(P
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 )
(DM::PRIMEP-P)
(DM::P-NAT)
(DM::P-IS-BIG)
(DM::FP)
(DM::F+
 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (10 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (5 5 (:TYPE-PRESCRIPTION NATP))
 (5 5 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (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))
 )
(DM::F-
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 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
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 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (5 5 (:TYPE-PRESCRIPTION NATP))
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 (5 5 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (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))
 )
(DM::F*
 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (10 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (5 5 (:TYPE-PRESCRIPTION NATP))
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 (5 5 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5 5 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (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))
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 (5 5 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 )
(DM::FEXPT)
(DM::FRCP)
(DM::NATP-FRCP
 (5 1 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (5 1 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
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 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 )
(DM::F/
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 (25 5 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (10 10 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (10 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (5 5 (:TYPE-PRESCRIPTION DM::NATP-FRCP))
 (5 5 (:TYPE-PRESCRIPTION NATP))
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 (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))
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 (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))
 )
(DM::MOD*0
 (907 907 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (907 907 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (907 907 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
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 (715 307 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (715 307 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
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 (649 21 (:REWRITE MOD-X-Y-=-X . 4))
 (649 21 (:REWRITE MOD-X-Y-=-X . 3))
 (620 21 (:REWRITE MOD-ZERO . 3))
 (606 39 (:REWRITE DEFAULT-MOD-RATIO))
 (572 21 (:REWRITE RTL::MOD-DOES-NOTHING))
 (530 265 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (436 21 (:REWRITE MOD-X-Y-=-X . 2))
 (345 21 (:REWRITE MOD-ZERO . 4))
 (307 307 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (307 307 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (307 307 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (307 307 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (265 265 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (265 265 (:TYPE-PRESCRIPTION NATP))
 (262 187 (:REWRITE DEFAULT-TIMES-2))
 (237 187 (:REWRITE DEFAULT-TIMES-1))
 (218 11 (:REWRITE |(* (* x y) z)|))
 (184 5 (:LINEAR MOD-BOUNDS-3))
 (148 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (147 21 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (147 21 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (136 98 (:REWRITE SIMPLIFY-SUMS-<))
 (136 98 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (136 98 (:REWRITE DEFAULT-LESS-THAN-2))
 (126 21 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (111 21 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (111 21 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (98 98 (:REWRITE THE-FLOOR-BELOW))
 (98 98 (:REWRITE THE-FLOOR-ABOVE))
 (98 98 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (98 98 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (98 98 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (98 98 (:REWRITE INTEGERP-<-CONSTANT))
 (98 98 (:REWRITE DEFAULT-LESS-THAN-1))
 (98 98 (:REWRITE CONSTANT-<-INTEGERP))
 (98 98 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (98 98 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (98 98 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (98 98 (:REWRITE |(< c (- x))|))
 (98 98 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (98 98 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (98 98 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (98 98 (:REWRITE |(< (/ x) (/ y))|))
 (98 98 (:REWRITE |(< (- x) c)|))
 (98 98 (:REWRITE |(< (- x) (- y))|))
 (90 45 (:REWRITE DEFAULT-DIVIDE))
 (88 3 (:LINEAR RTL::MOD-BND-2))
 (79 79 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (79 79 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
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 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (74 74 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (73 56 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (70 10 (:LINEAR MOD-BOUNDS-2))
 (64 64 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (60 60 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (60 39 (:REWRITE DEFAULT-MOD-2))
 (60 5 (:REWRITE |(* y (* x z))|))
 (56 56 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (56 56 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (56 56 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (56 56 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (56 56 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (56 56 (:REWRITE |(equal c (/ x))|))
 (56 56 (:REWRITE |(equal c (- x))|))
 (56 56 (:REWRITE |(equal (/ x) c)|))
 (56 56 (:REWRITE |(equal (/ x) (/ y))|))
 (56 56 (:REWRITE |(equal (- x) c)|))
 (56 56 (:REWRITE |(equal (- x) (- y))|))
 (48 38 (:META META-INTEGERP-CORRECT))
 (45 45 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (41 41 (:REWRITE |(< (/ x) 0)|))
 (41 41 (:REWRITE |(< (* x y) 0)|))
 (39 39 (:REWRITE DEFAULT-MOD-1))
 (38 38 (:REWRITE REDUCE-INTEGERP-+))
 (38 38 (:REWRITE INTEGERP-MINUS-X))
 (24 24 (:REWRITE |(* 0 x)|))
 (21 21 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (21 21 (:REWRITE |(mod x (- y))| . 3))
 (21 21 (:REWRITE |(mod x (- y))| . 2))
 (21 21 (:REWRITE |(mod x (- y))| . 1))
 (21 21 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (21 21 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (19 19 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (19 19 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (19 19 (:REWRITE |(< 0 (/ x))|))
 (19 19 (:REWRITE |(< 0 (* x y))|))
 (9 9 (:REWRITE DM::FACTOR-DIVIDES))
 (5 5 (:REWRITE |(* c (* d x))|))
 (3 3 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (3 3 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:REWRITE INTEGERP-/))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 )
(DM::MOD+REWRITE-1
 (5261 63 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4070 64 (:REWRITE MOD-ZERO . 4))
 (3521 64 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (3479 64 (:REWRITE MOD-X-Y-=-X . 4))
 (3479 64 (:REWRITE MOD-X-Y-=-X . 3))
 (3411 64 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3401 3401 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (3401 3401 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (3401 3401 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3124 101 (:REWRITE |(* y x)|))
 (3065 613 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (3065 613 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (3025 613 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3025 613 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2891 64 (:REWRITE DEFAULT-MOD-RATIO))
 (2848 40 (:LINEAR RTL::MOD-BND-2))
 (2796 64 (:REWRITE MOD-ZERO . 3))
 (2165 31 (:REWRITE |(* x (+ y z))|))
 (2069 271 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1610 595 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1273 264 (:REWRITE DEFAULT-TIMES-2))
 (1208 40 (:LINEAR MOD-BOUNDS-3))
 (1077 155 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (987 64 (:REWRITE MOD-X-Y-=-X . 2))
 (881 264 (:REWRITE DEFAULT-TIMES-1))
 (840 155 (:REWRITE DEFAULT-LESS-THAN-1))
 (750 48 (:REWRITE DEFAULT-PLUS-2))
 (688 80 (:LINEAR MOD-BOUNDS-2))
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 (672 64 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (672 64 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (668 15 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (613 613 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (613 613 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (613 613 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (613 613 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (613 613 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (613 613 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (595 595 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (595 595 (:TYPE-PRESCRIPTION NATP))
 (384 155 (:REWRITE DEFAULT-LESS-THAN-2))
 (368 64 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (368 64 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (368 64 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (304 64 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (304 64 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (304 64 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (287 64 (:REWRITE DEFAULT-MOD-1))
 (271 271 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (271 271 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (271 271 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (233 155 (:REWRITE SIMPLIFY-SUMS-<))
 (230 46 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (202 101 (:REWRITE DEFAULT-DIVIDE))
 (163 163 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (155 155 (:REWRITE THE-FLOOR-BELOW))
 (155 155 (:REWRITE THE-FLOOR-ABOVE))
 (155 155 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (155 155 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (155 155 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (155 155 (:REWRITE INTEGERP-<-CONSTANT))
 (155 155 (:REWRITE CONSTANT-<-INTEGERP))
 (155 155 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (155 155 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (155 155 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (155 155 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (155 155 (:REWRITE |(< c (- x))|))
 (155 155 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (155 155 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (155 155 (:REWRITE |(< (/ x) (/ y))|))
 (155 155 (:REWRITE |(< (- x) c)|))
 (155 155 (:REWRITE |(< (- x) (- y))|))
 (128 64 (:REWRITE DEFAULT-MOD-2))
 (102 102 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (101 101 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (64 64 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (64 64 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (64 64 (:REWRITE |(mod x (- y))| . 3))
 (64 64 (:REWRITE |(mod x (- y))| . 2))
 (64 64 (:REWRITE |(mod x (- y))| . 1))
 (64 64 (:REWRITE |(< (/ x) 0)|))
 (64 64 (:REWRITE |(< (* x y) 0)|))
 (51 51 (:REWRITE |(< (+ c/d x) y)|))
 (51 51 (:REWRITE |(< (+ (- c) x) y)|))
 (46 46 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (46 46 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (46 46 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (46 46 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (46 46 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (46 46 (:REWRITE |(equal c (/ x))|))
 (46 46 (:REWRITE |(equal c (- x))|))
 (46 46 (:REWRITE |(equal (/ x) c)|))
 (46 46 (:REWRITE |(equal (/ x) (/ y))|))
 (46 46 (:REWRITE |(equal (- x) c)|))
 (46 46 (:REWRITE |(equal (- x) (- y))|))
 (40 40 (:LINEAR RTL::MOD-BND-3))
 (39 39 (:REWRITE REDUCE-INTEGERP-+))
 (39 39 (:REWRITE INTEGERP-MINUS-X))
 (39 39 (:META META-INTEGERP-CORRECT))
 (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))|))
 (34 34 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (34 34 (:REWRITE NORMALIZE-ADDENDS))
 (16 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (15 15 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (15 15 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (12 12 (:REWRITE |(< y (+ (- c) x))|))
 (12 12 (:REWRITE |(< x (+ c/d y))|))
 (10 10 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (10 10 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 )
(DM::MOD+REWRITE-2
 (4000 58 (:REWRITE MOD-ZERO . 4))
 (3499 58 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (3349 58 (:REWRITE MOD-X-Y-=-X . 4))
 (3349 58 (:REWRITE MOD-X-Y-=-X . 3))
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 (3003 3003 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
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 (2689 58 (:REWRITE DEFAULT-MOD-RATIO))
 (2670 534 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2670 534 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2630 534 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2630 534 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2622 58 (:REWRITE MOD-ZERO . 3))
 (1851 41 (:REWRITE |(* x (+ y z))|))
 (1657 259 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1251 256 (:REWRITE DEFAULT-TIMES-2))
 (1156 518 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (992 36 (:LINEAR MOD-BOUNDS-3))
 (905 127 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (879 256 (:REWRITE DEFAULT-TIMES-1))
 (765 58 (:REWRITE MOD-X-Y-=-X . 2))
 (742 50 (:REWRITE DEFAULT-PLUS-2))
 (680 127 (:REWRITE DEFAULT-LESS-THAN-1))
 (674 21 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (632 72 (:LINEAR MOD-BOUNDS-2))
 (630 58 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (630 58 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (625 51 (:REWRITE RTL::MOD-DOES-NOTHING))
 (534 534 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (534 534 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (534 534 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (534 534 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (534 534 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (534 534 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (518 518 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (518 518 (:TYPE-PRESCRIPTION NATP))
 (392 58 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (392 58 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (392 58 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (344 127 (:REWRITE DEFAULT-LESS-THAN-2))
 (333 127 (:REWRITE SIMPLIFY-SUMS-<))
 (281 58 (:REWRITE DEFAULT-MOD-1))
 (259 259 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (259 259 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (259 259 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (255 50 (:REWRITE DEFAULT-PLUS-1))
 (238 58 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (238 58 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (238 58 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (210 34 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (174 87 (:REWRITE DEFAULT-DIVIDE))
 (169 169 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (127 127 (:REWRITE THE-FLOOR-BELOW))
 (127 127 (:REWRITE THE-FLOOR-ABOVE))
 (127 127 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (127 127 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (127 127 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (127 127 (:REWRITE INTEGERP-<-CONSTANT))
 (127 127 (:REWRITE CONSTANT-<-INTEGERP))
 (127 127 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (127 127 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (127 127 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (127 127 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (127 127 (:REWRITE |(< c (- x))|))
 (127 127 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (127 127 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (25 25 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (25 25 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (25 25 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (25 25 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (25 25 (:REWRITE |(equal c (/ x))|))
 (25 25 (:REWRITE |(equal c (- x))|))
 (25 25 (:REWRITE |(equal (/ x) c)|))
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 (18 18 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
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 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (12 12 (:REWRITE |(< y (+ (- c) x))|))
 (12 12 (:REWRITE |(< x (+ c/d y))|))
 (5 5 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (5 5 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (1 1 (:REWRITE INTEGERP-/))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 )
(DM::MOD*REWRITE-6
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 (2283 463 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (1918 26 (:REWRITE |(* y x)|))
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 (1414 12 (:REWRITE MOD-X-Y-=-X . 3))
 (1400 26 (:REWRITE |(* x (+ y z))|))
 (1304 12 (:REWRITE MOD-X-Y-=-X+Y . 2))
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 (1244 12 (:REWRITE MOD-ZERO . 4))
 (1238 132 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (906 104 (:REWRITE DEFAULT-TIMES-2))
 (894 447 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (820 64 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
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 (650 64 (:REWRITE DEFAULT-LESS-THAN-1))
 (586 12 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
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 (544 26 (:REWRITE DEFAULT-PLUS-2))
 (512 12 (:REWRITE MOD-X-Y-=-X . 2))
 (504 4 (:LINEAR RTL::MOD-BND-2))
 (463 463 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (463 463 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (463 463 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (463 463 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (463 463 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (447 447 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
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 (264 12 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (64 64 (:REWRITE THE-FLOOR-ABOVE))
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 (44 44 (:REWRITE |(< (+ (- c) x) y)|))
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 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
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 (26 26 (:REWRITE |(* c (* d x))|))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (24 24 (:REWRITE |(< (* x y) 0)|))
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 )
(DM::MOD*REWRITE-7
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 (1930 4 (:LINEAR MOD-BOUNDS-3))
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 (1226 12 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1178 589 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
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 (640 54 (:REWRITE DEFAULT-LESS-THAN-1))
 (633 633 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (633 633 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (633 633 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (633 633 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (633 633 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (589 589 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
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 (518 26 (:REWRITE |(* y x)|))
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 (500 4 (:LINEAR RTL::MOD-BND-2))
 (338 54 (:REWRITE SIMPLIFY-SUMS-<))
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 (264 12 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (264 12 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (202 12 (:REWRITE DEFAULT-MOD-1))
 (184 8 (:LINEAR MOD-BOUNDS-2))
 (182 182 (:REWRITE |(* c (* d x))|))
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 (144 144 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
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 (54 54 (:REWRITE THE-FLOOR-BELOW))
 (54 54 (:REWRITE THE-FLOOR-ABOVE))
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 (8 8 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
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 (4 4 (:LINEAR RTL::MOD-BND-3))
 )
(DM::MOD-REWRITE-1
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 (476 44 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (408 196 (:REWRITE DEFAULT-TIMES-1))
 (384 32 (:REWRITE |(* x (- y))|))
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 (32 32 (:REWRITE |(- (* c x))|))
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(DM::MOD-REWRITE-2
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 (4319 131 (:REWRITE |(* y x)|))
 (3978 94 (:REWRITE DEFAULT-MOD-RATIO))
 (3769 94 (:REWRITE MOD-ZERO . 3))
 (3391 172 (:REWRITE NORMALIZE-ADDENDS))
 (3210 41 (:REWRITE |(* x (+ y z))|))
 (2568 372 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2423 190 (:REWRITE |(+ y x)|))
 (2250 1065 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1956 190 (:DEFINITION FIX))
 (1878 385 (:REWRITE DEFAULT-TIMES-2))
 (1526 68 (:LINEAR MOD-BOUNDS-3))
 (1470 87 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1400 41 (:REWRITE |(* x (- y))|))
 (1111 1111 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1111 1111 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1111 1111 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1111 1111 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1111 1111 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1111 1111 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1093 385 (:REWRITE DEFAULT-TIMES-1))
 (1080 136 (:LINEAR MOD-BOUNDS-2))
 (1065 1065 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (1065 1065 (:TYPE-PRESCRIPTION NATP))
 (1047 238 (:REWRITE DEFAULT-LESS-THAN-2))
 (981 94 (:REWRITE MOD-X-Y-=-X . 2))
 (978 95 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (956 238 (:REWRITE DEFAULT-LESS-THAN-1))
 (938 159 (:REWRITE SIMPLIFY-SUMS-<))
 (889 163 (:REWRITE |(+ 0 x)|))
 (882 94 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (882 94 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (791 238 (:REWRITE |(< (- x) (- y))|))
 (742 50 (:REWRITE DEFAULT-MINUS))
 (674 21 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (626 238 (:REWRITE |(< (- x) c)|))
 (454 94 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (454 94 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (454 94 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (428 94 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (428 94 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (428 94 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (403 238 (:REWRITE |(< c (- x))|))
 (372 372 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (372 372 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (372 372 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (370 39 (:REWRITE INTEGERP-MINUS-X))
 (317 94 (:REWRITE DEFAULT-MOD-1))
 (262 131 (:REWRITE DEFAULT-DIVIDE))
 (238 238 (:REWRITE THE-FLOOR-BELOW))
 (238 238 (:REWRITE THE-FLOOR-ABOVE))
 (238 238 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (238 238 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (238 238 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (238 238 (:REWRITE INTEGERP-<-CONSTANT))
 (238 238 (:REWRITE CONSTANT-<-INTEGERP))
 (238 238 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (238 238 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (238 238 (:REWRITE |(< (/ x) (/ y))|))
 (221 56 (:REWRITE |(equal (- x) c)|))
 (221 56 (:REWRITE |(equal (- x) (- y))|))
 (213 213 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (205 40 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (190 95 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (188 94 (:REWRITE DEFAULT-MOD-2))
 (158 158 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (131 131 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (95 95 (:REWRITE |(+ x (- x))|))
 (94 94 (:REWRITE |(mod x (- y))| . 3))
 (94 94 (:REWRITE |(mod x (- y))| . 2))
 (94 94 (:REWRITE |(mod x (- y))| . 1))
 (77 77 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (68 68 (:LINEAR RTL::MOD-BND-3))
 (66 66 (:REWRITE |(< (/ x) 0)|))
 (66 66 (:REWRITE |(< (* x y) 0)|))
 (63 63 (:REWRITE |(< (+ c/d x) y)|))
 (63 63 (:REWRITE |(< (+ (- c) x) y)|))
 (56 56 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (56 56 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (56 56 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (56 56 (:REWRITE |(equal c (/ x))|))
 (56 56 (:REWRITE |(equal c (- x))|))
 (56 56 (:REWRITE |(equal (/ x) c)|))
 (56 56 (:REWRITE |(equal (/ x) (/ y))|))
 (43 43 (:REWRITE |(< y (+ (- c) x))|))
 (43 43 (:REWRITE |(< x (+ c/d y))|))
 (41 41 (:REWRITE |(- (* c x))|))
 (40 40 (:REWRITE |(< 0 (/ x))|))
 (40 40 (:REWRITE |(< 0 (* x y))|))
 (39 39 (:REWRITE REDUCE-INTEGERP-+))
 (39 39 (:META META-INTEGERP-CORRECT))
 (30 30 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (30 30 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (21 21 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
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 (20 20 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 16 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 10 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (10 10 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (10 5 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (5 5 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (5 5 (:REWRITE MOD-X-Y-=-X+Y . 1))
 )
(DM::MOD-EXPT-REWRITE-1
 (9297 41 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4147 42 (:REWRITE MOD-X-Y-=-X-Y . 2))
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 (2131 9 (:LINEAR RTL::MOD-BND-2))
 (2083 80 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2010 580 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1982 1982 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1982 1982 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1982 1982 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1982 1982 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1982 1982 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1934 326 (:REWRITE DEFAULT-TIMES-2))
 (1718 580 (:REWRITE DEFAULT-LESS-THAN-1))
 (1632 12 (:LINEAR MOD-BOUNDS-3))
 (1615 163 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1580 316 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
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 (1552 326 (:REWRITE DEFAULT-TIMES-1))
 (1516 316 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (1458 5 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1285 41 (:REWRITE MOD-X-Y-=-X . 2))
 (1276 140 (:LINEAR EXPT-<=-1-ONE))
 (1236 140 (:LINEAR EXPT->=-1-TWO))
 (1236 140 (:LINEAR EXPT->-1-TWO))
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 (1116 140 (:LINEAR EXPT->=-1-ONE))
 (1116 140 (:LINEAR EXPT-<=-1-TWO))
 (1100 42 (:REWRITE MOD-ZERO . 4))
 (1076 140 (:LINEAR EXPT-X->-X))
 (1076 140 (:LINEAR EXPT->-1-ONE))
 (1076 140 (:LINEAR EXPT-<-1-TWO))
 (978 269 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (888 580 (:REWRITE DEFAULT-LESS-THAN-2))
 (591 42 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (591 42 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (580 580 (:REWRITE THE-FLOOR-BELOW))
 (580 580 (:REWRITE THE-FLOOR-ABOVE))
 (580 580 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (580 580 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (580 580 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (580 580 (:REWRITE INTEGERP-<-CONSTANT))
 (580 580 (:REWRITE CONSTANT-<-INTEGERP))
 (580 580 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (580 580 (:REWRITE |(< c (- x))|))
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 (580 580 (:REWRITE |(< (- x) (- y))|))
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 (526 41 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
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 (476 24 (:LINEAR MOD-BOUNDS-2))
 (470 58 (:REWRITE DEFAULT-MOD-1))
 (320 5 (:REWRITE MOD-ZERO . 1))
 (316 316 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (316 316 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (316 316 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (316 316 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (316 316 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (297 8 (:REWRITE |(* (if a b c) x)|))
 (280 280 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (280 280 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (280 280 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (280 280 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (275 275 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (269 269 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (269 269 (:TYPE-PRESCRIPTION NATP))
 (267 137 (:REWRITE DEFAULT-PLUS-2))
 (245 75 (:REWRITE SIMPLIFY-SUMS-EQUAL))
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 (211 137 (:REWRITE DEFAULT-PLUS-1))
 (163 163 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (163 163 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (163 163 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
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 (155 155 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (155 155 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (155 155 (:REWRITE |(< 0 (/ x))|))
 (155 155 (:REWRITE |(< 0 (* x y))|))
 (151 55 (:META META-INTEGERP-CORRECT))
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 (140 140 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (140 140 (:LINEAR EXPT-LINEAR-LOWER-<))
 (120 120 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (116 116 (:REWRITE |(< (/ x) 0)|))
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 (115 58 (:REWRITE DEFAULT-MOD-2))
 (92 26 (:REWRITE DEFAULT-EXPT-1))
 (86 81 (:REWRITE |(equal (- x) c)|))
 (86 81 (:REWRITE |(equal (- x) (- y))|))
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 (55 55 (:REWRITE REDUCE-INTEGERP-+))
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 (41 41 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (41 41 (:REWRITE |(mod x (- y))| . 3))
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 (31 31 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (30 5 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (28 28 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
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 (26 26 (:REWRITE DEFAULT-EXPT-2))
 (25 25 (:REWRITE |(expt 1/c n)|))
 (25 25 (:REWRITE |(expt (- x) n)|))
 (25 1 (:REWRITE |(equal (expt x n) 0)|))
 (24 24 (:REWRITE |(< y (+ (- c) x))|))
 (24 24 (:REWRITE |(< x (+ c/d y))|))
 (24 19 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (17 17 (:REWRITE |(< (+ c/d x) y)|))
 (17 17 (:REWRITE |(< (+ (- c) x) y)|))
 (16 16 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (16 16 (:REWRITE |(* 0 x)|))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (15 3 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
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 (15 3 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (10 10 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 5 (:REWRITE DEFAULT-MINUS))
 (9 9 (:LINEAR RTL::MOD-BND-3))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:REWRITE |(* c (expt d n))|))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE |(* c (* d x))|))
 (3 3 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (2 2 (:REWRITE INTEGERP-/))
 (2 2 (:REWRITE |(equal (* x y) 0)|))
 (2 2 (:REWRITE |(* (/ c) (expt d n))|))
 )
(DM::MOD-EXPT-REWRITE-2
 (12735 228 (:REWRITE RTL::MOD-DOES-NOTHING))
 (10672 232 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (9515 232 (:REWRITE MOD-X-Y-=-X+Y . 2))
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 (8783 119 (:LINEAR EXPT-X->=-X))
 (8783 119 (:LINEAR EXPT->=-1-ONE))
 (8783 119 (:LINEAR EXPT-<=-1-TWO))
 (8758 119 (:LINEAR EXPT-X->-X))
 (8758 119 (:LINEAR EXPT->-1-ONE))
 (8758 119 (:LINEAR EXPT-<-1-TWO))
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 (5631 255 (:REWRITE DEFAULT-MOD-RATIO))
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 (5565 1125 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (5565 1125 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4914 1419 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4672 228 (:REWRITE MOD-X-Y-=-X . 2))
 (3486 551 (:REWRITE |(* y x)|))
 (3261 1423 (:REWRITE DEFAULT-LESS-THAN-2))
 (3134 1169 (:REWRITE DEFAULT-TIMES-2))
 (2968 1061 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2951 71 (:LINEAR MOD-BOUNDS-3))
 (2828 1423 (:REWRITE DEFAULT-LESS-THAN-1))
 (2572 1169 (:REWRITE DEFAULT-TIMES-1))
 (2255 1419 (:REWRITE SIMPLIFY-SUMS-<))
 (2053 1649 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1916 232 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1916 232 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1649 1649 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
