT-MOD-1))
 (90 90 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (90 90 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (81 81 (:REWRITE THE-FLOOR-BELOW))
 (81 81 (:REWRITE THE-FLOOR-ABOVE))
 (80 80 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (80 80 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (80 80 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (80 80 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (80 80 (:REWRITE INTEGERP-<-CONSTANT))
 (80 80 (:REWRITE DEFAULT-LESS-THAN-2))
 (80 80 (:REWRITE CONSTANT-<-INTEGERP))
 (80 80 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (80 80 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (80 80 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (80 80 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (80 80 (:REWRITE |(< c (- x))|))
 (80 80 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (80 80 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (80 80 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (80 80 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (80 80 (:REWRITE |(< (/ x) (/ y))|))
 (80 80 (:REWRITE |(< (- x) c)|))
 (80 80 (:REWRITE |(< (- x) (- y))|))
 (69 1 (:LINEAR MOD-BOUNDS-3))
 (64 32 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (46 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (43 7 (:REWRITE DEFAULT-PLUS-2))
 (39 3 (:REWRITE NORMALIZE-ADDENDS))
 (38 38 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (36 36 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (36 36 (:REWRITE DEFAULT-DIVIDE))
 (32 32 (:TYPE-PRESCRIPTION NATP))
 (32 32 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (32 32 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (32 32 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (32 32 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (31 31 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (30 30 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (28 28 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (28 28 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (28 28 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (28 28 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (28 2 (:LINEAR MOD-BOUNDS-2))
 (24 24 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (24 24 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (24 24 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (23 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (22 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (21 21 (:REWRITE REDUCE-INTEGERP-+))
 (21 21 (:REWRITE INTEGERP-MINUS-X))
 (21 21 (:META META-INTEGERP-CORRECT))
 (20 20 (:REWRITE DEFAULT-EXPT-2))
 (20 20 (:REWRITE DEFAULT-EXPT-1))
 (20 20 (:REWRITE |(expt 1/c n)|))
 (20 20 (:REWRITE |(expt (- x) n)|))
 (19 2 (:REWRITE |(+ y x)|))
 (17 7 (:REWRITE DEFAULT-PLUS-1))
 (14 14 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (14 14 (:LINEAR EXPT-LINEAR-UPPER-<))
 (14 14 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (14 14 (:LINEAR EXPT-LINEAR-LOWER-<))
 (14 14 (:LINEAR EXPT->-1-TWO))
 (14 14 (:LINEAR EXPT-<=-1-TWO))
 (14 14 (:LINEAR EXPT-<-1-ONE))
 (12 12 (:REWRITE |(expt c (* d n))|))
 (12 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (10 10 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (10 10 (:REWRITE DEFAULT-MOD-2))
 (10 10 (:REWRITE |(mod x (- y))| . 3))
 (10 10 (:REWRITE |(mod x (- y))| . 2))
 (10 10 (:REWRITE |(mod x (- y))| . 1))
 (10 10 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (10 10 (:REWRITE |(mod (- x) y)| . 3))
 (10 10 (:REWRITE |(mod (- x) y)| . 2))
 (10 10 (:REWRITE |(mod (- x) y)| . 1))
 (10 10 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (10 10 (:REWRITE |(- (* c x))|))
 (10 1 (:REWRITE |(+ 0 x)|))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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))|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (1 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 MOD-POSITIVE . 3))
 (1 1 (:REWRITE MOD-POSITIVE . 2))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::LOC)
(DM::MEMBER-MOD-POWERS
 (9713 36 (:REWRITE RTL::MOD-DOES-NOTHING))
 (5203 35 (:REWRITE MOD-X-Y-=-X . 3))
 (4958 35 (:REWRITE CANCEL-MOD-+))
 (4576 35 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4389 7 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (4078 7 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (3233 3233 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3233 3233 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3233 3233 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3233 3233 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3233 3233 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3036 290 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2833 35 (:REWRITE MOD-ZERO . 3))
 (2366 105 (:LINEAR EXPT->=-1-ONE))
 (2342 30 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2104 519 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1811 105 (:LINEAR EXPT-X->=-X))
 (1779 491 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1731 35 (:REWRITE |(integerp (- x))|))
 (1659 258 (:REWRITE DEFAULT-TIMES-1))
 (1639 105 (:LINEAR EXPT->=-1-TWO))
 (1639 105 (:LINEAR EXPT-<=-1-ONE))
 (1580 105 (:LINEAR EXPT-X->-X))
 (1580 105 (:LINEAR EXPT->-1-ONE))
 (1580 105 (:LINEAR EXPT-<-1-TWO))
 (1558 520 (:REWRITE DEFAULT-LESS-THAN-1))
 (1555 1555 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1555 1555 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1555 1555 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1549 36 (:REWRITE DEFAULT-MOD-RATIO))
 (1510 491 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1495 111 (:REWRITE |(* y x)|))
 (1487 476 (:REWRITE SIMPLIFY-SUMS-<))
 (1448 35 (:REWRITE |(* (- x) y)|))
 (1309 258 (:REWRITE DEFAULT-TIMES-2))
 (1243 211 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1195 211 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1195 211 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1195 211 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1168 35 (:REWRITE MOD-X-Y-=-X . 4))
 (1055 211 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (857 1 (:REWRITE |(< (if a b c) x)|))
 (837 35 (:REWRITE MOD-ZERO . 4))
 (837 35 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (837 35 (:REWRITE MOD-X-Y-=-X . 2))
 (837 35 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (837 35 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (630 494 (:REWRITE |(< (- x) c)|))
 (630 494 (:REWRITE |(< (- x) (- y))|))
 (618 159 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (541 57 (:REWRITE ACL2-NUMBERP-X))
 (535 225 (:REWRITE DEFAULT-PLUS-2))
 (520 520 (:REWRITE THE-FLOOR-BELOW))
 (520 520 (:REWRITE THE-FLOOR-ABOVE))
 (520 520 (:REWRITE DEFAULT-LESS-THAN-2))
 (519 519 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (519 519 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (506 35 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (506 35 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (506 35 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (506 35 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (506 35 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (494 494 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (494 494 (:REWRITE INTEGERP-<-CONSTANT))
 (494 494 (:REWRITE CONSTANT-<-INTEGERP))
 (494 494 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (494 494 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (494 494 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (494 494 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (494 494 (:REWRITE |(< c (- x))|))
 (494 494 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (494 494 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (494 494 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (494 494 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (494 494 (:REWRITE |(< (/ x) (/ y))|))
 (480 35 (:REWRITE MOD-CANCEL-*-CONST))
 (459 159 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (459 159 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (459 159 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (394 30 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (386 36 (:REWRITE DEFAULT-MOD-1))
 (376 4 (:LINEAR MOD-BOUNDS-3))
 (368 223 (:REWRITE DEFAULT-PLUS-1))
 (298 64 (:REWRITE NORMALIZE-ADDENDS))
 (290 290 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (290 290 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (290 290 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (290 26 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (242 38 (:REWRITE RATIONALP-X))
 (211 211 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (211 211 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (211 211 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (211 211 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (210 210 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (210 210 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (210 210 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (210 210 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (182 46 (:DEFINITION FIX))
 (159 159 (:TYPE-PRESCRIPTION NATP))
 (133 116 (:REWRITE DEFAULT-EXPT-2))
 (120 8 (:LINEAR MOD-BOUNDS-2))
 (116 116 (:REWRITE DEFAULT-EXPT-1))
 (115 115 (:REWRITE |(expt 1/c n)|))
 (115 115 (:REWRITE |(expt (- x) n)|))
 (112 112 (:REWRITE REDUCE-INTEGERP-+))
 (112 112 (:REWRITE INTEGERP-MINUS-X))
 (112 112 (:META META-INTEGERP-CORRECT))
 (111 111 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (110 110 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (110 110 (:REWRITE DEFAULT-DIVIDE))
 (106 31 (:REWRITE |(+ c (+ d x))|))
 (105 105 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (105 105 (:LINEAR EXPT-LINEAR-UPPER-<))
 (105 105 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (105 105 (:LINEAR EXPT-LINEAR-LOWER-<))
 (105 105 (:LINEAR EXPT->-1-TWO))
 (105 105 (:LINEAR EXPT-<-1-ONE))
 (92 4 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (70 7 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (50 1 (:REWRITE |(* (if a b c) x)|))
 (45 45 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (38 38 (:REWRITE REDUCE-RATIONALP-+))
 (38 38 (:REWRITE REDUCE-RATIONALP-*))
 (38 38 (:REWRITE RATIONALP-MINUS-X))
 (38 38 (:META META-RATIONALP-CORRECT))
 (36 36 (:REWRITE DEFAULT-MOD-2))
 (35 35 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (35 35 (:REWRITE |(mod x (- y))| . 3))
 (35 35 (:REWRITE |(mod x (- y))| . 2))
 (35 35 (:REWRITE |(mod x (- y))| . 1))
 (35 35 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (35 35 (:REWRITE |(mod (- x) y)| . 3))
 (35 35 (:REWRITE |(mod (- x) y)| . 2))
 (35 35 (:REWRITE |(mod (- x) y)| . 1))
 (35 35 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (35 35 (:REWRITE |(< x (+ c/d y))|))
 (35 35 (:REWRITE |(- (* c x))|))
 (30 30 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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))|))
 (30 15 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (28 28 (:REWRITE |(< (+ c/d x) y)|))
 (26 26 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (26 26 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (26 26 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (26 26 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (23 23 (:REWRITE |(< (+ (- c) x) y)|))
 (21 13 (:REWRITE DEFAULT-CAR))
 (19 19 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (19 19 (:REWRITE |(+ x (- x))|))
 (18 18 (:REWRITE |(equal (+ (- c) x) y)|))
 (16 16 (:REWRITE |(< (* x y) 0)|))
 (15 15 (:REWRITE |(< y (+ (- c) x))|))
 (15 10 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE DM::PERM-MEMBER))
 (11 11 (:REWRITE |(< (/ x) 0)|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (9 9 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 )
(DM::LOC-BOUNDS
 (506 70 (:REWRITE ACL2-NUMBERP-X))
 (366 27 (:REWRITE DEFAULT-PLUS-2))
 (218 38 (:REWRITE RATIONALP-X))
 (160 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (44 44 (:REWRITE REDUCE-INTEGERP-+))
 (44 44 (:REWRITE INTEGERP-MINUS-X))
 (44 44 (:META META-INTEGERP-CORRECT))
 (38 38 (:REWRITE REDUCE-RATIONALP-+))
 (38 38 (:REWRITE REDUCE-RATIONALP-*))
 (38 38 (:REWRITE RATIONALP-MINUS-X))
 (38 38 (:META META-RATIONALP-CORRECT))
 (32 16 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (32 16 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (26 26 (:REWRITE DEFAULT-CAR))
 (19 19 (:REWRITE DEFAULT-CDR))
 (19 11 (:REWRITE DEFAULT-LESS-THAN-2))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (18 18 (:REWRITE NORMALIZE-ADDENDS))
 (18 18 (:REWRITE DEFAULT-PLUS-1))
 (17 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (17 10 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE DM::PERM-MEMBER))
 (16 16 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (16 16 (:REWRITE |(equal c (/ x))|))
 (16 16 (:REWRITE |(equal c (- x))|))
 (16 16 (:REWRITE |(equal (/ x) c)|))
 (16 16 (:REWRITE |(equal (/ x) (/ y))|))
 (16 16 (:REWRITE |(equal (- x) c)|))
 (16 16 (:REWRITE |(equal (- x) (- y))|))
 (15 10 (:REWRITE SIMPLIFY-SUMS-<))
 (11 11 (:REWRITE THE-FLOOR-BELOW))
 (11 11 (:REWRITE THE-FLOOR-ABOVE))
 (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 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))|))
 (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-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))|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(DM::MOD-POWER-MUST-BE-1
 (21809 19 (:DEFINITION DM::MOD-POWERS))
 (4303 29 (:REWRITE MOD-X-Y-=-X . 3))
 (3855 29 (:REWRITE CANCEL-MOD-+))
 (3810 29 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (3357 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (2380 238 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2230 2230 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2230 2230 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2230 2230 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2230 2230 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2230 2230 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2230 88 (:LINEAR EXPT-X->=-X))
 (2073 29 (:REWRITE MOD-ZERO . 3))
 (1801 29 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1362 31 (:REWRITE DEFAULT-MOD-RATIO))
 (1342 215 (:REWRITE DEFAULT-TIMES-1))
 (1318 498 (:REWRITE DEFAULT-LESS-THAN-1))
 (1274 29 (:REWRITE |(integerp (- x))|))
 (1228 427 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1196 92 (:REWRITE |(* y x)|))
 (1192 391 (:REWRITE SIMPLIFY-SUMS-<))
 (1160 29 (:REWRITE |(* (- x) y)|))
 (1076 88 (:LINEAR EXPT->=-1-TWO))
 (1076 88 (:LINEAR EXPT-<=-1-ONE))
 (1043 215 (:REWRITE DEFAULT-TIMES-2))
 (1038 88 (:LINEAR EXPT-X->-X))
 (1038 88 (:LINEAR EXPT->-1-ONE))
 (1038 88 (:LINEAR EXPT-<-1-TWO))
 (1026 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1019 516 (:REWRITE DEFAULT-PLUS-2))
 (928 29 (:REWRITE MOD-X-Y-=-X . 4))
 (857 1 (:REWRITE |(< (if a b c) x)|))
 (802 802 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (802 802 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (802 802 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (737 11 (:DEFINITION DM::LOC))
 (667 29 (:REWRITE MOD-ZERO . 4))
 (667 29 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (667 29 (:REWRITE MOD-X-Y-=-X . 2))
 (667 29 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (667 29 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (651 176 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (633 89 (:REWRITE ACL2-NUMBERP-X))
 (579 505 (:REWRITE DEFAULT-PLUS-1))
 (499 498 (:REWRITE DEFAULT-LESS-THAN-2))
 (498 498 (:REWRITE THE-FLOOR-BELOW))
 (498 498 (:REWRITE THE-FLOOR-ABOVE))
 (496 496 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (496 496 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (428 428 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (428 428 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (428 428 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (428 428 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (428 428 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (428 428 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (428 428 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (428 428 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (428 428 (:REWRITE |(< (/ x) (/ y))|))
 (428 428 (:REWRITE |(< (- x) (- y))|))
 (427 427 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (427 427 (:REWRITE INTEGERP-<-CONSTANT))
 (427 427 (:REWRITE CONSTANT-<-INTEGERP))
 (427 427 (:REWRITE |(< (- x) c)|))
 (406 29 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (406 29 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (406 29 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (406 29 (:REWRITE MOD-CANCEL-*-CONST))
 (406 29 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (406 29 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (350 70 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (330 31 (:REWRITE DEFAULT-MOD-1))
 (294 70 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (274 70 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (274 70 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (274 70 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (272 47 (:REWRITE RATIONALP-X))
 (246 29 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (238 238 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (238 238 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (238 238 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (184 184 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (176 176 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (176 176 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (176 176 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (120 60 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (112 112 (:REWRITE |(< x (+ c/d y))|))
 (110 110 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (106 106 (:REWRITE REDUCE-INTEGERP-+))
 (106 106 (:REWRITE INTEGERP-MINUS-X))
 (106 106 (:META META-INTEGERP-CORRECT))
 (101 99 (:REWRITE DEFAULT-EXPT-2))
 (100 2 (:REWRITE |(* (if a b c) x)|))
 (99 99 (:REWRITE DEFAULT-EXPT-1))
 (97 97 (:REWRITE |(expt 1/c n)|))
 (97 97 (:REWRITE |(expt (- x) n)|))
 (92 92 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (90 90 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (90 90 (:REWRITE DEFAULT-DIVIDE))
 (89 89 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (89 89 (:LINEAR EXPT-LINEAR-UPPER-<))
 (89 89 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (89 89 (:LINEAR EXPT-LINEAR-LOWER-<))
 (88 88 (:LINEAR EXPT->-1-TWO))
 (88 88 (:LINEAR EXPT-<-1-ONE))
 (78 1 (:LINEAR MOD-BOUNDS-3))
 (74 27 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (70 70 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (70 70 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (70 70 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (70 70 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (60 60 (:TYPE-PRESCRIPTION NATP))
 (60 60 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (60 60 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (60 60 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (54 54 (:REWRITE |(< y (+ (- c) x))|))
 (47 47 (:REWRITE REDUCE-RATIONALP-+))
 (47 47 (:REWRITE REDUCE-RATIONALP-*))
 (47 47 (:REWRITE RATIONALP-MINUS-X))
 (47 47 (:REWRITE |(< (+ c/d x) y)|))
 (47 47 (:META META-RATIONALP-CORRECT))
 (38 38 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (37 37 (:REWRITE |(< 0 (* x y))|))
