src/HOL/SMT_Examples/SMT_Word_Examples.certs

more theorems on orderings

8e6fd56de8adc20c29f4bdb8c2c55e63988185a8 8 0
unsat
((set-logic <null>)
(proof
(let ((@x38 (monotonicity (rewrite (= (bvneg (_ bv5 4)) (_ bv11 4))) (= (= (_ bv11 4) (bvneg (_ bv5 4))) (= (_ bv11 4) (_ bv11 4))))))
(let ((@x42 (trans @x38 (rewrite (= (= (_ bv11 4) (_ bv11 4)) true)) (= (= (_ bv11 4) (bvneg (_ bv5 4))) true))))
(let ((@x49 (trans (monotonicity @x42 (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (bvneg (_ bv5 4)))) false))))
(mp (asserted (not (= (_ bv11 4) (bvneg (_ bv5 4))))) @x49 false))))))

aa1cdd144e99278cb2bdb51d68a75ec8d25b433d 7 0
unsat
((set-logic <null>)
(proof
(let ((@x35 (monotonicity (rewrite (= (= (_ bv11 4) (_ bv11 4)) true)) (= (not (= (_ bv11 4) (_ bv11 4))) (not true)))))
(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 4) (_ bv11 4))) false))))
(mp (asserted (not (= (_ bv11 4) (_ bv11 4)))) @x39 false)))))

a14afea8a52a1586ff44eff03b88f1717144d17a 7 0
unsat
((set-logic <null>)
(proof
(let ((@x38 (monotonicity (rewrite (= (bvult (_ bv23 8) (_ bv27 8)) true)) (= (not (bvult (_ bv23 8) (_ bv27 8))) (not true)))))
(let ((@x42 (trans @x38 (rewrite (= (not true) false)) (= (not (bvult (_ bv23 8) (_ bv27 8))) false))))
(mp (asserted (not (bvult (_ bv23 8) (_ bv27 8)))) @x42 false)))))

282d94be68c87485ea9ec13e80f6f2a51b18f5bd 9 0
unsat
((set-logic <null>)
(proof
(let ((@x38 (monotonicity (rewrite (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) (= (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)) (= (_ bv6 5) (_ bv6 5))))))
(let ((@x42 (trans @x38 (rewrite (= (= (_ bv6 5) (_ bv6 5)) true)) (= (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)) true))))
(let ((@x45 (monotonicity @x42 (= (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) (not true)))))
(let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5))) false))))
(mp (asserted (not (= (bvadd (_ bv27 5) (_ bv11 5)) (_ bv6 5)))) @x49 false)))))))

4df99826f79b2c96079a4c58ea51a58b8cc6199c 9 0
unsat
((set-logic <null>)
(proof
(let ((@x38 (monotonicity (rewrite (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) (= (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)) (= (_ bv21 8) (_ bv21 8))))))
(let ((@x42 (trans @x38 (rewrite (= (= (_ bv21 8) (_ bv21 8)) true)) (= (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)) true))))
(let ((@x45 (monotonicity @x42 (= (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) (not true)))))
(let ((@x49 (trans @x45 (rewrite (= (not true) false)) (= (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8))) false))))
(mp (asserted (not (= (bvmul (_ bv7 8) (_ bv3 8)) (_ bv21 8)))) @x49 false)))))))

45bf9e0a746f7dde46f8242e5851928c2671c7f2 9 0
unsat
((set-logic <null>)
(proof
(let ((@x43 (monotonicity (rewrite (= (bvsub (_ bv11 8) (_ bv27 8)) (_ bv240 8))) (rewrite (= (bvneg (_ bv16 8)) (_ bv240 8))) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) (= (_ bv240 8) (_ bv240 8))))))
(let ((@x47 (trans @x43 (rewrite (= (= (_ bv240 8) (_ bv240 8)) true)) (= (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))) true))))
(let ((@x50 (monotonicity @x47 (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) (not true)))))
(let ((@x54 (trans @x50 (rewrite (= (not true) false)) (= (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8)))) false))))
(mp (asserted (not (= (bvsub (_ bv11 8) (_ bv27 8)) (bvneg (_ bv16 8))))) @x54 false)))))))

