(RTL::ASSOCIATE
 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (10 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (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 NOT-INTEGERP-4B))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (5 5 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (5 5 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5 5 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5 5 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (5 5 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (5 5 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (5 5 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (5 5 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (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 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (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))
 )
(RTL::ASSOCIATE-PROPERTY
 (28115 7 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (22056 22 (:LINEAR MOD-BOUNDS-1))
 (15103 44 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12448 12 (:LINEAR RTL::MOD-BND-1))
 (10964 7 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (8019 39 (:REWRITE CANCEL-MOD-+))
 (5512 39 (:REWRITE MOD-X-Y-=-X . 3))
 (5216 39 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4806 1 (:REWRITE RTL::MOD-DISTINCT))
 (4790 39 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4785 39 (:REWRITE MOD-ZERO . 3))
 (4727 2 (:REWRITE ZP-OPEN))
 (4699 39 (:REWRITE MOD-X-Y-=-X . 4))
 (4192 39 (:REWRITE MOD-ZERO . 4))
 (4025 593 (:REWRITE DEFAULT-TIMES-2))
 (4015 803 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (3929 3929 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3929 3929 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3929 3929 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3929 3929 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3929 3929 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3903 593 (:REWRITE DEFAULT-TIMES-1))
 (3902 336 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (3800 39 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3752 3752 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3752 3752 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3752 3752 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3743 803 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (3267 803 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3267 803 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2996 39 (:REWRITE DEFAULT-MOD-RATIO))
 (2996 39 (:REWRITE |(* (- x) y)|))
 (2664 39 (:REWRITE |(integerp (- x))|))
 (2258 506 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2229 256 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2173 12 (:LINEAR RTL::MOD-BND-2))
 (1927 272 (:REWRITE DEFAULT-LESS-THAN-1))
 (1800 256 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1483 803 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1270 256 (:REWRITE SIMPLIFY-SUMS-<))
 (1123 11 (:LINEAR MOD-BOUNDS-3))
 (1109 44 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1071 39 (:REWRITE MOD-X-Y-=-X . 2))
 (1071 39 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1071 39 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (971 119 (:META META-INTEGERP-CORRECT))
 (803 803 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (803 803 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (803 803 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (803 803 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (791 45 (:REWRITE DEFAULT-MINUS))
 (760 272 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (720 272 (:REWRITE DEFAULT-LESS-THAN-2))
 (704 22 (:LINEAR MOD-BOUNDS-2))
 (684 76 (:REWRITE DEFAULT-PLUS-2))
 (666 333 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (633 39 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (633 39 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (633 39 (:REWRITE MOD-CANCEL-*-CONST))
 (562 41 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (506 506 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (506 506 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (506 506 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (463 39 (:REWRITE DEFAULT-MOD-1))
 (416 39 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (416 39 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (416 39 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (369 76 (:REWRITE DEFAULT-PLUS-1))
 (352 16 (:REWRITE RATIONALP-X))
 (342 14 (:LINEAR EXPT-<=-1-TWO))
 (336 336 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (336 336 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (336 336 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (333 333 (:TYPE-PRESCRIPTION NATP))
 (333 333 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (333 333 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (333 333 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (326 14 (:LINEAR EXPT-X->=-X))
 (272 272 (:REWRITE THE-FLOOR-BELOW))
 (272 272 (:REWRITE THE-FLOOR-ABOVE))
 (272 272 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (272 272 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (256 256 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (256 256 (:REWRITE INTEGERP-<-CONSTANT))
 (256 256 (:REWRITE CONSTANT-<-INTEGERP))
 (256 256 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (256 256 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (256 256 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (256 256 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (256 256 (:REWRITE |(< c (- x))|))
 (256 256 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (256 256 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (256 256 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (256 256 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (256 256 (:REWRITE |(< (/ x) (/ y))|))
 (256 256 (:REWRITE |(< (- x) c)|))
 (256 256 (:REWRITE |(< (- x) (- y))|))
 (256 39 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (256 39 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (256 39 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (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))
 (196 14 (:LINEAR EXPT->=-1-ONE))
 (188 3 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (180 10 (:REWRITE |(* y (* x z))|))
 (153 119 (:REWRITE INTEGERP-MINUS-X))
 (145 145 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (143 143 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (143 143 (:REWRITE DEFAULT-DIVIDE))
 (133 7 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (123 123 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (119 119 (:REWRITE REDUCE-INTEGERP-+))
 (118 118 (:REWRITE |(* c (* d x))|))
 (112 16 (:META META-RATIONALP-CORRECT))
 (109 19 (:REWRITE |(+ 0 x)|))
 (83 2 (:REWRITE MOD-POSITIVE . 3))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (73 73 (:REWRITE |(< (/ x) 0)|))
 (73 73 (:REWRITE |(< (* x y) 0)|))
 (71 71 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (66 66 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (52 52 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (47 47 (:REWRITE |(< 0 (* x y))|))
 (44 44 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (44 44 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (44 44 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (44 44 (:REWRITE |(equal c (/ x))|))
 (44 44 (:REWRITE |(equal c (- x))|))
 (44 44 (:REWRITE |(equal (/ x) c)|))
 (44 44 (:REWRITE |(equal (/ x) (/ y))|))
 (44 44 (:REWRITE |(equal (- x) c)|))
 (44 44 (:REWRITE |(equal (- x) (- y))|))
 (42 42 (:REWRITE |(- (* c x))|))
 (39 39 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (39 39 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (39 39 (:REWRITE DEFAULT-MOD-2))
 (39 39 (:REWRITE |(mod x (- y))| . 3))
 (39 39 (:REWRITE |(mod x (- y))| . 2))
 (39 39 (:REWRITE |(mod x (- y))| . 1))
 (39 39 (:REWRITE |(mod (- x) y)| . 3))
 (39 39 (:REWRITE |(mod (- x) y)| . 2))
 (39 39 (:REWRITE |(mod (- x) y)| . 1))
 (39 39 (:REWRITE |(< 0 (/ x))|))
 (33 33 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (32 32 (:REWRITE |(equal (* x y) 0)|))
 (32 32 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (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))
 (23 23 (:REWRITE DEFAULT-EXPT-2))
 (23 23 (:REWRITE DEFAULT-EXPT-1))
 (23 23 (:REWRITE |(expt 1/c n)|))
 (23 23 (:REWRITE |(expt (- x) n)|))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (16 16 (:REWRITE REDUCE-RATIONALP-+))
 (16 16 (:REWRITE REDUCE-RATIONALP-*))
 (16 16 (:REWRITE RATIONALP-MINUS-X))
 (16 16 (:REWRITE |(< x (+ c/d y))|))
 (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))
 (14 1 (:REWRITE MOD-NONPOSITIVE))
 (12 12 (:LINEAR RTL::MOD-BND-3))
 (9 5 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 8 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE MOD-POSITIVE . 2))
 (2 2 (:REWRITE MOD-POSITIVE . 1))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(RTL::ASSOCIATE-BNDS
 (5667 731 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5539 26 (:REWRITE MOD-X-Y-=-X . 3))
 (5451 731 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5451 731 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (5085 26 (:REWRITE CANCEL-MOD-+))
 (5053 26 (:REWRITE MOD-X-Y-=-X . 4))
 (4950 27 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4438 27 (:REWRITE MOD-ZERO . 4))
 (3655 731 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (3537 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (3343 3343 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3343 3343 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3343 3343 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3067 438 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2958 2958 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2958 2958 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2958 2958 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2958 2958 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2958 2958 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2680 32 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2630 438 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (2630 438 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (2630 438 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (2403 126 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2120 27 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1995 226 (:REWRITE DEFAULT-TIMES-1))
 (1969 226 (:REWRITE DEFAULT-TIMES-2))
 (1770 126 (:REWRITE SIMPLIFY-SUMS-<))
 (1675 25 (:REWRITE |(integerp (- x))|))
 (1579 27 (:REWRITE DEFAULT-MOD-RATIO))
 (1523 26 (:REWRITE |(* (- x) y)|))
 (1371 126 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1216 26 (:REWRITE MOD-X-Y-=-X . 2))
 (1216 26 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1216 26 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1100 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (902 126 (:REWRITE DEFAULT-LESS-THAN-1))
 (889 32 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (883 126 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (731 731 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (731 731 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (731 731 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (731 731 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (731 731 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (687 27 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (687 27 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (673 26 (:REWRITE MOD-CANCEL-*-CONST))
 (633 26 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (633 26 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (633 26 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (584 5 (:LINEAR MOD-BOUNDS-3))
 (531 56 (:META META-INTEGERP-CORRECT))
 (438 438 (:TYPE-PRESCRIPTION NATP))
 (424 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (380 29 (:REWRITE DEFAULT-MINUS))
 (346 126 (:REWRITE DEFAULT-LESS-THAN-2))
 (278 10 (:LINEAR MOD-BOUNDS-2))
 (273 25 (:REWRITE DEFAULT-PLUS-2))
 (267 30 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (256 27 (:REWRITE DEFAULT-MOD-1))
 (144 25 (:REWRITE DEFAULT-PLUS-1))
 (141 14 (:REWRITE NORMALIZE-ADDENDS))
 (140 5 (:REWRITE |(+ y x)|))
 (127 127 (:REWRITE THE-FLOOR-BELOW))
 (127 127 (:REWRITE THE-FLOOR-ABOVE))
 (127 127 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (126 126 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (126 126 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (126 126 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (126 126 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (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 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))|))
 (91 91 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (91 91 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (91 91 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (85 85 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (85 85 (:REWRITE DEFAULT-DIVIDE))
 (82 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (78 78 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (71 71 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (66 26 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (66 26 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (66 26 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (60 56 (:REWRITE INTEGERP-MINUS-X))
 (56 56 (:REWRITE REDUCE-INTEGERP-+))
 (46 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (45 3 (:REWRITE |(+ 0 x)|))
 (42 42 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (42 42 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (42 42 (:REWRITE |(< (/ x) 0)|))
 (42 42 (:REWRITE |(< (* x y) 0)|))
 (35 35 (:REWRITE |(* c (* d x))|))
 (32 32 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (32 32 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (32 32 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (32 32 (:REWRITE |(equal c (/ x))|))
 (32 32 (:REWRITE |(equal c (- x))|))
 (32 32 (:REWRITE |(equal (/ x) c)|))
 (32 32 (:REWRITE |(equal (/ x) (/ y))|))
 (32 32 (:REWRITE |(equal (- x) c)|))
 (32 32 (:REWRITE |(equal (- x) (- y))|))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (27 27 (:REWRITE DEFAULT-MOD-2))
 (27 27 (:REWRITE |(< 0 (/ x))|))
 (27 27 (:REWRITE |(< 0 (* x y))|))
 (27 27 (:REWRITE |(- (* c x))|))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (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))
 (25 1 (:REWRITE MOD-ZERO . 1))
 (22 22 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (22 22 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (16 1 (:REWRITE |(+ y (+ x z))|))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 12 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (11 11 (:REWRITE |(equal (* x y) 0)|))
 (10 10 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (7 7 (:LINEAR RTL::MOD-BND-3))
 (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)|))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (5 1 (:REWRITE MOD-ZERO . 2))
 (4 4 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 1 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (1 1 (:REWRITE MOD-POSITIVE . 3))
 (1 1 (:REWRITE MOD-POSITIVE . 2))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(RTL::ASSOCIATE-IS-UNIQUE
 (1547 1547 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1547 1547 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1375 275 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1343 275 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1034 19 (:REWRITE CANCEL-MOD-+))
 (1031 275 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1026 274 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (658 19 (:REWRITE MOD-X-Y-=-X . 3))
 (596 19 (:REWRITE MOD-ZERO . 3))
 (592 19 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (580 19 (:REWRITE MOD-X-Y-=-X . 4))
 (564 19 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (425 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (400 19 (:REWRITE |(integerp (- x))|))
 (390 26 (:REWRITE |(* (* x y) z)|))
 (367 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (355 19 (:REWRITE DEFAULT-MOD-RATIO))
 (355 19 (:REWRITE |(* (- x) y)|))
 (308 19 (:REWRITE MOD-ZERO . 4))
 (301 197 (:REWRITE DEFAULT-TIMES-2))
 (300 150 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (275 275 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (275 275 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (274 274 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (274 274 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (212 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (197 197 (:REWRITE DEFAULT-TIMES-1))
 (156 156 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (156 156 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (156 156 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (156 156 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (154 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (150 150 (:TYPE-PRESCRIPTION NATP))
 (150 150 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (150 150 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (150 150 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (150 150 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (139 27 (:REWRITE DEFAULT-MINUS))
 (127 19 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (125 4 (:LINEAR RTL::MOD-BND-2))
 (112 4 (:LINEAR MOD-BOUNDS-3))
 (102 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (101 101 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (99 99 (:REWRITE THE-FLOOR-BELOW))
 (99 99 (:REWRITE THE-FLOOR-ABOVE))
 (99 99 (:REWRITE SIMPLIFY-SUMS-<))
 (99 99 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (99 99 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (99 99 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (99 99 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (99 99 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (99 99 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (99 99 (:REWRITE INTEGERP-<-CONSTANT))
 (99 99 (:REWRITE DEFAULT-LESS-THAN-2))
 (99 99 (:REWRITE DEFAULT-LESS-THAN-1))
 (99 99 (:REWRITE CONSTANT-<-INTEGERP))
 (99 99 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (99 99 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (99 99 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (99 99 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (99 99 (:REWRITE |(< c (- x))|))
 (99 99 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (99 99 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (99 99 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (99 99 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (99 99 (:REWRITE |(< (/ x) (/ y))|))
 (99 99 (:REWRITE |(< (- x) c)|))
 (99 99 (:REWRITE |(< (- x) (- y))|))
 (95 19 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (95 19 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (95 19 (:REWRITE MOD-X-Y-=-X . 2))
 (95 19 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (95 19 (:REWRITE MOD-CANCEL-*-CONST))
 (95 19 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (95 19 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (95 19 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (95 19 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (70 70 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (70 70 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (70 70 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (70 70 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (63 63 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (63 63 (:REWRITE DEFAULT-DIVIDE))
 (61 61 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (54 16 (:REWRITE DEFAULT-PLUS-2))
 (47 43 (:REWRITE INTEGERP-MINUS-X))
 (43 43 (:REWRITE REDUCE-INTEGERP-+))
 (43 43 (:META META-INTEGERP-CORRECT))
 (40 8 (:LINEAR MOD-BOUNDS-2))
 (36 36 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (36 36 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (36 36 (:REWRITE |(< (/ x) 0)|))
 (36 36 (:REWRITE |(< (* x y) 0)|))
 (29 16 (:REWRITE DEFAULT-PLUS-1))
 (27 3 (:REWRITE |(+ y x)|))
 (26 26 (:REWRITE |(* c (* d x))|))
 (22 22 (:REWRITE |(- (* c x))|))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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 11 (:REWRITE NORMALIZE-ADDENDS))
 (19 19 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (19 19 (:REWRITE DEFAULT-MOD-2))
 (19 19 (:REWRITE DEFAULT-MOD-1))
 (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|))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (18 18 (:REWRITE |(< 0 (/ x))|))
 (18 18 (:REWRITE |(< 0 (* x y))|))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (14 14 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (11 11 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE |(equal (* x y) 0)|))
 (5 5 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (5 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 (3 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:REWRITE |(+ 0 x)|))
 )
(RTL::ASSOCIATE-OF-ASSOCIATE
 (2611 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1451 14 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1052 5 (:LINEAR RTL::MOD-BND-1))
 (955 191 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (921 921 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (921 921 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (867 191 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (602 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (563 191 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (497 11 (:REWRITE CANCEL-MOD-+))
 (463 171 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (377 11 (:REWRITE MOD-X-Y-=-X . 3))
 (343 11 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (325 11 (:REWRITE MOD-X-Y-=-X . 4))
 (316 11 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (275 11 (:REWRITE MOD-ZERO . 3))
 (200 11 (:REWRITE |(integerp (- x))|))
 (196 98 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (191 191 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (191 191 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (172 11 (:REWRITE MOD-ZERO . 4))
 (171 171 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (171 171 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (148 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (146 11 (:REWRITE DEFAULT-MOD-RATIO))
 (146 11 (:REWRITE |(* (- x) y)|))
 (121 13 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (105 7 (:REWRITE |(* (* x y) z)|))
 (102 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (101 73 (:REWRITE DEFAULT-TIMES-2))
 (98 98 (:TYPE-PRESCRIPTION NATP))
 (98 98 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (98 98 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (98 98 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (98 98 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (97 5 (:LINEAR RTL::MOD-BND-2))
 (73 73 (:REWRITE DEFAULT-TIMES-1))
 (69 13 (:REWRITE DEFAULT-MINUS))
 (65 65 (:REWRITE THE-FLOOR-BELOW))
 (65 65 (:REWRITE THE-FLOOR-ABOVE))
 (65 65 (:REWRITE SIMPLIFY-SUMS-<))
 (65 65 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (65 65 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (65 65 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (65 65 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (65 65 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (65 65 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (65 65 (:REWRITE INTEGERP-<-CONSTANT))
 (65 65 (:REWRITE DEFAULT-LESS-THAN-2))
 (65 65 (:REWRITE DEFAULT-LESS-THAN-1))
 (65 65 (:REWRITE CONSTANT-<-INTEGERP))
 (65 65 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (65 65 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (65 65 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (65 65 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (65 65 (:REWRITE |(< c (- x))|))
 (65 65 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (65 65 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (65 65 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (65 65 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (65 65 (:REWRITE |(< (/ x) (/ y))|))
 (65 65 (:REWRITE |(< (- x) c)|))
 (65 65 (:REWRITE |(< (- x) (- y))|))
 (55 11 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (55 11 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (55 11 (:REWRITE MOD-X-Y-=-X . 2))
 (55 11 (:REWRITE MOD-CANCEL-*-CONST))
 (55 11 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (55 11 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (52 4 (:LINEAR MOD-BOUNDS-3))
 (48 10 (:REWRITE DEFAULT-PLUS-2))
 (46 46 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (43 43 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (41 41 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (40 8 (:LINEAR MOD-BOUNDS-2))
 (39 11 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (39 11 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (39 11 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (37 37 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (37 37 (:REWRITE DEFAULT-DIVIDE))
 (30 26 (:REWRITE INTEGERP-MINUS-X))
 (27 27 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (27 27 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (27 27 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (27 27 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (27 11 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (27 11 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (27 11 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (27 3 (:REWRITE |(+ y x)|))
 (26 26 (:REWRITE REDUCE-INTEGERP-+))
 (26 26 (:META META-INTEGERP-CORRECT))
 (23 10 (:REWRITE DEFAULT-PLUS-1))
 (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)|))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (14 14 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (14 14 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (14 14 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (14 14 (:REWRITE |(equal c (/ x))|))
 (14 14 (:REWRITE |(equal c (- x))|))
 (14 14 (:REWRITE |(equal (/ x) c)|))
 (14 14 (:REWRITE |(equal (/ x) (/ y))|))
 (14 14 (:REWRITE |(equal (- x) c)|))
 (14 14 (:REWRITE |(equal (- x) (- y))|))
 (14 5 (:REWRITE NORMALIZE-ADDENDS))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (13 13 (:REWRITE |(< 0 (/ x))|))
 (13 13 (:REWRITE |(< 0 (* x y))|))
 (12 12 (:REWRITE |(- (* c x))|))
 (11 11 (:REWRITE DEFAULT-MOD-2))
 (11 11 (:REWRITE DEFAULT-MOD-1))
 (11 11 (:REWRITE |(mod x (- y))| . 3))
 (11 11 (:REWRITE |(mod x (- y))| . 2))
 (11 11 (:REWRITE |(mod x (- y))| . 1))
 (11 11 (:REWRITE |(mod (- x) y)| . 3))
 (11 11 (:REWRITE |(mod (- x) y)| . 2))
 (11 11 (:REWRITE |(mod (- x) y)| . 1))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (7 7 (:REWRITE |(* c (* d x))|))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 (5 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:REWRITE |(+ 0 x)|))
 )
(RTL::ASSOCIATE-EQUAL
 (65 13 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (65 13 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (58 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (58 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (58 58 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (22 11 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (21 13 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (13 13 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (13 13 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (11 11 (:TYPE-PRESCRIPTION NATP))
 (11 11 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (11 11 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (11 11 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (11 11 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (11 11 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (11 11 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (11 11 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (5 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (5 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (5 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(equal c (/ x))|))
 (4 4 (:REWRITE |(equal c (- x))|))
 (4 4 (:REWRITE |(equal (/ x) c)|))
 (4 4 (:REWRITE |(equal (/ x) (/ y))|))
 (4 4 (:REWRITE |(equal (- x) c)|))
 (4 4 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(RTL::ASSOCIATE-SQUARE
 (30460 9 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (15757 50 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (13364 9 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (9387 91 (:REWRITE MOD-X-Y-=-X . 3))
 (8626 91 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (8613 91 (:REWRITE CANCEL-MOD-+))