 (37 37 (:REWRITE |(< (+ (- c) x) y)|))
 (31 31 (:REWRITE DEFAULT-MOD-2))
 (30 30 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (30 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (29 29 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (29 29 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (29 29 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (29 29 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (29 29 (:REWRITE |(mod x (- y))| . 3))
 (29 29 (:REWRITE |(mod x (- y))| . 2))
 (29 29 (:REWRITE |(mod x (- y))| . 1))
 (29 29 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (29 29 (:REWRITE |(mod (- x) y)| . 3))
 (29 29 (:REWRITE |(mod (- x) y)| . 2))
 (29 29 (:REWRITE |(mod (- x) y)| . 1))
 (29 29 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (29 29 (:REWRITE |(equal c (/ x))|))
 (29 29 (:REWRITE |(equal c (- x))|))
 (29 29 (:REWRITE |(equal (/ x) c)|))
 (29 29 (:REWRITE |(equal (/ x) (/ y))|))
 (29 29 (:REWRITE |(equal (- x) c)|))
 (29 29 (:REWRITE |(equal (- x) (- y))|))
 (29 29 (:REWRITE |(- (* c x))|))
 (28 2 (:LINEAR MOD-BOUNDS-2))
 (17 17 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (17 17 (:REWRITE DEFAULT-CDR))
 (17 17 (:REWRITE DEFAULT-CAR))
 (17 17 (:REWRITE |(< 0 (/ x))|))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (12 12 (:REWRITE DM::PERM-MEMBER))
 (11 11 (:REWRITE |(< (* x y) 0)|))
 (7 7 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::DIVISOR-MUST-BE-1
 (5395 5 (:DEFINITION DM::MOD-POWERS))
 (1410 5 (:REWRITE RTL::MOD-DOES-NOTHING))
 (800 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (775 5 (:REWRITE MOD-X-Y-=-X . 3))
 (690 5 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (660 5 (:REWRITE CANCEL-MOD-+))
 (400 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (345 345 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (345 5 (:REWRITE MOD-ZERO . 3))
 (215 35 (:REWRITE DEFAULT-TIMES-1))
 (215 5 (:REWRITE |(integerp (- x))|))
 (210 15 (:LINEAR EXPT->=-1-ONE))
 (200 5 (:REWRITE DEFAULT-MOD-RATIO))
 (200 5 (:REWRITE |(* (- x) y)|))
 (195 15 (:REWRITE |(* y x)|))
 (192 57 (:REWRITE DEFAULT-LESS-THAN-1))
 (189 54 (:REWRITE SIMPLIFY-SUMS-<))
 (189 54 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (170 35 (:REWRITE DEFAULT-TIMES-2))
 (160 5 (:REWRITE MOD-X-Y-=-X . 4))
 (145 15 (:LINEAR EXPT->=-1-TWO))
 (145 15 (:LINEAR EXPT-<=-1-ONE))
 (140 15 (:LINEAR EXPT-X->-X))
 (140 15 (:LINEAR EXPT->-1-ONE))
 (140 15 (:LINEAR EXPT-<-1-TWO))
 (125 15 (:LINEAR EXPT-X->=-X))
 (115 5 (:REWRITE MOD-ZERO . 4))
 (115 5 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (115 5 (:REWRITE MOD-X-Y-=-X . 2))
 (115 5 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (115 5 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (99 54 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (87 3 (:DEFINITION MEMBER-EQUAL))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (73 19 (:REWRITE ACL2-NUMBERP-X))
 (70 5 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (70 5 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (70 5 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (70 5 (:REWRITE MOD-CANCEL-*-CONST))
 (70 5 (:REWRITE DEFAULT-MINUS))
 (70 5 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (70 5 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (60 2 (:DEFINITION REMOVE1-EQUAL))
 (57 57 (:REWRITE THE-FLOOR-BELOW))
 (57 57 (:REWRITE THE-FLOOR-ABOVE))
 (57 57 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (57 57 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (57 57 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (57 57 (:REWRITE DEFAULT-LESS-THAN-2))
 (56 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (54 54 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (54 54 (:REWRITE INTEGERP-<-CONSTANT))
 (54 54 (:REWRITE CONSTANT-<-INTEGERP))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (- x))|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (54 54 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< (/ x) (/ y))|))
 (54 54 (:REWRITE |(< (- x) c)|))
 (54 54 (:REWRITE |(< (- x) (- y))|))
 (50 5 (:REWRITE DEFAULT-MOD-1))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (40 40 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (40 8 (:REWRITE |(+ c (+ d x))|))
 (37 3 (:REWRITE ZP-OPEN))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (30 30 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (30 30 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (29 29 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (29 29 (:REWRITE DEFAULT-PLUS-2))
 (29 29 (:REWRITE DEFAULT-PLUS-1))
 (27 6 (:REWRITE RATIONALP-X))
 (25 25 (:REWRITE DEFAULT-EXPT-2))
 (25 25 (:REWRITE DEFAULT-EXPT-1))
 (25 25 (:REWRITE |(expt 1/c n)|))
 (25 25 (:REWRITE |(expt (- x) n)|))
 (24 3 (:DEFINITION DM::POSITIVES))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (21 21 (:REWRITE NORMALIZE-ADDENDS))
 (19 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (18 18 (:REWRITE REDUCE-INTEGERP-+))
 (18 18 (:REWRITE INTEGERP-MINUS-X))
 (18 18 (:META META-INTEGERP-CORRECT))
 (16 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (16 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (15 15 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (15 15 (:REWRITE DEFAULT-DIVIDE))
 (15 15 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (15 15 (:LINEAR EXPT-LINEAR-UPPER-<))
 (15 15 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (15 15 (:LINEAR EXPT-LINEAR-LOWER-<))
 (15 15 (:LINEAR EXPT->-1-TWO))
 (15 15 (:LINEAR EXPT-<=-1-TWO))
 (15 15 (:LINEAR EXPT-<-1-ONE))
 (11 11 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE DEFAULT-CDR))
 (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 REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:META META-RATIONALP-CORRECT))
 (5 5 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE |(mod x (- y))| . 3))
 (5 5 (:REWRITE |(mod x (- y))| . 2))
 (5 5 (:REWRITE |(mod x (- y))| . 1))
 (5 5 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(mod (- x) y)| . 3))
 (5 5 (:REWRITE |(mod (- x) y)| . 2))
 (5 5 (:REWRITE |(mod (- x) y)| . 1))
 (5 5 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(- (* c x))|))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (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 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(DM::MAX-ORDER-P-PRIME
 (1061 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (892 5 (:REWRITE RTL::MOD-DOES-NOTHING))
 (823 1 (:LINEAR RTL::MOD-BND-1))
 (670 5 (:REWRITE MOD-X-Y-=-X . 3))
 (660 5 (:REWRITE CANCEL-MOD-+))
 (605 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (585 5 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (486 9 (:DEFINITION DM::LEAST-DIVISOR-2))
 (420 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (418 418 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (418 418 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (418 418 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (418 418 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (418 418 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (345 5 (:REWRITE MOD-ZERO . 3))
 (302 92 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (284 11 (:LINEAR EXPT-X->=-X))
 (227 92 (:REWRITE DEFAULT-LESS-THAN-1))
 (226 37 (:REWRITE DEFAULT-TIMES-1))
 (220 85 (:REWRITE SIMPLIFY-SUMS-<))
 (220 85 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (215 5 (:REWRITE |(integerp (- x))|))
 (208 16 (:REWRITE |(* y x)|))
 (200 5 (:REWRITE DEFAULT-MOD-RATIO))
 (200 5 (:REWRITE |(* (- x) y)|))
 (197 197 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (197 197 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (197 197 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (193 11 (:LINEAR EXPT->=-1-TWO))
 (193 11 (:LINEAR EXPT-<=-1-ONE))
 (186 11 (:LINEAR EXPT-X->-X))
 (186 11 (:LINEAR EXPT->-1-ONE))
 (186 11 (:LINEAR EXPT-<-1-TWO))
 (181 37 (:REWRITE DEFAULT-TIMES-2))
 (160 32 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (160 5 (:REWRITE MOD-X-Y-=-X . 4))
 (130 85 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (115 5 (:REWRITE MOD-ZERO . 4))
 (115 5 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (115 5 (:REWRITE MOD-X-Y-=-X . 2))
 (115 5 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (115 5 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (112 32 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (92 92 (:REWRITE THE-FLOOR-BELOW))
 (92 92 (:REWRITE THE-FLOOR-ABOVE))
 (92 92 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (92 92 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (92 92 (:REWRITE DEFAULT-LESS-THAN-2))
 (88 32 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (88 32 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (88 32 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (85 85 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (85 85 (:REWRITE INTEGERP-<-CONSTANT))
 (85 85 (:REWRITE CONSTANT-<-INTEGERP))
 (85 85 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (85 85 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (85 85 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (85 85 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (85 85 (:REWRITE |(< c (- x))|))
 (85 85 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (85 85 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (85 85 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (85 85 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (85 85 (:REWRITE |(< (/ x) (/ y))|))
 (85 85 (:REWRITE |(< (- x) c)|))
 (85 85 (:REWRITE |(< (- x) (- y))|))
 (71 6 (:REWRITE DEFAULT-MINUS))
 (70 5 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (70 5 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (70 5 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (70 5 (:REWRITE MOD-CANCEL-*-CONST))
 (70 5 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (70 5 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (69 1 (:LINEAR MOD-BOUNDS-3))
 (59 23 (:REWRITE DEFAULT-PLUS-2))
 (50 5 (:REWRITE DEFAULT-MOD-1))
 (47 47 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (46 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (41 5 (:REWRITE NORMALIZE-ADDENDS))
 (36 18 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (34 6 (:REWRITE ACL2-NUMBERP-X))
 (33 23 (:REWRITE DEFAULT-PLUS-1))
 (32 32 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (32 32 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (32 32 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (32 32 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (29 8 (:REWRITE |(+ c (+ d x))|))
 (28 2 (:LINEAR MOD-BOUNDS-2))
 (23 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (23 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (22 22 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (22 22 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (22 22 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (22 22 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (21 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (19 2 (:REWRITE |(+ y x)|))
 (18 18 (:TYPE-PRESCRIPTION NATP))
 (18 18 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (18 18 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (18 18 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (18 18 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (18 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (17 17 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (17 17 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (17 8 (:REWRITE |(+ 0 x)|))
 (16 16 (:REWRITE REDUCE-INTEGERP-+))
 (16 16 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (16 16 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (16 16 (:REWRITE INTEGERP-MINUS-X))
 (16 16 (:REWRITE DEFAULT-DIVIDE))
 (16 16 (:META META-INTEGERP-CORRECT))
 (14 2 (:REWRITE RATIONALP-X))
 (12 12 (:REWRITE DEFAULT-EXPT-2))
 (12 12 (:REWRITE DEFAULT-EXPT-1))
 (12 12 (:REWRITE |(expt 1/c n)|))
 (12 12 (:REWRITE |(expt (- x) n)|))
 (11 11 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (11 11 (:LINEAR EXPT-LINEAR-UPPER-<))
 (11 11 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (11 11 (:LINEAR EXPT-LINEAR-LOWER-<))
 (11 11 (:LINEAR EXPT->-1-TWO))
 (11 11 (:LINEAR EXPT-<=-1-TWO))
 (11 11 (:LINEAR EXPT-<-1-ONE))
 (10 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE |(equal c (/ x))|))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (/ x) c)|))
 (6 6 (:REWRITE |(equal (/ x) (/ y))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (5 5 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE |(mod x (- y))| . 3))
 (5 5 (:REWRITE |(mod x (- y))| . 2))
 (5 5 (:REWRITE |(mod x (- y))| . 1))
 (5 5 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(mod (- x) y)| . 3))
 (5 5 (:REWRITE |(mod (- x) y)| . 2))
 (5 5 (:REWRITE |(mod (- x) y)| . 1))
 (5 5 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(- (* c x))|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE REDUCE-RATIONALP-+))
 (2 2 (:REWRITE REDUCE-RATIONALP-*))
 (2 2 (:REWRITE RATIONALP-MINUS-X))
 (2 2 (:META META-RATIONALP-CORRECT))
 (2 2 (:DEFINITION FIX))
 (1 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 (- x))|))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::PROD-POWERS
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 )
(DM::DISTINCT-FACTORS)
(DM::ALL-POSITIVE)
(DM::FACTORIZATION)
(DM::FACTOR-DIVIDES-1
 (21 3 (:REWRITE DEFAULT-TIMES-2))
 (13 3 (:REWRITE DEFAULT-TIMES-1))
 (11 11 (:REWRITE DEFAULT-PLUS-2))
 (11 11 (:REWRITE DEFAULT-PLUS-1))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE DEFAULT-EXPT-1))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (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))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (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 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-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (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 |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (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) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(DM::FACTOR-DIVIDES-2
 (212 52 (:REWRITE ACL2-NUMBERP-X))
 (162 18 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (80 20 (:REWRITE RATIONALP-X))
 (47 47 (:REWRITE DEFAULT-CAR))
 (38 38 (:REWRITE DM::PERM-MEMBER))
 (34 18 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (34 18 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (31 31 (:REWRITE DEFAULT-CDR))
 (29 29 (:REWRITE REDUCE-INTEGERP-+))
 (29 29 (:REWRITE INTEGERP-MINUS-X))
 (29 29 (:META META-INTEGERP-CORRECT))
 (26 26 (:REWRITE THE-FLOOR-BELOW))
 (26 26 (:REWRITE THE-FLOOR-ABOVE))
 (24 24 (:REWRITE SIMPLIFY-SUMS-<))
 (24 24 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (24 24 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (24 24 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (24 24 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (24 24 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (24 24 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (24 24 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (24 24 (:REWRITE INTEGERP-<-CONSTANT))
 (24 24 (:REWRITE DEFAULT-LESS-THAN-1))
 (24 24 (:REWRITE CONSTANT-<-INTEGERP))
 (24 24 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (24 24 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (24 24 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (24 24 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (24 24 (:REWRITE |(< c (- x))|))
 (24 24 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (24 24 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (24 24 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (24 24 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (24 24 (:REWRITE |(< (/ x) (/ y))|))
 (24 24 (:REWRITE |(< (- x) c)|))
 (24 24 (:REWRITE |(< (- x) (- y))|))
 (20 20 (:REWRITE REDUCE-RATIONALP-+))
 (20 20 (:REWRITE REDUCE-RATIONALP-*))
 (20 20 (:REWRITE RATIONALP-MINUS-X))
 (20 20 (:META META-RATIONALP-CORRECT))
 (18 18 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (18 18 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (18 18 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (18 18 (:REWRITE |(equal c (/ x))|))
 (18 18 (:REWRITE |(equal c (- x))|))
 (18 18 (:REWRITE |(equal (/ x) c)|))
 (18 18 (:REWRITE |(equal (/ x) (/ y))|))
 (18 18 (:REWRITE |(equal (- x) c)|))
 (18 18 (: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 |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (6 6 (:REWRITE ZP-OPEN))
 )
(DM::INTEGERP-PROD-POWERS
 (1237 84 (:REWRITE DM::FACTOR-DIVIDES-2))
 (377 97 (:REWRITE ACL2-NUMBERP-X))
 (318 39 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (140 35 (:REWRITE RATIONALP-X))
 (113 113 (:REWRITE THE-FLOOR-BELOW))
 (113 113 (:REWRITE THE-FLOOR-ABOVE))
 (113 113 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (113 113 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (113 113 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (113 113 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (113 113 (:REWRITE INTEGERP-<-CONSTANT))
 (113 113 (:REWRITE DEFAULT-LESS-THAN-2))
 (113 113 (:REWRITE DEFAULT-LESS-THAN-1))
 (113 113 (:REWRITE CONSTANT-<-INTEGERP))
 (113 113 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (113 113 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (113 113 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (113 113 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (113 113 (:REWRITE |(< c (- x))|))
 (113 113 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (113 113 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (113 113 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (113 113 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (113 113 (:REWRITE |(< (/ x) (/ y))|))
 (113 113 (:REWRITE |(< (- x) c)|))
 (113 113 (:REWRITE |(< (- x) (- y))|))
 (112 112 (:REWRITE SIMPLIFY-SUMS-<))
 (112 112 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (112 112 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (111 24 (:REWRITE DEFAULT-TIMES-1))
 (108 108 (:REWRITE REDUCE-INTEGERP-+))
 (108 108 (:REWRITE INTEGERP-MINUS-X))
 (108 108 (:META META-INTEGERP-CORRECT))
 (106 6 (:REWRITE |(* (if a b c) x)|))
 (84 84 (:REWRITE DM::PERM-MEMBER))
 (75 5 (:REWRITE DEFAULT-EXPT-1))
 (70 39 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (70 39 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (52 52 (:REWRITE |(< (/ x) 0)|))
 (52 52 (:REWRITE |(< (* x y) 0)|))
 (46 24 (:REWRITE DEFAULT-TIMES-2))
 (39 39 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (39 39 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (39 39 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (39 39 (:REWRITE |(equal c (/ x))|))
 (39 39 (:REWRITE |(equal c (- x))|))
 (39 39 (:REWRITE |(equal (/ x) c)|))
 (39 39 (:REWRITE |(equal (/ x) (/ y))|))
 (39 39 (:REWRITE |(equal (- x) c)|))
 (39 39 (:REWRITE |(equal (- x) (- y))|))
 (35 35 (:REWRITE REDUCE-RATIONALP-+))
 (35 35 (:REWRITE REDUCE-RATIONALP-*))
 (35 35 (:REWRITE RATIONALP-MINUS-X))
 (35 35 (:META META-RATIONALP-CORRECT))
 (28 2 (:REWRITE ZIP-OPEN))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT))
 (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))|))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE |(* 0 x)|))
 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-PROD-POWERS))
 )
(DM::POSITIVE-PROD-POWERS
