(|(* 2 (floor x y))|
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 (4837 2516 (:META META-INTEGERP-CORRECT))
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 (2932 2932 (:REWRITE |(* c (* d x))|))
 (2340 1164 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (2214 1797 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2214 1797 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2020 76 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (1879 1879 (:REWRITE DEFAULT-LESS-THAN-2))
 (1879 1879 (:REWRITE DEFAULT-LESS-THAN-1))
 (1834 1834 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1789 1789 (:REWRITE INTEGERP-<-CONSTANT))
 (1789 1789 (:REWRITE CONSTANT-<-INTEGERP))
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 (716 716 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (567 23 (:REWRITE |(equal x (/ y))|))
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 (460 460 (:REWRITE |(equal (/ x) (/ y))|))
 (460 460 (:REWRITE |(equal (- x) (- y))|))
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 (458 458 (:REWRITE |(equal c (- x))|))
 (458 458 (:REWRITE |(equal (- x) c)|))
 (375 86 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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 (324 302 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (240 60 (:REWRITE |(integerp (- x))|))
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 (193 171 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (182 14 (:REWRITE |(equal (floor (+ x y) z) x)|))
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 (165 165 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (165 165 (:REWRITE |(floor x (- y))| . 2))
 (165 165 (:REWRITE |(floor x (- y))| . 1))
 (165 165 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (165 165 (:REWRITE |(floor (- x) y)| . 2))
 (165 165 (:REWRITE |(floor (- x) y)| . 1))
 (165 165 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (154 154 (:REWRITE |(< (+ c/d x) y)|))
 (146 146 (:REWRITE |(< (+ (- c) x) y)|))
 (140 92 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (80 80 (:REWRITE |(< y (+ (- c) x))|))
 (80 80 (:REWRITE |(< x (+ c/d y))|))
 (76 76 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 (72 8 (:REWRITE |(<= 1 (* x (/ y))) with (< y 0)|))
 (72 8 (:REWRITE |(<= 1 (* x (/ y))) with (< 0 y)|))
 (72 8 (:REWRITE |(< (* x (/ y)) 1) with (< y 0)|))
 (72 8 (:REWRITE |(< (* x (/ y)) 1) with (< 0 y)|))
 (44 44 (:REWRITE |arith (* c (* d x))|))
 (42 3 (:REWRITE |(* (if a b c) x)|))
 (30 30 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (16 16 (:REWRITE FOLD-CONSTS-IN-+))
 (15 15 (:REWRITE |(not (equal x (/ y)))|))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-MOD))
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 (6 6 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (6 6 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (6 6 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (2 2 (:REWRITE |(/ (/ x))|))
 )
(UGLY-UNHIDE-HACK
 (1 1 (:TYPE-PRESCRIPTION UGLY-UNHIDE-HACK))
 )
(UGLY-UNHIDE-HACK-FN)
(UGLY-UNHIDE-HACK-THM-1
 (3 3 (:TYPE-PRESCRIPTION UGLY-UNHIDE-HACK))
 )
(UGLY-UNHIDE-HACK-THM-2
 (3 3 (:TYPE-PRESCRIPTION UGLY-UNHIDE-HACK))
 )
(UGLY-UNHIDE-HACK-LOOP-STOPPER-1
 (10 8 (:REWRITE DEFAULT-PLUS-1))
 (8 8 (:REWRITE DEFAULT-PLUS-2))
 (4 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (4 4 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (2 2 (: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 |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(UGLY-UNHIDE-HACK-LOOP-STOPPER)
(|(* 1/2 (floor x y))|
 (2124 2 (:REWRITE FLOOR-=-X/Y . 4))
 (1985 34 (:REWRITE FLOOR-ZERO . 3))
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 (993 993 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (719 134 (:REWRITE |(< (/ x) 0)|))
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 (523 262 (:META META-INTEGERP-CORRECT))
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 (442 39 (:REWRITE DEFAULT-FLOOR-RATIO))
 (417 417 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (332 320 (:REWRITE |(* c (* d x))|))
 (318 47 (:REWRITE |(* (- x) y)|))
 (300 224 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (300 224 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (262 262 (:REWRITE REDUCE-INTEGERP-+))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (260 260 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (254 254 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (252 12 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
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 (243 32 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (243 32 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (224 224 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (224 224 (:REWRITE DEFAULT-LESS-THAN-2))
 (224 224 (:REWRITE DEFAULT-LESS-THAN-1))
 (224 224 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (224 224 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (224 224 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (224 224 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (224 224 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (224 224 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (224 224 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (224 224 (:REWRITE |(< (/ x) (/ y))|))
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 (121 121 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (102 34 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (102 34 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (102 34 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (91 91 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (90 90 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (90 90 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (90 90 (:REWRITE |(< 0 (/ x))|))
 (90 90 (:REWRITE |(< 0 (* x y))|))
 (87 48 (:REWRITE INTEGERP-/))
 (85 31 (:REWRITE REDUCE-RATIONALP-*))
 (84 21 (:REWRITE |(integerp (- x))|))
 (69 69 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (45 45 (:REWRITE DEFAULT-MINUS))
 (34 34 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (34 34 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (34 34 (:REWRITE |(equal c (/ x))|))
 (34 34 (:REWRITE |(equal c (- x))|))
 (34 34 (:REWRITE |(equal (/ x) c)|))
 (34 34 (:REWRITE |(equal (/ x) (/ y))|))
 (34 34 (:REWRITE |(equal (- x) c)|))
 (34 34 (:REWRITE |(equal (- x) (- y))|))
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 (32 32 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (32 32 (:REWRITE |(floor x (- y))| . 2))
 (32 32 (:REWRITE |(floor x (- y))| . 1))
 (32 32 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (32 32 (:REWRITE |(floor (- x) y)| . 2))
 (32 32 (:REWRITE |(floor (- x) y)| . 1))
 (31 31 (:REWRITE REDUCE-RATIONALP-+))
 (31 31 (:REWRITE RATIONALP-MINUS-X))
 (31 31 (:META META-RATIONALP-CORRECT))
 (30 30 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (28 2 (:REWRITE |(* (if a b c) x)|))
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 (24 2 (:DEFINITION RFIX))
 (18 18 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 (18 1 (:REWRITE |(equal (floor (+ x y) z) x)|))
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 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 12 (:REWRITE NORMALIZE-ADDENDS))
 (11 11 (:TYPE-PRESCRIPTION UGLY-UNHIDE-HACK))
 (11 11 (:REWRITE |(equal (* x y) 0)|))
 (9 1 (:REWRITE RATIONALP-/))
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 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(* 2 (floor x y))| . 3))
 (1 1 (:REWRITE |(* 2 (floor x y))| . 2))
 )
(EXTRA-INTP-THM-1
 (8 8 (:REWRITE DEFAULT-TIMES-2))
 (8 8 (:REWRITE DEFAULT-TIMES-1))
 (5 5 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (4 4 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(* c (* d x))|))
 )
(EXTRA-INTP-THM-3
 (70 5 (:META META-INTEGERP-CORRECT))
 (63 2 (:REWRITE INTEGERP-/))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (27 27 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (11 11 (:REWRITE DEFAULT-TIMES-2))
 (11 11 (:REWRITE DEFAULT-TIMES-1))
 (9 1 (:REWRITE DEFAULT-FLOOR-RATIO))
 (7 7 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (6 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE DEFAULT-DIVIDE))
 (6 6 (:REWRITE |(equal c (/ x))|))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (/ x) c)|))
 (6 6 (:REWRITE |(equal (/ x) (/ y))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (4 1 (:REWRITE RATIONALP-X))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE |(* c (* d x))|))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE DEFAULT-FLOOR-2))
 (1 1 (:REWRITE DEFAULT-FLOOR-1))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(|(floor (+ x r) i)|
 (3702 3 (:REWRITE FLOOR-=-X/Y . 4))
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 (524 218 (:REWRITE DEFAULT-PLUS-1))
 (459 27 (:REWRITE CANCEL-FLOOR-+))
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 (388 44 (:REWRITE |(* (- x) y)|))
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 (385 385 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
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 (293 293 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (293 293 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (293 293 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (293 293 (:REWRITE INTEGERP-<-CONSTANT))
 (293 293 (:REWRITE DEFAULT-LESS-THAN-2))
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 (293 293 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (215 43 (:REWRITE |(integerp (- x))|))
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 (189 189 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (189 189 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (152 152 (:REWRITE EXTRA-INTP-THM-1))
 (132 8 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
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 (129 129 (:REWRITE |(< (/ x) 0)|))
 (129 129 (:REWRITE |(< (* x y) 0)|))
 (127 127 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (127 127 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (107 67 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (107 67 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (104 8 (:LINEAR MOD-BOUNDS-3))
 (96 28 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (92 92 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (90 90 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (87 19 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (74 74 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (74 74 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (74 74 (:REWRITE |(< 0 (/ x))|))