6dd848d7b26e0521039e21a5e2bafebc1fee8c9b 7 0
unsat
((set-logic <null>)
(proof
(let ((@x35 (monotonicity (rewrite (= (= (_ bv11 5) (_ bv11 5)) true)) (= (not (= (_ bv11 5) (_ bv11 5))) (not true)))))
(let ((@x39 (trans @x35 (rewrite (= (not true) false)) (= (not (= (_ bv11 5) (_ bv11 5))) false))))
(mp (asserted (not (= (_ bv11 5) (_ bv11 5)))) @x39 false)))))

00a7ff287d9c23d984163ea8e0cac8ac61008afd 11 0
unsat
((set-logic <null>)
(proof
(let ((@x42 (monotonicity (rewrite (= (bvneg (_ bv40 7)) (_ bv88 7))) (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvadd (_ bv88 7) (_ bv1 7))))))
(let ((@x47 (trans @x42 (rewrite (= (bvadd (_ bv88 7) (_ bv1 7)) (_ bv89 7))) (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (_ bv89 7)))))
(let ((@x52 (monotonicity @x47 (rewrite (= (bvneg (_ bv39 7)) (_ bv89 7))) (= (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))) (= (_ bv89 7) (_ bv89 7))))))
(let ((@x56 (trans @x52 (rewrite (= (= (_ bv89 7) (_ bv89 7)) true)) (= (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))) true))))
(let ((@x59 (monotonicity @x56 (= (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7)))) (not true)))))
(let ((@x63 (trans @x59 (rewrite (= (not true) false)) (= (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7)))) false))))
(mp (asserted (not (= (bvadd (bvneg (_ bv40 7)) (_ bv1 7)) (bvneg (_ bv39 7))))) @x63 false)))))))))

9673ca576ccae343db48aa68f876fd3a2515cc33 19 0
unsat
((set-logic <null>)
(proof
(let ((?x35 (bvadd b$ c$)))
(let ((?x36 (bvadd ?x35 a$)))
(let ((?x30 (bvmul (_ bv2 32) b$)))
(let ((?x31 (bvadd a$ ?x30)))
(let ((?x33 (bvadd ?x31 c$)))
(let ((?x34 (bvsub ?x33 b$)))
(let (($x37 (= ?x34 ?x36)))
(let (($x38 (not $x37)))
(let ((@x58 (rewrite (= (= (bvadd a$ b$ c$) (bvadd a$ b$ c$)) true))))
(let ((@x48 (rewrite (= (bvsub (bvadd a$ ?x30 c$) b$) (bvadd a$ b$ c$)))))
(let ((@x46 (monotonicity (rewrite (= ?x33 (bvadd a$ ?x30 c$))) (= ?x34 (bvsub (bvadd a$ ?x30 c$) b$)))))
(let ((@x56 (monotonicity (trans @x46 @x48 (= ?x34 (bvadd a$ b$ c$))) (rewrite (= ?x36 (bvadd a$ b$ c$))) (= $x37 (= (bvadd a$ b$ c$) (bvadd a$ b$ c$))))))
(let ((@x63 (monotonicity (trans @x56 @x58 (= $x37 true)) (= $x38 (not true)))))
(let ((@x67 (trans @x63 (rewrite (= (not true) false)) (= $x38 false))))
(mp (asserted $x38) @x67 false)))))))))))))))))