 (1237 84 (:REWRITE DM::FACTOR-DIVIDES-2))
 (377 97 (:REWRITE ACL2-NUMBERP-X))
 (318 39 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (152 126 (:REWRITE DEFAULT-LESS-THAN-2))
 (150 124 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (150 124 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (140 35 (:REWRITE RATIONALP-X))
 (138 6 (:REWRITE |(* (if a b c) x)|))
 (126 126 (:REWRITE THE-FLOOR-BELOW))
 (126 126 (:REWRITE THE-FLOOR-ABOVE))
 (126 126 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (126 126 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (126 126 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (126 126 (:REWRITE INTEGERP-<-CONSTANT))
 (126 126 (:REWRITE DEFAULT-LESS-THAN-1))
 (126 126 (:REWRITE CONSTANT-<-INTEGERP))
 (126 126 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (126 126 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (126 126 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (126 126 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (126 126 (:REWRITE |(< c (- x))|))
 (126 126 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (126 126 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (126 126 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (126 126 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (126 126 (:REWRITE |(< (/ x) (/ y))|))
 (126 126 (:REWRITE |(< (- x) c)|))
 (126 126 (:REWRITE |(< (- x) (- y))|))
 (124 124 (:REWRITE SIMPLIFY-SUMS-<))
 (111 24 (:REWRITE DEFAULT-TIMES-1))
 (97 97 (:REWRITE REDUCE-INTEGERP-+))
 (97 97 (:REWRITE INTEGERP-MINUS-X))
 (97 97 (:META META-INTEGERP-CORRECT))
 (90 24 (:REWRITE DEFAULT-TIMES-2))
 (84 84 (:REWRITE DM::PERM-MEMBER))
 (75 5 (:REWRITE DEFAULT-EXPT-1))
 (70 39 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (70 39 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (52 52 (:REWRITE |(< (/ x) 0)|))
 (52 52 (:REWRITE |(< (* x y) 0)|))
 (39 39 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (39 39 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (39 39 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (39 39 (:REWRITE |(equal c (/ x))|))
 (39 39 (:REWRITE |(equal c (- x))|))
 (39 39 (:REWRITE |(equal (/ x) c)|))
 (39 39 (:REWRITE |(equal (/ x) (/ y))|))
 (39 39 (:REWRITE |(equal (- x) c)|))
 (39 39 (:REWRITE |(equal (- x) (- y))|))
 (35 35 (:REWRITE REDUCE-RATIONALP-+))
 (35 35 (:REWRITE REDUCE-RATIONALP-*))
 (35 35 (:REWRITE RATIONALP-MINUS-X))
 (35 35 (:META META-RATIONALP-CORRECT))
 (28 2 (:REWRITE ZIP-OPEN))
 (19 19 (:REWRITE |(< 0 (/ x))|))
 (19 19 (:REWRITE |(< 0 (* x y))|))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (17 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE |(< x (if a b c))|))
 (2 2 (:REWRITE |(* 0 x)|))
 )
(DM::FACTOR-DIVIDES-3
 (1123 57 (:REWRITE DM::FACTOR-DIVIDES-2))
 (389 93 (:REWRITE ACL2-NUMBERP-X))
 (297 39 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (208 28 (:REWRITE DEFAULT-TIMES-1))
 (171 171 (:REWRITE DEFAULT-CAR))
 (148 37 (:REWRITE RATIONALP-X))
 (117 28 (:REWRITE DEFAULT-TIMES-2))
 (105 21 (:REWRITE DEFAULT-EXPT-2))
 (81 39 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (80 80 (:REWRITE REDUCE-INTEGERP-+))
 (80 80 (:REWRITE INTEGERP-MINUS-X))
 (80 80 (:META META-INTEGERP-CORRECT))
 (80 39 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (73 73 (:REWRITE THE-FLOOR-BELOW))
 (73 73 (:REWRITE THE-FLOOR-ABOVE))
 (73 73 (:REWRITE SIMPLIFY-SUMS-<))
 (73 73 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (73 73 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (73 73 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (73 73 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (73 73 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (73 73 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (73 73 (:REWRITE INTEGERP-<-CONSTANT))
 (73 73 (:REWRITE DEFAULT-LESS-THAN-2))
 (73 73 (:REWRITE DEFAULT-LESS-THAN-1))
 (73 73 (:REWRITE CONSTANT-<-INTEGERP))
 (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 |(< c (- x))|))
 (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|))
 (73 73 (:REWRITE |(< (/ x) (/ y))|))
 (73 73 (:REWRITE |(< (- x) c)|))
 (73 73 (:REWRITE |(< (- x) (- y))|))
 (68 68 (:REWRITE DEFAULT-CDR))
 (67 67 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (57 57 (:REWRITE DM::PERM-MEMBER))
 (44 22 (:REWRITE DEFAULT-PLUS-2))
 (39 39 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (39 39 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (39 39 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (39 39 (:REWRITE |(equal c (/ x))|))
 (39 39 (:REWRITE |(equal c (- x))|))
 (39 39 (:REWRITE |(equal (/ x) c)|))
 (39 39 (:REWRITE |(equal (/ x) (/ y))|))
 (39 39 (:REWRITE |(equal (- x) c)|))
 (39 39 (:REWRITE |(equal (- x) (- y))|))
 (37 37 (:REWRITE REDUCE-RATIONALP-+))
 (37 37 (:REWRITE REDUCE-RATIONALP-*))
 (37 37 (:REWRITE RATIONALP-MINUS-X))
 (37 37 (:META META-RATIONALP-CORRECT))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (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))
 (28 2 (:REWRITE ZIP-OPEN))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (23 23 (:REWRITE |(< (/ x) 0)|))
 (23 23 (:REWRITE |(< (* x y) 0)|))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (22 22 (:REWRITE NORMALIZE-ADDENDS))
 (22 22 (:REWRITE DEFAULT-PLUS-1))
 (16 4 (:REWRITE |(* 1 x)|))
 (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 |(expt 1/c n)|))
 (13 13 (:REWRITE |(expt (- x) n)|))
 (13 13 (:REWRITE |(< 0 (/ x))|))
 (13 13 (:REWRITE |(< 0 (* x y))|))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 5 (:REWRITE |(equal x (if a b c))|))
 (5 5 (:REWRITE |(equal (if a b c) x)|))
 (4 4 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 1 (:REWRITE DM::INTEGERP-PROD-POWERS))
 )
(DM::FACTOR-DIVIDES
 (177 2 (:DEFINITION DM::DISTINCT-FACTORS))
 (141 5 (:REWRITE DM::FACTOR-DIVIDES-2))
 (137 1 (:DEFINITION DM::PROD-POWERS))
 (135 2 (:DEFINITION MEMBER-EQUAL))
 (69 3 (:REWRITE |(* (if a b c) x)|))
 (68 2 (:DEFINITION NATP))
 (46 7 (:REWRITE DEFAULT-TIMES-1))
 (45 3 (:REWRITE DEFAULT-EXPT-2))
 (40 8 (:REWRITE ACL2-NUMBERP-X))
 (38 1 (:DEFINITION DM::ALL-POSITIVE))
 (37 2 (:REWRITE DEFAULT-EXPT-1))
 (36 2 (:REWRITE ZP-OPEN))
 (28 7 (:REWRITE DEFAULT-TIMES-2))
 (24 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (16 4 (:REWRITE RATIONALP-X))
 (14 2 (:DEFINITION LEN))
 (14 1 (:REWRITE ZIP-OPEN))
 (11 11 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE DEFAULT-CAR))
 (9 9 (:TYPE-PRESCRIPTION DM::PROD-POWERS))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-INTEGERP-CORRECT))
 (8 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 2 (:REWRITE |(* 1 x)|))
 (7 7 (:REWRITE THE-FLOOR-BELOW))
 (7 7 (:REWRITE THE-FLOOR-ABOVE))
 (7 7 (:REWRITE SIMPLIFY-SUMS-<))
 (7 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (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 DEFAULT-LESS-THAN-2))
 (7 7 (:REWRITE DEFAULT-LESS-THAN-1))
 (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))|))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (5 5 (:REWRITE DM::PERM-MEMBER))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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 (:META META-RATIONALP-CORRECT))
 (4 2 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:TYPE-PRESCRIPTION ZP))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-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 NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE |(expt 1/c n)|))
 (1 1 (:REWRITE |(expt (- x) n)|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(* 0 x)|))
 )
(DM::ALL-PRIME)
(DM::PRIME-FACTORIZATION)
(DM::ALL-PRIME-FACTORS-1
 (20 2 (:REWRITE DEFAULT-TIMES-2))
 (13 13 (:REWRITE THE-FLOOR-BELOW))
 (13 13 (:REWRITE THE-FLOOR-ABOVE))
 (13 13 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (13 13 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (13 13 (:REWRITE INTEGERP-<-CONSTANT))
 (13 13 (:REWRITE DEFAULT-LESS-THAN-2))
 (13 13 (:REWRITE DEFAULT-LESS-THAN-1))
 (13 13 (:REWRITE CONSTANT-<-INTEGERP))
 (13 13 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (13 13 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (13 13 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (13 13 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (13 13 (:REWRITE |(< c (- x))|))
 (13 13 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (13 13 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (13 13 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (13 13 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (13 13 (:REWRITE |(< (/ x) (/ y))|))
 (13 13 (:REWRITE |(< (- x) c)|))
 (13 13 (:REWRITE |(< (- x) (- y))|))
 (12 12 (:REWRITE DEFAULT-PLUS-2))
 (12 12 (:REWRITE DEFAULT-PLUS-1))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (10 10 (:REWRITE DM::FACTOR-DIVIDES))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (5 5 (:REWRITE SIMPLIFY-SUMS-<))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (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)|))
 (3 2 (:REWRITE DEFAULT-TIMES-1))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(DM::ALL-PRIME-FACTORS-2
 (4249 401 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4152 934 (:REWRITE ACL2-NUMBERP-X))
 (1857 385 (:REWRITE DM::FACTOR-DIVIDES-2))
 (1609 322 (:REWRITE RATIONALP-X))
 (1158 401 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1148 1148 (:REWRITE DEFAULT-CAR))
 (1135 401 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1019 1019 (:REWRITE THE-FLOOR-BELOW))
 (1019 1019 (:REWRITE THE-FLOOR-ABOVE))
 (1019 1019 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1019 1019 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1019 1019 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1019 1019 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1019 1019 (:REWRITE INTEGERP-<-CONSTANT))
 (1019 1019 (:REWRITE DEFAULT-LESS-THAN-2))
 (1019 1019 (:REWRITE DEFAULT-LESS-THAN-1))
 (1019 1019 (:REWRITE CONSTANT-<-INTEGERP))
 (1019 1019 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1019 1019 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1019 1019 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1019 1019 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1019 1019 (:REWRITE |(< c (- x))|))
 (1019 1019 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1019 1019 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1019 1019 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1019 1019 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1019 1019 (:REWRITE |(< (/ x) (/ y))|))
 (1019 1019 (:REWRITE |(< (- x) c)|))
 (1019 1019 (:REWRITE |(< (- x) (- y))|))
 (898 898 (:REWRITE SIMPLIFY-SUMS-<))
 (898 898 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (898 898 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (572 572 (:REWRITE REDUCE-INTEGERP-+))
 (572 572 (:REWRITE INTEGERP-MINUS-X))
 (572 572 (:META META-INTEGERP-CORRECT))
 (534 534 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (534 534 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (534 534 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (534 534 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (534 534 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (417 417 (:REWRITE DEFAULT-CDR))
 (401 401 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (401 401 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (401 401 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (401 401 (:REWRITE |(equal c (/ x))|))
 (401 401 (:REWRITE |(equal c (- x))|))
 (401 401 (:REWRITE |(equal (/ x) c)|))
 (401 401 (:REWRITE |(equal (/ x) (/ y))|))
 (401 401 (:REWRITE |(equal (- x) c)|))
 (401 401 (:REWRITE |(equal (- x) (- y))|))
 (387 387 (:REWRITE DM::PERM-MEMBER))
 (366 51 (:REWRITE DEFAULT-TIMES-1))
 (350 350 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (350 350 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (322 322 (:REWRITE REDUCE-RATIONALP-+))
 (322 322 (:REWRITE REDUCE-RATIONALP-*))
 (322 322 (:REWRITE RATIONALP-MINUS-X))
 (322 322 (:META META-RATIONALP-CORRECT))
 (264 264 (:REWRITE DM::FACTOR-DIVIDES))
 (187 187 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (187 187 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (187 187 (:REWRITE |(< (/ x) 0)|))
 (187 187 (:REWRITE |(< (* x y) 0)|))
 (179 51 (:REWRITE DEFAULT-TIMES-2))
 (161 46 (:REWRITE DM::FACTOR-DIVIDES-3))
 (136 68 (:REWRITE DEFAULT-PLUS-2))
 (68 68 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (68 68 (:REWRITE NORMALIZE-ADDENDS))
 (68 68 (:REWRITE DEFAULT-PLUS-1))
 (28 28 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (28 28 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (28 28 (:REWRITE |(< 0 (/ x))|))
 (28 28 (:REWRITE |(< 0 (* x y))|))
 (23 23 (:REWRITE |(expt 1/c n)|))
 (23 23 (:REWRITE |(expt (- x) n)|))
 (15 15 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (9 9 (:REWRITE |(equal x (if a b c))|))
 (9 9 (:REWRITE |(equal (if a b c) x)|))
 (8 8 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 1 (:REWRITE DM::INTEGERP-PROD-POWERS))
 )
(DM::ALL-PRIME-FACTORS
 (137 1 (:DEFINITION DM::PROD-POWERS))
 (86 5 (:REWRITE DM::FACTOR-DIVIDES-2))
 (69 3 (:REWRITE |(* (if a b c) x)|))
 (57 11 (:REWRITE ACL2-NUMBERP-X))
 (46 7 (:REWRITE DEFAULT-TIMES-1))
 (45 3 (:REWRITE DEFAULT-EXPT-2))
 (40 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (37 2 (:REWRITE DEFAULT-EXPT-1))
 (28 7 (:REWRITE DEFAULT-TIMES-2))
 (23 5 (:REWRITE RATIONALP-X))
 (14 1 (:REWRITE ZIP-OPEN))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE THE-FLOOR-BELOW))
 (11 11 (:REWRITE THE-FLOOR-ABOVE))
 (11 11 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (11 11 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:REWRITE INTEGERP-<-CONSTANT))
 (11 11 (:REWRITE DEFAULT-LESS-THAN-2))
 (11 11 (:REWRITE DEFAULT-LESS-THAN-1))
 (11 11 (:REWRITE CONSTANT-<-INTEGERP))
 (11 11 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (11 11 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (11 11 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (11 11 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (11 11 (:REWRITE |(< c (- x))|))
 (11 11 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (11 11 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (11 11 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (11 11 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (11 11 (:REWRITE |(< (/ x) (/ y))|))
 (11 11 (:REWRITE |(< (- x) c)|))
 (11 11 (:REWRITE |(< (- x) (- y))|))
 (11 11 (:META META-INTEGERP-CORRECT))
 (10 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 9 (:TYPE-PRESCRIPTION DM::PROD-POWERS))
 (9 9 (:REWRITE SIMPLIFY-SUMS-<))
 (9 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (9 9 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (8 2 (:REWRITE |(* 1 x)|))
 (5 5 (:REWRITE REDUCE-RATIONALP-+))
 (5 5 (:REWRITE REDUCE-RATIONALP-*))
 (5 5 (:REWRITE RATIONALP-MINUS-X))
 (5 5 (:REWRITE DM::PERM-MEMBER))
 (5 5 (:META META-RATIONALP-CORRECT))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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 2 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (3 3 (:TYPE-PRESCRIPTION EXPT))
 (3 3 (:REWRITE DM::FACTOR-DIVIDES))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-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 NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE DM::FACTOR-DIVIDES-3))
 (1 1 (:REWRITE |(expt 1/c n)|))
 (1 1 (:REWRITE |(expt (- x) n)|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(* 0 x)|))
 )
(DM::PRIME-WITNESS
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(DM::DIVIDES-FACTOR-1
 (392 392 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (392 392 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (392 392 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (182 33 (:META META-INTEGERP-CORRECT))
 (168 116 (:REWRITE DEFAULT-TIMES-2))
 (166 166 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (166 166 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (166 166 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (166 166 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (158 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (158 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (158 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (131 10 (:REWRITE INTEGERP-/))
 (124 116 (:REWRITE DEFAULT-TIMES-1))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-4G))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-3G))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-2G))
 (62 62 (:TYPE-PRESCRIPTION NOT-INTEGERP-1G))
 (60 60 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (38 34 (:REWRITE SIMPLIFY-SUMS-<))
 (38 34 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (38 34 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (38 34 (:REWRITE DEFAULT-LESS-THAN-1))
 (34 34 (:REWRITE THE-FLOOR-BELOW))
 (34 34 (:REWRITE THE-FLOOR-ABOVE))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (34 34 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (34 34 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (34 34 (:REWRITE INTEGERP-<-CONSTANT))
 (34 34 (:REWRITE DEFAULT-LESS-THAN-2))
 (34 34 (:REWRITE CONSTANT-<-INTEGERP))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (34 34 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< c (- x))|))
 (34 34 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (34 34 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (34 34 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) (/ y))|))
 (34 34 (:REWRITE |(< (- x) c)|))
 (34 34 (:REWRITE |(< (- x) (- y))|))
 (33 33 (:REWRITE REDUCE-INTEGERP-+))
 (33 33 (:REWRITE INTEGERP-MINUS-X))
 (30 30 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (30 30 (:REWRITE DEFAULT-DIVIDE))
 (29 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (17 3 (:REWRITE ACL2-NUMBERP-X))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-4F))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-3F))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-2F))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-1F))
 (16 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (15 11 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (15 11 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (13 13 (:REWRITE DM::FACTOR-DIVIDES))
 (12 12 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (12 12 (: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 (- x) (- y))|))
 (11 11 (:REWRITE |(* c (* d x))|))
 (7 1 (:REWRITE RATIONALP-X))
 (5 5 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(DM::DIVIDES-FACTOR-2
 (197 197 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (197 197 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (197 197 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (134 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (134 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (134 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (72 1 (:DEFINITION DM::LEAST-DIVISOR-2))
 (70 46 (:REWRITE DEFAULT-TIMES-2))
 (60 15 (:META META-INTEGERP-CORRECT))
 (58 46 (:REWRITE DEFAULT-TIMES-1))
 (47 5 (:REWRITE ACL2-NUMBERP-X))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3G))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2G))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1G))
 (39 3 (:REWRITE INTEGERP-/))
 (23 23 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (22 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (21 3 (:REWRITE RATIONALP-X))
