Kazimir Majorinc's Blog (currently not in use): One Hundred Propositional Tautologies (5)

The same like last post, but this time 1500 tautologies, and
these are in the infix form. It is very easy to change prefix
into infix in Newlisp. And vice versa - same function can be
used for changing infix to prefix. But, tautologies are great.

(set 'infix<->prefix 
  (lambda(L)
    (cond ((symbol? L) L)
          ((= (length L) 2) (map infix<->prefix L))
          ((= (length L) 3) (let((L1 (map infix<->prefix L)))
                                (list (nth 1 L1) (nth 0 L1) (nth 2 L1)))))))

Generated 1005725 formulas.
Filtered to 187105 tautologies in T1.
Filtered to 2730 tautologies in T2.
Filtered to 1581 tautologies in T3 and 1149 tautologies in M3.

*** T3 ***

1. true
2. (not false)
3. (not (not true))
4. (true and true)
5. (true or a)
6. (a or true)
7. (false -> a)
8. (a -> true)
9. (a -> a)
10. (a <-> a)
11. (not (false and a))
12. (not (a and false))
13. (not (false or false))
14. (not (true -> false))
15. (not (true <-> false))
16. (not (false <-> true))
17. (a or (not a))
18. ((not a) or a)
19. ((not true) -> a)
20. (false <-> (not true))
21. ((not true) <-> false)
22. (not (a and (not true)))
23. (not (a and (not a)))
24. (not ((not true) and a))
25. (not ((not a) and a))
26. (not (false or (not true)))
27. (not ((not true) or false))
28. (not (true -> (not true)))
29. (not (a <-> (not a)))
30. (not ((not a) <-> a))
31. (a or (a -> b))
32. (a or (false <-> a))
33. (a or (a <-> false))
34. ((a -> b) or a)
35. ((false <-> a) or a)
36. ((a <-> false) or a)
37. (a -> (not (not a)))
38. (a -> (true and a))
39. (a -> (a and true))
40. (a -> (a and a))
41. (a -> (a or b))
42. (a -> (b or a))
43. (a -> (b -> a))
44. (a -> (true <-> a))
45. (a -> (a <-> true))
46. ((not (not a)) -> a)
47. ((false and a) -> b)
48. ((a and false) -> b)
49. ((a and b) -> a)
50. ((a and b) -> b)
51. ((false or false) -> a)
52. ((false or a) -> a)
53. ((a or false) -> a)
54. ((a or a) -> a)
55. ((true -> false) -> a)
56. ((true -> a) -> a)
57. ((true <-> false) -> a)
58. ((true <-> a) -> a)
59. ((false <-> true) -> a)
60. ((a <-> true) -> a)
61. (false <-> (false and a))
62. (false <-> (a and false))
63. (a <-> (not (not a)))
64. (a <-> (true and a))
65. (a <-> (a and true))
66. (a <-> (a and a))
67. (a <-> (false or a))
68. (a <-> (a or false))
69. (a <-> (a or a))
70. (a <-> (true -> a))
71. (a <-> (true <-> a))
72. (a <-> (a <-> true))
73. ((not (not a)) <-> a)
74. ((true and a) <-> a)
75. ((false and a) <-> false)
76. ((a and true) <-> a)
77. ((a and false) <-> false)
78. ((a and a) <-> a)
79. ((false or a) <-> a)
80. ((a or false) <-> a)
81. ((a or a) <-> a)
82. ((true -> a) <-> a)
83. ((true <-> a) <-> a)
84. ((a <-> true) <-> a)
85. (not (a and (false and b)))
86. (not (a and (b and false)))
87. (not (a and (false or false)))
88. (not (a and (true -> false)))
89. (not (a and (a -> false)))
90. (not (a and (true <-> false)))
91. (not (a and (false <-> true)))
92. (not (a and (false <-> a)))
93. (not (a and (a <-> false)))
94. (not ((false and a) and b))
95. (not ((a and false) and b))
96. (not ((false or false) and a))
97. (not ((true -> false) and a))
98. (not ((a -> false) and a))
99. (not ((true <-> false) and a))
100. (not ((false <-> true) and a))
101. (not ((false <-> a) and a))
102. (not ((a <-> false) and a))
103. (not (false or (false and a)))
104. (not (false or (a and false)))
105. (not (false or (false or false)))
106. (not (false or (true -> false)))
107. (not (false or (true <-> false)))
108. (not (false or (false <-> true)))
109. (not ((not true) or (not true)))
110. (not ((false and a) or false))
111. (not ((a and false) or false))
112. (not ((false or false) or false))
113. (not ((true -> false) or false))
114. (not ((true <-> false) or false))
115. (not ((false <-> true) or false))
116. (not (true -> (false and a)))
117. (not (true -> (a and false)))
118. (not (true -> (false or false)))
119. (not (true -> (true -> false)))
120. (not (true -> (true <-> false)))
121. (not (true -> (false <-> true)))
122. (not (true <-> (false and a)))
123. (not (true <-> (a and false)))
124. (not (true <-> (false or false)))
125. (not (a <-> (a -> false)))
126. (not (a <-> (false <-> a)))
127. (not (a <-> (a <-> false)))
128. (not ((false and a) <-> true))
129. (not ((a and false) <-> true))
130. (not ((false or false) <-> true))
131. (not ((a -> false) <-> a))
132. (not ((false <-> a) <-> a))
133. (not ((a <-> false) <-> a))
134. (a or (not (not (not a))))
135. (a or (not (a and b)))
136. (a or (not (b and a)))
137. (a or (not (false or a)))
138. (a or (not (a or false)))
139. (a or (not (a or a)))
140. (a or (not (true -> a)))
141. (a or (not (true <-> a)))
142. (a or (not (a <-> true)))
143. (a or (true and (not a)))
144. (a or ((not a) and true))
145. (a or (b or (not a)))
146. (a or ((not a) or b))
147. (a or (b -> (not a)))
148. (a or (true <-> (not a)))
149. (a or (a <-> (not true)))
150. (a or ((not true) <-> a))
151. (a or ((not a) <-> true))
152. ((not a) or (true and a))
153. ((not a) or (a and true))
154. ((not a) or (a and a))
155. ((not a) or (a or b))
156. ((not a) or (b or a))
157. ((not a) or (b -> a))
158. ((not a) or (true <-> a))
159. ((not a) or (a <-> true))
160. ((true and a) or (not a))
161. ((a and true) or (not a))
162. ((a and a) or (not a))
163. ((a or b) or (not a))
164. ((a or b) or (not b))