b4600e6d14c88b633ac7bcc5b2e24af8539b0218 18 0
unsat
((set-logic <null>)
(proof
(let ((?x31 (bvmul (_ bv4 4) x$)))
(let (($x32 (= ?x31 (_ bv4 4))))
(let (($x43 (= (_ bv5 4) x$)))
(let (($x56 (not (or (not $x43) (= (_ bv4 4) ?x31)))))
(let ((@x48 (monotonicity (rewrite (= (= x$ (_ bv5 4)) $x43)) (= (not (= x$ (_ bv5 4))) (not $x43)))))
(let ((@x55 (monotonicity @x48 (rewrite (= $x32 (= (_ bv4 4) ?x31))) (= (or (not (= x$ (_ bv5 4))) $x32) (or (not $x43) (= (_ bv4 4) ?x31))))))
(let (($x34 (not (=> (= x$ (_ bv5 4)) $x32))))
(let ((@x39 (rewrite (= (=> (= x$ (_ bv5 4)) $x32) (or (not (= x$ (_ bv5 4))) $x32)))))
(let ((@x60 (trans (monotonicity @x39 (= $x34 (not (or (not (= x$ (_ bv5 4))) $x32)))) (monotonicity @x55 (= (not (or (not (= x$ (_ bv5 4))) $x32)) $x56)) (= $x34 $x56))))
(let ((@x67 (monotonicity (not-or-elim (mp (asserted $x34) @x60 $x56) $x43) (= ?x31 (bvmul (_ bv4 4) (_ bv5 4))))))
(let ((@x73 (monotonicity (trans @x67 (rewrite (= (bvmul (_ bv4 4) (_ bv5 4)) (_ bv4 4))) $x32) (= (= (_ bv4 4) ?x31) (= (_ bv4 4) (_ bv4 4))))))
(let ((@x77 (trans @x73 (rewrite (= (= (_ bv4 4) (_ bv4 4)) true)) (= (= (_ bv4 4) ?x31) true))))
(let ((@x84 (trans (monotonicity @x77 (= (not (= (_ bv4 4) ?x31)) (not true))) (rewrite (= (not true) false)) (= (not (= (_ bv4 4) ?x31)) false))))
(mp (not-or-elim (mp (asserted $x34) @x60 $x56) (not (= (_ bv4 4) ?x31))) @x84 false))))))))))))))))

d150015a66b6757a72346710966844993c0f3c27 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) (= (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)) (= (_ bv4 32) (_ bv4 32))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv4 32) (_ bv4 32)) true)) (= (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32))) false))))
(mp (asserted (not (= (bvand (_ bv6 32) (_ bv5 32)) (_ bv4 32)))) @x48 false)))))))

200e29aa9f19844d244c5c9755155eb956c5cf7c 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) (= (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)) (= (_ bv7 8) (_ bv7 8))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv7 8) (_ bv7 8)) true)) (= (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8))) false))))
(mp (asserted (not (= (bvor (_ bv6 8) (_ bv3 8)) (_ bv7 8)))) @x48 false)))))))

d7cc0827eb340c29b0f489145022e4b3e3610818 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) (= (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)) (= (_ bv15 8) (_ bv15 8))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv15 8) (_ bv15 8)) true)) (= (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8))) false))))
(mp (asserted (not (= (bvxor (_ bv240 8) (_ bv255 8)) (_ bv15 8)))) @x48 false)))))))

3838eb33edcd292c3a0ecbf1662b54af3940189f 8 0
unsat
((set-logic <null>)
(proof
(let ((@x36 (monotonicity (rewrite (= (bvnot (_ bv240 16)) (_ bv65295 16))) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) (= (_ bv65295 16) (_ bv65295 16))))))
(let ((@x40 (trans @x36 (rewrite (= (= (_ bv65295 16) (_ bv65295 16)) true)) (= (= (bvnot (_ bv240 16)) (_ bv65295 16)) true))))
(let ((@x47 (trans (monotonicity @x40 (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) (not true))) (rewrite (= (not true) false)) (= (not (= (bvnot (_ bv240 16)) (_ bv65295 16))) false))))
(mp (asserted (not (= (bvnot (_ bv240 16)) (_ bv65295 16)))) @x47 false))))))

14431ccb33137348161eb6ca6cfb2e57942c3f9d 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) (= (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)) (= (_ bv2843 12) (_ bv2843 12))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv2843 12) (_ bv2843 12)) true)) (= (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12))) false))))
(mp (asserted (not (= (concat (_ bv11 4) (_ bv27 8)) (_ bv2843 12)))) @x48 false)))))))