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 (43 43 (:REWRITE |(- (* c x))|))
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 (28 28 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (28 28 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (28 28 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (28 28 (:REWRITE |(equal c (/ x))|))
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 (27 27 (:REWRITE |(floor x (- y))| . 2))
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 (19 19 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (19 19 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (19 19 (:REWRITE MOD-CANCEL-*-CONST))
 (19 19 (:REWRITE |(mod x (- y))| . 3))
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 (19 19 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (19 19 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (16 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 16 (:LINEAR MOD-BOUNDS-2))
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 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
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 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:REWRITE |(+ c (+ d x))|))
 (5 5 (:REWRITE |(floor (+ x y) z) where (< 0 z)| . 3))
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 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (2 2 (:REWRITE |(equal (floor (+ x y) z) x)|))
 (1 1 (:REWRITE |(* x (- y))|))
 )
(MOD-X-I*J
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 (915 813 (:REWRITE DEFAULT-TIMES-2))
 (813 813 (:REWRITE DEFAULT-TIMES-1))
 (718 6 (:REWRITE FLOOR-ZERO . 3))
 (648 648 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (648 648 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (648 648 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (648 648 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (648 648 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (647 647 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (639 253 (:META META-INTEGERP-CORRECT))
 (509 113 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (449 17 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (449 17 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (444 378 (:REWRITE DEFAULT-PLUS-2))
 (430 430 (:REWRITE DEFAULT-LESS-THAN-2))
 (430 430 (:REWRITE DEFAULT-LESS-THAN-1))
 (426 426 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (426 426 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (426 426 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (426 426 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (426 426 (:REWRITE INTEGERP-<-CONSTANT))
 (426 426 (:REWRITE CONSTANT-<-INTEGERP))
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 (426 426 (:REWRITE |(< (- x) (- y))|))
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 (426 17 (:REWRITE MOD-X-Y-=-X+Y . 2))
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 (398 18 (:REWRITE DEFAULT-MOD-RATIO))
 (379 379 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
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 (313 93 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (286 286 (:REWRITE DEFAULT-DIVIDE))
 (281 16 (:REWRITE MOD-X-Y-=-X . 4))
 (281 16 (:REWRITE MOD-X-Y-=-X . 3))
 (255 255 (:REWRITE INTEGERP-MINUS-X))
 (237 237 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (204 204 (:REWRITE |(< 0 (/ x))|))
 (204 204 (:REWRITE |(< 0 (* x y))|))
 (203 203 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (203 203 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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 (188 16 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (180 180 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
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 (176 6 (:REWRITE FLOOR-X-Y-=--1 . 3))
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 (162 6 (:REWRITE EXTRA-INTP-THM-3))
 (144 17 (:REWRITE MOD-ZERO . 4))
 (138 28 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (137 122 (:REWRITE |(equal (/ x) c)|))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (128 128 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (124 4 (:REWRITE |(< x (if a b c))|))
 (122 122 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (122 122 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (122 122 (:REWRITE |(equal c (/ x))|))
 (122 122 (:REWRITE |(equal (/ x) (/ y))|))
 (122 122 (:REWRITE |(equal (- x) (- y))|))
 (121 121 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (121 121 (:REWRITE |(equal c (- x))|))
 (121 121 (:REWRITE |(equal (- x) c)|))
 (115 115 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (114 6 (:REWRITE CANCEL-FLOOR-+))
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 (100 100 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
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 (78 6 (:REWRITE FLOOR-=-X/Y . 3))
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 (66 66 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (66 66 (:REWRITE |(* c (* d x))|))
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 (12 12 (:REWRITE |(+ c (+ d x))|))
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 (11 11 (:REWRITE |(< x (+ c/d y))|))
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 (6 6 (:REWRITE |arith (* c (* d x))|))
 (6 6 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
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 (6 6 (:REWRITE DEFAULT-FLOOR-1))
 (6 6 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (6 6 (:REWRITE |(floor x (- y))| . 2))
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 (1 1 (:REWRITE |(equal x (/ y))|))
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 )
(MOD-X-I*J-V2
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 (3932 132 (:LINEAR MOD-BOUNDS-2))
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 (1046 452 (:REWRITE DEFAULT-PLUS-2))
 (950 848 (:REWRITE DEFAULT-TIMES-2))
 (922 157 (:META META-INTEGERP-CORRECT))
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 (757 757 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
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 (757 757 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (757 757 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
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 (475 475 (:REWRITE DEFAULT-LESS-THAN-2))
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 (471 471 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (471 471 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (471 471 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (471 471 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (471 471 (:REWRITE INTEGERP-<-CONSTANT))
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 (74 74 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (66 66 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (56 56 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (56 56 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (54 6 (:REWRITE DEFAULT-FLOOR-RATIO))
 (51 51 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (44 11 (:REWRITE RATIONALP-X))
 (40 8 (:REWRITE |(+ x x)|))
 (33 33 (:REWRITE DEFAULT-MINUS))
 (30 30 (:REWRITE |(equal (+ (- c) x) y)|))
 (30 6 (:REWRITE |(integerp (- x))|))
 (26 26 (:REWRITE |(- (* c x))|))
 (24 24 (:REWRITE |(equal (* x y) 0)|))
 (24 24 (:REWRITE |(+ c (+ d x))|))
 (16 16 (:REWRITE DEFAULT-MOD-2))
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 (14 14 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
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 (14 14 (:REWRITE MOD-CANCEL-*-CONST))
 (14 14 (:REWRITE |(mod x (- y))| . 3))
 (14 14 (:REWRITE |(mod x (- y))| . 2))
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 (14 14 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
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 (12 12 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (12 12 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (11 11 (:REWRITE REDUCE-RATIONALP-+))
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 (11 11 (:META META-RATIONALP-CORRECT))
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 (6 6 (:REWRITE |arith (- (* c x))|))
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 (6 6 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (6 6 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
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 (6 6 (:REWRITE EXTRA-INTP-THM-3))
 (6 6 (:REWRITE DEFAULT-FLOOR-2))
 (6 6 (:REWRITE DEFAULT-FLOOR-1))
 (6 6 (:REWRITE |(floor x (- y))| . 2))
 (6 6 (:REWRITE |(floor x (- y))| . 1))
 (6 6 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (6 6 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
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 (6 6 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (4 4 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE |arith (* (- x) y)|))
 (2 2 (:REWRITE |(* x (- y))|))
 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(/ (/ x))|))
 )
(MOD-X-I*J-X-2
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 (38335 195 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (21364 20 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (19718 406 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (9016 98 (:REWRITE FLOOR-ZERO . 3))
 (8440 669 (:REWRITE DEFAULT-PLUS-2))
 (7508 672 (:REWRITE |(* y (* x z))|))
 (5821 4105 (:REWRITE DEFAULT-TIMES-2))
 (5716 1582 (:META META-INTEGERP-CORRECT))
 (5142 600 (:REWRITE |(< (/ x) 0)|))
 (4678 98 (:REWRITE CANCEL-FLOOR-+))
 (4139 4105 (:REWRITE DEFAULT-TIMES-1))
 (3235 669 (:REWRITE DEFAULT-PLUS-1))
 (3156 98 (:REWRITE FLOOR-=-X/Y . 2))
 (3092 98 (:REWRITE FLOOR-=-X/Y . 3))
 (2981 266 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2634 98 (:REWRITE FLOOR-X-Y-=-1 . 3))
 (2634 98 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (2634 98 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (2634 98 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (2586 98 (:REWRITE FLOOR-ZERO . 5))
 (2586 98 (:REWRITE FLOOR-ZERO . 4))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
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 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (2540 2540 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
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 (2448 128 (:LINEAR MOD-BOUNDS-2))