 (4677 91 (:REWRITE MOD-ZERO . 3))
 (4666 481 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (3946 3946 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (3946 3946 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (3946 3946 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (3946 3946 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (3946 3946 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (3946 3946 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3854 3854 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3854 3854 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3087 220 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2926 91 (:REWRITE |(integerp (- x))|))
 (2777 91 (:REWRITE MOD-X-Y-=-X . 4))
 (2772 91 (:REWRITE DEFAULT-MOD-RATIO))
 (2772 91 (:REWRITE |(* (- x) y)|))
 (2727 697 (:REWRITE DEFAULT-TIMES-1))
 (2595 519 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2505 697 (:REWRITE DEFAULT-TIMES-2))
 (2355 519 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2327 91 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1944 702 (:REWRITE SIMPLIFY-SUMS-<))
 (1944 702 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1944 702 (:REWRITE DEFAULT-LESS-THAN-1))
 (1823 519 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1818 518 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1751 91 (:REWRITE MOD-ZERO . 4))
 (1514 110 (:LINEAR EXPT->=-1-TWO))
 (1514 110 (:LINEAR EXPT-<=-1-ONE))
 (1460 110 (:LINEAR EXPT-X->-X))
 (1460 110 (:LINEAR EXPT->-1-ONE))
 (1460 110 (:LINEAR EXPT-<-1-TWO))
 (1416 220 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1360 30 (:REWRITE |(* (* x y) z)|))
 (1283 91 (:REWRITE MOD-X-Y-=-X . 2))
 (1283 91 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1283 91 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1116 702 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1055 21 (:LINEAR MOD-BOUNDS-3))
 (972 97 (:REWRITE DEFAULT-MINUS))
 (869 91 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (869 91 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (869 91 (:REWRITE MOD-CANCEL-*-CONST))
 (795 220 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (780 26 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (702 702 (:REWRITE THE-FLOOR-BELOW))
 (702 702 (:REWRITE THE-FLOOR-ABOVE))
 (702 702 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (702 702 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (702 702 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (702 702 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (702 702 (:REWRITE INTEGERP-<-CONSTANT))
 (702 702 (:REWRITE DEFAULT-LESS-THAN-2))
 (702 702 (:REWRITE CONSTANT-<-INTEGERP))
 (702 702 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (702 702 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (702 702 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (702 702 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (702 702 (:REWRITE |(< c (- x))|))
 (702 702 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (702 702 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (702 702 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (702 702 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (702 702 (:REWRITE |(< (/ x) (/ y))|))
 (702 702 (:REWRITE |(< (- x) c)|))
 (702 702 (:REWRITE |(< (- x) (- y))|))
 (536 50 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (519 519 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (519 519 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (518 518 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (518 518 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (505 91 (:REWRITE DEFAULT-MOD-1))
 (495 91 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (495 91 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (495 91 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (481 481 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (481 481 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (481 481 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (465 91 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (465 91 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (465 91 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (440 440 (:REWRITE DEFAULT-EXPT-2))
 (440 440 (:REWRITE DEFAULT-EXPT-1))
 (440 440 (:REWRITE |(expt 1/c n)|))
 (440 440 (:REWRITE |(expt (- x) n)|))
 (433 47 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (390 42 (:LINEAR MOD-BOUNDS-2))
 (386 193 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (376 3 (:REWRITE |(equal (mod a n) (mod b n))|))
 (335 335 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (300 300 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (300 300 (:REWRITE DEFAULT-DIVIDE))
 (229 208 (:REWRITE INTEGERP-MINUS-X))
 (220 220 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (208 208 (:REWRITE REDUCE-INTEGERP-+))
 (208 208 (:META META-INTEGERP-CORRECT))
 (207 29 (:REWRITE DEFAULT-PLUS-2))
 (193 193 (:TYPE-PRESCRIPTION NATP))
 (193 193 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (193 193 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (193 193 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (193 193 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (110 110 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (110 110 (:LINEAR EXPT-LINEAR-UPPER-<))
 (110 110 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (110 110 (:LINEAR EXPT-LINEAR-LOWER-<))
 (110 110 (:LINEAR EXPT->-1-TWO))
 (110 110 (:LINEAR EXPT-<=-1-TWO))
 (110 110 (:LINEAR EXPT-<-1-ONE))
 (94 94 (:REWRITE |(- (* c x))|))
 (91 91 (:REWRITE DEFAULT-MOD-2))
 (91 91 (:REWRITE |(mod x (- y))| . 3))
 (91 91 (:REWRITE |(mod x (- y))| . 2))
 (91 91 (:REWRITE |(mod x (- y))| . 1))
 (91 91 (:REWRITE |(mod (- x) y)| . 3))
 (91 91 (:REWRITE |(mod (- x) y)| . 2))
 (91 91 (:REWRITE |(mod (- x) y)| . 1))
 (90 90 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (83 83 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (83 83 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (83 83 (:REWRITE |(< (/ x) 0)|))
 (83 83 (:REWRITE |(< (* x y) 0)|))
 (83 29 (:REWRITE DEFAULT-PLUS-1))
 (81 7 (:REWRITE |(+ y x)|))
 (66 15 (:REWRITE NORMALIZE-ADDENDS))
 (50 50 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (50 50 (:REWRITE |(equal c (/ x))|))
 (50 50 (:REWRITE |(equal c (- x))|))
 (50 50 (:REWRITE |(equal (/ x) c)|))
 (50 50 (:REWRITE |(equal (/ x) (/ y))|))
 (50 50 (:REWRITE |(equal (- x) c)|))
 (50 50 (:REWRITE |(equal (- x) (- y))|))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (38 38 (:REWRITE |(< 0 (/ x))|))
 (38 38 (:REWRITE |(< 0 (* x y))|))
 (36 36 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (36 9 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (35 35 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (30 30 (:REWRITE |(* c (* d x))|))
 (28 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (23 23 (:LINEAR RTL::MOD-BND-3))
 (16 1 (:REWRITE |(+ y (+ x z))|))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 3 (:REWRITE |(+ 0 x)|))
 (9 9 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (9 9 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 3 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (3 3 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 1 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 )
(RTL::FIND-ROOT
 (70 14 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (28 14 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (14 14 (:TYPE-PRESCRIPTION NATP))
 (14 14 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (14 14 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (14 14 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (14 14 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (14 14 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (14 14 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (14 14 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (14 14 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (14 14 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (14 14 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (14 14 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (14 14 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (7 7 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 )
(RTL::RESIDUE)
(RTL::NOT-RES-NO-ROOT-LEMMA
 (78612 57 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (42438 752 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (37763 277 (:REWRITE RTL::MOD-DOES-NOTHING))
 (37218 57 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (15035 165 (:REWRITE MOD-X-Y-=-X . 3))
 (10824 204 (:LINEAR MOD-BOUNDS-1))
 (9661 9661 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (9661 9661 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (9661 9661 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
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 (9132 204 (:LINEAR MOD-BOUNDS-2))
 (7313 7313 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (7313 7313 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (7313 7313 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (7313 7313 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (7313 7313 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (7313 7313 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6922 1898 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6922 1898 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (5553 1450 (:REWRITE DEFAULT-TIMES-2))
 (5420 178 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (5420 178 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (5420 178 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (5420 178 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (5096 1450 (:REWRITE DEFAULT-TIMES-1))
 (4460 235 (:LINEAR EXPT-<-1-TWO))
 (4448 165 (:REWRITE MOD-X-Y-=-X . 4))
 (4311 229 (:LINEAR EXPT->=-1-TWO))
 (4304 229 (:LINEAR EXPT-X->-X))
 (4304 229 (:LINEAR EXPT->-1-ONE))
 (4285 752 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4127 2408 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4127 2408 (:REWRITE DEFAULT-LESS-THAN-1))
 (4019 2408 (:REWRITE SIMPLIFY-SUMS-<))
 (3926 1898 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (3684 1898 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (3639 165 (:REWRITE MOD-X-Y-=-X . 2))
 (3639 165 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (3639 165 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (3612 102 (:LINEAR MOD-BOUNDS-3))
 (3534 309 (:REWRITE RATIONALP-X))
 (3444 733 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3416 2408 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2986 178 (:REWRITE MOD-ZERO . 4))
 (2486 165 (:REWRITE CANCEL-MOD-+))
 (2456 2456 (:REWRITE THE-FLOOR-BELOW))
 (2456 2456 (:REWRITE THE-FLOOR-ABOVE))
 (2408 2408 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2408 2408 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2408 2408 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2408 2408 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2408 2408 (:REWRITE INTEGERP-<-CONSTANT))
 (2408 2408 (:REWRITE CONSTANT-<-INTEGERP))
 (2408 2408 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2408 2408 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2408 2408 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2408 2408 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2408 2408 (:REWRITE |(< c (- x))|))
 (2408 2408 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2408 2408 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2408 2408 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2408 2408 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2408 2408 (:REWRITE |(< (/ x) (/ y))|))
 (2408 2408 (:REWRITE |(< (- x) c)|))
 (2408 2408 (:REWRITE |(< (- x) (- y))|))
 (1898 1898 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1898 1898 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1898 1898 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1898 1898 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (1863 1863 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1863 1863 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1786 1786 (:TYPE-PRESCRIPTION NATP))
 (1785 1785 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (1635 182 (:REWRITE DEFAULT-PLUS-2))
 (1632 24 (:REWRITE |(* x (if a b c))|))
 (1506 11 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1388 165 (:REWRITE MOD-CANCEL-*-CONST))
 (1111 207 (:REWRITE ACL2-NUMBERP-X))
 (1046 218 (:REWRITE DEFAULT-MOD-1))
 (1021 565 (:REWRITE DEFAULT-DIVIDE))
 (951 165 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (951 165 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (951 165 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (752 752 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (752 752 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (752 752 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (752 752 (:REWRITE |(equal c (/ x))|))
 (752 752 (:REWRITE |(equal c (- x))|))
 (752 752 (:REWRITE |(equal (/ x) c)|))
 (752 752 (:REWRITE |(equal (/ x) (/ y))|))
 (752 752 (:REWRITE |(equal (- x) c)|))
 (752 752 (:REWRITE |(equal (- x) (- y))|))
 (698 165 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (698 165 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (698 165 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (669 571 (:REWRITE INTEGERP-MINUS-X))
 (668 668 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (668 668 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (668 668 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (664 664 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (643 643 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (643 643 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (643 643 (:REWRITE |(< (/ x) 0)|))
 (643 643 (:REWRITE |(< (* x y) 0)|))
 (623 623 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (623 623 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (623 623 (:REWRITE |(< 0 (/ x))|))
 (623 623 (:REWRITE |(< 0 (* x y))|))
 (611 611 (:REWRITE DEFAULT-EXPT-2))
 (611 611 (:REWRITE DEFAULT-EXPT-1))
 (611 611 (:REWRITE |(expt 1/c n)|))
 (611 611 (:REWRITE |(expt (- x) n)|))
 (605 101 (:REWRITE NORMALIZE-ADDENDS))
 (571 571 (:REWRITE REDUCE-INTEGERP-+))
 (571 571 (:META META-INTEGERP-CORRECT))
 (544 182 (:REWRITE DEFAULT-PLUS-1))
 (541 541 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (527 527 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (498 37 (:REWRITE |(+ y x)|))
 (458 458 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (458 458 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (458 458 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (458 458 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (380 146 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (299 13 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (282 57 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (249 249 (:REWRITE RATIONALP-MINUS-X))
 (235 235 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (235 235 (:LINEAR EXPT-LINEAR-UPPER-<))
 (235 235 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (235 235 (:LINEAR EXPT-LINEAR-LOWER-<))
 (235 235 (:LINEAR EXPT-<=-1-TWO))
 (229 229 (:LINEAR EXPT->-1-TWO))
 (229 229 (:LINEAR EXPT-<-1-ONE))
 (223 223 (:REWRITE REDUCE-RATIONALP-+))
 (223 223 (:META META-RATIONALP-CORRECT))
 (165 165 (:REWRITE |(mod x (- y))| . 3))
 (165 165 (:REWRITE |(mod x (- y))| . 2))
 (165 165 (:REWRITE |(mod x (- y))| . 1))
 (165 165 (:REWRITE |(mod (- x) y)| . 3))
 (165 165 (:REWRITE |(mod (- x) y)| . 2))
 (165 165 (:REWRITE |(mod (- x) y)| . 1))
 (136 19 (:REWRITE |(+ 0 x)|))
 (128 30 (:REWRITE DEFAULT-MINUS))
 (108 108 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (108 108 (:LINEAR RTL::MOD-BND-3))
 (96 6 (:REWRITE |(+ y (+ x z))|))
 (82 82 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (60 60 (:REWRITE INTEGERP-/))
 (60 60 (:REWRITE |(* c (* d x))|))
 (57 57 (:REWRITE |(equal (+ (- c) x) y)|))
 (48 48 (:REWRITE |(* 0 x)|))
 (36 36 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (36 36 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (34 34 (:REWRITE |(not (equal x (/ y)))|))
 (34 34 (:REWRITE |(equal x (/ y))|))
 (26 26 (:REWRITE |(* (expt c m) (expt d n))|))
 (19 19 (:REWRITE |(+ x (- x))|))
 (13 13 (:REWRITE |(+ c (+ d x))|))
 (12 6 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (11 11 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (11 11 (:REWRITE |(- (* c x))|))
 (9 9 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (8 8 (:REWRITE |(< y (+ (- c) x))|))
 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 )
(RTL::NOT-RES-NO-ROOT
 (7910 274 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7299 258 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6044 28 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5843 17 (:REWRITE MOD-ZERO . 4))
 (5518 8 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (4541 17 (:REWRITE MOD-X-Y-=-X . 3))
 (4355 268 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (4322 32 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3652 17 (:REWRITE MOD-X-Y-=-X . 4))
 (3595 17 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3082 134 (:LINEAR EXPT-X->=-X))
 (2992 17 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2896 134 (:LINEAR EXPT-X->-X))
 (2896 134 (:LINEAR EXPT->-1-ONE))
 (2273 268 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (2083 2083 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (2083 2083 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2083 2083 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2083 2083 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2083 2083 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2083 2083 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1876 134 (:LINEAR EXPT->=-1-ONE))
 (1746 8 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1654 12 (:REWRITE |(< y (+ (- c) x))|))
 (1424 18 (:REWRITE |(equal (+ (- c) x) y)|))
 (1380 276 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1338 1338 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1338 1338 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1338 1338 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1275 235 (:REWRITE DEFAULT-PLUS-2))
 (1260 276 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (995 17 (:REWRITE MOD-ZERO . 3))
 (944 268 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (932 276 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (932 276 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (852 852 (:REWRITE DEFAULT-EXPT-2))
 (852 852 (:REWRITE DEFAULT-EXPT-1))
 (852 852 (:REWRITE |(expt 1/c n)|))
 (852 852 (:REWRITE |(expt (- x) n)|))
 (841 19 (:REWRITE |(< (+ (- c) x) y)|))
 (810 134 (:LINEAR EXPT->=-1-TWO))
 (810 134 (:LINEAR EXPT-<=-1-ONE))
 (784 240 (:REWRITE DEFAULT-TIMES-2))
 (784 134 (:LINEAR EXPT-<-1-TWO))
 (714 17 (:REWRITE DEFAULT-MOD-RATIO))
 (662 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (650 13 (:REWRITE |(* (* x y) z)|))
 (617 240 (:REWRITE DEFAULT-TIMES-1))
 (573 276 (:REWRITE DEFAULT-LESS-THAN-1))
 (555 235 (:REWRITE DEFAULT-PLUS-1))
 (519 258 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (504 12 (:REWRITE BUBBLE-DOWN-+-BUBBLE-DOWN))
 (476 276 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (456 28 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (429 15 (:REWRITE |(integerp (- x))|))
 (419 248 (:REWRITE SIMPLIFY-SUMS-<))
 (390 13 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (376 8 (:REWRITE |(* x (+ y z))|))
 (348 276 (:REWRITE DEFAULT-LESS-THAN-2))
 (326 276 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (310 22 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (276 276 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (276 276 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (276 276 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (276 276 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (276 276 (:REWRITE THE-FLOOR-BELOW))
 (276 276 (:REWRITE THE-FLOOR-ABOVE))
 (276 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (274 274 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (268 268 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (258 258 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (258 258 (:REWRITE INTEGERP-<-CONSTANT))
 (258 258 (:REWRITE CONSTANT-<-INTEGERP))
 (258 258 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (258 258 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (258 258 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (258 258 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (258 258 (:REWRITE |(< c (- x))|))
 (258 258 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (258 258 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (258 258 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (258 258 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (258 258 (:REWRITE |(< (/ x) (/ y))|))
 (258 258 (:REWRITE |(< (- x) c)|))
 (258 258 (:REWRITE |(< (- x) (- y))|))
 (224 112 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (175 17 (:REWRITE MOD-X-Y-=-X . 2))
 (175 17 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (175 17 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (162 31 (:REWRITE DEFAULT-MINUS))
 (134 134 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (134 134 (:LINEAR EXPT-LINEAR-UPPER-<))
 (134 134 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (134 134 (:LINEAR EXPT-LINEAR-LOWER-<))
 (134 134 (:LINEAR EXPT->-1-TWO))
 (134 134 (:LINEAR EXPT-<=-1-TWO))
 (134 134 (:LINEAR EXPT-<-1-ONE))
 (130 17 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (130 17 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (129 129 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (112 112 (:TYPE-PRESCRIPTION NATP))
 (112 112 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (112 112 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (112 112 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (112 112 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (109 2 (:LINEAR MOD-BOUNDS-3))
 (102 15 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (102 15 (:REWRITE MOD-CANCEL-*-CONST))
 (102 15 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (102 15 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (96 30 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (78 60 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (71 71 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (68 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (68 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (68 68 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (62 17 (:REWRITE DEFAULT-MOD-1))
 (61 61 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (61 61 (:REWRITE DEFAULT-DIVIDE))
 (54 6 (:REWRITE |(* y (* x z))|))
 (48 12 (:REWRITE |(+ (* c x) (* d x))|))
 (44 36 (:REWRITE INTEGERP-MINUS-X))
 (36 36 (:REWRITE REDUCE-INTEGERP-+))
 (36 36 (:META META-INTEGERP-CORRECT))
 (34 32 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (28 28 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (28 28 (:REWRITE |(equal c (/ x))|))
 (28 28 (:REWRITE |(equal c (- x))|))
 (28 28 (:REWRITE |(equal (/ x) c)|))
 (28 28 (:REWRITE |(equal (/ x) (/ y))|))
 (28 28 (:REWRITE |(equal (- x) c)|))
 (28 28 (:REWRITE |(equal (- x) (- y))|))
 (26 8 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (25 25 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (25 25 (:REWRITE |(< (+ c/d x) y)|))
 (23 23 (:REWRITE |(< (* x y) 0)|))
 (20 4 (:LINEAR MOD-BOUNDS-2))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (17 17 (:REWRITE DEFAULT-MOD-2))
 (17 17 (:REWRITE |(< (/ x) 0)|))
 (16 4 (:REWRITE |(+ x (* c x))|))
 (15 15 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (15 15 (:REWRITE |(mod x (- y))| . 3))
 (15 15 (:REWRITE |(mod x (- y))| . 2))
 (15 15 (:REWRITE |(mod x (- y))| . 1))
 (15 15 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (15 15 (:REWRITE |(mod (- x) y)| . 3))
 (15 15 (:REWRITE |(mod (- x) y)| . 2))
 (15 15 (:REWRITE |(mod (- x) y)| . 1))
 (15 15 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (14 14 (:REWRITE FOLD-CONSTS-IN-+))
 (14 14 (:REWRITE |(< x (+ c/d y))|))
 (14 14 (:REWRITE |(< 0 (* x y))|))
 (13 13 (:REWRITE |(* c (* d x))|))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (12 12 (:REWRITE |(< 0 (/ x))|))
 (12 12 (:REWRITE |(* 0 x)|))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (8 8 (:REWRITE |(* (/ c) (expt d n))|))
 (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))
 (4 4 (:TYPE-PRESCRIPTION ABS))
 (4 4 (:REWRITE |(* a (/ a))|))
 (4 4 (:REWRITE |(* 1 x)|))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (2 2 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (2 2 (:REWRITE |(* a (/ a) b)|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 )
(RTL::NOT-RES-NO-SELF-ASSOCIATE
 (10 2 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (10 2 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4 2 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (2 2 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (2 2 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2 2 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (2 2 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (2 2 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (2 2 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2 2 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (2 2 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (2 2 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (2 2 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 )
(RTL::ROOT1)
(RTL::RES-ROOT1-LEMMA
 (348154 234 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (186061 2652 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (171989 234 (:REWRITE MOD-X-Y-=-X+Y . 1))
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 (34860 1530 (:LINEAR EXPT->-1-ONE))
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 (29746 786 (:LINEAR MOD-BOUNDS-2))
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 (28559 28559 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (28559 28559 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (28559 28559 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (14991 3779 (:REWRITE DEFAULT-TIMES-2))
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 (12305 12305 (:REWRITE THE-FLOOR-BELOW))
 (12305 12305 (:REWRITE THE-FLOOR-ABOVE))
 (11985 11985 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (11985 11985 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (11985 11985 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (11980 11980 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (11980 11980 (:REWRITE INTEGERP-<-CONSTANT))
 (11980 11980 (:REWRITE CONSTANT-<-INTEGERP))
 (11980 11980 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (11980 11980 (:REWRITE |(< c (- x))|))
 (11980 11980 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (11980 11980 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (11980 11980 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (11980 11980 (:REWRITE |(< (/ x) (/ y))|))
 (11980 11980 (:REWRITE |(< (- x) c)|))
 (11980 11980 (:REWRITE |(< (- x) (- y))|))
 (11576 1422 (:REWRITE RATIONALP-X))
 (11162 529 (:REWRITE MOD-X-Y-=-X . 2))
 (11162 529 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (11162 529 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (10996 2470 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10816 4236 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (9504 4236 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (9504 4236 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (9504 4236 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (8635 1347 (:REWRITE DEFAULT-PLUS-2))
 (8373 4236 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (8364 529 (:REWRITE CANCEL-MOD-+))
 (8063 529 (:REWRITE MOD-ZERO . 4))
 (6260 1088 (:REWRITE ACL2-NUMBERP-X))
 (6069 597 (:REWRITE NORMALIZE-ADDENDS))
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 (4236 4236 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (4236 4236 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (4236 4236 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
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 (4219 4219 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (4194 4194 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (4137 4137 (:TYPE-PRESCRIPTION NATP))
 (3731 529 (:REWRITE MOD-CANCEL-*-CONST))
 (3414 3414 (:REWRITE DEFAULT-EXPT-2))
 (3414 3414 (:REWRITE DEFAULT-EXPT-1))
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 (3060 3060 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (3060 3060 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (2923 1347 (:REWRITE DEFAULT-PLUS-1))