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 (1649 1649 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1649 1649 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1423 1423 (:REWRITE THE-FLOOR-BELOW))
 (1423 1423 (:REWRITE THE-FLOOR-ABOVE))
 (1423 1423 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1423 1423 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1419 1419 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1419 1419 (:REWRITE INTEGERP-<-CONSTANT))
 (1419 1419 (:REWRITE CONSTANT-<-INTEGERP))
 (1419 1419 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (1419 1419 (:REWRITE |(< (- x) (- y))|))
 (1414 444 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
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 (1188 228 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
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 (941 941 (:TYPE-PRESCRIPTION NATP))
 (827 827 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (657 255 (:REWRITE DEFAULT-MOD-1))
 (650 443 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (630 18 (:REWRITE MOD-POSITIVE . 3))
 (628 228 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (628 228 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (628 228 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (575 463 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (563 563 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (521 521 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (521 521 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (521 521 (:REWRITE |(< (/ x) 0)|))
 (521 521 (:REWRITE |(< (* x y) 0)|))
 (510 255 (:REWRITE DEFAULT-MOD-2))
 (492 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (463 463 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (457 456 (:REWRITE |(equal (- x) (- y))|))
 (456 456 (:REWRITE |(equal c (/ x))|))
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 (456 456 (:REWRITE |(equal (/ x) c)|))
 (456 456 (:REWRITE |(equal (/ x) (/ y))|))
 (456 456 (:REWRITE |(equal (- x) c)|))
 (456 50 (:REWRITE DEFAULT-EXPT-1))
 (444 444 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (426 426 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (363 11 (:REWRITE |(* (if a b c) x)|))
 (327 18 (:REWRITE MOD-POSITIVE . 2))
 (309 309 (:REWRITE REDUCE-INTEGERP-+))
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 (298 298 (:REWRITE |(< 0 (* x y))|))
 (294 294 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (294 294 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (294 294 (:REWRITE |(< 0 (/ x))|))
 (257 116 (:REWRITE DEFAULT-PLUS-2))
 (238 238 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
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 (238 238 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (238 238 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (234 6 (:REWRITE ZP-OPEN))
 (228 228 (:REWRITE |(mod x (- y))| . 3))
 (228 228 (:REWRITE |(mod x (- y))| . 2))
 (228 228 (:REWRITE |(mod x (- y))| . 1))
 (144 116 (:REWRITE DEFAULT-PLUS-1))
 (119 119 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (119 119 (:LINEAR EXPT-LINEAR-UPPER-<))
 (119 119 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (119 119 (:LINEAR EXPT-LINEAR-LOWER-<))
 (100 4 (:REWRITE |(< y (+ (- c) x))|))
 (82 40 (:REWRITE NORMALIZE-ADDENDS))
 (65 65 (:LINEAR RTL::MOD-BND-3))
 (58 1 (:REWRITE |(+ x (if a b c))|))
 (50 50 (:REWRITE DEFAULT-EXPT-2))
 (50 50 (:REWRITE |(expt 1/c n)|))
 (50 50 (:REWRITE |(expt (- x) n)|))
 (39 39 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (27 27 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (25 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (23 23 (:REWRITE |(* 0 x)|))
 (18 18 (:REWRITE MOD-POSITIVE . 1))
 (15 15 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (13 12 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (12 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (11 11 (:REWRITE |(* c (expt d n))|))
 (10 10 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 1 (:REWRITE DEFAULT-MINUS))
 (1 1 (:REWRITE |(+ x (- x))|))
 )
(DM::MOD-EXPT-REWRITE
 (15179 151 (:LINEAR EXPT-<=-1-ONE))
 (14225 330 (:REWRITE RTL::MOD-DOES-NOTHING))
 (11321 338 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (10860 151 (:LINEAR EXPT->=-1-TWO))
 (10860 151 (:LINEAR EXPT->-1-TWO))
 (10860 151 (:LINEAR EXPT-<-1-ONE))
 (10383 338 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (10331 151 (:LINEAR EXPT-X->=-X))
 (10331 151 (:LINEAR EXPT->=-1-ONE))
 (10331 151 (:LINEAR EXPT-<=-1-TWO))
 (10300 151 (:LINEAR EXPT-X->-X))
 (10300 151 (:LINEAR EXPT->-1-ONE))
 (10300 151 (:LINEAR EXPT-<-1-TWO))
 (10272 338 (:REWRITE MOD-X-Y-=-X . 4))
 (9516 9516 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (9516 9516 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (9516 9516 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (8518 338 (:REWRITE MOD-ZERO . 3))
 (7002 338 (:REWRITE MOD-ZERO . 4))
 (6865 1373 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (6865 1373 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (6860 338 (:REWRITE DEFAULT-MOD-RATIO))
 (6841 1373 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6841 1373 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (6221 1637 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6162 302 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (5920 302 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (5606 330 (:REWRITE MOD-X-Y-=-X . 2))
 (4287 699 (:REWRITE |(* y x)|))
 (4199 103 (:LINEAR MOD-BOUNDS-3))
 (4068 1650 (:REWRITE DEFAULT-LESS-THAN-2))
 (3448 1650 (:REWRITE DEFAULT-LESS-THAN-1))
 (3330 1068 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2909 1408 (:REWRITE DEFAULT-TIMES-2))
 (2899 1408 (:REWRITE DEFAULT-TIMES-1))
 (2756 338 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (2756 338 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2720 1185 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2513 1637 (:REWRITE SIMPLIFY-SUMS-<))
 (2045 330 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2045 330 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (2045 330 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1838 206 (:LINEAR MOD-BOUNDS-2))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1719 1719 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1650 1650 (:REWRITE THE-FLOOR-BELOW))
 (1650 1650 (:REWRITE THE-FLOOR-ABOVE))
 (1650 1650 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1650 1650 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1638 1638 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1638 1638 (:REWRITE INTEGERP-<-CONSTANT))
 (1638 1638 (:REWRITE CONSTANT-<-INTEGERP))
 (1638 1638 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1638 1638 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1638 1638 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1638 1638 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1638 1638 (:REWRITE |(< c (- x))|))
 (1638 1638 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1638 1638 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1638 1638 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1638 1638 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1638 1638 (:REWRITE |(< (/ x) (/ y))|))
 (1638 1638 (:REWRITE |(< (- x) c)|))
 (1638 1638 (:REWRITE |(< (- x) (- y))|))
 (1418 709 (:REWRITE DEFAULT-DIVIDE))
 (1373 1373 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1373 1373 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1373 1373 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1373 1373 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1373 1373 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1185 1185 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (1185 1185 (:TYPE-PRESCRIPTION NATP))
 (1068 1068 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1068 1068 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1068 1068 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (980 28 (:REWRITE MOD-POSITIVE . 3))
 (771 516 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (728 338 (:REWRITE DEFAULT-MOD-1))
 (709 709 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (699 699 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (697 13 (:REWRITE ZP-OPEN))
 (676 338 (:REWRITE DEFAULT-MOD-2))
 (655 330 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (655 330 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (655 330 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (638 542 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (595 595 (:REWRITE |(< (/ x) 0)|))
 (595 595 (:REWRITE |(< (* x y) 0)|))
 (594 594 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (594 594 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (578 20 (:REWRITE |(equal (expt x n) 0)|))
 (542 542 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (536 536 (:REWRITE |(equal c (/ x))|))
 (536 536 (:REWRITE |(equal c (- x))|))
 (536 536 (:REWRITE |(equal (/ x) c)|))
 (536 536 (:REWRITE |(equal (/ x) (/ y))|))
 (536 536 (:REWRITE |(equal (- x) c)|))
 (536 536 (:REWRITE |(equal (- x) (- y))|))
 (518 28 (:REWRITE MOD-POSITIVE . 2))
 (516 516 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (516 516 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (504 504 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (396 49 (:REWRITE DEFAULT-EXPT-1))
 (372 372 (:REWRITE REDUCE-INTEGERP-+))
 (372 372 (:REWRITE INTEGERP-MINUS-X))
 (372 372 (:META META-INTEGERP-CORRECT))
 (372 18 (:REWRITE DM::MOD-EXPT-REWRITE-1))
 (351 351 (:REWRITE |(< 0 (* x y))|))
 (339 339 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (339 339 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (339 339 (:REWRITE |(< 0 (/ x))|))
 (330 330 (:REWRITE |(mod x (- y))| . 3))
 (330 330 (:REWRITE |(mod x (- y))| . 2))
 (330 330 (:REWRITE |(mod x (- y))| . 1))
 (302 302 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (302 302 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (300 12 (:REWRITE |(< y (+ (- c) x))|))
 (151 151 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (151 151 (:LINEAR EXPT-LINEAR-UPPER-<))
 (151 151 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (151 151 (:LINEAR EXPT-LINEAR-LOWER-<))
 (95 95 (:LINEAR RTL::MOD-BND-3))
 (49 49 (:REWRITE DEFAULT-EXPT-2))
 (49 49 (:REWRITE |(expt 1/c n)|))
 (49 49 (:REWRITE |(expt (- x) n)|))
 (33 33 (:REWRITE DEFAULT-PLUS-2))
 (33 33 (:REWRITE DEFAULT-PLUS-1))
 (28 28 (:REWRITE MOD-POSITIVE . 1))
 (24 6 (:REWRITE |(+ c (+ d x))|))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (21 21 (:REWRITE NORMALIZE-ADDENDS))
 (20 10 (:REWRITE |(* 1 x)|))
 (12 12 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (6 6 (:REWRITE |(+ 0 x)|))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (2 2 (:REWRITE INTEGERP-/))
 )
(DM::MOD-EXPT-REWRITE-3
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 (1939 187 (:REWRITE DEFAULT-TIMES-2))
 (1761 15 (:REWRITE MOD-ZERO . 3))
 (1515 15 (:REWRITE DEFAULT-MOD-RATIO))
 (1357 15 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1302 15 (:REWRITE MOD-X-Y-=-X . 4))
 (1302 15 (:REWRITE MOD-X-Y-=-X . 3))
 (1286 4 (:LINEAR MOD-BOUNDS-3))
 (1222 15 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1133 15 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1110 15 (:REWRITE MOD-ZERO . 4))
 (1080 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1029 1029 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (973 29 (:REWRITE |(* y (* x z))|))
 (959 187 (:REWRITE DEFAULT-TIMES-1))
 (846 846 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (846 846 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (846 846 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
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 (815 163 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (775 163 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (775 163 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (745 65 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (740 4 (:LINEAR RTL::MOD-BND-2))
 (658 159 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (603 65 (:REWRITE DEFAULT-LESS-THAN-1))
 (511 31 (:REWRITE |(* y x)|))
 (482 15 (:REWRITE MOD-X-Y-=-X . 2))
 (325 34 (:META META-INTEGERP-CORRECT))
 (309 65 (:REWRITE SIMPLIFY-SUMS-<))
 (264 8 (:LINEAR MOD-BOUNDS-2))
 (245 15 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (245 15 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (230 15 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (230 15 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (230 15 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (199 65 (:REWRITE DEFAULT-LESS-THAN-2))
 (163 163 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (163 163 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (163 163 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (163 163 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (163 163 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (163 163 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (159 159 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (159 159 (:TYPE-PRESCRIPTION NATP))
 (155 15 (:REWRITE DEFAULT-MOD-1))
 (144 23 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (98 98 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (65 65 (:REWRITE THE-FLOOR-BELOW))
 (65 65 (:REWRITE THE-FLOOR-ABOVE))
 (65 65 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (65 65 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (65 65 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (65 65 (:REWRITE INTEGERP-<-CONSTANT))
 (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))|))
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 (42 9 (:REWRITE DEFAULT-EXPT-1))
 (41 41 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (34 34 (:REWRITE REDUCE-INTEGERP-+))
 (34 34 (:REWRITE INTEGERP-MINUS-X))
 (31 31 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (30 15 (:REWRITE DEFAULT-MOD-2))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (29 29 (:REWRITE |(< (/ x) 0)|))
 (29 29 (:REWRITE |(< (* x y) 0)|))
 (29 29 (:REWRITE |(* c (* d x))|))
 (26 26 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (23 23 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (23 23 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (23 23 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (23 23 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (23 23 (:REWRITE |(equal c (/ x))|))
 (23 23 (:REWRITE |(equal c (- x))|))
 (23 23 (:REWRITE |(equal (/ x) c)|))
 (23 23 (:REWRITE |(equal (/ x) (/ y))|))
 (23 23 (:REWRITE |(equal (- x) c)|))
 (23 23 (:REWRITE |(equal (- x) (- y))|))
 (15 15 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (15 15 (:REWRITE INTEGERP-/))
 (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)) z) not rewriting-goal-literal|))
 (14 14 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (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 y))|))
 (11 11 (:REWRITE |(equal (* x y) 0)|))
 (11 11 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (10 10 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (9 9 (:REWRITE DEFAULT-EXPT-2))
 (9 9 (:REWRITE |(expt 1/c n)|))
 (9 9 (:REWRITE |(expt (- x) n)|))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 )
(DM::MOD-EXPT-REWRITE-4
 (5134 260 (:REWRITE DEFAULT-TIMES-2))
 (4106 12 (:REWRITE DEFAULT-MOD-RATIO))
 (4026 12 (:REWRITE MOD-ZERO . 3))
 (3086 52 (:REWRITE |(* y (* x z))|))
 (2685 537 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2685 537 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2653 537 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2653 537 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2466 92 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2354 2354 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2354 2354 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2354 2354 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2282 260 (:REWRITE DEFAULT-TIMES-1))
 (2246 12 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2204 12 (:REWRITE MOD-X-Y-=-X . 4))
 (2204 12 (:REWRITE MOD-X-Y-=-X . 3))
 (2044 12 (:REWRITE MOD-ZERO . 4))
 (1994 12 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1926 12 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1794 4 (:LINEAR MOD-BOUNDS-3))
 (1340 54 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1080 54 (:REWRITE DEFAULT-LESS-THAN-1))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1046 1046 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1018 509 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (778 26 (:REWRITE |(* y x)|))
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 (538 54 (:REWRITE SIMPLIFY-SUMS-<))
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 (537 537 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (537 537 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (537 537 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (537 537 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (509 509 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (509 509 (:TYPE-PRESCRIPTION NATP))
 (436 28 (:META META-INTEGERP-CORRECT))
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 (396 12 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (384 12 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (384 12 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (384 12 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (306 54 (:REWRITE DEFAULT-LESS-THAN-2))
 (264 8 (:LINEAR MOD-BOUNDS-2))
 (262 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (130 130 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (92 92 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (92 92 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (92 92 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (78 78 (:REWRITE |(* c (* d x))|))
 (54 54 (:REWRITE THE-FLOOR-BELOW))
 (54 54 (:REWRITE THE-FLOOR-ABOVE))
 (54 54 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (54 54 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (54 54 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (54 54 (:REWRITE INTEGERP-<-CONSTANT))
 (54 54 (:REWRITE CONSTANT-<-INTEGERP))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (- x))|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (54 54 (:REWRITE |(< (/ x) (/ y))|))
 (54 54 (:REWRITE |(< (- x) c)|))
 (54 54 (:REWRITE |(< (- x) (- y))|))
 (52 26 (:REWRITE DEFAULT-DIVIDE))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (28 28 (:REWRITE REDUCE-INTEGERP-+))
 (28 28 (:REWRITE INTEGERP-MINUS-X))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE |(< (/ x) 0)|))
 (24 24 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (24 24 (:REWRITE |(< (* x y) 0)|))
 (24 12 (:REWRITE DEFAULT-MOD-2))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (20 20 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (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))|))
 (14 14 (:REWRITE INTEGERP-/))
 (12 12 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (12 12 (:REWRITE |(mod x (- y))| . 3))
 (12 12 (:REWRITE |(mod x (- y))| . 2))
 (12 12 (:REWRITE |(mod x (- y))| . 1))
 (12 12 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (12 12 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (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 |(equal (* x y) 0)|))
 (10 10 (:REWRITE |(< 0 (/ x))|))
 (10 10 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 )
(DM::MOD-EXPT-REWRITE-5
 (7338 364 (:REWRITE DEFAULT-TIMES-2))
 (5598 12 (:REWRITE DEFAULT-MOD-RATIO))
 (5164 12 (:REWRITE MOD-ZERO . 3))
 (4642 78 (:REWRITE |(* y (* x z))|))
 (3166 118 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (3060 364 (:REWRITE DEFAULT-TIMES-1))
 (2925 585 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2925 585 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2893 585 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2893 585 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2546 2546 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2546 2546 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2546 2546 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2302 4 (:LINEAR MOD-BOUNDS-3))
 (2246 12 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2204 12 (:REWRITE MOD-X-Y-=-X . 4))
 (2204 12 (:REWRITE MOD-X-Y-=-X . 3))
 (2044 12 (:REWRITE MOD-ZERO . 4))
 (1994 12 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1926 12 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1340 54 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1150 1150 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1098 549 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1080 54 (:REWRITE DEFAULT-LESS-THAN-1))
 (778 26 (:REWRITE |(* y x)|))
 (740 4 (:LINEAR RTL::MOD-BND-2))
 (712 12 (:REWRITE MOD-X-Y-=-X . 2))
 (585 585 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (585 585 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (585 585 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (585 585 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (585 585 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (585 585 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (549 549 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (549 549 (:TYPE-PRESCRIPTION NATP))
 (538 54 (:REWRITE SIMPLIFY-SUMS-<))
 (436 28 (:META META-INTEGERP-CORRECT))
 (396 12 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (396 12 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (384 12 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (384 12 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (384 12 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (322 12 (:REWRITE DEFAULT-MOD-1))
 (306 54 (:REWRITE DEFAULT-LESS-THAN-2))
 (264 8 (:LINEAR MOD-BOUNDS-2))
 (262 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (182 182 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (130 130 (:REWRITE |(* c (* d x))|))
 (118 118 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (118 118 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (118 118 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (54 54 (:REWRITE THE-FLOOR-BELOW))
 (54 54 (:REWRITE THE-FLOOR-ABOVE))
 (54 54 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (54 54 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (54 54 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (54 54 (:REWRITE INTEGERP-<-CONSTANT))
 (54 54 (:REWRITE CONSTANT-<-INTEGERP))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (- x))|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (54 54 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< (/ x) (/ y))|))
 (54 54 (:REWRITE |(< (- x) c)|))
 (54 54 (:REWRITE |(< (- x) (- y))|))
 (52 26 (:REWRITE DEFAULT-DIVIDE))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (28 28 (:REWRITE REDUCE-INTEGERP-+))
 (28 28 (:REWRITE INTEGERP-MINUS-X))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE |(< (/ x) 0)|))
 (24 24 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (24 24 (:REWRITE |(< (* x y) 0)|))
 (24 12 (:REWRITE DEFAULT-MOD-2))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (20 20 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (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))|))
 (14 14 (:REWRITE INTEGERP-/))
 (12 12 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (12 12 (:REWRITE |(mod x (- y))| . 3))
 (12 12 (:REWRITE |(mod x (- y))| . 2))
 (12 12 (:REWRITE |(mod x (- y))| . 1))
 (12 12 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (12 12 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (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 |(equal (* x y) 0)|))
 (10 10 (:REWRITE |(< 0 (/ x))|))
 (10 10 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 )
(DM::MOD-EQUAL-0
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 (6816 24 (:LINEAR MOD-BOUNDS-1))
 (4472 59 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4079 7 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (3192 12 (:LINEAR RTL::MOD-BND-1))
 (1936 1936 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1936 1936 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1936 1936 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1645 47 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1533 45 (:REWRITE MOD-X-Y-=-X . 4))
 (1533 45 (:REWRITE MOD-X-Y-=-X . 3))
 (1513 47 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1165 233 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1129 45 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1053 233 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (997 233 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (997 233 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (904 47 (:REWRITE MOD-ZERO . 4))
 (680 252 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (569 47 (:REWRITE DEFAULT-MOD-RATIO))
 (348 12 (:LINEAR RTL::MOD-BND-2))
 (334 54 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (252 252 (:REWRITE THE-FLOOR-BELOW))
 (252 252 (:REWRITE THE-FLOOR-ABOVE))
 (252 252 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (252 252 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (252 252 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (252 252 (:REWRITE INTEGERP-<-CONSTANT))
 (252 252 (:REWRITE DEFAULT-LESS-THAN-2))
 (252 252 (:REWRITE DEFAULT-LESS-THAN-1))
 (252 252 (:REWRITE CONSTANT-<-INTEGERP))
 (252 252 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (252 252 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (252 252 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (252 252 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (252 252 (:REWRITE |(< c (- x))|))
 (252 252 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (252 252 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (252 252 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (252 252 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (252 252 (:REWRITE |(< (/ x) (/ y))|))
 (252 252 (:REWRITE |(< (- x) c)|))
 (252 252 (:REWRITE |(< (- x) (- y))|))
 (252 12 (:LINEAR MOD-BOUNDS-3))
 (243 243 (:REWRITE SIMPLIFY-SUMS-<))
 (235 47 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (235 47 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (233 233 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (233 233 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (233 233 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (233 233 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (233 233 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (225 45 (:REWRITE MOD-X-Y-=-X . 2))
 (224 14 (:REWRITE |(+ y (+ x z))|))
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 (189 45 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (189 45 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (179 179 (:REWRITE DEFAULT-TIMES-1))
 (156 156 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (156 69 (:REWRITE REDUCE-INTEGERP-+))
 (135 135 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (130 65 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (130 46 (:REWRITE NORMALIZE-ADDENDS))
 (120 24 (:LINEAR MOD-BOUNDS-2))
 (113 113 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (113 113 (:REWRITE DEFAULT-DIVIDE))
 (104 104 (:REWRITE |(< (/ x) 0)|))
 (104 104 (:REWRITE |(< (* x y) 0)|))
 (100 100 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (100 100 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (88 22 (:REWRITE |(+ y x)|))
 (85 69 (:REWRITE INTEGERP-MINUS-X))
 (81 45 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (81 45 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (81 45 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (72 24 (:REWRITE DEFAULT-MINUS))
 (69 69 (:META META-INTEGERP-CORRECT))
 (65 65 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (65 65 (:TYPE-PRESCRIPTION NATP))
 (63 3 (:REWRITE |(equal (mod a n) (mod b n))|))
 (59 59 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (59 59 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (59 59 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (59 59 (:REWRITE |(equal c (/ x))|))
 (59 59 (:REWRITE |(equal c (- x))|))
 (59 59 (:REWRITE |(equal (/ x) c)|))
 (59 59 (:REWRITE |(equal (/ x) (/ y))|))
 (59 59 (:REWRITE |(equal (- x) c)|))
 (59 59 (:REWRITE |(equal (- x) (- y))|))
 (52 52 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (48 3 (:REWRITE |(integerp (- x))|))
 (47 47 (:REWRITE DEFAULT-MOD-2))
 (47 47 (:REWRITE DEFAULT-MOD-1))
 (47 47 (:REWRITE |(< 0 (/ x))|))
 (47 47 (:REWRITE |(< 0 (* x y))|))
 (46 46 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (46 46 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (45 45 (:REWRITE |(mod x (- y))| . 3))
 (45 45 (:REWRITE |(mod x (- y))| . 2))
 (45 45 (:REWRITE |(mod x (- y))| . 1))
 (44 44 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (36 36 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (32 32 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (28 28 (:DEFINITION FIX))
 (28 14 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (22 22 (:REWRITE |(+ 0 x)|))
 (14 14 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (14 14 (:REWRITE |(+ x (- x))|))
 (12 12 (:REWRITE |(- (* c x))|))
 (12 12 (:LINEAR RTL::MOD-BND-3))
 (9 9 (:REWRITE |(equal (+ (- c) x) y)|))
 (9 1 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (8 8 (:REWRITE |(< (+ c/d x) y)|))
 (8 8 (:REWRITE |(< (+ (- c) x) y)|))
 (7 7 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (5 5 (:REWRITE |(< y (+ (- c) x))|))
 (5 5 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (1 1 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 )
(DM::FRCP-LEMMA
 (5942 23 (:REWRITE RTL::MOD-DOES-NOTHING))
 (2534 23 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2441 23 (:REWRITE MOD-X-Y-=-X . 4))
 (2441 23 (:REWRITE MOD-X-Y-=-X . 3))
 (2291 23 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1973 55 (:REWRITE DEFAULT-MOD-RATIO))
 (1870 6 (:LINEAR MOD-BOUNDS-3))
 (1844 229 (:REWRITE DEFAULT-TIMES-2))
 (1480 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1478 23 (:REWRITE MOD-ZERO . 3))
 (1442 320 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1319 1319 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1319 1319 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1319 1319 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1298 96 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1262 229 (:REWRITE DEFAULT-TIMES-1))
 (1260 268 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1260 268 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1225 1225 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1181 5 (:LINEAR RTL::MOD-BND-2))
 (1172 268 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1172 268 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1136 320 (:REWRITE DEFAULT-LESS-THAN-1))
 (995 70 (:REWRITE |(* y x)|))
 (954 65 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (880 4 (:REWRITE |(* (* x y) z)|))
 (849 23 (:REWRITE MOD-ZERO . 4))
 (843 23 (:REWRITE MOD-X-Y-=-X . 2))
 (726 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (722 320 (:REWRITE SIMPLIFY-SUMS-<))
 (673 85 (:LINEAR EXPT-<=-1-ONE))
 (652 85 (:LINEAR EXPT->=-1-TWO))
 (652 85 (:LINEAR EXPT->-1-TWO))
 (652 85 (:LINEAR EXPT-<-1-ONE))
 (589 85 (:LINEAR EXPT-X->=-X))
 (589 85 (:LINEAR EXPT->=-1-ONE))
 (589 85 (:LINEAR EXPT-<=-1-TWO))
 (568 85 (:LINEAR EXPT-X->-X))
 (568 85 (:LINEAR EXPT->-1-ONE))
 (568 85 (:LINEAR EXPT-<-1-TWO))
 (527 320 (:REWRITE DEFAULT-LESS-THAN-2))
 (455 13 (:REWRITE |(* (if a b c) x)|))
 (436 12 (:LINEAR MOD-BOUNDS-2))
 (404 202 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (385 55 (:REWRITE DEFAULT-MOD-1))
 (348 4 (:REWRITE |(* y (* x z))|))
 (326 23 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (326 23 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (320 320 (:REWRITE THE-FLOOR-BELOW))
 (320 320 (:REWRITE THE-FLOOR-ABOVE))
 (320 320 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (320 320 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (320 320 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (320 320 (:REWRITE INTEGERP-<-CONSTANT))
 (320 320 (:REWRITE CONSTANT-<-INTEGERP))
 (320 320 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (320 320 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (320 320 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (320 320 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (320 320 (:REWRITE |(< c (- x))|))
 (320 320 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (320 320 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (303 23 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (303 23 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (303 23 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (276 268 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (268 268 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (268 268 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (268 268 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (251 115 (:REWRITE DEFAULT-PLUS-2))
 (211 35 (:META META-INTEGERP-CORRECT))
 (202 202 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (202 202 (:TYPE-PRESCRIPTION NATP))
 (177 177 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (175 115 (:REWRITE DEFAULT-PLUS-1))