 (2448 128 (:LINEAR MOD-BOUNDS-1))
 (2434 2434 (:REWRITE DEFAULT-DIVIDE))
 (2214 89 (:REWRITE |(integerp (- x))|))
 (2072 184 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<-2))
 (2008 2008 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1974 98 (:REWRITE DEFAULT-FLOOR-RATIO))
 (1934 756 (:REWRITE INTEGERP-/))
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 (1582 1582 (:REWRITE INTEGERP-MINUS-X))
 (1498 1498 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (1440 110 (:REWRITE |(* (- x) y)|))
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 (1379 1379 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1379 1379 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
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 (1379 1379 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1379 1379 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1379 1379 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
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 (1093 1076 (:REWRITE DEFAULT-LESS-THAN-1))
 (1064 1064 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1064 1064 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1064 1064 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1064 1064 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1064 1064 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1064 1064 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
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 (1064 1064 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (1064 1064 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1064 1064 (:REWRITE |(< (/ x) (/ y))|))
 (1064 1064 (:REWRITE |(< (- x) (- y))|))
 (1016 982 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (994 994 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (994 994 (:REWRITE INTEGERP-<-CONSTANT))
 (994 994 (:REWRITE CONSTANT-<-INTEGERP))
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 (994 994 (:REWRITE |(< (- x) c)|))
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 (981 9 (:REWRITE FLOOR-=-X/Y . 4))
 (910 25 (:REWRITE MOD-ZERO . 4))
 (895 19 (:REWRITE MOD-X-Y-=-X . 4))
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 (810 810 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (768 768 (:REWRITE |(* c (* d x))|))
 (755 398 (:REWRITE |(equal (- x) (- y))|))
 (724 25 (:REWRITE MOD-X-Y-=-X-Y . 3))
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 (724 25 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (600 600 (:REWRITE |(< (* x y) 0)|))
 (518 518 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (518 518 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (472 25 (:REWRITE DEFAULT-MOD-RATIO))
 (466 98 (:REWRITE FLOOR-ZERO . 2))
 (458 386 (:REWRITE |(equal (- x) c)|))
 (456 456 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (456 456 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (456 456 (:REWRITE |(< 0 (/ x))|))
 (456 456 (:REWRITE |(< 0 (* x y))|))
 (418 406 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (417 89 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (408 14 (:REWRITE MOD-X-I*J))
 (398 398 (:REWRITE |(equal c (/ x))|))
 (398 398 (:REWRITE |(equal (/ x) (/ y))|))
 (396 396 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (386 386 (:REWRITE |(equal c (- x))|))
 (384 12 (:REWRITE |(< x (if a b c))|))
 (382 382 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (371 75 (:REWRITE |(+ c (+ d x))|))
 (368 368 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (340 340 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (340 116 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (340 116 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (313 19 (:REWRITE MOD-X-Y-=-X . 2))
 (313 19 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (313 19 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (296 19 (:REWRITE CANCEL-MOD-+))
 (276 8 (:REWRITE |(equal x (/ y))|))
 (244 244 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (194 194 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (192 10 (:REWRITE EXTRA-INTP-THM-3))
 (188 4 (:REWRITE |(equal x (- (/ y)))|))
 (185 117 (:REWRITE DEFAULT-MINUS))
 (177 177 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (172 172 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (172 172 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (160 160 (:REWRITE |(/ (/ x))|))
 (131 115 (:REWRITE |(- (* c x))|))
 (128 16 (:REWRITE |(* a (/ a))|))
 (100 100 (:REWRITE |(equal (+ (- c) x) y)|))
 (98 98 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (98 98 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (98 98 (:REWRITE FLOOR-CANCEL-*-CONST))
 (98 98 (:REWRITE DEFAULT-FLOOR-2))
 (98 98 (:REWRITE DEFAULT-FLOOR-1))
 (98 98 (:REWRITE |(floor x (- y))| . 2))
 (98 98 (:REWRITE |(floor x (- y))| . 1))
 (98 98 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (98 98 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (98 98 (:REWRITE |(floor (- x) y)| . 2))
 (98 98 (:REWRITE |(floor (- x) y)| . 1))
 (98 98 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (98 98 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (82 82 (:REWRITE |(equal (* x y) 0)|))
 (76 76 (:REWRITE |arith (* c (* d x))|))
 (60 15 (:REWRITE RATIONALP-X))
 (56 4 (:REWRITE |(equal (* (/ x) y) -1)|))
 (42 25 (:REWRITE DEFAULT-MOD-1))
 (36 19 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
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 (30 30 (:REWRITE FOLD-CONSTS-IN-+))
 (30 6 (:REWRITE |(+ x x)|))
 (25 25 (:REWRITE DEFAULT-MOD-2))
 (20 20 (:REWRITE ARITH-NORMALIZE-ADDENDS))
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 (20 20 (:REWRITE |(* 1 x)|))
 (19 19 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (18 18 (:REWRITE |(mod x (- y))| . 3))
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 (15 15 (:META META-RATIONALP-CORRECT))
 (12 12 (:TYPE-PRESCRIPTION ABS))
 (9 9 (:REWRITE |(equal (floor (+ x y) z) x)|))
 (9 1 (:REWRITE MOD-ZERO . 1))
 (8 8 (:REWRITE |(< (* (/ x) y) 1) with (< x 0)|))
 (8 8 (:REWRITE |(< (* (/ x) y) 1) with (< 0 x)|))
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 (1 1 (:REWRITE FLOOR-POSITIVE . 4))
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 (1 1 (:REWRITE |(mod (floor x y) z)| . 3))
 (1 1 (:REWRITE |(mod (floor x y) z)| . 2))
 )
(MOD-X+I*K-I*J
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 (2066 73 (:REWRITE MOD-X-Y-=-X . 4))
 (2001 1711 (:REWRITE DEFAULT-TIMES-2))
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 (1711 1711 (:REWRITE DEFAULT-TIMES-1))
 (1591 73 (:REWRITE MOD-X-Y-=-X+Y . 2))
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 (1222 73 (:REWRITE DEFAULT-MOD-RATIO))
 (1146 286 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1048 79 (:REWRITE |(* (- x) y)|))
 (1007 73 (:REWRITE MOD-ZERO . 4))
 (916 326 (:REWRITE DEFAULT-PLUS-2))
 (780 5 (:REWRITE CANCEL-FLOOR-+))
 (683 683 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (683 683 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
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 (683 683 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (683 683 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (683 683 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (683 683 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (683 683 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (665 25 (:REWRITE FLOOR-=-X/Y . 3))
 (644 644 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (536 67 (:REWRITE |(/ (* x y))|))
 (521 401 (:REWRITE DEFAULT-LESS-THAN-1))
 (510 510 (:REWRITE DEFAULT-DIVIDE))
 (485 68 (:REWRITE |(integerp (- x))|))
 (473 326 (:REWRITE DEFAULT-PLUS-1))
 (427 427 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (415 25 (:REWRITE DEFAULT-FLOOR-RATIO))
 (402 262 (:META META-INTEGERP-CORRECT))
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 (401 401 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (401 401 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (401 401 (:REWRITE DEFAULT-LESS-THAN-2))
 (386 386 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (386 386 (:REWRITE INTEGERP-<-CONSTANT))
 (386 386 (:REWRITE CONSTANT-<-INTEGERP))
 (386 386 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (139 139 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (135 95 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (131 131 (:REWRITE |(< 0 (* x y))|))
 (130 10 (:REWRITE INTEGERP-/))
 (122 122 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (119 119 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (116 116 (:REWRITE |(< 0 (/ x))|))
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 (91 91 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (91 91 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (91 91 (:REWRITE |(equal c (/ x))|))
 (91 91 (:REWRITE |(equal (/ x) (/ y))|))
 (91 91 (:REWRITE |(equal (- x) (- y))|))
 (91 91 (:REWRITE |(* c (* d x))|))
 (90 90 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (90 90 (:REWRITE DEFAULT-MINUS))
 (90 90 (:REWRITE |(equal c (- x))|))
 (90 90 (:REWRITE |(equal (- x) c)|))
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 (58 58 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (58 58 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (43 43 (:REWRITE |(mod x (- y))| . 3))
 (43 43 (:REWRITE |(mod x (- y))| . 2))
 (43 43 (:REWRITE |(mod x (- y))| . 1))
 (43 43 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
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 (43 43 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (43 43 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (39 39 (:REWRITE |arith (* c (* d x))|))
 (38 38 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
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 (35 35 (:REWRITE MOD-X-I*J-V2))
 (30 30 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
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 (23 23 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (23 23 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (23 23 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (23 23 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (23 23 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (20 5 (:REWRITE |(floor (+ x r) i)|))
 (19 19 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (18 18 (:REWRITE |(+ c (+ d x))|))
 (15 15 (:REWRITE |(equal (* x y) 0)|))