 (2796 296 (:REWRITE |(+ y x)|))
 (2772 2658 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2686 2686 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (2680 2654 (:REWRITE |(equal (- x) c)|))
 (2658 2658 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2654 2654 (:REWRITE |(equal c (/ x))|))
 (2654 2654 (:REWRITE |(equal c (- x))|))
 (2654 2654 (:REWRITE |(equal (/ x) c)|))
 (2654 2654 (:REWRITE |(equal (/ x) (/ y))|))
 (2654 2654 (:REWRITE |(equal (- x) (- y))|))
 (2652 2652 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2503 2321 (:REWRITE INTEGERP-MINUS-X))
 (2321 2321 (:REWRITE REDUCE-INTEGERP-+))
 (2321 2321 (:META META-INTEGERP-CORRECT))
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 (2246 2246 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2246 2246 (:REWRITE |(< 0 (/ x))|))
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 (2185 529 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (2163 2163 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2163 2163 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2163 2163 (:REWRITE |(< (/ x) 0)|))
 (2163 2163 (:REWRITE |(< (* x y) 0)|))
 (2130 234 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2089 529 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2075 529 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
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 (1971 529 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1851 1851 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
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 (1530 1530 (:LINEAR EXPT-<-1-ONE))
 (1300 50 (:REWRITE |(mod (+ 1 x) y)|))
 (1210 1210 (:REWRITE RATIONALP-MINUS-X))
 (1164 426 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1128 1128 (:REWRITE REDUCE-RATIONALP-+))
 (1128 1128 (:META META-RATIONALP-CORRECT))
 (612 18 (:REWRITE MOD-ZERO . 2))
 (608 40 (:REWRITE |(+ y (+ x z))|))
 (529 529 (:REWRITE |(mod x (- y))| . 3))
 (529 529 (:REWRITE |(mod x (- y))| . 2))
 (529 529 (:REWRITE |(mod x (- y))| . 1))
 (529 529 (:REWRITE |(mod (- x) y)| . 3))
 (529 529 (:REWRITE |(mod (- x) y)| . 2))
 (529 529 (:REWRITE |(mod (- x) y)| . 1))
 (502 502 (:REWRITE |(equal (+ (- c) x) y)|))
 (415 415 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (411 411 (:LINEAR RTL::MOD-BND-3))
 (338 156 (:REWRITE DEFAULT-MINUS))
 (282 282 (:REWRITE INTEGERP-/))
 (182 182 (:REWRITE |(+ x (- x))|))
 (176 22 (:REWRITE |(integerp (- x))|))
 (162 150 (:REWRITE |(+ c (+ d x))|))
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 (118 118 (:REWRITE |(not (equal x (/ y)))|))
 (118 118 (:REWRITE |(equal x (/ y))|))
 (82 82 (:REWRITE |(* (expt c m) (expt d n))|))
 (72 36 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (52 2 (:REWRITE NOT-INTEGERP-/-2))
 (52 2 (:REWRITE NOT-INTEGERP-/-1))
 (38 38 (:REWRITE |(- (* c x))|))
 (24 24 (:REWRITE |(* c (* d x))|))
 (20 20 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (20 20 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (20 20 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (18 18 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 16 (:REWRITE |(< y (+ (- c) x))|))
 (16 16 (:REWRITE |(< x (+ c/d y))|))
 (8 8 (:REWRITE |(< (+ c/d x) y)|))
 (8 8 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (5 5 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (5 5 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (3 3 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (2 2 (:REWRITE |(- (- x))|))
 )
(RTL::RES-ROOT1
 (63458 965 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (58397 829 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (47380 68 (:REWRITE MOD-ZERO . 4))
 (42406 134 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (36425 20 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (35501 164 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (33819 2028 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (32253 68 (:REWRITE MOD-X-Y-=-X . 3))
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 (22794 1014 (:LINEAR EXPT->-1-ONE))
 (19618 1014 (:LINEAR EXPT-X->=-X))
 (19611 68 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (19090 1014 (:LINEAR EXPT-X->-X))
 (14590 14590 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (14590 14590 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (14590 14590 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (14590 14590 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (14590 14590 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (14196 1014 (:LINEAR EXPT->=-1-ONE))
 (13629 20 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (13444 75 (:REWRITE |(< y (+ (- c) x))|))
 (13136 20 (:LINEAR MOD-BOUNDS-1))
 (11685 86 (:REWRITE |(equal (+ (- c) x) y)|))
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 (6828 136 (:REWRITE |(< (+ (- c) x) y)|))
 (6165 6165 (:REWRITE DEFAULT-EXPT-2))
 (6165 6165 (:REWRITE DEFAULT-EXPT-1))
 (6165 6165 (:REWRITE |(expt 1/c n)|))
 (6165 6165 (:REWRITE |(expt (- x) n)|))
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 (3942 2028 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (3780 90 (:REWRITE BUBBLE-DOWN-+-BUBBLE-DOWN))
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 (2928 1014 (:LINEAR EXPT->=-1-TWO))
 (2928 1014 (:LINEAR EXPT-<=-1-ONE))
 (2908 829 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2820 60 (:REWRITE |(* x (+ y z))|))
 (2730 1014 (:LINEAR EXPT-<-1-TWO))
 (2522 2522 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2522 2522 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2522 2522 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2365 250 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
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 (2028 2028 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1526 986 (:REWRITE DEFAULT-LESS-THAN-2))
 (1435 287 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
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 (1096 68 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1096 68 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1014 1014 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1014 1014 (:LINEAR EXPT-LINEAR-UPPER-<))
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 (1014 1014 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1014 1014 (:LINEAR EXPT->-1-TWO))
 (1014 1014 (:LINEAR EXPT-<=-1-TWO))
 (1014 1014 (:LINEAR EXPT-<-1-ONE))
 (986 986 (:REWRITE THE-FLOOR-BELOW))
 (986 986 (:REWRITE THE-FLOOR-ABOVE))
 (965 965 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (953 134 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (829 829 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (829 829 (:REWRITE INTEGERP-<-CONSTANT))
 (829 829 (:REWRITE CONSTANT-<-INTEGERP))
 (829 829 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (829 829 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (829 829 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (829 829 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (829 829 (:REWRITE |(< c (- x))|))
 (829 829 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (829 829 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (829 829 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (829 829 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (829 829 (:REWRITE |(< (/ x) (/ y))|))
 (829 829 (:REWRITE |(< (- x) c)|))
 (829 829 (:REWRITE |(< (- x) (- y))|))
 (718 68 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (718 68 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (712 221 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (615 287 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (611 143 (:REWRITE DEFAULT-MINUS))
 (575 104 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (508 53 (:REWRITE MOD-CANCEL-*-CONST))
 (498 10 (:LINEAR MOD-BOUNDS-3))
 (453 318 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (449 449 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (421 53 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (421 53 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (421 53 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (419 419 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (407 205 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (360 90 (:REWRITE |(+ (* c x) (* d x))|))
 (360 54 (:REWRITE RATIONALP-X))
 (287 287 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (287 287 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (287 287 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (284 284 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (259 259 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (259 259 (:REWRITE DEFAULT-DIVIDE))
 (250 250 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (250 250 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (250 250 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (208 20 (:LINEAR MOD-BOUNDS-2))
 (205 205 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (202 202 (:TYPE-PRESCRIPTION NATP))
 (202 202 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (202 202 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (196 183 (:REWRITE INTEGERP-MINUS-X))
 (183 183 (:REWRITE REDUCE-INTEGERP-+))
 (183 183 (:META META-INTEGERP-CORRECT))
 (181 181 (:REWRITE |(< (+ c/d x) y)|))
 (179 164 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (140 53 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (140 53 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (140 53 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (136 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (134 134 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (134 134 (:REWRITE |(equal c (/ x))|))
 (134 134 (:REWRITE |(equal c (- x))|))
 (134 134 (:REWRITE |(equal (/ x) c)|))
 (134 134 (:REWRITE |(equal (/ x) (/ y))|))
 (134 134 (:REWRITE |(equal (- x) c)|))
 (134 134 (:REWRITE |(equal (- x) (- y))|))
 (120 30 (:REWRITE |(+ x (* c x))|))
 (106 106 (:REWRITE |(< x (+ c/d y))|))
 (105 105 (:REWRITE FOLD-CONSTS-IN-+))
 (103 103 (:REWRITE |(< (* x y) 0)|))
 (96 96 (:REWRITE |(expt x 0)|))
 (91 1 (:REWRITE MOD-ZERO . 1))
 (90 90 (:REWRITE |(* 0 x)|))
 (89 23 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (86 86 (:REWRITE DEFAULT-MOD-2))
 (65 20 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (60 60 (:REWRITE |(* (/ c) (expt d n))|))
 (58 58 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (58 58 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (58 58 (:REWRITE |(< (/ x) 0)|))
 (56 56 (:REWRITE |(< 0 (* x y))|))
 (54 54 (:REWRITE RATIONALP-MINUS-X))
 (53 53 (:REWRITE |(mod x (- y))| . 3))
 (53 53 (:REWRITE |(mod x (- y))| . 2))
 (53 53 (:REWRITE |(mod x (- y))| . 1))
 (53 53 (:REWRITE |(mod (- x) y)| . 3))
 (53 53 (:REWRITE |(mod (- x) y)| . 2))
 (53 53 (:REWRITE |(mod (- x) y)| . 1))
 (42 42 (:REWRITE REDUCE-RATIONALP-+))
 (42 42 (:META META-RATIONALP-CORRECT))
 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (41 41 (:REWRITE |(< 0 (/ x))|))
 (39 39 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (30 30 (:TYPE-PRESCRIPTION ABS))
 (26 26 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (23 1 (:REWRITE MOD-ZERO . 2))
 (15 15 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (15 15 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (15 15 (:REWRITE |(* a (/ a) b)|))
 (12 12 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (12 12 (:LINEAR RTL::MOD-BND-3))
 )
(RTL::ROOT2)
(RTL::RES-ROOT2
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 (21772 49 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (19820 58 (:REWRITE RTL::MOD-DOES-NOTHING))
 (13565 10 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (13136 20 (:LINEAR MOD-BOUNDS-1))
 (10968 12 (:LINEAR RTL::MOD-BND-2))
 (8843 55 (:REWRITE MOD-X-Y-=-X . 3))
 (7894 55 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (7865 484 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
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 (6357 55 (:REWRITE MOD-ZERO . 4))
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 (5286 5286 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (5286 5286 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (5286 5286 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (5286 5286 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (5286 5286 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (4007 942 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3947 55 (:REWRITE MOD-ZERO . 3))
 (3388 242 (:LINEAR EXPT->=-1-ONE))
 (3370 484 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (3128 242 (:LINEAR EXPT->=-1-TWO))
 (3128 242 (:LINEAR EXPT-<=-1-ONE))
 (3098 571 (:REWRITE DEFAULT-PLUS-2))
 (2894 242 (:LINEAR EXPT-X->-X))
 (2894 242 (:LINEAR EXPT->-1-ONE))
 (2894 242 (:LINEAR EXPT-<-1-TWO))
 (2837 798 (:REWRITE DEFAULT-TIMES-2))
 (2644 955 (:REWRITE DEFAULT-LESS-THAN-1))
 (2443 798 (:REWRITE DEFAULT-TIMES-1))
 (2148 2148 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2148 2148 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2148 2148 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1833 571 (:REWRITE DEFAULT-PLUS-1))
 (1810 484 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1325 265 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1171 955 (:REWRITE DEFAULT-LESS-THAN-2))
 (1113 265 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1113 265 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1089 53 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1049 55 (:REWRITE MOD-X-Y-=-X . 2))
 (1049 55 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1049 55 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1017 1017 (:REWRITE DEFAULT-EXPT-2))
 (1017 1017 (:REWRITE DEFAULT-EXPT-1))
 (1015 1015 (:REWRITE |(expt 1/c n)|))
 (955 955 (:REWRITE THE-FLOOR-BELOW))
 (955 955 (:REWRITE THE-FLOOR-ABOVE))
 (954 954 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (954 954 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (954 954 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (942 942 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (942 942 (:REWRITE INTEGERP-<-CONSTANT))
 (942 942 (:REWRITE CONSTANT-<-INTEGERP))
 (942 942 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (942 942 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (942 942 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (942 942 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (942 942 (:REWRITE |(< c (- x))|))
 (942 942 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (942 942 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (942 942 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (942 942 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (942 942 (:REWRITE |(< (/ x) (/ y))|))
 (942 942 (:REWRITE |(< (- x) c)|))
 (942 942 (:REWRITE |(< (- x) (- y))|))
 (662 55 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (662 55 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (617 265 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (614 82 (:REWRITE DEFAULT-MINUS))
 (498 10 (:LINEAR MOD-BOUNDS-3))
 (488 47 (:REWRITE MOD-CANCEL-*-CONST))
 (484 484 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (457 457 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (444 36 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (415 47 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (415 47 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (415 47 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (379 379 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (379 379 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (379 379 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (346 175 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (265 265 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (265 265 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (265 265 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (261 261 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (243 131 (:META META-INTEGERP-CORRECT))
 (242 242 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (242 242 (:LINEAR EXPT-LINEAR-UPPER-<))
 (242 242 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (242 242 (:LINEAR EXPT-LINEAR-LOWER-<))
 (242 242 (:LINEAR EXPT->-1-TWO))
 (242 242 (:LINEAR EXPT-<=-1-TWO))
 (242 242 (:LINEAR EXPT-<-1-ONE))
 (208 20 (:LINEAR MOD-BOUNDS-2))
 (190 190 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (190 190 (:REWRITE DEFAULT-DIVIDE))
 (175 175 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (171 171 (:TYPE-PRESCRIPTION NATP))
 (171 171 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (171 171 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (148 112 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (146 47 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (146 47 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (146 47 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (144 131 (:REWRITE INTEGERP-MINUS-X))
 (136 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (131 131 (:REWRITE REDUCE-INTEGERP-+))
 (105 105 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (91 1 (:REWRITE MOD-ZERO . 1))
 (60 9 (:REWRITE RATIONALP-X))
 (58 58 (:REWRITE DEFAULT-MOD-2))
 (55 10 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (54 54 (:REWRITE |(< (/ x) 0)|))
 (54 54 (:REWRITE |(< (* x y) 0)|))
 (53 53 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (53 53 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (53 53 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (53 53 (:REWRITE |(equal c (/ x))|))
 (53 53 (:REWRITE |(equal c (- x))|))
 (53 53 (:REWRITE |(equal (/ x) c)|))
 (53 53 (:REWRITE |(equal (/ x) (/ y))|))
 (53 53 (:REWRITE |(equal (- x) c)|))
 (53 53 (:REWRITE |(equal (- x) (- y))|))
 (50 50 (:REWRITE |(< (+ c/d x) y)|))
 (50 50 (:REWRITE |(< (+ (- c) x) y)|))
 (47 47 (:REWRITE |(mod x (- y))| . 3))
 (47 47 (:REWRITE |(mod x (- y))| . 2))
 (47 47 (:REWRITE |(mod x (- y))| . 1))
 (47 47 (:REWRITE |(mod (- x) y)| . 3))
 (47 47 (:REWRITE |(mod (- x) y)| . 2))
 (47 47 (:REWRITE |(mod (- x) y)| . 1))
 (41 41 (:REWRITE |(< 0 (* x y))|))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (32 32 (:REWRITE |(< y (+ (- c) x))|))
 (32 32 (:REWRITE |(< x (+ c/d y))|))
 (32 32 (:REWRITE |(* (/ c) (expt d n))|))
 (29 29 (:REWRITE |(< 0 (/ x))|))
 (28 4 (:REWRITE ACL2-NUMBERP-X))
 (26 26 (:REWRITE |(+ c (+ d x))|))
 (23 23 (:REWRITE |(equal (+ (- c) x) y)|))
 (23 1 (:REWRITE MOD-ZERO . 2))
 (19 19 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (19 19 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (19 19 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (16 16 (:REWRITE FOLD-CONSTS-IN-+))
 (12 12 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (12 12 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (12 12 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (12 12 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (12 12 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (12 12 (:LINEAR RTL::MOD-BND-3))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:META META-RATIONALP-CORRECT))
 (6 6 (:REWRITE |(* c (* d x))|))
 (2 2 (:REWRITE |(expt (- c) n)|))
 )
(RTL::ROOT1-ROOT2
 (7490 43 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (6742 407 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5362 33 (:REWRITE MOD-X-Y-=-X . 3))
 (5162 5 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (4485 276 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (4116 43 (:REWRITE MOD-ZERO . 4))
 (4088 43 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3174 138 (:LINEAR EXPT-X->=-X))
 (2615 2615 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (2615 2615 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2615 2615 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2615 2615 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2615 2615 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2615 2615 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2256 418 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2142 33 (:REWRITE MOD-X-Y-=-X . 4))
 (1947 563 (:REWRITE DEFAULT-TIMES-1))
 (1932 138 (:LINEAR EXPT->=-1-ONE))
 (1906 1906 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1906 1906 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1906 1906 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1855 563 (:REWRITE DEFAULT-TIMES-2))
 (1816 8 (:LINEAR MOD-BOUNDS-1))
 (1771 367 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1429 43 (:REWRITE DEFAULT-MOD-RATIO))
 (1358 5 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1300 276 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1183 251 (:REWRITE DEFAULT-PLUS-2))
 (1167 367 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1162 138 (:LINEAR EXPT->=-1-TWO))
 (1162 138 (:LINEAR EXPT-<=-1-ONE))
 (1153 251 (:REWRITE DEFAULT-PLUS-1))
 (1074 138 (:LINEAR EXPT-X->-X))
 (1074 138 (:LINEAR EXPT->-1-ONE))
 (1074 138 (:LINEAR EXPT-<-1-TWO))
 (1062 5 (:LINEAR RTL::MOD-BND-1))
 (938 439 (:REWRITE DEFAULT-LESS-THAN-1))
 (818 386 (:REWRITE SIMPLIFY-SUMS-<))
 (744 276 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (710 425 (:REWRITE |(< (- x) c)|))
 (675 136 (:REWRITE DEFAULT-MINUS))
 (664 439 (:REWRITE DEFAULT-LESS-THAN-2))
 (659 49 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (655 367 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (590 428 (:REWRITE |(< (- x) (- y))|))
 (580 580 (:REWRITE DEFAULT-EXPT-2))
 (580 580 (:REWRITE DEFAULT-EXPT-1))
 (580 580 (:REWRITE |(expt 1/c n)|))
 (580 580 (:REWRITE |(expt (- x) n)|))
 (548 428 (:REWRITE |(< c (- x))|))
 (492 8 (:LINEAR MOD-BOUNDS-2))
 (459 33 (:REWRITE MOD-X-Y-=-X . 2))
 (459 33 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (459 33 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (439 439 (:REWRITE THE-FLOOR-BELOW))
 (439 439 (:REWRITE THE-FLOOR-ABOVE))
 (439 439 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (439 439 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (439 439 (:REWRITE REDUCE-ADDITIVE-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))|))
 (418 418 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (418 418 (:REWRITE INTEGERP-<-CONSTANT))
 (418 418 (:REWRITE CONSTANT-<-INTEGERP))
 (411 43 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (411 43 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (367 367 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (367 367 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (363 363 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (358 358 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (354 180 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (316 28 (:REWRITE RATIONALP-X))
 (303 69 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (300 20 (:REWRITE ACL2-NUMBERP-X))
 (276 276 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (261 34 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (259 43 (:REWRITE DEFAULT-MOD-1))
 (236 30 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (232 4 (:LINEAR MOD-BOUNDS-3))
 (226 226 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (226 226 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (225 30 (:REWRITE MOD-CANCEL-*-CONST))
 (210 210 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (185 5 (:LINEAR RTL::MOD-BND-2))
 (180 180 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (175 175 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (175 175 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (174 174 (:TYPE-PRESCRIPTION NATP))
 (154 53 (:REWRITE |(equal (- x) c)|))
 (153 27 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (142 142 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (142 142 (:REWRITE DEFAULT-DIVIDE))
 (138 138 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (138 138 (:LINEAR EXPT-LINEAR-UPPER-<))
 (138 138 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (138 138 (:LINEAR EXPT-LINEAR-LOWER-<))
 (138 138 (:LINEAR EXPT->-1-TWO))
 (138 138 (:LINEAR EXPT-<=-1-TWO))
 (138 138 (:LINEAR EXPT-<-1-ONE))
 (138 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (132 20 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (132 20 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (113 83 (:REWRITE INTEGERP-MINUS-X))
 (98 98 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (98 53 (:REWRITE |(equal (- x) (- y))|))
 (96 16 (:REWRITE |(* (/ x) (expt x n))|))
 (83 83 (:REWRITE REDUCE-INTEGERP-+))
 (83 83 (:META META-INTEGERP-CORRECT))
 (61 61 (:REWRITE |(- (* c x))|))
 (58 30 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (53 53 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (53 53 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (53 53 (:REWRITE |(equal c (/ x))|))
 (53 53 (:REWRITE |(equal c (- x))|))
 (53 53 (:REWRITE |(equal (/ x) c)|))
 (53 53 (:REWRITE |(equal (/ x) (/ y))|))
 (49 49 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (49 49 (:REWRITE |(< (/ x) 0)|))
 (49 49 (:REWRITE |(< (* x y) 0)|))
 (48 20 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (48 20 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (45 45 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (43 43 (:REWRITE DEFAULT-MOD-2))
 (38 38 (:REWRITE |(< 0 (* x y))|))
 (34 34 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (34 34 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (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))
 (28 28 (:REWRITE REDUCE-RATIONALP-+))
 (28 28 (:REWRITE REDUCE-RATIONALP-*))
 (28 28 (:REWRITE RATIONALP-MINUS-X))
 (28 28 (:META META-RATIONALP-CORRECT))
 (27 27 (:REWRITE |(< 0 (/ x))|))
 (27 27 (:REWRITE |(+ c (+ d x))|))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (18 18 (:REWRITE |(< (+ c/d x) y)|))
 (18 18 (:REWRITE |(< (+ (- c) x) y)|))
 (16 16 (:REWRITE |(expt x 1)|))
 (16 16 (:REWRITE |(* a (/ a))|))
 (16 16 (:REWRITE |(* 1 x)|))
 (16 16 (:REWRITE |(* (/ c) (expt d n))|))
 (14 14 (:REWRITE |(equal (+ (- c) x) y)|))
 (14 5 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (13 13 (:REWRITE |(< y (+ (- c) x))|))
 (13 13 (:REWRITE |(< x (+ c/d y))|))
 (11 11 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (11 11 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (11 11 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (11 11 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (10 10 (:REWRITE |(* c (* d x))|))
 (8 2 (:REWRITE |(+ x x)|))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 (3 3 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 )
(RTL::ASSOCIATE-ROOTS
 (20 4 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (20 4 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (8 8 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (8 4 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (4 4 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (4 4 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (4 4 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (4 4 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (4 4 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (4 4 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4 4 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (4 4 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (4 4 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 )
(RTL::ONLY-2-ROOTS-LEMMA-1
 (103329 20 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (77506 20 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (31408 354 (:REWRITE RTL::MOD-DOES-NOTHING))
 (18468 455 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (18172 350 (:REWRITE MOD-X-Y-=-X . 3))
 (18168 350 (:REWRITE MOD-X-Y-=-X . 4))
 (17438 354 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (16278 354 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (14024 14024 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (14024 14024 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (14024 14024 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (13742 350 (:REWRITE CANCEL-MOD-+))
 (12970 354 (:REWRITE MOD-ZERO . 4))
 (10980 2196 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (9616 2196 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (8984 2196 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (8984 2196 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (8230 104 (:LINEAR RTL::MOD-BND-2))
 (5785 705 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5498 2778 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5359 354 (:REWRITE DEFAULT-MOD-RATIO))
 (5224 2840 (:REWRITE DEFAULT-TIMES-1))
 (5053 401 (:REWRITE DEFAULT-PLUS-2))
 (4990 2790 (:REWRITE DEFAULT-LESS-THAN-1))