165. ((a -> b) or (not b))
166. ((true <-> a) or (not a))
167. ((a <-> true) or (not a))
168. ((not (not (not a))) or a)
169. ((not (a and b)) or a)
170. ((not (a and b)) or b)
171. ((not (false or a)) or a)
172. ((not (a or false)) or a)
173. ((not (a or a)) or a)
174. ((not (true -> a)) or a)
175. ((not (true <-> a)) or a)
176. ((not (a <-> true)) or a)
177. ((true and (not a)) or a)
178. (((not a) and true) or a)
179. ((a or (not b)) or b)
180. (((not a) or b) or a)
181. ((a -> (not b)) or b)
182. ((true <-> (not a)) or a)
183. ((a <-> (not true)) or a)
184. (((not true) <-> a) or a)
185. (((not a) <-> true) or a)
186. (a -> (not (a -> false)))
187. (a -> (not (false <-> a)))
188. (a -> (not (a <-> false)))
189. (a -> ((not a) -> b))
190. (a -> (false <-> (not a)))
191. (a -> ((not a) <-> false))
192. ((not a) -> (a -> b))
193. ((not a) -> (false <-> a))
194. ((not a) -> (a <-> false))
195. ((a -> false) -> (not a))
196. ((false <-> a) -> (not a))
197. ((a <-> false) -> (not a))
198. ((not (a -> b)) -> a)
199. ((not (false <-> a)) -> a)
200. ((not (a <-> false)) -> a)
201. ((a and (not true)) -> b)
202. ((a and (not a)) -> b)
203. (((not true) and a) -> b)
204. (((not a) and a) -> b)
205. ((false or (not true)) -> a)
206. ((a or (not true)) -> a)
207. (((not true) or false) -> a)
208. (((not true) or a) -> a)
209. ((true -> (not true)) -> a)
210. (((not a) -> false) -> a)
211. (((not a) -> a) -> a)
212. ((false <-> (not a)) -> a)
213. ((a <-> (not a)) -> b)
214. (((not a) <-> false) -> a)
215. (((not a) <-> a) -> b)
216. (false <-> (a and (not true)))
217. (false <-> (a and (not a)))
218. (false <-> ((not true) and a))
219. (false <-> ((not a) and a))
220. (false <-> (true -> (not true)))
221. (false <-> (a <-> (not a)))
222. (false <-> ((not a) <-> a))
223. (a <-> (not (a -> false)))
224. (a <-> (not (false <-> a)))
225. (a <-> (not (a <-> false)))
226. (a <-> (a or (not true)))
227. (a <-> ((not true) or a))
228. (a <-> ((not a) -> false))
229. (a <-> ((not a) -> a))
230. (a <-> (false <-> (not a)))
231. (a <-> ((not a) <-> false))
232. ((not true) <-> (false and a))
233. ((not true) <-> (a and false))
234. ((not true) <-> (false or false))
235. ((not a) <-> (a -> false))
236. ((not a) <-> (false <-> a))
237. ((not a) <-> (a <-> false))
238. ((false and a) <-> (not true))
239. ((a and false) <-> (not true))
240. ((false or false) <-> (not true))
241. ((a -> false) <-> (not a))
242. ((false <-> a) <-> (not a))
243. ((a <-> false) <-> (not a))
244. ((not (a -> false)) <-> a)
245. ((not (false <-> a)) <-> a)
246. ((not (a <-> false)) <-> a)
247. ((a and (not true)) <-> false)
248. ((a and (not a)) <-> false)
249. (((not true) and a) <-> false)
250. (((not a) and a) <-> false)
251. ((a or (not true)) <-> a)
252. (((not true) or a) <-> a)
253. ((true -> (not true)) <-> false)
254. (((not a) -> false) <-> a)
255. (((not a) -> a) <-> a)
256. ((false <-> (not a)) <-> a)
257. ((a <-> (not a)) <-> false)
258. (((not a) <-> false) <-> a)
259. (((not a) <-> a) <-> false)
260. (not (a and (not (not (not a)))))
261. (not (a and (not (true and a))))
262. (not (a and (not (a and true))))
263. (not (a and (not (a and a))))
264. (not (a and (not (a or b))))
265. (not (a and (not (b or a))))
266. (not (a and (not (b -> a))))
267. (not (a and (not (true <-> a))))
268. (not (a and (not (a <-> true))))
269. (not (a and (b and (not true))))
270. (not (a and (b and (not a))))
271. (not (a and (b and (not b))))
272. (not (a and ((not true) and b)))
273. (not (a and ((not a) and b)))
274. (not (a and ((not b) and b)))
275. (not (a and (false or (not true))))
276. (not (a and (false or (not a))))
277. (not (a and ((not true) or false)))
278. (not (a and ((not a) or false)))
279. (not (a and (true -> (not true))))
280. (not (a and (true -> (not a))))
281. (not (a and (a -> (not true))))
282. (not (a and (a -> (not a))))
283. (not (a and (true <-> (not a))))
284. (not (a and (a <-> (not true))))
285. (not (a and (b <-> (not b))))
286. (not (a and ((not true) <-> a)))
287. (not (a and ((not a) <-> true)))
288. (not (a and ((not b) <-> b)))
289. (not ((not a) and (a and b)))
290. (not ((not a) and (b and a)))
291. (not ((not a) and (false or a)))
292. (not ((not a) and (a or false)))
293. (not ((not a) and (a or a)))
294. (not ((not a) and (true -> a)))
295. (not ((not a) and (true <-> a)))
296. (not ((not a) and (a <-> true)))
297. (not ((a and b) and (not a)))
298. (not ((a and b) and (not b)))
299. (not ((false or a) and (not a)))
300. (not ((a or false) and (not a)))
301. (not ((a or a) and (not a)))
302. (not ((true -> a) and (not a)))
303. (not ((true <-> a) and (not a)))
304. (not ((a <-> true) and (not a)))
305. (not ((not (not (not a))) and a))
306. (not ((not (true and a)) and a))
307. (not ((not (a and true)) and a))
308. (not ((not (a and a)) and a))
309. (not ((not (a or b)) and a))
310. (not ((not (a or b)) and b))
311. (not ((not (a -> b)) and b))
312. (not ((not (true <-> a)) and a))
313. (not ((not (a <-> true)) and a))
314. (not ((a and (not true)) and b))
315. (not ((a and (not a)) and b))
316. (not ((a and (not b)) and b))
317. (not (((not true) and a) and b))
318. (not (((not a) and a) and b))
319. (not (((not a) and b) and a))
320. (not ((false or (not true)) and a))
321. (not ((false or (not a)) and a))
322. (not (((not true) or false) and a))
323. (not (((not a) or false) and a))
324. (not ((true -> (not true)) and a))