 (15 15 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (15 15 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (15 15 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (15 15 (:REWRITE |(< x (/ y)) with (< 0 y)|))
 (15 15 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (14 14 (:REWRITE REDUCE-RATIONALP-+))
 (14 14 (:REWRITE REDUCE-RATIONALP-*))
 (14 14 (:REWRITE RATIONALP-MINUS-X))
 (14 14 (:META META-RATIONALP-CORRECT))
 (13 13 (:REWRITE |(< y (+ (- c) x))|))
 (13 13 (:REWRITE |(< x (+ c/d y))|))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 10 (:REWRITE |arith (- (* c x))|))
 (10 10 (:REWRITE |arith (* (- x) y)|))
 (10 10 (:REWRITE FLOOR-X-Y-=-1 . 3))
 (10 10 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (9 9 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (6 6 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
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 (5 5 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 3))
 (5 5 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 2))
 (5 5 (:REWRITE |(- (- x))|))
 (4 1 (:REWRITE |(+ x x)|))
 (3 3 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (2 2 (:REWRITE |(equal (mod (+ x y) z) x)|))
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 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(* x (- y))|))
 )
(FLOOR-X+I*K-I*J
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 (2781 56 (:REWRITE FLOOR-ZERO . 3))
 (2498 2388 (:REWRITE DEFAULT-TIMES-2))
 (2399 56 (:REWRITE CANCEL-FLOOR-+))
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 (1896 56 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (1876 61 (:REWRITE FLOOR-=-X/Y . 3))
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 (1616 56 (:REWRITE FLOOR-ZERO . 5))
 (1506 56 (:REWRITE FLOOR-ZERO . 4))
 (1505 541 (:META META-INTEGERP-CORRECT))
 (1352 61 (:REWRITE DEFAULT-FLOOR-RATIO))
 (1291 300 (:REWRITE DEFAULT-PLUS-2))
 (1203 353 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1143 78 (:REWRITE |(* (- x) y)|))
 (1091 1091 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (967 56 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (952 77 (:REWRITE |(integerp (- x))|))
 (928 928 (:REWRITE DEFAULT-DIVIDE))
 (892 300 (:REWRITE DEFAULT-PLUS-1))
 (680 680 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (668 21 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (622 21 (:REWRITE MOD-X-Y-=-X . 4))
 (589 479 (:REWRITE DEFAULT-LESS-THAN-1))
 (543 543 (:REWRITE INTEGERP-MINUS-X))
 (526 166 (:REWRITE INTEGERP-/))
 (479 479 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (479 479 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (479 479 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (479 479 (:REWRITE DEFAULT-LESS-THAN-2))
 (466 21 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (464 464 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (464 464 (:REWRITE INTEGERP-<-CONSTANT))
 (464 464 (:REWRITE CONSTANT-<-INTEGERP))
 (464 464 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (464 464 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
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 (464 464 (:REWRITE |(< (/ x) (/ y))|))
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 (464 464 (:REWRITE |(< (- x) (- y))|))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 4))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (441 441 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (441 441 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (441 441 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (441 441 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (441 441 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (412 12 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
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 (404 16 (:REWRITE CANCEL-MOD-+))
 (373 21 (:REWRITE MOD-ZERO . 3))
 (364 364 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (364 364 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
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 (364 364 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (364 364 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (359 359 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (359 359 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (359 359 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (359 359 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (359 359 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (359 359 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (303 21 (:REWRITE MOD-ZERO . 4))
 (295 295 (:REWRITE |(* c (* d x))|))
 (289 21 (:REWRITE DEFAULT-MOD-RATIO))
 (286 60 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (280 54 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (231 231 (:REWRITE EXTRA-INTP-THM-1))
 (224 224 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (170 105 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (160 160 (:REWRITE |(< (/ x) 0)|))
 (160 160 (:REWRITE |(< (* x y) 0)|))
 (157 157 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (157 157 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (145 105 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (141 141 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (136 136 (:REWRITE |(< 0 (* x y))|))
 (121 121 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (121 121 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (121 121 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (121 121 (:REWRITE |(< 0 (/ x))|))
 (107 62 (:REWRITE |(equal (/ x) c)|))
 (85 17 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (78 78 (:REWRITE DEFAULT-MINUS))
 (77 77 (:REWRITE |(- (* c x))|))
 (72 18 (:REWRITE RATIONALP-X))
 (62 62 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (62 62 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (62 62 (:REWRITE |(equal c (/ x))|))
 (62 62 (:REWRITE |(equal (/ x) (/ y))|))
 (62 62 (:REWRITE |(equal (- x) (- y))|))
 (61 61 (:REWRITE DEFAULT-FLOOR-2))
 (61 61 (:REWRITE DEFAULT-FLOOR-1))
 (60 60 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (60 60 (:REWRITE |(equal c (- x))|))
 (60 60 (:REWRITE |(equal (- x) c)|))
 (58 58 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (56 56 (:REWRITE FLOOR-ZERO . 2))
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 (46 46 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (46 46 (:REWRITE |(floor x (- y))| . 2))
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 (20 5 (:REWRITE |(floor (+ x r) i)|))
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 (16 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
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 (15 15 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
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 (9 9 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:REWRITE |(< y (+ (- c) x))|))
 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (8 8 (:LINEAR MOD-BOUNDS-2))
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 (6 6 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
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 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(* x (- y))|))
 )
(FLOOR-EQUAL-I-OVER-J-REWRITE
 (462 6 (:REWRITE FLOOR-ZERO . 3))
 (268 20 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<-2))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (213 213 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (178 6 (:REWRITE FLOOR-ZERO . 5))
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 (175 73 (:REWRITE DEFAULT-TIMES-2))
 (172 6 (:REWRITE FLOOR-X-Y-=-1 . 3))
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 (172 6 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (172 6 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (115 13 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (115 13 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (77 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (74 6 (:REWRITE CANCEL-FLOOR-+))
 (73 73 (:REWRITE DEFAULT-TIMES-1))
 (48 48 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (48 48 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (48 48 (:REWRITE DEFAULT-LESS-THAN-2))
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 (39 6 (:REWRITE FLOOR-=-X/Y . 2))
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 (27 27 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (26 26 (:REWRITE |(< (/ x) 0)|))
 (26 26 (:REWRITE |(< (* x y) 0)|))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (22 22 (:REWRITE |(< 0 (/ x))|))
 (22 22 (:REWRITE |(< 0 (* x y))|))
 (20 20 (:REWRITE REDUCE-INTEGERP-+))
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 (13 13 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (13 13 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (13 13 (:REWRITE |(equal c (/ x))|))
 (13 13 (:REWRITE |(equal c (- x))|))
 (13 13 (:REWRITE |(equal (/ x) c)|))
 (13 13 (:REWRITE |(equal (/ x) (/ y))|))
 (13 13 (:REWRITE |(equal (- x) c)|))
 (13 13 (:REWRITE |(equal (- x) (- y))|))
 (12 12 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:META META-RATIONALP-CORRECT))
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 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (7 7 (:REWRITE DEFAULT-FLOOR-2))
 (7 7 (:REWRITE DEFAULT-FLOOR-1))
 (6 6 (:REWRITE FLOOR-ZERO . 2))
 (6 6 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
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 (6 6 (:REWRITE FLOOR-CANCEL-*-CONST))
 (6 6 (:REWRITE DEFAULT-MINUS))
 (6 6 (:REWRITE |(floor x (- y))| . 2))
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 (6 6 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 (6 6 (:REWRITE |(- (* c x))|))
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 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (2 2 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 )
(MOD-PLUS-MOD-N
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 (2373 2373 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2373 2373 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
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 (1749 866 (:REWRITE DEFAULT-PLUS-2))
 (1669 1669 (:REWRITE DEFAULT-TIMES-2))
 (1669 1669 (:REWRITE DEFAULT-TIMES-1))
 (1512 177 (:REWRITE DEFAULT-MOD-RATIO))
 (1328 866 (:REWRITE DEFAULT-PLUS-1))
 (1284 1274 (:REWRITE DEFAULT-LESS-THAN-2))
 (1284 1274 (:REWRITE DEFAULT-LESS-THAN-1))
 (1274 1274 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1274 1274 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1274 1274 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1274 1274 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1274 1274 (:REWRITE INTEGERP-<-CONSTANT))
