(EXTEND-WITH-PROOF
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 (576 554 (:REWRITE DEFAULT-CDR))
 (360 263 (:REWRITE DEFAULT-<-2))
 (307 263 (:REWRITE DEFAULT-<-1))
 (304 19 (:DEFINITION DRAT-HINT-LISTP))
 (228 19 (:DEFINITION DRAT-HINT-P))
 (165 55 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (132 123 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (114 87 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (27 27 (:TYPE-PRESCRIPTION HONS-ACONS))
 (4 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 )
(FORMULA-FAL-P-DELETE-CLAUSES-FAL
 (27 24 (:REWRITE DEFAULT-CDR))
 (27 24 (:REWRITE DEFAULT-CAR))
 (27 9 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (19 14 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (9 9 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE DEFAULT-<-1))
 (5 5 (:TYPE-PRESCRIPTION HONS-ACONS))
 )
(FORMULA-FAL-MAX-DELETE-CLAUSES-FAL
 (77 10 (:DEFINITION MAX))
 (70 48 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (61 46 (:REWRITE DEFAULT-CDR))
 (61 46 (:REWRITE DEFAULT-CAR))
 (42 14 (:REWRITE DEFAULT-<-2))
 (29 20 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (24 14 (:REWRITE DEFAULT-<-1))
 (22 22 (:TYPE-PRESCRIPTION HONS-ACONS))
 (12 12 (:TYPE-PRESCRIPTION CLAUSE-OR-ASSIGNMENT-P))
 (12 4 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (12 4 (:DEFINITION POSP))
 )
(FORMULA-P-DELETE-CLAUSES-FAL
 (24 2 (:DEFINITION FORMULA-FAL-MAX))
 (17 15 (:REWRITE DEFAULT-CAR))
 (16 14 (:REWRITE DEFAULT-CDR))
 (12 1 (:DEFINITION FORMULA-FAL-P))
 (10 6 (:REWRITE DEFAULT-<-2))
 (10 2 (:DEFINITION MAX))
 (8 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 5 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (4 1 (:DEFINITION DELETE-CLAUSES-FAL))
 (3 3 (:TYPE-PRESCRIPTION CLAUSE-OR-ASSIGNMENT-P))
 (3 1 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (3 1 (:DEFINITION POSP))
 (1 1 (:DEFINITION HONS-ACONS))
 )
(FORMULA-P-ADD-PROOF-CLAUSE
 (22 22 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (16 11 (:REWRITE DEFAULT-<-1))
 (15 11 (:REWRITE DEFAULT-<-2))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 1 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 )
(HONS-ASSOC-EQUAL-DELETE-CLAUSES-FAL-MEMBER-EQUAL-CASE
 (70 55 (:REWRITE DEFAULT-CAR))
 (44 28 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (39 29 (:REWRITE DEFAULT-CDR))
 (16 16 (:TYPE-PRESCRIPTION HONS-ACONS))
 )
(HONS-ASSOC-EQUAL-DELETE-CLAUSES-FAL
 (164 134 (:REWRITE DEFAULT-CAR))
 (86 66 (:REWRITE DEFAULT-CDR))
 (66 42 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (48 48 (:TYPE-PRESCRIPTION HONS-ACONS))
 )
(DELETE-CLAUSES-FAL-PRESERVES-EVALUATE-FORMULA-FAL
 (240 240 (:REWRITE DEFAULT-CAR))
 (208 198 (:REWRITE DEFAULT-CDR))
 (135 45 (:DEFINITION MEMBER-EQUAL))
 (48 16 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (38 19 (:REWRITE DEFAULT-UNARY-MINUS))
 (36 12 (:REWRITE FOLD-CONSTS-IN-+))
 (35 35 (:REWRITE DEFAULT-+-2))
 (35 35 (:REWRITE DEFAULT-+-1))
 (32 8 (:DEFINITION DELETE-CLAUSES-FAL))
 (23 11 (:REWRITE ZP-OPEN))
 (20 20 (:REWRITE DEFAULT-<-2))
 (20 20 (:REWRITE DEFAULT-<-1))
 (19 19 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 8 (:DEFINITION HONS-ACONS))
 )
(DELETE-CLAUSES-FAL-PRESERVES-SATISFIABLE
 (100 2 (:DEFINITION EVALUATE-FORMULA-FAL))
 (42 2 (:DEFINITION EVALUATE-CLAUSE))
 (28 27 (:REWRITE DEFAULT-CAR))
 (25 24 (:REWRITE DEFAULT-CDR))
 (22 2 (:DEFINITION EVALUATE-LITERAL))
 (18 2 (:DEFINITION HONS-GET))
 (16 2 (:DEFINITION HONS-ASSOC-EQUAL))
 (12 12 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (12 4 (:DEFINITION MEMBER-EQUAL))
 (12 1 (:DEFINITION FORMULA-FAL-P))
 (12 1 (:DEFINITION FORMULA-FAL-MAX))
 (8 6 (:REWRITE DEFAULT-<-2))
 (8 2 (:REWRITE ZP-OPEN))
 (7 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:TYPE-PRESCRIPTION EVALUATE-CLAUSE))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (5 1 (:DEFINITION MAX))
 (4 4 (:TYPE-PRESCRIPTION TRUE-LISTP-LOOKUP-FORMULA-INDEX))
 (4 4 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (4 4 (:DEFINITION UNDEFP$INLINE))