 (4978 2778 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4880 2840 (:REWRITE DEFAULT-TIMES-2))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (4851 4851 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3818 2778 (:REWRITE SIMPLIFY-SUMS-<))
 (3310 2790 (:REWRITE DEFAULT-LESS-THAN-2))
 (3030 2786 (:REWRITE |(< (- x) c)|))
 (2980 776 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2914 2790 (:REWRITE |(< c (- x))|))
 (2896 401 (:REWRITE DEFAULT-PLUS-1))
 (2790 2790 (:REWRITE THE-FLOOR-BELOW))
 (2790 2790 (:REWRITE THE-FLOOR-ABOVE))
 (2790 2790 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2790 2790 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2790 2790 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (2790 2790 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2790 2790 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2790 2790 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2790 2790 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2790 2790 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2790 2790 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2790 2790 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2790 2790 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2790 2790 (:REWRITE |(< (/ x) (/ y))|))
 (2790 2790 (:REWRITE |(< (- x) (- y))|))
 (2790 350 (:REWRITE MOD-X-Y-=-X . 2))
 (2790 350 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (2790 350 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (2778 2778 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2778 2778 (:REWRITE INTEGERP-<-CONSTANT))
 (2778 2778 (:REWRITE CONSTANT-<-INTEGERP))
 (2752 776 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2668 388 (:LINEAR EXPT-<=-1-ONE))
 (2645 489 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2592 388 (:LINEAR EXPT->=-1-TWO))
 (2592 388 (:LINEAR EXPT->-1-TWO))
 (2592 388 (:LINEAR EXPT-<-1-ONE))
 (2364 388 (:LINEAR EXPT-X->=-X))
 (2364 388 (:LINEAR EXPT->=-1-ONE))
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 (2290 354 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2288 388 (:LINEAR EXPT-X->-X))
 (2288 388 (:LINEAR EXPT->-1-ONE))
 (2288 388 (:LINEAR EXPT-<-1-TWO))
 (2262 350 (:REWRITE MOD-CANCEL-*-CONST))
 (2230 104 (:LINEAR MOD-BOUNDS-3))
 (2196 2196 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (2196 2196 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (2196 2196 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (2196 2196 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1934 350 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1930 346 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1930 346 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1538 1538 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1508 426 (:REWRITE DEFAULT-MINUS))
 (1404 52 (:REWRITE |(equal (expt x n) 0)|))
 (1280 208 (:LINEAR MOD-BOUNDS-2))
 (1186 593 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
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 (1174 1174 (:REWRITE DEFAULT-DIVIDE))
 (920 20 (:REWRITE |(* (* x y) z)|))
 (888 888 (:REWRITE |(< (/ x) 0)|))
 (888 888 (:REWRITE |(< (* x y) 0)|))
 (880 880 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (880 880 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (874 354 (:REWRITE DEFAULT-MOD-1))
 (779 545 (:REWRITE |(equal (- x) (- y))|))
 (776 776 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (776 776 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (760 16 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (705 705 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (705 705 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (705 705 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (686 350 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (666 346 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (666 346 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (662 662 (:REWRITE |(< 0 (/ x))|))
 (662 662 (:REWRITE |(< 0 (* x y))|))
 (658 658 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (658 658 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (601 545 (:REWRITE |(equal (- x) c)|))
 (593 593 (:TYPE-PRESCRIPTION NATP))
 (593 593 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (593 593 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (593 593 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (593 593 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (569 101 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (545 545 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (545 545 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (545 545 (:REWRITE |(equal c (/ x))|))
 (545 545 (:REWRITE |(equal c (- x))|))
 (545 545 (:REWRITE |(equal (/ x) c)|))
 (545 545 (:REWRITE |(equal (/ x) (/ y))|))
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 (350 350 (:REWRITE |(mod x (- y))| . 3))
 (350 350 (:REWRITE |(mod x (- y))| . 2))
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 (350 350 (:REWRITE |(mod (- x) y)| . 3))
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 (320 10 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (270 10 (:REWRITE |(* y (* x z))|))
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 (183 183 (:REWRITE REDUCE-INTEGERP-+))
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 (88 88 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
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 (75 3 (:REWRITE MOD-ZERO . 1))
 (70 70 (:REWRITE |(equal (+ (- c) x) y)|))
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 (44 44 (:REWRITE |(expt (- x) n)|))
 (28 7 (:REWRITE |(+ x x)|))
 (26 26 (:REWRITE |(+ c (+ d x))|))
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 (14 14 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (10 10 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:REWRITE |(* c (* d x))|))
 (6 6 (:REWRITE |(equal (* x y) 0)|))
 (6 6 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (3 3 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 )
(RTL::ONLY-2-ROOTS-LEMMA-2
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 (11905 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8509 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (5092 36 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4991 34 (:REWRITE MOD-X-Y-=-X . 3))
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 (2937 309 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2730 168 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2443 2443 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (2443 2443 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2443 2443 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2443 2443 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2443 2443 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (1462 34 (:REWRITE |(integerp (- x))|))
 (1321 112 (:REWRITE |(* y x)|))
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 (1176 84 (:LINEAR EXPT->=-1-ONE))
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 (1084 84 (:LINEAR EXPT->-1-ONE))
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 (844 252 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (638 34 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (638 34 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (606 363 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
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 (507 44 (:REWRITE DEFAULT-MINUS))
 (414 36 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (414 36 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (391 34 (:REWRITE MOD-CANCEL-*-CONST))
 (390 13 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (366 366 (:REWRITE DEFAULT-EXPT-2))
 (366 366 (:REWRITE DEFAULT-EXPT-1))
 (366 366 (:REWRITE |(expt 1/c n)|))
 (366 366 (:REWRITE |(expt (- x) n)|))
 (363 363 (:REWRITE THE-FLOOR-BELOW))
 (363 363 (:REWRITE THE-FLOOR-ABOVE))
 (363 363 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (363 363 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (363 363 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (363 363 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (363 363 (:REWRITE INTEGERP-<-CONSTANT))
 (363 363 (:REWRITE DEFAULT-LESS-THAN-2))
 (363 363 (:REWRITE CONSTANT-<-INTEGERP))
 (363 363 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (363 363 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (363 363 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (363 363 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (363 363 (:REWRITE |(< c (- x))|))
 (363 363 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (363 363 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (363 363 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (363 363 (:REWRITE |(< (/ x) (/ y))|))
 (363 363 (:REWRITE |(< (- x) c)|))
 (363 363 (:REWRITE |(< (- x) (- y))|))
 (338 13 (:REWRITE |(* y (* x z))|))
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 (320 34 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (320 34 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (309 309 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (309 309 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (309 309 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (270 36 (:REWRITE DEFAULT-MOD-1))
 (255 255 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (255 255 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (252 252 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (252 252 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (232 116 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (226 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (193 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (177 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (168 168 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (118 34 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (118 34 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (118 34 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (116 116 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (116 116 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (116 116 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (112 112 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (112 112 (:REWRITE DEFAULT-DIVIDE))
 (112 15 (:REWRITE DEFAULT-PLUS-2))
 (88 75 (:REWRITE INTEGERP-MINUS-X))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<=))
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 (84 84 (:LINEAR EXPT->-1-TWO))
 (84 84 (:LINEAR EXPT-<=-1-TWO))
 (84 84 (:LINEAR EXPT-<-1-ONE))
 (75 75 (:REWRITE REDUCE-INTEGERP-+))
 (75 75 (:META META-INTEGERP-CORRECT))
 (47 15 (:REWRITE DEFAULT-PLUS-1))
 (44 8 (:REWRITE NORMALIZE-ADDENDS))
 (37 37 (:REWRITE |(- (* c x))|))
 (36 36 (:REWRITE DEFAULT-MOD-2))
 (34 34 (:REWRITE |(mod x (- y))| . 3))
 (34 34 (:REWRITE |(mod x (- y))| . 2))
 (34 34 (:REWRITE |(mod x (- y))| . 1))
 (34 34 (:REWRITE |(mod (- x) y)| . 3))
 (34 34 (:REWRITE |(mod (- x) y)| . 2))
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 (30 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (23 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (20 20 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (16 16 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (16 16 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (16 16 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (13 13 (:REWRITE |(* c (* d x))|))
 (10 1 (:REWRITE |(+ 0 x)|))
 (8 8 (:LINEAR RTL::MOD-BND-3))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (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))|))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(RTL::ONLY-2-ROOTS
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 (6429 33 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4444 14 (:LINEAR MOD-BOUNDS-1))
 (3225 7 (:REWRITE MOD-X-Y-=-X+Y . 1))
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 (2665 164 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2507 33 (:REWRITE MOD-X-Y-=-X . 4))
 (2422 33 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1922 33 (:REWRITE MOD-ZERO . 4))
 (1886 82 (:LINEAR EXPT-X->=-X))
 (1761 1761 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (1370 1370 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1370 1370 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (1228 164 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
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 (651 164 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
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 (550 181 (:REWRITE DEFAULT-PLUS-1))
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 (450 45 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (438 438 (:REWRITE THE-FLOOR-BELOW))
 (438 438 (:REWRITE THE-FLOOR-ABOVE))
 (438 438 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (438 438 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (438 438 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (435 435 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (435 435 (:REWRITE INTEGERP-<-CONSTANT))
 (435 435 (:REWRITE CONSTANT-<-INTEGERP))
 (435 435 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (435 435 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (435 435 (:REWRITE |(< (- x) c)|))
 (435 435 (:REWRITE |(< (- x) (- y))|))
 (412 6 (:REWRITE |(* x (+ y z))|))
 (344 344 (:REWRITE DEFAULT-EXPT-2))
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 (343 343 (:REWRITE |(expt 1/c n)|))
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 (309 33 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (309 33 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (287 38 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (277 3 (:REWRITE |(equal (mod a n) (mod b n))|))
 (237 47 (:REWRITE DEFAULT-MINUS))
 (237 33 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (237 33 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (232 232 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (232 232 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (232 232 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (232 232 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (231 231 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (204 102 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (200 31 (:REWRITE MOD-CANCEL-*-CONST))
 (164 164 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (148 16 (:REWRITE |(* y (* x z))|))
 (147 7 (:LINEAR MOD-BOUNDS-3))
 (123 31 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (123 31 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (123 31 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (113 113 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (113 113 (:REWRITE DEFAULT-DIVIDE))
 (108 31 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (108 31 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (108 31 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (106 78 (:META META-INTEGERP-CORRECT))
 (105 33 (:REWRITE DEFAULT-MOD-1))
 (102 102 (:TYPE-PRESCRIPTION NATP))
 (102 102 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (102 102 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (102 102 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (102 102 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (86 78 (:REWRITE INTEGERP-MINUS-X))
 (82 82 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (82 82 (:LINEAR EXPT-LINEAR-UPPER-<))
 (82 82 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (82 82 (:LINEAR EXPT-LINEAR-LOWER-<))
 (82 82 (:LINEAR EXPT->-1-TWO))
 (82 82 (:LINEAR EXPT-<=-1-TWO))
 (82 82 (:LINEAR EXPT-<-1-ONE))
 (78 78 (:REWRITE REDUCE-INTEGERP-+))
 (77 77 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (77 77 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (77 77 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (70 14 (:LINEAR MOD-BOUNDS-2))
 (65 65 (:REWRITE |(< (/ x) 0)|))
 (65 65 (:REWRITE |(< (* x y) 0)|))
 (61 61 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (61 61 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (45 45 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (45 45 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (45 45 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (45 45 (:REWRITE |(equal c (/ x))|))
 (45 45 (:REWRITE |(equal c (- x))|))
 (45 45 (:REWRITE |(equal (/ x) c)|))
 (45 45 (:REWRITE |(equal (/ x) (/ y))|))
 (45 45 (:REWRITE |(equal (- x) c)|))
 (45 45 (:REWRITE |(equal (- x) (- y))|))
 (44 35 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (37 37 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (36 36 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (34 34 (:REWRITE |(< 0 (* x y))|))
 (33 33 (:REWRITE DEFAULT-MOD-2))
 (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)| . 3))
 (31 31 (:REWRITE |(mod (- x) y)| . 2))
 (31 31 (:REWRITE |(mod (- x) y)| . 1))
 (31 31 (:REWRITE |(< 0 (/ x))|))
 (28 28 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (28 28 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (25 7 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (13 13 (:REWRITE |(< (+ c/d x) y)|))
 (13 13 (:REWRITE |(< (+ (- c) x) y)|))
 (12 12 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (9 9 (:REWRITE |(< y (+ (- c) x))|))
 (9 9 (:REWRITE |(< x (+ c/d y))|))
 (9 9 (:LINEAR RTL::MOD-BND-3))
 (8 8 (:REWRITE |(+ c (+ d x))|))
 (8 8 (:REWRITE |(* (/ c) (expt d n))|))
 (4 4 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE |(* a (/ a))|))
 (4 4 (:REWRITE |(* 1 x)|))
 (3 3 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (3 3 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (3 3 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (3 3 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (2 2 (:REWRITE |(* c (* d x))|))
 (1 1 (:REWRITE |(expt (- c) n)|))
 )
(RTL::ROOTS-DISTINCT
 (40538 28 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (15268 28 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (13070 140 (:REWRITE MOD-X-Y-=-X . 3))
 (12435 140 (:REWRITE CANCEL-MOD-+))
 (11535 140 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (9547 9547 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (9547 9547 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (9547 9547 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (8485 1697 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (8425 1697 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (8114 8114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (8114 8114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (8114 8114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (8114 8114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (8114 8114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6940 694 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (6540 140 (:REWRITE MOD-ZERO . 3))
 (6277 1697 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6277 1697 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4675 140 (:REWRITE MOD-X-Y-=-X . 4))
 (4485 1697 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (4422 210 (:LINEAR EXPT-<-1-TWO))
 (4265 140 (:REWRITE |(integerp (- x))|))
 (4101 968 (:REWRITE DEFAULT-TIMES-1))
 (3935 140 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3650 140 (:REWRITE |(* (- x) y)|))
 (3453 1428 (:REWRITE SIMPLIFY-SUMS-<))
 (3453 1428 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3433 968 (:REWRITE DEFAULT-TIMES-2))
 (3342 170 (:LINEAR EXPT-X->-X))
 (3342 170 (:LINEAR EXPT->-1-ONE))
 (2765 140 (:REWRITE MOD-ZERO . 4))
 (2563 55 (:LINEAR MOD-BOUNDS-3))
 (2516 170 (:LINEAR EXPT->=-1-TWO))
 (2103 1428 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2072 1080 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2050 140 (:REWRITE MOD-X-Y-=-X . 2))
 (2050 140 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (2050 140 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1826 194 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1697 1697 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1697 1697 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1697 1697 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1697 1697 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1666 340 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1431 1431 (:REWRITE THE-FLOOR-BELOW))
 (1431 1431 (:REWRITE THE-FLOOR-ABOVE))
 (1431 1431 (:REWRITE DEFAULT-LESS-THAN-2))
 (1428 1428 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1428 1428 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1428 1428 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1428 1428 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1428 1428 (:REWRITE INTEGERP-<-CONSTANT))
 (1428 1428 (:REWRITE CONSTANT-<-INTEGERP))
 (1428 1428 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1428 1428 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1428 1428 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1428 1428 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1428 1428 (:REWRITE |(< c (- x))|))
 (1428 1428 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1428 1428 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1428 1428 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1428 1428 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1428 1428 (:REWRITE |(< (/ x) (/ y))|))
 (1428 1428 (:REWRITE |(< (- x) c)|))
 (1428 1428 (:REWRITE |(< (- x) (- y))|))
 (1375 140 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1375 140 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1375 140 (:REWRITE MOD-CANCEL-*-CONST))
 (1206 150 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1198 110 (:LINEAR MOD-BOUNDS-2))
 (1141 439 (:REWRITE DEFAULT-PLUS-2))
 (1080 1080 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1080 1080 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (1080 1080 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (1007 140 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1007 140 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1007 140 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1006 73 (:REWRITE ACL2-NUMBERP-X))
 (992 992 (:TYPE-PRESCRIPTION NATP))
 (816 6 (:REWRITE |(equal (mod a n) (mod b n))|))
 (771 771 (:REWRITE DEFAULT-EXPT-2))
 (771 771 (:REWRITE DEFAULT-EXPT-1))
 (771 771 (:REWRITE |(expt 1/c n)|))
 (771 771 (:REWRITE |(expt (- x) n)|))
 (694 694 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (694 694 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (694 694 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (689 689 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (627 439 (:REWRITE DEFAULT-PLUS-1))
 (546 6 (:REWRITE MOD-ZERO . 1))
 (530 83 (:REWRITE RATIONALP-X))
 (508 140 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (508 140 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (508 140 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (495 495 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (495 495 (:REWRITE DEFAULT-DIVIDE))
 (491 413 (:REWRITE INTEGERP-MINUS-X))
 (413 413 (:REWRITE REDUCE-INTEGERP-+))
 (413 413 (:META META-INTEGERP-CORRECT))
 (343 343 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (340 340 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (322 322 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (322 322 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (322 322 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (210 210 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (210 210 (:LINEAR EXPT-LINEAR-UPPER-<))
 (210 210 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (210 210 (:LINEAR EXPT-LINEAR-LOWER-<))
 (210 210 (:LINEAR EXPT-<=-1-TWO))
 (207 9 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (194 194 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (194 194 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (194 194 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (194 194 (:REWRITE |(equal c (/ x))|))
 (194 194 (:REWRITE |(equal c (- x))|))
 (194 194 (:REWRITE |(equal (/ x) c)|))
 (194 194 (:REWRITE |(equal (/ x) (/ y))|))
 (194 194 (:REWRITE |(equal (- x) c)|))
 (194 194 (:REWRITE |(equal (- x) (- y))|))
 (190 28 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (170 170 (:LINEAR EXPT->-1-TWO))
 (170 170 (:LINEAR EXPT-<-1-ONE))
 (160 160 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (160 160 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (160 160 (:REWRITE |(< 0 (/ x))|))
 (160 160 (:REWRITE |(< 0 (* x y))|))
 (151 151 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (151 151 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (151 151 (:REWRITE |(< (/ x) 0)|))
 (151 151 (:REWRITE |(< (* x y) 0)|))
 (146 146 (:REWRITE |(- (* c x))|))
 (142 142 (:REWRITE DEFAULT-MOD-2))
 (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)| . 3))
 (140 140 (:REWRITE |(mod (- x) y)| . 2))
 (140 140 (:REWRITE |(mod (- x) y)| . 1))
 (138 6 (:REWRITE MOD-ZERO . 2))
 (83 83 (:REWRITE RATIONALP-MINUS-X))
 (81 81 (:REWRITE REDUCE-RATIONALP-+))
 (81 81 (:META META-RATIONALP-CORRECT))
 (75 75 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (63 63 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (63 63 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (58 58 (:REWRITE |(equal (+ (- c) x) y)|))
 (57 57 (:LINEAR RTL::MOD-BND-3))
 (9 9 (:REWRITE |(+ c (+ d x))|))
 (6 6 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 )
(RTL::ASSOCIATES)
(RTL::MEMBER-ASSOCIATES
 (611 165 (:REWRITE ACL2-NUMBERP-X))
 (597 84 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (232 34 (:REWRITE ZP-OPEN))
 (223 55 (:REWRITE RATIONALP-X))
 (151 84 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (151 84 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (145 145 (:REWRITE RTL::PERM-MEMBER))
 (90 18 (:REWRITE |(+ c (+ d x))|))
 (84 84 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (84 84 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (84 84 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (84 84 (:REWRITE |(equal c (/ x))|))
 (84 84 (:REWRITE |(equal c (- x))|))
 (84 84 (:REWRITE |(equal (/ x) c)|))
 (84 84 (:REWRITE |(equal (/ x) (/ y))|))
 (84 84 (:REWRITE |(equal (- x) c)|))
 (84 84 (:REWRITE |(equal (- x) (- y))|))
 (80 70 (:REWRITE DEFAULT-CDR))
 (80 70 (:REWRITE DEFAULT-CAR))
 (79 79 (:REWRITE DEFAULT-PLUS-2))
 (79 79 (:REWRITE DEFAULT-PLUS-1))
 (75 75 (:REWRITE REDUCE-INTEGERP-+))
 (75 75 (:REWRITE INTEGERP-MINUS-X))
 (75 75 (:META META-INTEGERP-CORRECT))
 (61 61 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (61 61 (:REWRITE NORMALIZE-ADDENDS))
 (55 55 (:REWRITE REDUCE-RATIONALP-+))
 (55 55 (:REWRITE REDUCE-RATIONALP-*))
 (55 55 (:REWRITE RATIONALP-MINUS-X))
 (55 55 (:META META-RATIONALP-CORRECT))
 (40 40 (:REWRITE THE-FLOOR-BELOW))
 (40 40 (:REWRITE THE-FLOOR-ABOVE))
 (40 40 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (40 40 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (40 40 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (40 40 (:REWRITE INTEGERP-<-CONSTANT))
 (40 40 (:REWRITE DEFAULT-LESS-THAN-2))
 (40 40 (:REWRITE DEFAULT-LESS-THAN-1))
 (40 40 (:REWRITE CONSTANT-<-INTEGERP))
 (40 40 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (40 40 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (40 40 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (40 40 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (40 40 (:REWRITE |(< c (- x))|))
 (40 40 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (40 40 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (40 40 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (40 40 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (40 40 (:REWRITE |(< (/ x) (/ y))|))
 (40 40 (:REWRITE |(< (- x) c)|))
 (40 40 (:REWRITE |(< (- x) (- y))|))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (40 8 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (38 38 (:REWRITE SIMPLIFY-SUMS-<))
 (38 38 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (38 38 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (38 38 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (20 20 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (16 8 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (12 6 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (8 8 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (8 8 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (6 6 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6 6 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (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 (: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 |(equal (+ (- c) x) y)|))
 (6 6 (:REWRITE |(< y (+ (- c) x))|))
 (6 6 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:REWRITE |(< 0 (/ x))|))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 (4 4 (:REWRITE |(< (+ c/d x) y)|))
 (4 4 (:REWRITE |(< (+ (- c) x) y)|))