 (1274 1274 (:REWRITE CONSTANT-<-INTEGERP))
 (1274 1274 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1274 1274 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (1034 1014 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (823 823 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
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 (572 562 (:META META-INTEGERP-CORRECT))
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 (552 552 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (552 552 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (552 552 (:REWRITE |(< 0 (/ x))|))
 (552 552 (:REWRITE |(< 0 (* x y))|))
 (550 169 (:REWRITE MOD-X-Y-=-X . 2))
 (550 169 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (550 169 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (546 546 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (546 546 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (546 546 (:REWRITE |(< (/ x) 0)|))
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 (317 317 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (315 315 (:REWRITE INTEGERP-MINUS-X))
 (302 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (285 25 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (285 25 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (278 25 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (278 25 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (165 165 (:REWRITE DEFAULT-DIVIDE))
 (164 164 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (160 160 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (160 160 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (160 160 (:REWRITE |(< 0 (/ x))|))
 (160 160 (:REWRITE |(< 0 (* x y))|))
 (156 24 (:REWRITE MOD-X-Y-=-X . 2))
 (156 24 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (156 24 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (153 153 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (153 153 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (153 153 (:REWRITE |(< (/ x) 0)|))
 (153 153 (:REWRITE |(< (* x y) 0)|))
 (138 84 (:REWRITE INTEGERP-/))
 (128 84 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (109 109 (:REWRITE |(* c (* d x))|))
 (102 36 (:REWRITE DEFAULT-MINUS))
 (96 96 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (92 26 (:REWRITE DEFAULT-MOD-1))
 (89 89 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (88 22 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (88 22 (:REWRITE MOD-CANCEL-*-CONST))
 (88 22 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (88 22 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (84 18 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (72 57 (:REWRITE |(equal (/ x) c)|))
 (66 66 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (64 16 (:REWRITE RATIONALP-X))
 (57 57 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (57 57 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (57 57 (:REWRITE |(equal c (/ x))|))
 (57 57 (:REWRITE |(equal (/ x) (/ y))|))
 (57 57 (:REWRITE |(equal (- x) (- y))|))
 (56 56 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (56 56 (:REWRITE |(equal c (- x))|))
 (56 56 (:REWRITE |(equal (- x) c)|))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (28 28 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (28 28 (:REWRITE |(- (* c x))|))
 (27 27 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (26 26 (:REWRITE DEFAULT-MOD-2))
 (22 22 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (22 22 (:REWRITE |(mod x (- y))| . 3))
 (22 22 (:REWRITE |(mod x (- y))| . 2))
 (22 22 (:REWRITE |(mod x (- y))| . 1))
 (22 22 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (22 22 (:REWRITE |(mod (- x) y)| . 3))
 (22 22 (:REWRITE |(mod (- x) y)| . 2))
 (22 22 (:REWRITE |(mod (- x) y)| . 1))
 (22 22 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(equal (+ (- c) x) y)|))
 (16 16 (:REWRITE REDUCE-RATIONALP-+))
 (16 16 (:REWRITE REDUCE-RATIONALP-*))
 (16 16 (:REWRITE RATIONALP-MINUS-X))
 (16 16 (:META META-RATIONALP-CORRECT))
 (15 15 (:REWRITE |(equal (* x y) 0)|))
 (15 15 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (15 15 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (14 14 (:REWRITE |(< (+ c/d x) y)|))
 (14 14 (:REWRITE |(< (+ (- c) x) y)|))
 (13 13 (:REWRITE |(+ c (+ d x))|))
 (11 11 (:REWRITE |(< y (+ (- c) x))|))
 (11 11 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (5 5 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (3 3 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (2 2 (:REWRITE EXTRA-INTP-THM-1))
 (2 2 (:REWRITE |(* x (- y))|))
 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(/ (/ x))|))
 )
(IND-FN)
(MOD-THEOREM-TWO-HELPER-HELPER
 (8400 8400 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (5544 830 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (5512 830 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (2310 1990 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (2214 1990 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (1438 1438 (:REWRITE |(- (* c x))|))
 (1420 1420 (:REWRITE DEFAULT-MOD-2))
 (1375 1375 (:REWRITE EXTRA-INTP-THM-1))
 (1270 1270 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (1270 1270 (:REWRITE |(mod x (- y))| . 3))
 (1270 1270 (:REWRITE |(mod x (- y))| . 2))
 (1270 1270 (:REWRITE |(mod x (- y))| . 1))
 (1270 1270 (:REWRITE |(mod (- x) y)| . 3))
 (1270 1270 (:REWRITE |(mod (- x) y)| . 2))
 (1249 1249 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (1249 1249 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (1191 1191 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1154 346 (:REWRITE MOD-ZERO . 2))
 (684 524 (:REWRITE DEFAULT-EXPT-1))
 (524 524 (:REWRITE DEFAULT-EXPT-2))
 (518 518 (:REWRITE |(expt 1/c n)|))
 (518 518 (:REWRITE |(expt (- x) n)|))
 (443 443 (:REWRITE ZP-OPEN))
 (352 176 (:REWRITE RATIONALP-X))
 (232 232 (:REWRITE |(+ c (+ d x))|))
 (176 176 (:REWRITE REDUCE-RATIONALP-+))
 (176 176 (:REWRITE REDUCE-RATIONALP-*))
 (176 176 (:REWRITE RATIONALP-MINUS-X))
 (176 176 (:META META-RATIONALP-CORRECT))
 (168 168 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (119 119 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (107 107 (:REWRITE |(equal (+ (- c) x) y)|))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-ZERO . 4))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (105 105 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (96 96 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (87 87 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (87 87 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (80 80 (:REWRITE |arith (expt x c)|))
 (80 80 (:REWRITE |arith (expt 1/c n)|))
 (78 78 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (73 73 (:REWRITE FOLD-CONSTS-IN-+))
 (63 63 (:REWRITE |(< (+ c/d x) y)|))
 (63 63 (:REWRITE |(< (+ (- c) x) y)|))
 (52 52 (:REWRITE |(< y (+ (- c) x))|))
 (52 52 (:REWRITE |(< x (+ c/d y))|))
 (52 6 (:REWRITE NOT-INTEGERP-/-1))
 (41 41 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 3))
 (41 41 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 2))
 (39 39 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (39 39 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (39 39 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (29 6 (:REWRITE NOT-INTEGERP-/-2))
 (15 15 (:REWRITE |arith (* c (* d x))|))
 (12 12 (:REWRITE MOD-POSITIVE . 3))
 (12 12 (:REWRITE MOD-POSITIVE . 2))
 (12 12 (:REWRITE MOD-NEGATIVE . 3))
 (12 12 (:REWRITE MOD-NEGATIVE . 2))
 (8 8 (:REWRITE |(not (equal x (/ y)))|))
 (8 8 (:REWRITE |(equal x (/ y))|))
 (4 4 (:REWRITE |arith (- (* c x))|))
 (3 3 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (3 3 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (3 3 (:REWRITE |(< x (/ y)) with (< y 0)|))
 )
(MOD-THEOREM-TWO-HELPER
 (980 6 (:REWRITE MOD-ZERO . 4))
 (838 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (758 6 (:REWRITE CANCEL-MOD-+))
 (708 6 (:REWRITE MOD-X-Y-=-X . 4))
 (708 6 (:REWRITE MOD-X-Y-=-X . 3))
 (672 18 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (475 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (449 449 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (441 441 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (441 441 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (441 441 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (441 441 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (441 441 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (441 441 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (441 441 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (441 441 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (414 57 (:REWRITE DEFAULT-TIMES-1))
 (397 8 (:LINEAR MOD-BOUNDS-3))
 (391 57 (:REWRITE DEFAULT-TIMES-2))
 (370 16 (:LINEAR MOD-BOUNDS-2))
 (370 16 (:LINEAR MOD-BOUNDS-1))
 (313 6 (:REWRITE MOD-ZERO . 3))
 (292 2 (:REWRITE |(equal (expt x n) 0)|))
 (266 2 (:REWRITE |(expt x (+ m n)) non-zero x|))
 (261 6 (:REWRITE DEFAULT-MOD-RATIO))
 (261 6 (:REWRITE |(* (- x) y)|))
 (255 6 (:REWRITE |(integerp (- x))|))
 (254 18 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (205 5 (:REWRITE |(* (* x y) z)|))
 (168 17 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (120 34 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (120 34 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (112 6 (:REWRITE MOD-X-Y-=-X . 2))
 (112 6 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (112 6 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (102 19 (:META META-INTEGERP-CORRECT))
 (96 10 (:REWRITE DEFAULT-PLUS-2))
 (77 34 (:REWRITE DEFAULT-LESS-THAN-2))
 (77 34 (:REWRITE DEFAULT-LESS-THAN-1))
 (70 6 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (70 6 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (70 6 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (70 6 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (62 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (61 9 (:REWRITE DEFAULT-EXPT-1))
 (60 8 (:LINEAR EXPT-X->=-X))
 (60 8 (:LINEAR EXPT-X->-X))
 (60 8 (:LINEAR EXPT->=-1-TWO))
 (60 8 (:LINEAR EXPT->=-1-ONE))
 (60 8 (:LINEAR EXPT->-1-TWO))
 (60 8 (:LINEAR EXPT->-1-ONE))
 (60 8 (:LINEAR EXPT-<=-1-TWO))
 (60 8 (:LINEAR EXPT-<=-1-ONE))
 (60 8 (:LINEAR EXPT-<-1-TWO))
 (60 8 (:LINEAR EXPT-<-1-ONE))
 (60 7 (:REWRITE DEFAULT-MINUS))
 (59 6 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (59 6 (:REWRITE DEFAULT-MOD-1))