325. (not ((true -> (not a)) and a))
326. (not ((a -> (not true)) and a))
327. (not ((a -> (not a)) and a))
328. (not ((true <-> (not a)) and a))
329. (not ((a <-> (not true)) and a))
330. (not ((a <-> (not a)) and b))
331. (not (((not true) <-> a) and a))
332. (not (((not a) <-> true) and a))
333. (not (((not a) <-> a) and b))
334. (not (false or (a and (not true))))
335. (not (false or (a and (not a))))
336. (not (false or ((not true) and a)))
337. (not (false or ((not a) and a)))
338. (not (false or (false or (not true))))
339. (not (false or ((not true) or false)))
340. (not (false or (true -> (not true))))
341. (not (false or (a <-> (not a))))
342. (not (false or ((not a) <-> a)))
343. (not ((not true) or (false and a)))
344. (not ((not true) or (a and false)))
345. (not ((not true) or (false or false)))
346. (not ((not true) or (true -> false)))
347. (not ((not true) or (true <-> false)))
348. (not ((not true) or (false <-> true)))
349. (not ((false and a) or (not true)))
350. (not ((a and false) or (not true)))
351. (not ((false or false) or (not true)))
352. (not ((true -> false) or (not true)))
353. (not ((true <-> false) or (not true)))
354. (not ((false <-> true) or (not true)))
355. (not ((a and (not true)) or false))
356. (not ((a and (not a)) or false))
357. (not (((not true) and a) or false))
358. (not (((not a) and a) or false))
359. (not ((false or (not true)) or false))
360. (not (((not true) or false) or false))
361. (not ((true -> (not true)) or false))
362. (not ((a <-> (not a)) or false))
363. (not (((not a) <-> a) or false))
364. (not (true -> (a and (not true))))
365. (not (true -> (a and (not a))))
366. (not (true -> ((not true) and a)))
367. (not (true -> ((not a) and a)))
368. (not (true -> (false or (not true))))
369. (not (true -> ((not true) or false)))
370. (not (true -> (true -> (not true))))
371. (not (true -> (a <-> (not a))))
372. (not (true -> ((not a) <-> a)))
373. (not (true <-> (a and (not true))))
374. (not (true <-> (a and (not a))))
375. (not (true <-> ((not true) and a)))
376. (not (true <-> ((not a) and a)))
377. (not (true <-> (a <-> (not a))))
378. (not (true <-> ((not a) <-> a)))
379. (not (a <-> (not (not (not a)))))
380. (not (a <-> (not (true and a))))
381. (not (a <-> (not (a and true))))
382. (not (a <-> (not (a and a))))
383. (not (a <-> (not (false or a))))
384. (not (a <-> (not (a or false))))
385. (not (a <-> (not (a or a))))
386. (not (a <-> (not (true -> a))))
387. (not (a <-> (not (true <-> a))))
388. (not (a <-> (not (a <-> true))))
389. (not (a <-> (true and (not a))))
390. (not (a <-> ((not a) and true)))
391. (not (a <-> (false or (not a))))
392. (not (a <-> ((not a) or false)))
393. (not (a <-> (true -> (not a))))
394. (not (a <-> (a -> (not true))))
395. (not (a <-> (a -> (not a))))
396. (not (a <-> (true <-> (not a))))
397. (not (a <-> (a <-> (not true))))
398. (not (a <-> ((not true) <-> a)))
399. (not (a <-> ((not a) <-> true)))
400. (not ((not a) <-> (true and a)))

401. (not ((not a) <-> (a and true)))
402. (not ((not a) <-> (a and a)))
403. (not ((not a) <-> (false or a)))
404. (not ((not a) <-> (a or false)))
405. (not ((not a) <-> (a or a)))
406. (not ((not a) <-> (true -> a)))
407. (not ((not a) <-> (true <-> a)))
408. (not ((not a) <-> (a <-> true)))
409. (not ((true and a) <-> (not a)))
410. (not ((a and true) <-> (not a)))
411. (not ((a and a) <-> (not a)))
412. (not ((false or a) <-> (not a)))
413. (not ((a or false) <-> (not a)))
414. (not ((a or a) <-> (not a)))
415. (not ((true -> a) <-> (not a)))
416. (not ((true <-> a) <-> (not a)))
417. (not ((a <-> true) <-> (not a)))
418. (not ((not (not (not a))) <-> a))
419. (not ((not (true and a)) <-> a))
420. (not ((not (a and true)) <-> a))
421. (not ((not (a and a)) <-> a))
422. (not ((not (false or a)) <-> a))
423. (not ((not (a or false)) <-> a))
424. (not ((not (a or a)) <-> a))
425. (not ((not (true -> a)) <-> a))
426. (not ((not (true <-> a)) <-> a))
427. (not ((not (a <-> true)) <-> a))
428. (not ((true and (not a)) <-> a))
429. (not ((a and (not true)) <-> true))
430. (not ((a and (not a)) <-> true))
431. (not (((not true) and a) <-> true))
432. (not (((not a) and true) <-> a))
433. (not (((not a) and a) <-> true))
434. (not ((false or (not a)) <-> a))
435. (not (((not a) or false) <-> a))
436. (not ((true -> (not a)) <-> a))
437. (not ((a -> (not true)) <-> a))
438. (not ((a -> (not a)) <-> a))
439. (not ((true <-> (not a)) <-> a))
440. (not ((a <-> (not true)) <-> a))
441. (not ((a <-> (not a)) <-> true))
442. (not (((not true) <-> a) <-> a))
443. (not (((not a) <-> true) <-> a))
444. (not (((not a) <-> a) <-> true))
445. (a or (not (not (a -> b))))
446. (a or (not (not (false <-> a))))
447. (a or (not (not (a <-> false))))
448. (a or (not (a or (not true))))
449. (a or (not ((not true) or a)))
450. (a or (not ((not a) -> false)))
451. (a or (not ((not a) -> a)))
452. (a or (not (false <-> (not a))))
453. (a or (not ((not a) <-> false)))
454. (a or (true and (a -> b)))
455. (a or (true and (false <-> a)))
456. (a or (true and (a <-> false)))
457. (a or ((not a) and (not a)))
458. (a or ((a -> b) and true))
459. (a or ((false <-> a) and true))
460. (a or ((a <-> false) and true))
461. (a or (b or (a -> c)))
462. (a or (b or (false <-> a)))
463. (a or (b or (a <-> false)))
464. (a or (b or (a <-> b)))
465. (a or (b or (b <-> a)))
466. (a or ((a -> b) or c))