 (170 170 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (170 170 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (170 170 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (170 170 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (157 80 (:REWRITE DEFAULT-DIVIDE))
 (152 152 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (113 69 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (106 48 (:REWRITE NORMALIZE-ADDENDS))
 (106 2 (:REWRITE |(equal (expt x n) 0)|))
 (104 55 (:REWRITE DEFAULT-MOD-2))
 (96 96 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (96 96 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (96 96 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (85 85 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (85 85 (:LINEAR EXPT-LINEAR-UPPER-<))
 (85 85 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (85 85 (:LINEAR EXPT-LINEAR-LOWER-<))
 (84 84 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (84 84 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (84 84 (:REWRITE |(< 0 (/ x))|))
 (84 84 (:REWRITE |(< 0 (* x y))|))
 (80 80 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (77 63 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (69 69 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (69 67 (:REWRITE |(equal (- x) c)|))
 (69 67 (:REWRITE |(equal (- x) (- y))|))
 (68 68 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (68 68 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (68 68 (:REWRITE |(< (/ x) 0)|))
 (68 68 (:REWRITE |(< (* x y) 0)|))
 (67 67 (:REWRITE |(equal c (/ x))|))
 (67 67 (:REWRITE |(equal c (- x))|))
 (67 67 (:REWRITE |(equal (/ x) c)|))
 (67 67 (:REWRITE |(equal (/ x) (/ y))|))
 (65 65 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (51 51 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (48 48 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A-EXPT))
 (48 48 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A-EXPT))
 (48 48 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A-EXPT))
 (48 48 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A-EXPT))
 (46 46 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (36 1 (:REWRITE MOD-ZERO . 1))
 (35 35 (:REWRITE REDUCE-INTEGERP-+))
 (35 35 (:REWRITE INTEGERP-MINUS-X))
 (35 20 (:REWRITE DEFAULT-EXPT-2))
 (33 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (32 32 (:REWRITE |(* 0 x)|))
 (30 30 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (30 2 (:REWRITE |(equal x (/ y))|))
 (28 2 (:REWRITE |(not (equal x (/ y)))|))
 (23 23 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (23 23 (:REWRITE |(mod x (- y))| . 3))
 (23 23 (:REWRITE |(mod x (- y))| . 2))
 (23 23 (:REWRITE |(mod x (- y))| . 1))
 (23 23 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (23 23 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (23 1 (:REWRITE MOD-ZERO . 2))
 (20 20 (:REWRITE DEFAULT-EXPT-1))
 (20 20 (:REWRITE |(expt 1/c n)|))
 (20 20 (:REWRITE |(expt (- x) n)|))
 (20 5 (:REWRITE |(+ 0 x)|))
 (19 17 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (16 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (15 15 (:REWRITE |(* c (expt d n))|))
 (10 10 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:REWRITE INTEGERP-/))
 (4 4 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (4 4 (:REWRITE |(* c (* d x))|))
 (4 2 (:REWRITE DEFAULT-MINUS))
 (3 3 (:REWRITE DM::FACTOR-DIVIDES))
 (3 3 (:REWRITE |(* 1 x)|))
 (2 2 (:REWRITE |(+ x (- x))|))
 )
(DM::FRCP-INVERTS
 (608 22 (:REWRITE |(* (* x y) z)|))
 (571 11 (:REWRITE MOD-ZERO . 3))
 (425 11 (:REWRITE MOD-X-Y-=-X . 4))
 (412 412 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (412 412 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (399 11 (:REWRITE DEFAULT-MOD-RATIO))
 (385 11 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (330 66 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (330 66 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (298 66 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (297 155 (:REWRITE DEFAULT-TIMES-2))
 (292 22 (:REWRITE |(* y (* x z))|))
 (289 10 (:REWRITE RTL::MOD-DOES-NOTHING))
 (263 11 (:REWRITE MOD-ZERO . 4))
 (218 155 (:REWRITE DEFAULT-TIMES-1))
 (114 2 (:LINEAR MOD-BOUNDS-3))
 (100 15 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (95 57 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (79 40 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (78 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (75 11 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (73 25 (:META META-INTEGERP-CORRECT))
 (70 10 (:REWRITE MOD-X-Y-=-X . 2))
 (69 69 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (69 40 (:REWRITE SIMPLIFY-SUMS-<))
 (68 40 (:REWRITE DEFAULT-LESS-THAN-1))
 (66 66 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (66 66 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (66 66 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (65 65 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (65 65 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (65 11 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (65 11 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (60 10 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (57 57 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (57 57 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (57 57 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (51 40 (:REWRITE DEFAULT-LESS-THAN-2))
 (41 40 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (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 INTEGERP-<-CONSTANT))
 (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))|))
 (35 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (25 25 (:REWRITE REDUCE-INTEGERP-+))
 (25 25 (:REWRITE INTEGERP-MINUS-X))
 (24 24 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (24 4 (:LINEAR MOD-BOUNDS-2))
 (23 23 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (23 23 (:REWRITE DEFAULT-DIVIDE))
 (22 22 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (22 22 (:REWRITE |(* c (* d x))|))
 (21 21 (:TYPE-PRESCRIPTION NATP))
 (21 11 (:REWRITE DEFAULT-MOD-1))
 (20 10 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (20 10 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (17 3 (:REWRITE |(+ y x)|))
 (16 4 (:REWRITE NORMALIZE-ADDENDS))
 (15 15 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (15 15 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (15 15 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (15 15 (:REWRITE |(equal c (/ x))|))
 (15 15 (:REWRITE |(equal c (- x))|))
 (15 15 (:REWRITE |(equal (/ x) c)|))
 (15 15 (:REWRITE |(equal (/ x) (/ y))|))
 (15 15 (:REWRITE |(equal (- x) c)|))
 (15 15 (:REWRITE |(equal (- x) (- y))|))
 (15 14 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (14 9 (:REWRITE DEFAULT-PLUS-2))
 (12 12 (:REWRITE INTEGERP-/))
 (12 9 (:REWRITE DEFAULT-PLUS-1))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (11 11 (:REWRITE DEFAULT-MOD-2))
 (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 MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (10 10 (:REWRITE |(mod x (- y))| . 3))
 (10 10 (:REWRITE |(mod x (- y))| . 2))
 (10 10 (:REWRITE |(mod x (- y))| . 1))
 (10 10 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (10 10 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (10 10 (:REWRITE |(equal (* x y) 0)|))
 (10 10 (:REWRITE |(< 0 (/ x))|))
 (10 10 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (7 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:DEFINITION FIX))
 (2 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2 1 (:REWRITE |(+ 0 x)|))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (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 DEFAULT-MINUS))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(DM::FRCP-COR
 (1792 33 (:REWRITE MOD-ZERO . 3))
 (1301 33 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1264 33 (:REWRITE DEFAULT-MOD-RATIO))
 (1208 33 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1182 33 (:REWRITE MOD-X-Y-=-X . 4))
 (1182 33 (:REWRITE MOD-X-Y-=-X . 3))
 (1168 1168 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1168 1168 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1168 1168 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1074 404 (:REWRITE DEFAULT-TIMES-2))
 (1030 33 (:REWRITE RTL::MOD-DOES-NOTHING))
 (815 163 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (815 163 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (791 163 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (791 163 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (710 33 (:REWRITE MOD-X-Y-=-X . 2))
 (686 33 (:REWRITE MOD-ZERO . 4))
 (635 404 (:REWRITE DEFAULT-TIMES-1))
 (554 10 (:LINEAR MOD-BOUNDS-3))
 (466 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (300 164 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (296 148 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (289 9 (:LINEAR RTL::MOD-BND-2))
 (254 164 (:REWRITE SIMPLIFY-SUMS-<))
 (245 33 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (245 33 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (240 164 (:REWRITE DEFAULT-LESS-THAN-2))
 (224 164 (:REWRITE DEFAULT-LESS-THAN-1))
 (212 33 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (212 33 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (212 33 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (203 203 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (201 64 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (177 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (177 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (177 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (167 59 (:META META-INTEGERP-CORRECT))
 (164 164 (:REWRITE THE-FLOOR-BELOW))
 (164 164 (:REWRITE THE-FLOOR-ABOVE))
 (164 164 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (164 164 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (164 164 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (164 164 (:REWRITE INTEGERP-<-CONSTANT))
 (164 164 (:REWRITE CONSTANT-<-INTEGERP))
 (164 164 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (164 164 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (164 164 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (164 164 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (164 164 (:REWRITE |(< c (- x))|))
 (164 164 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (164 164 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (164 164 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (164 164 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (164 164 (:REWRITE |(< (/ x) (/ y))|))
 (164 164 (:REWRITE |(< (- x) c)|))
 (164 164 (:REWRITE |(< (- x) (- y))|))
 (163 163 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (163 163 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (163 163 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (163 163 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (163 163 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (148 148 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (148 148 (:TYPE-PRESCRIPTION NATP))
 (148 74 (:REWRITE DEFAULT-DIVIDE))
 (148 20 (:LINEAR MOD-BOUNDS-2))
 (102 102 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (101 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (93 93 (:REWRITE |(* c (* d x))|))
 (74 74 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (71 71 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (71 71 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (71 71 (:REWRITE |(< (/ x) 0)|))
 (71 71 (:REWRITE |(< (* x y) 0)|))
 (66 33 (:REWRITE DEFAULT-MOD-2))
 (65 64 (:REWRITE |(equal (- x) c)|))
 (65 64 (:REWRITE |(equal (- x) (- y))|))
 (65 63 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (64 64 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (64 64 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (64 64 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (64 64 (:REWRITE |(equal c (/ x))|))
 (64 64 (:REWRITE |(equal c (- x))|))
 (64 64 (:REWRITE |(equal (/ x) c)|))
 (64 64 (:REWRITE |(equal (/ x) (/ y))|))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (59 59 (:REWRITE REDUCE-INTEGERP-+))
 (59 59 (:REWRITE INTEGERP-MINUS-X))
 (47 33 (:REWRITE DEFAULT-MOD-1))
 (43 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (33 33 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (33 33 (:REWRITE |(mod x (- y))| . 3))
 (33 33 (:REWRITE |(mod x (- y))| . 2))
 (33 33 (:REWRITE |(mod x (- y))| . 1))
 (33 33 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (33 33 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (32 32 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (31 31 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (31 31 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (31 31 (:REWRITE |(< 0 (/ x))|))
 (31 31 (:REWRITE |(< 0 (* x y))|))
 (20 3 (:REWRITE |(+ y x)|))
 (19 9 (:REWRITE DEFAULT-PLUS-2))
 (19 4 (:REWRITE NORMALIZE-ADDENDS))
 (18 18 (:REWRITE INTEGERP-/))
 (17 9 (:REWRITE DEFAULT-PLUS-1))
 (14 14 (:REWRITE |(equal (* x y) 0)|))
 (14 14 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (9 9 (:LINEAR RTL::MOD-BND-3))
 (7 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4 2 (:DEFINITION FIX))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 1 (:REWRITE DEFAULT-MINUS))
 (2 1 (:REWRITE |(+ 0 x)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(DM::FRCP-PROD
 (4141 35 (:REWRITE |(* (* x y) z)|))
 (3953 21 (:REWRITE RTL::MOD-DOES-NOTHING))
 (3646 21 (:REWRITE MOD-ZERO . 3))
 (3586 21 (:REWRITE MOD-X-Y-=-X . 4))
 (3586 21 (:REWRITE MOD-X-Y-=-X . 3))
 (3387 21 (:REWRITE MOD-ZERO . 4))
 (3219 265 (:REWRITE DEFAULT-TIMES-2))
 (3216 21 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3141 21 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2827 265 (:REWRITE DEFAULT-TIMES-1))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2722 2722 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2573 21 (:REWRITE DEFAULT-MOD-RATIO))
 (2114 5 (:LINEAR MOD-BOUNDS-3))
 (2062 35 (:REWRITE |(* y (* x z))|))
 (1986 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1963 163 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1613 163 (:REWRITE DEFAULT-LESS-THAN-1))
 (1226 1226 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1226 1226 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1226 1226 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1190 238 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1190 238 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1142 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1142 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (845 21 (:REWRITE MOD-X-Y-=-X . 2))
 (519 27 (:META META-INTEGERP-CORRECT))
 (513 163 (:REWRITE DEFAULT-LESS-THAN-2))
 (475 21 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (475 21 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (475 21 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (475 21 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (454 10 (:LINEAR MOD-BOUNDS-2))
 (391 21 (:REWRITE DEFAULT-MOD-1))
 (325 25 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (238 238 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (238 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (238 238 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (238 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (238 238 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (208 36 (:LINEAR EXPT-<=-1-ONE))
 (202 36 (:LINEAR EXPT->=-1-TWO))
 (202 36 (:LINEAR EXPT->-1-TWO))
 (202 36 (:LINEAR EXPT-<-1-ONE))
 (180 36 (:LINEAR EXPT-X->=-X))
 (180 36 (:LINEAR EXPT->=-1-ONE))
 (180 36 (:LINEAR EXPT-<=-1-TWO))
 (174 36 (:LINEAR EXPT-X->-X))
 (174 36 (:LINEAR EXPT->-1-ONE))
 (174 36 (:LINEAR EXPT-<-1-TWO))
 (163 163 (:REWRITE THE-FLOOR-BELOW))
 (163 163 (:REWRITE THE-FLOOR-ABOVE))
 (163 163 (:REWRITE SIMPLIFY-SUMS-<))
 (163 163 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (163 163 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (163 163 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (163 163 (:REWRITE INTEGERP-<-CONSTANT))
 (163 163 (:REWRITE CONSTANT-<-INTEGERP))
 (163 163 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (163 163 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (163 163 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (163 163 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (163 163 (:REWRITE |(< c (- x))|))
 (163 163 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (163 163 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (163 163 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (163 163 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (163 163 (:REWRITE |(< (/ x) (/ y))|))
 (163 163 (:REWRITE |(< (- x) c)|))
 (163 163 (:REWRITE |(< (- x) (- y))|))
 (137 137 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (131 5 (:REWRITE |(equal (expt x n) 0)|))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (87 87 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (72 72 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (72 72 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (72 72 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (72 72 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (49 49 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (49 49 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (49 49 (:REWRITE |(< (/ x) 0)|))
 (49 49 (:REWRITE |(< (* x y) 0)|))
 (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 |(< (* x y) 0) rationalp (* x y)|))
 (36 36 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (36 36 (:LINEAR EXPT-LINEAR-UPPER-<))
 (36 36 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (36 36 (:LINEAR EXPT-LINEAR-LOWER-<))
 (35 35 (:REWRITE |(* c (* d x))|))
 (30 30 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (30 30 (:REWRITE |(equal c (/ x))|))
 (30 30 (:REWRITE |(equal c (- x))|))
 (30 30 (:REWRITE |(equal (/ x) c)|))
 (30 30 (:REWRITE |(equal (/ x) (/ y))|))
 (30 30 (:REWRITE |(equal (- x) c)|))
 (30 30 (:REWRITE |(equal (- x) (- y))|))
 (27 27 (:REWRITE REDUCE-INTEGERP-+))
 (27 27 (:REWRITE INTEGERP-MINUS-X))
 (27 27 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (25 25 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (25 25 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (21 21 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (21 21 (:REWRITE DEFAULT-MOD-2))
 (21 21 (:REWRITE |(mod x (- y))| . 3))
 (21 21 (:REWRITE |(mod x (- y))| . 2))
 (21 21 (:REWRITE |(mod x (- y))| . 1))
 (21 21 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (21 21 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (21 21 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (21 21 (:REWRITE |(equal (* x y) 0)|))
 (15 15 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (12 12 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (12 12 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (5 5 (:REWRITE DEFAULT-EXPT-2))
 (5 5 (:REWRITE DEFAULT-EXPT-1))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 )
(DM::MOD-FRCP
 (11259 44 (:REWRITE MOD-ZERO . 4))
 (9788 44 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (8594 44 (:REWRITE MOD-X-Y-=-X . 4))
 (8582 44 (:REWRITE MOD-X-Y-=-X . 3))
 (7662 44 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (7312 494 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (7288 494 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (7288 494 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (6150 22 (:LINEAR RTL::MOD-BND-2))
 (5569 44 (:REWRITE DEFAULT-MOD-RATIO))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (5417 5417 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (5352 494 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (5352 494 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (5349 491 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4580 44 (:REWRITE MOD-ZERO . 3))
 (3317 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (3159 276 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2954 28 (:LINEAR MOD-BOUNDS-3))
 (2951 75 (:REWRITE |(* y x)|))
 (2801 150 (:REWRITE DEFAULT-TIMES-2))
 (2801 150 (:REWRITE DEFAULT-TIMES-1))
 (2656 2656 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2656 2656 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2656 2656 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2505 276 (:REWRITE DEFAULT-LESS-THAN-1))
 (2470 494 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1920 44 (:REWRITE MOD-X-Y-=-X . 2))
 (1881 44 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1881 44 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1651 44 (:REWRITE DEFAULT-MOD-1))
 (1492 56 (:LINEAR MOD-BOUNDS-2))
 (1405 44 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1405 44 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1405 44 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1362 276 (:REWRITE SIMPLIFY-SUMS-<))
 (898 276 (:REWRITE DEFAULT-LESS-THAN-2))
 (878 16 (:REWRITE |(equal (expt x n) 0)|))
 (618 114 (:LINEAR EXPT-<=-1-ONE))
 (600 114 (:LINEAR EXPT->=-1-TWO))
 (600 114 (:LINEAR EXPT->-1-TWO))
 (600 114 (:LINEAR EXPT-<-1-ONE))
 (546 114 (:LINEAR EXPT-X->=-X))
 (546 114 (:LINEAR EXPT->=-1-ONE))
 (546 114 (:LINEAR EXPT-<=-1-TWO))
 (528 114 (:LINEAR EXPT-X->-X))
 (528 114 (:LINEAR EXPT->-1-ONE))
 (528 114 (:LINEAR EXPT-<-1-TWO))
 (518 8 (:REWRITE MOD-NEGATIVE . 3))
 (506 71 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (494 494 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (494 494 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (494 494 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (494 494 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (494 494 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (491 491 (:TYPE-PRESCRIPTION NATP))
 (476 44 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (476 44 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (476 44 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (455 103 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (278 278 (:REWRITE THE-FLOOR-BELOW))
 (278 278 (:REWRITE THE-FLOOR-ABOVE))
 (276 276 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (276 276 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (276 276 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (276 276 (:REWRITE INTEGERP-<-CONSTANT))
 (276 276 (:REWRITE CONSTANT-<-INTEGERP))
 (276 276 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (276 276 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (276 276 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (276 276 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (276 276 (:REWRITE |(< c (- x))|))
 (276 276 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (276 276 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (276 276 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (276 276 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (276 276 (:REWRITE |(< (/ x) (/ y))|))
 (276 276 (:REWRITE |(< (- x) c)|))
 (276 276 (:REWRITE |(< (- x) (- y))|))
 (228 228 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (228 228 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (228 228 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (228 228 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (171 3 (:REWRITE MOD-ZERO . 1))
 (150 75 (:REWRITE DEFAULT-DIVIDE))
 (133 133 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (132 3 (:REWRITE MOD-POSITIVE . 3))
 (114 114 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (114 114 (:LINEAR EXPT-LINEAR-UPPER-<))
 (114 114 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (114 114 (:LINEAR EXPT-LINEAR-LOWER-<))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (106 106 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (103 103 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (96 16 (:REWRITE |(+ c (+ d x))|))
 (90 3 (:REWRITE MOD-ZERO . 2))
 (88 44 (:REWRITE DEFAULT-MOD-2))
 (87 87 (:REWRITE |(equal c (/ x))|))
 (87 87 (:REWRITE |(equal c (- x))|))
 (87 87 (:REWRITE |(equal (/ x) c)|))
 (87 87 (:REWRITE |(equal (/ x) (/ y))|))
 (87 87 (:REWRITE |(equal (- x) c)|))
 (87 87 (:REWRITE |(equal (- x) (- y))|))
 (75 75 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (75 75 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (73 73 (:REWRITE |(< 0 (/ x))|))
 (73 73 (:REWRITE |(< 0 (* x y))|))
 (71 71 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (71 71 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (68 34 (:REWRITE DEFAULT-PLUS-2))
 (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)|))
 (58 58 (:REWRITE |(< (* x y) 0)|))
 (58 8 (:REWRITE MOD-NEGATIVE . 2))
 (55 55 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (54 3 (:REWRITE MOD-NONPOSITIVE))
 (44 44 (:REWRITE |(mod x (- y))| . 3))
 (44 44 (:REWRITE |(mod x (- y))| . 2))
 (44 44 (:REWRITE |(mod x (- y))| . 1))
 (42 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (34 34 (:REWRITE DEFAULT-PLUS-1))
 (32 32 (:REWRITE REDUCE-INTEGERP-+))
 (32 32 (:REWRITE INTEGERP-MINUS-X))
 (32 32 (:META META-INTEGERP-CORRECT))
 (32 16 (:REWRITE |(+ 0 x)|))
 (22 22 (:LINEAR RTL::MOD-BND-3))
 (8 8 (:REWRITE MOD-NEGATIVE . 1))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 3 (:REWRITE MOD-POSITIVE . 2))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 2 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (3 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (3 3 (:REWRITE MOD-POSITIVE . 1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-EXPT-1))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 )
(DM::FRCP-MOD
 (42854 217 (:REWRITE RTL::MOD-DOES-NOTHING))
 (11736 106 (:LINEAR EXPT-<=-1-ONE))
 (10717 217 (:REWRITE MOD-ZERO . 4))
 (10616 217 (:REWRITE MOD-X-Y-=-X . 3))
 (9667 217 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (9029 217 (:REWRITE MOD-X-Y-=-X . 4))
 (8896 217 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (8381 106 (:LINEAR EXPT->=-1-TWO))
 (8381 106 (:LINEAR EXPT->-1-TWO))
 (8381 106 (:LINEAR EXPT-<-1-ONE))
 (8299 8299 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (8299 8299 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (8299 8299 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (7995 106 (:LINEAR EXPT-X->=-X))
 (7995 106 (:LINEAR EXPT->=-1-ONE))
 (7995 106 (:LINEAR EXPT-<=-1-TWO))
 (7976 106 (:LINEAR EXPT-X->-X))
 (7976 106 (:LINEAR EXPT->-1-ONE))
 (7976 106 (:LINEAR EXPT-<-1-TWO))
 (7813 1434 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (7789 1434 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (7789 1434 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (7170 1434 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (6792 217 (:REWRITE MOD-ZERO . 3))
 (4973 1044 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4583 217 (:REWRITE DEFAULT-MOD-RATIO))
 (3634 15 (:REWRITE |(equal (expt x n) 0)|))
 (3111 1216 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2986 458 (:REWRITE |(* y x)|))
 (2976 78 (:LINEAR MOD-BOUNDS-3))
 (2896 1060 (:REWRITE DEFAULT-LESS-THAN-2))
 (2884 1060 (:REWRITE DEFAULT-LESS-THAN-1))
 (2492 699 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (2125 1434 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (2070 916 (:REWRITE DEFAULT-TIMES-2))
 (2070 916 (:REWRITE DEFAULT-TIMES-1))
 (2066 1044 (:REWRITE SIMPLIFY-SUMS-<))
 (1907 1216 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (1823 217 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1823 217 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1466 217 (:REWRITE MOD-X-Y-=-X . 2))
 (1434 1434 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1434 1434 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1434 1434 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1434 1434 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1317 1317 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (1308 156 (:LINEAR MOD-BOUNDS-2))
 (1217 217 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1217 217 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1217 217 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1060 1060 (:REWRITE THE-FLOOR-BELOW))
 (1060 1060 (:REWRITE THE-FLOOR-ABOVE))
 (1060 1060 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1060 1060 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1044 1044 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1044 1044 (:REWRITE INTEGERP-<-CONSTANT))
 (1044 1044 (:REWRITE CONSTANT-<-INTEGERP))
 (1044 1044 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1044 1044 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1044 1044 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1044 1044 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1044 1044 (:REWRITE |(< c (- x))|))
 (1044 1044 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1044 1044 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1044 1044 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1044 1044 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1044 1044 (:REWRITE |(< (/ x) (/ y))|))
 (1044 1044 (:REWRITE |(< (- x) c)|))
 (1044 1044 (:REWRITE |(< (- x) (- y))|))
 (916 458 (:REWRITE DEFAULT-DIVIDE))
 (766 63 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (699 699 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (699 699 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (699 699 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (630 18 (:REWRITE MOD-POSITIVE . 3))
 (614 614 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (606 217 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (606 217 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (606 217 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (604 274 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (556 8 (:REWRITE ZP-OPEN))
 (515 217 (:REWRITE DEFAULT-MOD-1))
 (458 458 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (458 458 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (456 244 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (434 217 (:REWRITE DEFAULT-MOD-2))
 (390 390 (:REWRITE |(< (* x y) 0)|))
 (382 382 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (382 382 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (382 382 (:REWRITE |(< (/ x) 0)|))
 (339 18 (:REWRITE MOD-POSITIVE . 2))
 (296 4 (:REWRITE DM::MOD-EXPT-REWRITE-2))
 (292 4 (:REWRITE DM::MOD-EXPT-REWRITE-1))
 (274 274 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (259 259 (:REWRITE |(equal c (/ x))|))
 (259 259 (:REWRITE |(equal c (- x))|))
 (259 259 (:REWRITE |(equal (/ x) c)|))
 (259 259 (:REWRITE |(equal (/ x) (/ y))|))
 (259 259 (:REWRITE |(equal (- x) c)|))
 (259 259 (:REWRITE |(equal (- x) (- y))|))
 (248 8 (:REWRITE |(< (+ (- c) x) y)|))
 (244 244 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (244 244 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (242 242 (:REWRITE REDUCE-INTEGERP-+))
 (242 242 (:REWRITE INTEGERP-MINUS-X))
 (242 242 (:META META-INTEGERP-CORRECT))
 (225 225 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (220 8 (:REWRITE |(< y (+ (- c) x))|))
 (218 218 (:REWRITE |(< 0 (* x y))|))
 (217 217 (:REWRITE |(mod x (- y))| . 3))
 (217 217 (:REWRITE |(mod x (- y))| . 2))
 (217 217 (:REWRITE |(mod x (- y))| . 1))
 (212 212 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (212 212 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (212 212 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (212 212 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (210 210 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (210 210 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (210 210 (:REWRITE |(< 0 (/ x))|))
 (180 4 (:REWRITE MOD-THEOREM-TWO))
 (106 106 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (106 106 (:LINEAR EXPT-LINEAR-UPPER-<))
 (106 106 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (106 106 (:LINEAR EXPT-LINEAR-LOWER-<))
 (90 15 (:REWRITE |(+ c (+ d x))|))
 (72 72 (:LINEAR RTL::MOD-BND-3))
 (64 32 (:REWRITE DEFAULT-PLUS-2))
 (48 4 (:REWRITE MOD-ZERO . 1))
 (40 7 (:REWRITE DEFAULT-EXPT-1))
 (32 32 (:REWRITE DEFAULT-PLUS-1))
 (30 15 (:REWRITE |(+ 0 x)|))
 (28 4 (:REWRITE MOD-ZERO . 2))
 (18 18 (:REWRITE MOD-POSITIVE . 1))
 (14 7 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:TYPE-PRESCRIPTION ZP))
 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (8 8 (:REWRITE |(< (+ c/d x) y)|))
 (8 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (7 7 (:REWRITE |(expt 1/c n)|))
 (7 7 (:REWRITE |(expt (- x) n)|))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (4 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 )
(DM::PRIME-DIVIDES-1)
(DM::FRCP-EXPT
 (22671 14 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (20734 104 (:REWRITE RTL::MOD-DOES-NOTHING))
 (13770 254 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (13513 121 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (10437 117 (:REWRITE MOD-X-Y-=-X . 4))
 (8097 117 (:REWRITE MOD-ZERO . 3))
 (7638 144 (:REWRITE DEFAULT-MOD-RATIO))
 (7371 6815 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (6815 6815 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (6815 6815 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (6815 6815 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (6815 6815 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6570 14 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (5757 698 (:REWRITE DEFAULT-TIMES-2))
 (5281 644 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5201 1064 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4223 698 (:REWRITE DEFAULT-TIMES-1))