 (59 6 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (59 6 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (51 3 (:REWRITE INTEGERP-/))
 (49 6 (:REWRITE MOD-CANCEL-*-CONST))
 (45 6 (:REWRITE NORMALIZE-ADDENDS))
 (34 34 (:REWRITE SIMPLIFY-SUMS-<))
 (34 34 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (34 34 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (34 34 (:REWRITE INTEGERP-<-CONSTANT))
 (34 34 (:REWRITE CONSTANT-<-INTEGERP))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (34 34 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< c (- x))|))
 (34 34 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (34 34 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (34 34 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) (/ y))|))
 (34 34 (:REWRITE |(< (- x) c)|))
 (34 34 (:REWRITE |(< (- x) (- y))|))
 (31 31 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (31 10 (:REWRITE DEFAULT-PLUS-1))
 (30 2 (:REWRITE |(+ y x)|))
 (28 28 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (25 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (22 22 (:REWRITE DEFAULT-DIVIDE))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (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))|))
 (19 19 (:REWRITE REDUCE-INTEGERP-+))
 (19 19 (:REWRITE INTEGERP-MINUS-X))
 (18 18 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (17 17 (:REWRITE |(< 0 (/ x))|))
 (17 17 (:REWRITE |(< 0 (* x y))|))
 (17 17 (:REWRITE |(< (/ x) 0)|))
 (17 17 (:REWRITE |(< (* x y) 0)|))
 (16 16 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (16 16 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (16 16 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (16 16 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (11 3 (:REWRITE MOD-ZERO . 1))
 (11 1 (:REWRITE |(+ 0 x)|))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (10 10 (:REWRITE REMOVE-WEAK-INEQUALITIES))
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 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<))
 (7 7 (:REWRITE EXTRA-INTP-THM-1))
 (7 7 (:REWRITE |(expt 1/c n)|))
 (7 7 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (6 6 (:REWRITE DEFAULT-MOD-2))
 (6 6 (:REWRITE |(mod x (- y))| . 3))
 (6 6 (:REWRITE |(mod x (- y))| . 2))
 (6 6 (:REWRITE |(mod x (- y))| . 1))
 (6 6 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (6 6 (:REWRITE |(mod (- x) y)| . 3))
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 (6 6 (:REWRITE |(mod (- x) y)| . 1))
 (6 6 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (6 6 (:REWRITE |(- (* c x))|))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE |(* c (* d x))|))
 (3 3 (:REWRITE MOD-ZERO . 2))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(MOD-THEOREM-TWO
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 (4517 25 (:REWRITE MOD-ZERO . 4))
 (3328 54 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3049 25 (:REWRITE MOD-X-Y-=-X . 3))
 (2970 25 (:REWRITE MOD-X-Y-=-X . 4))
 (2716 19 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (2692 52 (:LINEAR MOD-BOUNDS-3))
 (2636 104 (:LINEAR MOD-BOUNDS-2))
 (2636 104 (:LINEAR MOD-BOUNDS-1))
 (2126 24 (:REWRITE CANCEL-MOD-+))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1432 1432 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1432 1432 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1394 10 (:REWRITE |(equal (expt x n) 0)|))
 (1338 1338 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1338 1338 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
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 (1338 1338 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1338 1338 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1338 1338 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1325 183 (:REWRITE DEFAULT-TIMES-1))
 (1225 62 (:REWRITE |(* y x)|))
 (1160 183 (:REWRITE DEFAULT-TIMES-2))
 (1121 25 (:REWRITE MOD-ZERO . 3))
 (775 54 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (717 25 (:REWRITE DEFAULT-MOD-RATIO))
 (689 24 (:REWRITE |(integerp (- x))|))
 (649 24 (:REWRITE |(* (- x) y)|))
 (548 192 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (529 50 (:REWRITE DEFAULT-PLUS-2))
 (504 51 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (449 192 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (381 25 (:REWRITE MOD-X-Y-=-X . 2))
 (381 25 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (371 193 (:REWRITE DEFAULT-LESS-THAN-2))
 (371 193 (:REWRITE DEFAULT-LESS-THAN-1))
 (300 40 (:LINEAR EXPT-X->=-X))
 (300 40 (:LINEAR EXPT-X->-X))
 (300 40 (:LINEAR EXPT->=-1-TWO))
 (300 40 (:LINEAR EXPT->=-1-ONE))
 (300 40 (:LINEAR EXPT->-1-TWO))
 (300 40 (:LINEAR EXPT->-1-ONE))
 (300 40 (:LINEAR EXPT-<=-1-TWO))
 (300 40 (:LINEAR EXPT-<=-1-ONE))
 (300 40 (:LINEAR EXPT-<-1-TWO))
 (300 40 (:LINEAR EXPT-<-1-ONE))
 (244 50 (:REWRITE DEFAULT-PLUS-1))
 (224 25 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (224 25 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (224 25 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (224 25 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (203 25 (:REWRITE DEFAULT-MOD-1))
 (193 193 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (193 193 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (193 193 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (193 193 (:REWRITE REDUCE-ADDITIVE-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|))
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 (193 193 (:REWRITE |(< (/ x) (/ y))|))
 (193 193 (:REWRITE |(< (- x) c)|))
 (193 193 (:REWRITE |(< (- x) (- y))|))
 (192 192 (:REWRITE SIMPLIFY-SUMS-<))
 (192 27 (:REWRITE DEFAULT-MINUS))
 (189 24 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (189 24 (:REWRITE MOD-CANCEL-*-CONST))
 (189 24 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (189 24 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (153 3 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (148 19 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (132 80 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (132 80 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (120 16 (:REWRITE DEFAULT-EXPT-1))
 (102 6 (:REWRITE INTEGERP-/))
 (101 101 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (101 101 (:REWRITE DEFAULT-DIVIDE))
 (100 66 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (95 95 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (95 95 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (95 95 (:REWRITE |(< 0 (/ x))|))
 (95 95 (:REWRITE |(< 0 (* x y))|))
 (94 94 (:REWRITE |(< (/ x) 0)|))
 (94 94 (:REWRITE |(< (* x y) 0)|))
 (93 93 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (93 93 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (89 89 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (80 80 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (80 80 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (76 76 (:REWRITE REDUCE-INTEGERP-+))
 (76 76 (:REWRITE INTEGERP-MINUS-X))
 (76 76 (:META META-INTEGERP-CORRECT))
 (66 66 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (64 64 (:REWRITE |(equal c (/ x))|))
 (64 64 (:REWRITE |(equal c (- x))|))
 (64 64 (:REWRITE |(equal (/ x) c)|))
 (64 64 (:REWRITE |(equal (/ x) (/ y))|))
 (64 64 (:REWRITE |(equal (- x) c)|))
 (64 64 (:REWRITE |(equal (- x) (- y))|))
 (54 54 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (51 51 (:REWRITE EXTRA-INTP-THM-1))
 (50 4 (:REWRITE |(mod (+ 1 x) y)|))
 (48 48 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (40 40 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (40 40 (:LINEAR EXPT-LINEAR-UPPER-<))
 (40 40 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (40 40 (:LINEAR EXPT-LINEAR-LOWER-<))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (25 25 (:REWRITE DEFAULT-MOD-2))
 (24 24 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (24 24 (:REWRITE |(mod x (- y))| . 3))
 (24 24 (:REWRITE |(mod x (- y))| . 2))
 (24 24 (:REWRITE |(mod x (- y))| . 1))
 (24 24 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (24 24 (:REWRITE |(mod (- x) y)| . 3))
 (24 24 (:REWRITE |(mod (- x) y)| . 2))
 (24 24 (:REWRITE |(mod (- x) y)| . 1))
 (24 24 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (20 20 (:REWRITE |(- (* c x))|))
 (17 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (16 16 (:REWRITE DEFAULT-EXPT-2))
 (16 16 (:REWRITE |(expt 1/c n)|))
 (16 16 (:REWRITE |(expt (- x) n)|))
 (10 10 (:REWRITE MOD-ZERO . 2))
 (10 10 (:REWRITE MOD-ZERO . 1))
 (9 9 (:REWRITE |(equal (+ (- c) x) y)|))
 (8 4 (:REWRITE |(* -1 x)|))
 (6 6 (:REWRITE |(* 1 x)|))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE MOD-POSITIVE . 3))
 (1 1 (:REWRITE MOD-POSITIVE . 2))
 (1 1 (:REWRITE MOD-POSITIVE . 1))
 (1 1 (:REWRITE MOD-NONPOSITIVE))
 (1 1 (:REWRITE MOD-NONNEGATIVE))
 (1 1 (:REWRITE MOD-NEGATIVE . 3))
 (1 1 (:REWRITE MOD-NEGATIVE . 2))
 (1 1 (:REWRITE MOD-NEGATIVE . 1))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(TWO-XXX
 (28096 6 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (20806 6 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (14886 83 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (14423 19 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (13118 80 (:REWRITE CANCEL-MOD-+))
 (11971 80 (:REWRITE MOD-X-Y-=-X . 3))
 (11277 1604 (:REWRITE DEFAULT-TIMES-2))
 (9843 9843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (9843 9843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (9843 9843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (9843 9843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (9843 9843 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (7976 80 (:REWRITE MOD-ZERO . 3))
 (5020 969 (:REWRITE DEFAULT-PLUS-2))
 (4965 83 (:REWRITE DEFAULT-MOD-RATIO))
 (4689 4689 (:TYPE-PRESCRIPTION INTEGERP-/-EXPT-1))
 (4415 1604 (:REWRITE DEFAULT-TIMES-1))
 (3775 36 (:LINEAR MOD-BOUNDS-3))
 (3371 338 (:REWRITE DEFAULT-DIVIDE))
 (3219 240 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3116 260 (:META META-INTEGERP-CORRECT))
 (2573 31 (:REWRITE |(integerp (expt x n))|))
 (2502 80 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (2502 80 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (2488 110 (:REWRITE |(* (- x) y)|))
 (2443 73 (:REWRITE |(integerp (- x))|))
 (2266 496 (:REWRITE DEFAULT-LESS-THAN-2))
 (2236 969 (:REWRITE DEFAULT-PLUS-1))
 (2072 748 (:REWRITE DEFAULT-MINUS))
 (2052 9 (:REWRITE MOD-X-I*J))
 (1906 80 (:REWRITE MOD-X-Y-=-X . 4))
 (1903 132 (:LINEAR EXPT-X->-X))