 )
(RTL::SUBSET-POSITIVES-ASSOCIATES
 (1221 333 (:REWRITE ACL2-NUMBERP-X))
 (1114 113 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (919 61 (:REWRITE ZP-OPEN))
 (444 111 (:REWRITE RATIONALP-X))
 (270 54 (:REWRITE |(+ c (+ d x))|))
 (226 113 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (226 113 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (189 189 (:REWRITE RTL::PERM-MEMBER))
 (187 175 (:REWRITE DEFAULT-CAR))
 (169 169 (:REWRITE DEFAULT-PLUS-2))
 (169 169 (:REWRITE DEFAULT-PLUS-1))
 (146 135 (:REWRITE DEFAULT-CDR))
 (115 115 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (115 115 (:REWRITE NORMALIZE-ADDENDS))
 (113 113 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (113 113 (:REWRITE REDUCE-INTEGERP-+))
 (113 113 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (113 113 (:REWRITE INTEGERP-MINUS-X))
 (113 113 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (113 113 (:REWRITE |(equal c (/ x))|))
 (113 113 (:REWRITE |(equal c (- x))|))
 (113 113 (:REWRITE |(equal (/ x) c)|))
 (113 113 (:REWRITE |(equal (/ x) (/ y))|))
 (113 113 (:REWRITE |(equal (- x) c)|))
 (113 113 (:REWRITE |(equal (- x) (- y))|))
 (113 113 (:META META-INTEGERP-CORRECT))
 (111 111 (:REWRITE REDUCE-RATIONALP-+))
 (111 111 (:REWRITE REDUCE-RATIONALP-*))
 (111 111 (:REWRITE RATIONALP-MINUS-X))
 (111 111 (:META META-RATIONALP-CORRECT))
 (28 28 (:REWRITE THE-FLOOR-BELOW))
 (28 28 (:REWRITE THE-FLOOR-ABOVE))
 (28 28 (:REWRITE SIMPLIFY-SUMS-<))
 (28 28 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (28 28 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (28 28 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (28 28 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (28 28 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (28 28 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (28 28 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (28 28 (:REWRITE INTEGERP-<-CONSTANT))
 (28 28 (:REWRITE DEFAULT-LESS-THAN-2))
 (28 28 (:REWRITE DEFAULT-LESS-THAN-1))
 (28 28 (:REWRITE CONSTANT-<-INTEGERP))
 (28 28 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (28 28 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (28 28 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (28 28 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (28 28 (:REWRITE |(< c (- x))|))
 (28 28 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (28 28 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (28 28 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (28 28 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (28 28 (:REWRITE |(< (/ x) (/ y))|))
 (28 28 (:REWRITE |(< (- x) c)|))
 (28 28 (:REWRITE |(< (- x) (- y))|))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (26 26 (:REWRITE |(< y (+ (- c) x))|))
 (26 26 (:REWRITE |(< x (+ c/d y))|))
 (26 26 (:REWRITE |(< 0 (/ x))|))
 (26 26 (:REWRITE |(< 0 (* x y))|))
 (14 14 (:REWRITE |(equal (+ (- c) 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)|))
 )
(RTL::MEMBER-SELF-ASSOCIATE
 (239 34 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (237 63 (:REWRITE ACL2-NUMBERP-X))
 (87 21 (:REWRITE RATIONALP-X))
 (65 34 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (65 34 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (46 46 (:REWRITE RTL::PERM-MEMBER))
 (37 37 (:REWRITE REDUCE-INTEGERP-+))
 (37 37 (:REWRITE INTEGERP-MINUS-X))
 (37 37 (:META META-INTEGERP-CORRECT))
 (34 34 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (34 34 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (34 34 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (34 34 (:REWRITE |(equal c (/ x))|))
 (34 34 (:REWRITE |(equal c (- x))|))
 (34 34 (:REWRITE |(equal (/ x) c)|))
 (34 34 (:REWRITE |(equal (/ x) (/ y))|))
 (34 34 (:REWRITE |(equal (- x) c)|))
 (34 34 (:REWRITE |(equal (- x) (- y))|))
 (26 24 (:REWRITE DEFAULT-CAR))
 (24 22 (:REWRITE DEFAULT-CDR))
 (21 21 (:REWRITE REDUCE-RATIONALP-+))
 (21 21 (:REWRITE REDUCE-RATIONALP-*))
 (21 21 (:REWRITE RATIONALP-MINUS-X))
 (21 21 (:META META-RATIONALP-CORRECT))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (18 18 (:REWRITE NORMALIZE-ADDENDS))
 (18 18 (:REWRITE DEFAULT-PLUS-2))
 (18 18 (:REWRITE DEFAULT-PLUS-1))
 (17 17 (:REWRITE THE-FLOOR-BELOW))
 (17 17 (:REWRITE THE-FLOOR-ABOVE))
 (17 17 (:REWRITE SIMPLIFY-SUMS-<))
 (17 17 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (17 17 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (17 17 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (17 17 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (17 17 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (17 17 (:REWRITE INTEGERP-<-CONSTANT))
 (17 17 (:REWRITE DEFAULT-LESS-THAN-2))
 (17 17 (:REWRITE DEFAULT-LESS-THAN-1))
 (17 17 (:REWRITE CONSTANT-<-INTEGERP))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (- x))|))
 (17 17 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) (/ y))|))
 (17 17 (:REWRITE |(< (- x) c)|))
 (17 17 (:REWRITE |(< (- x) (- y))|))
 (8 2 (:REWRITE RTL::MEMBER-ASSOCIATES))
 (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))|))
 )
(RTL::DISTINCT-POSITIVES-ASSOCIATES-LEMMA
 (9378 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (5072 93 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2584 8 (:LINEAR MOD-BOUNDS-1))
 (2248 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1966 6 (:LINEAR RTL::MOD-BND-1))
 (1656 24 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1437 1437 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1437 1437 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1437 1437 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1245 249 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1245 249 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1150 18 (:REWRITE MOD-X-Y-=-X . 3))
 (1052 18 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1040 64 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (909 249 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (909 249 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (888 18 (:REWRITE CANCEL-MOD-+))
 (764 64 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (736 32 (:LINEAR EXPT-X->=-X))
 (732 32 (:LINEAR EXPT->=-1-TWO))
 (732 32 (:LINEAR EXPT-<=-1-ONE))
 (728 93 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (656 32 (:LINEAR EXPT-X->-X))
 (656 32 (:LINEAR EXPT->-1-ONE))
 (656 32 (:LINEAR EXPT-<-1-TWO))
 (637 249 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (624 18 (:REWRITE MOD-X-Y-=-X . 4))
 (590 18 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (526 526 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (484 132 (:REWRITE ACL2-NUMBERP-X))
 (474 18 (:REWRITE MOD-ZERO . 3))
 (448 32 (:LINEAR EXPT->=-1-ONE))
 (421 367 (:REWRITE SIMPLIFY-SUMS-<))
 (421 367 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (421 367 (:REWRITE DEFAULT-LESS-THAN-1))
 (385 367 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (376 64 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (367 367 (:REWRITE THE-FLOOR-BELOW))
 (367 367 (:REWRITE THE-FLOOR-ABOVE))
 (367 367 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (367 367 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (367 367 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (367 367 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (367 367 (:REWRITE INTEGERP-<-CONSTANT))
 (367 367 (:REWRITE DEFAULT-LESS-THAN-2))
 (367 367 (:REWRITE CONSTANT-<-INTEGERP))
 (367 367 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (367 367 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (367 367 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (367 367 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (367 367 (:REWRITE |(< c (- x))|))
 (367 367 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (367 367 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (367 367 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (367 367 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (367 367 (:REWRITE |(< (/ x) (/ y))|))
 (367 367 (:REWRITE |(< (- x) c)|))
 (367 367 (:REWRITE |(< (- x) (- y))|))
 (359 208 (:REWRITE DEFAULT-PLUS-2))
 (342 18 (:REWRITE |(integerp (- x))|))
 (334 18 (:REWRITE MOD-ZERO . 4))
 (330 91 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (280 208 (:REWRITE DEFAULT-PLUS-1))
 (276 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (249 249 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (249 249 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (249 249 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (249 249 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (240 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (240 18 (:REWRITE DEFAULT-MOD-RATIO))
 (240 18 (:REWRITE |(* (- x) y)|))
 (225 225 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (224 191 (:REWRITE DEFAULT-CAR))
 (195 123 (:REWRITE NORMALIZE-ADDENDS))
 (186 6 (:LINEAR RTL::MOD-BND-2))
 (184 92 (:REWRITE DEFAULT-TIMES-1))
 (176 44 (:REWRITE RATIONALP-X))
 (168 84 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (167 144 (:REWRITE DEFAULT-CDR))
 (164 92 (:REWRITE DEFAULT-TIMES-2))
 (134 126 (:REWRITE INTEGERP-MINUS-X))
 (130 130 (:REWRITE DEFAULT-EXPT-2))
 (130 130 (:REWRITE DEFAULT-EXPT-1))
 (130 130 (:REWRITE |(expt 1/c n)|))
 (130 130 (:REWRITE |(expt (- x) n)|))
 (126 126 (:REWRITE REDUCE-INTEGERP-+))
 (126 126 (:META META-INTEGERP-CORRECT))
 (126 18 (:REWRITE MOD-X-Y-=-X . 2))
 (126 18 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (126 18 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (121 121 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (120 120 (:REWRITE RTL::PERM-MEMBER))
 (120 22 (:REWRITE DEFAULT-MINUS))
 (108 18 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (108 18 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (108 18 (:REWRITE MOD-CANCEL-*-CONST))
 (104 8 (:REWRITE |(* y x)|))
 (100 6 (:REWRITE |(+ y x)|))
 (94 94 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (94 94 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (93 93 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (93 93 (:REWRITE |(equal c (/ x))|))
 (93 93 (:REWRITE |(equal c (- x))|))
 (93 93 (:REWRITE |(equal (/ x) c)|))
 (93 93 (:REWRITE |(equal (/ x) (/ y))|))
 (93 93 (:REWRITE |(equal (- x) c)|))
 (93 93 (:REWRITE |(equal (- x) (- y))|))
 (84 84 (:TYPE-PRESCRIPTION NATP))
 (84 84 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (84 84 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (84 84 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (84 84 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (84 4 (:LINEAR MOD-BOUNDS-3))
 (77 77 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (77 77 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (77 77 (:REWRITE |(< 0 (/ x))|))
 (77 77 (:REWRITE |(< 0 (* x y))|))
 (74 18 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (74 18 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (74 18 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (64 64 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (62 62 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (62 62 (:REWRITE DEFAULT-DIVIDE))
 (52 18 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (52 18 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (52 18 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (46 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (44 44 (:REWRITE REDUCE-RATIONALP-+))
 (44 44 (:REWRITE REDUCE-RATIONALP-*))
 (44 44 (:REWRITE RATIONALP-MINUS-X))
 (44 44 (:META META-RATIONALP-CORRECT))
 (40 8 (:LINEAR MOD-BOUNDS-2))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (38 38 (:REWRITE |(< (/ x) 0)|))
 (38 38 (:REWRITE |(< (* x y) 0)|))
 (37 37 (:REWRITE |(< (+ c/d x) y)|))
 (37 37 (:REWRITE |(< (+ (- c) x) y)|))
 (36 18 (:REWRITE DEFAULT-MOD-1))
 (35 9 (:REWRITE |(equal (+ (- c) x) y)|))
 (32 32 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (32 32 (:LINEAR EXPT-LINEAR-UPPER-<))
 (32 32 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (32 32 (:LINEAR EXPT-LINEAR-LOWER-<))
 (32 32 (:LINEAR EXPT->-1-TWO))
 (32 32 (:LINEAR EXPT-<=-1-TWO))
 (32 32 (:LINEAR EXPT-<-1-ONE))
 (26 26 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (24 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (20 20 (:REWRITE |(- (* c x))|))
 (18 18 (:REWRITE DEFAULT-MOD-2))
 (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)| . 3))
 (18 18 (:REWRITE |(mod (- x) y)| . 2))
 (18 18 (:REWRITE |(mod (- x) y)| . 1))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (12 6 (:REWRITE RTL::ASSOCIATE-OF-ASSOCIATE))
 (10 10 (:REWRITE |(< y (+ (- c) x))|))
 (10 10 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE |(+ x (- x))|))
 )
(RTL::DISTINCT-POSITIVES-ASSOCIATES
 (328 9 (:REWRITE RTL::PIGEONHOLE-PRINCIPLE-LEMMA-1))
 (125 1 (:DEFINITION RTL::ASSOCIATES))
 (119 4 (:DEFINITION MEMBER-EQUAL))
 (44 12 (:REWRITE ACL2-NUMBERP-X))
 (42 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (36 1 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (29 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (27 25 (:REWRITE DEFAULT-PLUS-1))
 (26 25 (:REWRITE DEFAULT-PLUS-2))
 (23 5 (:REWRITE |(+ c (+ d x))|))
 (16 4 (:REWRITE RATIONALP-X))
 (15 15 (:TYPE-PRESCRIPTION RTL::ASSOCIATE))
 (13 13 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE THE-FLOOR-BELOW))
 (11 11 (:REWRITE THE-FLOOR-ABOVE))
 (11 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (11 11 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (11 11 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (11 11 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (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))|))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 9 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (8 8 (:REWRITE RTL::PERM-MEMBER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:REWRITE |(< 0 (/ x))|))
 (7 7 (:REWRITE |(< 0 (* x y))|))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (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 |(< (+ c/d x) y)|))
 (3 3 (:REWRITE |(< (+ (- c) x) y)|))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(+ 0 x)|))
 (1 1 (:TYPE-PRESCRIPTION RTL::RESIDUE))
 )
(RTL::LDPU-INDUCTION)
(RTL::LEN-DISTINCT-POSITIVES-UPPER
 (88 24 (:REWRITE ACL2-NUMBERP-X))
 (80 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (56 2 (:DEFINITION REMOVE1-EQUAL))
 (32 8 (:REWRITE RATIONALP-X))
 (19 19 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE DEFAULT-CDR))
 (17 15 (:REWRITE DEFAULT-PLUS-2))
 (16 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (16 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (15 15 (:REWRITE DEFAULT-PLUS-1))
 (12 12 (:REWRITE RTL::PERM-MEMBER))
 (11 11 (:REWRITE THE-FLOOR-BELOW))
 (11 11 (:REWRITE THE-FLOOR-ABOVE))
 (11 11 (:REWRITE SIMPLIFY-SUMS-<))
 (11 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (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 PREFER-POSITIVE-ADDENDS-<))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (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))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (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))
 (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 |(< (+ c/d x) y)|))
 (3 3 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 )
(RTL::LEN-REMOVE
 (28 1 (:DEFINITION REMOVE1-EQUAL))
 (27 1 (:DEFINITION MEMBER-EQUAL))
 (22 6 (:REWRITE ACL2-NUMBERP-X))
 (20 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (14 2 (:DEFINITION LEN))
 (8 4 (:REWRITE DEFAULT-PLUS-2))
 (8 2 (:REWRITE RATIONALP-X))
 (5 5 (:REWRITE DEFAULT-CDR))
 (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 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (4 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE REDUCE-RATIONALP-+))
 (2 2 (:REWRITE REDUCE-RATIONALP-*))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE RATIONALP-MINUS-X))
 (2 2 (:REWRITE RTL::PERM-MEMBER))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:META META-RATIONALP-CORRECT))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(RTL::SUBSETP-REMOVE
 (1166 318 (:REWRITE ACL2-NUMBERP-X))
 (1060 106 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (424 106 (:REWRITE RATIONALP-X))
 (222 22 (:REWRITE RTL::NOT-MEMBER-REMOVE1))
 (212 106 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (212 106 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (165 165 (:REWRITE DEFAULT-CAR))
 (138 138 (:REWRITE RTL::PERM-MEMBER))
 (122 122 (:REWRITE DEFAULT-CDR))
 (106 106 (:REWRITE REDUCE-RATIONALP-+))
 (106 106 (:REWRITE REDUCE-RATIONALP-*))
 (106 106 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (106 106 (:REWRITE REDUCE-INTEGERP-+))
 (106 106 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (106 106 (:REWRITE RATIONALP-MINUS-X))
 (106 106 (:REWRITE INTEGERP-MINUS-X))
 (106 106 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (106 106 (:REWRITE |(equal c (/ x))|))
 (106 106 (:REWRITE |(equal c (- x))|))
 (106 106 (:REWRITE |(equal (/ x) c)|))
 (106 106 (:REWRITE |(equal (/ x) (/ y))|))
 (106 106 (:REWRITE |(equal (- x) c)|))
 (106 106 (:REWRITE |(equal (- x) (- y))|))
 (106 106 (:META META-RATIONALP-CORRECT))
 (106 106 (:META META-INTEGERP-CORRECT))
 )
(RTL::LEN-SUBSETP-POSITIVES
 (176 48 (:REWRITE ACL2-NUMBERP-X))
 (160 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (84 3 (:DEFINITION REMOVE1-EQUAL))
 (64 16 (:REWRITE RATIONALP-X))
 (55 50 (:REWRITE DEFAULT-PLUS-2))
 (52 50 (:REWRITE DEFAULT-PLUS-1))
 (34 1 (:REWRITE RTL::NOT-MEMBER-REMOVE1))
 (32 32 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (32 30 (:REWRITE DEFAULT-CDR))
 (32 28 (:REWRITE DEFAULT-CAR))
 (32 16 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (32 16 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (28 4 (:DEFINITION LEN))
 (26 26 (:REWRITE RTL::PERM-MEMBER))
 (26 22 (:REWRITE DEFAULT-LESS-THAN-1))
 (24 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (24 20 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (22 22 (:REWRITE THE-FLOOR-BELOW))
 (22 22 (:REWRITE THE-FLOOR-ABOVE))
 (22 22 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:REWRITE DEFAULT-LESS-THAN-2))
 (20 20 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (20 20 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (20 20 (:REWRITE REDUCE-INTEGERP-+))
 (20 20 (:REWRITE INTEGERP-MINUS-X))
 (20 20 (:REWRITE INTEGERP-<-CONSTANT))
 (20 20 (:REWRITE CONSTANT-<-INTEGERP))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (- x))|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) (/ y))|))
 (20 20 (:REWRITE |(< (- x) c)|))
 (20 20 (:REWRITE |(< (- x) (- y))|))
 (20 20 (:META META-INTEGERP-CORRECT))
 (16 16 (:REWRITE REDUCE-RATIONALP-+))
 (16 16 (:REWRITE REDUCE-RATIONALP-*))
 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (16 16 (:REWRITE RATIONALP-MINUS-X))
 (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))|))
 (16 16 (:META META-RATIONALP-CORRECT))
 (13 13 (:REWRITE |(< x (+ c/d y))|))
 (12 12 (:REWRITE |(< y (+ (- c) x))|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (9 9 (: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 |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 )
(RTL::PIGEONHOLE-PRINCIPLE-2
 (790 25 (:REWRITE RTL::PIGEONHOLE-PRINCIPLE-LEMMA-1))
 (547 34 (:REWRITE RTL::PERM-MEMBER))
 (510 3 (:REWRITE RTL::MEMBER-POSITIVES))
 (474 17 (:DEFINITION MEMBER-EQUAL))
 (360 3 (:DEFINITION RTL::PERM))
 (220 60 (:REWRITE ACL2-NUMBERP-X))
 (200 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (84 3 (:DEFINITION REMOVE1-EQUAL))
 (82 7 (:DEFINITION RTL::POSITIVES))
 (80 20 (:REWRITE RATIONALP-X))
 (63 63 (:REWRITE DEFAULT-CAR))
 (58 48 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (58 48 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (58 48 (:REWRITE DEFAULT-LESS-THAN-2))
 (56 56 (:REWRITE DEFAULT-CDR))
 (53 48 (:REWRITE SIMPLIFY-SUMS-<))
 (51 48 (:REWRITE DEFAULT-LESS-THAN-1))
 (48 48 (:REWRITE THE-FLOOR-BELOW))
 (48 48 (:REWRITE THE-FLOOR-ABOVE))
 (48 48 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (48 48 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (48 48 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (48 48 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (48 48 (:REWRITE INTEGERP-<-CONSTANT))
 (48 48 (:REWRITE CONSTANT-<-INTEGERP))
 (48 48 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (48 48 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (48 48 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (48 48 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (48 48 (:REWRITE |(< c (- x))|))
 (48 48 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (48 48 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (48 48 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (48 48 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (48 48 (:REWRITE |(< (/ x) (/ y))|))
 (48 48 (:REWRITE |(< (- x) c)|))
 (48 48 (:REWRITE |(< (- x) (- y))|))
 (42 6 (:DEFINITION LEN))
 (40 40 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (40 20 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (40 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (35 35 (:REWRITE REDUCE-INTEGERP-+))
 (35 35 (:REWRITE INTEGERP-MINUS-X))
 (35 35 (:META META-INTEGERP-CORRECT))
 (30 23 (:REWRITE DEFAULT-PLUS-2))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (26 26 (:REWRITE |(< 0 (/ x))|))
 (26 26 (:REWRITE |(< 0 (* x y))|))
 (23 23 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (23 23 (:REWRITE NORMALIZE-ADDENDS))
 (23 23 (:REWRITE DEFAULT-PLUS-1))
 (20 20 (:REWRITE REDUCE-RATIONALP-+))
 (20 20 (:REWRITE REDUCE-RATIONALP-*))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE RATIONALP-MINUS-X))
 (20 20 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (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 (:META META-RATIONALP-CORRECT))
 (5 5 (:REWRITE |(< (+ c/d x) y)|))
 (5 5 (:REWRITE |(< (+ (- c) 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)|))
 )
(RTL::PERM-ASSOCIATES-POSITIVES
 (444 3 (:DEFINITION RTL::DISTINCT-POSITIVES))
 (328 9 (:REWRITE RTL::PIGEONHOLE-PRINCIPLE-LEMMA-1))
 (233 5 (:REWRITE ZP-OPEN))
 (125 1 (:DEFINITION RTL::ASSOCIATES))
 (119 4 (:DEFINITION MEMBER-EQUAL))
 (44 12 (:REWRITE ACL2-NUMBERP-X))
 (42 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (36 1 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (29 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (23 5 (:REWRITE |(+ c (+ d x))|))
 (17 16 (:REWRITE DEFAULT-PLUS-2))
 (16 16 (:REWRITE DEFAULT-PLUS-1))
 (16 4 (:REWRITE RATIONALP-X))
 (15 15 (:TYPE-PRESCRIPTION RTL::ASSOCIATE))
 (13 13 (:REWRITE DEFAULT-CAR))
 (12 12 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE SIMPLIFY-SUMS-<))
 (10 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (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 PREFER-POSITIVE-ADDENDS-<))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (10 10 (:REWRITE DEFAULT-CDR))
 (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))|))
 (10 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE NORMALIZE-ADDENDS))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (8 8 (:REWRITE RTL::PERM-MEMBER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:REWRITE |(< 0 (/ x))|))
 (7 7 (:REWRITE |(< 0 (* x y))|))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:META META-RATIONALP-CORRECT))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (2 2 (:REWRITE |(+ 0 x)|))
 (1 1 (:TYPE-PRESCRIPTION RTL::RESIDUE))
 )
(RTL::TIMES-LIST-ASSOCIATES-FACT)
(RTL::PERM-LEN
 (84 3 (:DEFINITION REMOVE1-EQUAL))
 (82 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (77 21 (:REWRITE ACL2-NUMBERP-X))
 (28 7 (:REWRITE RATIONALP-X))
 (26 11 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (26 11 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (24 24 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE DEFAULT-CDR))
 (16 8 (:REWRITE DEFAULT-PLUS-2))
 (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))|))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:REWRITE NORMALIZE-ADDENDS))
 (8 8 (:REWRITE DEFAULT-PLUS-1))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:REWRITE REDUCE-RATIONALP-*))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE RATIONALP-MINUS-X))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-RATIONALP-CORRECT))
 (7 7 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(RTL::LEN-POSITIVES
 (18 2 (:REWRITE ACL2-NUMBERP-X))
 (16 10 (:REWRITE DEFAULT-PLUS-2))
 (12 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE DEFAULT-PLUS-1))
 (10 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 2 (:REWRITE RATIONALP-X))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE THE-FLOOR-BELOW))
 (6 6 (:REWRITE THE-FLOOR-ABOVE))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE DEFAULT-LESS-THAN-2))
 (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))|))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (5 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) c)|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE ZP-OPEN))
 (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 SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE REDUCE-RATIONALP-+))
 (2 2 (:REWRITE REDUCE-RATIONALP-*))
 (2 2 (:REWRITE RATIONALP-MINUS-X))
 (2 2 (:META META-RATIONALP-CORRECT))
 )
(RTL::LEN-ASSOCIATES
 (378 9 (:REWRITE ZP-OPEN))
 (375 3 (:DEFINITION RTL::ASSOCIATES))
 (242 5 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (162 10 (:REWRITE RTL::PERM-MEMBER))
 (151 1 (:REWRITE RTL::MEMBER-POSITIVES))
 (148 5 (:DEFINITION MEMBER-EQUAL))
 (87 9 (:REWRITE |(equal (+ (- c) x) y)|))
 (84 2 (:DEFINITION RTL::POSITIVES))
 (77 21 (:REWRITE ACL2-NUMBERP-X))
 (76 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (60 2 (:DEFINITION REMOVE1-EQUAL))
 (59 12 (:REWRITE |(+ c (+ d x))|))
 (47 16 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (45 45 (:TYPE-PRESCRIPTION RTL::ASSOCIATE))
 (39 35 (:REWRITE DEFAULT-PLUS-2))
 (35 35 (:REWRITE DEFAULT-PLUS-1))
 (34 2 (:REWRITE |(< (+ (- c) x) y)|))
 (28 7 (:REWRITE RATIONALP-X))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (22 22 (:REWRITE NORMALIZE-ADDENDS))
 (20 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (20 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (16 16 (:REWRITE THE-FLOOR-BELOW))
 (16 16 (:REWRITE THE-FLOOR-ABOVE))
 (16 16 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (16 16 (:REWRITE DEFAULT-LESS-THAN-2))
 (16 16 (:REWRITE DEFAULT-LESS-THAN-1))
 (14 14 (:REWRITE SIMPLIFY-SUMS-<))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (14 14 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (14 14 (:REWRITE INTEGERP-<-CONSTANT))
 (14 14 (:REWRITE CONSTANT-<-INTEGERP))
 (14 14 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (14 14 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (14 14 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (14 14 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (14 14 (:REWRITE |(< c (- x))|))
 (14 14 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (14 14 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (14 14 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (14 14 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (14 14 (:REWRITE |(< (/ x) (/ y))|))
 (14 14 (:REWRITE |(< (- x) c)|))
 (14 14 (:REWRITE |(< (- x) (- y))|))
 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (12 12 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE |(< 0 (* x y))|))
 (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 REDUCE-INTEGERP-+))
 (10 10 (:REWRITE INTEGERP-MINUS-X))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (10 10 (:REWRITE |(< 0 (/ x))|))
 (10 10 (:META META-INTEGERP-CORRECT))
 (9 1 (:DEFINITION LEN))
 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:REWRITE REDUCE-RATIONALP-*))
 (7 7 (:REWRITE RATIONALP-MINUS-X))
 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:META META-RATIONALP-CORRECT))
 (3 3 (:TYPE-PRESCRIPTION RTL::RESIDUE))
 (2 2 (:TYPE-PRESCRIPTION ZP))
 (2 2 (: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 |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(+ 0 x)|))
 )
(RTL::LEN-ASSOCIATES-EVEN
 (9378 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (4983 43 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2584 8 (:LINEAR MOD-BOUNDS-1))
 (2248 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1966 6 (:LINEAR RTL::MOD-BND-1))
 (1650 18 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1215 1215 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1215 1215 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1215 1215 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1150 18 (:REWRITE MOD-X-Y-=-X . 3))