880bee16a8f6469b14122277b92e87533ef6a071 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) (= (_ bv207 10) (_ bv207 10))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv207 10) (_ bv207 10)) true)) (= (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10))) false))))
(mp (asserted (not (= (concat (_ bv3 4) (_ bv15 6)) (_ bv207 10)))) @x48 false)))))))

b48f55cefc567df166d8e9967c53372c30620183 8 0
unsat
((set-logic <null>)
(proof
(let ((@x36 (monotonicity (rewrite (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) (= (_ bv3 2) (_ bv3 2))))))
(let ((@x40 (trans @x36 (rewrite (= (= (_ bv3 2) (_ bv3 2)) true)) (= (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)) true))))
(let ((@x47 (trans (monotonicity @x40 (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) (not true))) (rewrite (= (not true) false)) (= (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2))) false))))
(mp (asserted (not (= ((_ extract 2 1) (_ bv6 4)) (_ bv3 2)))) @x47 false))))))

446b3cb9d63aa1f488dc092ed3fb111d2ad50b4e 9 0
unsat
((set-logic <null>)
(proof
(let ((@x36 (monotonicity (rewrite (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) (= (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)) (= (_ bv10 10) (_ bv10 10))))))
(let ((@x40 (trans @x36 (rewrite (= (= (_ bv10 10) (_ bv10 10)) true)) (= (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)) true))))
(let ((@x43 (monotonicity @x40 (= (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) (not true)))))
(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10))) false))))
(mp (asserted (not (= ((_ zero_extend 6) (_ bv10 4)) (_ bv10 10)))) @x47 false)))))))

956d8b6229140c8c4aa869ab0f3765697ab8ff25 9 0
unsat
((set-logic <null>)
(proof
(let ((@x36 (monotonicity (rewrite (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) (= (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)) (= (_ bv58 6) (_ bv58 6))))))
(let ((@x40 (trans @x36 (rewrite (= (= (_ bv58 6) (_ bv58 6)) true)) (= (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)) true))))
(let ((@x43 (monotonicity @x40 (= (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) (not true)))))
(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6))) false))))
(mp (asserted (not (= ((_ sign_extend 2) (_ bv10 4)) (_ bv58 6)))) @x47 false)))))))

24e98aaba1a95c03812c938201b3faa04d97c341 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) (= (_ bv76 8) (_ bv76 8))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv76 8) (_ bv76 8)) true)) (= (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8))) false))))
(mp (asserted (not (= (bvshl (_ bv19 8) (_ bv2 8)) (_ bv76 8)))) @x48 false)))))))

c13d08f3c98afca39a5c9317ed8ca7b7d4e35b5a 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) (= (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)) (= (_ bv6 8) (_ bv6 8))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv6 8) (_ bv6 8)) true)) (= (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8))) false))))
(mp (asserted (not (= (bvlshr (_ bv25 8) (_ bv2 8)) (_ bv6 8)))) @x48 false)))))))

053f04ff749dbee44bfba8828181ab0a78473f75 9 0
unsat
((set-logic <null>)
(proof
(let ((@x37 (monotonicity (rewrite (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) (= (_ bv4 8) (_ bv4 8))))))
(let ((@x41 (trans @x37 (rewrite (= (= (_ bv4 8) (_ bv4 8)) true)) (= (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)) true))))
(let ((@x44 (monotonicity @x41 (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) (not true)))))
(let ((@x48 (trans @x44 (rewrite (= (not true) false)) (= (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8))) false))))
(mp (asserted (not (= (bvashr (_ bv19 8) (_ bv2 8)) (_ bv4 8)))) @x48 false)))))))