 (4206 47 (:REWRITE |(* (* x y) z)|))
 (4055 4055 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4055 4055 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4055 4055 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3814 1067 (:REWRITE DEFAULT-LESS-THAN-1))
 (3810 1064 (:REWRITE SIMPLIFY-SUMS-<))
 (3496 215 (:REWRITE |(* y x)|))
 (3464 121 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3320 664 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (3307 27 (:LINEAR MOD-BOUNDS-3))
 (3061 677 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3061 677 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2913 255 (:LINEAR EXPT->=-1-TWO))
 (2863 255 (:LINEAR EXPT->-1-TWO))
 (2863 255 (:LINEAR EXPT-<-1-ONE))
 (2784 104 (:REWRITE MOD-X-Y-=-X . 2))
 (2758 255 (:LINEAR EXPT->=-1-ONE))
 (2687 255 (:LINEAR EXPT-X->=-X))
 (2641 255 (:LINEAR EXPT-<=-1-TWO))
 (2623 1067 (:REWRITE DEFAULT-LESS-THAN-2))
 (2615 255 (:LINEAR EXPT-X->-X))
 (2615 255 (:LINEAR EXPT->-1-ONE))
 (2615 255 (:LINEAR EXPT-<-1-TWO))
 (2065 121 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (2065 121 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1673 47 (:REWRITE |(* y (* x z))|))
 (1657 242 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1626 104 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1626 104 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1626 104 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1452 144 (:REWRITE DEFAULT-MOD-1))
 (1209 206 (:REWRITE DEFAULT-PLUS-2))
 (1067 1067 (:REWRITE THE-FLOOR-BELOW))
 (1067 1067 (:REWRITE THE-FLOOR-ABOVE))
 (1067 1067 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1067 1067 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1067 1067 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1067 1067 (:REWRITE INTEGERP-<-CONSTANT))
 (1067 1067 (:REWRITE CONSTANT-<-INTEGERP))
 (1067 1067 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1067 1067 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1067 1067 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1067 1067 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1067 1067 (:REWRITE |(< c (- x))|))
 (1067 1067 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1067 1067 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1067 1067 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1067 1067 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1067 1067 (:REWRITE |(< (/ x) (/ y))|))
 (1067 1067 (:REWRITE |(< (- x) c)|))
 (1067 1067 (:REWRITE |(< (- x) (- y))|))
 (1056 54 (:LINEAR MOD-BOUNDS-2))
 (677 677 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (677 677 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (677 677 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (664 664 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (664 664 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (652 510 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (644 644 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (644 644 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (644 644 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (640 510 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (640 137 (:META META-INTEGERP-CORRECT))
 (640 88 (:REWRITE NORMALIZE-ADDENDS))
 (601 601 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (585 206 (:REWRITE DEFAULT-PLUS-1))
 (510 510 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (510 510 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (500 250 (:REWRITE DEFAULT-DIVIDE))
 (445 317 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (345 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (332 12 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (321 309 (:REWRITE |(equal (- x) (- y))|))
 (317 317 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (309 309 (:REWRITE |(equal c (/ x))|))
 (309 309 (:REWRITE |(equal c (- x))|))
 (309 309 (:REWRITE |(equal (/ x) c)|))
 (309 309 (:REWRITE |(equal (/ x) (/ y))|))
 (309 309 (:REWRITE |(equal (- x) c)|))
 (298 10 (:REWRITE |(* (if a b c) x)|))
 (297 297 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (297 297 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (297 297 (:REWRITE |(< 0 (/ x))|))
 (297 297 (:REWRITE |(< 0 (* x y))|))
 (288 144 (:REWRITE DEFAULT-MOD-2))
 (255 255 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (255 255 (:LINEAR EXPT-LINEAR-UPPER-<))
 (255 255 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (255 255 (:LINEAR EXPT-LINEAR-LOWER-<))
 (254 254 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (250 250 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (248 104 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (248 104 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (248 104 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (189 189 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (186 14 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (153 137 (:REWRITE INTEGERP-MINUS-X))
 (137 137 (:REWRITE REDUCE-INTEGERP-+))
 (134 134 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (110 110 (:TYPE-PRESCRIPTION NATP))
 (110 110 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (104 104 (:REWRITE |(mod x (- y))| . 3))
 (104 104 (:REWRITE |(mod x (- y))| . 2))
 (104 104 (:REWRITE |(mod x (- y))| . 1))
 (81 81 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (76 76 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (67 57 (:REWRITE DEFAULT-EXPT-1))
 (61 1 (:REWRITE |(+ x (if a b c))|))
 (57 57 (:REWRITE DEFAULT-EXPT-2))
 (57 57 (:REWRITE |(expt 1/c n)|))
 (57 57 (:REWRITE |(expt (- x) n)|))
 (47 47 (:REWRITE |(* c (* d x))|))
 (44 22 (:REWRITE |(* 1 x)|))
 (43 22 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (41 13 (:REWRITE DEFAULT-MINUS))
 (37 37 (:REWRITE |(equal (+ (- c) x) y)|))
 (34 34 (:REWRITE INTEGERP-/))
 (26 26 (:LINEAR RTL::MOD-BND-3))
 (23 23 (:REWRITE |(* 0 x)|))
 (20 20 (:REWRITE |(equal (* x y) 0)|))
 (20 20 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (12 12 (:REWRITE |(+ x (- x))|))
 (10 10 (:REWRITE |(* c (expt d n))|))
 (7 7 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(DM::PRIME-DIVIDES-EXPT
 (22 2 (:REWRITE DEFAULT-TIMES-2))
 (12 12 (:REWRITE DEFAULT-PLUS-2))
 (12 12 (:REWRITE DEFAULT-PLUS-1))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE NORMALIZE-ADDENDS))
 (7 7 (:REWRITE DM::FACTOR-DIVIDES))
 (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)|))
 (3 2 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (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-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (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 |(equal (+ (- c) 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 (expt d n))|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(DM::MOD-EXPT-0
 (1371 8 (:REWRITE RTL::MOD-DOES-NOTHING))
 (570 8 (:REWRITE MOD-X-Y-=-X . 4))
 (570 8 (:REWRITE MOD-X-Y-=-X . 3))
 (550 8 (:REWRITE MOD-ZERO . 4))
 (538 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (532 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (441 2 (:LINEAR RTL::MOD-BND-2))
 (368 368 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (368 368 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (368 368 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (327 8 (:REWRITE MOD-ZERO . 3))
 (310 62 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (283 283 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (250 90 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (220 90 (:REWRITE DEFAULT-LESS-THAN-1))
 (206 62 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (179 8 (:REWRITE DEFAULT-MOD-RATIO))
 (152 44 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (150 90 (:REWRITE SIMPLIFY-SUMS-<))
 (142 62 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (142 62 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (140 44 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (134 22 (:LINEAR EXPT-<=-1-ONE))
 (130 22 (:LINEAR EXPT->=-1-TWO))
 (130 22 (:LINEAR EXPT->-1-TWO))
 (130 22 (:LINEAR EXPT-<-1-ONE))
 (121 11 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (120 90 (:REWRITE DEFAULT-LESS-THAN-2))
 (118 22 (:LINEAR EXPT-X->=-X))
 (118 22 (:LINEAR EXPT->=-1-ONE))
 (118 22 (:LINEAR EXPT-<=-1-TWO))
 (116 3 (:LINEAR MOD-BOUNDS-3))
 (114 22 (:LINEAR EXPT-X->-X))
 (114 22 (:LINEAR EXPT->-1-ONE))
 (114 22 (:LINEAR EXPT-<-1-TWO))
 (114 3 (:REWRITE |(equal (expt x n) 0)|))
 (100 8 (:REWRITE MOD-X-Y-=-X . 2))
 (98 7 (:REWRITE |(* y x)|))
 (96 26 (:REWRITE DEFAULT-TIMES-2))
 (96 26 (:REWRITE DEFAULT-TIMES-1))
 (90 90 (:REWRITE THE-FLOOR-BELOW))
 (90 90 (:REWRITE THE-FLOOR-ABOVE))
 (90 90 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (90 90 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (90 90 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (90 90 (:REWRITE INTEGERP-<-CONSTANT))
 (90 90 (:REWRITE CONSTANT-<-INTEGERP))
 (90 90 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (90 90 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (90 90 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (90 90 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (90 90 (:REWRITE |(< c (- x))|))
 (90 90 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (90 90 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (90 90 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (90 90 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (90 90 (:REWRITE |(< (/ x) (/ y))|))
 (90 90 (:REWRITE |(< (- x) c)|))
 (90 90 (:REWRITE |(< (- x) (- y))|))
 (84 42 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (70 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (70 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (70 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (70 8 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (70 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (62 62 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (62 62 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (62 62 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (62 62 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (50 6 (:LINEAR MOD-BOUNDS-2))
 (46 46 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (44 44 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (42 42 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (42 42 (:TYPE-PRESCRIPTION NATP))
 (40 40 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (38 8 (:REWRITE DEFAULT-MOD-1))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (24 24 (:REWRITE |(< 0 (/ x))|))
 (24 24 (:REWRITE |(< 0 (* x y))|))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (22 22 (:REWRITE |(< (/ x) 0)|))
 (22 22 (:REWRITE |(< (* x y) 0)|))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<))
 (19 19 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (19 19 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (19 19 (:REWRITE DEFAULT-DIVIDE))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (17 17 (:REWRITE |(equal c (/ x))|))
 (17 17 (:REWRITE |(equal c (- x))|))
 (17 17 (:REWRITE |(equal (/ x) c)|))
 (17 17 (:REWRITE |(equal (/ x) (/ y))|))
 (17 17 (:REWRITE |(equal (- x) c)|))
 (17 17 (:REWRITE |(equal (- x) (- y))|))
 (16 16 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (14 14 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (14 14 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (14 14 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (14 14 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (11 11 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (11 11 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (11 11 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:META META-INTEGERP-CORRECT))
 (8 8 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (8 8 (:REWRITE DEFAULT-MOD-2))
 (8 8 (:REWRITE |(mod x (- y))| . 3))
 (8 8 (:REWRITE |(mod x (- y))| . 2))
 (8 8 (:REWRITE |(mod x (- y))| . 1))
 (8 8 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2 2 (:REWRITE DM::FACTOR-DIVIDES))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (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)|))
 )
(DM::MOD-FRCP-0
 (3241 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (3020 22 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (2407 22 (:REWRITE MOD-ZERO . 4))
 (2125 22 (:REWRITE MOD-X-Y-=-X . 4))
 (2125 22 (:REWRITE MOD-X-Y-=-X . 3))
 (1986 22 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1961 66 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1603 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1442 1442 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1442 1442 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1442 1442 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1393 9 (:LINEAR RTL::MOD-BND-2))
 (1360 272 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1360 272 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1346 22 (:REWRITE MOD-ZERO . 3))
 (1343 22 (:REWRITE DEFAULT-MOD-RATIO))
 (1308 272 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1308 272 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1182 338 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (993 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (978 338 (:REWRITE DEFAULT-LESS-THAN-1))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (955 955 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (827 49 (:REWRITE |(* y x)|))
 (757 12 (:LINEAR MOD-BOUNDS-3))
 (729 98 (:REWRITE DEFAULT-TIMES-2))
 (729 98 (:REWRITE DEFAULT-TIMES-1))
 (719 338 (:REWRITE SIMPLIFY-SUMS-<))
 (692 76 (:LINEAR EXPT-<=-1-ONE))
 (686 22 (:REWRITE MOD-X-Y-=-X . 2))
 (670 76 (:LINEAR EXPT->=-1-TWO))
 (670 76 (:LINEAR EXPT->-1-TWO))
 (670 76 (:LINEAR EXPT-<-1-ONE))
 (604 76 (:LINEAR EXPT-X->=-X))
 (604 76 (:LINEAR EXPT->=-1-ONE))
 (604 76 (:LINEAR EXPT-<=-1-TWO))
 (582 76 (:LINEAR EXPT-X->-X))
 (582 76 (:LINEAR EXPT->-1-ONE))
 (582 76 (:LINEAR EXPT-<-1-TWO))
 (520 338 (:REWRITE DEFAULT-LESS-THAN-2))
 (472 22 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (472 22 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (454 24 (:LINEAR MOD-BOUNDS-2))
 (454 9 (:REWRITE |(equal (expt x n) 0)|))
 (402 22 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (402 22 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (402 22 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (345 22 (:REWRITE DEFAULT-MOD-1))
 (341 152 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (341 152 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (339 339 (:REWRITE THE-FLOOR-BELOW))
 (339 339 (:REWRITE THE-FLOOR-ABOVE))
 (338 338 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (338 338 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (338 338 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (338 338 (:REWRITE INTEGERP-<-CONSTANT))
 (338 338 (:REWRITE CONSTANT-<-INTEGERP))
 (338 338 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (338 338 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (338 338 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (338 338 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (338 338 (:REWRITE |(< c (- x))|))
 (338 338 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (338 338 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (338 338 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (338 338 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (338 338 (:REWRITE |(< (/ x) (/ y))|))
 (338 338 (:REWRITE |(< (- x) c)|))
 (338 338 (:REWRITE |(< (- x) (- y))|))
 (320 152 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (313 152 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (312 4 (:REWRITE MOD-ZERO . 1))
 (272 272 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (272 272 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (272 272 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (272 272 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (272 272 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (257 257 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (257 83 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (253 253 (:TYPE-PRESCRIPTION NATP))
 (220 220 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (186 47 (:REWRITE DEFAULT-PLUS-2))
 (182 3 (:REWRITE MOD-NEGATIVE . 3))
 (152 152 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (141 4 (:REWRITE MOD-ZERO . 2))
 (112 13 (:REWRITE NORMALIZE-ADDENDS))
 (107 47 (:REWRITE DEFAULT-PLUS-1))
 (98 49 (:REWRITE DEFAULT-DIVIDE))
 (97 97 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (97 97 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (97 97 (:REWRITE |(< 0 (/ x))|))
 (97 97 (:REWRITE |(< 0 (* x y))|))
 (96 9 (:REWRITE |(+ y x)|))
 (87 63 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (83 83 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (78 75 (:REWRITE |(equal (- x) c)|))
 (78 75 (:REWRITE |(equal (- x) (- y))|))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (76 76 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (76 76 (:LINEAR EXPT-LINEAR-UPPER-<))
 (76 76 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (76 76 (:LINEAR EXPT-LINEAR-LOWER-<))
 (75 75 (:REWRITE |(equal c (/ x))|))
 (75 75 (:REWRITE |(equal c (- x))|))
 (75 75 (:REWRITE |(equal (/ x) c)|))
 (75 75 (:REWRITE |(equal (/ x) (/ y))|))
 (70 22 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (70 22 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (70 22 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (66 66 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (59 59 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (59 59 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (59 59 (:REWRITE |(< (/ x) 0)|))
 (59 59 (:REWRITE |(< (* x y) 0)|))
 (57 3 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (52 52 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (51 11 (:REWRITE |(+ c (+ d x))|))
 (49 49 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (49 49 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (46 14 (:REWRITE |(+ 0 x)|))
 (44 22 (:REWRITE DEFAULT-MOD-2))
 (41 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (33 1 (:REWRITE MOD-POSITIVE . 3))
 (29 29 (:REWRITE REDUCE-INTEGERP-+))
 (29 29 (:REWRITE INTEGERP-MINUS-X))
 (29 29 (:META META-INTEGERP-CORRECT))
 (27 3 (:REWRITE MOD-NEGATIVE . 2))
 (22 22 (:REWRITE |(mod x (- y))| . 3))
 (22 22 (:REWRITE |(mod x (- y))| . 2))
 (22 22 (:REWRITE |(mod x (- y))| . 1))
 (18 1 (:REWRITE MOD-NONPOSITIVE))
 (13 13 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (12 6 (:DEFINITION FIX))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:LINEAR RTL::MOD-BND-3))
 (6 6 (:REWRITE |(equal (+ (- c) x) y)|))
 (6 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 3 (:REWRITE DEFAULT-MINUS))
 (5 5 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 3 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE MOD-NEGATIVE . 1))
 (3 3 (:REWRITE DEFAULT-EXPT-1))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (3 3 (:REWRITE |(+ x (- x))|))
 (2 1 (:REWRITE MOD-POSITIVE . 2))
 (1 1 (:REWRITE MOD-POSITIVE . 1))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(DM::F/CANCEL
 (2540 36 (:REWRITE MOD-ZERO . 3))
 (1831 607 (:REWRITE DEFAULT-TIMES-2))
 (1826 36 (:REWRITE DEFAULT-MOD-RATIO))
 (1559 36 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1447 36 (:REWRITE MOD-X-Y-=-X . 3))
 (1443 36 (:REWRITE MOD-X-Y-=-X . 4))
 (1416 36 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1321 1321 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1321 1321 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1321 1321 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1246 36 (:REWRITE RTL::MOD-DOES-NOTHING))
 (1070 214 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1070 214 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1005 607 (:REWRITE DEFAULT-TIMES-1))
 (899 36 (:REWRITE MOD-ZERO . 4))
 (894 214 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (894 214 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (763 36 (:REWRITE MOD-X-Y-=-X . 2))
 (726 242 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (698 10 (:LINEAR MOD-BOUNDS-3))
 (613 73 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (526 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (413 178 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (362 181 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (317 9 (:LINEAR RTL::MOD-BND-2))
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(DM::F/MOD
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(DM::F*/-1
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(DM::F*/
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 (251 251 (:REWRITE |(< (- x) c)|))
 (251 251 (:REWRITE |(< (- x) (- y))|))
 (250 250 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (237 92 (:META META-INTEGERP-CORRECT))
 (236 118 (:REWRITE DEFAULT-DIVIDE))
 (187 39 (:REWRITE DEFAULT-PLUS-2))
 (176 24 (:LINEAR MOD-BOUNDS-2))
 (155 155 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (118 118 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (108 104 (:REWRITE |(equal (- x) (- y))|))
 (108 92 (:REWRITE INTEGERP-MINUS-X))
 (107 107 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (107 107 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (107 107 (:REWRITE |(< (/ x) 0)|))
 (107 107 (:REWRITE |(< (* x y) 0)|))
 (106 12 (:REWRITE |(+ y x)|))
 (105 104 (:REWRITE |(equal (- x) c)|))
 (104 104 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (104 104 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (104 104 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (104 104 (:REWRITE |(equal c (/ x))|))
 (104 104 (:REWRITE |(equal c (- x))|))
 (104 104 (:REWRITE |(equal (/ x) c)|))
 (104 104 (:REWRITE |(equal (/ x) (/ y))|))
 (102 51 (:REWRITE DEFAULT-MOD-2))
 (100 39 (:REWRITE DEFAULT-PLUS-1))
 (92 92 (:REWRITE REDUCE-INTEGERP-+))
 (90 90 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (72 18 (:REWRITE NORMALIZE-ADDENDS))
 (70 70 (:REWRITE |(* c (* d x))|))
 (67 51 (:REWRITE DEFAULT-MOD-1))
 (53 53 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (53 53 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (51 51 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (51 51 (:REWRITE |(mod x (- y))| . 3))
 (51 51 (:REWRITE |(mod x (- y))| . 2))
 (51 51 (:REWRITE |(mod x (- y))| . 1))
 (51 51 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (51 51 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (48 48 (:REWRITE |(< 0 (/ x))|))
 (48 48 (:REWRITE |(< 0 (* x y))|))
 (45 45 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (36 1 (:REWRITE MOD-ZERO . 1))
 (27 7 (:REWRITE DEFAULT-MINUS))
 (25 25 (:REWRITE INTEGERP-/))
 (24 10 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (24 4 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (23 1 (:REWRITE MOD-ZERO . 2))
 (20 20 (:REWRITE |(equal (* x y) 0)|))
 (20 20 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (16 8 (:DEFINITION FIX))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE |(equal (+ (- c) x) y)|))
 (11 11 (:LINEAR RTL::MOD-BND-3))
 (8 5 (:REWRITE |(+ 0 x)|))
 (8 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE |(+ x (- x))|))
 (4 4 (:REWRITE |(+ c (+ d x))|))
 (3 3 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (3 3 (:REWRITE |(- (* c x))|))
 )
(DM::ODD-CHAR
 (671 671 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (671 671 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (671 671 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (591 147 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (591 147 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (487 147 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (487 147 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (385 12 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (366 12 (:REWRITE MOD-ZERO . 3))
 (361 12 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (357 22 (:REWRITE DEFAULT-MOD-RATIO))
 (348 12 (:REWRITE MOD-X-Y-=-X . 4))
 (348 12 (:REWRITE MOD-X-Y-=-X . 3))
 (302 12 (:REWRITE RTL::MOD-DOES-NOTHING))
 (244 122 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (235 12 (:REWRITE MOD-X-Y-=-X . 2))
 (207 37 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (189 110 (:REWRITE DEFAULT-TIMES-2))
 (186 12 (:REWRITE MOD-ZERO . 4))
 (179 13 (:REWRITE |(* (* x y) z)|))
 (175 37 (:REWRITE |(* y x)|))
 (160 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (155 147 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (147 147 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (147 147 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (147 147 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (137 110 (:REWRITE DEFAULT-TIMES-1))
 (122 122 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (122 122 (:TYPE-PRESCRIPTION NATP))
 (120 3 (:LINEAR MOD-BOUNDS-3))
 (102 55 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (99 2 (:REWRITE MOD-ZERO . 1))
 (89 51 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (84 12 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (84 12 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (79 2 (:LINEAR RTL::MOD-BND-2))
 (77 55 (:REWRITE DEFAULT-LESS-THAN-2))
 (76 54 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (74 54 (:REWRITE SIMPLIFY-SUMS-<))
 (72 12 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (72 12 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (72 12 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (68 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (60 54 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (55 55 (:REWRITE THE-FLOOR-BELOW))
 (55 55 (:REWRITE THE-FLOOR-ABOVE))
 (55 55 (:REWRITE DEFAULT-LESS-THAN-1))
 (54 54 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (54 54 (:REWRITE INTEGERP-<-CONSTANT))
 (54 54 (:REWRITE CONSTANT-<-INTEGERP))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (54 54 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< c (- x))|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (54 54 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (54 54 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (54 54 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (54 54 (:REWRITE |(< (/ x) (/ y))|))
 (54 54 (:REWRITE |(< (- x) c)|))
 (54 54 (:REWRITE |(< (- x) (- y))|))
 (54 27 (:REWRITE DEFAULT-DIVIDE))
 (51 51 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (51 51 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (51 51 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (48 48 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (46 2 (:REWRITE MOD-ZERO . 2))
 (45 25 (:META META-INTEGERP-CORRECT))
 (42 6 (:LINEAR MOD-BOUNDS-2))
 (39 37 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (39 37 (:REWRITE |(equal (- x) c)|))
 (39 37 (:REWRITE |(equal (- x) (- y))|))
 (38 38 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (38 38 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (37 37 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (37 37 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (37 37 (:REWRITE |(equal c (/ x))|))
 (37 37 (:REWRITE |(equal c (- x))|))
 (37 37 (:REWRITE |(equal (/ x) c)|))
 (37 37 (:REWRITE |(equal (/ x) (/ y))|))
 (37 35 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (36 6 (:REWRITE |(+ y x)|))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (34 22 (:REWRITE DEFAULT-MOD-2))
 (33 33 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (30 18 (:REWRITE DEFAULT-PLUS-1))
 (30 6 (:REWRITE NORMALIZE-ADDENDS))
 (28 18 (:REWRITE DEFAULT-PLUS-2))
 (27 27 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (25 25 (:REWRITE REDUCE-INTEGERP-+))
 (25 25 (:REWRITE INTEGERP-MINUS-X))
 (24 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (23 23 (:REWRITE |(< (* x y) 0)|))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (22 22 (:REWRITE DEFAULT-MOD-1))
 (22 22 (:REWRITE |(< (/ x) 0)|))
 (15 15 (:TYPE-PRESCRIPTION ABS))
 (13 13 (:REWRITE DM::FACTOR-DIVIDES))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (12 12 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (12 12 (:REWRITE |(mod x (- y))| . 3))
 (12 12 (:REWRITE |(mod x (- y))| . 2))
 (12 12 (:REWRITE |(mod x (- y))| . 1))
 (12 12 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (12 12 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (11 11 (:REWRITE |(< 0 (/ x))|))
 (11 11 (:REWRITE |(< 0 (* x y))|))
 (11 1 (:REWRITE |(* y (* x z))|))
 (10 10 (:REWRITE |(* 0 x)|))
 (10 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (8 8 (:REWRITE |(* c (* d x))|))
 (8 4 (:DEFINITION FIX))
 (6 4 (:REWRITE |(+ 0 x)|))
 (5 5 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE INTEGERP-/))
 (4 4 (:REWRITE |(equal (+ (- c) x) y)|))
 (4 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 2 (:REWRITE DEFAULT-MINUS))
 (4 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (2 2 (:REWRITE |(equal (* x y) 0)|))
 (2 2 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (1 1 (:REWRITE |(* a (/ a) b)|))
 )
(DM::INF)
(X)
(Y)
(A)
(DM::ECP)
(DM::INTEGERP-EC-X
 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(DM::INTEGERP-EC-Y
 (10 5 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (4 1 (:REWRITE DM::INTEGERP-EC-X))
 (3 2 (:REWRITE SIMPLIFY-SUMS-<))
 (3 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-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 REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(DM::A2-4-NONRESIDUE-1)
(DM::A2-4-NONRESIDUE-2)
(DM::NATP-P-1/2
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 )
(DM::A2-4-NONRESIDUE
 (2600 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1824 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (982 2 (:REWRITE RTL::MOD-DOES-NOTHING))
 (980 13 (:LINEAR EXPT-<=-1-TWO))
 (862 6 (:REWRITE |(equal (+ (- c) x) y)|))
 (712 18 (:REWRITE |(< x (+ c/d y))|))
 (703 1 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (580 13 (:LINEAR EXPT-X->=-X))
 (580 13 (:LINEAR EXPT-X->-X))
 (577 13 (:LINEAR EXPT->-1-ONE))
 (546 2 (:REWRITE MOD-X-Y-=-X . 3))
 (506 2 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (494 13 (:LINEAR EXPT->=-1-ONE))
 (462 462 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (462 462 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (462 462 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (294 42 (:REWRITE DEFAULT-EXPT-2))
 (294 9 (:REWRITE |(< y (+ (- c) x))|))
 (291 44 (:REWRITE DEFAULT-PLUS-2))
 (250 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (247 247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (247 247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (247 247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (247 247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (247 247 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (210 2 (:REWRITE MOD-ZERO . 3))
 (200 33 (:REWRITE DEFAULT-TIMES-2))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (175 175 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (168 32 (:REWRITE NORMALIZE-ADDENDS))
 (143 3 (:REWRITE |(+ y (+ x z))|))
 (124 34 (:REWRITE DEFAULT-LESS-THAN-1))
 (124 2 (:REWRITE DEFAULT-MOD-RATIO))
 (122 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (114 2 (:REWRITE MOD-X-Y-=-X . 2))
 (112 34 (:REWRITE DEFAULT-LESS-THAN-2))
 (112 16 (:REWRITE SIMPLIFY-SUMS-<))
 (110 22 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (110 22 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (110 22 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (110 22 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (100 2 (:REWRITE MOD-X-Y-=-X . 4))
 (98 33 (:REWRITE DEFAULT-TIMES-1))
 (93 44 (:REWRITE DEFAULT-PLUS-1))
 (91 13 (:LINEAR EXPT-<-1-TWO))
 (80 2 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (70 2 (:REWRITE MOD-ZERO . 4))
 (70 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (57 3 (:REWRITE |(+ y x)|))
 (42 42 (:REWRITE DEFAULT-EXPT-1))
 (42 42 (:REWRITE |(expt 1/c n)|))
 (42 42 (:REWRITE |(expt (- x) n)|))
 (42 2 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (42 2 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (40 2 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (40 2 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (40 2 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (34 34 (:REWRITE THE-FLOOR-BELOW))
 (34 34 (:REWRITE THE-FLOOR-ABOVE))
 (32 2 (:REWRITE DEFAULT-MOD-1))
 (32 2 (:REWRITE |(+ 0 x)|))
 (28 28 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (26 26 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (26 26 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (26 26 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (26 26 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (25 25 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (25 25 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (22 22 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (22 22 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (22 22 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (22 22 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (22 22 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (22 22 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (22 22 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (19 19 (:REWRITE |(< 0 (* x y))|))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (18 9 (:REWRITE |(* a (/ a) b)|))