 (1052 18 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1040 64 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (945 189 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (945 189 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (888 18 (:REWRITE CANCEL-MOD-+))
 (764 64 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (736 32 (:LINEAR EXPT-X->=-X))
 (732 32 (:LINEAR EXPT->=-1-TWO))
 (732 32 (:LINEAR EXPT-<=-1-ONE))
 (705 189 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (705 189 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (656 32 (:LINEAR EXPT-X->-X))
 (656 32 (:LINEAR EXPT->-1-ONE))
 (656 32 (:LINEAR EXPT-<-1-TWO))
 (624 18 (:REWRITE MOD-X-Y-=-X . 4))
 (590 18 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (478 478 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (478 478 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (478 478 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (478 478 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (478 478 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (478 478 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (474 18 (:REWRITE MOD-ZERO . 3))
 (457 189 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (448 32 (:LINEAR EXPT->=-1-ONE))
 (376 64 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (342 18 (:REWRITE |(integerp (- x))|))
 (335 43 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (334 18 (:REWRITE MOD-ZERO . 4))
 (312 258 (:REWRITE SIMPLIFY-SUMS-<))
 (312 258 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (312 258 (:REWRITE DEFAULT-LESS-THAN-1))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (276 258 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (276 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (258 258 (:REWRITE THE-FLOOR-BELOW))
 (258 258 (:REWRITE THE-FLOOR-ABOVE))
 (258 258 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (258 258 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (258 258 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (258 258 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (258 258 (:REWRITE INTEGERP-<-CONSTANT))
 (258 258 (:REWRITE DEFAULT-LESS-THAN-2))
 (258 258 (:REWRITE CONSTANT-<-INTEGERP))
 (258 258 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (258 258 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (258 258 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (258 258 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (258 258 (:REWRITE |(< c (- x))|))
 (258 258 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (258 258 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (258 258 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (258 258 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (258 258 (:REWRITE |(< (/ x) (/ y))|))
 (258 258 (:REWRITE |(< (- x) c)|))
 (258 258 (:REWRITE |(< (- x) (- y))|))
 (241 41 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (240 18 (:REWRITE DEFAULT-MOD-RATIO))
 (240 18 (:REWRITE |(* (- x) y)|))
 (201 39 (:REWRITE DEFAULT-PLUS-2))
 (191 99 (:REWRITE DEFAULT-TIMES-1))
 (189 189 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (189 189 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (189 189 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (189 189 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (186 6 (:LINEAR RTL::MOD-BND-2))
 (178 99 (:REWRITE DEFAULT-TIMES-2))
 (138 138 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (130 130 (:REWRITE DEFAULT-EXPT-2))
 (130 130 (:REWRITE DEFAULT-EXPT-1))
 (130 130 (:REWRITE |(expt 1/c n)|))
 (130 130 (:REWRITE |(expt (- x) n)|))
 (126 18 (:REWRITE MOD-X-Y-=-X . 2))
 (126 18 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (126 18 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (120 60 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (120 22 (:REWRITE DEFAULT-MINUS))
 (111 39 (:REWRITE DEFAULT-PLUS-1))
 (108 18 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (108 18 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (108 18 (:REWRITE MOD-CANCEL-*-CONST))
 (104 8 (:REWRITE |(* y x)|))
 (100 28 (:REWRITE NORMALIZE-ADDENDS))
 (100 6 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (100 6 (:REWRITE |(+ y x)|))
 (84 4 (:LINEAR MOD-BOUNDS-3))
 (74 18 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (74 18 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (74 18 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (73 65 (:REWRITE INTEGERP-MINUS-X))
 (66 18 (:REWRITE ACL2-NUMBERP-X))
 (65 65 (:REWRITE REDUCE-INTEGERP-+))
 (65 65 (:META META-INTEGERP-CORRECT))
 (64 64 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (62 62 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (62 62 (:REWRITE DEFAULT-DIVIDE))
 (60 60 (:TYPE-PRESCRIPTION NATP))
 (60 60 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (60 60 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (60 60 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (60 60 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (52 18 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (52 18 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (52 18 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (46 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (43 43 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (43 43 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (43 43 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (43 43 (:REWRITE |(equal c (/ x))|))
 (43 43 (:REWRITE |(equal c (- x))|))
 (43 43 (:REWRITE |(equal (/ x) c)|))
 (43 43 (:REWRITE |(equal (/ x) (/ y))|))
 (43 43 (:REWRITE |(equal (- x) c)|))
 (43 43 (:REWRITE |(equal (- x) (- y))|))
 (40 8 (:LINEAR MOD-BOUNDS-2))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (38 38 (:REWRITE |(< (/ x) 0)|))
 (38 38 (:REWRITE |(< (* x y) 0)|))
 (36 18 (:REWRITE DEFAULT-MOD-1))
 (32 32 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (32 32 (:LINEAR EXPT-LINEAR-UPPER-<))
 (32 32 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (32 32 (:LINEAR EXPT-LINEAR-LOWER-<))
 (32 32 (:LINEAR EXPT->-1-TWO))
 (32 32 (:LINEAR EXPT-<=-1-TWO))
 (32 32 (:LINEAR EXPT-<-1-ONE))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (24 6 (:REWRITE RATIONALP-X))
 (24 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (23 23 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (20 20 (:REWRITE |(- (* c x))|))
 (20 2 (:REWRITE |(+ 0 x)|))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (18 18 (:REWRITE DEFAULT-MOD-2))
 (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)| . 3))
 (18 18 (:REWRITE |(mod (- x) y)| . 2))
 (18 18 (:REWRITE |(mod (- x) y)| . 1))
 (18 18 (:REWRITE |(< 0 (/ x))|))
 (18 18 (:REWRITE |(< 0 (* x y))|))
 (18 16 (:REWRITE DEFAULT-CDR))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (12 12 (:REWRITE RTL::PERM-MEMBER))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE |(equal (+ (- c) x) y)|))
 (6 6 (:META META-RATIONALP-CORRECT))
 (6 6 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (2 2 (:REWRITE |(+ x (- x))|))
 )
(RTL::TIMES-LIST-ASSOCIATES-LEMMA-1
 (54540 27 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (29377 196 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (27636 27 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (18663 120 (:REWRITE CANCEL-MOD-+))
 (13978 2330 (:REWRITE DEFAULT-TIMES-2))
 (12463 120 (:REWRITE MOD-ZERO . 3))
 (10008 120 (:REWRITE MOD-X-Y-=-X . 3))
 (9844 120 (:REWRITE MOD-X-Y-=-X . 4))
 (9837 9837 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (9837 9837 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (9837 9837 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (9254 120 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (9126 2022 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (9021 2065 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (9021 2065 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (8792 120 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (8749 121 (:REWRITE DEFAULT-MOD-RATIO))
 (8633 120 (:REWRITE |(* (- x) y)|))
 (8462 2330 (:REWRITE DEFAULT-TIMES-1))
 (7988 1502 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (7945 120 (:REWRITE MOD-ZERO . 4))
 (6335 6335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (6335 6335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (6335 6335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (6335 6335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (6335 6335 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5734 120 (:REWRITE |(integerp (- x))|))
 (3805 639 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3346 640 (:REWRITE DEFAULT-LESS-THAN-1))
 (3335 639 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3159 32 (:LINEAR MOD-BOUNDS-3))
 (2915 495 (:META META-INTEGERP-CORRECT))
 (2750 460 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (2293 2065 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (2248 196 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2071 32 (:LINEAR RTL::MOD-BND-2))
 (2065 2065 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (2065 2065 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (2065 2065 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (2022 2022 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1917 639 (:REWRITE SIMPLIFY-SUMS-<))
 (1912 7 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1868 120 (:REWRITE MOD-X-Y-=-X . 2))
 (1868 120 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1868 120 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1516 138 (:REWRITE DEFAULT-MINUS))
 (1502 1502 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1502 1502 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1274 640 (:REWRITE DEFAULT-LESS-THAN-2))
 (1272 184 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1234 120 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1234 120 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1234 120 (:REWRITE MOD-CANCEL-*-CONST))
 (864 110 (:REWRITE DEFAULT-PLUS-2))
 (768 120 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (768 120 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (768 120 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (765 121 (:REWRITE DEFAULT-MOD-1))
 (686 343 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (640 640 (:REWRITE THE-FLOOR-BELOW))
 (640 640 (:REWRITE THE-FLOOR-ABOVE))
 (639 639 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (639 639 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (639 639 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (639 639 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (639 639 (:REWRITE INTEGERP-<-CONSTANT))
 (639 639 (:REWRITE CONSTANT-<-INTEGERP))
 (639 639 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (639 639 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (639 639 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (639 639 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (639 639 (:REWRITE |(< c (- x))|))
 (639 639 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (639 639 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (639 639 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (639 639 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (639 639 (:REWRITE |(< (/ x) (/ y))|))
 (639 639 (:REWRITE |(< (- x) c)|))
 (639 639 (:REWRITE |(< (- x) (- y))|))
 (620 64 (:LINEAR MOD-BOUNDS-2))
 (594 234 (:REWRITE INTEGERP-/))
 (586 120 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (562 120 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (562 120 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (559 495 (:REWRITE INTEGERP-MINUS-X))
 (495 495 (:REWRITE REDUCE-INTEGERP-+))
 (460 460 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (460 460 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (460 460 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (433 433 (:REWRITE |(* c (* d x))|))
 (410 410 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (410 410 (:REWRITE DEFAULT-DIVIDE))
 (398 398 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (398 110 (:REWRITE DEFAULT-PLUS-1))
 (367 52 (:REWRITE NORMALIZE-ADDENDS))
 (343 343 (:TYPE-PRESCRIPTION NATP))
 (343 343 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (337 337 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (337 337 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (274 274 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (274 274 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (274 274 (:REWRITE |(< (/ x) 0)|))
 (274 274 (:REWRITE |(< (* x y) 0)|))
 (268 268 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (233 233 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (196 196 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (196 196 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (196 196 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (196 196 (:REWRITE |(equal c (/ x))|))
 (196 196 (:REWRITE |(equal c (- x))|))
 (196 196 (:REWRITE |(equal (/ x) c)|))
 (196 196 (:REWRITE |(equal (/ x) (/ y))|))
 (196 196 (:REWRITE |(equal (- x) c)|))
 (196 196 (:REWRITE |(equal (- x) (- y))|))
 (189 9 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (159 27 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (151 65 (:REWRITE |(* (if a b c) x)|))
 (127 127 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (127 127 (:REWRITE |(- (* c x))|))
 (124 124 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (124 124 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (124 124 (:REWRITE |(< 0 (/ x))|))
 (124 124 (:REWRITE |(< 0 (* x y))|))
 (121 121 (:REWRITE DEFAULT-MOD-2))
 (120 120 (:REWRITE |(mod x (- y))| . 3))
 (120 120 (:REWRITE |(mod x (- y))| . 2))
 (120 120 (:REWRITE |(mod x (- y))| . 1))
 (120 120 (:REWRITE |(mod (- x) y)| . 3))
 (120 120 (:REWRITE |(mod (- x) y)| . 2))
 (120 120 (:REWRITE |(mod (- x) y)| . 1))
 (102 102 (:REWRITE |(equal (* x y) 0)|))
 (102 102 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (101 3 (:REWRITE MOD-ZERO . 1))
 (96 1 (:REWRITE |(< (if a b c) x)|))
 (88 16 (:REWRITE |(+ 0 x)|))
 (64 64 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (48 3 (:REWRITE |(+ y (+ x z))|))
 (40 40 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (32 32 (:REWRITE |(equal (+ (- c) x) y)|))
 (32 32 (:LINEAR RTL::MOD-BND-3))
 (15 3 (:REWRITE MOD-ZERO . 2))
 (14 14 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (14 14 (:REWRITE DEFAULT-EXPT-2))
 (14 14 (:REWRITE DEFAULT-EXPT-1))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (14 14 (:REWRITE |(expt (- x) n)|))
 (12 12 (:REWRITE |(+ x (- x))|))
 (9 9 (:REWRITE |(+ c (+ d x))|))
 (7 7 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (6 3 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (6 2 (:REWRITE RTL::MOD-DISTINCT))
 (4 4 (:TYPE-PRESCRIPTION RTL::PRIMEP))
 (2 2 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(RTL::TIMES-LIST-ASSOCIATES-LEMMA-2
 (301820 30 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (293419 30 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (143878 388 (:REWRITE RTL::MOD-DOES-NOTHING))
 (98787 538 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (73501 388 (:REWRITE MOD-ZERO . 4))
 (65238 366 (:REWRITE MOD-X-Y-=-X . 3))
 (64723 366 (:REWRITE MOD-X-Y-=-X . 4))
 (64392 388 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (59958 388 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (41443 109 (:LINEAR RTL::MOD-BND-2))
 (33256 366 (:REWRITE CANCEL-MOD-+))
 (32242 6162 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (27924 6236 (:REWRITE DEFAULT-LESS-THAN-1))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (27393 27393 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (27176 6162 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (25591 3278 (:REWRITE DEFAULT-TIMES-1))
 (24347 24347 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (24347 24347 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (24347 24347 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (21524 21524 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (21524 21524 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (21524 21524 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (20644 3278 (:REWRITE DEFAULT-TIMES-2))
 (17418 6214 (:REWRITE |(< (- x) c)|))
 (16294 6162 (:REWRITE SIMPLIFY-SUMS-<))
 (15704 388 (:REWRITE DEFAULT-MOD-RATIO))
 (14755 2395 (:LINEAR EXPT-<=-1-ONE))
 (14343 2395 (:LINEAR EXPT->=-1-TWO))
 (14343 2395 (:LINEAR EXPT->-1-TWO))
 (14343 2395 (:LINEAR EXPT-<-1-ONE))
 (14135 2827 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (13551 2827 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (13107 2395 (:LINEAR EXPT-X->=-X))
 (13107 2395 (:LINEAR EXPT->=-1-ONE))
 (13107 2395 (:LINEAR EXPT-<=-1-TWO))
 (12695 2395 (:LINEAR EXPT-X->-X))
 (12695 2395 (:LINEAR EXPT->-1-ONE))
 (12695 2395 (:LINEAR EXPT-<-1-TWO))
 (11975 2827 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (11975 2827 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (11762 6236 (:REWRITE DEFAULT-LESS-THAN-2))
 (11288 366 (:REWRITE MOD-X-Y-=-X . 2))
 (11288 366 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (11288 366 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (11155 844 (:REWRITE DEFAULT-PLUS-2))
 (10435 6236 (:REWRITE |(< c (- x))|))
 (10427 591 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (7803 6236 (:REWRITE |(< (- x) (- y))|))
 (7006 388 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (7006 388 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (6644 844 (:REWRITE DEFAULT-PLUS-1))
 (6559 366 (:REWRITE MOD-CANCEL-*-CONST))
 (6536 104 (:LINEAR MOD-BOUNDS-3))
 (6445 616 (:REWRITE |(equal (- x) c)|))
 (6236 6236 (:REWRITE THE-FLOOR-BELOW))
 (6236 6236 (:REWRITE THE-FLOOR-ABOVE))
 (6236 6236 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (6236 6236 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (6236 6236 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (6236 6236 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (6236 6236 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (6236 6236 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (6236 6236 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (6236 6236 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (6236 6236 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (6236 6236 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (6236 6236 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (6236 6236 (:REWRITE |(< (/ x) (/ y))|))
 (6162 6162 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6162 6162 (:REWRITE INTEGERP-<-CONSTANT))
 (6162 6162 (:REWRITE CONSTANT-<-INTEGERP))
 (5546 366 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (5524 344 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (5524 344 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5454 388 (:REWRITE DEFAULT-MOD-1))
 (5429 618 (:REWRITE DEFAULT-MINUS))
 (4790 4790 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (4790 4790 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (4790 4790 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (4790 4790 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (3888 208 (:LINEAR MOD-BOUNDS-2))
 (3195 2827 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (2914 2914 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2827 2827 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (2827 2827 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (2827 2827 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (2827 2827 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (2395 2395 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (2395 2395 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2395 2395 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (2395 2395 (:LINEAR EXPT-LINEAR-LOWER-<))
 (2295 123 (:REWRITE |(* (* x y) z)|))
 (2181 318 (:REWRITE |(equal (expt x n) 0)|))
 (1852 42 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (1680 1680 (:REWRITE |(< 0 (/ x))|))
 (1680 1680 (:REWRITE |(< 0 (* x y))|))
 (1658 1658 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1658 1658 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1505 616 (:REWRITE |(equal (- x) (- y))|))
 (1504 1504 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1379 366 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1304 86 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1285 1285 (:REWRITE |(< (/ x) 0)|))
 (1285 1285 (:REWRITE |(< (* x y) 0)|))
 (1282 1282 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1282 1282 (:REWRITE DEFAULT-DIVIDE))
 (1264 40 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (1233 1233 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1233 1233 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1092 36 (:REWRITE ZP-OPEN))
 (1080 540 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1036 204 (:REWRITE |(equal (+ (- c) x) y)|))
 (932 344 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (932 344 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (648 648 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (648 648 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (616 616 (:REWRITE |(equal c (/ x))|))
 (616 616 (:REWRITE |(equal c (- x))|))
 (616 616 (:REWRITE |(equal (/ x) c)|))
 (616 616 (:REWRITE |(equal (/ x) (/ y))|))
 (591 591 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (540 540 (:TYPE-PRESCRIPTION NATP))
 (540 540 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (540 540 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (540 540 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (540 540 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (510 5 (:REWRITE |(equal (mod a n) (mod b n))|))
 (440 120 (:REWRITE ACL2-NUMBERP-X))
 (426 426 (:REWRITE |(- (* c x))|))
 (405 405 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (388 388 (:REWRITE DEFAULT-MOD-2))
 (366 366 (:REWRITE |(mod x (- y))| . 3))
 (366 366 (:REWRITE |(mod x (- y))| . 2))
 (366 366 (:REWRITE |(mod x (- y))| . 1))
 (366 366 (:REWRITE |(mod (- x) y)| . 3))
 (366 366 (:REWRITE |(mod (- x) y)| . 2))
 (334 334 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (328 198 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (319 319 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (314 279 (:META META-INTEGERP-CORRECT))
 (299 279 (:REWRITE INTEGERP-MINUS-X))
 (279 279 (:REWRITE REDUCE-INTEGERP-+))
 (198 198 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (198 198 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (198 198 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (198 9 (:DEFINITION RTL::TIMES-LIST))
 (183 4 (:REWRITE MOD-ZERO . 1))
 (160 40 (:REWRITE RATIONALP-X))
 (126 126 (:REWRITE |(* c (* d x))|))
 (109 109 (:LINEAR RTL::MOD-BND-3))
 (92 92 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (92 92 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (81 9 (:REWRITE |(* (if a b c) x)|))
 (80 80 (:REWRITE RTL::PERM-MEMBER))
 (76 68 (:REWRITE DEFAULT-CDR))
 (70 10 (:REWRITE DEFAULT-EXPT-2))
 (49 49 (:REWRITE DEFAULT-CAR))
 (45 30 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (44 11 (:REWRITE |(+ x x)|))
 (40 40 (:REWRITE REDUCE-RATIONALP-+))
 (40 40 (:REWRITE REDUCE-RATIONALP-*))
 (40 40 (:REWRITE RATIONALP-MINUS-X))
 (40 40 (:META META-RATIONALP-CORRECT))
 (36 9 (:DEFINITION IFIX))
 (34 34 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (32 32 (:TYPE-PRESCRIPTION RTL::RESIDUE))
 (32 32 (:REWRITE |(< y (+ (- c) x))|))
 (32 32 (:REWRITE |(< x (+ c/d y))|))
 (28 4 (:REWRITE MOD-ZERO . 2))
 (26 26 (:REWRITE FOLD-CONSTS-IN-+))
 (18 18 (:REWRITE RTL::TIMES-LIST-EQUAL-FACT))
 (15 15 (:REWRITE |(equal (* x y) 0)|))
 (15 15 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (10 10 (:REWRITE DEFAULT-EXPT-1))
 (10 10 (:REWRITE |(expt 1/c n)|))
 (10 10 (:REWRITE |(expt (- x) n)|))
 (9 9 (:REWRITE |(* 0 x)|))
 (5 5 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (5 5 (:REWRITE |(expt c (* d n))|))
 )
(RTL::TIMES-LIST-ASSOCIATES-LEMMA-3
 (374537 14 (:REWRITE RTL::TIMES-LIST-ASSOCIATES-LEMMA-2))
 (72027 217 (:REWRITE RTL::MOD-DOES-NOTHING))
 (65830 32 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (55016 3706 (:REWRITE |(< (- x) c)|))
 (53446 217 (:REWRITE MOD-ZERO . 4))
 (48685 217 (:REWRITE MOD-X-Y-=-X . 3))
 (46915 217 (:REWRITE MOD-X-Y-=-X . 4))
 (45887 217 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (37554 346 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (31973 59 (:LINEAR RTL::MOD-BND-2))
 (31527 217 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (31283 553 (:REWRITE |(* (- x) y)|))
 (30962 32 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (26727 217 (:REWRITE CANCEL-MOD-+))
 (26234 217 (:REWRITE MOD-ZERO . 3))
 (25487 441 (:REWRITE |(integerp (- x))|))
 (24062 444 (:REWRITE |(equal (- x) c)|))
 (23110 3804 (:REWRITE |(< c (- x))|))
 (22351 2783 (:REWRITE DEFAULT-TIMES-1))
 (21875 217 (:REWRITE |(mod (- x) y)| . 3))
 (21522 21522 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (21522 21522 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (21522 21522 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (19915 217 (:REWRITE |(mod (- x) y)| . 2))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (19865 19865 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (18452 1013 (:REWRITE DEFAULT-MINUS))
 (16612 3482 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (16076 3860 (:REWRITE DEFAULT-LESS-THAN-1))
 (15117 2783 (:REWRITE DEFAULT-TIMES-2))
 (14805 217 (:REWRITE DEFAULT-MOD-RATIO))
 (14130 3482 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (10554 10554 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (10554 10554 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (10554 10554 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (10524 3804 (:REWRITE |(< (- x) (- y))|))
 (9926 3860 (:REWRITE DEFAULT-LESS-THAN-2))
 (8451 1641 (:LINEAR EXPT-<=-1-ONE))
 (8446 3482 (:REWRITE SIMPLIFY-SUMS-<))
 (8224 1641 (:LINEAR EXPT->=-1-TWO))
 (8224 1641 (:LINEAR EXPT->-1-TWO))
 (8224 1641 (:LINEAR EXPT-<-1-ONE))
 (7543 1641 (:LINEAR EXPT-X->=-X))
 (7543 1641 (:LINEAR EXPT->=-1-ONE))
 (7543 1641 (:LINEAR EXPT-<=-1-TWO))
 (7434 434 (:REWRITE |(- (- x))|))
 (7394 56 (:LINEAR MOD-BOUNDS-3))
 (7316 1641 (:LINEAR EXPT-X->-X))
 (7316 1641 (:LINEAR EXPT->-1-ONE))
 (7316 1641 (:LINEAR EXPT-<-1-TWO))
 (6515 1303 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (6123 1303 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (6051 217 (:REWRITE MOD-X-Y-=-X . 2))
 (6051 217 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (6051 217 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (5596 3860 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5223 1303 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5223 1303 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (5033 346 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (4375 20 (:REWRITE |(equal (mod a n) (mod b n))|))
 (3860 3860 (:REWRITE THE-FLOOR-BELOW))
 (3860 3860 (:REWRITE THE-FLOOR-ABOVE))
 (3860 3860 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3860 3860 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3804 3804 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3804 3804 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3804 3804 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3804 3804 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3804 3804 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3804 3804 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3804 3804 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3804 3804 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3804 3804 (:REWRITE |(< (/ x) (/ y))|))
 (3568 217 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (3568 217 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (3563 217 (:REWRITE MOD-CANCEL-*-CONST))
 (3482 3482 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3482 3482 (:REWRITE INTEGERP-<-CONSTANT))
 (3482 3482 (:REWRITE CONSTANT-<-INTEGERP))
 (3282 3282 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (3282 3282 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (3282 3282 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (3282 3282 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (3051 217 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (3051 217 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (3051 217 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2926 74 (:REWRITE ZP-OPEN))
 (2830 47 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (2700 217 (:REWRITE DEFAULT-MOD-1))
 (2186 340 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2058 109 (:REWRITE |(* (* x y) z)|))
 (2012 444 (:REWRITE |(equal (- x) (- y))|))
 (2000 112 (:LINEAR MOD-BOUNDS-2))