 (19 19 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (19 19 (:REWRITE DEFAULT-DIVIDE))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:REWRITE DM::FACTOR-DIVIDES))
 (8 8 (:REWRITE THE-FLOOR-BELOW))
 (8 8 (:REWRITE THE-FLOOR-ABOVE))
 (8 8 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (8 8 (:REWRITE INTEGERP-<-CONSTANT))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-2))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 8 (:REWRITE CONSTANT-<-INTEGERP))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (- x))|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) (/ y))|))
 (8 8 (:REWRITE |(< (- x) c)|))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (8 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 7 (:REWRITE SIMPLIFY-SUMS-<))
 (7 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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 (* d x))|))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:META META-RATIONALP-CORRECT))
 )
(DM::DIVIDES-FACTOR-3
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(DM::DIVIDES-FACTOR-4
 (3 3 (:REWRITE THE-FLOOR-BELOW))
 (3 3 (:REWRITE THE-FLOOR-ABOVE))
 (3 3 (:REWRITE SIMPLIFY-SUMS-<))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 3 (:REWRITE INTEGERP-<-CONSTANT))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-2))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-1))
 (3 3 (:REWRITE CONSTANT-<-INTEGERP))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (- x))|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE ZP-OPEN))
 (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 DM::FACTOR-DIVIDES))
 )
(DM::DIVIDES-FACTOR
 (3288 24 (:DEFINITION DM::PROD-POWERS))
 (1656 72 (:REWRITE |(* (if a b c) x)|))
 (1116 180 (:REWRITE DEFAULT-TIMES-1))
 (1080 72 (:REWRITE DEFAULT-EXPT-2))
 (888 48 (:REWRITE DEFAULT-EXPT-1))
 (686 180 (:REWRITE DEFAULT-TIMES-2))
 (624 80 (:REWRITE ACL2-NUMBERP-X))
 (336 24 (:REWRITE ZIP-OPEN))
 (304 7 (:DEFINITION MEMBER-EQUAL))
 (272 62 (:REWRITE RATIONALP-X))
 (192 48 (:REWRITE |(* 1 x)|))
 (145 35 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (121 121 (:REWRITE REDUCE-INTEGERP-+))
 (121 121 (:REWRITE INTEGERP-MINUS-X))
 (121 121 (:META META-INTEGERP-CORRECT))
 (110 2 (:DEFINITION DM::LEAST-DIVISOR-2))
 (102 3 (:REWRITE DM::FACTOR-DIVIDES-3))
 (72 72 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (72 72 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (72 72 (:TYPE-PRESCRIPTION EXPT))
 (72 72 (:REWRITE DEFAULT-CDR))
 (72 72 (:REWRITE DEFAULT-CAR))
 (62 62 (:REWRITE REDUCE-RATIONALP-+))
 (62 62 (:REWRITE REDUCE-RATIONALP-*))
 (62 62 (:REWRITE RATIONALP-MINUS-X))
 (62 62 (:META META-RATIONALP-CORRECT))
 (55 35 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (55 35 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (35 35 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (35 35 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (35 35 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (35 35 (:REWRITE |(equal c (/ x))|))
 (35 35 (:REWRITE |(equal c (- x))|))
 (35 35 (:REWRITE |(equal (/ x) c)|))
 (35 35 (:REWRITE |(equal (/ x) (/ y))|))
 (35 35 (:REWRITE |(equal (- x) c)|))
 (35 35 (:REWRITE |(equal (- x) (- y))|))
 (29 29 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (29 29 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (29 29 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (26 26 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (26 24 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (26 24 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (26 24 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (26 24 (:REWRITE DEFAULT-LESS-THAN-2))
 (24 24 (:REWRITE THE-FLOOR-BELOW))
 (24 24 (:REWRITE THE-FLOOR-ABOVE))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 24 (:REWRITE SIMPLIFY-SUMS-<))
 (24 24 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (24 24 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (24 24 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (24 24 (:REWRITE INTEGERP-<-CONSTANT))
 (24 24 (:REWRITE DEFAULT-LESS-THAN-1))
 (24 24 (:REWRITE CONSTANT-<-INTEGERP))
 (24 24 (:REWRITE |(expt 1/c n)|))
 (24 24 (:REWRITE |(expt (- x) n)|))
 (24 24 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (24 24 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (24 24 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (24 24 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (24 24 (:REWRITE |(< c (- x))|))
 (24 24 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (24 24 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (24 24 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (24 24 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (24 24 (:REWRITE |(< (/ x) (/ y))|))
 (24 24 (:REWRITE |(< (- x) c)|))
 (24 24 (:REWRITE |(< (- x) (- y))|))
 (23 23 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (15 15 (:REWRITE DM::PERM-MEMBER))
 (8 8 (:REWRITE DM::FACTOR-DIVIDES))
 (8 4 (:REWRITE DEFAULT-PLUS-2))
 (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))|))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 )
(DM::MAX-ORDER-BY-FACTORIZATION
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(DM::MAX-ORDER-BY-FACTORIZATION-ROOTP
 (41087 119 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (39451 5875 (:REWRITE DEFAULT-TIMES-1))
 (38598 2905 (:REWRITE RATIONALP-X))
 (36889 8443 (:REWRITE DEFAULT-LESS-THAN-1))
 (27466 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (27466 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (23961 5875 (:REWRITE DEFAULT-TIMES-2))
 (22303 22303 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (22303 22303 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (22303 22303 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (21455 119 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (21342 21342 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (21342 21342 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (17788 2324 (:REWRITE ACL2-NUMBERP-X))
 (17299 703 (:LINEAR EXPT-<=-1-ONE))
 (16729 703 (:LINEAR EXPT->=-1-TWO))
 (16729 703 (:LINEAR EXPT->-1-TWO))
 (16729 703 (:LINEAR EXPT-<-1-ONE))
 (15271 703 (:LINEAR EXPT-X->=-X))
 (15271 703 (:LINEAR EXPT->=-1-ONE))
 (15271 703 (:LINEAR EXPT-<=-1-TWO))
 (14701 703 (:LINEAR EXPT-X->-X))
 (14701 703 (:LINEAR EXPT->-1-ONE))
 (14701 703 (:LINEAR EXPT-<-1-TWO))
 (13634 7398 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (13055 7398 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (12383 140 (:REWRITE MOD-X-Y-=-X . 3))
 (11938 324 (:REWRITE DM::FACTOR-DIVIDES-2))
 (11566 133 (:DEFINITION DM::DISTINCT-FACTORS))
 (11410 7398 (:REWRITE SIMPLIFY-SUMS-<))
 (11333 140 (:REWRITE MOD-ZERO . 4))
 (11033 140 (:REWRITE MOD-X-Y-=-X . 4))
 (9905 1357 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (8878 8878 (:REWRITE THE-FLOOR-BELOW))
 (8878 8878 (:REWRITE THE-FLOOR-ABOVE))
 (8704 13 (:LINEAR RTL::MOD-BND-2))
 (8595 1357 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (8249 140 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (8231 140 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (7572 26 (:LINEAR MOD-BOUNDS-2))
 (7572 26 (:LINEAR MOD-BOUNDS-1))
 (7407 7398 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (7398 7398 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (7398 7398 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (7398 7398 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (7398 7398 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7398 7398 (:REWRITE INTEGERP-<-CONSTANT))
 (7398 7398 (:REWRITE CONSTANT-<-INTEGERP))
 (7398 7398 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (7398 7398 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (7398 7398 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (7398 7398 (:REWRITE |(< c (- x))|))
 (7398 7398 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (7398 7398 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (7398 7398 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (7398 7398 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (7398 7398 (:REWRITE |(< (/ x) (/ y))|))
 (7398 7398 (:REWRITE |(< (- x) c)|))
 (7398 7398 (:REWRITE |(< (- x) (- y))|))
 (7397 140 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (7397 140 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (6701 1357 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6605 1357 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (5986 1357 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (5921 140 (:REWRITE MOD-ZERO . 3))
 (5436 498 (:REWRITE DEFAULT-MOD-1))
 (5299 140 (:REWRITE MOD-X-Y-=-X . 2))
 (5299 140 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (5299 140 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (4839 3879 (:REWRITE REDUCE-INTEGERP-+))
 (4724 1538 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4629 1357 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (4629 1357 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (4629 1357 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (4629 1357 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (4629 1357 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (4629 1357 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (4629 1357 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (4629 1357 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4283 140 (:REWRITE CANCEL-MOD-+))
 (4111 839 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (3879 3879 (:REWRITE INTEGERP-MINUS-X))
 (3879 3879 (:META META-INTEGERP-CORRECT))
 (3792 1002 (:REWRITE |(< (/ x) 0)|))
 (3638 107 (:DEFINITION NATP))
 (3522 1357 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (3511 140 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (3511 140 (:REWRITE MOD-CANCEL-*-CONST))
 (3511 140 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (3135 140 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (2739 2739 (:REWRITE RATIONALP-MINUS-X))
 (2735 2735 (:REWRITE REDUCE-RATIONALP-+))
 (2735 2735 (:META META-RATIONALP-CORRECT))
 (2413 2413 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2371 2371 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2371 2371 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2371 2371 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2095 25 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (1988 1988 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1988 1988 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1988 1988 (:REWRITE |(< 0 (/ x))|))
 (1988 1988 (:REWRITE |(< 0 (* x y))|))
 (1963 105 (:REWRITE |(equal x (/ y))|))
 (1777 1279 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1763 1108 (:REWRITE DEFAULT-PLUS-1))
 (1761 1761 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1538 1538 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1444 94 (:REWRITE |(mod (+ 1 x) y)|))
 (1428 1428 (:REWRITE |(equal c (/ x))|))
 (1428 1428 (:REWRITE |(equal c (- x))|))
 (1428 1428 (:REWRITE |(equal (/ x) c)|))
 (1428 1428 (:REWRITE |(equal (/ x) (/ y))|))
 (1428 1428 (:REWRITE |(equal (- x) (- y))|))
 (1406 1406 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1406 1406 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1406 1406 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1406 1406 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1357 1357 (:TYPE-PRESCRIPTION NATP))
 (1351 1351 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1330 1330 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1188 108 (:REWRITE |(+ y (+ x z))|))
 (1170 130 (:REWRITE |(equal (expt x n) 1)|))
 (1002 1002 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1002 1002 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1002 1002 (:REWRITE |(< (* x y) 0)|))
 (892 418 (:REWRITE INTEGERP-/))
 (887 887 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (754 29 (:REWRITE NOT-INTEGERP-/-2))
 (754 29 (:REWRITE NOT-INTEGERP-/-1))
 (748 112 (:REWRITE |(equal (expt x n) 0)|))
 (744 744 (:REWRITE DEFAULT-CAR))
 (724 724 (:TYPE-PRESCRIPTION DM::DISTINCT-FACTORS))
 (703 703 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (703 703 (:LINEAR EXPT-LINEAR-UPPER-<))
 (703 703 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (703 703 (:LINEAR EXPT-LINEAR-LOWER-<))
 (640 124 (:REWRITE |(integerp (expt x n))|))
 (535 171 (:REWRITE |(* (- x) y)|))
 (489 165 (:REWRITE |(+ c (+ d x))|))
 (474 474 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (394 394 (:REWRITE DEFAULT-CDR))
 (335 327 (:REWRITE DEFAULT-MINUS))
 (324 324 (:REWRITE DM::PERM-MEMBER))
 (171 171 (:REWRITE |(expt 1/c n)|))
 (171 171 (:REWRITE |(expt (- x) n)|))
 (140 140 (:REWRITE MOD-CANCEL-*-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|))
 (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|))
 (130 13 (:LINEAR MOD-BOUNDS-3))
 (107 107 (:REWRITE |(equal (+ (- c) x) y)|))
 (73 73 (:REWRITE |(* x (- y))|))
 (60 60 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (57 57 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (32 32 (:REWRITE |(equal (* x y) 0)|))
 (23 23 (:REWRITE |(not (equal x (- (/ y))))|))
 (23 23 (:REWRITE |(equal x (- (/ y)))|))
 (13 13 (:LINEAR RTL::MOD-BND-3))
 (12 12 (:REWRITE |(- (* c x))|))
 (1 1 (:TYPE-PRESCRIPTION ZP))
 (1 1 (:REWRITE ZP-OPEN))
 )
(DM::MAX-ORDER-BY-FACTORIZATION-MAX-ORDER-P
 (23997 13 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (13018 94 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12331 87 (:LINEAR EXPT-<=-1-TWO))
 (7609 87 (:LINEAR EXPT-X->=-X))
 (5993 5993 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (5993 5993 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (5993 5993 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (5048 647 (:REWRITE RATIONALP-X))
 (3590 896 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2900 42 (:REWRITE DEFAULT-MOD-RATIO))
 (2623 985 (:REWRITE DEFAULT-LESS-THAN-1))
 (2622 617 (:REWRITE DEFAULT-TIMES-1))
 (2618 1241 (:REWRITE DEFAULT-PLUS-2))
 (2556 2556 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2556 2556 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2556 2556 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2556 2556 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2556 2556 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2457 18 (:REWRITE CANCEL-MOD-+))
 (2393 18 (:REWRITE MOD-X-Y-=-X . 3))
 (2087 18 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1905 381 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1881 381 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1829 87 (:LINEAR EXPT->=-1-TWO))
 (1829 87 (:LINEAR EXPT-<=-1-ONE))
 (1762 87 (:LINEAR EXPT-X->-X))
 (1762 87 (:LINEAR EXPT->-1-ONE))
 (1762 87 (:LINEAR EXPT-<-1-TWO))
 (1728 617 (:REWRITE DEFAULT-TIMES-2))
 (1700 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1584 48 (:REWRITE |(<= x (/ y)) with (< y 0)|))
 (1584 48 (:REWRITE |(<= x (/ y)) with (< 0 y)|))
 (1584 48 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (1584 48 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (1572 1241 (:REWRITE DEFAULT-PLUS-1))
 (1553 381 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1553 381 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1513 381 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1505 985 (:REWRITE DEFAULT-LESS-THAN-2))
 (1323 18 (:REWRITE MOD-ZERO . 3))
 (1085 833 (:REWRITE REDUCE-INTEGERP-+))
 (1058 936 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (985 985 (:REWRITE THE-FLOOR-BELOW))
 (985 985 (:REWRITE THE-FLOOR-ABOVE))
 (951 30 (:REWRITE |(integerp (- x))|))
 (936 936 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (936 936 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (925 65 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (896 896 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (896 896 (:REWRITE INTEGERP-<-CONSTANT))
 (896 896 (:REWRITE CONSTANT-<-INTEGERP))
 (896 896 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (896 896 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (896 896 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (896 896 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (896 896 (:REWRITE |(< c (- x))|))
 (896 896 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (896 896 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (896 896 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (896 896 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (896 896 (:REWRITE |(< (/ x) (/ y))|))
 (896 896 (:REWRITE |(< (- x) c)|))
 (896 896 (:REWRITE |(< (- x) (- y))|))
 (864 96 (:REWRITE RATIONALP-/))
 (833 833 (:REWRITE INTEGERP-MINUS-X))
 (833 833 (:META META-INTEGERP-CORRECT))
 (823 1 (:LINEAR RTL::MOD-BND-1))
 (812 124 (:REWRITE ACL2-NUMBERP-X))
 (741 39 (:REWRITE |(* (- x) y)|))
 (697 94 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (660 12 (:DEFINITION DM::LEAST-DIVISOR-2))
 (576 18 (:REWRITE MOD-X-Y-=-X . 4))
 (554 42 (:REWRITE DEFAULT-MOD-1))
 (551 551 (:REWRITE REDUCE-RATIONALP-+))
 (551 551 (:REWRITE REDUCE-RATIONALP-*))
 (551 551 (:REWRITE RATIONALP-MINUS-X))
 (551 551 (:META META-RATIONALP-CORRECT))
 (527 67 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (517 65 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (501 501 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (414 18 (:REWRITE MOD-ZERO . 4))
 (414 18 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (414 18 (:REWRITE MOD-X-Y-=-X . 2))
 (414 18 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (414 18 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (381 381 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (381 381 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (381 381 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (381 381 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (366 183 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (299 13 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (286 52 (:REWRITE DEFAULT-MINUS))
 (280 81 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (252 18 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (252 18 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (252 18 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (252 18 (:REWRITE MOD-CANCEL-*-CONST))
 (252 18 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (252 18 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (234 234 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (226 214 (:REWRITE |(+ c (+ d x))|))
 (214 214 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (183 183 (:TYPE-PRESCRIPTION NATP))
 (183 183 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (183 183 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (183 183 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (174 174 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (174 174 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (174 174 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (174 174 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (144 108 (:REWRITE INTEGERP-/))
 (140 140 (:REWRITE |(< x (+ c/d y))|))
 (136 136 (:REWRITE |(< y (+ (- c) x))|))
 (134 134 (:REWRITE |(< (+ c/d x) y)|))
 (134 134 (:REWRITE |(< (+ (- c) x) y)|))
 (133 133 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (130 13 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (120 120 (:REWRITE DEFAULT-CDR))
 (119 119 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (111 111 (:REWRITE DEFAULT-CAR))