 (17 1 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (16 16 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (16 16 (:REWRITE INTEGERP-<-CONSTANT))
 (16 16 (:REWRITE CONSTANT-<-INTEGERP))
 (16 16 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (16 16 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (16 16 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (16 16 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (16 16 (:REWRITE |(< c (- x))|))
 (16 16 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (16 16 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (16 16 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (16 16 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (16 16 (:REWRITE |(< (/ x) (/ y))|))
 (16 16 (:REWRITE |(< (- x) c)|))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (13 13 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (13 13 (:LINEAR EXPT-LINEAR-UPPER-<))
 (13 13 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (13 13 (:LINEAR EXPT-LINEAR-LOWER-<))
 (13 13 (:LINEAR EXPT->=-1-TWO))
 (13 13 (:LINEAR EXPT->-1-TWO))
 (13 13 (:LINEAR EXPT-<=-1-ONE))
 (13 13 (:LINEAR EXPT-<-1-ONE))
 (12 12 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (12 6 (:DEFINITION FIX))
 (10 9 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (9 9 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (9 8 (:REWRITE |(equal (- x) (- y))|))
 (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 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 4 (:REWRITE DEFAULT-DIVIDE))
 (8 2 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (5 1 (:REWRITE |(+ x x)|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (4 2 (:REWRITE DEFAULT-MOD-2))
 (3 3 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE DM::FACTOR-DIVIDES))
 (2 2 (:REWRITE |(mod x (- y))| . 3))
 (2 2 (:REWRITE |(mod x (- y))| . 2))
 (2 2 (:REWRITE |(mod x (- y))| . 1))
 (2 2 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (2 1 (:REWRITE DEFAULT-MINUS))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1 1 (:TYPE-PRESCRIPTION ABS))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 )
(DM::EC-X-0-1
 (4115 23 (:REWRITE |(* y x)|))
 (3613 32 (:REWRITE |(* x (+ y z))|))
 (3605 11 (:REWRITE RTL::MOD-DOES-NOTHING))
 (2898 11 (:REWRITE MOD-ZERO . 3))
 (2595 11 (:REWRITE DEFAULT-MOD-RATIO))
 (2219 1 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1808 11 (:REWRITE MOD-X-Y-=-X . 3))
 (1780 90 (:REWRITE DEFAULT-PLUS-2))
 (1688 11 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1655 11 (:REWRITE MOD-X-Y-=-X . 4))
 (1605 151 (:REWRITE DEFAULT-TIMES-2))
 (1542 11 (:REWRITE MOD-ZERO . 4))
 (1520 300 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1368 1368 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1264 17 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1252 107 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (1053 90 (:REWRITE DEFAULT-PLUS-1))
 (1048 2 (:LINEAR MOD-BOUNDS-3))
 (895 205 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (827 46 (:META META-INTEGERP-CORRECT))
 (788 11 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (735 205 (:REWRITE DEFAULT-LESS-THAN-1))
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 (122 122 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
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(DM::EC-X-0-2
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(DM::EC-X-0-3
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(DM::EC-X-0-8)
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(DM::EC-X-0-12)
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 (80 80 (:REWRITE |(< x (+ c/d y))|))
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 (79 79 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
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 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 )
(DM::EC-X-0-14
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 )
(DM::EC-X-0-15
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(DM::EC-X-0-16
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 (167 167 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (167 167 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (167 167 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (167 167 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (167 167 (:REWRITE |(< c (- x))|))
 (167 167 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (167 167 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (167 167 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (167 167 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (167 167 (:REWRITE |(< (/ x) (/ y))|))
 (167 167 (:REWRITE |(< (- x) c)|))
 (167 167 (:REWRITE |(< (- x) (- y))|))
 (166 21 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (166 21 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (166 21 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (166 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (121 2 (:LINEAR MOD-BOUNDS-3))
 (112 36 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (98 19 (:REWRITE DEFAULT-PLUS-2))
 (85 85 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (80 40 (:REWRITE DEFAULT-DIVIDE))
 (78 78 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (78 78 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (75 25 (:REWRITE DEFAULT-MOD-1))
 (75 6 (:REWRITE |(+ y x)|))
 (75 3 (:REWRITE |(equal (expt x n) 0)|))
 (73 13 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (71 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (71 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (71 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (71 19 (:REWRITE DEFAULT-PLUS-1))
 (71 13 (:REWRITE DEFAULT-EXPT-1))
 (62 8 (:REWRITE NORMALIZE-ADDENDS))
 (59 2 (:LINEAR RTL::MOD-BND-2))
 (54 54 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (54 54 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (54 54 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (54 54 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (46 25 (:REWRITE DEFAULT-MOD-2))
 (43 41 (:REWRITE |(equal (- x) (- y))|))
 (42 41 (:REWRITE |(equal (- x) c)|))
 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (41 41 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (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 REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (41 41 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (41 41 (:REWRITE |(equal c (/ x))|))
 (41 41 (:REWRITE |(equal c (- x))|))
 (41 41 (:REWRITE |(equal (/ x) c)|))
 (41 41 (:REWRITE |(equal (/ x) (/ y))|))
 (41 41 (:REWRITE |(< 0 (/ x))|))
 (41 41 (:REWRITE |(< 0 (* x y))|))
 (41 41 (:REWRITE |(< (/ x) 0)|))
 (41 41 (:REWRITE |(< (* x y) 0)|))
 (40 40 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (38 38 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (36 1 (:REWRITE MOD-ZERO . 1))
 (31 31 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (30 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (28 4 (:LINEAR MOD-BOUNDS-2))
 (27 27 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (27 27 (:LINEAR EXPT-LINEAR-UPPER-<))
 (27 27 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (27 27 (:LINEAR EXPT-LINEAR-LOWER-<))
 (27 22 (:REWRITE INTEGERP-MINUS-X))
 (22 22 (:REWRITE REDUCE-INTEGERP-+))
 (22 22 (:META META-INTEGERP-CORRECT))
 (22 1 (:REWRITE MOD-ZERO . 2))
 (21 21 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (21 21 (:REWRITE |(mod x (- y))| . 3))
 (21 21 (:REWRITE |(mod x (- y))| . 2))
 (21 21 (:REWRITE |(mod x (- y))| . 1))
 (21 21 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (21 21 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (18 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (14 3 (:REWRITE |(+ 0 x)|))
 (13 13 (:REWRITE DEFAULT-EXPT-2))
 (13 13 (:REWRITE |(expt 1/c n)|))
 (13 13 (:REWRITE |(expt (- x) n)|))
 (10 3 (:REWRITE DEFAULT-MINUS))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE DM::FACTOR-DIVIDES))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (5 5 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:REWRITE |(equal (* x y) 0)|))
 (2 2 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(- (* c x))|))
 )
(DM::EC-X-0-17
 (85616 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (62986 191 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (51653 53 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (39706 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (27605 179 (:REWRITE |(+ y (+ x z))|))
 (22710 910 (:REWRITE DEFAULT-PLUS-2))
 (16466 26 (:REWRITE MOD-X-Y-=-X . 3))
 (16408 26 (:REWRITE MOD-X-Y-=-X . 4))
 (15770 26 (:REWRITE MOD-ZERO . 4))
 (15683 26 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (15657 26 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (15079 910 (:REWRITE DEFAULT-PLUS-1))
 (14732 26 (:REWRITE RTL::MOD-DOES-NOTHING))
 (13680 26 (:REWRITE MOD-ZERO . 3))
 (12135 12135 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (12135 12135 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (12135 12135 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (12135 12135 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (12135 12135 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (12132 12132 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (11131 510 (:REWRITE DEFAULT-TIMES-2))
 (9110 26 (:REWRITE DEFAULT-MOD-RATIO))
 (7933 661 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (6935 135 (:META META-INTEGERP-CORRECT))
 (5846 8 (:LINEAR MOD-BOUNDS-3))
 (5670 191 (:REWRITE DEFAULT-LESS-THAN-1))
 (5658 246 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (5279 6 (:LINEAR RTL::MOD-BND-2))
 (4127 116 (:REWRITE SIMPLIFY-SUMS-<))
 (3797 155 (:REWRITE INTEGERP-MINUS-X))
 (3300 150 (:REWRITE |(+ 0 x)|))
 (3031 510 (:REWRITE DEFAULT-TIMES-1))
 (2746 191 (:REWRITE DEFAULT-LESS-THAN-2))
 (2316 90 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (2225 89 (:REWRITE |(+ (* c x) (* d x))|))
 (1992 97 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1793 26 (:REWRITE MOD-X-Y-=-X . 2))
 (1464 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1170 18 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (1136 26 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1136 26 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (989 38 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (983 983 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (983 983 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (983 983 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (980 26 (:REWRITE DEFAULT-MOD-1))
 (954 26 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (954 26 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (954 26 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (943 39 (:REWRITE DEFAULT-MINUS))
 (748 16 (:LINEAR MOD-BOUNDS-2))
 (670 134 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (670 134 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (661 661 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (661 661 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (661 661 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (630 134 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (630 134 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (246 246 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (246 246 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (246 246 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (218 218 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (210 18 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (191 191 (:REWRITE THE-FLOOR-BELOW))
 (191 191 (:REWRITE THE-FLOOR-ABOVE))
 (191 191 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (191 191 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (191 191 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (191 191 (:REWRITE INTEGERP-<-CONSTANT))
 (191 191 (:REWRITE CONSTANT-<-INTEGERP))
 (191 191 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (191 191 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (191 191 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (191 191 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (191 191 (:REWRITE |(< c (- x))|))
 (191 191 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (191 191 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (191 191 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (191 191 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (191 191 (:REWRITE |(< (/ x) (/ y))|))
 (191 191 (:REWRITE |(< (- x) c)|))
 (191 191 (:REWRITE |(< (- x) (- y))|))
 (182 26 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (182 26 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (172 26 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (161 2 (:REWRITE |(integerp (- x))|))
 (146 146 (:REWRITE |(* c (* d x))|))
 (135 135 (:REWRITE REDUCE-INTEGERP-+))
 (134 134 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (134 134 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (134 134 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (134 134 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (134 134 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (123 123 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (122 122 (:REWRITE |(< (+ c/d x) y)|))
 (122 122 (:REWRITE |(< (+ (- c) x) y)|))
 (112 56 (:REWRITE DEFAULT-DIVIDE))
 (112 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (106 106 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (89 89 (:REWRITE |(* 0 x)|))
 (85 85 (:TYPE-PRESCRIPTION NATP))
 (68 18 (:REWRITE DEFAULT-EXPT-1))
 (56 56 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (56 56 (:REWRITE |(< y (+ (- c) x))|))
 (56 56 (:REWRITE |(< x (+ c/d y))|))
 (54 53 (:REWRITE |(equal (- x) (- y))|))
 (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)|))
 (52 26 (:REWRITE DEFAULT-MOD-2))
 (45 45 (:REWRITE |(+ c (+ d x))|))
 (44 44 (:REWRITE FOLD-CONSTS-IN-+))
 (42 42 (:REWRITE INTEGERP-/))
 (42 42 (:REWRITE |(< (/ x) 0)|))
 (42 42 (:REWRITE |(< (* x y) 0)|))
 (32 32 (:REWRITE |(< 0 (/ x))|))
 (32 32 (:REWRITE |(< 0 (* x y))|))
 (31 31 (:REWRITE |(equal (+ (- c) x) y)|))
 (30 30 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (26 26 (:REWRITE |(mod x (- y))| . 3))
 (26 26 (:REWRITE |(mod x (- y))| . 2))
 (26 26 (:REWRITE |(mod x (- y))| . 1))
 (21 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (21 21 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (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-EXPT-2))
 (18 18 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (14 14 (:REWRITE |(expt 1/c n)|))
 (10 10 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (10 10 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (6 6 (:LINEAR RTL::MOD-BND-3))
 (2 2 (:REWRITE DM::FACTOR-DIVIDES))
 (1 1 (:REWRITE |(expt (- c) n)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 )
(DM::EC-X-0
 (4296 16 (:REWRITE RTL::MOD-DOES-NOTHING))
 (3292 16 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (3246 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (3183 16 (:REWRITE MOD-X-Y-=-X . 3))
 (2550 16 (:REWRITE MOD-ZERO . 3))
 (1740 22 (:REWRITE |(* x (+ y z))|))
 (1695 17 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1610 1610 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1610 1610 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1610 1610 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1610 1610 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1610 1610 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1610 1610 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1545 184 (:REWRITE DEFAULT-TIMES-2))
 (1539 63 (:LINEAR EXPT-X->=-X))
 (1391 76 (:REWRITE DEFAULT-PLUS-2))
 (883 76 (:REWRITE DEFAULT-PLUS-1))
 (882 63 (:LINEAR EXPT->=-1-ONE))
 (817 2 (:REWRITE MOD-ZERO . 1))
 (766 193 (:REWRITE SIMPLIFY-SUMS-<))
 (766 193 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (760 193 (:REWRITE DEFAULT-LESS-THAN-1))
 (711 63 (:LINEAR EXPT->=-1-TWO))
 (711 63 (:LINEAR EXPT-<=-1-ONE))
 (687 16 (:REWRITE MOD-X-Y-=-X . 4))
 (684 63 (:LINEAR EXPT-X->-X))
 (684 63 (:LINEAR EXPT->-1-ONE))
 (684 63 (:LINEAR EXPT-<-1-TWO))
 (667 184 (:REWRITE DEFAULT-TIMES-1))
 (630 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (502 16 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (492 16 (:REWRITE MOD-X-Y-=-X . 2))
 (470 16 (:REWRITE MOD-ZERO . 4))
 (457 41 (:META META-INTEGERP-CORRECT))
 (427 427 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (427 427 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (420 14 (:REWRITE |(* y (* x z))|))
 (366 4 (:REWRITE |(+ (+ x y) z)|))
 (282 16 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (282 16 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (281 16 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (281 16 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (281 16 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (252 6 (:REWRITE |(* (* x y) z)|))
 (240 48 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (240 48 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (208 48 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (199 193 (:REWRITE DEFAULT-LESS-THAN-2))
 (193 193 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (193 193 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (193 193 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (193 193 (:REWRITE THE-FLOOR-BELOW))
 (193 193 (:REWRITE THE-FLOOR-ABOVE))
 (193 193 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (193 193 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (193 193 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (193 193 (:REWRITE INTEGERP-<-CONSTANT))
 (193 193 (:REWRITE CONSTANT-<-INTEGERP))
 (193 193 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (193 193 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (193 193 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (193 193 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (193 193 (:REWRITE |(< c (- x))|))
 (193 193 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (193 193 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (193 193 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (193 193 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (193 193 (:REWRITE |(< (/ x) (/ y))|))
 (193 193 (:REWRITE |(< (- x) c)|))
 (193 193 (:REWRITE |(< (- x) (- y))|))
 (192 4 (:REWRITE |(+ y (+ x z))|))
 (175 49 (:REWRITE NORMALIZE-ADDENDS))
 (166 6 (:REWRITE REDUCE-RATIONALP-*))
 (162 6 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (132 132 (:REWRITE DEFAULT-EXPT-2))
 (132 132 (:REWRITE DEFAULT-EXPT-1))
 (132 132 (:REWRITE |(expt 1/c n)|))
 (132 132 (:REWRITE |(expt (- x) n)|))
 (126 126 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (126 126 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (126 126 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (126 126 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (117 117 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (82 2 (:REWRITE MOD-ZERO . 2))
 (82 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (82 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (80 80 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (63 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (63 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (63 63 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (63 63 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (63 63 (:LINEAR EXPT-LINEAR-UPPER-<))
 (63 63 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (63 63 (:LINEAR EXPT-LINEAR-LOWER-<))
 (63 63 (:LINEAR EXPT->-1-TWO))
 (63 63 (:LINEAR EXPT-<=-1-TWO))
 (63 63 (:LINEAR EXPT-<-1-ONE))
 (62 47 (:REWRITE DEFAULT-DIVIDE))
 (54 6 (:REWRITE RATIONALP-X))
 (51 15 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (48 48 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (48 48 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (48 48 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (47 47 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (47 47 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (47 47 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (47 47 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (41 41 (:REWRITE REDUCE-INTEGERP-+))
 (41 41 (:REWRITE INTEGERP-MINUS-X))
 (40 4 (:REWRITE |(+ 0 x)|))
 (38 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (28 14 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (26 22 (:LINEAR DM::P-IS-BIG))
 (22 4 (:DEFINITION RFIX))
 (21 18 (:REWRITE DEFAULT-MOD-2))
 (21 17 (:REWRITE |(equal (/ x) c)|))
 (21 17 (:REWRITE |(equal (/ x) (/ y))|))
 (20 20 (:REWRITE |(* c (* d x))|))
 (19 19 (:REWRITE |(+ c (+ d x))|))
 (18 18 (:REWRITE |(< (+ c/d x) y)|))
 (18 18 (:REWRITE |(< (+ (- c) x) y)|))
 (18 2 (:REWRITE ACL2-NUMBERP-X))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (17 17 (:REWRITE FOLD-CONSTS-IN-+))
 (17 17 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (17 17 (:REWRITE |(equal c (/ x))|))
 (17 17 (:REWRITE |(equal c (- x))|))
 (17 17 (:REWRITE |(equal (- x) c)|))
 (17 17 (:REWRITE |(equal (- x) (- y))|))
 (16 16 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (16 16 (:REWRITE DEFAULT-CAR))
 (16 16 (:REWRITE |(mod x (- y))| . 3))
 (16 16 (:REWRITE |(mod x (- y))| . 2))
 (16 16 (:REWRITE |(mod x (- y))| . 1))
 (16 16 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (16 16 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (14 14 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (14 14 (:TYPE-PRESCRIPTION NATP))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (12 4 (:REWRITE |(equal x (/ y))|))
 (10 10 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (8 8 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (8 8 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (8 4 (:REWRITE |(not (equal x (/ y)))|))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (6 6 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (6 6 (:REWRITE |(< (/ x) 0)|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
 (6 6 (:META META-RATIONALP-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (4 4 (:REWRITE |(equal (+ (- c) x) y)|))
 (4 4 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(DM::EC-Y-0
 (2302 2 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (1354 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (926 4 (:REWRITE RTL::MOD-DOES-NOTHING))
 (701 2 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (533 4 (:REWRITE MOD-X-Y-=-X . 3))
 (515 4 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (409 21 (:LINEAR EXPT-X->=-X))
 (361 21 (:LINEAR EXPT-<=-1-ONE))
 (354 21 (:LINEAR EXPT->=-1-TWO))
 (320 21 (:LINEAR EXPT-X->-X))
 (320 21 (:LINEAR EXPT->-1-ONE))
 (320 21 (:LINEAR EXPT-<-1-TWO))
 (319 21 (:LINEAR EXPT->=-1-ONE))
 (284 284 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (284 284 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (284 284 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (284 284 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (284 284 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (284 284 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (245 4 (:REWRITE MOD-ZERO . 3))
 (245 4 (:REWRITE MOD-X-Y-=-X . 4))
 (230 120 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (225 4 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (214 120 (:REWRITE DEFAULT-LESS-THAN-1))
 (210 21 (:LINEAR EXPT->-1-TWO))
 (210 21 (:LINEAR EXPT-<-1-ONE))
 (200 120 (:REWRITE SIMPLIFY-SUMS-<))
 (197 2 (:REWRITE MOD-ZERO . 1))
 (190 190 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (190 190 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (189 21 (:LINEAR EXPT-<=-1-TWO))
 (166 6 (:REWRITE REDUCE-RATIONALP-*))
 (150 30 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (150 30 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (139 46 (:REWRITE DEFAULT-TIMES-2))
 (139 46 (:REWRITE DEFAULT-TIMES-1))
 (136 120 (:REWRITE DEFAULT-LESS-THAN-2))
 (133 4 (:REWRITE MOD-X-Y-=-X . 2))
 (120 120 (:REWRITE THE-FLOOR-BELOW))
 (120 120 (:REWRITE THE-FLOOR-ABOVE))
 (120 120 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (120 120 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (120 120 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (120 120 (:REWRITE INTEGERP-<-CONSTANT))
 (120 120 (:REWRITE CONSTANT-<-INTEGERP))
 (120 120 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (120 120 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (120 120 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (120 120 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (120 120 (:REWRITE |(< c (- x))|))
 (120 120 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (120 120 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (120 120 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (120 120 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (120 120 (:REWRITE |(< (/ x) (/ y))|))
 (120 120 (:REWRITE |(< (- x) c)|))
 (120 120 (:REWRITE |(< (- x) (- y))|))
 (118 30 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (107 16 (:REWRITE DEFAULT-PLUS-2))
 (89 4 (:REWRITE MOD-ZERO . 4))
 (83 5 (:REWRITE NORMALIZE-ADDENDS))
 (71 2 (:REWRITE MOD-ZERO . 2))
 (63 4 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (63 4 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (61 4 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (61 4 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (61 4 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (56 5 (:REWRITE |(+ y x)|))
 (54 6 (:REWRITE RATIONALP-X))
 (52 52 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (52 16 (:REWRITE DEFAULT-PLUS-1))
 (48 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (44 22 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (42 42 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (42 42 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (42 42 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (42 42 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (41 23 (:REWRITE DEFAULT-DIVIDE))
 (38 18 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (31 31 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (30 30 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (30 30 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (30 30 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (29 29 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (29 29 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (24 20 (:REWRITE |(equal (/ x) c)|))
 (24 20 (:REWRITE |(equal (/ x) (/ y))|))
 (24 4 (:REWRITE |(+ 0 x)|))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (23 23 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (23 23 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (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)|))
 (23 23 (:REWRITE |(< 0 (/ x))|))
 (23 23 (:REWRITE |(< 0 (* x y))|))
 (22 22 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (22 22 (:TYPE-PRESCRIPTION NATP))
 (22 4 (:DEFINITION RFIX))
 (22 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (21 21 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (21 21 (:LINEAR EXPT-LINEAR-UPPER-<))
 (21 21 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (21 21 (:LINEAR EXPT-LINEAR-LOWER-<))
 (21 20 (:REWRITE |(equal (- x) c)|))
 (21 20 (:REWRITE |(equal (- x) (- y))|))
 (21 11 (:LINEAR DM::P-IS-BIG))
 (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))|))
 (18 2 (:REWRITE ACL2-NUMBERP-X))
 (16 16 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (16 16 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:META META-INTEGERP-CORRECT))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (13 13 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (13 13 (:REWRITE |(< (/ x) 0)|))
 (13 13 (:REWRITE |(< (* x y) 0)|))
 (12 4 (:REWRITE |(equal x (/ y))|))
 (10 10 (:REWRITE DEFAULT-CAR))
 (10 6 (:REWRITE DEFAULT-MOD-2))
 (8 8 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (8 4 (:REWRITE |(not (equal x (/ y)))|))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:META META-RATIONALP-CORRECT))
 (6 4 (:DEFINITION FIX))
 (4 4 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE |(mod x (- y))| . 3))
 (4 4 (:REWRITE |(mod x (- y))| . 2))
 (4 4 (:REWRITE |(mod x (- y))| . 1))
 (4 4 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (3 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 2 (:REWRITE DEFAULT-MINUS))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 )
(DM::EC-)
(DM::EC+)
(DM::EC+SLOPE)
(DM::INTEGERP-EC+SLOPE
 (83678 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (52494 22 (:LINEAR MOD-BOUNDS-1))
 (43191 81 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (27168 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (24550 10 (:LINEAR RTL::MOD-BND-2))
 (22734 64 (:REWRITE RTL::MOD-DOES-NOTHING))
 (20468 64 (:REWRITE MOD-ZERO . 3))
 (19610 10 (:LINEAR RTL::MOD-BND-1))
 (17483 1768 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
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 (12847 64 (:REWRITE MOD-X-Y-=-X-Y . 2))
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 (8412 8412 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
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 (8412 8412 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (2072 304 (:LINEAR EXPT-<=-1-ONE))
 (2012 961 (:REWRITE DEFAULT-LESS-THAN-2))
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 (2004 304 (:LINEAR EXPT->-1-ONE))
 (2004 304 (:LINEAR EXPT-<-1-TWO))
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 (1748 1748 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1748 1748 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1748 1748 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1692 846 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (1375 64 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1375 64 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1228 52 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (1228 52 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
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 (1072 64 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1072 64 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1072 64 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (966 961 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (963 961 (:REWRITE |(< (- x) c)|))
 (962 961 (:REWRITE |(< c (- x))|))
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 (961 961 (:REWRITE THE-FLOOR-ABOVE))
 (961 961 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (961 961 (:REWRITE INTEGERP-<-CONSTANT))
 (961 961 (:REWRITE CONSTANT-<-INTEGERP))
 (961 961 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (961 961 (:REWRITE |(< (/ x) (/ y))|))
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 (930 186 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (930 186 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (930 186 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (741 741 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (626 35 (:REWRITE DEFAULT-MINUS))
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 (608 608 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (608 608 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (608 608 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (585 585 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (585 585 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (554 20 (:REWRITE |(+ y (+ x z))|))
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 (367 64 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (367 64 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (122 122 (:REWRITE |(+ c (+ d x))|))
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 (57 57 (:REWRITE |(< x (+ c/d y))|))
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 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-EC+SLOPE))
 )
(DM::EC+X
 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-EC+SLOPE))
 (1 1 (:TYPE-PRESCRIPTION DM::ECP))
 )
(DM::EC+Y
 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-EC+SLOPE))
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 )
(DM::EC+REWRITE)
(DM::EC--
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 (5722 360 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (4984 2492 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (4369 351 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4369 351 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (4369 351 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (4245 381 (:REWRITE DEFAULT-MOD-1))
 (4021 3235 (:REWRITE |(< c (- x))|))
 (3863 3235 (:REWRITE |(< (- x) (- y))|))
 (3787 147 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (3787 147 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (3465 35 (:REWRITE |(- (+ x y))|))
 (3251 371 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3243 3235 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3243 3235 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3235 3235 (:REWRITE THE-FLOOR-BELOW))
 (3235 3235 (:REWRITE THE-FLOOR-ABOVE))