467. (a or ((false <-> a) or b))
468. (a or ((a <-> false) or b))
469. (a or ((a <-> b) or b))
470. (a or ((b <-> a) or b))
471. (a or (b -> (a -> c)))
472. (a or (b -> (false <-> a)))
473. (a or (b -> (a <-> false)))
474. (a or ((not (not a)) -> b))
475. (a or ((a and b) -> c))
476. (a or ((b and a) -> c))
477. (a or ((false or a) -> b))
478. (a or ((a or false) -> b))
479. (a or ((a or a) -> b))
480. (a or ((a or b) -> b))
481. (a or ((b or a) -> b))
482. (a or ((true -> a) -> b))
483. (a or ((true <-> a) -> b))
484. (a or ((a <-> true) -> b))
485. (a or (true <-> (a -> b)))
486. (a or (true <-> (false <-> a)))
487. (a or (true <-> (a <-> false)))
488. (a or (false <-> (not (not a))))
489. (a or (false <-> (a and b)))
490. (a or (false <-> (b and a)))
491. (a or (false <-> (a or a)))
492. (a or (false <-> (true -> a)))
493. (a or (false <-> (true <-> a)))
494. (a or (false <-> (a <-> true)))
495. (a or (a <-> (false and b)))
496. (a or (a <-> (a and b)))
497. (a or (a <-> (b and false)))
498. (a or (a <-> (b and a)))
499. (a or (a <-> (false or false)))
500. (a or (a <-> (true -> false)))
501. (a or (a <-> (true <-> false)))
502. (a or (a <-> (false <-> true)))
503. (a or (b <-> (a or b)))
504. (a or (b <-> (b or a)))
505. (a or ((not (not a)) <-> false))
506. (a or ((false and b) <-> a))
507. (a or ((a and b) <-> false))
508. (a or ((a and b) <-> a))
509. (a or ((b and false) <-> a))
510. (a or ((b and a) <-> false))
511. (a or ((b and a) <-> a))
512. (a or ((false or false) <-> a))
513. (a or ((a or a) <-> false))
514. (a or ((a or b) <-> b))
515. (a or ((b or a) <-> b))
516. (a or ((true -> false) <-> a))
517. (a or ((true -> a) <-> false))
518. (a or ((a -> b) <-> true))
519. (a or ((true <-> false) <-> a))
520. (a or ((true <-> a) <-> false))
521. (a or ((false <-> true) <-> a))
522. (a or ((false <-> a) <-> true))
523. (a or ((a <-> true) <-> false))
524. (a or ((a <-> false) <-> true))
525. ((not a) or (not (a -> false)))
526. ((not a) or (not (false <-> a)))
527. ((not a) or (not (a <-> false)))
528. ((not (not a)) or (a -> b))
529. ((not (not a)) or (false <-> a))
530. ((not (not a)) or (a <-> false))
531. ((true and a) or (a -> b))
532. ((true and a) or (false <-> a))
533. ((true and a) or (a <-> false))
534. ((a and true) or (a -> b))
535. ((a and true) or (false <-> a))
536. ((a and true) or (a <-> false))
537. ((a and a) or (a -> b))
538. ((a and a) or (false <-> a))
539. ((a and a) or (a <-> false))
540. ((a or b) or (a -> c))
541. ((a or b) or (b -> c))
542. ((a or b) or (false <-> a))
543. ((a or b) or (false <-> b))
544. ((a or b) or (a <-> false))
545. ((a or b) or (a <-> b))
546. ((a or b) or (b <-> false))
547. ((a or b) or (b <-> a))
548. ((a -> b) or (not (not a)))
549. ((a -> b) or (true and a))
550. ((a -> b) or (a and true))
551. ((a -> b) or (a and a))
552. ((a -> b) or (a or c))
553. ((a -> b) or (c or a))
554. ((a -> b) or (b -> c))
555. ((a -> b) or (c -> a))
556. ((a -> b) or (true <-> a))
557. ((a -> b) or (false <-> b))
558. ((a -> b) or (a <-> true))
559. ((a -> b) or (b <-> false))
560. ((true <-> a) or (a -> b))
561. ((true <-> a) or (false <-> a))
562. ((true <-> a) or (a <-> false))
563. ((false <-> a) or (not (not a)))
564. ((false <-> a) or (true and a))
565. ((false <-> a) or (a and true))
566. ((false <-> a) or (a and a))
567. ((false <-> a) or (a or b))
568. ((false <-> a) or (b or a))
569. ((false <-> a) or (b -> a))
570. ((false <-> a) or (true <-> a))
571. ((false <-> a) or (a <-> true))
572. ((a <-> true) or (a -> b))
573. ((a <-> true) or (false <-> a))
574. ((a <-> true) or (a <-> false))
575. ((a <-> false) or (not (not a)))
576. ((a <-> false) or (true and a))
577. ((a <-> false) or (a and true))
578. ((a <-> false) or (a and a))
579. ((a <-> false) or (a or b))
580. ((a <-> false) or (b or a))
581. ((a <-> false) or (b -> a))
582. ((a <-> false) or (true <-> a))
583. ((a <-> false) or (a <-> true))
584. ((a <-> b) or (a or b))
585. ((a <-> b) or (b or a))
586. ((not (a -> false)) or (not a))
587. ((not (false <-> a)) or (not a))
588. ((not (a <-> false)) or (not a))
589. ((not (not (a -> b))) or a)
590. ((not (not (false <-> a))) or a)
591. ((not (not (a <-> false))) or a)
592. ((not (a or (not true))) or a)
593. ((not ((not true) or a)) or a)
594. ((not ((not a) -> false)) or a)
595. ((not ((not a) -> a)) or a)
596. ((not (false <-> (not a))) or a)
597. ((not ((not a) <-> false)) or a)
598. ((true and (a -> b)) or a)
599. ((true and (false <-> a)) or a)
600. ((true and (a <-> false)) or a)
601. (((not a) and (not a)) or a)
602. (((a -> b) and true) or a)
603. (((false <-> a) and true) or a)
604. (((a <-> false) and true) or a)
605. ((a or (b -> c)) or b)
606. ((a or (false <-> b)) or b)
607. ((a or (a <-> b)) or b)
608. ((a or (b <-> false)) or b)
609. ((a or (b <-> a)) or b)
610. (((a -> b) or c) or a)
611. (((false <-> a) or b) or a)
612. (((a <-> false) or b) or a)
613. (((a <-> b) or a) or b)
614. (((a <-> b) or b) or a)
615. ((a -> (b -> c)) or b)
616. ((a -> (false <-> b)) or b)
617. ((a -> (b <-> false)) or b)
618. (((not (not a)) -> b) or a)
619. (((a and b) -> c) or a)
620. (((a and b) -> c) or b)
621. (((false or a) -> b) or a)
622. (((a or false) -> b) or a)
623. (((a or a) -> b) or a)
624. (((a or b) -> a) or b)
625. (((a or b) -> b) or a)
626. (((true -> a) -> b) or a)
627. (((true <-> a) -> b) or a)
628. (((a <-> true) -> b) or a)