 (1688 1688 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1641 1641 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1641 1641 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1641 1641 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (1641 1641 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1546 150 (:REWRITE |(equal (+ (- c) x) y)|))
 (1443 1303 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1303 1303 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1303 1303 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1303 1303 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1303 1303 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1250 565 (:REWRITE DEFAULT-PLUS-2))
 (1189 1189 (:REWRITE |(< 0 (* x y))|))
 (1149 1149 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1133 1133 (:REWRITE |(< 0 (/ x))|))
 (1063 154 (:REWRITE |(equal (expt x n) 0)|))
 (1035 1035 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1035 1035 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (942 942 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (942 942 (:REWRITE DEFAULT-DIVIDE))
 (846 774 (:REWRITE INTEGERP-MINUS-X))
 (808 808 (:REWRITE |(< (/ x) 0)|))
 (808 808 (:REWRITE |(< (* x y) 0)|))
 (806 774 (:META META-INTEGERP-CORRECT))
 (774 774 (:REWRITE REDUCE-INTEGERP-+))
 (734 217 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (734 217 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (734 217 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (722 565 (:REWRITE DEFAULT-PLUS-1))
 (646 323 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (584 584 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (584 584 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (559 559 (:REWRITE |(- (* c x))|))
 (545 169 (:REWRITE ACL2-NUMBERP-X))
 (488 488 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (488 488 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (444 444 (:REWRITE |(equal c (/ x))|))
 (444 444 (:REWRITE |(equal c (- x))|))
 (444 444 (:REWRITE |(equal (/ x) c)|))
 (444 444 (:REWRITE |(equal (/ x) (/ y))|))
 (440 20 (:DEFINITION RTL::TIMES-LIST))
 (355 292 (:REWRITE NORMALIZE-ADDENDS))
 (346 346 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (323 323 (:TYPE-PRESCRIPTION NATP))
 (323 323 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (323 323 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (323 323 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (323 323 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (292 168 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (286 286 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (217 217 (:REWRITE DEFAULT-MOD-2))
 (217 217 (:REWRITE |(mod x (- y))| . 3))
 (217 217 (:REWRITE |(mod x (- y))| . 2))
 (217 217 (:REWRITE |(mod x (- y))| . 1))
 (217 217 (:REWRITE |(mod (- x) y)| . 1))
 (212 212 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (188 47 (:REWRITE RATIONALP-X))
 (180 20 (:REWRITE |(* (if a b c) x)|))
 (173 173 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (168 168 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (168 168 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (168 168 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (151 16 (:REWRITE |(+ y x)|))
 (145 32 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (133 19 (:REWRITE DEFAULT-EXPT-2))
 (111 111 (:REWRITE |(* c (* d x))|))
 (94 94 (:REWRITE RTL::PERM-MEMBER))
 (91 89 (:REWRITE DEFAULT-CDR))
 (80 20 (:DEFINITION IFIX))
 (72 72 (:REWRITE |(< x (+ c/d y))|))
 (67 67 (:REWRITE DEFAULT-CAR))
 (65 62 (:REWRITE |(+ 0 x)|))
 (59 59 (:LINEAR RTL::MOD-BND-3))
 (47 47 (:REWRITE REDUCE-RATIONALP-+))
 (47 47 (:REWRITE REDUCE-RATIONALP-*))
 (47 47 (:REWRITE RATIONALP-MINUS-X))
 (47 47 (:META META-RATIONALP-CORRECT))
 (44 44 (:TYPE-PRESCRIPTION RTL::RESIDUE))
 (40 40 (:REWRITE RTL::TIMES-LIST-EQUAL-FACT))
 (36 6 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (34 34 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (34 34 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (32 32 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (20 20 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (20 20 (:REWRITE |(* 0 x)|))
 (19 19 (:REWRITE DEFAULT-EXPT-1))
 (19 19 (:REWRITE |(expt 1/c n)|))
 (19 19 (:REWRITE |(expt (- x) n)|))
 (17 17 (:REWRITE |(expt c (* d n))|))
 (16 16 (:REWRITE |(< y (+ (- c) x))|))
 (14 14 (:REWRITE |(equal (* x y) 0)|))
 (14 14 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (12 12 (:DEFINITION FIX))
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:REWRITE |(+ x (- x))|))
 )
(RTL::FIRST-POWER
 (62 2 (:LINEAR EXPT-<=-1-ONE))
 (60 2 (:LINEAR EXPT->=-1-TWO))
 (60 2 (:LINEAR EXPT->-1-TWO))
 (60 2 (:LINEAR EXPT-<-1-ONE))
 (54 2 (:LINEAR EXPT-X->=-X))
 (54 2 (:LINEAR EXPT->=-1-ONE))
 (54 2 (:LINEAR EXPT-<=-1-TWO))
 (52 2 (:LINEAR EXPT-X->-X))
 (52 2 (:LINEAR EXPT->-1-ONE))
 (52 2 (:LINEAR EXPT-<-1-TWO))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (25 25 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (20 20 (:REWRITE THE-FLOOR-BELOW))
 (20 20 (:REWRITE THE-FLOOR-ABOVE))
 (20 20 (:REWRITE SIMPLIFY-SUMS-<))
 (20 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (20 20 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (20 20 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (20 20 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (20 20 (:REWRITE INTEGERP-<-CONSTANT))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-2))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-1))
 (20 20 (:REWRITE CONSTANT-<-INTEGERP))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (- x))|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) (/ y))|))
 (20 20 (:REWRITE |(< (- x) c)|))
 (20 20 (:REWRITE |(< (- x) (- y))|))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (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 (: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 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (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-LINEAR-UPPER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE DEFAULT-EXPT-2))
 (1 1 (:REWRITE DEFAULT-EXPT-1))
 (1 1 (:REWRITE |(expt 1/c n)|))
 (1 1 (:REWRITE |(expt (- x) n)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(RTL::HACK-1
 (62 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (58 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (58 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (58 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (58 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (58 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (22 2 (:REWRITE DEFAULT-TIMES-2))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (3 3 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:REWRITE DEFAULT-PLUS-1))
 (3 3 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE DEFAULT-EXPT-1))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (3 2 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (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 (:META META-INTEGERP-CORRECT))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (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-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-SUMS-<))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(RTL::HACK-2
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (105 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (88 8 (:REWRITE DEFAULT-TIMES-2))
 (12 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11 11 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (11 8 (:REWRITE DEFAULT-TIMES-1))
 (4 4 (:REWRITE DEFAULT-EXPT-2))
 (4 4 (:REWRITE DEFAULT-EXPT-1))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (4 2 (:REWRITE COLLECT-*-PROBLEM-FINDER))
 (4 1 (:REWRITE RATIONALP-X))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:META META-INTEGERP-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION FMT-TO-COMMENT-WINDOW))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE |(* c (expt d n))|))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (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-SUMS-<))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(* c (* d x))|))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(RTL::HACK-3
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (42 42 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (42 42 (: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))
 )
(RTL::TIMES-LIST-ASSOCIATES
 (15124 14 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (11594 161 (:REWRITE MOD-ZERO . 4))
 (11208 147 (:REWRITE MOD-X-Y-=-X . 3))
 (11017 162 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (10583 147 (:REWRITE MOD-X-Y-=-X . 4))
 (10348 275 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9480 147 (:REWRITE CANCEL-MOD-+))
 (8384 8384 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (8384 8384 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (8384 8384 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (7981 1621 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (6765 1621 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5493 1621 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (5471 14 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (4246 1339 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4213 4213 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (4213 4213 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (4213 4213 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (4213 4213 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (4213 4213 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (4184 1359 (:REWRITE |(< (- x) c)|))
 (4166 1243 (:REWRITE DEFAULT-TIMES-1))
 (4113 4113 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (4113 4113 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (4113 4113 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (4078 164 (:REWRITE DEFAULT-MOD-RATIO))
 (3739 3739 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (3600 1339 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3459 1243 (:REWRITE DEFAULT-TIMES-2))
 (2934 275 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2633 1339 (:REWRITE SIMPLIFY-SUMS-<))
 (2589 1368 (:REWRITE |(< c (- x))|))
 (2386 276 (:REWRITE DEFAULT-MINUS))
 (2202 290 (:REWRITE |(equal (- x) c)|))
 (2132 292 (:LINEAR EXPT-<=-1-ONE))
 (2094 292 (:LINEAR EXPT->=-1-TWO))
 (2082 35 (:LINEAR RTL::MOD-BND-2))
 (2057 1373 (:REWRITE DEFAULT-LESS-THAN-2))
 (1984 292 (:LINEAR EXPT-X->=-X))
 (1866 292 (:LINEAR EXPT-X->-X))
 (1866 292 (:LINEAR EXPT->-1-ONE))
 (1866 292 (:LINEAR EXPT-<-1-TWO))
 (1865 1621 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (1834 1368 (:REWRITE |(< (- x) (- y))|))
 (1800 266 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1793 147 (:REWRITE MOD-X-Y-=-X . 2))
 (1793 147 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (1793 147 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (1696 292 (:LINEAR EXPT->=-1-ONE))
 (1621 1621 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1621 1621 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1621 1621 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1590 1590 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1560 584 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1444 162 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1444 162 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1394 292 (:LINEAR EXPT->-1-TWO))
 (1394 292 (:LINEAR EXPT-<-1-ONE))
 (1373 1373 (:REWRITE THE-FLOOR-BELOW))
 (1373 1373 (:REWRITE THE-FLOOR-ABOVE))
 (1368 1368 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1368 1368 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1368 1368 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1368 1368 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1368 1368 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1368 1368 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1368 1368 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1368 1368 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1368 1368 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1368 1368 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1368 1368 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1368 1368 (:REWRITE |(< (/ x) (/ y))|))
 (1339 1339 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1339 1339 (:REWRITE INTEGERP-<-CONSTANT))
 (1339 1339 (:REWRITE CONSTANT-<-INTEGERP))
 (1284 584 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1280 292 (:LINEAR EXPT-<=-1-TWO))
 (1244 622 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1226 214 (:REWRITE DEFAULT-PLUS-2))
 (1181 147 (:REWRITE MOD-CANCEL-*-CONST))
 (948 147 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (902 30 (:LINEAR MOD-BOUNDS-3))
 (896 584 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (873 164 (:REWRITE DEFAULT-MOD-1))
 (802 135 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (802 135 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (798 2 (:REWRITE |(< (if a b c) x)|))
 (715 715 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (622 622 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (622 622 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (622 622 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (622 622 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (584 584 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (524 30 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (504 504 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (504 504 (:REWRITE DEFAULT-DIVIDE))
 (453 147 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (429 101 (:REWRITE ACL2-NUMBERP-X))
 (422 34 (:REWRITE |(equal (expt x n) 0)|))
 (421 135 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (421 135 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (412 290 (:REWRITE |(equal (- x) (- y))|))
 (412 60 (:LINEAR MOD-BOUNDS-2))
 (385 377 (:REWRITE INTEGERP-MINUS-X))
 (377 377 (:REWRITE REDUCE-INTEGERP-+))
 (377 377 (:META META-INTEGERP-CORRECT))
 (377 3 (:REWRITE |(equal (mod a n) (mod b n))|))
 (374 374 (:REWRITE |(< (/ x) 0)|))
 (374 374 (:REWRITE |(< (* x y) 0)|))
 (354 354 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (354 354 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (343 160 (:REWRITE NORMALIZE-ADDENDS))
 (315 214 (:REWRITE DEFAULT-PLUS-1))
 (301 292 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (292 292 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (292 292 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (292 292 (:LINEAR EXPT-LINEAR-UPPER-<))
 (292 292 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (292 292 (:LINEAR EXPT-LINEAR-LOWER-<))
 (290 290 (:REWRITE |(equal c (/ x))|))
 (290 290 (:REWRITE |(equal c (- x))|))
 (290 290 (:REWRITE |(equal (/ x) c)|))
 (290 290 (:REWRITE |(equal (/ x) (/ y))|))
 (278 278 (:REWRITE |(< 0 (/ x))|))
 (278 278 (:REWRITE |(< 0 (* x y))|))
 (275 275 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (274 21 (:REWRITE |(* (if a b c) x)|))
 (269 269 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (269 269 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (204 23 (:REWRITE |(+ y x)|))
 (176 176 (:REWRITE |(- (* c x))|))
 (164 164 (:REWRITE DEFAULT-MOD-2))
 (164 41 (:REWRITE RATIONALP-X))
 (161 161 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (155 155 (:REWRITE DEFAULT-EXPT-1))
 (155 155 (:REWRITE |(expt 1/c n)|))
 (155 155 (:REWRITE |(expt (- x) n)|))
 (148 148 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (147 147 (:REWRITE |(mod x (- y))| . 3))
 (147 147 (:REWRITE |(mod x (- y))| . 2))
 (147 147 (:REWRITE |(mod x (- y))| . 1))
 (146 146 (:REWRITE |(mod (- x) y)| . 2))
 (119 101 (:REWRITE DEFAULT-CDR))
 (102 10 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (76 76 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (76 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (70 70 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (65 59 (:REWRITE DEFAULT-CAR))
 (60 60 (:REWRITE RTL::PERM-MEMBER))
 (56 56 (:REWRITE RTL::TIMES-LIST-EQUAL-FACT))
 (53 3 (:REWRITE |(+ y (+ x z))|))
 (41 41 (:REWRITE REDUCE-RATIONALP-+))
 (41 41 (:REWRITE REDUCE-RATIONALP-*))
 (41 41 (:REWRITE RATIONALP-MINUS-X))
 (41 41 (:META META-RATIONALP-CORRECT))
 (40 14 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (36 10 (:REWRITE |(+ 0 x)|))
 (35 35 (:LINEAR RTL::MOD-BND-3))
 (19 19 (:REWRITE |(* 0 x)|))
 (16 16 (:REWRITE |(expt c (* d n))|))
 (14 14 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (12 12 (:REWRITE |(equal x (if a b c))|))
 (12 12 (:REWRITE |(equal (if a b c) x)|))
 (11 11 (:REWRITE |(+ x (- x))|))
 (9 9 (:TYPE-PRESCRIPTION ABS))
 (8 8 (:REWRITE |(equal (* x y) 0)|))
 (7 2 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (4 4 (:REWRITE |(+ x (if a b c))|))
 (4 2 (:REWRITE |(* -1 x)|))
 (4 1 (:REWRITE |(+ x x)|))
 (3 3 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (3 3 (:REWRITE |(* c (* d x))|))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 )
(RTL::EULER-LEMMA
 (1940 388 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1811 20 (:REWRITE MOD-ZERO . 4))
 (1801 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1713 1713 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1713 1713 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1713 1713 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1640 18 (:REWRITE MOD-X-Y-=-X . 3))
 (1614 22 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1491 26 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1328 388 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1280 388 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1280 388 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1234 18 (:REWRITE MOD-X-Y-=-X . 4))
 (1195 18 (:REWRITE CANCEL-MOD-+))
 (1011 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1008 1008 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (925 188 (:REWRITE |(< (- x) c)|))
 (804 2 (:REWRITE |(< (if a b c) x)|))
 (788 388 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (714 24 (:REWRITE DEFAULT-MOD-RATIO))
 (675 207 (:REWRITE DEFAULT-TIMES-1))
 (638 26 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (637 183 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (596 192 (:REWRITE DEFAULT-LESS-THAN-1))
 (557 29 (:REWRITE |(equal (- x) c)|))
 (539 207 (:REWRITE DEFAULT-TIMES-2))
 (525 183 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (498 4 (:DEFINITION RTL::ASSOCIATES))
 (486 190 (:REWRITE |(< c (- x))|))
 (446 52 (:REWRITE DEFAULT-MINUS))
 (422 211 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (404 25 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (388 388 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (388 388 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (388 388 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (388 388 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (375 375 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (375 375 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (375 375 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (367 67 (:LINEAR EXPT-<=-1-ONE))
 (357 67 (:LINEAR EXPT->=-1-TWO))
 (357 67 (:LINEAR EXPT->-1-TWO))
 (357 67 (:LINEAR EXPT-<-1-ONE))
 (327 67 (:LINEAR EXPT-X->=-X))
 (327 67 (:LINEAR EXPT->=-1-ONE))
 (327 67 (:LINEAR EXPT-<=-1-TWO))
 (317 67 (:LINEAR EXPT-X->-X))
 (317 67 (:LINEAR EXPT->-1-ONE))
 (317 67 (:LINEAR EXPT-<-1-TWO))
 (310 190 (:REWRITE |(< (- x) (- y))|))
 (302 192 (:REWRITE DEFAULT-LESS-THAN-2))
 (295 91 (:REWRITE DEFAULT-PLUS-2))
 (272 8 (:REWRITE ZP-OPEN))
 (256 4 (:DEFINITION RTL::FACT))
 (246 18 (:REWRITE MOD-X-Y-=-X . 2))
 (246 18 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (246 18 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (211 211 (:TYPE-PRESCRIPTION NATP))
 (211 211 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (211 211 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (211 211 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (204 22 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (204 22 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (192 192 (:REWRITE THE-FLOOR-BELOW))
 (192 192 (:REWRITE THE-FLOOR-ABOVE))
 (190 190 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (190 190 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (190 190 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (190 190 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (190 190 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (190 190 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (190 190 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (190 190 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (190 190 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (190 190 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (190 190 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (190 190 (:REWRITE |(< (/ x) (/ y))|))
 (183 183 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (183 183 (:REWRITE INTEGERP-<-CONSTANT))
 (183 183 (:REWRITE CONSTANT-<-INTEGERP))
 (168 18 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (168 18 (:REWRITE MOD-CANCEL-*-CONST))
 (144 24 (:REWRITE DEFAULT-MOD-1))
 (144 4 (:REWRITE RTL::MEMBER-SELF-ASSOCIATE))
 (136 16 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (136 16 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (134 134 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (134 134 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (134 134 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (134 134 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (120 4 (:DEFINITION MEMBER-EQUAL))
 (119 15 (:REWRITE |(equal (+ (- c) x) y)|))
 (100 91 (:REWRITE DEFAULT-PLUS-1))
 (88 88 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (81 81 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (81 17 (:REWRITE |(+ c (+ d x))|))
 (72 4 (:REWRITE |(* (+ x y) z)|))
 (67 67 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (67 67 (:LINEAR EXPT-LINEAR-UPPER-<))
 (67 67 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (67 67 (:LINEAR EXPT-LINEAR-LOWER-<))
 (66 66 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (66 66 (:REWRITE DEFAULT-DIVIDE))
 (63 63 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (60 60 (:TYPE-PRESCRIPTION RTL::ASSOCIATE))
 (59 29 (:REWRITE |(equal (- x) (- y))|))
 (58 2 (:LINEAR MOD-BOUNDS-3))
 (50 50 (:REWRITE REDUCE-INTEGERP-+))
 (50 50 (:REWRITE INTEGERP-MINUS-X))
 (50 50 (:META META-INTEGERP-CORRECT))
 (49 49 (:REWRITE |(< 0 (/ x))|))
 (49 49 (:REWRITE |(< 0 (* x y))|))
 (47 47 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (47 47 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (44 12 (:REWRITE ACL2-NUMBERP-X))
 (41 41 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (33 33 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (33 33 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (29 29 (:REWRITE |(equal c (/ x))|))
 (29 29 (:REWRITE |(equal c (- x))|))
 (29 29 (:REWRITE |(equal (/ x) c)|))
 (29 29 (:REWRITE |(equal (/ x) (/ y))|))
 (27 27 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (26 26 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (26 26 (:REWRITE |(< (/ x) 0)|))
 (26 26 (:REWRITE |(< (* x y) 0)|))
 (25 25 (:REWRITE |(- (* c x))|))
 (24 24 (:REWRITE DEFAULT-MOD-2))
 (24 4 (:LINEAR MOD-BOUNDS-2))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (18 18 (:REWRITE MOD-CANCEL-*-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)| . 3))
 (18 18 (:REWRITE |(mod (- x) y)| . 2))
 (18 7 (:REWRITE |(* -1 x)|))
 (16 16 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (16 16 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (16 4 (:REWRITE RATIONALP-X))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (8 8 (:REWRITE RTL::PERM-MEMBER))
 (8 8 (:REWRITE |(equal (expt x n) 0)|))
 (8 8 (:REWRITE |(< y (+ (- c) x))|))
 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (7 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE DEFAULT-EXPT-1))
 (5 5 (:REWRITE |(expt 1/c n)|))
 (5 5 (:REWRITE |(expt (- x) n)|))
 (4 4 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (4 4 (:REWRITE RTL::TIMES-LIST-EQUAL-FACT))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:META META-RATIONALP-CORRECT))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE |(equal x (if a b c))|))
 (3 3 (:REWRITE |(equal (if a b c) x)|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (2 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2 1 (:REWRITE |(+ 0 x)|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE |(+ x (if a b c))|))
 (1 1 (:REWRITE |(* 1 x)|))
 )
(RTL::FIND-ROOT-1
 (94700 45 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (48886 556 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (41165 45 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (26799 280 (:REWRITE RTL::MOD-DOES-NOTHING))
 (13400 126 (:LINEAR MOD-BOUNDS-1))
 (12837 222 (:REWRITE MOD-X-Y-=-X . 3))
 (8632 222 (:REWRITE MOD-ZERO . 3))
 (7882 7882 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (7882 7882 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (7882 7882 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (7670 126 (:LINEAR MOD-BOUNDS-2))
 (6531 6531 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (6531 6531 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (6531 6531 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (6531 6531 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (6531 6531 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (6531 6531 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5645 1129 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (5581 1516 (:REWRITE DEFAULT-TIMES-2))
 (5083 1516 (:REWRITE DEFAULT-TIMES-1))
 (5061 1129 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (5061 1129 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5061 1129 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5061 1129 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4587 222 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (4587 222 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4587 222 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (4587 222 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (4062 211 (:LINEAR EXPT-X->-X))
 (4062 211 (:LINEAR EXPT->-1-ONE))
 (3929 211 (:LINEAR EXPT->=-1-TWO))
 (3886 211 (:LINEAR EXPT-<-1-TWO))
 (3594 222 (:REWRITE MOD-X-Y-=-X . 4))
 (3568 134 (:REWRITE RTL::HACK-3))
 (3440 355 (:REWRITE RATIONALP-X))
 (3366 222 (:REWRITE MOD-X-Y-=-X . 2))
 (3366 222 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (3366 222 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (3211 63 (:LINEAR MOD-BOUNDS-3))
 (3173 1733 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3173 1733 (:REWRITE DEFAULT-LESS-THAN-1))
 (3110 1733 (:REWRITE SIMPLIFY-SUMS-<))
 (3041 556 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2766 222 (:REWRITE MOD-ZERO . 4))
 (2525 1733 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2307 222 (:REWRITE CANCEL-MOD-+))
 (2258 1129 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2106 541 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1763 1763 (:REWRITE THE-FLOOR-BELOW))
 (1763 1763 (:REWRITE THE-FLOOR-ABOVE))
 (1733 1733 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1733 1733 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1733 1733 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1733 1733 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1733 1733 (:REWRITE INTEGERP-<-CONSTANT))
 (1733 1733 (:REWRITE CONSTANT-<-INTEGERP))
 (1733 1733 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1733 1733 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1733 1733 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1733 1733 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1733 1733 (:REWRITE |(< c (- x))|))
 (1733 1733 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1733 1733 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1733 1733 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1733 1733 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1733 1733 (:REWRITE |(< (/ x) (/ y))|))
 (1733 1733 (:REWRITE |(< (- x) c)|))
 (1733 1733 (:REWRITE |(< (- x) (- y))|))
 (1702 222 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1702 222 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1360 20 (:REWRITE |(* x (if a b c))|))
 (1293 222 (:REWRITE MOD-CANCEL-*-CONST))
 (1262 222 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1235 120 (:REWRITE DEFAULT-PLUS-2))
 (1139 248 (:REWRITE DEFAULT-MOD-1))
 (1129 1129 (:TYPE-PRESCRIPTION NATP))