 (3235 3235 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3235 3235 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3235 3235 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3235 3235 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3235 3235 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3235 3235 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3235 3235 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3235 3235 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3235 3235 (:REWRITE |(< (/ x) (/ y))|))
 (3035 3035 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3035 3035 (:REWRITE INTEGERP-<-CONSTANT))
 (3035 3035 (:REWRITE CONSTANT-<-INTEGERP))
 (2941 53 (:REWRITE RATIONALP-X))
 (2720 200 (:LINEAR MOD-BOUNDS-2))
 (2560 2560 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2526 1940 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (2496 1940 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (2496 1940 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (2496 1940 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (2496 1940 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (2274 106 (:REWRITE |(integerp (- x))|))
 (1861 45 (:REWRITE REDUCE-RATIONALP-*))
 (1840 1840 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1840 1840 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1840 1840 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1840 1840 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1716 565 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1698 1698 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (1698 1698 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (1698 1698 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (1647 351 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1647 351 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1647 351 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1371 1371 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1149 1149 (:REWRITE REDUCE-INTEGERP-+))
 (1149 786 (:REWRITE NORMALIZE-ADDENDS))
 (1121 565 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (1102 546 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (1102 546 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (1036 847 (:REWRITE DEFAULT-DIVIDE))
 (1003 1003 (:REWRITE |(< 0 (/ x))|))
 (1003 1003 (:REWRITE |(< 0 (* x y))|))
 (997 997 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (997 997 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (920 920 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (920 920 (:LINEAR EXPT-LINEAR-UPPER-<))
 (920 920 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (920 920 (:LINEAR EXPT-LINEAR-LOWER-<))
 (919 8 (:REWRITE |(+ y (+ x z))|))
 (847 847 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (841 29 (:REWRITE |(equal (expt x n) 0)|))
 (778 778 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (762 16 (:DEFINITION RFIX))
 (720 16 (:REWRITE |(* (* x y) z)|))
 (681 468 (:REWRITE |(equal (- x) (- y))|))
 (667 408 (:REWRITE |(- (* c x))|))
 (623 147 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (565 565 (:TYPE-PRESCRIPTION NATP))
 (484 468 (:REWRITE |(equal (/ x) c)|))
 (484 468 (:REWRITE |(equal (/ x) (/ y))|))
 (476 468 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (468 468 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (468 468 (:REWRITE |(equal c (/ x))|))
 (468 468 (:REWRITE |(equal c (- x))|))
 (441 441 (:REWRITE |(< (+ c/d x) y)|))
 (441 441 (:REWRITE |(< (+ (- c) x) y)|))
 (437 19 (:REWRITE MOD-POSITIVE . 3))
 (425 381 (:REWRITE DEFAULT-MOD-2))
 (407 28 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (379 379 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (373 373 (:REWRITE |(+ c (+ d x))|))
 (368 368 (:REWRITE |(* c (* d x))|))
 (366 366 (:REWRITE FOLD-CONSTS-IN-+))
 (351 351 (:REWRITE |(mod x (- y))| . 3))
 (351 351 (:REWRITE |(mod x (- y))| . 2))
 (351 351 (:REWRITE |(mod x (- y))| . 1))
 (321 321 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (219 219 (:REWRITE |(< (/ x) 0)|))
 (219 219 (:REWRITE |(< (* x y) 0)|))
 (198 198 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (195 15 (:REWRITE ACL2-NUMBERP-X))
 (191 191 (:REWRITE INTEGERP-/))
 (175 7 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (170 170 (:REWRITE |(equal (+ (- c) x) y)|))
 (147 147 (:REWRITE |(< y (+ (- c) x))|))
 (147 147 (:REWRITE |(< x (+ c/d y))|))
 (94 2 (:REWRITE RATIONALP-MOD))
 (93 93 (:LINEAR RTL::MOD-BND-3))
 (87 13 (:REWRITE MOD-NONPOSITIVE))
 (72 16 (:DEFINITION FIX))
 (70 42 (:REWRITE DEFAULT-CAR))
 (59 31 (:REWRITE DEFAULT-CDR))
 (53 6 (:REWRITE MOD-ZERO . 1))
 (48 16 (:REWRITE |(equal x (/ y))|))
 (45 45 (:REWRITE REDUCE-RATIONALP-+))
 (45 45 (:REWRITE RATIONALP-MINUS-X))
 (45 45 (:META META-RATIONALP-CORRECT))
 (43 19 (:REWRITE MOD-POSITIVE . 2))
 (36 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (32 16 (:REWRITE |(not (equal x (/ y)))|))
 (32 6 (:REWRITE MOD-ZERO . 2))
 (27 27 (:REWRITE DEFAULT-EXPT-2))
 (27 27 (:REWRITE DEFAULT-EXPT-1))
 (27 27 (:REWRITE |(expt 1/c n)|))
 (27 27 (:REWRITE |(expt (- x) n)|))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (25 25 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:TYPE-PRESCRIPTION ABS))
 (20 2 (:REWRITE RTL::RATIONALP-MOD))
 (19 19 (:REWRITE MOD-POSITIVE . 1))
 (18 2 (:REWRITE INTEGERP-MOD-2))
 (18 2 (:REWRITE INTEGERP-MOD-1))
 (18 2 (:REWRITE RTL::INTEGERP-MOD))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (8 8 (:REWRITE |(equal (* x y) 0)|))
 (8 8 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (8 8 (:REWRITE |(+ x (- x))|))
 (7 1 (:REWRITE MOD-NONNEGATIVE))
 (7 1 (:REWRITE MOD-NEGATIVE . 3))
 (2 1 (:REWRITE MOD-NEGATIVE . 2))
 (2 1 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (1 1 (:REWRITE MOD-NEGATIVE . 1))
 )
(DM::EC-ECP
 (251035 19 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (129828 299 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (81505 19 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (73884 44 (:LINEAR RTL::MOD-BND-2))
 (69196 186 (:REWRITE RTL::MOD-DOES-NOTHING))
 (59076 190 (:REWRITE MOD-ZERO . 3))
 (51520 630 (:REWRITE |(* x (+ y z))|))
 (37311 190 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (33658 190 (:REWRITE MOD-X-Y-=-X . 4))
 (32429 3319 (:REWRITE DEFAULT-TIMES-2))
 (30417 190 (:REWRITE MOD-ZERO . 4))
 (24925 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (24925 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (24925 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (24925 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (24925 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (24685 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (24685 24685 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (19954 798 (:REWRITE DEFAULT-PLUS-2))
 (17677 1607 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (17386 1016 (:META META-INTEGERP-CORRECT))
 (15289 2751 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (14897 52 (:LINEAR MOD-BOUNDS-3))
 (12673 3319 (:REWRITE DEFAULT-TIMES-1))
 (12232 2796 (:REWRITE DEFAULT-LESS-THAN-1))
 (12097 2751 (:REWRITE SIMPLIFY-SUMS-<))
 (10304 322 (:REWRITE |(* y (* x z))|))
 (8591 190 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (8490 6 (:REWRITE |(equal (mod a n) (mod b n))|))
 (8234 798 (:REWRITE DEFAULT-PLUS-1))
 (7529 186 (:REWRITE MOD-X-Y-=-X . 2))
 (6632 890 (:LINEAR EXPT->=-1-TWO))
 (6632 890 (:LINEAR EXPT->-1-TWO))
 (6632 890 (:LINEAR EXPT-<-1-ONE))
 (6493 6381 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (6493 6381 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (6493 6381 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (6038 890 (:LINEAR EXPT-X->=-X))
 (6038 890 (:LINEAR EXPT->=-1-ONE))
 (6038 890 (:LINEAR EXPT-<=-1-TWO))
 (6038 890 (:LINEAR EXPT-<=-1-ONE))
 (6010 2796 (:REWRITE DEFAULT-LESS-THAN-2))
 (5840 890 (:LINEAR EXPT-X->-X))
 (5840 890 (:LINEAR EXPT->-1-ONE))
 (5840 890 (:LINEAR EXPT-<-1-TWO))
 (5755 2790 (:REWRITE |(< (- x) c)|))
 (5717 1093 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (5717 1093 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5378 5354 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (5378 5354 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (5378 5354 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (5264 1022 (:REWRITE INTEGERP-MINUS-X))
 (4319 190 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (4319 190 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (3668 140 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (3668 140 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (3569 211 (:REWRITE DEFAULT-MOD-1))
 (3342 186 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (3342 186 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (3342 186 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (3253 1093 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3253 1093 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (3249 2796 (:REWRITE |(< c (- x))|))
 (2970 30 (:REWRITE |(- (+ x y))|))
 (2908 2796 (:REWRITE |(< (- x) (- y))|))
 (2803 2796 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2803 2796 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2796 2796 (:REWRITE THE-FLOOR-BELOW))
 (2796 2796 (:REWRITE THE-FLOOR-ABOVE))
 (2796 2796 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2796 2796 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2796 2796 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2796 2796 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2796 2796 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2796 2796 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2796 2796 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2796 2796 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2796 2796 (:REWRITE |(< (/ x) (/ y))|))
 (2751 2751 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2751 2751 (:REWRITE INTEGERP-<-CONSTANT))
 (2751 2751 (:REWRITE CONSTANT-<-INTEGERP))
 (2261 52 (:REWRITE RATIONALP-X))
 (2206 2206 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2096 104 (:LINEAR MOD-BOUNDS-2))
 (1951 293 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1780 1780 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1780 1780 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (1780 1780 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1780 1780 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1607 1607 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (1607 1607 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (1607 1607 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (1534 44 (:REWRITE REDUCE-RATIONALP-*))
 (1204 1204 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1184 578 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1149 1093 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1133 186 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1133 186 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1133 186 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1121 1093 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1121 1093 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1121 1093 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1121 1093 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1016 1016 (:REWRITE REDUCE-INTEGERP-+))
 (965 731 (:REWRITE NORMALIZE-ADDENDS))
 (952 37 (:REWRITE |(integerp (- x))|))
 (903 334 (:REWRITE |(equal (- x) c)|))
 (890 890 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (890 890 (:LINEAR EXPT-LINEAR-UPPER-<))
 (890 890 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (890 890 (:LINEAR EXPT-LINEAR-LOWER-<))
 (813 813 (:REWRITE |(< 0 (/ x))|))
 (813 813 (:REWRITE |(< 0 (* x y))|))
 (807 807 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (807 807 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (742 576 (:REWRITE DEFAULT-DIVIDE))
 (725 725 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (654 6 (:REWRITE |(+ y (+ x z))|))
 (630 14 (:REWRITE |(* (* x y) z)|))
 (609 21 (:REWRITE |(equal (expt x n) 0)|))
 (606 578 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (606 16 (:DEFINITION RFIX))
 (588 560 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (588 560 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (578 578 (:TYPE-PRESCRIPTION NATP))
 (576 576 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (532 140 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (420 420 (:REWRITE |(< (+ c/d x) y)|))
 (420 420 (:REWRITE |(< (+ (- c) x) y)|))
 (393 171 (:REWRITE |(- (* c x))|))
 (362 334 (:REWRITE |(equal (- x) (- y))|))
 (351 351 (:REWRITE |(+ c (+ d x))|))
 (350 334 (:REWRITE |(equal (/ x) c)|))
 (350 334 (:REWRITE |(equal (/ x) (/ y))|))
 (348 348 (:REWRITE |(* c (* d x))|))
 (345 345 (:REWRITE FOLD-CONSTS-IN-+))
 (345 105 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (345 105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (341 334 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (334 334 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (334 334 (:REWRITE |(equal c (/ x))|))
 (334 334 (:REWRITE |(equal c (- x))|))
 (319 19 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (299 299 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (250 250 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (242 211 (:REWRITE DEFAULT-MOD-2))
 (218 26 (:REWRITE DM::INTEGERP-EC-Y))
 (188 188 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (186 186 (:REWRITE |(mod x (- y))| . 3))
 (186 186 (:REWRITE |(mod x (- y))| . 2))
 (186 186 (:REWRITE |(mod x (- y))| . 1))
 (186 14 (:REWRITE ACL2-NUMBERP-X))
 (182 182 (:REWRITE INTEGERP-/))
 (158 158 (:REWRITE |(equal (+ (- c) x) y)|))
 (150 6 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (148 36 (:REWRITE DEFAULT-CAR))
 (140 140 (:REWRITE |(< y (+ (- c) x))|))
 (140 140 (:REWRITE |(< x (+ c/d y))|))
 (88 2 (:REWRITE RATIONALP-MOD))
 (81 25 (:REWRITE DEFAULT-CDR))
 (67 3 (:REWRITE MOD-POSITIVE . 3))
 (62 62 (:REWRITE |(< (/ x) 0)|))
 (62 62 (:REWRITE |(< (* x y) 0)|))
 (51 23 (:REWRITE DEFAULT-EXPT-1))
 (48 16 (:REWRITE |(equal x (/ y))|))
 (44 44 (:REWRITE REDUCE-RATIONALP-+))
 (44 44 (:REWRITE RATIONALP-MINUS-X))
 (44 44 (:META META-RATIONALP-CORRECT))
 (44 44 (:LINEAR RTL::MOD-BND-3))
 (32 16 (:REWRITE |(not (equal x (/ y)))|))
 (30 2 (:REWRITE MOD-NONPOSITIVE))
 (28 7 (:REWRITE DM::INTEGERP-EC-X))
 (27 3 (:REWRITE MOD-POSITIVE . 2))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (23 23 (:REWRITE DEFAULT-EXPT-2))
 (22 22 (:REWRITE |(expt 1/c n)|))
 (21 21 (:TYPE-PRESCRIPTION ABS))
 (18 2 (:REWRITE RTL::RATIONALP-MOD))
 (16 2 (:REWRITE INTEGERP-MOD-2))
 (16 2 (:REWRITE INTEGERP-MOD-1))
 (16 2 (:REWRITE RTL::INTEGERP-MOD))
 (12 12 (:DEFINITION FIX))
 (7 7 (:REWRITE |(equal (* x y) 0)|))
 (7 7 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (7 1 (:REWRITE MOD-ZERO . 1))
 (6 6 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:REWRITE |(+ x (- x))|))
 (6 1 (:REWRITE MOD-ZERO . 2))
 (6 1 (:REWRITE MOD-NONNEGATIVE))
 (6 1 (:REWRITE MOD-NEGATIVE . 3))
 (3 3 (:REWRITE MOD-POSITIVE . 1))
 (2 1 (:REWRITE MOD-NEGATIVE . 2))
 (1 1 (:REWRITE MOD-NEGATIVE . 1))
 (1 1 (:REWRITE |(expt (- c) n)|))
 )
(DM::CONSP-EC-
 (212 10 (:REWRITE RATIONALP-X))
 (182 8 (:REWRITE REDUCE-RATIONALP-*))
 (180 90 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (104 61 (:REWRITE DEFAULT-TIMES-2))
 (98 98 (:TYPE-PRESCRIPTION DM::ECP))
 (85 61 (:REWRITE DEFAULT-TIMES-1))
 (81 1 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (77 1 (:REWRITE MOD-X-Y-=-X . 3))
 (76 1 (:REWRITE MOD-X-Y-=-X . 4))
 (68 7 (:REWRITE |(< (- x) c)|))
 (62 1 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (53 3 (:REWRITE |(integerp (- x))|))
 (49 1 (:REWRITE MOD-ZERO . 4))
 (48 2 (:REWRITE ACL2-NUMBERP-X))
 (47 1 (:REWRITE MOD-X-Y-=-X . 2))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (39 8 (:REWRITE |(< c (- x))|))
 (38 19 (:REWRITE DEFAULT-DIVIDE))
 (37 1 (:REWRITE MOD-ZERO . 3))
 (36 4 (:DEFINITION RFIX))
 (32 1 (:REWRITE RTL::MOD-DOES-NOTHING))
 (26 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (26 11 (:REWRITE |(equal (- x) c)|))
 (26 1 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (26 1 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (25 1 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (25 1 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (25 1 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (19 19 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (18 18 (:REWRITE |(- (* c x))|))
 (15 11 (:REWRITE |(equal (/ x) c)|))
 (15 11 (:REWRITE |(equal (/ x) (/ y))|))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (13 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 4 (:REWRITE DM::INTEGERP-EC-Y))
 (12 4 (:REWRITE |(equal x (/ y))|))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:REWRITE |(equal c (/ x))|))
 (11 11 (:REWRITE |(equal c (- x))|))
 (11 11 (:REWRITE |(equal (- x) (- y))|))
 (11 11 (:META META-INTEGERP-CORRECT))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (10 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 8 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 5 (:REWRITE DEFAULT-MOD-2))
 (9 5 (:REWRITE DEFAULT-MOD-1))
 (8 8 (:REWRITE THE-FLOOR-BELOW))
 (8 8 (:REWRITE THE-FLOOR-ABOVE))
 (8 8 (:REWRITE REDUCE-RATIONALP-+))
 (8 8 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE RATIONALP-MINUS-X))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) (/ y))|))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (8 8 (:META META-RATIONALP-CORRECT))
 (8 4 (:REWRITE |(not (equal x (/ y)))|))
 (7 5 (:REWRITE SIMPLIFY-SUMS-<))
 (7 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (7 3 (:LINEAR DM::P-IS-BIG))
 (7 1 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (7 1 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5 5 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(- (- x))|))
 (4 2 (:REWRITE DEFAULT-PLUS-2))
 (4 1 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (3 1 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (3 1 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (3 1 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (3 1 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (3 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (3 1 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (3 1 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (3 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (3 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (3 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (3 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (3 1 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (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 MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE |(mod x (- y))| . 3))
 (1 1 (:REWRITE |(mod x (- y))| . 2))
 (1 1 (:REWRITE |(mod x (- y))| . 1))
 (1 1 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 )
(DM::CAR-EC-
 (212 10 (:REWRITE RATIONALP-X))
 (182 8 (:REWRITE REDUCE-RATIONALP-*))
 (180 90 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (104 61 (:REWRITE DEFAULT-TIMES-2))
 (85 61 (:REWRITE DEFAULT-TIMES-1))
 (81 3 (:REWRITE DEFAULT-CAR))
 (81 1 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (77 1 (:REWRITE MOD-X-Y-=-X . 3))
 (76 1 (:REWRITE MOD-X-Y-=-X . 4))
 (68 7 (:REWRITE |(< (- x) c)|))
 (62 1 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (53 3 (:REWRITE |(integerp (- x))|))
 (49 1 (:REWRITE MOD-ZERO . 4))
 (48 2 (:REWRITE ACL2-NUMBERP-X))
 (47 1 (:REWRITE MOD-X-Y-=-X . 2))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (42 42 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (39 8 (:REWRITE |(< c (- x))|))
 (38 19 (:REWRITE DEFAULT-DIVIDE))
 (37 1 (:REWRITE MOD-ZERO . 3))
 (36 4 (:DEFINITION RFIX))
 (32 1 (:REWRITE RTL::MOD-DOES-NOTHING))
 (26 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (26 11 (:REWRITE |(equal (- x) c)|))
 (26 1 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (26 1 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (25 1 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (25 1 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (25 1 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (19 19 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (18 18 (:REWRITE |(- (* c x))|))
 (15 11 (:REWRITE |(equal (/ x) c)|))
 (15 11 (:REWRITE |(equal (/ x) (/ y))|))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (14 14 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (13 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 4 (:REWRITE DM::INTEGERP-EC-Y))
 (12 4 (:REWRITE |(equal x (/ y))|))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:REWRITE |(equal c (/ x))|))
 (11 11 (:REWRITE |(equal c (- x))|))
 (11 11 (:REWRITE |(equal (- x) (- y))|))
 (11 11 (:META META-INTEGERP-CORRECT))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (10 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 8 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 5 (:REWRITE DEFAULT-MOD-2))
 (9 5 (:REWRITE DEFAULT-MOD-1))
 (8 8 (:REWRITE THE-FLOOR-BELOW))
 (8 8 (:REWRITE THE-FLOOR-ABOVE))
 (8 8 (:REWRITE REDUCE-RATIONALP-+))
 (8 8 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE RATIONALP-MINUS-X))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) (/ y))|))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (8 8 (:META META-RATIONALP-CORRECT))
 (8 4 (:REWRITE |(not (equal x (/ y)))|))
 (7 5 (:REWRITE SIMPLIFY-SUMS-<))
 (7 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (7 3 (:LINEAR DM::P-IS-BIG))
 (7 1 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (7 1 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (5 5 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(- (- x))|))
 (4 2 (:REWRITE DEFAULT-PLUS-2))
 (4 1 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (4 1 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (3 1 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (3 1 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (3 1 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (3 1 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (3 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3 1 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (3 1 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (3 1 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (3 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (3 1 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (3 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (3 1 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (3 1 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:TYPE-PRESCRIPTION MOD))
 (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 MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE |(mod x (- y))| . 3))
 (1 1 (:REWRITE |(mod x (- y))| . 2))
 (1 1 (:REWRITE |(mod x (- y))| . 1))
 (1 1 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1 1 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 )
(DM::CDR-EC-
 (2256 124 (:REWRITE ACL2-NUMBERP-X))
 (1832 120 (:REWRITE RATIONALP-X))
 (748 4 (:LINEAR MOD-BOUNDS-2))
 (748 4 (:LINEAR MOD-BOUNDS-1))
 (740 370 (:REWRITE DEFAULT-TIMES-1))
 (568 4 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (556 4 (:REWRITE MOD-X-Y-=-X . 3))
 (540 4 (:REWRITE MOD-X-Y-=-X . 4))
 (526 4 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (466 4 (:REWRITE MOD-ZERO . 4))
 (464 116 (:REWRITE REDUCE-RATIONALP-*))
 (412 4 (:REWRITE MOD-X-Y-=-X . 2))
 (386 84 (:REWRITE DEFAULT-PLUS-2))
 (366 4 (:REWRITE MOD-ZERO . 3))
 (330 330 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (330 330 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (330 330 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (324 4 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (324 4 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (324 4 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (324 2 (:LINEAR MOD-BOUNDS-3))
 (278 4 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (278 4 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (270 4 (:REWRITE RTL::MOD-DOES-NOTHING))
 (256 2 (:LINEAR RTL::MOD-BND-2))
 (252 96 (:REWRITE DM::INTEGERP-EC-Y))
 (246 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (238 24 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (234 28 (:REWRITE |(< (- x) c)|))
 (196 14 (:DEFINITION FIX))
 (184 30 (:REWRITE |(< (- x) (- y))|))
 (160 80 (:REWRITE DEFAULT-DIVIDE))
 (133 23 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (133 23 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (126 126 (:REWRITE REDUCE-INTEGERP-+))
 (126 126 (:REWRITE INTEGERP-MINUS-X))
 (126 126 (:META META-INTEGERP-CORRECT))
 (118 118 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (116 116 (:REWRITE REDUCE-RATIONALP-+))
 (116 116 (:REWRITE RATIONALP-MINUS-X))
 (116 116 (:META META-RATIONALP-CORRECT))
 (114 114 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (114 114 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (114 114 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (106 30 (:REWRITE |(< c (- x))|))
 (106 6 (:REWRITE |(integerp (- x))|))
 (84 84 (:REWRITE DEFAULT-PLUS-1))
 (81 3 (:REWRITE DEFAULT-CDR))
 (80 80 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (78 78 (:REWRITE |(- (* c x))|))
 (72 8 (:DEFINITION RFIX))
 (70 26 (:REWRITE |(equal (- x) c)|))
 (64 23 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (52 24 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (50 30 (:REWRITE DEFAULT-LESS-THAN-1))
 (44 30 (:REWRITE DEFAULT-LESS-THAN-2))
 (41 23 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (41 23 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (41 23 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (41 23 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (41 23 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (41 23 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (41 23 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (41 23 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (41 23 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (41 23 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (41 23 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (41 23 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (41 23 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (40 26 (:REWRITE |(equal (- x) (- y))|))
 (40 24 (:REWRITE SIMPLIFY-SUMS-<))
 (34 26 (:REWRITE |(equal (/ x) c)|))
 (34 26 (:REWRITE |(equal (/ x) (/ y))|))
 (30 30 (:REWRITE THE-FLOOR-BELOW))
 (30 30 (:REWRITE THE-FLOOR-ABOVE))
 (30 30 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (30 30 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (30 30 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (30 30 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (30 30 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (30 30 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (30 30 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (30 30 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (30 30 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (30 30 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (30 30 (:REWRITE |(< (/ x) (/ y))|))
 (30 14 (:REWRITE DEFAULT-MOD-1))
 (28 14 (:REWRITE DEFAULT-MOD-2))
 (26 26 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (26 26 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (26 26 (:REWRITE |(equal c (/ x))|))
 (26 26 (:REWRITE |(equal c (- x))|))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 24 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (24 24 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (24 24 (:REWRITE INTEGERP-<-CONSTANT))
 (24 24 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (24 24 (:REWRITE CONSTANT-<-INTEGERP))
 (24 8 (:REWRITE |(equal x (/ y))|))
 (23 23 (:TYPE-PRESCRIPTION NATP))
 (16 16 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (16 8 (:REWRITE |(not (equal x (/ y)))|))
 (12 12 (:REWRITE |(< (/ x) 0)|))
 (12 12 (:REWRITE |(< (* x y) 0)|))
 (10 10 (:REWRITE |(< 0 (/ x))|))
 (10 10 (:REWRITE |(< 0 (* x y))|))
 (10 10 (:REWRITE |(< (+ c/d x) y)|))
 (10 10 (:REWRITE |(< (+ (- c) x) y)|))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (8 8 (:REWRITE |(- (- x))|))
 (4 4 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE |(mod x (- y))| . 3))
 (4 4 (:REWRITE |(mod x (- y))| . 2))
 (4 4 (:REWRITE |(mod x (- y))| . 1))
 (4 4 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:LINEAR RTL::MOD-BND-3))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(DM::EC-INVERSE-UNIQUE
 (2584 13 (:REWRITE RTL::MOD-DOES-NOTHING))
 (2137 122 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1978 13 (:REWRITE MOD-ZERO . 3))
 (1699 13 (:REWRITE MOD-X-Y-=-X . 3))
 (1687 13 (:REWRITE MOD-X-Y-=-X . 4))
 (1679 13 (:REWRITE MOD-ZERO . 4))
 (1667 13 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1623 30 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1611 13 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1453 380 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (1250 13 (:REWRITE DEFAULT-MOD-RATIO))
 (1039 159 (:REWRITE DEFAULT-TIMES-2))
 (957 163 (:REWRITE DEFAULT-PLUS-2))
 (873 11 (:REWRITE ACL2-NUMBERP-X))
 (680 163 (:REWRITE DEFAULT-PLUS-1))
 (637 19 (:REWRITE |(+ y (+ x z))|))
 (548 159 (:REWRITE DEFAULT-TIMES-1))
 (504 131 (:REWRITE DEFAULT-LESS-THAN-1))
 (483 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (461 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (431 8 (:REWRITE RATIONALP-X))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (415 415 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (380 380 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (380 380 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (380 380 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (359 128 (:REWRITE |(< (- x) c)|))
 (331 107 (:REWRITE SIMPLIFY-SUMS-<))
 (306 131 (:REWRITE DEFAULT-LESS-THAN-2))
 (299 71 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (299 71 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (299 71 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (299 71 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (267 51 (:REWRITE NORMALIZE-ADDENDS))
 (267 35 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (267 34 (:META META-INTEGERP-CORRECT))
 (248 131 (:REWRITE |(< c (- x))|))
 (192 30 (:LINEAR EXPT-<=-1-ONE))
 (188 30 (:LINEAR EXPT->=-1-TWO))
 (188 30 (:LINEAR EXPT->-1-TWO))
 (188 30 (:LINEAR EXPT-<-1-ONE))
 (186 6 (:REWRITE |(* (* x y) z)|))
 (180 13 (:REWRITE MOD-X-Y-=-X . 2))
 (176 30 (:LINEAR EXPT-X->=-X))
 (176 30 (:LINEAR EXPT->=-1-ONE))
 (176 30 (:LINEAR EXPT-<=-1-TWO))
 (172 30 (:LINEAR EXPT-X->-X))
 (172 30 (:LINEAR EXPT->-1-ONE))
 (172 30 (:LINEAR EXPT-<-1-TWO))
 (172 13 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (172 13 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (167 131 (:REWRITE |(< (- x) (- y))|))
 (159 13 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (159 13 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (159 13 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (143 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (143 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (143 143 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (140 131 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (140 131 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (131 131 (:REWRITE THE-FLOOR-BELOW))
 (131 131 (:REWRITE THE-FLOOR-ABOVE))
 (131 131 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (131 131 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (131 131 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (131 131 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (131 131 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (131 131 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (131 131 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (131 131 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (131 131 (:REWRITE |(< (/ x) (/ y))|))
 (129 30 (:REWRITE DEFAULT-MINUS))
 (128 71 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (122 122 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (122 122 (:REWRITE INTEGERP-<-CONSTANT))
 (122 122 (:REWRITE CONSTANT-<-INTEGERP))
 (114 6 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (113 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (113 21 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (109 34 (:REWRITE |(equal (- x) c)|))
 (108 36 (:DEFINITION FIX))
 (98 6 (:REWRITE |(* x (- y))|))
 (94 13 (:REWRITE DEFAULT-MOD-1))
 (89 89 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (73 33 (:LINEAR DM::P-IS-BIG))
 (73 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (73 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (71 71 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (71 71 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (71 71 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (71 71 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (71 71 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (71 71 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (71 71 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (66 66 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (66 3 (:REWRITE |(integerp (- x))|))
 (61 15 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (60 60 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (60 60 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (60 60 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (60 60 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (57 57 (:TYPE-PRESCRIPTION NATP))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (55 34 (:REWRITE INTEGERP-MINUS-X))