42de7906f9755bf3d790213172b0ec7fab46237c 9 0
unsat
((set-logic <null>)
(proof
(let ((@x36 (monotonicity (rewrite (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) (= (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)) (= (_ bv9 4) (_ bv9 4))))))
(let ((@x40 (trans @x36 (rewrite (= (= (_ bv9 4) (_ bv9 4)) true)) (= (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)) true))))
(let ((@x43 (monotonicity @x40 (= (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) (not true)))))
(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4))) false))))
(mp (asserted (not (= ((_ rotate_right 2) (_ bv6 4)) (_ bv9 4)))) @x47 false)))))))

6b83b0b418738896f8c64ad12f5670cb5bf96e0f 9 0
unsat
((set-logic <null>)
(proof
(let ((@x36 (monotonicity (rewrite (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) (= (_ bv13 4) (_ bv13 4))))))
(let ((@x40 (trans @x36 (rewrite (= (= (_ bv13 4) (_ bv13 4)) true)) (= (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)) true))))
(let ((@x43 (monotonicity @x40 (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) (not true)))))
(let ((@x47 (trans @x43 (rewrite (= (not true) false)) (= (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4))) false))))
(mp (asserted (not (= ((_ rotate_left 1) (_ bv14 4)) (_ bv13 4)))) @x47 false)))))))

5c4e275bed2d91897e820ccd6744b0a775a6e26e 17 0
unsat
((set-logic <null>)
(proof
(let ((?x31 (bvand x$ (_ bv255 16))))
(let ((?x29 (bvand x$ (_ bv65280 16))))
(let ((?x32 (bvor ?x29 ?x31)))
(let (($x33 (= ?x32 x$)))
(let (($x34 (not $x33)))
(let ((@x59 (symm (commutativity (= (= x$ ?x32) $x33)) (= $x33 (= x$ ?x32)))))
(let ((@x35 (asserted $x34)))
(let ((@x63 (mp @x35 (monotonicity @x59 (= $x34 (not (= x$ ?x32)))) (not (= x$ ?x32)))))
(let (($x52 (= x$ ?x32)))
(let ((@x26 (true-axiom true)))
(let (($x53 (or $x52 false false false false false false false false false false false false false false false false)))
(let ((@x55 (unit-resolution ((_ th-lemma bv) $x53) @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 $x52)))
(unit-resolution @x55 @x63 false)))))))))))))))