629. ((true <-> (a -> b)) or a)
630. ((true <-> (false <-> a)) or a)
631. ((true <-> (a <-> false)) or a)
632. ((false <-> (not (not a))) or a)
633. ((false <-> (a and b)) or a)
634. ((false <-> (a and b)) or b)
635. ((false <-> (a or a)) or a)
636. ((false <-> (true -> a)) or a)
637. ((false <-> (true <-> a)) or a)
638. ((false <-> (a <-> true)) or a)
639. ((a <-> (false and b)) or a)
640. ((a <-> (a and b)) or a)
641. ((a <-> (b and false)) or a)
642. ((a <-> (b and a)) or a)
643. ((a <-> (false or false)) or a)
644. ((a <-> (a or b)) or b)
645. ((a <-> (b or a)) or b)
646. ((a <-> (true -> false)) or a)
647. ((a <-> (true <-> false)) or a)
648. ((a <-> (false <-> true)) or a)
649. (((not (not a)) <-> false) or a)
650. (((false and a) <-> b) or b)
651. (((a and false) <-> b) or b)
652. (((a and b) <-> false) or a)
653. (((a and b) <-> false) or b)
654. (((a and b) <-> a) or a)
655. (((a and b) <-> b) or b)
656. (((false or false) <-> a) or a)
657. (((a or a) <-> false) or a)
658. (((a or b) <-> a) or b)
659. (((a or b) <-> b) or a)
660. (((true -> false) <-> a) or a)
661. (((true -> a) <-> false) or a)
662. (((a -> b) <-> true) or a)
663. (((true <-> false) <-> a) or a)
664. (((true <-> a) <-> false) or a)
665. (((false <-> true) <-> a) or a)
666. (((false <-> a) <-> true) or a)
667. (((a <-> true) <-> false) or a)
668. (((a <-> false) <-> true) or a)
669. (a -> (not (not (not (not a)))))
670. (a -> (not (not (true and a))))
671. (a -> (not (not (a and true))))
672. (a -> (not (not (a and a))))
673. (a -> (not (not (a or b))))
674. (a -> (not (not (b or a))))
675. (a -> (not (not (b -> a))))
676. (a -> (not (not (true <-> a))))
677. (a -> (not (not (a <-> true))))
678. (a -> (not (b and (not a))))
679. (a -> (not ((not a) and b)))
680. (a -> (not (false or (not a))))
681. (a -> (not ((not a) or false)))
682. (a -> (not (true -> (not a))))
683. (a -> (not (a -> (not true))))
684. (a -> (not (a -> (not a))))
685. (a -> (not (true <-> (not a))))
686. (a -> (not (a <-> (not true))))
687. (a -> (not ((not true) <-> a)))
688. (a -> (not ((not a) <-> true)))
689. (a -> (true and (not (not a))))
690. (a -> (true and (true and a)))
691. (a -> (true and (a and true)))
692. (a -> (true and (a and a)))
693. (a -> (true and (a or b)))
694. (a -> (true and (b or a)))
695. (a -> (true and (b -> a)))
696. (a -> (true and (true <-> a)))
697. (a -> (true and (a <-> true)))
698. (a -> (a and (not (not a))))
699. (a -> (a and (true and a)))
700. (a -> (a and (a and true)))
701. (a -> (a and (a and a)))
702. (a -> (a and (a or b)))
703. (a -> (a and (b or a)))
704. (a -> (a and (b -> a)))
705. (a -> (a and (true <-> a)))
706. (a -> (a and (a <-> true)))
707. (a -> ((not (not a)) and true))
708. (a -> ((not (not a)) and a))
709. (a -> ((true and a) and true))
710. (a -> ((true and a) and a))
711. (a -> ((a and true) and true))
712. (a -> ((a and true) and a))
713. (a -> ((a and a) and true))
714. (a -> ((a and a) and a))
715. (a -> ((a or b) and true))
716. (a -> ((a or b) and a))
717. (a -> ((b or a) and true))
718. (a -> ((b or a) and a))
719. (a -> ((b -> a) and true))
720. (a -> ((b -> a) and a))
721. (a -> ((true <-> a) and true))
722. (a -> ((true <-> a) and a))
723. (a -> ((a <-> true) and true))
724. (a -> ((a <-> true) and a))
725. (a -> (b or (not (not a))))
726. (a -> (b or (true and a)))
727. (a -> (b or (a and true)))
728. (a -> (b or (a and a)))
729. (a -> (b or (a or c)))
730. (a -> (b or (c or a)))
731. (a -> (b or (c -> a)))
732. (a -> (b or (true <-> a)))
733. (a -> (b or (a <-> true)))
734. (a -> ((not (not a)) or b))
735. (a -> ((true and a) or b))
736. (a -> ((a and true) or b))
737. (a -> ((a and a) or b))
738. (a -> ((a or b) or c))
739. (a -> ((b or a) or c))
740. (a -> ((b -> a) or c))
741. (a -> ((true <-> a) or b))
742. (a -> ((a <-> true) or b))
743. (a -> (b -> (not (not a))))
744. (a -> (b -> (true and a)))
745. (a -> (b -> (a and true)))
746. (a -> (b -> (a and a)))
747. (a -> (b -> (a and b)))
748. (a -> (b -> (b and a)))
749. (a -> (b -> (a or c)))
750. (a -> (b -> (c or a)))
751. (a -> (b -> (c -> a)))
752. (a -> (b -> (true <-> a)))
753. (a -> (b -> (a <-> true)))
754. (a -> (b -> (a <-> b)))
755. (a -> (b -> (b <-> a)))
756. (a -> ((a -> false) -> b))
757. (a -> ((a -> b) -> b))
758. (a -> ((false <-> a) -> b))
759. (a -> ((a <-> false) -> b))
760. (a -> ((a <-> b) -> b))
761. (a -> ((b <-> a) -> b))
762. (a -> (true <-> (not (not a))))
763. (a -> (true <-> (a and a)))
764. (a -> (true <-> (a or b)))
765. (a -> (true <-> (b or a)))
766. (a -> (true <-> (b -> a)))
767. (a -> (a <-> (a or b)))
768. (a -> (a <-> (b or a)))
769. (a -> (a <-> (b -> a)))
770. (a -> (b <-> (a and b)))
771. (a -> (b <-> (b and a)))
772. (a -> (b <-> (a -> b)))
773. (a -> (b <-> (a <-> b)))
774. (a -> (b <-> (b <-> a)))
775. (a -> ((not true) <-> (not a)))
776. (a -> ((not a) <-> (not true)))
777. (a -> ((not (not a)) <-> true))
778. (a -> ((a and a) <-> true))
779. (a -> ((a and b) <-> b))
780. (a -> ((b and a) <-> b))
781. (a -> ((a or b) <-> true))
782. (a -> ((a or b) <-> a))
783. (a -> ((b or a) <-> true))
784. (a -> ((b or a) <-> a))
785. (a -> ((a -> b) <-> b))
786. (a -> ((b -> a) <-> true))
787. (a -> ((b -> a) <-> a))
788. (a -> ((a <-> b) <-> b))
789. (a -> ((b <-> a) <-> b))
790. ((not a) -> (not (a and b)))
791. ((not a) -> (not (b and a)))
792. ((not a) -> (not (false or a)))
793. ((not a) -> (not (a or false)))