 (54 18 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (52 26 (:REWRITE DEFAULT-DIVIDE))
 (43 34 (:REWRITE |(equal (- x) (- y))|))
 (42 27 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (39 1 (:REWRITE |(equal (expt x n) 0)|))
 (38 35 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (36 18 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (35 8 (:REWRITE |(+ c (+ d x))|))
 (34 34 (:REWRITE REDUCE-INTEGERP-+))
 (34 34 (:REWRITE |(equal c (/ x))|))
 (34 34 (:REWRITE |(equal c (- x))|))
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 (34 34 (:REWRITE |(equal (/ x) (/ y))|))
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(DM::X=-2
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 (9 3 (:REWRITE DM::INTEGERP-EC-X))
 (8 2 (:REWRITE DM::INTEGERP-EC-Y))
 (4 4 (:REWRITE |(equal (* x y) 0)|))
 (4 4 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:REWRITE |(* (- x) y)|))
 )
(DM::X=-3
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 (121286 320 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (118535 55 (:LINEAR MOD-BOUNDS-1))
 (79271 24 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (68143 175 (:REWRITE RTL::MOD-DOES-NOTHING))
 (55495 25 (:LINEAR RTL::MOD-BND-2))
 (46805 175 (:REWRITE MOD-ZERO . 3))
 (43425 25 (:LINEAR RTL::MOD-BND-1))
 (39847 3713 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (38012 175 (:REWRITE MOD-X-Y-=-X . 3))
 (36405 175 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (33781 175 (:REWRITE MOD-X-Y-=-X . 4))
 (31034 175 (:REWRITE MOD-ZERO . 4))
 (29028 175 (:REWRITE DEFAULT-MOD-RATIO))
 (24561 2458 (:REWRITE DEFAULT-TIMES-2))
 (23703 1851 (:REWRITE DEFAULT-PLUS-2))
 (23529 23445 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (23445 23445 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (23445 23445 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (23078 22994 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (22192 3905 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (18174 371 (:REWRITE |(equal (- x) c)|))
 (14286 1851 (:REWRITE DEFAULT-PLUS-1))
 (12978 3713 (:REWRITE DEFAULT-LESS-THAN-1))
 (12852 175 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (12221 1111 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (12180 3618 (:REWRITE SIMPLIFY-SUMS-<))
 (11880 724 (:META META-INTEGERP-CORRECT))
 (10212 30 (:LINEAR MOD-BOUNDS-3))
 (9682 1014 (:LINEAR EXPT->=-1-TWO))
 (9682 1014 (:LINEAR EXPT->-1-TWO))
 (9682 1014 (:LINEAR EXPT-<-1-ONE))
 (9230 1014 (:LINEAR EXPT-<=-1-ONE))
 (9221 2458 (:REWRITE DEFAULT-TIMES-1))
 (8830 1014 (:LINEAR EXPT-X->=-X))
 (8830 1014 (:LINEAR EXPT->=-1-ONE))
 (8830 1014 (:LINEAR EXPT-<=-1-TWO))
 (8546 1014 (:LINEAR EXPT-X->-X))
 (8546 1014 (:LINEAR EXPT->-1-ONE))
 (8546 1014 (:LINEAR EXPT-<-1-TWO))
 (7673 3713 (:REWRITE DEFAULT-LESS-THAN-2))
 (7168 224 (:REWRITE |(* y (* x z))|))
 (6005 175 (:REWRITE MOD-X-Y-=-X . 2))
 (5898 5 (:REWRITE |(equal (mod a n) (mod b n))|))
 (4910 4910 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4910 4910 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4910 4910 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4161 3713 (:REWRITE |(< (- x) (- y))|))
 (3937 3713 (:REWRITE |(< (- x) c)|))
 (3916 728 (:REWRITE INTEGERP-MINUS-X))
 (3905 3905 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (3905 3905 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (3905 3905 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (3825 3713 (:REWRITE |(< c (- x))|))
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 (3720 3713 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3713 3713 (:REWRITE THE-FLOOR-BELOW))
 (3713 3713 (:REWRITE THE-FLOOR-ABOVE))
 (3713 3713 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3713 3713 (:REWRITE INTEGERP-<-CONSTANT))
 (3713 3713 (:REWRITE CONSTANT-<-INTEGERP))
 (3713 3713 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (3713 3713 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3713 3713 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (3713 3713 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3713 3713 (:REWRITE |(< (/ x) (/ y))|))
 (3619 175 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (3619 175 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2995 599 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2995 599 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2863 175 (:REWRITE DEFAULT-MOD-1))
 (2748 9 (:REWRITE MOD-ZERO . 1))
 (2744 210 (:REWRITE DEFAULT-MINUS))
 (2535 599 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (2485 175 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2485 175 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (2485 175 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2478 126 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (2478 126 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (2028 2028 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (2028 2028 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2028 2028 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (2028 2028 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1876 278 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1621 1621 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1380 60 (:LINEAR MOD-BOUNDS-2))
 (1281 175 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1281 175 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1281 175 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1164 42 (:REWRITE |(equal (expt x n) 0)|))
 (1111 1111 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (1111 1111 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (1111 1111 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (1052 164 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1037 1037 (:REWRITE |(< 0 (/ x))|))
 (1037 1037 (:REWRITE |(< 0 (* x y))|))
 (1024 126 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (1018 1018 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1018 1018 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1014 1014 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1014 1014 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1014 1014 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (1014 1014 (:LINEAR EXPT-LINEAR-LOWER-<))
 (797 797 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (774 371 (:REWRITE |(equal (- x) (- y))|))
 (724 724 (:REWRITE REDUCE-INTEGERP-+))
 (630 14 (:REWRITE |(* (* x y) z)|))
 (628 9 (:REWRITE MOD-ZERO . 2))
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 (599 599 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (599 599 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (599 599 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (464 399 (:REWRITE DEFAULT-DIVIDE))
 (464 232 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (451 24 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (406 406 (:REWRITE |(< (+ c/d x) y)|))
 (406 406 (:REWRITE |(< (+ (- c) x) y)|))
 (399 399 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (378 371 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (371 371 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (371 371 (:REWRITE |(equal c (/ x))|))
 (371 371 (:REWRITE |(equal c (- x))|))
 (371 371 (:REWRITE |(equal (/ x) c)|))
 (371 371 (:REWRITE |(equal (/ x) (/ y))|))
 (358 14 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (320 320 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (296 182 (:LINEAR DM::P-IS-BIG))
 (278 278 (:REWRITE |(+ c (+ d x))|))
 (264 264 (:REWRITE FOLD-CONSTS-IN-+))
 (246 246 (:REWRITE |(* c (* d x))|))
 (232 232 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (232 232 (:TYPE-PRESCRIPTION NATP))
 (226 226 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (225 77 (:REWRITE |(- (* c x))|))
 (203 175 (:REWRITE DEFAULT-MOD-2))
 (201 26 (:REWRITE |(- (- x))|))
 (186 186 (:REWRITE |(equal (+ (- c) x) y)|))
 (184 4 (:REWRITE |(integerp (- x))|))
 (175 175 (:REWRITE |(mod x (- y))| . 3))
 (175 175 (:REWRITE |(mod x (- y))| . 2))
 (175 175 (:REWRITE |(mod x (- y))| . 1))
 (175 175 (:REWRITE |(< (/ x) 0)|))
 (175 175 (:REWRITE |(< (* x y) 0)|))
 (168 168 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (164 164 (:REWRITE |(< y (+ (- c) x))|))
 (164 164 (:REWRITE |(< x (+ c/d y))|))
 (152 68 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (152 68 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (137 137 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (137 137 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (128 128 (:REWRITE DEFAULT-CDR))
 (126 126 (:REWRITE INTEGERP-/))
 (115 115 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (115 115 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (57 41 (:REWRITE DEFAULT-EXPT-1))
 (41 41 (:REWRITE DEFAULT-EXPT-2))
 (41 41 (:REWRITE |(expt 1/c n)|))
 (41 41 (:REWRITE |(expt (- x) n)|))
 (36 36 (:REWRITE DEFAULT-CAR))
 (30 9 (:REWRITE DM::INTEGERP-EC-Y))
 (27 9 (:REWRITE DM::INTEGERP-EC-X))
 (25 25 (:LINEAR RTL::MOD-BND-3))
 (21 21 (:TYPE-PRESCRIPTION ABS))
 (7 7 (:REWRITE |(equal (* x y) 0)|))
 (7 7 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (4 4 (:REWRITE |(* (- x) y)|))
 )
(DM::X=-4
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 (580520 2277 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (352761 245 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (265431 1422 (:REWRITE RTL::MOD-DOES-NOTHING))
 (212701 1432 (:REWRITE MOD-ZERO . 3))
 (205062 3047 (:REWRITE |(* y x)|))
 (164524 2129 (:REWRITE |(* x (+ y z))|))
 (155850 1432 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (145762 1432 (:REWRITE MOD-X-Y-=-X . 4))
 (145373 1432 (:REWRITE DEFAULT-MOD-RATIO))
 (124981 1432 (:REWRITE MOD-ZERO . 4))
 (108718 13460 (:REWRITE DEFAULT-TIMES-2))
 (97831 20205 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (88024 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (88024 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (88024 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (88024 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (88024 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (87862 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (87862 87862 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (70371 5302 (:REWRITE DEFAULT-PLUS-2))
 (67068 13030 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (62392 16 (:REWRITE ACL2-NUMBERP-X))
 (62376 56 (:REWRITE DM::INTEGERP-EC-X))
 (62304 12 (:REWRITE RATIONALP-X))
 (56624 1432 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (54062 337 (:LINEAR MOD-BOUNDS-3))
 (53768 4888 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
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 (46951 12914 (:REWRITE SIMPLIFY-SUMS-<))
 (46115 43067 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (46115 43067 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (46115 43067 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (43418 13460 (:REWRITE DEFAULT-TIMES-1))
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 (32064 1002 (:REWRITE |(* y (* x z))|))
 (28372 58 (:REWRITE |(equal (mod a n) (mod b n))|))
 (27545 6267 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (26551 13863 (:REWRITE DEFAULT-LESS-THAN-2))
 (25457 3365 (:LINEAR EXPT->=-1-TWO))
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 (23165 3365 (:LINEAR EXPT-<=-1-ONE))
 (22401 3365 (:LINEAR EXPT-X->-X))
 (22401 3365 (:LINEAR EXPT->-1-ONE))
 (22401 3365 (:LINEAR EXPT-<-1-TWO))
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 (20871 13863 (:REWRITE |(< c (- x))|))
 (20205 20205 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (20205 20205 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (20205 20205 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (16171 3780 (:REWRITE INTEGERP-MINUS-X))
 (16134 1422 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (16134 1422 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (16134 1422 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (14763 13863 (:REWRITE |(< (- x) (- y))|))
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 (14002 1432 (:REWRITE DEFAULT-MOD-1))
 (13893 13863 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (13893 13863 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (13863 13863 (:REWRITE THE-FLOOR-BELOW))
 (13863 13863 (:REWRITE THE-FLOOR-ABOVE))
 (13863 13863 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (13863 13863 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (13863 13863 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (13863 13863 (:REWRITE |(< (/ x) (/ y))|))
 (13573 2545 (:REWRITE DEFAULT-MINUS))
 (13030 13030 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (13030 13030 (:REWRITE INTEGERP-<-CONSTANT))
 (13030 13030 (:REWRITE CONSTANT-<-INTEGERP))
 (11643 527 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (11643 527 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
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 (10399 2743 (:REWRITE |(equal (- x) c)|))
 (9582 674 (:LINEAR MOD-BOUNDS-2))
 (8967 125 (:REWRITE |(- (+ x y))|))
 (8712 396 (:REWRITE |(integerp (- x))|))
 (8489 8489 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (7769 333 (:REWRITE |(+ y (+ x z))|))
 (7061 6267 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
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 (5833 203 (:REWRITE |(equal (expt x n) 0)|))
 (5612 1422 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (5612 1422 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
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 (3763 3763 (:REWRITE REDUCE-INTEGERP-+))
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 (2743 2743 (:REWRITE |(equal (/ x) c)|))
 (2743 2743 (:REWRITE |(equal (/ x) (/ y))|))
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 (529 529 (:REWRITE |(< x (+ c/d y))|))
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 (281 281 (:REWRITE |(+ x (- x))|))
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 (102 102 (:REWRITE DEFAULT-EXPT-1))
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 (102 102 (:REWRITE |(expt (- x) n)|))
 (90 90 (:TYPE-PRESCRIPTION ABS))
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 (12 12 (:REWRITE REDUCE-RATIONALP-*))
 (12 12 (:REWRITE RATIONALP-MINUS-X))
 (12 12 (:META META-RATIONALP-CORRECT))
 )
(DM::X=
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 (365612 1296 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (255561 928 (:REWRITE RTL::MOD-DOES-NOTHING))
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 (180979 2205 (:REWRITE |(* x (+ y z))|))
 (166018 928 (:REWRITE MOD-X-Y-=-X . 3))
 (162279 114 (:REWRITE DM::INTEGERP-EC-Y))
 (152308 928 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (142916 928 (:REWRITE DEFAULT-MOD-RATIO))
 (140662 928 (:REWRITE MOD-X-Y-=-X . 4))
 (139732 106 (:REWRITE DM::INTEGERP-EC-X))
 (125447 928 (:REWRITE MOD-ZERO . 4))
 (118420 11090 (:REWRITE DEFAULT-TIMES-2))
 (108307 108259 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (108307 108259 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (108307 108259 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (108307 108259 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (108259 108259 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (108259 108259 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (106145 19235 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (81472 3328 (:REWRITE DEFAULT-PLUS-2))
 (65500 5953 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (63881 105 (:REWRITE ACL2-NUMBERP-X))
 (63492 57 (:REWRITE RATIONALP-X))
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 (32705 928 (:REWRITE MOD-X-Y-=-X . 2))
 (31180 6236 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
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 (23190 3192 (:LINEAR EXPT->-1-TWO))
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 (21156 3192 (:LINEAR EXPT->=-1-ONE))
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 (21156 3192 (:LINEAR EXPT-<=-1-ONE))
 (20478 3192 (:LINEAR EXPT-X->-X))
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 (12318 928 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
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 (10382 10338 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (10338 10338 (:REWRITE |(< (/ x) (/ y))|))
 (10231 10228 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (10228 10228 (:REWRITE CONSTANT-<-INTEGERP))
 (8889 1256 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7817 7817 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (7385 241 (:REWRITE |(equal (expt x n) 0)|))
 (7348 928 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (7348 928 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (7348 928 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (6384 6384 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
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 (6384 6384 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (6384 6384 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (6290 286 (:LINEAR MOD-BOUNDS-2))
 (6237 6237 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (6237 6237 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (4248 41 (:REWRITE |(+ y (+ x z))|))
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 (3192 3192 (:LINEAR EXPT-LINEAR-UPPER-<))
 (3192 3192 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (3192 3192 (:LINEAR EXPT-LINEAR-LOWER-<))
 (2926 2926 (:REWRITE |(< 0 (/ x))|))
 (2926 2926 (:REWRITE |(< 0 (* x y))|))
 (2925 2925 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2925 2925 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2913 2913 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2348 77 (:REWRITE |(integerp (- x))|))
 (2089 1572 (:REWRITE |(equal (- x) c)|))
 (2035 123 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (1961 1947 (:REWRITE DEFAULT-DIVIDE))
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 (1629 260 (:REWRITE |(- (* c x))|))
 (1616 1572 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1577 1572 (:REWRITE |(equal (- x) (- y))|))
 (1572 1572 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1572 1572 (:REWRITE |(equal c (/ x))|))
 (1572 1572 (:REWRITE |(equal c (- x))|))
 (1572 1572 (:REWRITE |(equal (/ x) c)|))
 (1572 1572 (:REWRITE |(equal (/ x) (/ y))|))
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 (1357 1357 (:REWRITE |(+ c (+ d x))|))
 (1325 1325 (:REWRITE |(* c (* d x))|))
 (1319 1319 (:REWRITE FOLD-CONSTS-IN-+))
 (1296 1296 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1058 1058 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1024 112 (:REWRITE |(* (- x) y)|))
 (935 928 (:REWRITE DEFAULT-MOD-2))
 (932 38 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (928 928 (:REWRITE |(mod x (- y))| . 3))
 (928 928 (:REWRITE |(mod x (- y))| . 2))
 (928 928 (:REWRITE |(mod x (- y))| . 1))
 (889 219 (:REWRITE |(- (- x))|))
 (673 673 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (636 636 (:REWRITE INTEGERP-/))
 (629 629 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (615 615 (:REWRITE |(equal (+ (- c) x) y)|))
 (568 568 (:TYPE-PRESCRIPTION NATP))
 (494 494 (:REWRITE |(< y (+ (- c) x))|))
 (494 494 (:REWRITE |(< x (+ c/d y))|))
 (476 428 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (476 428 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (474 474 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (474 474 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (436 408 (:REWRITE DEFAULT-CAR))
 (240 240 (:REWRITE DEFAULT-EXPT-2))
 (240 240 (:REWRITE DEFAULT-EXPT-1))
 (240 240 (:REWRITE |(expt 1/c n)|))
 (240 240 (:REWRITE |(expt (- x) n)|))
 (231 231 (:REWRITE DEFAULT-CDR))
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 (198 198 (:REWRITE |(< (* x y) 0)|))
 (132 132 (:TYPE-PRESCRIPTION ABS))
 (130 130 (:LINEAR RTL::MOD-BND-3))
 (88 88 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (88 88 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (86 80 (:DEFINITION FIX))
 (57 57 (:REWRITE REDUCE-RATIONALP-+))
 (57 57 (:REWRITE REDUCE-RATIONALP-*))
 (57 57 (:REWRITE RATIONALP-MINUS-X))
 (57 57 (:META META-RATIONALP-CORRECT))
 (44 44 (:REWRITE |(equal (* x y) 0)|))
 (44 44 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (43 40 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (40 40 (:REWRITE |(+ x (- x))|))
 (4 2 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 )
(DM::R=-R-1
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 (18121 68 (:REWRITE RTL::MOD-DOES-NOTHING))
 (16263 70 (:REWRITE MOD-ZERO . 3))
 (15914 169 (:REWRITE |(* y x)|))
 (14069 9 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (13174 164 (:REWRITE |(* x (+ y z))|))
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 (8502 907 (:REWRITE DEFAULT-TIMES-2))
 (8086 6 (:REWRITE DM::INTEGERP-EC-X))
 (8052 6 (:REWRITE DM::INTEGERP-EC-Y))
 (7863 70 (:REWRITE MOD-ZERO . 4))
 (7356 7356 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (7356 7356 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (7356 7356 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (7356 7356 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (4600 442 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (4241 248 (:META META-INTEGERP-CORRECT))
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 (2196 444 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
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 (1554 723 (:REWRITE DEFAULT-LESS-THAN-2))
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 (1292 646 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (1215 227 (:LINEAR EXPT-<=-1-TWO))
 (995 77 (:REWRITE DEFAULT-MOD-1))
 (982 10 (:REWRITE |(- (+ x y))|))
 (778 68 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (778 68 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
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 (730 723 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (730 723 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
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 (723 723 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (553 68 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (553 68 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (454 454 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (454 454 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (454 454 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (454 454 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
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 (227 227 (:LINEAR EXPT-LINEAR-UPPER-<))
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 (175 175 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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 (87 86 (:REWRITE |(equal (- x) c)|))
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 (86 86 (:REWRITE |(equal (/ x) c)|))
 (86 86 (:REWRITE |(equal (/ x) (/ y))|))
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 (80 80 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
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 (76 76 (:REWRITE |(expt 1/c n)|))
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 (72 6 (:REWRITE |(* x (- y))|))
 (68 68 (:REWRITE |(mod x (- y))| . 3))
 (68 68 (:REWRITE |(mod x (- y))| . 2))
 (68 68 (:REWRITE |(mod x (- y))| . 1))
 (61 61 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
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 (48 48 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
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 (29 29 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
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 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (8 8 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (8 8 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (8 2 (:REWRITE RATIONALP-X))
 (6 6 (:REWRITE |(* 0 x)|))
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 (3 3 (:REWRITE |(equal (* x y) 0)|))
 (2 2 (:REWRITE REDUCE-RATIONALP-+))
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 (2 2 (:REWRITE RATIONALP-MINUS-X))
 (2 2 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (2 2 (:META META-RATIONALP-CORRECT))
 )
(O)
(DM::R=-R
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 (78110 479 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (58145 242 (:REWRITE RTL::MOD-DOES-NOTHING))
 (48887 50 (:REWRITE DM::INTEGERP-EC-X))
 (42822 242 (:REWRITE MOD-ZERO . 3))
 (42038 527 (:REWRITE |(* y x)|))
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 (33420 405 (:REWRITE |(* x (+ y z))|))
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 (31211 242 (:REWRITE MOD-X-Y-=-X . 4))
 (31178 260 (:REWRITE DEFAULT-MOD-RATIO))
 (28959 37 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (28172 242 (:REWRITE MOD-ZERO . 4))
 (26735 39 (:REWRITE DM::INTEGERP-EC-Y))
 (24531 71 (:REWRITE ACL2-NUMBERP-X))
 (24176 62 (:REWRITE RATIONALP-X))
 (23898 2522 (:REWRITE DEFAULT-TIMES-2))
 (22368 22203 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (22368 22203 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
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 (22368 22203 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
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 (7075 5 (:REWRITE |(equal (mod a n) (mod b n))|))
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 (5227 1215 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (2868 2853 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2868 2853 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2857 2853 (:REWRITE |(< (- x) (- y))|))
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 (1485 33 (:REWRITE |(* (* x y) z)|))
 (1265 101 (:REWRITE |(* (- x) y)|))
 (1241 1241 (:REWRITE REMOVE-WEAK-INEQUALITIES))
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 (306 121 (:REWRITE |(- (* c x))|))
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 (295 130 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
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 (262 262 (:REWRITE |(* c (* d x))|))
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 (248 248 (:REWRITE FOLD-CONSTS-IN-+))
 (242 242 (:REWRITE |(mod x (- y))| . 3))
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 (242 242 (:REWRITE |(mod x (- y))| . 1))
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 (148 148 (:REWRITE |(< (* x y) 0)|))
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 (88 88 (:REWRITE |(< y (+ (- c) x))|))
 (88 88 (:REWRITE |(< x (+ c/d y))|))
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 (69 69 (:REWRITE |(expt 1/c n)|))
 (69 69 (:REWRITE |(expt (- x) n)|))
 (68 60 (:DEFINITION FIX))
 (62 62 (:REWRITE REDUCE-RATIONALP-+))
 (62 62 (:REWRITE REDUCE-RATIONALP-*))
 (62 62 (:REWRITE RATIONALP-MINUS-X))
 (62 62 (:META META-RATIONALP-CORRECT))
 (58 16 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (45 45 (:TYPE-PRESCRIPTION ABS))
 (39 34 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (38 38 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (26 26 (:REWRITE |(+ x (- x))|))
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(DM::Y0)
(DM::Y1)
(DM::Y2)
(DM::X0)
(DM::X1)
(DM::X2)
(DM::P0)
(DM::P1)
(DM::P2)
(DM::ECP-ASSUMPTION)
(DM::NATP-X0
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(DM::NATP-X1
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 (9125 104 (:REWRITE |(* x (+ y z))|))
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 (1802 53 (:REWRITE |(* y (* x z))|))
 (1781 446 (:REWRITE DEFAULT-TIMES-1))
 (1499 1 (:REWRITE |(equal (mod a n) (mod b n))|))
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 (432 431 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (431 431 (:REWRITE THE-FLOOR-BELOW))
 (431 431 (:REWRITE THE-FLOOR-ABOVE))
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 (431 431 (:REWRITE INTEGERP-<-CONSTANT))
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 (431 431 (:REWRITE |(< (/ x) (/ y))|))
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 (1 1 (:REWRITE |(equal (* x y) 0)|))
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 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(DM::NATP-X2
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 (318 240 (:REWRITE NORMALIZE-ADDENDS))
 (306 306 (:REWRITE REDUCE-INTEGERP-+))
 (286 286 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (286 286 (:LINEAR EXPT-LINEAR-UPPER-<))
 (286 286 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (286 286 (:LINEAR EXPT-LINEAR-LOWER-<))
 (278 54 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (278 54 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (278 54 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (246 246 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (246 246 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (246 246 (:REWRITE |(< 0 (/ x))|))
 (246 246 (:REWRITE |(< 0 (* x y))|))
 (238 238 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (228 2 (:REWRITE |(+ y (+ x z))|))
 (206 6 (:REWRITE |(equal (expt x n) 0)|))
 (192 4 (:REWRITE |(* (* x y) z)|))
 (168 46 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (152 152 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (152 152 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (152 152 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (152 152 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (152 152 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (138 138 (:REWRITE |(< (+ c/d x) y)|))
 (138 138 (:REWRITE |(< (+ (- c) x) y)|))
 (124 124 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (124 124 (:REWRITE DEFAULT-DIVIDE))
 (118 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (116 116 (:REWRITE |(+ c (+ d x))|))
 (114 114 (:REWRITE FOLD-CONSTS-IN-+))
 (114 114 (:REWRITE |(* c (* d x))|))
 (92 2 (:REWRITE |(integerp (- x))|))
 (88 10 (:REWRITE |(- (* c x))|))
 (76 74 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (74 74 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (74 74 (:REWRITE |(equal c (/ x))|))
 (74 74 (:REWRITE |(equal c (- x))|))
 (74 74 (:REWRITE |(equal (/ x) c)|))
 (74 74 (:REWRITE |(equal (/ x) (/ y))|))
 (74 74 (:REWRITE |(equal (- x) c)|))
 (74 74 (:REWRITE |(equal (- x) (- y))|))
 (68 68 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (62 62 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (60 60 (:REWRITE INTEGERP-/))
 (54 54 (:REWRITE DEFAULT-MOD-2))
 (54 54 (:REWRITE |(mod x (- y))| . 3))
 (54 54 (:REWRITE |(mod x (- y))| . 2))
 (54 54 (:REWRITE |(mod x (- y))| . 1))
 (52 52 (:REWRITE |(equal (+ (- c) x) y)|))
 (50 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (46 46 (:REWRITE |(< y (+ (- c) x))|))
 (46 46 (:REWRITE |(< x (+ c/d y))|))
 (44 4 (:REWRITE |(- (- x))|))
 (34 34 (:LINEAR DM::P-IS-BIG))
 (22 2 (:REWRITE |(+ 0 x)|))
 (10 10 (:LINEAR RTL::MOD-BND-3))
 (10 6 (:REWRITE DEFAULT-EXPT-1))
 (9 9 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION ABS))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (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 |(equal (* x y) 0)|))
 (2 2 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(* (- x) y)|))
 )
(DM::NATP-Y0
 (3 1 (:REWRITE SIMPLIFY-SUMS-<))
 (3 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (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 INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (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) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 )
(DM::NATP-Y1
 (46860 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (29543 11 (:LINEAR MOD-BOUNDS-1))
 (24082 34 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (15199 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (13815 5 (:LINEAR RTL::MOD-BND-2))
 (11688 27 (:REWRITE RTL::MOD-DOES-NOTHING))
 (10855 5 (:LINEAR RTL::MOD-BND-1))
 (10689 62 (:REWRITE |(* y x)|))
 (10325 27 (:REWRITE MOD-ZERO . 3))
 (9335 737 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (9125 104 (:REWRITE |(* x (+ y z))|))
 (7000 27 (:REWRITE MOD-X-Y-=-X . 3))
 (6929 27 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (6326 27 (:REWRITE DEFAULT-MOD-RATIO))
 (5967 27 (:REWRITE MOD-X-Y-=-X . 4))
 (5589 446 (:REWRITE DEFAULT-TIMES-2))
 (5435 27 (:REWRITE MOD-ZERO . 4))
 (4831 813 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (4006 4006 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (3436 128 (:REWRITE DEFAULT-PLUS-2))
 (3180 265 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (3071 152 (:META META-INTEGERP-CORRECT))
 (3043 431 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2646 6 (:LINEAR MOD-BOUNDS-3))
 (2246 431 (:REWRITE DEFAULT-LESS-THAN-1))
 (2151 431 (:REWRITE SIMPLIFY-SUMS-<))
 (1802 53 (:REWRITE |(* y (* x z))|))
 (1784 446 (:REWRITE DEFAULT-TIMES-1))
 (1519 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1454 128 (:REWRITE DEFAULT-PLUS-1))
 (1357 143 (:LINEAR EXPT-<=-1-ONE))
 (1310 143 (:LINEAR EXPT->=-1-TWO))
 (1310 143 (:LINEAR EXPT->-1-TWO))
 (1310 143 (:LINEAR EXPT-<-1-ONE))
 (1279 27 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1279 27 (:REWRITE MOD-X-Y-=-X . 2))