 (1895 755 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1895 755 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1888 273 (:REWRITE INTEGERP-MINUS-X))
 (1855 755 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1855 755 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1796 80 (:REWRITE MOD-ZERO . 4))
 (1795 132 (:LINEAR EXPT-X->=-X))
 (1785 83 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (1785 83 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (1782 80 (:REWRITE MOD-X-Y-=-X . 2))
 (1548 72 (:LINEAR MOD-BOUNDS-2))
 (1392 232 (:REWRITE |(- (+ x y))|))
 (1389 428 (:REWRITE |(< (- x) c)|))
 (1105 496 (:REWRITE DEFAULT-LESS-THAN-1))
 (1013 154 (:REWRITE ODD-EXPT-THM))
 (903 80 (:REWRITE MOD-CANCEL-*-CONST))
 (880 32 (:LINEAR LINEAR-FLOOR-BOUNDS-1))
 (852 12 (:REWRITE BUBBLE-DOWN-*-BUBBLE-DOWN))
 (830 83 (:REWRITE DEFAULT-MOD-2))
 (755 755 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (755 755 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (755 755 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (755 755 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (747 747 (:REWRITE DEFAULT-EXPT-2))
 (747 747 (:REWRITE DEFAULT-EXPT-1))
 (733 733 (:REWRITE |(expt 1/c n)|))
 (733 733 (:REWRITE |(expt (- x) n)|))
 (714 428 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (681 154 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (643 154 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-<))
 (619 138 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (586 4 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (585 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (580 17 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (580 4 (:REWRITE FLOOR-ZERO . 3))
 (550 77 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (546 73 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (546 73 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (546 4 (:REWRITE FLOOR-ZERO . 4))
 (541 373 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (520 520 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (503 491 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (503 491 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (498 50 (:REWRITE DEFAULT-FLOOR-RATIO))
 (490 1 (:REWRITE EVEN-AND-ODD-ALTERNATE))
 (485 373 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (485 373 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (485 373 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (437 428 (:REWRITE |(< (- x) (- y))|))
 (436 4 (:REWRITE CANCEL-FLOOR-+))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (429 373 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (428 428 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (428 428 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (428 428 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (428 428 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (428 428 (:REWRITE |(< c (- x))|))
 (428 428 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (428 428 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (428 428 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (428 428 (:REWRITE |(< (/ x) (/ y))|))
 (397 397 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (397 397 (:REWRITE INTEGERP-<-CONSTANT))
 (397 397 (:REWRITE CONSTANT-<-INTEGERP))
 (396 99 (:REWRITE |(- (* c x))|))
 (396 9 (:REWRITE |(* (- (/ c)) (expt d n))|))
 (385 73 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (385 73 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (346 11 (:REWRITE |(< (+ (- c) x) y)|))
 (338 132 (:LINEAR EXPT-<=-1-TWO))
 (333 46 (:REWRITE |(floor x 2)| . 2))
 (306 9 (:REWRITE |(* (/ c) (expt d n))|))
 (272 16 (:REWRITE |(* x (expt x n))|))
 (268 4 (:REWRITE FLOOR-=-X/Y . 3))
 (264 264 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (264 264 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (264 264 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (260 4 (:REWRITE FLOOR-=-X/Y . 2))
 (223 223 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (171 9 (:REWRITE MOD-X-I*J-V2))
 (164 164 (:REWRITE |(< 0 (* x y))|))
 (162 162 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (162 162 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (162 162 (:REWRITE |(< 0 (/ x))|))
 (143 83 (:REWRITE DEFAULT-MOD-1))
 (138 2 (:REWRITE |(+ x x)|))
 (132 132 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (132 132 (:LINEAR EXPT-LINEAR-UPPER-<))
 (132 132 (:LINEAR EXPT-LINEAR-LOWER-<))
 (132 132 (:LINEAR EXPT->=-1-TWO))
 (132 132 (:LINEAR EXPT->-1-TWO))
 (132 132 (:LINEAR EXPT-<=-1-ONE))
 (132 132 (:LINEAR EXPT-<-1-TWO))
 (132 132 (:LINEAR EXPT-<-1-ONE))
 (127 127 (:REWRITE |(* c (* d x))|))
 (116 65 (:REWRITE |(< x (+ c/d y))|))
 (86 50 (:REWRITE DEFAULT-FLOOR-2))
 (84 4 (:REWRITE FLOOR-ZERO . 2))
 (84 4 (:REWRITE FLOOR-X-Y-=-1 . 3))
 (84 4 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (84 4 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (73 73 (:REWRITE |(mod x (- y))| . 3))
 (73 73 (:REWRITE |(mod x (- y))| . 2))
 (73 73 (:REWRITE |(mod x (- y))| . 1))
 (73 73 (:REWRITE |(mod (- x) y)| . 3))
 (73 73 (:REWRITE |(mod (- x) y)| . 2))
 (73 73 (:REWRITE |(mod (- x) y)| . 1))
 (61 61 (:REWRITE |(< (* x y) 0)|))
 (60 6 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (57 57 (:REWRITE |(< (/ x) 0)|))
 (52 52 (:REWRITE EXTRA-INTP-THM-1))
 (50 50 (:REWRITE DEFAULT-FLOOR-1))
 (48 4 (:REWRITE FLOOR-ZERO . 5))
 (48 4 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (48 4 (:REWRITE FLOOR-CANCEL-*-CONST))
 (48 4 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (48 4 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (40 21 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (36 36 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (35 20 (:REWRITE |(equal (/ x) c)|))
 (31 31 (:REWRITE |(- (- x))|))
 (29 20 (:REWRITE |(equal (- x) (- y))|))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (25 25 (:TYPE-PRESCRIPTION ABS))
 (22 21 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE |(equal c (/ x))|))
 (20 20 (:REWRITE |(equal (/ x) (/ y))|))
 (19 19 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (19 19 (:REWRITE |(equal c (- x))|))
 (19 19 (:REWRITE |(equal (- x) c)|))
 (16 16 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (16 16 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (12 12 (:REWRITE |arith (expt x c)|))
 (12 12 (:REWRITE |arith (expt 1/c n)|))
 (12 12 (:REWRITE BUBBLE-DOWN-*-MATCH-3))
 (10 10 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:REWRITE |(equal (+ (- c) x) y)|))
 (7 7 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (6 6 (:REWRITE ARITH-NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (5 5 (:REWRITE |(< y (+ (- c) x))|))
 (5 5 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (4 4 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (4 4 (:REWRITE FLOOR-ZERO . 1))
 (4 4 (:REWRITE FLOOR-POSITIVE . 4))
 (4 4 (:REWRITE FLOOR-POSITIVE . 3))
 (4 4 (:REWRITE FLOOR-POSITIVE . 2))
 (4 4 (:REWRITE FLOOR-POSITIVE . 1))
 (4 4 (:REWRITE FLOOR-NONPOSITIVE . 3))
 (4 4 (:REWRITE FLOOR-NONPOSITIVE . 2))
 (4 4 (:REWRITE FLOOR-NONPOSITIVE . 1))
 (4 4 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE FLOOR-=-X/Y . 4))
 (4 4 (:REWRITE |(mod (floor x y) z)| . 5))
 (4 4 (:REWRITE |(mod (floor x y) z)| . 4))
 (4 4 (:REWRITE |(mod (floor x y) z)| . 3))
 (4 4 (:REWRITE |(mod (floor x y) z)| . 2))
 (4 4 (:REWRITE |(floor x (- y))| . 2))
 (4 4 (:REWRITE |(floor x (- y))| . 1))
 (4 4 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(floor (- x) y)| . 2))
 (4 4 (:REWRITE |(floor (- x) y)| . 1))
 (4 4 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(equal (floor (+ x y) z) x)|))
 (4 1 (:REWRITE RATIONALP-X))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-SCATTER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE MOD-X-Y-=-X . 1))
 (2 2 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 3))
 (1 1 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 2))
 (1 1 (:REWRITE |(/ (/ x))|))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(MOD-THEOREM-THREE
 (3032 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (2496 8 (:LINEAR MOD-BOUNDS-3))
 (2330 20 (:REWRITE |(* (* x y) z)|))
 (1882 156 (:REWRITE DEFAULT-TIMES-2))
 (1831 23 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1731 9 (:REWRITE CANCEL-MOD-+))
 (1578 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (1212 60 (:META META-INTEGERP-CORRECT))
 (1180 156 (:REWRITE DEFAULT-TIMES-1))
 (1107 9 (:REWRITE MOD-ZERO . 3))
 (1099 9 (:REWRITE MOD-X-Y-=-X . 4))
 (1099 9 (:REWRITE MOD-X-Y-=-X . 3))
 (1050 9 (:REWRITE MOD-ZERO . 4))
 (956 20 (:REWRITE |(* y (* x z))|))
 (800 16 (:LINEAR MOD-BOUNDS-2))
 (800 16 (:LINEAR MOD-BOUNDS-1))
 (702 9 (:REWRITE DEFAULT-MOD-RATIO))
 (702 9 (:REWRITE |(* (- x) y)|))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (675 675 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (616 616 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (616 616 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (616 616 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (616 616 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (616 616 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (616 616 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (616 616 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (616 616 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (616 616 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (608 9 (:REWRITE |(integerp (- x))|))
 (370 10 (:REWRITE |(integerp (expt x n))|))
 (324 23 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (242 54 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (242 54 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (197 9 (:REWRITE MOD-X-Y-=-X . 2))
 (197 9 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (197 9 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (195 22 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (148 54 (:REWRITE DEFAULT-LESS-THAN-2))
 (148 54 (:REWRITE DEFAULT-LESS-THAN-1))
 (146 8 (:REWRITE DEFAULT-PLUS-2))
 (112 16 (:REWRITE INTEGERP-/))
 (104 10 (:REWRITE DEFAULT-MINUS))
 (103 9 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (103 9 (:REWRITE MOD-CANCEL-*-CONST))
 (103 9 (:REWRITE DEFAULT-MOD-1))
 (103 9 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (103 9 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (82 2 (:REWRITE |(equal (expt x n) 0)|))
 (77 77 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (76 4 (:REWRITE NORMALIZE-ADDENDS))