1d4a0e2a4449a8adbcf5a134bf7f2b0ee940d954 51 0
unsat
((set-logic <null>)
(proof
(let ((?x31 (bvand w$ (_ bv255 16))))
(let (($x32 (= ?x31 w$)))
(let (($x64 (not $x32)))
(let ((@x318 (symm (commutativity (= (= w$ ?x31) $x32)) (= $x32 (= w$ ?x31)))))
(let (($x57 (not (or (bvule (_ bv256 16) w$) $x32))))
(let ((@x49 (monotonicity (rewrite (= (bvult w$ (_ bv256 16)) (not (bvule (_ bv256 16) w$)))) (= (not (bvult w$ (_ bv256 16))) (not (not (bvule (_ bv256 16) w$)))))))
(let ((@x53 (trans @x49 (rewrite (= (not (not (bvule (_ bv256 16) w$))) (bvule (_ bv256 16) w$))) (= (not (bvult w$ (_ bv256 16))) (bvule (_ bv256 16) w$)))))
(let ((@x56 (monotonicity @x53 (= (or (not (bvult w$ (_ bv256 16))) $x32) (or (bvule (_ bv256 16) w$) $x32)))))
(let ((@x59 (monotonicity @x56 (= (not (or (not (bvult w$ (_ bv256 16))) $x32)) $x57))))
(let (($x34 (not (=> (bvult w$ (_ bv256 16)) $x32))))
(let ((@x39 (rewrite (= (=> (bvult w$ (_ bv256 16)) $x32) (or (not (bvult w$ (_ bv256 16))) $x32)))))
(let ((@x42 (monotonicity @x39 (= $x34 (not (or (not (bvult w$ (_ bv256 16))) $x32))))))
(let ((@x65 (not-or-elim (mp (asserted $x34) (trans @x42 @x59 (= $x34 $x57)) $x57) $x64)))
(let ((@x322 (mp @x65 (monotonicity @x318 (= $x64 (not (= w$ ?x31)))) (not (= w$ ?x31)))))
(let (($x300 (= w$ ?x31)))
(let (($x81 (= ((_ extract 15 15) w$) (_ bv1 1))))
(let (($x264 (not $x81)))
(let (($x74 (= ((_ extract 8 8) w$) (_ bv1 1))))
(let (($x75 (= ((_ extract 9 9) w$) (_ bv1 1))))
(let (($x82 (and $x75 $x74)))
(let (($x83 (or $x75 $x74 $x82)))
(let (($x76 (= ((_ extract 10 10) w$) (_ bv1 1))))
(let (($x84 (and $x76 $x83)))
(let (($x85 (or $x76 $x75 $x74 $x82 $x84)))
(let (($x77 (= ((_ extract 11 11) w$) (_ bv1 1))))
(let (($x86 (and $x77 $x85)))
(let (($x87 (or $x77 $x76 $x75 $x74 $x82 $x84 $x86)))
(let (($x78 (= ((_ extract 12 12) w$) (_ bv1 1))))
(let (($x88 (and $x78 $x87)))
(let (($x89 (or $x78 $x77 $x76 $x75 $x74 $x82 $x84 $x86 $x88)))
(let (($x79 (= ((_ extract 13 13) w$) (_ bv1 1))))
(let (($x90 (and $x79 $x89)))
(let (($x91 (or $x79 $x78 $x77 $x76 $x75 $x74 $x82 $x84 $x86 $x88 $x90)))
(let (($x80 (= ((_ extract 14 14) w$) (_ bv1 1))))
(let (($x92 (and $x80 $x91)))
(let (($x93 (or $x80 $x79 $x78 $x77 $x76 $x75 $x74 $x82 $x84 $x86 $x88 $x90 $x92)))
(let (($x94 (and $x81 $x93)))
(let (($x95 (or $x81 $x80 $x79 $x78 $x77 $x76 $x75 $x74 $x82 $x84 $x86 $x88 $x90 $x92 $x94)))
(let (($x297 (not $x95)))
(let (($x43 (bvule (_ bv256 16) w$)))
(let (($x44 (not $x43)))
(let ((@x63 (not-or-elim (mp (asserted $x34) (trans @x42 @x59 (= $x34 $x57)) $x57) $x44)))
(let ((@x303 (unit-resolution ((_ th-lemma bv) (or $x43 $x297)) @x63 $x297)))
(let ((@x26 (true-axiom true)))
(let (($x312 (or $x300 false false false false false false false false $x74 $x75 $x76 $x77 $x78 $x79 $x80 $x81)))
(let ((@x314 (unit-resolution ((_ th-lemma bv) $x312) @x26 @x26 @x26 @x26 @x26 @x26 @x26 @x26 (unit-resolution (def-axiom (or $x95 (not $x74))) @x303 (not $x74)) (unit-resolution (def-axiom (or $x95 (not $x75))) @x303 (not $x75)) (unit-resolution (def-axiom (or $x95 (not $x76))) @x303 (not $x76)) (unit-resolution (def-axiom (or $x95 (not $x77))) @x303 (not $x77)) (unit-resolution (def-axiom (or $x95 (not $x78))) @x303 (not $x78)) (unit-resolution (def-axiom (or $x95 (not $x79))) @x303 (not $x79)) (unit-resolution (def-axiom (or $x95 (not $x80))) @x303 (not $x80)) (unit-resolution (def-axiom (or $x95 $x264)) @x303 $x264) $x300)))
(unit-resolution @x314 @x322 false)))))))))))))))))))))))))))))))))))))))))))))))))