 (1228 431 (:REWRITE DEFAULT-LESS-THAN-2))
 (1214 143 (:LINEAR EXPT-X->=-X))
 (1214 143 (:LINEAR EXPT->=-1-ONE))
 (1214 143 (:LINEAR EXPT-<=-1-TWO))
 (1182 143 (:LINEAR EXPT-X->-X))
 (1182 143 (:LINEAR EXPT->-1-ONE))
 (1182 143 (:LINEAR EXPT-<-1-TWO))
 (911 153 (:REWRITE INTEGERP-MINUS-X))
 (813 813 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (813 813 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (813 813 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (737 737 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (737 737 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (737 737 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (707 27 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (707 27 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (674 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (674 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (599 27 (:REWRITE DEFAULT-MOD-1))
 (594 27 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (594 27 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (594 27 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (527 5 (:REWRITE |(- (+ x y))|))
 (432 431 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (432 431 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (431 431 (:REWRITE THE-FLOOR-BELOW))
 (431 431 (:REWRITE THE-FLOOR-ABOVE))
 (431 431 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (431 431 (:REWRITE INTEGERP-<-CONSTANT))
 (431 431 (:REWRITE CONSTANT-<-INTEGERP))
 (431 431 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (431 431 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (431 431 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (431 431 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (431 431 (:REWRITE |(< c (- x))|))
 (431 431 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (431 431 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (431 431 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (431 431 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (431 431 (:REWRITE |(< (/ x) (/ y))|))
 (431 431 (:REWRITE |(< (- x) c)|))
 (431 431 (:REWRITE |(< (- x) (- y))|))
 (365 73 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (365 73 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (365 73 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (365 73 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (336 12 (:LINEAR MOD-BOUNDS-2))
 (329 329 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (316 13 (:REWRITE DEFAULT-MINUS))
 (286 286 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (286 286 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (286 286 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (286 286 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (265 265 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (265 265 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (265 265 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (247 33 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (185 185 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (162 120 (:REWRITE NORMALIZE-ADDENDS))
 (152 152 (:REWRITE REDUCE-INTEGERP-+))
 (143 143 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (143 143 (:LINEAR EXPT-LINEAR-UPPER-<))
 (143 143 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (143 143 (:LINEAR EXPT-LINEAR-LOWER-<))
 (140 27 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (140 27 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (140 27 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (123 123 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (123 123 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (123 123 (:REWRITE |(< 0 (/ x))|))
 (123 123 (:REWRITE |(< 0 (* x y))|))
 (119 119 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (117 3 (:REWRITE |(equal (expt x n) 0)|))
 (116 1 (:REWRITE |(+ y (+ x z))|))
 (96 2 (:REWRITE |(* (* x y) z)|))
 (84 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (73 73 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (73 73 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (73 73 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (73 73 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (73 73 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (69 69 (:REWRITE |(< (+ c/d x) y)|))
 (69 69 (:REWRITE |(< (+ (- c) x) y)|))
 (62 62 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (62 62 (:REWRITE DEFAULT-DIVIDE))
 (60 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (58 58 (:REWRITE |(+ c (+ d x))|))
 (57 57 (:REWRITE FOLD-CONSTS-IN-+))
 (57 57 (:REWRITE |(* c (* d x))|))
 (49 1 (:REWRITE |(integerp (- x))|))
 (44 5 (:REWRITE |(- (* c x))|))
 (38 37 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (37 37 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (37 37 (:REWRITE |(equal c (/ x))|))
 (37 37 (:REWRITE |(equal c (- x))|))
 (37 37 (:REWRITE |(equal (/ x) c)|))
 (37 37 (:REWRITE |(equal (/ x) (/ y))|))
 (37 37 (:REWRITE |(equal (- x) c)|))
 (37 37 (:REWRITE |(equal (- x) (- y))|))
 (34 34 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (31 31 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (30 30 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (30 30 (:REWRITE INTEGERP-/))
 (27 27 (:REWRITE DEFAULT-MOD-2))
 (27 27 (:REWRITE |(mod x (- y))| . 3))
 (27 27 (:REWRITE |(mod x (- y))| . 2))
 (27 27 (:REWRITE |(mod x (- y))| . 1))
 (27 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (26 26 (:REWRITE |(equal (+ (- c) x) y)|))
 (23 23 (:REWRITE |(< y (+ (- c) x))|))
 (23 23 (:REWRITE |(< x (+ c/d y))|))
 (22 2 (:REWRITE |(- (- x))|))
 (17 17 (:LINEAR DM::P-IS-BIG))
 (12 1 (:REWRITE |(+ 0 x)|))
 (9 5 (:REWRITE DEFAULT-CAR))
 (6 3 (:REWRITE DEFAULT-EXPT-1))
 (5 5 (:LINEAR RTL::MOD-BND-3))
 (5 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:TYPE-PRESCRIPTION ABS))
 (3 3 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(DM::NATP-Y2
 (93720 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (59086 22 (:LINEAR MOD-BOUNDS-1))
 (48164 68 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (30398 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (27630 10 (:LINEAR RTL::MOD-BND-2))
 (23376 54 (:REWRITE RTL::MOD-DOES-NOTHING))
 (21710 10 (:LINEAR RTL::MOD-BND-1))
 (21378 124 (:REWRITE |(* y x)|))
 (20650 54 (:REWRITE MOD-ZERO . 3))
 (18694 1498 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (18250 208 (:REWRITE |(* x (+ y z))|))
 (14000 54 (:REWRITE MOD-X-Y-=-X . 3))
 (13858 54 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (12652 54 (:REWRITE DEFAULT-MOD-RATIO))
 (11934 54 (:REWRITE MOD-X-Y-=-X . 4))
 (11178 892 (:REWRITE DEFAULT-TIMES-2))
 (10870 54 (:REWRITE MOD-ZERO . 4))
 (9662 1626 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (8021 8021 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6872 256 (:REWRITE DEFAULT-PLUS-2))
 (6360 530 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (6142 304 (:META META-INTEGERP-CORRECT))
 (6083 861 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5292 12 (:LINEAR MOD-BOUNDS-3))
 (4490 861 (:REWRITE DEFAULT-LESS-THAN-1))
 (4299 861 (:REWRITE SIMPLIFY-SUMS-<))
 (3604 106 (:REWRITE |(* y (* x z))|))
 (3568 892 (:REWRITE DEFAULT-TIMES-1))
 (3038 2 (:REWRITE |(equal (mod a n) (mod b n))|))
 (2908 256 (:REWRITE DEFAULT-PLUS-1))
 (2714 286 (:LINEAR EXPT-<=-1-ONE))
 (2620 286 (:LINEAR EXPT->=-1-TWO))
 (2620 286 (:LINEAR EXPT->-1-TWO))
 (2620 286 (:LINEAR EXPT-<-1-ONE))
 (2558 54 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (2558 54 (:REWRITE MOD-X-Y-=-X . 2))
 (2454 861 (:REWRITE DEFAULT-LESS-THAN-2))
 (2428 286 (:LINEAR EXPT-X->=-X))
 (2428 286 (:LINEAR EXPT->=-1-ONE))
 (2428 286 (:LINEAR EXPT-<=-1-TWO))
 (2364 286 (:LINEAR EXPT-X->-X))
 (2364 286 (:LINEAR EXPT->-1-ONE))
 (2364 286 (:LINEAR EXPT-<-1-TWO))
 (1822 306 (:REWRITE INTEGERP-MINUS-X))
 (1626 1626 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (1626 1626 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (1626 1626 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1498 1498 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1498 1498 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1498 1498 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1414 54 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1414 54 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1348 46 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (1348 46 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (1198 54 (:REWRITE DEFAULT-MOD-1))
 (1188 54 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1188 54 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1188 54 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1054 10 (:REWRITE |(- (+ x y))|))
 (863 861 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (863 861 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (861 861 (:REWRITE THE-FLOOR-BELOW))
 (861 861 (:REWRITE THE-FLOOR-ABOVE))
 (861 861 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (861 861 (:REWRITE INTEGERP-<-CONSTANT))
 (861 861 (:REWRITE CONSTANT-<-INTEGERP))
 (861 861 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (861 861 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (861 861 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (861 861 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (861 861 (:REWRITE |(< c (- x))|))
 (861 861 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (861 861 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (861 861 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (861 861 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (861 861 (:REWRITE |(< (/ x) (/ y))|))
 (861 861 (:REWRITE |(< (- x) c)|))
 (861 861 (:REWRITE |(< (- x) (- y))|))
 (760 152 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (760 152 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (760 152 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (760 152 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (672 24 (:LINEAR MOD-BOUNDS-2))
 (658 658 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (632 26 (:REWRITE DEFAULT-MINUS))
 (572 572 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (572 572 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (572 572 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (572 572 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (530 530 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (530 530 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (530 530 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (494 66 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (369 369 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (324 240 (:REWRITE NORMALIZE-ADDENDS))
 (304 304 (:REWRITE REDUCE-INTEGERP-+))
 (286 286 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (286 286 (:LINEAR EXPT-LINEAR-UPPER-<))
 (286 286 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (286 286 (:LINEAR EXPT-LINEAR-LOWER-<))
 (280 54 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (280 54 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (280 54 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (246 246 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (246 246 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (246 246 (:REWRITE |(< 0 (/ x))|))
 (246 246 (:REWRITE |(< 0 (* x y))|))
 (238 238 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (234 6 (:REWRITE |(equal (expt x n) 0)|))
 (232 2 (:REWRITE |(+ y (+ x z))|))
 (192 4 (:REWRITE |(* (* x y) z)|))
 (168 46 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (152 152 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (152 152 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (152 152 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (152 152 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (152 152 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (138 138 (:REWRITE |(< (+ c/d x) y)|))
 (138 138 (:REWRITE |(< (+ (- c) x) y)|))
 (124 124 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (124 124 (:REWRITE DEFAULT-DIVIDE))
 (120 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (116 116 (:REWRITE |(+ c (+ d x))|))
 (114 114 (:REWRITE FOLD-CONSTS-IN-+))
 (114 114 (:REWRITE |(* c (* d x))|))
 (98 2 (:REWRITE |(integerp (- x))|))
 (88 10 (:REWRITE |(- (* c x))|))
 (76 74 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (74 74 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (74 74 (:REWRITE |(equal c (/ x))|))
 (74 74 (:REWRITE |(equal c (- x))|))
 (74 74 (:REWRITE |(equal (/ x) c)|))
 (74 74 (:REWRITE |(equal (/ x) (/ y))|))
 (74 74 (:REWRITE |(equal (- x) c)|))
 (74 74 (:REWRITE |(equal (- x) (- y))|))
 (68 68 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (62 62 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (60 60 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (60 60 (:REWRITE INTEGERP-/))
 (54 54 (:REWRITE DEFAULT-MOD-2))
 (54 54 (:REWRITE |(mod x (- y))| . 3))
 (54 54 (:REWRITE |(mod x (- y))| . 2))
 (54 54 (:REWRITE |(mod x (- y))| . 1))
 (54 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (52 52 (:REWRITE |(equal (+ (- c) x) y)|))
 (46 46 (:REWRITE |(< y (+ (- c) x))|))
 (46 46 (:REWRITE |(< x (+ c/d y))|))
 (44 4 (:REWRITE |(- (- x))|))
 (34 34 (:LINEAR DM::P-IS-BIG))
 (24 2 (:REWRITE |(+ 0 x)|))
 (17 9 (:REWRITE DEFAULT-CAR))
 (12 6 (:REWRITE DEFAULT-EXPT-1))
 (10 10 (:LINEAR RTL::MOD-BND-3))
 (9 5 (:REWRITE DEFAULT-CDR))
 (6 6 (:TYPE-PRESCRIPTION ABS))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (4 4 (:DEFINITION FIX))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(equal (* x y) 0)|))
 (2 2 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:REWRITE |(+ x (- x))|))
 (2 2 (:REWRITE |(* (- x) y)|))
 )
(DM::MOD-XI-YI
 (140580 9 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (88629 33 (:LINEAR MOD-BOUNDS-1))
 (72258 108 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (45597 9 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (41445 15 (:LINEAR RTL::MOD-BND-2))
 (35064 81 (:REWRITE RTL::MOD-DOES-NOTHING))
 (32565 15 (:LINEAR RTL::MOD-BND-1))
 (32127 198 (:REWRITE |(* y x)|))
 (31149 87 (:REWRITE MOD-ZERO . 3))
 (27375 312 (:REWRITE |(* x (+ y z))|))
 (20823 87 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (19074 87 (:REWRITE DEFAULT-MOD-RATIO))
 (18147 87 (:REWRITE MOD-X-Y-=-X . 4))
 (16803 1362 (:REWRITE DEFAULT-TIMES-2))
 (16455 87 (:REWRITE MOD-ZERO . 4))
 (14529 2457 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (12045 12045 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (10308 384 (:REWRITE DEFAULT-PLUS-2))
 (9540 795 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (9219 462 (:META META-INTEGERP-CORRECT))
 (9133 1296 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (7938 18 (:LINEAR MOD-BOUNDS-3))
 (6738 1296 (:REWRITE DEFAULT-LESS-THAN-1))
 (6451 1296 (:REWRITE SIMPLIFY-SUMS-<))
 (5406 159 (:REWRITE |(* y (* x z))|))
 (5388 1362 (:REWRITE DEFAULT-TIMES-1))
 (4557 3 (:REWRITE |(equal (mod a n) (mod b n))|))
 (4362 384 (:REWRITE DEFAULT-PLUS-1))
 (4071 429 (:LINEAR EXPT-<=-1-ONE))
 (3930 429 (:LINEAR EXPT->=-1-TWO))
 (3930 429 (:LINEAR EXPT->-1-TWO))
 (3930 429 (:LINEAR EXPT-<-1-ONE))
 (3879 87 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (3837 81 (:REWRITE MOD-X-Y-=-X . 2))
 (3691 1296 (:REWRITE DEFAULT-LESS-THAN-2))
 (3642 429 (:LINEAR EXPT-X->=-X))
 (3642 429 (:LINEAR EXPT->=-1-ONE))
 (3642 429 (:LINEAR EXPT-<=-1-TWO))
 (3546 429 (:LINEAR EXPT-X->-X))
 (3546 429 (:LINEAR EXPT->-1-ONE))
 (3546 429 (:LINEAR EXPT-<-1-TWO))
 (2739 465 (:REWRITE INTEGERP-MINUS-X))
 (2691 2691 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2691 2691 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2691 2691 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2457 2457 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2457 2457 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2457 2457 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2157 87 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (2157 87 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2022 69 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (2022 69 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (1809 87 (:REWRITE DEFAULT-MOD-1))
 (1782 81 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1782 81 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1782 81 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1581 15 (:REWRITE |(- (+ x y))|))
 (1455 291 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1455 291 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1455 291 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1455 291 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1299 1296 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1299 1296 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1296 1296 (:REWRITE THE-FLOOR-BELOW))
 (1296 1296 (:REWRITE THE-FLOOR-ABOVE))
 (1296 1296 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1296 1296 (:REWRITE INTEGERP-<-CONSTANT))
 (1296 1296 (:REWRITE CONSTANT-<-INTEGERP))
 (1296 1296 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1296 1296 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1296 1296 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1296 1296 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1296 1296 (:REWRITE |(< c (- x))|))
 (1296 1296 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1296 1296 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1296 1296 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1296 1296 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1296 1296 (:REWRITE |(< (/ x) (/ y))|))
 (1296 1296 (:REWRITE |(< (- x) c)|))
 (1296 1296 (:REWRITE |(< (- x) (- y))|))
 (1008 36 (:LINEAR MOD-BOUNDS-2))
 (999 999 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (948 39 (:REWRITE DEFAULT-MINUS))
 (858 858 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (858 858 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (858 858 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (858 858 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (795 795 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (795 795 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (795 795 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (747 105 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (558 558 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (486 360 (:REWRITE NORMALIZE-ADDENDS))
 (462 462 (:REWRITE REDUCE-INTEGERP-+))
 (429 429 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (429 429 (:LINEAR EXPT-LINEAR-UPPER-<))
 (429 429 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (429 429 (:LINEAR EXPT-LINEAR-LOWER-<))
 (420 81 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (420 81 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (420 81 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (375 375 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (375 375 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (375 375 (:REWRITE |(< 0 (/ x))|))
 (375 375 (:REWRITE |(< 0 (* x y))|))
 (357 357 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (351 9 (:REWRITE |(equal (expt x n) 0)|))
 (348 3 (:REWRITE |(+ y (+ x z))|))
 (291 291 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (291 291 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (291 291 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (291 291 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (291 291 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (288 6 (:REWRITE |(* (* x y) z)|))
 (252 69 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (207 207 (:REWRITE |(< (+ c/d x) y)|))
 (207 207 (:REWRITE |(< (+ (- c) x) y)|))
 (198 198 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (198 198 (:REWRITE DEFAULT-DIVIDE))
 (180 9 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (174 174 (:REWRITE |(+ c (+ d x))|))
 (171 171 (:REWRITE FOLD-CONSTS-IN-+))
 (171 171 (:REWRITE |(* c (* d x))|))
 (147 3 (:REWRITE |(integerp (- x))|))
 (132 15 (:REWRITE |(- (* c x))|))
 (120 117 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (117 117 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (117 117 (:REWRITE |(equal c (/ x))|))
 (117 117 (:REWRITE |(equal c (- x))|))
 (117 117 (:REWRITE |(equal (/ x) c)|))
 (117 117 (:REWRITE |(equal (/ x) (/ y))|))
 (117 117 (:REWRITE |(equal (- x) c)|))
 (117 117 (:REWRITE |(equal (- x) (- y))|))
 (108 108 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (96 96 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (93 93 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (90 90 (:REWRITE INTEGERP-/))
 (87 87 (:REWRITE DEFAULT-MOD-2))
 (81 81 (:REWRITE |(mod x (- y))| . 3))
 (81 81 (:REWRITE |(mod x (- y))| . 2))
 (81 81 (:REWRITE |(mod x (- y))| . 1))
 (81 3 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (78 78 (:REWRITE |(equal (+ (- c) x) y)|))
 (69 69 (:REWRITE |(< y (+ (- c) x))|))
 (69 69 (:REWRITE |(< x (+ c/d y))|))
 (66 6 (:REWRITE |(- (- x))|))
 (51 51 (:LINEAR DM::P-IS-BIG))
 (36 36 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (36 3 (:REWRITE |(+ 0 x)|))
 (24 12 (:REWRITE DEFAULT-CAR))
 (18 9 (:REWRITE DEFAULT-EXPT-1))
 (15 15 (:LINEAR RTL::MOD-BND-3))
 (12 6 (:REWRITE DEFAULT-CDR))
 (9 9 (:TYPE-PRESCRIPTION ABS))
 (9 9 (:REWRITE DEFAULT-EXPT-2))
 (9 9 (:REWRITE |(expt 1/c n)|))
 (9 9 (:REWRITE |(expt (- x) n)|))
 (6 6 (:DEFINITION FIX))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (3 3 (:REWRITE |(equal (* x y) 0)|))
 (3 3 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (3 3 (:REWRITE |(+ x (- x))|))
 (3 3 (:REWRITE |(* (- x) y)|))
 )
(DM::P0+P1<>P0-1
 (51499 31 (:REWRITE RTL::MOD-DOES-NOTHING))
 (36373 206 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (25975 2084 (:REWRITE DEFAULT-TIMES-2))
 (19486 2084 (:REWRITE DEFAULT-TIMES-1))
 (16623 3327 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (16623 3327 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (13270 99 (:REWRITE RATIONALP-X))
 (10246 31 (:REWRITE MOD-ZERO . 4))
 (10136 31 (:REWRITE MOD-X-Y-=-X . 3))
 (9900 31 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (9822 31 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (9546 31 (:REWRITE MOD-X-Y-=-X . 4))
 (8835 876 (:REWRITE DEFAULT-PLUS-2))
 (7972 7972 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (7972 7972 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (7972 7972 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (7625 3258 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (7396 150 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7003 93 (:REWRITE REDUCE-RATIONALP-*))
 (5743 34 (:LINEAR RTL::MOD-BND-2))
 (5500 31 (:REWRITE MOD-ZERO . 3))
 (5328 876 (:REWRITE DEFAULT-PLUS-1))
 (4851 3327 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (4851 3327 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4091 36 (:LINEAR MOD-BOUNDS-3))
 (4066 31 (:REWRITE MOD-X-Y-=-X . 2))
 (3830 72 (:LINEAR MOD-BOUNDS-2))
 (3708 36 (:DEFINITION RFIX))
 (3327 3327 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (3327 3327 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (3327 3327 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (3327 3327 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (3327 3327 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (3289 136 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3258 3258 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (3255 3255 (:TYPE-PRESCRIPTION NATP))
 (3148 31 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (3148 31 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2943 2943 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (2943 2943 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (2810 242 (:REWRITE DEFAULT-LESS-THAN-1))
 (2791 2791 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2791 2791 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2791 2791 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2261 65 (:REWRITE DEFAULT-MOD-1))
 (2253 285 (:META META-INTEGERP-CORRECT))
 (2229 3 (:REWRITE DEFAULT-CDR))
 (2229 3 (:REWRITE DEFAULT-CAR))
 (2132 241 (:REWRITE |(< (- x) c)|))
 (1874 400 (:REWRITE DEFAULT-MINUS))
 (1786 31 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1786 31 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1786 31 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1673 146 (:REWRITE SIMPLIFY-SUMS-<))
 (1484 288 (:REWRITE INTEGERP-MINUS-X))
 (1362 31 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1362 31 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1362 31 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (1125 1125 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1071 79 (:META META-RATIONALP-CORRECT))
 (1058 242 (:REWRITE DEFAULT-LESS-THAN-2))
 (1029 11 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (784 34 (:REWRITE |(* (- x) y)|))
 (738 12 (:REWRITE RATIONALP-MOD))
 (709 161 (:REWRITE |(equal (- x) c)|))
 (688 344 (:REWRITE DEFAULT-DIVIDE))
 (669 13 (:REWRITE DM::MOD*REWRITE-2))
 (635 22 (:REWRITE |(integerp (- x))|))
 (587 242 (:REWRITE |(< c (- x))|))
 (551 11 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (524 25 (:REWRITE INTEGERP-MOD-2))
 (524 25 (:REWRITE INTEGERP-MOD-1))
 (524 25 (:REWRITE RTL::INTEGERP-MOD))
 (447 103 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (438 242 (:REWRITE |(< (- x) (- y))|))
 (398 398 (:REWRITE |(* c (* d x))|))
 (382 12 (:REWRITE RTL::RATIONALP-MOD))
 (344 344 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (329 329 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (312 312 (:REWRITE |(- (* c x))|))
 (285 285 (:REWRITE REDUCE-INTEGERP-+))
 (242 242 (:REWRITE THE-FLOOR-BELOW))
 (242 242 (:REWRITE THE-FLOOR-ABOVE))
 (242 242 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (242 242 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (242 242 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (242 242 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (242 242 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (242 242 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (242 242 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (242 242 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (242 242 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (242 242 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (242 242 (:REWRITE |(< (/ x) (/ y))|))
 (212 161 (:REWRITE |(equal (- x) (- y))|))
 (206 206 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (206 206 (:REWRITE INTEGERP-<-CONSTANT))
 (206 206 (:REWRITE CONSTANT-<-INTEGERP))
 (189 161 (:REWRITE |(equal (/ x) c)|))
 (189 161 (:REWRITE |(equal (/ x) (/ y))|))
 (175 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (168 7 (:REWRITE MOD-THEOREM-ONE-B))
 (161 161 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (161 161 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (161 161 (:REWRITE |(equal c (/ x))|))
 (161 161 (:REWRITE |(equal c (- x))|))
 (150 150 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (143 143 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (132 132 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (130 65 (:REWRITE DEFAULT-MOD-2))
 (127 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (87 87 (:REWRITE |(+ c (+ d x))|))
 (84 28 (:REWRITE |(equal x (/ y))|))
 (77 77 (:REWRITE |(< (/ x) 0)|))
 (77 77 (:REWRITE |(< (* x y) 0)|))
 (63 63 (:REWRITE |(< 0 (/ x))|))
 (63 63 (:REWRITE |(< 0 (* x y))|))
 (56 28 (:REWRITE |(not (equal x (/ y)))|))
 (51 51 (:REWRITE |(< (+ c/d x) y)|))
 (51 51 (:REWRITE |(< (+ (- c) x) y)|))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (50 50 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (47 47 (:REWRITE FOLD-CONSTS-IN-+))
 (46 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (37 37 (:REWRITE |(< y (+ (- c) x))|))
 (37 37 (:REWRITE |(< x (+ c/d y))|))
 (34 34 (:LINEAR RTL::MOD-BND-3))
 (31 31 (:REWRITE INTEGERP-/))
 (31 31 (:REWRITE |(mod x (- y))| . 3))
 (31 31 (:REWRITE |(mod x (- y))| . 2))
 (31 31 (:REWRITE |(mod x (- y))| . 1))
 (17 17 (:REWRITE |(equal (+ (- c) x) y)|))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (16 16 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (11 11 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (10 2 (:REWRITE |(+ x x)|))
 (6 6 (:REWRITE |(equal (* x y) 0)|))
 (6 6 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 )
(DM::P0+P1<>P0-2
 (492 8 (:REWRITE DEFAULT-MOD-RATIO))
 (462 462 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (462 462 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (462 462 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (462 15 (:REWRITE |(* y x)|))
 (374 8 (:REWRITE MOD-ZERO . 3))
 (366 6 (:REWRITE |(* x (+ y z))|))
 (365 89 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (365 89 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (365 89 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (365 89 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (354 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (306 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (291 8 (:REWRITE MOD-X-Y-=-X . 3))
 (268 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (258 8 (:REWRITE RTL::MOD-DOES-NOTHING))
 (193 66 (:REWRITE DEFAULT-TIMES-2))
 (181 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (180 8 (:REWRITE MOD-ZERO . 4))
 (175 27 (:REWRITE |(< (- x) c)|))
 (175 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (174 8 (:REWRITE MOD-X-Y-=-X . 4))
 (162 46 (:REWRITE DEFAULT-PLUS-1))
 (161 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (156 46 (:REWRITE DEFAULT-PLUS-2))
 (123 66 (:REWRITE DEFAULT-TIMES-1))
 (115 1 (:LINEAR MOD-BOUNDS-3))
 (105 5 (:REWRITE |(* (* x y) z)|))
 (89 89 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (88 88 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (76 4 (:REWRITE |(* (- x) y)|))
 (74 2 (:REWRITE MOD-ZERO . 1))
 (71 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (71 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (71 71 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (68 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (68 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (67 22 (:REWRITE |(equal (- x) c)|))
 (65 23 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (63 8 (:REWRITE MOD-X-Y-=-X . 2))
 (60 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (60 8 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (60 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (58 19 (:REWRITE DEFAULT-MINUS))
 (58 16 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (58 14 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (55 23 (:REWRITE SIMPLIFY-SUMS-<))
 (53 4 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (51 27 (:REWRITE DEFAULT-LESS-THAN-2))
 (50 50 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (49 27 (:REWRITE DEFAULT-LESS-THAN-1))
 (49 2 (:REWRITE |(+ y (+ x z))|))
 (48 16 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (44 2 (:REWRITE |(integerp (- x))|))
 (42 42 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (42 12 (:META META-INTEGERP-CORRECT))
 (40 6 (:REWRITE |(+ y x)|))
 (33 27 (:REWRITE |(< (- x) (- y))|))
 (30 15 (:REWRITE DEFAULT-DIVIDE))
 (29 27 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (29 27 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (29 22 (:REWRITE |(equal (- x) (- y))|))
 (27 27 (:REWRITE THE-FLOOR-BELOW))
 (27 27 (:REWRITE THE-FLOOR-ABOVE))
 (27 27 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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(DM::P0+P1<>P0-10
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(DM::P0+P1<>P0-11
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(DM::P0+P1<>P0-12
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(DM::P0+P1=P0-P1-6)
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(DM::P0+P1=P0-P1-8
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(DM::P0+P1=P0-P1-10)
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(DM::P0+P1=P0-P1-17
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(DM::P0+P1=P0-P1-18
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 (139 139 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
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 (8 8 (:REWRITE |(equal (+ (- c) x) y)|))
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(DM::P0+P1=P0-P1-19
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 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
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(DM::P0+P1=P0-P1-20
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 )
(DM::P0+P1=P0-P1-21)
(DM::P0+P1=P0-P1-22
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(DM::P0+P1=P0-P1-23)
(DM::P0+P1=P0-P1-24
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(DM::P0+P1=P0-P1-25
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(DM::P0+P1=P0-P1-26
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(DM::P0+P1=P0-P1-27
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(DM::P0+P1=P0-P1-28)
(DM::P0+P1=P0-P1-29
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(DM::P0+P1=P0-P1-30
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(DM::P0+P1=P0-P1-31
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(DM::P0+P1=P0-P1)
