(SQUARE
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(SQUARE-PSD
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(SQUARE-TYPE
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(PROB-0)
(PROB-1)
(PROB-2)
(PROB-3
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 (7 7 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
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(PROB-4)
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(CONE-CF-0-TYPE
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(CONE-CF-0-PSD
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(CONE-CF-1
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(CONE-CF-1-TYPE
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(CONE-CF-1-PSD
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(CONE-CF-2
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(CONE-CF-2-TYPE
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(CONE-CF-2-PSD
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 (1312 1312 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
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 (66 66 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
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(CONE-CF-3
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 )
(CONE-CF-3-TYPE
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(CONE-CF-3-PSD
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 (6 6 (:REWRITE |(< x (+ c/d y))|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (5 5 (:REWRITE |(* (- x) y)|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (4 4 (:REWRITE DEFAULT-DIVIDE))
 (3 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE |(<= x (/ y)) with (< y 0)|))
 (2 2 (:REWRITE |(<= (/ x) y) with (< x 0)|))
 (2 2 (:REWRITE |(<= (/ x) y) with (< 0 x)|))
 (2 2 (:REWRITE |(< x (/ y)) with (< y 0)|))
 (2 2 (:REWRITE |(< (/ x) y) with (< x 0)|))
 (2 2 (:REWRITE |(< (/ x) y) with (< 0 x)|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(MONOID-CF-0)
(CERT)
(CERT-KEY
 (7909 342 (:REWRITE DEFAULT-PLUS-2))
 (5071 342 (:REWRITE DEFAULT-PLUS-1))
 (2216 223 (:REWRITE DEFAULT-TIMES-2))
 (1188 1188 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1188 1188 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1188 1188 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1188 1188 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1188 1188 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (776 776 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (776 776 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (776 776 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (442 46 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (365 223 (:REWRITE DEFAULT-TIMES-1))
 (280 34 (:REWRITE DEFAULT-MINUS))
 (114 114 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (71 71 (:REWRITE |(+ c (+ d x))|))
 (52 52 (:REWRITE FOLD-CONSTS-IN-+))
 (21 21 (:REWRITE DEFAULT-EXPT-2))
 (21 21 (:REWRITE DEFAULT-EXPT-1))
 (17 17 (:REWRITE |(expt 1/c n)|))
 (16 4 (:REWRITE RATIONALP-X))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(expt (- c) n)|))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE |(* c (expt d n))|))
 )
(CERT-CONTRA-M-0
 (838 58 (:REWRITE DEFAULT-PLUS-2))
 (560 60 (:REWRITE DEFAULT-TIMES-2))
 (391 58 (:REWRITE DEFAULT-PLUS-1))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (358 358 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (326 26 (:REWRITE DEFAULT-MINUS))
 (130 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (129 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (102 60 (:REWRITE DEFAULT-TIMES-1))
 (66 6 (:REWRITE SIMPLIFY-SUMS-<))
 (50 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (24 24 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (20 10 (:REWRITE |(< (- x) (- y))|))
 (17 17 (:REWRITE |(+ c (+ d x))|))
 (16 4 (:REWRITE RATIONALP-X))
 (14 14 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (9 9 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (9 9 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (9 9 (:REWRITE INTEGERP-<-CONSTANT))
 (9 9 (:REWRITE DEFAULT-EXPT-2))
 (9 9 (:REWRITE DEFAULT-EXPT-1))
 (9 9 (:REWRITE CONSTANT-<-INTEGERP))
 (7 7 (:REWRITE |(expt 1/c n)|))
 (7 7 (:REWRITE |(expt (- x) n)|))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (5 5 (:REWRITE |(* (- x) y)|))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 4 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(CERT-CONTRA-C-0)
(CERT-CONTRA-C-1)
(CERT-CONTRA-C-2)
(CERT-CONTRA-C-3)
(CERT-CONTRA
 (80 26 (:REWRITE DEFAULT-PLUS-2))
 (50 26 (:REWRITE DEFAULT-PLUS-1))
 (17 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (17 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (16 7 (:REWRITE DEFAULT-LESS-THAN-1))
 (16 4 (:REWRITE RATIONALP-X))
 (15 7 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (14 14 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE FOLD-CONSTS-IN-+))
 (10 10 (:REWRITE |(+ c (+ d x))|))
 (9 7 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (8 7 (:REWRITE DEFAULT-LESS-THAN-2))
 (7 7 (:REWRITE THE-FLOOR-BELOW))
 (7 7 (:REWRITE THE-FLOOR-ABOVE))
 (7 7 (:REWRITE SIMPLIFY-SUMS-<))
 (7 7 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (7 7 (:REWRITE INTEGERP-<-CONSTANT))
 (7 7 (:REWRITE CONSTANT-<-INTEGERP))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (7 7 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< c (- x))|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (7 7 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (7 7 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (7 7 (:REWRITE |(< (/ x) (/ y))|))
 (7 7 (:REWRITE |(< (- x) c)|))
 (7 7 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (5 5 (:REWRITE |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 4 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(MAIN
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 (75 39 (:REWRITE DEFAULT-PLUS-1))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (21 21 (:REWRITE NORMALIZE-ADDENDS))
 (15 15 (:REWRITE FOLD-CONSTS-IN-+))
 (15 15 (:REWRITE |(+ c (+ d x))|))
 (6 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(FINAL
 (1348 128 (:REWRITE DEFAULT-TIMES-2))
 (1174 74 (:REWRITE DEFAULT-PLUS-2))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (696 696 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (576 74 (:REWRITE DEFAULT-PLUS-1))
 (366 26 (:REWRITE DEFAULT-MINUS))
 (210 128 (:REWRITE DEFAULT-TIMES-1))
 (207 17 (:REWRITE DEFAULT-LESS-THAN-2))
 (193 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (151 11 (:REWRITE SIMPLIFY-SUMS-<))
 (144 144 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (57 17 (:REWRITE DEFAULT-LESS-THAN-1))
 (40 40 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (32 8 (:REWRITE RATIONALP-X))
 (27 17 (:REWRITE |(< (- x) (- y))|))
 (25 25 (:REWRITE |(+ c (+ d x))|))
 (23 23 (:REWRITE FOLD-CONSTS-IN-+))
 (23 23 (:REWRITE DEFAULT-EXPT-2))
 (23 23 (:REWRITE DEFAULT-EXPT-1))
 (17 17 (:REWRITE THE-FLOOR-BELOW))
 (17 17 (:REWRITE THE-FLOOR-ABOVE))
 (17 17 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (17 17 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (17 17 (:REWRITE |(expt 1/c n)|))
 (17 17 (:REWRITE |(expt (- x) n)|))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (17 17 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
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 (17 17 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (17 17 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (17 17 (:REWRITE |(< (/ x) (/ y))|))
 (16 16 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (16 16 (:REWRITE INTEGERP-<-CONSTANT))
 (16 16 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE |(< (/ x) 0)|))
 (10 10 (:REWRITE |(< (* x y) 0)|))
 (8 8 (:REWRITE REDUCE-RATIONALP-+))
 (8 8 (:REWRITE REDUCE-RATIONALP-*))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE RATIONALP-MINUS-X))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-RATIONALP-CORRECT))
 (8 8 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (5 5 (:REWRITE |(< y (+ (- c) x))|))
 (5 5 (:REWRITE |(< x (+ c/d y))|))
 (5 5 (:REWRITE |(* (- x) y)|))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