 (109 109 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (109 109 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (101 101 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (99 99 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (99 99 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (94 94 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (94 94 (:REWRITE |(equal c (/ x))|))
 (94 94 (:REWRITE |(equal c (- x))|))
 (94 94 (:REWRITE |(equal (/ x) c)|))
 (94 94 (:REWRITE |(equal (/ x) (/ y))|))
 (94 94 (:REWRITE |(equal (- x) c)|))
 (94 94 (:REWRITE |(equal (- x) (- y))|))
 (87 87 (:REWRITE |(< 0 (* x y))|))
 (87 87 (:REWRITE |(< (/ x) 0)|))
 (87 87 (:REWRITE |(< (* x y) 0)|))
 (87 87 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (87 87 (:LINEAR EXPT-LINEAR-UPPER-<))
 (87 87 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (87 87 (:LINEAR EXPT-LINEAR-LOWER-<))
 (87 87 (:LINEAR EXPT->-1-TWO))
 (87 87 (:LINEAR EXPT-<-1-ONE))
 (85 85 (:REWRITE |(< 0 (/ x))|))
 (73 73 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (69 1 (:LINEAR MOD-BOUNDS-3))
 (57 57 (:REWRITE |(expt 1/c n)|))
 (57 57 (:REWRITE |(expt (- x) n)|))
 (42 42 (:REWRITE DEFAULT-MOD-2))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (36 36 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (35 35 (:REWRITE DM::FACTOR-DIVIDES))
 (30 30 (:REWRITE DM::PERM-MEMBER))
 (28 2 (:LINEAR MOD-BOUNDS-2))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (18 18 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (18 18 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (18 18 (:REWRITE |(mod x (- y))| . 3))
 (18 18 (:REWRITE |(mod x (- y))| . 2))
 (18 18 (:REWRITE |(mod x (- y))| . 1))
 (18 18 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (18 18 (:REWRITE |(mod (- x) y)| . 3))
 (18 18 (:REWRITE |(mod (- x) y)| . 2))
 (18 18 (:REWRITE |(mod (- x) y)| . 1))
 (18 18 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (18 18 (:REWRITE |(- (* c x))|))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (6 6 (:REWRITE |(* x (- y))|))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::LUCAS
 (11083 346 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (9296 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (7446 18 (:REWRITE |(< (if a b c) x)|))
 (5228 34 (:LINEAR EXPT-<=-1-TWO))
 (4967 26 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2848 34 (:LINEAR EXPT-X->=-X))
 (2454 309 (:REWRITE RATIONALP-X))
 (2012 2012 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2012 2012 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2012 2012 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1603 346 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1496 128 (:REWRITE NORMALIZE-ADDENDS))
 (1130 17 (:REWRITE DEFAULT-MOD-RATIO))
 (1083 8 (:REWRITE CANCEL-MOD-+))
 (1061 8 (:REWRITE MOD-X-Y-=-X . 3))
 (1028 76 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (1007 368 (:REWRITE DEFAULT-LESS-THAN-1))
 (937 937 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (937 937 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (937 937 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (937 937 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (937 937 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (925 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (901 160 (:REWRITE DEFAULT-TIMES-1))
 (867 416 (:REWRITE DEFAULT-PLUS-2))
 (859 274 (:REWRITE SIMPLIFY-SUMS-<))
 (823 1 (:LINEAR RTL::MOD-BND-1))
 (792 24 (:REWRITE |(<= x (/ y)) with (< y 0)|))
 (792 24 (:REWRITE |(<= x (/ y)) with (< 0 y)|))
 (792 24 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (792 24 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (750 75 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (710 34 (:LINEAR EXPT->=-1-TWO))
 (710 34 (:LINEAR EXPT-<=-1-ONE))
 (684 34 (:LINEAR EXPT-X->-X))
 (684 34 (:LINEAR EXPT->-1-ONE))
 (684 34 (:LINEAR EXPT-<-1-TWO))
 (579 8 (:REWRITE MOD-ZERO . 3))
 (560 368 (:REWRITE DEFAULT-LESS-THAN-2))
 (529 160 (:REWRITE DEFAULT-TIMES-2))
 (528 416 (:REWRITE DEFAULT-PLUS-1))
 (472 350 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (467 371 (:REWRITE REDUCE-INTEGERP-+))
 (452 128 (:REWRITE |(+ 0 x)|))
 (432 48 (:REWRITE RATIONALP-/))
 (419 14 (:REWRITE |(integerp (- x))|))
 (388 80 (:REWRITE |(+ y x)|))
 (371 371 (:REWRITE INTEGERP-MINUS-X))
 (371 371 (:META META-INTEGERP-CORRECT))
 (368 368 (:REWRITE THE-FLOOR-BELOW))
 (368 368 (:REWRITE THE-FLOOR-ABOVE))
 (350 350 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (350 350 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (346 346 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (346 346 (:REWRITE INTEGERP-<-CONSTANT))
 (346 346 (:REWRITE CONSTANT-<-INTEGERP))
 (346 346 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (346 346 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (346 346 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (346 346 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (346 346 (:REWRITE |(< c (- x))|))
 (346 346 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (346 346 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (346 346 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (346 346 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (346 346 (:REWRITE |(< (/ x) (/ y))|))
 (346 346 (:REWRITE |(< (- x) c)|))
 (346 346 (:REWRITE |(< (- x) (- y))|))
 (323 11 (:REWRITE |(* (- x) y)|))
 (320 64 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (320 64 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (312 64 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (312 64 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (312 64 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (261 261 (:REWRITE REDUCE-RATIONALP-+))
 (261 261 (:REWRITE REDUCE-RATIONALP-*))
 (261 261 (:REWRITE RATIONALP-MINUS-X))
 (261 261 (:META META-RATIONALP-CORRECT))
 (256 8 (:REWRITE MOD-X-Y-=-X . 4))
 (243 39 (:REWRITE ACL2-NUMBERP-X))
 (236 26 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (218 17 (:REWRITE DEFAULT-MOD-1))
 (216 24 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (216 24 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (216 24 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (216 24 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (193 193 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (184 8 (:REWRITE MOD-ZERO . 4))
 (184 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (184 8 (:REWRITE MOD-X-Y-=-X . 2))
 (184 8 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (184 8 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (152 152 (:DEFINITION FIX))
 (119 15 (:REWRITE DEFAULT-MINUS))
 (112 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (112 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (112 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (112 8 (:REWRITE MOD-CANCEL-*-CONST))
 (112 8 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (112 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (93 3 (:DEFINITION MEMBER-EQUAL))
 (92 80 (:REWRITE |(+ c (+ d x))|))
 (92 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (88 22 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (76 76 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (76 76 (:REWRITE |(+ x (- x))|))
 (75 75 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (75 75 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (75 75 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (72 54 (:REWRITE INTEGERP-/))
 (69 1 (:LINEAR MOD-BOUNDS-3))
 (68 68 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (68 68 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (68 68 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (68 68 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (64 64 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (64 64 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (64 64 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (64 64 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (52 52 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (52 52 (:REWRITE |(< x (+ c/d y))|))
 (48 48 (:REWRITE |(< y (+ (- c) x))|))
 (48 48 (:REWRITE |(< (+ c/d x) y)|))
 (48 48 (:REWRITE |(< (+ (- c) x) y)|))
 (43 43 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (40 20 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (40 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (37 37 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (34 34 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (34 34 (:LINEAR EXPT-LINEAR-UPPER-<))
 (34 34 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (34 34 (:LINEAR EXPT-LINEAR-LOWER-<))
 (34 34 (:LINEAR EXPT->-1-TWO))
 (34 34 (:LINEAR EXPT-<-1-ONE))
 (30 30 (:REWRITE DEFAULT-CDR))
 (29 29 (:REWRITE |(< 0 (* x y))|))
 (28 28 (:REWRITE |(< (/ x) 0)|))
 (28 28 (:REWRITE |(< (* x y) 0)|))
 (28 2 (:LINEAR MOD-BOUNDS-2))
 (27 27 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (27 27 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (27 27 (:REWRITE DEFAULT-CAR))
 (27 27 (:REWRITE |(< 0 (/ x))|))
 (26 26 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (26 26 (:REWRITE |(equal c (/ x))|))
 (26 26 (:REWRITE |(equal c (- x))|))
 (26 26 (:REWRITE |(equal (/ x) c)|))
 (26 26 (:REWRITE |(equal (/ x) (/ y))|))
 (26 26 (:REWRITE |(equal (- x) c)|))
 (26 26 (:REWRITE |(equal (- x) (- y))|))
 (24 6 (:REWRITE DM::FACTOR-DIVIDES-2))
 (20 20 (:TYPE-PRESCRIPTION NATP))
 (20 20 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (20 20 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (20 20 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (17 17 (:REWRITE DEFAULT-MOD-2))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
 (11 11 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (11 11 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (8 8 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (8 8 (:REWRITE |(mod x (- y))| . 3))
 (8 8 (:REWRITE |(mod x (- y))| . 2))
 (8 8 (:REWRITE |(mod x (- y))| . 1))
 (8 8 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(mod (- x) y)| . 3))
 (8 8 (:REWRITE |(mod (- x) y)| . 2))
 (8 8 (:REWRITE |(mod (- x) y)| . 1))
 (8 8 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(- (* c x))|))
 (6 6 (:REWRITE DM::PERM-MEMBER))
 (6 6 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (5 5 (:REWRITE DM::FACTOR-DIVIDES))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-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 |(* x (- y))|))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (1 1 (:LINEAR RTL::MOD-BND-3))
 )
(DM::FAST-MOD-EXPT-MUL
 (90 18 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (64 4 (:REWRITE RTL::INTEGERP-FL))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (44 44 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (42 18 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (42 18 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (42 18 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (42 18 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (24 12 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (18 18 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (18 18 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (18 18 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (18 18 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (12 12 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (12 12 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (12 12 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (12 12 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (12 12 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (8 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (5 5 (:REWRITE THE-FLOOR-BELOW))
 (5 5 (:REWRITE THE-FLOOR-ABOVE))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-2))
 (5 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (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-<))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (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))|))
 (4 4 (:META META-INTEGERP-CORRECT))
 (4 4 (:LINEAR RTL::FL-MONOTONE-LINEAR))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-TIMES-2))
 (2 2 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:LINEAR RTL::N<=FL-LINEAR))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE DEFAULT-MINUS))
 )
(DM::FAST-MOD-EXPT)
(DM::EMM-1
 (9640 36 (:REWRITE RTL::MOD-DOES-NOTHING))
 (6278 65 (:REWRITE |(* (* x y) z)|))
 (5608 20 (:REWRITE CANCEL-MOD-+))
 (4461 489 (:REWRITE DEFAULT-TIMES-2))
 (4400 880 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (4380 880 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (4380 880 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (4380 880 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4033 489 (:REWRITE DEFAULT-TIMES-1))
 (3983 3983 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3983 3983 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3983 3983 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3728 20 (:REWRITE MOD-ZERO . 3))
 (3527 235 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (3456 20 (:REWRITE MOD-X-Y-=-X . 4))
 (3341 65 (:REWRITE |(* y (* x z))|))
 (3052 20 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2948 20 (:REWRITE MOD-ZERO . 4))
 (2596 20 (:REWRITE DEFAULT-MOD-RATIO))
 (2596 20 (:REWRITE |(* (- x) y)|))
 (2473 20 (:REWRITE MOD-X-Y-=-X . 3))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2210 2210 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1985 93 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1854 5 (:LINEAR MOD-BOUNDS-3))
 (1681 93 (:REWRITE SIMPLIFY-SUMS-<))
 (1681 93 (:REWRITE DEFAULT-LESS-THAN-1))
 (1536 20 (:REWRITE |(integerp (- x))|))
 (1485 93 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (880 880 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (880 880 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (880 880 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (880 880 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (880 880 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (833 45 (:META META-INTEGERP-CORRECT))
 (708 20 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (708 20 (:REWRITE MOD-X-Y-=-X . 2))
 (708 20 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (708 20 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (410 10 (:LINEAR MOD-BOUNDS-2))
 (404 20 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (404 20 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (404 20 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (404 20 (:REWRITE MOD-CANCEL-*-CONST))
 (404 20 (:REWRITE DEFAULT-MINUS))
 (397 93 (:REWRITE DEFAULT-LESS-THAN-2))
 (324 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (324 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (324 20 (:REWRITE DEFAULT-MOD-1))
 (244 20 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (244 20 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (235 235 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (235 235 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (235 235 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (128 48 (:REWRITE DEFAULT-EXPT-1))
 (96 16 (: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 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))|))
 (65 65 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (65 65 (:REWRITE DEFAULT-DIVIDE))
 (65 65 (:REWRITE |(* c (* d x))|))
 (48 48 (:REWRITE DEFAULT-EXPT-2))
 (45 45 (:REWRITE REDUCE-INTEGERP-+))
 (45 45 (:REWRITE INTEGERP-MINUS-X))
 (40 40 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (32 32 (:REWRITE |(expt 1/c n)|))
 (32 32 (:REWRITE |(expt (- x) n)|))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (20 20 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (20 20 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (20 20 (:REWRITE DEFAULT-MOD-2))
 (20 20 (:REWRITE |(mod x (- y))| . 3))
 (20 20 (:REWRITE |(mod x (- y))| . 2))
 (20 20 (:REWRITE |(mod x (- y))| . 1))
 (20 20 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(mod (- x) y)| . 3))
 (20 20 (:REWRITE |(mod (- x) y)| . 2))
 (20 20 (:REWRITE |(mod (- x) y)| . 1))
 (20 20 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(equal c (/ x))|))
 (20 20 (:REWRITE |(equal c (- x))|))
 (20 20 (:REWRITE |(equal (/ x) c)|))
 (20 20 (:REWRITE |(equal (/ x) (/ y))|))
 (20 20 (:REWRITE |(equal (- x) c)|))
 (20 20 (:REWRITE |(equal (- x) (- y))|))
 (20 20 (:REWRITE |(equal (* x y) 0)|))
 (20 20 (:REWRITE |(< 0 (/ x))|))
 (20 20 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (20 20 (:REWRITE |(< 0 (* x y))|))
 (20 20 (:REWRITE |(- (* c x))|))
 (10 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (8 8 (:REWRITE |(expt c (* d n))|))
 (5 5 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (5 5 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (5 5 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (5 5 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 )
(DM::EMM-2
 (144320 148 (:REWRITE RTL::MOD-DOES-NOTHING))
 (19082 124 (:REWRITE CANCEL-MOD-+))
 (15705 124 (:REWRITE MOD-X-Y-=-X . 4))
 (15575 124 (:REWRITE MOD-X-Y-=-X . 3))
 (14050 124 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (12698 166 (:LINEAR EXPT->=-1-TWO))
 (12698 166 (:LINEAR EXPT->-1-TWO))
 (12698 166 (:LINEAR EXPT-<-1-ONE))
 (12660 1130 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (12368 166 (:LINEAR EXPT-X->=-X))
 (12368 166 (:LINEAR EXPT->=-1-ONE))
 (12368 166 (:LINEAR EXPT-<=-1-TWO))
 (12318 166 (:LINEAR EXPT-X->-X))
 (12318 166 (:LINEAR EXPT->-1-ONE))
 (12318 166 (:LINEAR EXPT-<-1-TWO))
 (12104 124 (:REWRITE MOD-ZERO . 4))
 (11462 166 (:LINEAR EXPT-<=-1-ONE))
 (11460 332 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (11274 332 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (10565 10565 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (10565 10565 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (10565 10565 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
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 (8 8 (:REWRITE MOD-POSITIVE . 1))
 (8 8 (:REWRITE |(expt c (* d n))|))
 (6 6 (:TYPE-PRESCRIPTION ABS))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (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 |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 )
(DM::EMM-5
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 (358 358 (:REWRITE THE-FLOOR-ABOVE))
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(DM::EMM-6
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 )
(DM::EMM-7
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 (980 124 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (155 155 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (155 155 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
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 (124 124 (:REWRITE |(- (* c x))|))
 (106 14 (:REWRITE DEFAULT-EXPT-1))
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 (29 29 (:LINEAR RTL::MOD-BND-3))
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 (12 12 (:REWRITE |(expt 1/c n)|))
 (12 12 (:REWRITE |(expt (- x) n)|))
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 (8 8 (:REWRITE MOD-POSITIVE . 1))
 (8 8 (:REWRITE DEFAULT-PLUS-2))
 (8 8 (:REWRITE DEFAULT-PLUS-1))
 (5 5 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:TYPE-PRESCRIPTION ABS))
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 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE |(expt c (* d n))|))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE |(* c (expt d n))|))