 (73 9 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (73 9 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (73 9 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (73 9 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (68 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (60 60 (:REWRITE REDUCE-INTEGERP-+))
 (60 60 (:REWRITE INTEGERP-MINUS-X))
 (54 54 (:REWRITE SIMPLIFY-SUMS-<))
 (54 54 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (54 54 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (54 54 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (54 54 (:REWRITE REDUCE-ADDITIVE-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 2 (:REWRITE |(+ y x)|))
 (51 8 (:REWRITE DEFAULT-PLUS-1))
 (47 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (40 7 (:REWRITE DEFAULT-EXPT-1))
 (33 33 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (33 33 (:REWRITE DEFAULT-DIVIDE))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (27 27 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (27 27 (:REWRITE |(< 0 (/ x))|))
 (27 27 (:REWRITE |(< 0 (* x y))|))
 (27 27 (:REWRITE |(< (/ x) 0)|))
 (27 27 (:REWRITE |(< (* x y) 0)|))
 (25 25 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (25 25 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (25 25 (:REWRITE |(equal c (/ x))|))
 (25 25 (:REWRITE |(equal c (- x))|))
 (25 25 (:REWRITE |(equal (/ x) c)|))
 (25 25 (:REWRITE |(equal (/ x) (/ y))|))
 (25 25 (:REWRITE |(equal (- x) c)|))
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 (8 8 (:LINEAR EXPT->-1-ONE))
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 (8 8 (:LINEAR EXPT-<=-1-ONE))
 (8 8 (:LINEAR EXPT-<-1-TWO))
 (8 8 (:LINEAR EXPT-<-1-ONE))
 (7 7 (:REWRITE DEFAULT-EXPT-2))
 (7 7 (:REWRITE |(expt 1/c n)|))
 (7 7 (:REWRITE |(expt (- x) n)|))
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 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(MOD-MULT-2
 (348 4 (:LINEAR MOD-BOUNDS-2))
 (344 4 (:LINEAR MOD-BOUNDS-1))
 (280 40 (:REWRITE ACL2-NUMBERP-X))
 (192 8 (:REWRITE |(* x (if a b c))|))
 (176 24 (:REWRITE DEFAULT-DIVIDE))
 (164 20 (:REWRITE DEFAULT-LESS-THAN-2))
 (160 16 (:REWRITE DEFAULT-LESS-THAN-1))
 (120 30 (:REWRITE RATIONALP-X))
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 (42 1 (:REWRITE MOD-X-Y-=-X-Y . 3))
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 (42 1 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (42 1 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (33 2 (:REWRITE DEFAULT-MOD-RATIO))
 (31 31 (:REWRITE REDUCE-INTEGERP-+))
 (31 31 (:REWRITE INTEGERP-MINUS-X))
 (31 31 (:META META-INTEGERP-CORRECT))
 (30 30 (:REWRITE REDUCE-RATIONALP-+))
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 (30 30 (:REWRITE RATIONALP-MINUS-X))
 (30 30 (:META META-RATIONALP-CORRECT))
 (29 1 (:REWRITE MOD-ZERO . 4))
 (20 2 (:LINEAR MOD-BOUNDS-3))
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 (19 19 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
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 (16 16 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (13 1 (:REWRITE |(* (if a b c) x)|))
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 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (6 6 (:REWRITE |(< 0 (/ x))|))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 (6 6 (:REWRITE |(< (/ x) 0)|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
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 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
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 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
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 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 )
(MOD-PROD
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 (108 4 (:REWRITE |(* (* x y) z)|))
 (84 2 (:LINEAR MOD-BOUNDS-3))
 (81 6 (:REWRITE DEFAULT-MOD-RATIO))
 (78 45 (:REWRITE DEFAULT-TIMES-2))
 (60 60 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (60 60 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (60 60 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (60 60 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (60 60 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (60 3 (:REWRITE MOD-X-Y-=-X . 4))
 (60 3 (:REWRITE MOD-X-Y-=-X . 3))
 (59 59 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (59 59 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (59 59 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
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 (58 3 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (58 3 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (58 3 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (52 3 (:REWRITE MOD-ZERO . 3))
 (45 45 (:REWRITE DEFAULT-TIMES-1))
 (32 4 (:REWRITE |(/ (* x y))|))
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 (30 3 (:REWRITE MOD-X-Y-=-X . 2))
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 (30 3 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (30 3 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
 (28 1 (:REWRITE MOD-X-I*J))
 (23 23 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
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 (21 21 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (21 21 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (18 18 (:REWRITE |(equal c (/ x))|))
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 (18 18 (:REWRITE |(equal (- x) (- y))|))
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 (17 17 (:REWRITE |(equal c (- x))|))
 (17 17 (:REWRITE |(equal (- x) c)|))
 (13 13 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
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 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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 (11 11 (:REWRITE |(< 0 (* x y))|))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
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 (10 10 (:REWRITE |(< (* x y) 0)|))
 (10 4 (:REWRITE |(* (if a b c) x)|))
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 (4 4 (:REWRITE |(* c (* d x))|))
 (4 1 (:REWRITE MOD-X-I*J-V2))
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 (2 2 (:REWRITE |(mod x (- y))| . 3))
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 (1 1 (:REWRITE |(equal x (/ y))|))
 )
(MOD-MULT
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 (247 247 (:REWRITE PREFER-POSITIVE-EXPONENTS-SCATTER-EXPONENTS-<))
 (224 224 (:REWRITE NORMALIZE-FACTORS-SCATTER-EXPONENTS))
 (182 6 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (182 6 (:REWRITE |(mod (+ x y) z) where (<= 0 z)| . 1))
 (168 168 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (160 160 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (160 160 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (160 160 (:REWRITE |(< 0 (/ x))|))
 (160 160 (:REWRITE |(< 0 (* x y))|))
 (153 153 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (153 153 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (153 153 (:REWRITE |(< (/ x) 0)|))
 (153 153 (:REWRITE |(< (* x y) 0)|))
 (145 145 (:REWRITE DEFAULT-DIVIDE))
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 (138 28 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
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 (110 110 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
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 (109 109 (:REWRITE |(equal c (- x))|))
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 (98 16 (:REWRITE |(mod (+ x (mod a b)) y)|))
 (98 16 (:REWRITE |(mod (+ x (- (mod a b))) y)|))
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 (68 17 (:REWRITE RATIONALP-X))
 (34 34 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (34 34 (:REWRITE |(+ c (+ d x))|))
 (29 29 (:REWRITE |(equal (+ (- c) x) y)|))
 (28 28 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (24 24 (:REWRITE FOLD-CONSTS-IN-+))
 (24 24 (:REWRITE |(< (+ c/d x) y)|))
 (24 24 (:REWRITE |(< (+ (- c) x) y)|))
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 (21 21 (:REWRITE |(< x (+ c/d y))|))
 (20 20 (:REWRITE DEFAULT-MOD-2))
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 (20 20 (:REWRITE ARITH-NORMALIZE-ADDENDS))
 (18 18 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (18 4 (:REWRITE |(+ (if a b c) x)|))
 (17 17 (:REWRITE REDUCE-RATIONALP-+))
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 (12 12 (:REWRITE |(mod x (- y))| . 3))
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 )
(MOD-SUMS-CANCEL-1
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 (342 38 (:LINEAR MOD-BOUNDS-3))
 (326 23 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (285 23 (:REWRITE MOD-ZERO . 4))
 (225 23 (:REWRITE MOD-ZERO . 3))
 (186 23 (:REWRITE CANCEL-MOD-+))
 (179 135 (:REWRITE SIMPLIFY-SUMS-<))
 (179 135 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
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 (18 2 (:LINEAR LINEAR-FLOOR-BOUNDS-3))
 (18 2 (:LINEAR LINEAR-FLOOR-BOUNDS-2))
 (18 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (17 17 (:REWRITE REDUCE-RATIONALP-+))
 (17 17 (:REWRITE REDUCE-RATIONALP-*))
 (17 17 (:REWRITE RATIONALP-MINUS-X))
 (17 17 (:META META-RATIONALP-CORRECT))
 (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) 0)|))
 (16 16 (:REWRITE |(< (* x y) 0)|))
 (16 4 (:REWRITE |(integerp (- x))|))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (12 12 (:REWRITE |(< 0 (/ x))|))
 (12 12 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE |(equal c (/ x))|))
 (8 8 (:REWRITE |(equal c (- x))|))
 (8 8 (:REWRITE |(equal (/ x) c)|))
 (8 8 (:REWRITE |(equal (/ x) (/ y))|))
 (8 8 (:REWRITE |(equal (- x) c)|))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (7 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (4 4 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4 4 (:REWRITE FLOOR-CANCEL-*-CONST))
 (4 4 (:REWRITE |(floor x (- y))| . 2))
 (4 4 (:REWRITE |(floor x (- y))| . 1))
 (4 4 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (4 4 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(floor (- x) y)| . 2))
 (4 4 (:REWRITE |(floor (- x) y)| . 1))
 (4 4 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (4 4 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (4 4 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (4 4 (:REWRITE |(< (* x (/ y)) 0) rationalp (* x (/ y))|))
 (4 4 (:REWRITE |(- (* c x))|))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