794. ((not a) -> (not (a or a)))
795. ((not a) -> (not (true -> a)))
796. ((not a) -> (not (true <-> a)))
797. ((not a) -> (not (a <-> true)))
798. ((not a) -> (a <-> (not true)))
799. ((not a) -> ((not true) <-> a))
800. ((not (not a)) -> (true and a))

801. ((not (not a)) -> (a and true))
802. ((not (not a)) -> (a and a))
803. ((not (not a)) -> (a or b))
804. ((not (not a)) -> (b or a))
805. ((not (not a)) -> (b -> a))
806. ((not (not a)) -> (true <-> a))
807. ((not (not a)) -> (a <-> true))
808. ((a and b) -> (not (not a)))
809. ((a and b) -> (not (not b)))
810. ((a and b) -> (true and a))
811. ((a and b) -> (true and b))
812. ((a and b) -> (a and true))
813. ((a and b) -> (a and a))
814. ((a and b) -> (b and true))
815. ((a and b) -> (b and a))
816. ((a and b) -> (b and b))
817. ((a and b) -> (a or c))
818. ((a and b) -> (b or c))
819. ((a and b) -> (c or a))
820. ((a and b) -> (c or b))
821. ((a and b) -> (c -> a))
822. ((a and b) -> (c -> b))
823. ((a and b) -> (true <-> a))
824. ((a and b) -> (true <-> b))
825. ((a and b) -> (a <-> true))
826. ((a and b) -> (a <-> b))
827. ((a and b) -> (b <-> true))
828. ((a and b) -> (b <-> a))
829. ((false or a) -> (not (not a)))
830. ((false or a) -> (true and a))
831. ((false or a) -> (a and true))
832. ((false or a) -> (a and a))
833. ((false or a) -> (a or b))
834. ((false or a) -> (b or a))
835. ((false or a) -> (b -> a))
836. ((false or a) -> (true <-> a))
837. ((false or a) -> (a <-> true))
838. ((a or false) -> (not (not a)))
839. ((a or false) -> (true and a))
840. ((a or false) -> (a and true))
841. ((a or false) -> (a and a))
842. ((a or false) -> (a or b))
843. ((a or false) -> (b or a))
844. ((a or false) -> (b -> a))
845. ((a or false) -> (true <-> a))
846. ((a or false) -> (a <-> true))
847. ((a or a) -> (not (not a)))
848. ((a or a) -> (true and a))
849. ((a or a) -> (a and true))
850. ((a or a) -> (a and a))
851. ((a or a) -> (a or b))
852. ((a or a) -> (b or a))
853. ((a or a) -> (b -> a))
854. ((a or a) -> (true <-> a))
855. ((a or a) -> (a <-> true))
856. ((a or b) -> (b or a))
857. ((true -> a) -> (not (not a)))
858. ((true -> a) -> (true and a))
859. ((true -> a) -> (a and true))
860. ((true -> a) -> (a and a))
861. ((true -> a) -> (a or b))
862. ((true -> a) -> (b or a))
863. ((true -> a) -> (b -> a))
864. ((true -> a) -> (true <-> a))
865. ((true -> a) -> (a <-> true))
866. ((a -> false) -> (a -> b))
867. ((a -> false) -> (false <-> a))
868. ((a -> false) -> (a <-> false))
869. ((true <-> a) -> (not (not a)))
870. ((true <-> a) -> (true and a))
871. ((true <-> a) -> (a and true))
872. ((true <-> a) -> (a and a))
873. ((true <-> a) -> (a or b))
874. ((true <-> a) -> (b or a))
875. ((true <-> a) -> (b -> a))
876. ((false <-> a) -> (a -> b))
877. ((a <-> true) -> (not (not a)))
878. ((a <-> true) -> (true and a))
879. ((a <-> true) -> (a and true))
880. ((a <-> true) -> (a and a))
881. ((a <-> true) -> (a or b))
882. ((a <-> true) -> (b or a))
883. ((a <-> true) -> (b -> a))
884. ((a <-> false) -> (a -> b))
885. ((a <-> b) -> (a -> b))
886. ((a <-> b) -> (b -> a))
887. ((a <-> b) -> (b <-> a))
888. ((not (true and a)) -> (not a))
889. ((not (a and true)) -> (not a))
890. ((not (a and a)) -> (not a))
891. ((not (a or b)) -> (not a))
892. ((not (a or b)) -> (not b))
893. ((not (a -> b)) -> (not b))
894. ((not (true <-> a)) -> (not a))
895. ((not (a <-> true)) -> (not a))
896. ((a -> (not true)) -> (not a))
897. ((a -> (not a)) -> (not a))
898. ((a <-> (not true)) -> (not a))
899. (((not true) <-> a) -> (not a))
900. ((not (not (not (not a)))) -> a)
901. ((not (not (a and b))) -> a)
902. ((not (not (a and b))) -> b)
903. ((not (not (false or a))) -> a)
904. ((not (not (a or false))) -> a)
905. ((not (not (a or a))) -> a)
906. ((not (not (true -> a))) -> a)
907. ((not (not (true <-> a))) -> a)
908. ((not (not (a <-> true))) -> a)
909. ((not (true and (not a))) -> a)
910. ((not ((not a) and true)) -> a)
911. ((not (a or (not b))) -> b)
912. ((not ((not a) or b)) -> a)
913. ((not (a -> (not b))) -> b)
914. ((not (true <-> (not a))) -> a)
915. ((not (a <-> (not true))) -> a)
916. ((not ((not true) <-> a)) -> a)
917. ((not ((not a) <-> true)) -> a)
918. ((a and (not (not b))) -> b)
919. ((a and (false and b)) -> c)
920. ((a and (b and false)) -> c)
921. ((a and (b and c)) -> b)
922. ((a and (b and c)) -> c)
923. ((a and (false or false)) -> b)
924. ((a and (false or b)) -> b)
925. ((a and (b or false)) -> b)
926. ((a and (b or b)) -> b)
927. ((a and (true -> false)) -> b)
928. ((a and (true -> b)) -> b)
929. ((a and (a -> false)) -> b)
930. ((a and (a -> b)) -> b)
931. ((a and (true <-> false)) -> b)
932. ((a and (true <-> b)) -> b)
933. ((a and (false <-> true)) -> b)
934. ((a and (false <-> a)) -> b)
935. ((a and (a <-> false)) -> b)
936. ((a and (a <-> b)) -> b)
937. ((a and (b <-> true)) -> b)
938. ((a and (b <-> a)) -> b)
939. (((not (not a)) and b) -> a)
940. (((false and a) and b) -> c)
941. (((a and false) and b) -> c)
942. (((a and b) and c) -> a)
943. (((a and b) and c) -> b)
944. (((false or false) and a) -> b)
945. (((false or a) and b) -> a)
946. (((a or false) and b) -> a)
947. (((a or a) and b) -> a)
948. (((true -> false) and a) -> b)
949. (((true -> a) and b) -> a)
950. (((a -> false) and a) -> b)
951. (((a -> b) and a) -> b)
952. (((true <-> false) and a) -> b)
953. (((true <-> a) and b) -> a)
954. (((false <-> true) and a) -> b)