 )
(DM::EMM-8
 (6208 62 (:REWRITE |(* (* x y) z)|))
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 (3084 12 (:REWRITE CANCEL-MOD-+))
 (2808 20 (:REWRITE DEFAULT-MOD-RATIO))
 (2397 622 (:REWRITE DEFAULT-TIMES-1))
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 (2004 12 (:REWRITE |(* (- x) y)|))
 (1749 211 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
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 (1635 1635 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1635 1635 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1635 1635 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1635 1635 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1534 26 (:REWRITE BUBBLE-DOWN-*-BUBBLE-DOWN))
 (1440 12 (:REWRITE MOD-X-Y-=-X . 4))
 (1306 3 (:LINEAR MOD-BOUNDS-3))
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 (1203 1203 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (1150 230 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (727 61 (:REWRITE SIMPLIFY-SUMS-<))
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 (648 8 (:REWRITE |(* (if a b c) x)|))
 (645 645 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
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 (416 8 (:REWRITE |(integerp (- x))|))
 (284 12 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (284 12 (:REWRITE MOD-X-Y-=-X . 2))
 (284 12 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (284 12 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (243 27 (:META META-INTEGERP-CORRECT))
 (230 230 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (230 230 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (230 230 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (230 230 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (224 16 (:REWRITE DEFAULT-MINUS))
 (211 211 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
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 (211 211 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
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 (172 12 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
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 (145 33 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (61 61 (:REWRITE |(< (- x) (- y))|))
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 (33 33 (:REWRITE |(equal (/ x) c)|))
 (33 33 (:REWRITE |(equal (/ x) (/ y))|))
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 (33 33 (:REWRITE |(equal (- x) (- y))|))
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 (24 24 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (21 21 (:REWRITE NORMALIZE-ADDENDS))
 (21 21 (:REWRITE DEFAULT-EXPT-2))
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 (21 21 (:REWRITE |(expt 1/c n)|))
 (21 21 (:REWRITE |(expt (- x) n)|))
 (21 21 (:REWRITE |(* c (expt d n))|))
 (20 20 (:REWRITE DEFAULT-MOD-2))
 (19 19 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
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 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (12 12 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (12 12 (:REWRITE |(mod x (- y))| . 3))
 (12 12 (:REWRITE |(mod x (- y))| . 2))
 (12 12 (:REWRITE |(mod x (- y))| . 1))
 (12 12 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (12 12 (:REWRITE |(mod (- x) y)| . 3))
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 (12 12 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (12 12 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (12 12 (:REWRITE |(< 0 (* x y))|))
 (12 12 (:REWRITE |(- (* c x))|))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (3 3 (:LINEAR RTL::MOD-BND-3))
 )
(DM::EMM-9
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 (35934 220 (:REWRITE DEFAULT-MOD-RATIO))
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 (22640 22640 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (22640 22640 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (22640 22640 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (19731 217 (:REWRITE |(integerp (- x))|))
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 (18136 8712 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (14632 1449 (:REWRITE DEFAULT-LESS-THAN-1))
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 (12803 184 (:LINEAR EXPT->-1-TWO))
 (12803 184 (:LINEAR EXPT-<-1-ONE))
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 (12503 184 (:LINEAR EXPT->=-1-ONE))
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 (12436 184 (:LINEAR EXPT-X->-X))
 (12436 184 (:LINEAR EXPT->-1-ONE))
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 (9335 217 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (9335 217 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (4010 217 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (438 438 (:REWRITE |(equal (/ x) (/ y))|))
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 (258 57 (:REWRITE DEFAULT-PLUS-1))
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 (220 220 (:REWRITE DEFAULT-MOD-2))
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 (217 217 (:REWRITE |(mod x (- y))| . 3))
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 (184 184 (:LINEAR EXPT-LINEAR-UPPER-<=))
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 (183 183 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (125 125 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (121 8 (:REWRITE |(+ 0 x)|))
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 (45 45 (:REWRITE |(expt (- x) n)|))
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 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
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 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (11 11 (:REWRITE |(< (/ x) 0)|))
 (11 11 (:REWRITE |(< (* x y) 0)|))
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 (7 7 (:REWRITE ZIP-OPEN))
 (6 6 (:TYPE-PRESCRIPTION ABS))
 (6 6 (:REWRITE |(+ x (- x))|))
 (6 6 (:REWRITE |(+ c (+ d x))|))
 (4 4 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (4 4 (:REWRITE |(* c (expt d n))|))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 )
(DM::FAST-MOD-EXPT-MUL-REWRITE
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 (17540 17540 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (15303 215 (:REWRITE DEFAULT-MOD-RATIO))
 (15115 197 (:REWRITE |(* (- x) y)|))
 (15092 13 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (14293 3233 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (14293 3233 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (12544 157 (:LINEAR EXPT->=-1-TWO))
 (12544 157 (:LINEAR EXPT->-1-TWO))
 (12544 157 (:LINEAR EXPT-<-1-ONE))
 (12229 157 (:LINEAR EXPT-X->=-X))
 (12229 157 (:LINEAR EXPT->=-1-ONE))
 (12229 157 (:LINEAR EXPT-<=-1-TWO))
 (12184 157 (:LINEAR EXPT-X->-X))
 (12184 157 (:LINEAR EXPT->-1-ONE))
 (12184 157 (:LINEAR EXPT-<-1-TWO))
 (11896 194 (:REWRITE |(integerp (- x))|))
 (11323 157 (:LINEAR EXPT-<=-1-ONE))
 (11254 311 (:REWRITE |(* y (* x z))|))
 (10421 1329 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (7964 1337 (:REWRITE DEFAULT-LESS-THAN-1))
 (7737 1329 (:REWRITE SIMPLIFY-SUMS-<))
 (6535 1329 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5146 194 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (5146 194 (:REWRITE MOD-X-Y-=-X . 2))
 (5146 194 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (5146 194 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (4717 514 (:META META-INTEGERP-CORRECT))
 (4604 39 (:LINEAR MOD-BOUNDS-3))
 (4457 8 (:REWRITE MOD-THEOREM-ONE-B))
 (3878 1337 (:REWRITE DEFAULT-LESS-THAN-2))
 (3473 3233 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (3262 309 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3233 3233 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (3233 3233 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (3233 3233 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (3233 3233 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (3152 207 (:REWRITE DEFAULT-MINUS))
 (3058 194 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (3058 194 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2872 2 (:REWRITE MOD-THEOREM-TWO))
 (2820 194 (:REWRITE MOD-CANCEL-*-CONST))
 (2349 87 (:REWRITE |(equal (expt x n) 0)|))
 (2303 215 (:REWRITE DEFAULT-MOD-1))
 (2268 2268 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2268 2268 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2268 2268 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1912 194 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1912 194 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1912 194 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1799 807 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1765 298 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1741 3 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1340 194 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1337 1337 (:REWRITE THE-FLOOR-BELOW))
 (1337 1337 (:REWRITE THE-FLOOR-ABOVE))
 (1332 1332 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1332 1332 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1332 1332 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1332 1332 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1332 1332 (:REWRITE INTEGERP-<-CONSTANT))
 (1332 1332 (:REWRITE CONSTANT-<-INTEGERP))
 (1332 1332 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1332 1332 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1332 1332 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1332 1332 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1332 1332 (:REWRITE |(< c (- x))|))
 (1332 1332 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1332 1332 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1332 1332 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1332 1332 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1332 1332 (:REWRITE |(< (/ x) (/ y))|))
 (1332 1332 (:REWRITE |(< (- x) c)|))
 (1332 1332 (:REWRITE |(< (- x) (- y))|))
 (1296 48 (:REWRITE |(integerp (expt x n))|))
 (1228 78 (:LINEAR MOD-BOUNDS-2))
 (1088 103 (:REWRITE DEFAULT-PLUS-2))
 (1004 194 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1004 194 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (992 807 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (992 807 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (992 807 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (807 807 (:TYPE-PRESCRIPTION NATP))
 (623 623 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (623 623 (:REWRITE DEFAULT-DIVIDE))
 (557 514 (:REWRITE INTEGERP-MINUS-X))
 (528 6 (:REWRITE MOD-POSITIVE . 3))
 (517 103 (:REWRITE DEFAULT-PLUS-1))
 (514 514 (:REWRITE REDUCE-INTEGERP-+))
 (435 435 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (396 396 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (396 396 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (396 396 (:REWRITE |(equal c (/ x))|))
 (396 396 (:REWRITE |(equal c (- x))|))
 (396 396 (:REWRITE |(equal (/ x) c)|))
 (396 396 (:REWRITE |(equal (/ x) (/ y))|))
 (396 396 (:REWRITE |(equal (- x) c)|))
 (396 396 (:REWRITE |(equal (- x) (- y))|))
 (354 66 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (344 338 (:REWRITE |(* c (* d x))|))
 (332 332 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (332 332 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (332 332 (:REWRITE |(< 0 (/ x))|))
 (332 332 (:REWRITE |(< 0 (* x y))|))
 (314 314 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (314 314 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (314 314 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (314 314 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (311 35 (:REWRITE DEFAULT-EXPT-1))
 (309 309 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (283 7 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (271 271 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (215 215 (:REWRITE DEFAULT-MOD-2))
 (199 13 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (194 194 (:REWRITE |(mod x (- y))| . 3))
 (194 194 (:REWRITE |(mod x (- y))| . 2))
 (194 194 (:REWRITE |(mod x (- y))| . 1))
 (194 194 (:REWRITE |(mod (- x) y)| . 3))
 (194 194 (:REWRITE |(mod (- x) y)| . 2))
 (194 194 (:REWRITE |(mod (- x) y)| . 1))
 (170 170 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (157 157 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (157 157 (:LINEAR EXPT-LINEAR-UPPER-<))
 (157 157 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (157 157 (:LINEAR EXPT-LINEAR-LOWER-<))
 (102 1 (:REWRITE DM::MOD-DISTINCT))
 (100 1 (:DEFINITION DM::PRIMEP))
 (97 97 (:REWRITE |(equal (* x y) 0)|))
 (97 97 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (96 20 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (66 66 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (66 66 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (66 66 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (64 2 (:REWRITE RTL::FL*1/INT-REWRITE-ALT))
 (56 1 (:REWRITE DM::LEAST-DIVISOR-REWRITE))
 (55 1 (:DEFINITION DM::LEAST-DIVISOR-2))
 (47 35 (:REWRITE DEFAULT-EXPT-2))
 (43 43 (:LINEAR RTL::MOD-BND-3))
 (39 39 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (29 29 (:REWRITE |(expt 1/c n)|))
 (29 29 (:REWRITE |(expt (- x) n)|))
 (28 28 (:REWRITE |(equal (+ (- c) x) y)|))
 (21 21 (:REWRITE |(mod x 2)| . 2))
 (20 20 (:TYPE-PRESCRIPTION DM::LEAST-DIVISOR-2))
 (17 3 (:REWRITE ACL2-NUMBERP-X))
 (16 16 (:REWRITE |(< (/ x) 0)|))
 (16 16 (:REWRITE |(< (* x y) 0)|))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (10 10 (:LINEAR RTL::FL-MONOTONE-LINEAR))
 (7 7 (:REWRITE |(+ x (- x))|))
 (7 7 (:REWRITE |(+ c (+ d x))|))
 (7 1 (:REWRITE RATIONALP-X))
 (6 6 (:REWRITE MOD-POSITIVE . 2))
 (6 6 (:REWRITE MOD-POSITIVE . 1))
 (6 6 (:REWRITE |(expt c (* d n))|))
 (5 5 (:LINEAR RTL::N<=FL-LINEAR))
 (3 3 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:TYPE-PRESCRIPTION DM::PRIMEP))
 (1 1 (:TYPE-PRESCRIPTION DM::DIVIDES))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE DM::FACTOR-DIVIDES))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(DM::FAST-MOD-EXPT-REWRITE
 (8843 1 (:DEFINITION DM::FAST-MOD-EXPT-MUL))
 (4707 21 (:REWRITE RTL::MOD-DOES-NOTHING))
 (3881 1 (:REWRITE MOD-THEOREM-THREE))
 (3065 19 (:REWRITE CANCEL-MOD-+))
 (2307 19 (:REWRITE MOD-X-Y-=-X . 3))
 (2230 19 (:REWRITE MOD-X-Y-=-X . 4))
 (1989 19 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1939 19 (:REWRITE MOD-ZERO . 4))
 (1792 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1634 145 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1531 19 (:REWRITE MOD-ZERO . 3))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1333 1333 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1267 179 (:REWRITE DEFAULT-TIMES-1))
 (1180 1180 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1180 1180 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1180 1180 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1090 218 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1066 179 (:REWRITE DEFAULT-TIMES-2))
 (1062 218 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1010 218 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1010 218 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1003 20 (:REWRITE DEFAULT-MOD-RATIO))
 (925 184 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (886 15 (:REWRITE |(integerp (- x))|))
 (843 19 (:REWRITE |(* (- x) y)|))
 (759 185 (:REWRITE DEFAULT-LESS-THAN-1))
 (758 184 (:REWRITE SIMPLIFY-SUMS-<))
 (697 14 (:REWRITE |(* (* x y) z)|))
 (591 184 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (469 19 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (469 19 (:REWRITE MOD-X-Y-=-X . 2))
 (469 19 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (469 19 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (464 12 (:REWRITE |(equal (expt x n) 0)|))
 (356 185 (:REWRITE DEFAULT-LESS-THAN-2))
 (299 20 (:REWRITE DEFAULT-MINUS))
 (298 37 (:LINEAR EXPT->=-1-TWO))
 (298 37 (:LINEAR EXPT->-1-TWO))
 (298 37 (:LINEAR EXPT-<-1-ONE))
 (287 42 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (286 50 (:REWRITE INTEGERP-MINUS-X))
 (282 19 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (282 19 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (277 74 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (274 19 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (274 19 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (274 19 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (271 37 (:LINEAR EXPT-X->=-X))
 (271 37 (:LINEAR EXPT->=-1-ONE))
 (271 37 (:LINEAR EXPT-<=-1-TWO))
 (271 37 (:LINEAR EXPT-<=-1-ONE))
 (262 37 (:LINEAR EXPT-X->-X))
 (262 37 (:LINEAR EXPT->-1-ONE))
 (262 37 (:LINEAR EXPT-<-1-TWO))
 (256 74 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (252 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (250 19 (:REWRITE MOD-CANCEL-*-CONST))
 (246 3 (:REWRITE |(* y (* x z))|))
 (220 46 (:META META-INTEGERP-CORRECT))
 (218 218 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (218 218 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (218 218 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (218 218 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (218 218 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (207 20 (:REWRITE DEFAULT-MOD-1))
 (187 184 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (187 184 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (185 185 (:REWRITE THE-FLOOR-BELOW))
 (185 185 (:REWRITE THE-FLOOR-ABOVE))
 (184 184 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (184 184 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (184 184 (:REWRITE INTEGERP-<-CONSTANT))
 (184 184 (:REWRITE CONSTANT-<-INTEGERP))
 (184 184 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (184 184 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (184 184 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (184 184 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (184 184 (:REWRITE |(< c (- x))|))
 (184 184 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (184 184 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (184 184 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (184 184 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (184 184 (:REWRITE |(< (/ x) (/ y))|))
 (184 184 (:REWRITE |(< (- x) c)|))
 (184 184 (:REWRITE |(< (- x) (- y))|))
 (159 42 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (148 2 (:LINEAR MOD-BOUNDS-3))
 (145 145 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (145 145 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (145 145 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (134 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (130 130 (:TYPE-PRESCRIPTION RTL::FL-DEF))
 (108 88 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (100 41 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (88 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (83 83 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (81 3 (:REWRITE |(integerp (expt x n))|))
 (74 74 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (74 74 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (64 1 (:REWRITE MOD-THEOREM-ONE-A))
 (63 10 (:REWRITE DEFAULT-PLUS-2))
 (61 19 (:REWRITE |(- (* c x))|))
 (60 4 (:LINEAR MOD-BOUNDS-2))
 (57 54 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (56 56 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (56 56 (:REWRITE DEFAULT-DIVIDE))