 (1129 1129 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1129 1129 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1129 1129 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1129 1129 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1129 1129 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1129 1129 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1129 1129 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (1129 1129 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (1120 120 (:REWRITE |(mod (+ 1 x) y)|))
 (997 157 (:REWRITE ACL2-NUMBERP-X))
 (879 499 (:REWRITE DEFAULT-DIVIDE))
 (723 723 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (723 723 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (723 723 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (644 579 (:REWRITE INTEGERP-MINUS-X))
 (620 5 (:REWRITE |(equal (mod a n) (mod b n))|))
 (579 579 (:REWRITE REDUCE-INTEGERP-+))
 (579 579 (:META META-INTEGERP-CORRECT))
 (570 570 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (570 570 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (570 570 (:REWRITE |(equal c (/ x))|))
 (570 570 (:REWRITE |(equal c (- x))|))
 (570 570 (:REWRITE |(equal (/ x) c)|))
 (570 570 (:REWRITE |(equal (/ x) (/ y))|))
 (570 570 (:REWRITE |(equal (- x) c)|))
 (570 570 (:REWRITE |(equal (- x) (- y))|))
 (556 556 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (546 546 (:REWRITE DEFAULT-EXPT-2))
 (546 546 (:REWRITE DEFAULT-EXPT-1))
 (546 546 (:REWRITE |(expt 1/c n)|))
 (546 546 (:REWRITE |(expt (- x) n)|))
 (486 486 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (479 479 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (460 70 (:REWRITE NORMALIZE-ADDENDS))
 (458 222 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (458 222 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (422 422 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (422 422 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (422 422 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (422 422 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (418 222 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (387 117 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (341 341 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (341 341 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (341 341 (:REWRITE |(< (/ x) 0)|))
 (341 341 (:REWRITE |(< (* x y) 0)|))
 (335 335 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (335 335 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (335 335 (:REWRITE |(< 0 (/ x))|))
 (335 335 (:REWRITE |(< 0 (* x y))|))
 (315 120 (:REWRITE DEFAULT-PLUS-1))
 (289 289 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (280 20 (:REWRITE |(+ y x)|))
 (255 255 (:REWRITE RATIONALP-MINUS-X))
 (230 10 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (225 225 (:REWRITE REDUCE-RATIONALP-+))
 (225 225 (:META META-RATIONALP-CORRECT))
 (225 45 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (222 222 (:REWRITE |(mod x (- y))| . 3))
 (222 222 (:REWRITE |(mod x (- y))| . 2))
 (222 222 (:REWRITE |(mod x (- y))| . 1))
 (222 222 (:REWRITE |(mod (- x) y)| . 3))
 (222 222 (:REWRITE |(mod (- x) y)| . 2))
 (222 222 (:REWRITE |(mod (- x) y)| . 1))
 (211 211 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (211 211 (:LINEAR EXPT-LINEAR-UPPER-<))
 (211 211 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (211 211 (:LINEAR EXPT-LINEAR-LOWER-<))
 (211 211 (:LINEAR EXPT->-1-TWO))
 (211 211 (:LINEAR EXPT-<=-1-TWO))
 (211 211 (:LINEAR EXPT-<-1-ONE))
 (141 141 (:REWRITE INTEGERP-/))
 (104 104 (:REWRITE RTL::FIRST-POWER))
 (100 10 (:REWRITE |(+ 0 x)|))
 (85 20 (:REWRITE DEFAULT-MINUS))
 (68 68 (:LINEAR RTL::MOD-BND-3))
 (60 60 (:REWRITE |(* c (* d x))|))
 (55 55 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (50 5 (:REWRITE |(+ y (+ x z))|))
 (45 45 (:REWRITE |(equal (+ (- c) x) y)|))
 (40 40 (:REWRITE |(* 0 x)|))
 (30 30 (:REWRITE |(not (equal x (/ y)))|))
 (30 30 (:REWRITE |(equal x (/ y))|))
 (30 30 (:REWRITE |(* (expt c m) (expt d n))|))
 (15 15 (:REWRITE |(+ x (- x))|))
 (10 10 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (10 10 (:REWRITE |(+ c (+ d x))|))
 (10 5 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (5 5 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (5 5 (:REWRITE |(- (* c x))|))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 )
(RTL::RESIDUE-1
 (3 3 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE SIMPLIFY-SUMS-<))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE NORMALIZE-ADDENDS))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 )
(RTL::POWER-OF-1
 (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-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))
 )
(RTL::MOD-MINUS-1
 (267 267 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (267 267 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (267 267 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (195 39 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (187 39 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (187 39 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (187 39 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (163 39 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (72 2 (:LINEAR RTL::MOD-BND-1))
 (64 8 (:REWRITE DEFAULT-MOD-RATIO))
 (40 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (40 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (40 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (39 39 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (39 39 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (39 39 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (39 39 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (34 2 (:LINEAR MOD-BOUNDS-3))
 (20 10 (:REWRITE |(* -1 x)|))
 (20 4 (:LINEAR MOD-BOUNDS-2))
 (17 12 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (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))
 (11 11 (:REWRITE DEFAULT-TIMES-2))
 (11 11 (:REWRITE DEFAULT-TIMES-1))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE DEFAULT-PLUS-2))
 (10 10 (:REWRITE DEFAULT-PLUS-1))
 (10 10 (:REWRITE DEFAULT-MINUS))
 (10 10 (:REWRITE DEFAULT-DIVIDE))
 (10 10 (:REWRITE |(* (- x) y)|))
 (10 2 (:REWRITE |(integerp (- x))|))
 (8 8 (:REWRITE DEFAULT-MOD-2))
 (8 8 (:REWRITE DEFAULT-MOD-1))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE INTEGERP-/))
 (2 2 (:META META-INTEGERP-CORRECT))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:LINEAR RTL::MOD-BND-2))
 (1 1 (:REWRITE ZP-OPEN))
 )
(RTL::WILSON
 (364 7 (:REWRITE CANCEL-MOD-+))
 (313 313 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (313 313 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (277 56 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (241 7 (:REWRITE MOD-X-Y-=-X . 3))
 (238 7 (:REWRITE RTL::MOD-DOES-NOTHING))
 (235 7 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (175 7 (:REWRITE MOD-ZERO . 3))
 (145 56 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (145 56 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (138 54 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (133 7 (:REWRITE |(integerp (- x))|))
 (113 8 (:REWRITE |(* (- x) y)|))
 (112 56 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (112 7 (:REWRITE DEFAULT-MOD-RATIO))
 (105 21 (:REWRITE |(* y x)|))
 (80 52 (:REWRITE DEFAULT-TIMES-1))
 (76 52 (:REWRITE DEFAULT-TIMES-2))
 (64 1 (:DEFINITION RTL::FACT))
 (61 33 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (56 56 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (56 56 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (56 56 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (56 56 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (56 56 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (56 7 (:REWRITE MOD-X-Y-=-X . 4))
 (54 54 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (54 54 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (49 7 (:REWRITE MOD-ZERO . 4))
 (49 7 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (49 7 (:REWRITE MOD-X-Y-=-X . 2))
 (49 7 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (49 7 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (44 8 (:REWRITE DEFAULT-MINUS))
 (42 7 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (42 7 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (42 7 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (42 7 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (42 7 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (39 20 (:REWRITE SIMPLIFY-SUMS-<))
 (39 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (39 20 (:REWRITE DEFAULT-LESS-THAN-1))
 (37 7 (:REWRITE MOD-CANCEL-*-CONST))
 (34 1 (:REWRITE ZP-OPEN))
 (33 33 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (33 33 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (33 33 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (33 33 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (29 1 (:LINEAR MOD-BOUNDS-3))
 (28 28 (:TYPE-PRESCRIPTION NATP))
 (27 20 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (23 23 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (21 21 (:REWRITE DEFAULT-DIVIDE))
 (20 20 (:REWRITE THE-FLOOR-BELOW))
 (20 20 (:REWRITE THE-FLOOR-ABOVE))
 (20 20 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (20 20 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (20 20 (:REWRITE INTEGERP-<-CONSTANT))
 (20 20 (:REWRITE DEFAULT-LESS-THAN-2))
 (20 20 (:REWRITE CONSTANT-<-INTEGERP))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (20 20 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< c (- x))|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (20 20 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (20 20 (:REWRITE |(< (/ x) (/ y))|))
 (20 20 (:REWRITE |(< (- x) c)|))
 (20 20 (:REWRITE |(< (- x) (- y))|))
 (18 1 (:REWRITE |(* (+ x y) z)|))
 (14 14 (:REWRITE REDUCE-INTEGERP-+))
 (14 14 (:REWRITE INTEGERP-MINUS-X))
 (14 14 (:META META-INTEGERP-CORRECT))
 (14 7 (:REWRITE DEFAULT-MOD-1))
 (12 2 (:LINEAR MOD-BOUNDS-2))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (7 7 (:REWRITE DEFAULT-MOD-2))
 (7 7 (:REWRITE |(mod x (- y))| . 3))
 (7 7 (:REWRITE |(mod x (- y))| . 2))
 (7 7 (:REWRITE |(mod x (- y))| . 1))
 (7 7 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (7 7 (:REWRITE |(mod (- x) y)| . 3))
 (7 7 (:REWRITE |(mod (- x) y)| . 2))
 (7 7 (:REWRITE |(mod (- x) y)| . 1))
 (7 7 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (7 7 (:REWRITE |(- (* c x))|))
 (6 5 (:REWRITE DEFAULT-PLUS-2))
 (6 5 (:REWRITE DEFAULT-PLUS-1))
 (5 1 (:REWRITE |(+ c (+ d x))|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (3 1 (:REWRITE |(* -1 x)|))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (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 2 (:LINEAR RTL::MOD-BND-3))
 (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 SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(RTL::P-1-EVEN
 (200 200 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (200 200 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (200 200 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (141 29 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (141 29 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (69 29 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (68 28 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (37 37 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (36 18 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (32 4 (:REWRITE DEFAULT-MOD-RATIO))
 (29 29 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (29 29 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (28 28 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (28 28 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (18 18 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (18 18 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (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))
 (15 15 (:REWRITE DEFAULT-TIMES-2))
 (15 15 (:REWRITE DEFAULT-TIMES-1))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4 4 (:REWRITE DEFAULT-MOD-2))
 (4 4 (:REWRITE DEFAULT-MOD-1))
 (4 4 (:REWRITE |(mod x 2)| . 2))
 (3 3 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(RTL::EULER-CRITERION
 (4706 29 (:REWRITE MOD-ZERO . 4))
 (4212 27 (:REWRITE MOD-X-Y-=-X . 3))
 (4097 29 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (4083 27 (:REWRITE MOD-X-Y-=-X . 4))
 (3797 29 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (3476 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (3422 27 (:REWRITE CANCEL-MOD-+))
 (3311 3311 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3311 3311 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2732 47 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2561 2561 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2284 458 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2037 494 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1884 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1780 505 (:REWRITE DEFAULT-LESS-THAN-1))
 (1731 494 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1728 458 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1721 293 (:REWRITE DEFAULT-TIMES-1))
 (1684 4 (:LINEAR RTL::MOD-BND-2))
 (1680 458 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1661 453 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1430 31 (:REWRITE DEFAULT-MOD-RATIO))
 (1385 500 (:REWRITE |(< (- x) c)|))
 (1337 293 (:REWRITE DEFAULT-TIMES-2))
 (1271 191 (:LINEAR EXPT-<=-1-ONE))
 (1235 191 (:LINEAR EXPT->=-1-TWO))
 (1235 191 (:LINEAR EXPT->-1-TWO))
 (1235 191 (:LINEAR EXPT-<-1-ONE))
 (1127 191 (:LINEAR EXPT-X->=-X))
 (1127 191 (:LINEAR EXPT->=-1-ONE))
 (1127 191 (:LINEAR EXPT-<=-1-TWO))
 (1125 494 (:REWRITE SIMPLIFY-SUMS-<))
 (1091 191 (:LINEAR EXPT-X->-X))
 (1091 191 (:LINEAR EXPT->-1-ONE))
 (1091 191 (:LINEAR EXPT-<-1-TWO))
 (947 503 (:REWRITE |(< c (- x))|))
 (919 47 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (833 505 (:REWRITE DEFAULT-LESS-THAN-2))
 (815 75 (:REWRITE DEFAULT-MINUS))
 (804 2 (:REWRITE |(< (if a b c) x)|))
 (741 27 (:REWRITE MOD-X-Y-=-X . 2))
 (741 27 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (741 27 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (633 503 (:REWRITE |(< (- x) (- y))|))
 (578 50 (:REWRITE |(equal (- x) c)|))
 (575 43 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (505 505 (:REWRITE THE-FLOOR-BELOW))
 (505 505 (:REWRITE THE-FLOOR-ABOVE))
 (503 503 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (503 503 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (503 503 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (503 503 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (503 503 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (503 503 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (503 503 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (503 503 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (503 503 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (503 503 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (503 503 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (503 503 (:REWRITE |(< (/ x) (/ y))|))
 (494 494 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (494 494 (:REWRITE INTEGERP-<-CONSTANT))
 (494 494 (:REWRITE CONSTANT-<-INTEGERP))
 (470 29 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (470 29 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (458 458 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (458 458 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (453 453 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (453 453 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (449 449 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (449 449 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (449 449 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (438 27 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (410 205 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (408 27 (:REWRITE MOD-CANCEL-*-CONST))
 (400 129 (:REWRITE DEFAULT-PLUS-2))
 (390 24 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (390 24 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (382 382 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (382 382 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (382 382 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (382 382 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (376 4 (:LINEAR MOD-BOUNDS-3))
 (370 31 (:REWRITE DEFAULT-MOD-1))
 (222 222 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (205 205 (:TYPE-PRESCRIPTION NATP))
 (205 205 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (205 205 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (205 205 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (192 3 (:DEFINITION RTL::FACT))
 (191 191 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (191 191 (:LINEAR EXPT-LINEAR-UPPER-<))
 (191 191 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (191 191 (:LINEAR EXPT-LINEAR-LOWER-<))
 (169 129 (:REWRITE DEFAULT-PLUS-1))
 (152 8 (:LINEAR MOD-BOUNDS-2))
 (139 139 (:REWRITE |(< 0 (/ x))|))
 (139 139 (:REWRITE |(< 0 (* x y))|))
 (136 136 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (136 136 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (125 125 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (102 3 (:REWRITE ZP-OPEN))
 (99 2 (:REWRITE |(* (if a b c) x)|))
 (92 92 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (92 92 (:REWRITE DEFAULT-DIVIDE))
 (89 89 (:REWRITE |(< (/ x) 0)|))
 (89 89 (:REWRITE |(< (* x y) 0)|))
 (83 83 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (83 83 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (80 50 (:REWRITE |(equal (- x) (- y))|))
 (79 79 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (74 20 (:REWRITE |(equal (+ (- c) x) y)|))
 (72 24 (:REWRITE |(equal (expt x n) 0)|))
 (70 70 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (61 6 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (54 54 (:REWRITE REDUCE-INTEGERP-+))
 (54 54 (:REWRITE INTEGERP-MINUS-X))
 (54 54 (:META META-INTEGERP-CORRECT))
 (54 52 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (54 3 (:REWRITE |(* (+ x y) z)|))
 (52 52 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE |(equal c (/ x))|))
 (50 50 (:REWRITE |(equal c (- x))|))
 (50 50 (:REWRITE |(equal (/ x) c)|))
 (50 50 (:REWRITE |(equal (/ x) (/ y))|))
 (47 47 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (36 36 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (34 34 (:REWRITE |(- (* c x))|))
 (31 31 (:REWRITE DEFAULT-MOD-2))
 (27 27 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (27 27 (:REWRITE |(mod x (- y))| . 3))
 (27 27 (:REWRITE |(mod x (- y))| . 2))
 (27 27 (:REWRITE |(mod x (- y))| . 1))
 (27 27 (:REWRITE |(mod (- x) y)| . 3))
 (27 27 (:REWRITE |(mod (- x) y)| . 2))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 24 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (24 24 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (22 6 (:REWRITE |(+ 0 x)|))
 (21 9 (:REWRITE |(+ c (+ d x))|))
 (18 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (11 11 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (11 11 (:REWRITE DEFAULT-EXPT-1))
 (11 11 (:REWRITE |(expt 1/c n)|))
 (11 11 (:REWRITE |(expt (- x) n)|))
 (8 2 (:REWRITE |(+ x x)|))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 (3 3 (:REWRITE |(equal x (if a b c))|))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE |(* x (- y))|))
 (1 1 (:REWRITE |(+ x (if a b c))|))
 (1 1 (:REWRITE |(* 1 x)|))
 )
(RTL::EVENP-ODDP
 (235 5 (:REWRITE RTL::MOD-DOES-NOTHING))
 (195 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (154 154 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (154 154 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (154 154 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (106 22 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (99 5 (:REWRITE DEFAULT-MOD-RATIO))
 (78 50 (:REWRITE DEFAULT-PLUS-2))
 (60 44 (:REWRITE DEFAULT-TIMES-2))
 (55 23 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (55 5 (:REWRITE |(+ y (+ x z))|))
 (54 22 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (50 50 (:REWRITE DEFAULT-PLUS-1))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (47 47 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (44 44 (:REWRITE DEFAULT-TIMES-1))
 (30 30 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (30 30 (:REWRITE NORMALIZE-ADDENDS))
 (28 28 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (26 13 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (23 23 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (22 22 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (22 22 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (22 22 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (13 13 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (13 13 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (13 13 (:TYPE-PRESCRIPTION NATP))
 (13 13 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (13 13 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (13 13 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (13 13 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE SIMPLIFY-SUMS-<))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE DEFAULT-MOD-2))
 (5 5 (:REWRITE DEFAULT-MOD-1))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (5 5 (:REWRITE |(mod x 2)| . 2))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) c)|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE |(< (+ c/d x) y)|))
 )
(RTL::EXPT-MINUS-1
 (345 69 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (339 339 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (339 339 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (339 339 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (339 339 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (69 69 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (69 69 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (47 47 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (47 47 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (41 17 (:REWRITE DEFAULT-PLUS-2))
 (32 20 (:REWRITE DEFAULT-TIMES-2))
 (20 20 (:REWRITE DEFAULT-TIMES-1))
 (17 17 (:REWRITE DEFAULT-PLUS-1))
 (13 13 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (13 13 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (7 3 (:REWRITE RTL::P-1-EVEN))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION RTL::PRIMEP))
 (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 (:REWRITE DEFAULT-EXPT-2))
 (2 2 (:REWRITE DEFAULT-EXPT-1))
 (2 2 (:LINEAR EXPT-X->=-X))
 (2 2 (:LINEAR EXPT-X->-X))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-UPPER-<))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (2 2 (:LINEAR EXPT-LINEAR-LOWER-<))
 (2 2 (:LINEAR EXPT->=-1-TWO))
 (2 2 (:LINEAR EXPT->=-1-ONE))
 (2 2 (:LINEAR EXPT->-1-TWO))
 (2 2 (:LINEAR EXPT->-1-ONE))
 (2 2 (:LINEAR EXPT-<=-1-TWO))
 (2 2 (:LINEAR EXPT-<=-1-ONE))
 (2 2 (:LINEAR EXPT-<-1-TWO))
 (2 2 (:LINEAR EXPT-<-1-ONE))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 )
(RTL::FIRST-SUPPLEMENT
 (779 779 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (779 779 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (779 779 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (707 143 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (683 143 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (411 143 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (409 141 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (299 8 (:REWRITE CANCEL-MOD-+))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (284 284 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (248 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (240 8 (:REWRITE MOD-X-Y-=-X . 3))
 (195 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (195 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (195 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (186 94 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (143 143 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (143 143 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (141 141 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (141 141 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (141 8 (:REWRITE MOD-ZERO . 3))
 (137 17 (:REWRITE |(* (- x) y)|))
 (120 104 (:REWRITE DEFAULT-TIMES-2))
 (120 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (120 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (120 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (120 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (116 104 (:REWRITE DEFAULT-TIMES-1))
 (114 9 (:REWRITE DEFAULT-MOD-RATIO))
 (94 94 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (94 94 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (94 94 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (84 15 (:REWRITE INTEGERP-MINUS-X))
 (75 31 (:REWRITE DEFAULT-PLUS-2))
 (68 68 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (60 4 (:LINEAR MOD-BOUNDS-3))
 (56 12 (:REWRITE DEFAULT-MINUS))
 (55 55 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (52 11 (:REWRITE |(- (* c x))|))
 (48 8 (:LINEAR MOD-BOUNDS-1))
 (42 34 (:REWRITE DEFAULT-LESS-THAN-1))
 (42 12 (:REWRITE REDUCE-INTEGERP-+))
 (40 8 (:REWRITE MOD-ZERO . 4))
 (40 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (40 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (40 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (40 8 (:REWRITE MOD-X-Y-=-X . 4))
 (40 8 (:REWRITE MOD-X-Y-=-X . 2))
 (40 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (40 8 (:REWRITE MOD-CANCEL-*-CONST))
 (40 8 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (40 8 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (40 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (40 8 (:LINEAR MOD-BOUNDS-2))
 (39 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (39 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (37 33 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (37 33 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (34 34 (:REWRITE THE-FLOOR-BELOW))
 (34 34 (:REWRITE THE-FLOOR-ABOVE))
 (34 34 (:REWRITE DEFAULT-LESS-THAN-2))
 (33 33 (:REWRITE SIMPLIFY-SUMS-<))
 (33 33 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (33 33 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (33 33 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (33 33 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (33 33 (:REWRITE INTEGERP-<-CONSTANT))
 (33 33 (:REWRITE CONSTANT-<-INTEGERP))
 (33 33 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (33 33 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (33 33 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (33 33 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (33 33 (:REWRITE |(< c (- x))|))
 (33 33 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (33 33 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (33 33 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (33 33 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (33 33 (:REWRITE |(< (/ x) (/ y))|))
 (33 33 (:REWRITE |(< (- x) c)|))
 (33 33 (:REWRITE |(< (- x) (- y))|))
 (33 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (31 31 (:REWRITE DEFAULT-PLUS-1))
 (27 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (27 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (27 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (27 27 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (25 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-4G))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-3G))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-2G))
 (24 24 (:TYPE-PRESCRIPTION NOT-INTEGERP-1G))
 (23 23 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (23 23 (:REWRITE NORMALIZE-ADDENDS))
 (17 17 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (13 9 (:REWRITE DEFAULT-MOD-1))
 (13 1 (:REWRITE |(* (if a b c) x)|))
 (12 12 (:META META-INTEGERP-CORRECT))
 (10 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (9 9 (:REWRITE DEFAULT-MOD-2))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (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))) rewriting-goal-literal|))
 (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 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 4 (:LINEAR RTL::MOD-BND-2))
 (8 4 (:LINEAR RTL::MOD-BND-1))
 (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))|))
 (5 1 (:REWRITE |(< (if a b c) x)|))
 (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))|))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 (4 1 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE |(equal x (if a b c))|))
 (2 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2 1 (:REWRITE |(* -1 x)|))
 (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 NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1 1 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(+ 0 x)|))
 (1 1 (:REWRITE |(* 1 x)|))
 )