955. (((false <-> a) and a) -> b)
956. (((a <-> true) and b) -> a)
957. (((a <-> false) and a) -> b)
958. (((a <-> b) and a) -> b)
959. (((a <-> b) and b) -> a)
960. ((false or (not (not a))) -> a)
961. ((false or (false and a)) -> b)
962. ((false or (a and false)) -> b)
963. ((false or (a and b)) -> a)
964. ((false or (a and b)) -> b)
965. ((false or (false or false)) -> a)
966. ((false or (false or a)) -> a)
967. ((false or (a or false)) -> a)
968. ((false or (a or a)) -> a)
969. ((false or (true -> false)) -> a)
970. ((false or (true -> a)) -> a)
971. ((false or (true <-> false)) -> a)
972. ((false or (true <-> a)) -> a)
973. ((false or (false <-> true)) -> a)
974. ((false or (a <-> true)) -> a)
975. ((a or (not (not a))) -> a)
976. ((a or (false and b)) -> a)
977. ((a or (a and b)) -> a)
978. ((a or (b and false)) -> a)
979. ((a or (b and a)) -> a)
980. ((a or (false or false)) -> a)
981. ((a or (false or a)) -> a)
982. ((a or (a or false)) -> a)
983. ((a or (a or a)) -> a)
984. ((a or (true -> false)) -> a)
985. ((a or (true -> a)) -> a)
986. ((a or (true <-> false)) -> a)
987. ((a or (true <-> a)) -> a)
988. ((a or (false <-> true)) -> a)
989. ((a or (a <-> true)) -> a)
990. (((not true) or (not true)) -> a)
991. (((not (not a)) or false) -> a)
992. (((not (not a)) or a) -> a)
993. (((false and a) or false) -> b)
994. (((false and a) or b) -> b)
995. (((a and false) or false) -> b)
996. (((a and false) or b) -> b)
997. (((a and b) or false) -> a)
998. (((a and b) or false) -> b)
999. (((a and b) or a) -> a)
1000. (((a and b) or b) -> b)
1001. (((false or false) or false) -> a)
1002. (((false or false) or a) -> a)
1003. (((false or a) or false) -> a)
1004. (((false or a) or a) -> a)
1005. (((a or false) or false) -> a)
1006. (((a or false) or a) -> a)
1007. (((a or a) or false) -> a)
1008. (((a or a) or a) -> a)
1009. (((true -> false) or false) -> a)
1010. (((true -> false) or a) -> a)
1011. (((true -> a) or false) -> a)
1012. (((true -> a) or a) -> a)
1013. (((true <-> false) or false) -> a)
1014. (((true <-> false) or a) -> a)
1015. (((true <-> a) or false) -> a)
1016. (((true <-> a) or a) -> a)
1017. (((false <-> true) or false) -> a)
1018. (((false <-> true) or a) -> a)
1019. (((a <-> true) or false) -> a)
1020. (((a <-> true) or a) -> a)
1021. ((true -> (not (not a))) -> a)
1022. ((true -> (false and a)) -> b)
1023. ((true -> (a and false)) -> b)
1024. ((true -> (a and b)) -> a)
1025. ((true -> (a and b)) -> b)
1026. ((true -> (false or false)) -> a)
1027. ((true -> (false or a)) -> a)
1028. ((true -> (a or false)) -> a)
1029. ((true -> (a or a)) -> a)
1030. ((true -> (true -> false)) -> a)
1031. ((true -> (true -> a)) -> a)
1032. ((true -> (true <-> false)) -> a)
1033. ((true -> (true <-> a)) -> a)
1034. ((true -> (false <-> true)) -> a)
1035. ((true -> (a <-> true)) -> a)
1036. (((not a) -> (not true)) -> a)
1037. (((a -> b) -> false) -> a)
1038. (((a -> b) -> a) -> a)
1039. (((false <-> a) -> false) -> a)
1040. (((false <-> a) -> a) -> a)
1041. (((a <-> false) -> false) -> a)
1042. (((a <-> false) -> a) -> a)
1043. ((true <-> (not (not a))) -> a)
1044. ((true <-> (false and a)) -> b)
1045. ((true <-> (a and false)) -> b)
1046. ((true <-> (a and b)) -> a)
1047. ((true <-> (a and b)) -> b)
1048. ((true <-> (false or false)) -> a)
1049. ((true <-> (false or a)) -> a)
1050. ((true <-> (a or false)) -> a)
1051. ((true <-> (a or a)) -> a)
1052. ((false <-> (a -> b)) -> a)
1053. ((a <-> (a -> false)) -> b)
1054. ((a <-> (a -> b)) -> a)
1055. ((a <-> (a -> b)) -> b)
1056. ((a <-> (false <-> a)) -> b)
1057. ((a <-> (a <-> false)) -> b)
1058. ((a <-> (a <-> b)) -> b)
1059. ((a <-> (b <-> a)) -> b)
1060. (((not true) <-> (not a)) -> a)
1061. (((not a) <-> (not true)) -> a)
1062. (((not (not a)) <-> true) -> a)
1063. (((false and a) <-> true) -> b)
1064. (((a and false) <-> true) -> b)
1065. (((a and b) <-> true) -> a)
1066. (((a and b) <-> true) -> b)
1067. (((false or false) <-> true) -> a)
1068. (((false or a) <-> true) -> a)
1069. (((a or false) <-> true) -> a)
1070. (((a or a) <-> true) -> a)
1071. (((a -> false) <-> a) -> b)
1072. (((a -> b) <-> false) -> a)
1073. (((a -> b) <-> a) -> a)
1074. (((a -> b) <-> a) -> b)
1075. (((false <-> a) <-> a) -> b)
1076. (((a <-> false) <-> a) -> b)
1077. (((a <-> b) <-> a) -> b)
1078. (((a <-> b) <-> b) -> a)
1079. (false <-> (a and (false and b)))
1080. (false <-> (a and (b and false)))
1081. (false <-> (a and (false or false)))
1082. (false <-> (a and (true -> false)))
1083. (false <-> (a and (a -> false)))
1084. (false <-> (a and (true <-> false)))
1085. (false <-> (a and (false <-> true)))
1086. (false <-> (a and (false <-> a)))
1087. (false <-> (a and (a <-> false)))
1088. (false <-> ((false and a) and b))
1089. (false <-> ((a and false) and b))
1090. (false <-> ((false or false) and a))
1091. (false <-> ((true -> false) and a))
1092. (false <-> ((a -> false) and a))
1093. (false <-> ((true <-> false) and a))
1094. (false <-> ((false <-> true) and a))
1095. (false <-> ((false <-> a) and a))
1096. (false <-> ((a <-> false) and a))
1097. (false <-> ((not true) or (not true)))
1098. (false <-> (true -> (false and a)))
1099. (false <-> (true -> (a and false)))
1100. (false <-> (true <-> (false and a)))
1101. (false <-> (true <-> (a and false)))
1102. (false <-> (a <-> (a -> false)))
1103. (false <-> ((false and a) <-> true))
1104. (false <-> ((a and false) <-> true))