 (56 10 (:REWRITE DEFAULT-EXPT-1))
 (54 54 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (54 54 (:REWRITE |(equal c (/ x))|))
 (54 54 (:REWRITE |(equal c (- x))|))
 (54 54 (:REWRITE |(equal (/ x) c)|))
 (54 54 (:REWRITE |(equal (/ x) (/ y))|))
 (54 54 (:REWRITE |(equal (- x) c)|))
 (54 54 (:REWRITE |(equal (- x) (- y))|))
 (54 27 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (50 50 (:REWRITE |(< 0 (/ x))|))
 (50 50 (:REWRITE |(< 0 (* x y))|))
 (46 46 (:REWRITE REDUCE-INTEGERP-+))
 (45 6 (:REWRITE NORMALIZE-ADDENDS))
 (42 42 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (37 37 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (37 37 (:LINEAR EXPT-LINEAR-UPPER-<))
 (37 37 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (37 37 (:LINEAR EXPT-LINEAR-LOWER-<))
 (33 4 (:REWRITE ZP-OPEN))
 (31 10 (:REWRITE DEFAULT-PLUS-1))
 (30 2 (:REWRITE |(+ y x)|))
 (28 28 (:TYPE-PRESCRIPTION NATP))
 (27 27 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (27 27 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (27 27 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (27 19 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (27 19 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (27 19 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (25 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (20 20 (:REWRITE DEFAULT-MOD-2))
 (19 19 (:REWRITE |(mod x (- y))| . 3))
 (19 19 (:REWRITE |(mod x (- y))| . 2))
 (19 19 (:REWRITE |(mod x (- y))| . 1))
 (19 19 (:REWRITE |(mod (- x) y)| . 3))
 (19 19 (:REWRITE |(mod (- x) y)| . 2))
 (19 19 (:REWRITE |(mod (- x) y)| . 1))
 (18 18 (:REWRITE |(* c (* d x))|))
 (16 2 (:LINEAR RTL::FL-DEF))
 (15 1 (:REWRITE |(mod x 2)| . 1))
 (13 13 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (13 13 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (13 10 (:REWRITE DEFAULT-EXPT-2))
 (12 2 (:REWRITE BUBBLE-DOWN-*-MATCH-1))
 (12 1 (:REWRITE |(expt (expt x m) n)|))
 (11 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (11 1 (:REWRITE |(+ 0 x)|))
 (10 2 (:REWRITE |(* x x)|))
 (9 9 (:TYPE-PRESCRIPTION ABS))
 (9 9 (:REWRITE |(expt 1/c n)|))
 (9 9 (:REWRITE |(expt (- x) n)|))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 1 (:REWRITE |(< x (if a b c))|))
 (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 RTL::INTEGERP-FL))
 (4 4 (:REWRITE |(equal (* x y) 0)|))
 (4 4 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:LINEAR RTL::FL-MONOTONE-LINEAR))
 (4 4 (:DEFINITION FIX))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 3 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:LINEAR RTL::N<=FL-LINEAR))
 (1 1 (:REWRITE |(mod x 2)| . 2))
 (1 1 (:REWRITE |(expt c (* d n))|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(DM::FAST-MAX-FACT
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(DM::FPFR-1
 (685 5 (:DEFINITION DM::PROD-POWERS))
 (345 15 (:REWRITE |(* (if a b c) x)|))
 (282 10 (:REWRITE DM::FACTOR-DIVIDES-2))
 (234 39 (:REWRITE DEFAULT-TIMES-1))
 (225 15 (:REWRITE DEFAULT-EXPT-2))
 (185 10 (:REWRITE DEFAULT-EXPT-1))
 (144 39 (:REWRITE DEFAULT-TIMES-2))
 (143 23 (:REWRITE ACL2-NUMBERP-X))
 (70 5 (:REWRITE ZIP-OPEN))
 (60 15 (:REWRITE RATIONALP-X))
 (49 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (40 10 (:REWRITE |(* 1 x)|))
 (32 32 (:REWRITE REDUCE-INTEGERP-+))
 (32 32 (:REWRITE INTEGERP-MINUS-X))
 (32 32 (:META META-INTEGERP-CORRECT))
 (30 30 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (30 30 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (30 30 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (28 28 (:REWRITE DEFAULT-CDR))
 (28 28 (:REWRITE DEFAULT-CAR))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (18 18 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (17 11 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (17 11 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (16 15 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (16 15 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (16 15 (:REWRITE DEFAULT-LESS-THAN-2))
 (15 15 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (15 15 (:TYPE-PRESCRIPTION EXPT))
 (15 15 (:REWRITE THE-FLOOR-BELOW))
 (15 15 (:REWRITE THE-FLOOR-ABOVE))
 (15 15 (:REWRITE SIMPLIFY-SUMS-<))
 (15 15 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (15 15 (:REWRITE REDUCE-RATIONALP-+))
 (15 15 (:REWRITE REDUCE-RATIONALP-*))
 (15 15 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (15 15 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (15 15 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (15 15 (:REWRITE RATIONALP-MINUS-X))
 (15 15 (:REWRITE INTEGERP-<-CONSTANT))
 (15 15 (:REWRITE DEFAULT-LESS-THAN-1))
 (15 15 (:REWRITE CONSTANT-<-INTEGERP))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (15 15 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (15 15 (:REWRITE |(< c (- x))|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (15 15 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (15 15 (:REWRITE |(< (/ x) (/ y))|))
 (15 15 (:REWRITE |(< (- x) c)|))
 (15 15 (:REWRITE |(< (- x) (- y))|))
 (15 15 (:META META-RATIONALP-CORRECT))
 (13 13 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (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 (- x) (- y))|))
 (10 10 (:REWRITE DM::PERM-MEMBER))
 (8 4 (:REWRITE DEFAULT-PLUS-2))
 (7 7 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (5 5 (:REWRITE |(expt 1/c n)|))
 (5 5 (:REWRITE |(expt (- x) n)|))
 (5 5 (:REWRITE |(* 0 x)|))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 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 |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (2 2 (:REWRITE DEFAULT-DIVIDE))
 )
(DM::FPFR-2
 (103 1 (:DEFINITION DM::DISTINCT-FACTORS))
 (34 1 (:DEFINITION NATP))
 (31 1 (:DEFINITION MEMBER-EQUAL))
 (11 3 (:REWRITE ACL2-NUMBERP-X))
 (10 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 1 (:REWRITE RATIONALP-X))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (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-INTEGERP-+))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE DM::PERM-MEMBER))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (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) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (2 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (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 REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE RATIONALP-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 |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(DM::FPFR-3
 (822 6 (:DEFINITION DM::PROD-POWERS))
 (414 18 (:REWRITE |(* (if a b c) x)|))
 (399 15 (:REWRITE DM::FACTOR-DIVIDES-2))
 (283 49 (:REWRITE DEFAULT-TIMES-1))
 (270 18 (:REWRITE DEFAULT-EXPT-2))
 (222 12 (:REWRITE DEFAULT-EXPT-1))
 (210 34 (:REWRITE ACL2-NUMBERP-X))
 (175 49 (:REWRITE DEFAULT-TIMES-2))
 (88 22 (:REWRITE RATIONALP-X))
 (84 6 (:REWRITE ZIP-OPEN))
 (69 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (48 12 (:REWRITE |(* 1 x)|))
 (43 43 (:REWRITE REDUCE-INTEGERP-+))
 (43 43 (:REWRITE INTEGERP-MINUS-X))
 (43 43 (:META META-INTEGERP-CORRECT))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (38 38 (:REWRITE DEFAULT-CAR))
 (36 36 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE THE-FLOOR-BELOW))
 (22 22 (:REWRITE THE-FLOOR-ABOVE))
 (22 22 (:REWRITE REDUCE-RATIONALP-+))
 (22 22 (:REWRITE REDUCE-RATIONALP-*))
 (22 22 (:REWRITE RATIONALP-MINUS-X))
 (22 22 (:META META-RATIONALP-CORRECT))
 (22 21 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (22 21 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (21 21 (:REWRITE SIMPLIFY-SUMS-<))
 (21 21 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (21 21 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (21 21 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (21 21 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (21 21 (:REWRITE INTEGERP-<-CONSTANT))
 (21 21 (:REWRITE DEFAULT-LESS-THAN-1))
 (21 21 (:REWRITE CONSTANT-<-INTEGERP))
 (21 21 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (21 21 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (21 21 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (21 21 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (21 21 (:REWRITE |(< c (- x))|))
 (21 21 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (21 21 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (21 21 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (21 21 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (21 21 (:REWRITE |(< (/ x) (/ y))|))
 (21 21 (:REWRITE |(< (- x) c)|))
 (21 21 (:REWRITE |(< (- x) (- y))|))
 (21 13 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (21 13 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (18 18 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (18 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (18 18 (:TYPE-PRESCRIPTION EXPT))
 (18 18 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (15 15 (:REWRITE DM::PERM-MEMBER))
 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (13 13 (:REWRITE |(equal c (/ x))|))
 (13 13 (:REWRITE |(equal c (- x))|))
 (13 13 (:REWRITE |(equal (/ x) c)|))
 (13 13 (:REWRITE |(equal (/ x) (/ y))|))
 (13 13 (:REWRITE |(equal (- x) c)|))
 (13 13 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 4 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (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 |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE |(< (/ x) 0)|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (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 |(< 0 (* x y))|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 )
(DM::FPFR-4
 (282 10 (:REWRITE DM::FACTOR-DIVIDES-2))
 (146 24 (:REWRITE RATIONALP-X))
 (138 138 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (138 138 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (138 138 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (116 20 (:REWRITE ACL2-NUMBERP-X))
 (110 32 (:REWRITE DEFAULT-TIMES-1))
 (74 32 (:REWRITE DEFAULT-TIMES-2))
 (66 2 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (66 2 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (62 22 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (51 22 (:REWRITE DEFAULT-PLUS-2))
 (47 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (36 24 (:REWRITE DEFAULT-LESS-THAN-1))
 (35 35 (:REWRITE REDUCE-INTEGERP-+))
 (35 35 (:REWRITE INTEGERP-MINUS-X))
 (35 35 (:META META-INTEGERP-CORRECT))
 (28 20 (:REWRITE SIMPLIFY-SUMS-<))
 (24 24 (:REWRITE THE-FLOOR-BELOW))
 (24 24 (:REWRITE THE-FLOOR-ABOVE))
 (24 24 (:REWRITE DEFAULT-LESS-THAN-2))
 (24 22 (:REWRITE DEFAULT-PLUS-1))
 (22 22 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (22 22 (:REWRITE REDUCE-RATIONALP-+))
 (22 22 (:REWRITE REDUCE-RATIONALP-*))
 (22 22 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (22 22 (:REWRITE RATIONALP-MINUS-X))
 (22 22 (:REWRITE INTEGERP-<-CONSTANT))
 (22 22 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (22 22 (:REWRITE CONSTANT-<-INTEGERP))
 (22 22 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (22 22 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (22 22 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (22 22 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (22 22 (:REWRITE |(< c (- x))|))
 (22 22 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (22 22 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (22 22 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (22 22 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (22 22 (:REWRITE |(< (/ x) (/ y))|))
 (22 22 (:REWRITE |(< (- x) c)|))
 (22 22 (:REWRITE |(< (- x) (- y))|))
 (22 22 (:META META-RATIONALP-CORRECT))
 (20 20 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (18 2 (:REWRITE RATIONALP-/))
 (18 2 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (18 2 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (15 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (15 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE DM::PERM-MEMBER))
 (9 9 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (9 9 (:REWRITE REDUCE-ADDITIVE-CONSTANT-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))|))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6 6 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (6 6 (:TYPE-PRESCRIPTION EXPT))
 (6 6 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (6 6 (:REWRITE |(< (/ x) 0)|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (5 5 (:REWRITE |(< 0 (/ x))|))
 (5 5 (:REWRITE |(< 0 (* 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))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (2 2 (:REWRITE INTEGERP-/))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE |(* x (- y))|))
 (2 2 (:REWRITE |(* (- x) y)|))
 )
(DM::SUBSETP-MEMBER
 (2036 53 (:REWRITE DM::FACTOR-DIVIDES-2))
 (1923 21 (:DEFINITION DM::DISTINCT-FACTORS))
 (680 20 (:DEFINITION NATP))
 (253 69 (:REWRITE ACL2-NUMBERP-X))
 (230 23 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (131 131 (:TYPE-PRESCRIPTION DM::DISTINCT-FACTORS))
 (93 93 (:REWRITE DEFAULT-CAR))
 (92 23 (:REWRITE RATIONALP-X))
 (65 65 (:REWRITE DEFAULT-CDR))
 (53 53 (:REWRITE DM::PERM-MEMBER))
 (46 23 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (46 23 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (44 44 (:REWRITE THE-FLOOR-BELOW))
 (44 44 (:REWRITE THE-FLOOR-ABOVE))
 (44 44 (:REWRITE SIMPLIFY-SUMS-<))
 (44 44 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (44 44 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (44 44 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (44 44 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (44 44 (:REWRITE REDUCE-INTEGERP-+))
 (44 44 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (44 44 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (44 44 (:REWRITE INTEGERP-MINUS-X))
 (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))|))
 (44 44 (:META META-INTEGERP-CORRECT))
 (23 23 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (23 23 (:REWRITE REDUCE-RATIONALP-+))
 (23 23 (:REWRITE REDUCE-RATIONALP-*))
 (23 23 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (23 23 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (23 23 (:REWRITE RATIONALP-MINUS-X))
 (23 23 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (23 23 (:REWRITE |(equal c (/ x))|))
 (23 23 (:REWRITE |(equal c (- x))|))
 (23 23 (:REWRITE |(equal (/ x) c)|))
 (23 23 (:REWRITE |(equal (/ x) (/ y))|))
 (23 23 (:REWRITE |(equal (- x) c)|))
 (23 23 (:REWRITE |(equal (- x) (- y))|))
 (23 23 (:META META-RATIONALP-CORRECT))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (21 21 (:REWRITE |(< (/ x) 0)|))
 (21 21 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:TYPE-PRESCRIPTION ZP))
 (1 1 (:REWRITE ZP-OPEN))
 )
(DM::SUBSETP-CONS
 (5797 135 (:REWRITE DM::FACTOR-DIVIDES-2))
 (5693 55 (:DEFINITION DM::DISTINCT-FACTORS))
 (1870 55 (:DEFINITION NATP))
 (649 177 (:REWRITE ACL2-NUMBERP-X))
 (590 59 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (391 391 (:TYPE-PRESCRIPTION DM::DISTINCT-FACTORS))
 (245 245 (:REWRITE DEFAULT-CAR))
 (236 59 (:REWRITE RATIONALP-X))
 (168 168 (:REWRITE DEFAULT-CDR))
 (135 135 (:REWRITE DM::PERM-MEMBER))
 (122 122 (:REWRITE THE-FLOOR-BELOW))
 (122 122 (:REWRITE THE-FLOOR-ABOVE))
 (122 122 (:REWRITE SIMPLIFY-SUMS-<))
 (122 122 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (122 122 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (122 122 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (122 122 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (122 122 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (122 122 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (122 122 (:REWRITE INTEGERP-<-CONSTANT))
 (122 122 (:REWRITE DEFAULT-LESS-THAN-2))
 (122 122 (:REWRITE DEFAULT-LESS-THAN-1))
 (122 122 (:REWRITE CONSTANT-<-INTEGERP))
 (122 122 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (122 122 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (122 122 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (122 122 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (122 122 (:REWRITE |(< c (- x))|))
 (122 122 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (122 122 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (122 122 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (122 122 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (122 122 (:REWRITE |(< (/ x) (/ y))|))
 (122 122 (:REWRITE |(< (- x) c)|))
 (122 122 (:REWRITE |(< (- x) (- y))|))
 (120 120 (:REWRITE REDUCE-INTEGERP-+))
 (120 120 (:REWRITE INTEGERP-MINUS-X))
 (120 120 (:META META-INTEGERP-CORRECT))
 (118 59 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (118 59 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (61 61 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (61 61 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (61 61 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (61 61 (:REWRITE |(< (/ x) 0)|))
 (61 61 (:REWRITE |(< (* x y) 0)|))
 (59 59 (:REWRITE REDUCE-RATIONALP-+))
 (59 59 (:REWRITE REDUCE-RATIONALP-*))
 (59 59 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (59 59 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (59 59 (:REWRITE RATIONALP-MINUS-X))
 (59 59 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (59 59 (:REWRITE |(equal c (/ x))|))
 (59 59 (:REWRITE |(equal c (- x))|))
 (59 59 (:REWRITE |(equal (/ x) c)|))
 (59 59 (:REWRITE |(equal (/ x) (/ y))|))
 (59 59 (:REWRITE |(equal (- x) c)|))
 (59 59 (:REWRITE |(equal (- x) (- y))|))
 (59 59 (:META META-RATIONALP-CORRECT))
 )
(DM::SUBSETP-SELF
 (2444 59 (:REWRITE DM::FACTOR-DIVIDES-2))
 (2407 19 (:DEFINITION DM::DISTINCT-FACTORS))
 (646 19 (:DEFINITION NATP))
 (264 72 (:REWRITE ACL2-NUMBERP-X))
 (240 24 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (125 125 (:TYPE-PRESCRIPTION DM::DISTINCT-FACTORS))
 (120 120 (:REWRITE DEFAULT-CAR))
 (96 24 (:REWRITE RATIONALP-X))
 (88 88 (:REWRITE DEFAULT-CDR))
 (59 59 (:REWRITE DM::PERM-MEMBER))
 (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-INTEGERP-+))
 (48 48 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (48 48 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (48 48 (:REWRITE INTEGERP-MINUS-X))
 (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))|))
 (48 48 (:META META-INTEGERP-CORRECT))
 (48 24 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (48 24 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (24 24 (:REWRITE REDUCE-RATIONALP-+))
 (24 24 (:REWRITE REDUCE-RATIONALP-*))
 (24 24 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (24 24 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (24 24 (:REWRITE RATIONALP-MINUS-X))
 (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))|))
 (24 24 (:REWRITE |(< (/ x) 0)|))
 (24 24 (:REWRITE |(< (* x y) 0)|))
 (24 24 (:META META-RATIONALP-CORRECT))
 )
(DM::FPFR-5
 (10017 7 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (7234 129 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6255 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (6255 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6196 31 (:REWRITE MOD-ZERO . 4))
 (6168 31 (:REWRITE CANCEL-MOD-+))
 (5459 31 (:REWRITE MOD-X-Y-=-X . 4))
 (5420 5420 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (5420 5420 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (5420 5420 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4881 31 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4127 277 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (4021 31 (:REWRITE MOD-X-Y-=-X . 3))