 (4 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 1 (:DEFINITION DELETE-CLAUSES-FAL))
 (3 1 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (3 1 (:DEFINITION POSP))
 (2 2 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (2 2 (:DEFINITION HONS-EQUAL))
 (1 1 (:DEFINITION HONS-ACONS))
 )
(FORMULA-P-IMPLIES-NATP-FORMULA-MAX)
(NOT-SATISFIABLE-ADD-PROOF-CLAUSE-NIL
 (6 6 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE SATISFIABLE-SUFF))
 )
(VERIFY-CLAUSE-IMPLIES-UNSATISFIABLE
 (105 105 (:REWRITE DEFAULT-CAR))
 (58 58 (:REWRITE DEFAULT-CDR))
 (13 13 (:REWRITE DEFAULT-<-2))
 (13 13 (:REWRITE DEFAULT-<-1))
 (6 2 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (3 3 (:REWRITE SATISFIABLE-SUFF))
 )
(EXTEND-WITH-PROOF-PRESERVES-SATISFIABLE
 (688 652 (:REWRITE DEFAULT-CAR))
 (476 463 (:REWRITE DEFAULT-CDR))
 (157 115 (:REWRITE DEFAULT-<-1))
 (131 115 (:REWRITE DEFAULT-<-2))
 (124 31 (:DEFINITION DELETE-CLAUSES-FAL))
 (88 88 (:TYPE-PRESCRIPTION ADD-PROOF-CLAUSE))
 (48 24 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (48 16 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (31 31 (:DEFINITION HONS-ACONS))
 (28 14 (:REWRITE DEFAULT-+-2))
 (27 27 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (22 22 (:REWRITE SATISFIABLE-SUFF))
 (14 14 (:REWRITE DEFAULT-+-1))
 (1 1 (:TYPE-PRESCRIPTION POSP))
 )
(MAIN-LEMMA)
(PROOF-CONTRADICTION-P-IMPLIES-FALSE-LEMMA
 (5 5 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE DEFAULT-<-1))
 )
(PROOF-CONTRADICTION-P-IMPLIES-FALSE
 (816 734 (:REWRITE DEFAULT-CAR))
 (457 417 (:REWRITE DEFAULT-CDR))
 (231 11 (:DEFINITION EVALUATE-CLAUSE))
 (208 13 (:DEFINITION DRAT-HINT-LISTP))
 (201 131 (:REWRITE DEFAULT-<-1))
 (192 32 (:DEFINITION POS-LISTP))
 (156 13 (:DEFINITION DRAT-HINT-P))
 (155 85 (:REWRITE DEFAULT-+-2))
 (131 131 (:REWRITE DEFAULT-<-2))
 (126 11 (:DEFINITION HONS-ASSOC-EQUAL))
 (121 11 (:DEFINITION EVALUATE-LITERAL))
 (104 26 (:DEFINITION DELETE-CLAUSES-FAL))
 (91 31 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (85 85 (:REWRITE DEFAULT-+-1))
 (82 22 (:TYPE-PRESCRIPTION TRUE-LISTP-LOOKUP-FORMULA-INDEX))
 (66 66 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (66 22 (:DEFINITION MEMBER-EQUAL))
 (40 40 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (36 12 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (26 26 (:DEFINITION HONS-ACONS))
 (22 22 (:TYPE-PRESCRIPTION FORMULA-FAL-P))
 (22 11 (:REWRITE DEFAULT-UNARY-MINUS))
 (16 16 (:REWRITE CAR-CONS))
 (11 11 (:DEFINITION HONS-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION DELETE-CLAUSES))
 (4 4 (:REWRITE CDR-CONS))
 )
(PROOF-CONTRADICTION-P-IMPLIES-NOT-SATISFIABLE
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 (60 1 (:DEFINITION PROOFP))
 (53 1 (:DEFINITION PROOF-ENTRY-P))
 (44 2 (:DEFINITION ADD-STEP-P))
 (35 1 (:REWRITE MAIN-LEMMA))
 (35 1 (:REWRITE EXTEND-WITH-PROOF-PRESERVES-SATISFIABLE))
 (33 33 (:REWRITE DEFAULT-CAR))
 (32 32 (:REWRITE DEFAULT-CDR))
 (18 3 (:DEFINITION POS-LISTP))
 (16 1 (:DEFINITION DRAT-HINT-LISTP))
 (15 5 (:DEFINITION POSP))
 (14 14 (:TYPE-PRESCRIPTION VERIFY-PROOF))
 (14 2 (:DEFINITION DELETE-CLAUSES))
 (12 1 (:DEFINITION DRAT-HINT-P))
 (9 7 (:REWRITE DEFAULT-<-2))
 (8 2 (:DEFINITION DELETE-CLAUSES-FAL))
 (7 7 (:REWRITE DEFAULT-<-1))
 (6 1 (:DEFINITION PROOF-CONTRADICTION-P))
 (4 4 (:TYPE-PRESCRIPTION VERIFY-CLAUSE))
 (4 4 (:TYPE-PRESCRIPTION POS-LISTP))
 (4 2 (:DEFINITION WEAK-ADD-STEP-P))
 (3 1 (:REWRITE CLAUSE-OR-ASSIGNMENT-P-CDR))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:DEFINITION HONS-ACONS))
 (1 1 (:TYPE-PRESCRIPTION DRAT-HINT-LISTP))
 (1 1 (:REWRITE SATISFIABLE-SUFF))
 )
(MAIN-THEOREM
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 (491 485 (:REWRITE DEFAULT-CDR))
 (156 128 (:REWRITE DEFAULT-<-1))
 (142 128 (:REWRITE DEFAULT-<-2))
 (52 13 (:DEFINITION DELETE-CLAUSES-FAL))
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 (30 18 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (13 13 (:DEFINITION HONS-ACONS))
 (7 7 (:REWRITE SATISFIABLE-SUFF))
 (6 6 (:TYPE-PRESCRIPTION DELETE-CLAUSES-FAL))
 (1 1 (:TYPE-PRESCRIPTION POSP))
 )