115ab22c9945d493b971e69a38d9e608c5b40a71 29 0
unsat
((set-logic <null>)
(proof
(let ((?x28 (bv2int$ (_ bv0 2))))
(let (($x183 (<= ?x28 0)))
(let (($x184 (not $x183)))
(let (($x175 (forall ((?v0 (_ BitVec 2)) )(! (let ((?x47 (bv2int$ ?v0)))
(let (($x53 (<= ?x47 0)))
(not $x53))) :pattern ( (bv2int$ ?v0) ) :qid k!9))
))
(let (($x57 (forall ((?v0 (_ BitVec 2)) )(! (let ((?x47 (bv2int$ ?v0)))
(let (($x53 (<= ?x47 0)))
(not $x53))) :qid k!9))
))
(let ((@x177 (refl (= (not (<= (bv2int$ ?0) 0)) (not (<= (bv2int$ ?0) 0))))))
(let ((@x112 (refl (~ (not (<= (bv2int$ ?0) 0)) (not (<= (bv2int$ ?0) 0))))))
(let (($x49 (forall ((?v0 (_ BitVec 2)) )(! (let ((?x47 (bv2int$ ?v0)))
(< 0 ?x47)) :qid k!9))
))
(let ((@x56 (rewrite (= (< 0 (bv2int$ ?0)) (not (<= (bv2int$ ?0) 0))))))
(let ((@x115 (mp~ (mp (asserted $x49) (quant-intro @x56 (= $x49 $x57)) $x57) (nnf-pos @x112 (~ $x57 $x57)) $x57)))
(let ((@x180 (mp @x115 (quant-intro @x177 (= $x57 $x175)) $x175)))
(let (($x187 (not $x175)))
(let (($x188 (or $x187 $x184)))
(let ((@x189 ((_ quant-inst (_ bv0 2)) $x188)))
(let (($x29 (= ?x28 0)))
(let ((@x30 (asserted $x29)))
(unit-resolution ((_ th-lemma arith triangle-eq) (or (not $x29) $x183)) @x30 (unit-resolution @x189 @x180 $x184) false)))))))))))))))))))

d14e7b8f0d1858316e700b4eb09e7d03e57cf9c3 16 0
unsat
((set-logic <null>)
(proof
(let ((?x32 (p$ true)))
(let (($x29 (bvule (_ bv0 4) a$)))
(let (($x30 (ite $x29 true false)))
(let ((?x31 (p$ $x30)))
(let (($x33 (= ?x31 ?x32)))
(let (($x34 (not $x33)))
(let ((@x52 (monotonicity (monotonicity (rewrite (= $x29 true)) (= (p$ $x29) ?x32)) (= (= (p$ $x29) ?x32) (= ?x32 ?x32)))))
(let ((@x56 (trans @x52 (rewrite (= (= ?x32 ?x32) true)) (= (= (p$ $x29) ?x32) true))))
(let ((@x63 (trans (monotonicity @x56 (= (not (= (p$ $x29) ?x32)) (not true))) (rewrite (= (not true) false)) (= (not (= (p$ $x29) ?x32)) false))))
(let ((@x43 (monotonicity (monotonicity (rewrite (= $x30 $x29)) (= ?x31 (p$ $x29))) (= $x33 (= (p$ $x29) ?x32)))))
(let ((@x46 (monotonicity @x43 (= $x34 (not (= (p$ $x29) ?x32))))))
(mp (asserted $x34) (trans @x46 @x63 (= $x34 false)) false))))))))))))))

6182523304a5597432fa1bb8dd16e804ddd8d7ee 12 0
unsat
((set-logic <null>)
(proof
(let ((?x31 (p$ true)))
(let (($x29 (bvule (_ bv0 4) a$)))
(let ((?x30 (p$ $x29)))
(let (($x32 (= ?x30 ?x31)))
(let ((@x42 (monotonicity (monotonicity (rewrite (= $x29 true)) $x32) (= $x32 (= ?x31 ?x31)))))
(let ((@x49 (monotonicity (trans @x42 (rewrite (= (= ?x31 ?x31) true)) (= $x32 true)) (= (not $x32) (not true)))))
(let ((@x53 (trans @x49 (rewrite (= (not true) false)) (= (not $x32) false))))
(mp (asserted (not $x32)) @x53 false))))))))))