 (3546 31 (:REWRITE MOD-ZERO . 3))
 (3439 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (3439 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3439 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (3439 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3439 3439 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3426 50 (:REWRITE DEFAULT-MOD-RATIO))
 (3070 498 (:REWRITE DEFAULT-TIMES-1))
 (2960 80 (:REWRITE DM::FACTOR-DIVIDES-2))
 (2908 928 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2889 967 (:REWRITE DEFAULT-LESS-THAN-1))
 (2864 32 (:DEFINITION DM::DISTINCT-FACTORS))
 (2348 922 (:REWRITE SIMPLIFY-SUMS-<))
 (2264 41 (:REWRITE |(integerp (- x))|))
 (2148 498 (:REWRITE DEFAULT-TIMES-2))
 (2104 132 (:LINEAR EXPT->=-1-TWO))
 (2104 132 (:LINEAR EXPT->-1-TWO))
 (2104 132 (:LINEAR EXPT-<-1-ONE))
 (1907 31 (:REWRITE |(equal (expt x n) 0)|))
 (1900 132 (:LINEAR EXPT-X->=-X))
 (1900 132 (:LINEAR EXPT->=-1-ONE))
 (1900 132 (:LINEAR EXPT-<=-1-TWO))
 (1900 132 (:LINEAR EXPT-<=-1-ONE))
 (1832 132 (:LINEAR EXPT-X->-X))
 (1832 132 (:LINEAR EXPT->-1-ONE))
 (1832 132 (:LINEAR EXPT-<-1-TWO))
 (1780 46 (:REWRITE |(* (- x) y)|))
 (1421 967 (:REWRITE DEFAULT-LESS-THAN-2))
 (1328 210 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1288 210 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1288 210 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1155 132 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1063 31 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1063 31 (:REWRITE MOD-X-Y-=-X . 2))
 (1063 31 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1063 31 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1050 210 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (967 967 (:REWRITE THE-FLOOR-BELOW))
 (967 967 (:REWRITE THE-FLOOR-ABOVE))
 (950 34 (:REWRITE |(* (if a b c) x)|))
 (934 206 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (928 928 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (928 928 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (928 928 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (928 928 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (928 928 (:REWRITE INTEGERP-<-CONSTANT))
 (928 928 (:REWRITE CONSTANT-<-INTEGERP))
 (928 928 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (928 928 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (928 928 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (928 928 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (928 928 (:REWRITE |(< c (- x))|))
 (928 928 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (928 928 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (928 928 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (928 928 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (928 928 (:REWRITE |(< (/ x) (/ y))|))
 (928 928 (:REWRITE |(< (- x) c)|))
 (928 928 (:REWRITE |(< (- x) (- y))|))
 (774 50 (:REWRITE DEFAULT-MOD-1))
 (728 206 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (728 206 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (728 206 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (648 5 (:LINEAR MOD-BOUNDS-3))
 (631 53 (:REWRITE DEFAULT-MINUS))
 (624 184 (:REWRITE DEFAULT-PLUS-2))
 (609 31 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (609 31 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (609 31 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (609 31 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (609 31 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (531 107 (:REWRITE ACL2-NUMBERP-X))
 (506 89 (:REWRITE RATIONALP-X))
 (426 266 (:REWRITE REDUCE-INTEGERP-+))
 (423 31 (:REWRITE MOD-CANCEL-*-CONST))
 (416 416 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (278 184 (:REWRITE DEFAULT-PLUS-1))
 (277 277 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (277 277 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (277 277 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (276 111 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (266 266 (:REWRITE INTEGERP-MINUS-X))
 (266 266 (:META META-INTEGERP-CORRECT))
 (264 264 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (264 264 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (264 264 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (264 264 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (235 235 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (235 235 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (235 235 (:REWRITE |(< 0 (/ x))|))
 (235 235 (:REWRITE |(< 0 (* x y))|))
 (222 10 (:LINEAR MOD-BOUNDS-2))
 (210 210 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (210 210 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (210 210 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (210 210 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (210 210 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (208 208 (:TYPE-PRESCRIPTION DM::DISTINCT-FACTORS))
 (198 6 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (198 6 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (175 7 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (171 19 (:REWRITE |(not (equal x (/ y)))|))
 (171 19 (:REWRITE |(equal x (/ y))|))
 (165 165 (:REWRITE DEFAULT-CAR))
 (147 147 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (143 143 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (143 143 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (143 143 (:REWRITE |(equal c (/ x))|))
 (143 143 (:REWRITE |(equal c (- x))|))
 (143 143 (:REWRITE |(equal (/ x) c)|))
 (143 143 (:REWRITE |(equal (/ x) (/ y))|))
 (143 143 (:REWRITE |(equal (- x) c)|))
 (143 143 (:REWRITE |(equal (- x) (- y))|))
 (132 132 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (132 132 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (132 132 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (132 132 (:LINEAR EXPT-LINEAR-UPPER-<))
 (132 132 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (132 132 (:LINEAR EXPT-LINEAR-LOWER-<))
 (102 102 (:REWRITE DEFAULT-CDR))
 (96 3 (:REWRITE |(* y (* x z))|))
 (84 6 (:REWRITE |(* a (/ a))|))
 (83 83 (:REWRITE REDUCE-RATIONALP-+))
 (83 83 (:REWRITE REDUCE-RATIONALP-*))
 (83 83 (:REWRITE RATIONALP-MINUS-X))
 (83 83 (:META META-RATIONALP-CORRECT))
 (80 80 (:REWRITE DM::PERM-MEMBER))
 (77 7 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (66 66 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (66 66 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (64 64 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (62 62 (:REWRITE |(< (/ x) 0)|))
 (62 62 (:REWRITE |(< (* x y) 0)|))
 (56 56 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (56 56 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (54 6 (:REWRITE RATIONALP-/))
 (54 6 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (54 6 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (50 50 (:REWRITE DEFAULT-MOD-2))
 (46 16 (:REWRITE INTEGERP-/))
 (43 43 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (37 37 (:REWRITE |(* 1 x)|))
 (35 35 (:REWRITE DEFAULT-EXPT-1))
 (31 31 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (31 31 (:REWRITE |(mod x (- y))| . 3))
 (31 31 (:REWRITE |(mod x (- y))| . 2))
 (31 31 (:REWRITE |(mod x (- y))| . 1))
 (31 31 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (31 31 (:REWRITE |(mod (- x) y)| . 3))
 (31 31 (:REWRITE |(mod (- x) y)| . 2))
 (31 31 (:REWRITE |(mod (- x) y)| . 1))
 (31 31 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (31 31 (:REWRITE |(- (* c x))|))
 (26 26 (:REWRITE |(expt 1/c n)|))
 (26 26 (:REWRITE |(expt (- x) n)|))
 (25 25 (:REWRITE |(equal (+ (- c) x) y)|))
 (24 24 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (24 24 (:REWRITE |(+ c (+ d x))|))
 (15 15 (:REWRITE |(* x (- y))|))
 (10 10 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (8 8 (:TYPE-PRESCRIPTION DM::FAST-MOD-EXPT))
 (6 6 (:REWRITE |(< (+ c/d x) y)|))
 (6 6 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 )
(DM::FAST-MAX-FACT-REWRITE)
(DM::FIND-PRIM-ROOT
 (1225 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (676 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (383 78 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (340 1 (:REWRITE RTL::MOD-DOES-NOTHING))
 (220 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (212 7 (:LINEAR EXPT-<=-1-TWO))
 (202 7 (:LINEAR EXPT-X->=-X))
 (183 147 (:REWRITE DEFAULT-PLUS-2))
 (155 1 (:REWRITE MOD-X-Y-=-X . 3))
 (138 1 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (137 7 (:LINEAR EXPT->=-1-TWO))
 (137 7 (:LINEAR EXPT-<=-1-ONE))
 (132 7 (:LINEAR EXPT-X->-X))
 (132 7 (:LINEAR EXPT->-1-ONE))
 (132 7 (:LINEAR EXPT-<-1-TWO))
 (132 1 (:REWRITE CANCEL-MOD-+))
 (114 87 (:REWRITE DEFAULT-LESS-THAN-1))
 (104 104 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (104 104 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (104 104 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (104 104 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (104 104 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (98 7 (:LINEAR EXPT->=-1-ONE))
 (90 63 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (87 87 (:REWRITE THE-FLOOR-BELOW))
 (87 87 (:REWRITE THE-FLOOR-ABOVE))
 (87 87 (:REWRITE DEFAULT-LESS-THAN-2))
 (80 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (78 78 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (78 78 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (69 1 (:REWRITE MOD-ZERO . 3))
 (68 68 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (68 68 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (68 68 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (68 68 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (68 68 (:REWRITE |(< c (- x))|))
 (68 68 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (68 68 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (68 68 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (68 68 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (68 68 (:REWRITE |(< (/ x) (/ y))|))
 (68 68 (:REWRITE |(< (- x) (- y))|))
 (63 63 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (63 63 (:REWRITE INTEGERP-<-CONSTANT))
 (63 63 (:REWRITE CONSTANT-<-INTEGERP))
 (58 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (58 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (58 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (56 26 (:REWRITE |(+ c (+ d x))|))
 (43 7 (:REWRITE DEFAULT-TIMES-1))
 (43 1 (:REWRITE |(integerp (- x))|))
 (41 41 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (40 8 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (40 8 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (40 1 (:REWRITE DEFAULT-MOD-RATIO))
 (40 1 (:REWRITE |(* (- x) y)|))
 (39 3 (:REWRITE |(* y x)|))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (34 7 (:REWRITE DEFAULT-TIMES-2))
 (32 1 (:REWRITE MOD-X-Y-=-X . 4))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (23 1 (:REWRITE MOD-ZERO . 4))
 (23 1 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (23 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (23 1 (:REWRITE MOD-X-Y-=-X . 2))
 (23 1 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (23 1 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (22 22 (:REWRITE |(< x (+ c/d y))|))
 (21 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 18 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (16 4 (:REWRITE RATIONALP-X))
 (14 14 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (14 14 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (14 14 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (14 14 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (14 1 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (14 1 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (14 1 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (14 1 (:REWRITE MOD-CANCEL-*-CONST))
 (14 1 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (14 1 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (12 12 (:REWRITE |(< y (+ (- c) x))|))
 (12 12 (:REWRITE |(< 0 (* x y))|))
 (11 11 (:REWRITE |(< (+ c/d x) y)|))
 (11 11 (:REWRITE |(< (+ (- c) x) y)|))
 (11 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 1 (:REWRITE DEFAULT-MOD-1))
 (10 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (9 9 (:REWRITE |(< (/ x) 0)|))
 (9 9 (:REWRITE |(< (* x y) 0)|))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (8 8 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (8 8 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (8 8 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (8 8 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (8 8 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:REWRITE DEFAULT-EXPT-1))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:REWRITE |(< 0 (/ x))|))
 (7 7 (:META META-INTEGERP-CORRECT))
 (7 7 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (7 7 (:LINEAR EXPT-LINEAR-UPPER-<))
 (7 7 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (7 7 (:LINEAR EXPT-LINEAR-LOWER-<))
 (7 7 (:LINEAR EXPT->-1-TWO))
 (7 7 (:LINEAR EXPT-<-1-ONE))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (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 REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE DEFAULT-DIVIDE))
 (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 ZP-OPEN))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (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 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1 1 (:REWRITE DM::FPFR-5))
 (1 1 (:REWRITE DM::FAST-MAX-FACT-REWRITE))
 (1 1 (:REWRITE DEFAULT-MOD-2))
 (1 1 (:REWRITE |(mod x (- y))| . 3))
 (1 1 (:REWRITE |(mod x (- y))| . 2))
 (1 1 (:REWRITE |(mod x (- y))| . 1))
 (1 1 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(mod (- x) y)| . 3))
 (1 1 (:REWRITE |(mod (- x) y)| . 2))
 (1 1 (:REWRITE |(mod (- x) y)| . 1))
 (1 1 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(DM::CERTIFICATE-25519)
(DM::CERTIFY-PRIMES
 (28044 6 (:DEFINITION MOD-EXPT))
 (25486 73 (:REWRITE RTL::MOD-DOES-NOTHING))
 (22530 847 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (21510 18 (:REWRITE |(equal (if a b c) x)|))
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 (11776 39 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11012 91 (:LINEAR EXPT-<=-1-TWO))
 (6226 91 (:LINEAR EXPT-X->=-X))
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 (4188 37 (:REWRITE MOD-X-Y-=-X-Y . 2))
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 (1478 250 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (1430 250 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1334 934 (:REWRITE DEFAULT-LESS-THAN-2))
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 (968 776 (:REWRITE REDUCE-INTEGERP-+))
 (942 36 (:REWRITE |(* (if a b c) x)|))
 (934 934 (:REWRITE THE-FLOOR-BELOW))
 (934 934 (:REWRITE THE-FLOOR-ABOVE))
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 (898 898 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (864 864 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (864 864 (:REWRITE INTEGERP-<-CONSTANT))
 (864 864 (:REWRITE CONSTANT-<-INTEGERP))
 (864 864 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (864 864 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (864 864 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (864 864 (:REWRITE |(< c (- x))|))
 (864 864 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (864 864 (:REWRITE |(< (/ x) (/ y))|))
 (864 864 (:REWRITE |(< (- x) c)|))
 (864 864 (:REWRITE |(< (- x) (- y))|))
 (864 96 (:REWRITE RATIONALP-/))
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 (851 37 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (851 37 (:REWRITE MOD-X-Y-=-X . 2))
 (851 37 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (851 37 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (776 776 (:REWRITE INTEGERP-MINUS-X))
 (776 776 (:META META-INTEGERP-CORRECT))
 (656 90 (:REWRITE DEFAULT-MINUS))
 (646 55 (:REWRITE DEFAULT-MOD-1))
 (626 68 (:REWRITE DEFAULT-EXPT-2))
 (595 17 (:REWRITE |(+ (if a b c) x)|))
 (527 17 (:REWRITE NUMERATOR-NEGATIVE))
 (518 37 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (518 37 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (518 37 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (518 37 (:REWRITE MOD-CANCEL-*-CONST))
 (518 37 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (518 37 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (509 509 (:REWRITE REDUCE-RATIONALP-+))
 (509 509 (:REWRITE REDUCE-RATIONALP-*))
 (509 509 (:REWRITE RATIONALP-MINUS-X))
 (509 509 (:META META-RATIONALP-CORRECT))
 (464 464 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (444 60 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (438 6 (:REWRITE |(expt x (if a b c))|))
 (432 48 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (432 48 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (432 48 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (432 48 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (414 6 (:LINEAR MOD-BOUNDS-3))
 (384 60 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (384 60 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (384 60 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (326 326 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (326 326 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (326 326 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (299 13 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (273 39 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (264 264 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (261 147 (:REWRITE DEFAULT-DIVIDE))
 (250 250 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (250 250 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (250 250 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (250 250 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (192 6 (:REWRITE |(* x (if a b c))|))
 (182 182 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (182 182 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (182 182 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (182 182 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (170 17 (:DEFINITION LENGTH))
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 (153 153 (:TYPE-PRESCRIPTION NUMERATOR-ZERO))
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 (153 153 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
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 (153 153 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (147 147 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
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 (130 13 (:REWRITE |(equal (mod (+ x y) z) x)|))
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 (107 107 (:REWRITE |(< (* x y) 0)|))
 (104 104 (:REWRITE |(< y (+ (- c) x))|))
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 (76 76 (:REWRITE |(< 0 (* x y))|))
 (72 3 (:REWRITE |(* x (+ y z))|))
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 (3 3 (:REWRITE |(* x (- y))|))
 )
(DM::CERTIFY-PRIME)
(DM::CERTIFY-25519)
(DM::CERTIFICATION-LEMMA
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 (33 33 (:REWRITE |(equal c (/ x))|))
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 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 )
(DM::CERTIFICATION-THEOREM)
(DM::PRIMEP-25519)