1105. (false <-> ((a -> false) <-> a))
1106. (a <-> (not (not (not (not a)))))
1107. (a <-> (not (not (true and a))))
1108. (a <-> (not (not (a and true))))
1109. (a <-> (not (not (a and a))))
1110. (a <-> (not (not (false or a))))
1111. (a <-> (not (not (a or false))))
1112. (a <-> (not (not (a or a))))
1113. (a <-> (not (not (true -> a))))
1114. (a <-> (not (not (true <-> a))))
1115. (a <-> (not (not (a <-> true))))
1116. (a <-> (not (true and (not a))))
1117. (a <-> (not ((not a) and true)))
1118. (a <-> (not (false or (not a))))
1119. (a <-> (not ((not a) or false)))
1120. (a <-> (not (true -> (not a))))
1121. (a <-> (not (a -> (not true))))
1122. (a <-> (not (a -> (not a))))
1123. (a <-> (not (true <-> (not a))))
1124. (a <-> (not (a <-> (not true))))
1125. (a <-> (not ((not true) <-> a)))
1126. (a <-> (not ((not a) <-> true)))
1127. (a <-> (true and (not (not a))))
1128. (a <-> (true and (true and a)))
1129. (a <-> (true and (a and true)))
1130. (a <-> (true and (a and a)))
1131. (a <-> (true and (false or a)))
1132. (a <-> (true and (a or false)))
1133. (a <-> (true and (a or a)))
1134. (a <-> (true and (true -> a)))
1135. (a <-> (true and (true <-> a)))
1136. (a <-> (true and (a <-> true)))
1137. (a <-> (a and (not (not a))))
1138. (a <-> (a and (true and a)))
1139. (a <-> (a and (a and true)))
1140. (a <-> (a and (a and a)))
1141. (a <-> (a and (a or b)))
1142. (a <-> (a and (b or a)))
1143. (a <-> (a and (b -> a)))
1144. (a <-> (a and (true <-> a)))
1145. (a <-> (a and (a <-> true)))
1146. (a <-> ((not (not a)) and true))
1147. (a <-> ((not (not a)) and a))
1148. (a <-> ((true and a) and true))
1149. (a <-> ((true and a) and a))
1150. (a <-> ((a and true) and true))
1151. (a <-> ((a and true) and a))
1152. (a <-> ((a and a) and true))
1153. (a <-> ((a and a) and a))
1154. (a <-> ((false or a) and true))
1155. (a <-> ((a or false) and true))
1156. (a <-> ((a or a) and true))
1157. (a <-> ((a or b) and a))
1158. (a <-> ((b or a) and a))
1159. (a <-> ((true -> a) and true))
1160. (a <-> ((b -> a) and a))
1161. (a <-> ((true <-> a) and true))
1162. (a <-> ((true <-> a) and a))
1163. (a <-> ((a <-> true) and true))
1164. (a <-> ((a <-> true) and a))
1165. (a <-> (false or (not (not a))))
1166. (a <-> (false or (true and a)))
1167. (a <-> (false or (a and true)))
1168. (a <-> (false or (a and a)))
1169. (a <-> (false or (false or a)))
1170. (a <-> (false or (a or false)))
1171. (a <-> (false or (a or a)))
1172. (a <-> (false or (true -> a)))
1173. (a <-> (false or (true <-> a)))
1174. (a <-> (false or (a <-> true)))
1175. (a <-> (a or (not (not a))))
1176. (a <-> (a or (false and b)))
1177. (a <-> (a or (a and b)))
1178. (a <-> (a or (b and false)))
1179. (a <-> (a or (b and a)))
1180. (a <-> (a or (false or false)))
1181. (a <-> (a or (false or a)))
1182. (a <-> (a or (a or false)))
1183. (a <-> (a or (a or a)))
1184. (a <-> (a or (true -> false)))
1185. (a <-> (a or (true -> a)))
1186. (a <-> (a or (true <-> false)))
1187. (a <-> (a or (true <-> a)))
1188. (a <-> (a or (false <-> true)))
1189. (a <-> (a or (a <-> true)))
1190. (a <-> ((not (not a)) or false))
1191. (a <-> ((not (not a)) or a))
1192. (a <-> ((true and a) or false))
1193. (a <-> ((false and b) or a))
1194. (a <-> ((a and true) or false))
1195. (a <-> ((a and a) or false))
1196. (a <-> ((a and b) or a))
1197. (a <-> ((b and false) or a))
1198. (a <-> ((b and a) or a))
1199. (a <-> ((false or false) or a))
1200. (a <-> ((false or a) or false))

1201. (a <-> ((false or a) or a))
1202. (a <-> ((a or false) or false))
1203. (a <-> ((a or false) or a))
1204. (a <-> ((a or a) or false))
1205. (a <-> ((a or a) or a))
1206. (a <-> ((true -> false) or a))
1207. (a <-> ((true -> a) or false))
1208. (a <-> ((true -> a) or a))
1209. (a <-> ((true <-> false) or a))
1210. (a <-> ((true <-> a) or false))
1211. (a <-> ((true <-> a) or a))
1212. (a <-> ((false <-> true) or a))
1213. (a <-> ((a <-> true) or false))
1214. (a <-> ((a <-> true) or a))
1215. (a <-> (true -> (not (not a))))
1216. (a <-> (true -> (true and a)))
1217. (a <-> (true -> (a and true)))
1218. (a <-> (true -> (a and a)))
1219. (a <-> (true -> (false or a)))
1220. (a <-> (true -> (a or false)))
1221. (a <-> (true -> (a or a)))
1222. (a <-> (true -> (true -> a)))
1223. (a <-> (true -> (true <-> a)))
1224. (a <-> (true -> (a <-> true)))
1225. (a <-> ((not a) -> (not true)))
1226. (a <-> ((a -> false) -> false))
1227. (a <-> ((a -> b) -> a))
1228. (a <-> ((false <-> a) -> false))
1229. (a <-> ((false <-> a) -> a))
1230. (a <-> ((a <-> false) -> false))
1231. (a <-> ((a <-> false) -> a))
1232. (a <-> (true <-> (not (not a))))
1233. (a <-> (true <-> (true and a)))
1234. (a <-> (true <-> (a and true)))
1235. (a <-> (true <-> (a and a)))
1236. (a <-> (true <-> (false or a)))
1237. (a <-> (true <-> (a or false)))
1238. (a <-> (true <-> (a or a)))
1239. (a <-> (true <-> (true -> a)))
1240. (a <-> (false <-> (a -> false)))
1241. (a <-> (b <-> (a <-> b)))
1242. (a <-> (b <-> (b <-> a)))
1243. (a <-> ((not true) <-> (not a)))
1244. (a <-> ((not a) <-> (not true)))
1245. (a <-> ((not (not a)) <-> true))
1246. (a <-> ((true and a) <-> true))
1247. (a <-> ((a and true) <-> true))
1248. (a <-> ((a and a) <-> true))
1249. (a <-> ((false or a) <-> true))
1250. (a <-> ((a or false) <-> true))
1251. (a <-> ((a or a) <-> true))
1252. (a <-> ((true -> a) <-> true))
1253. (a <-> ((a -> false) <-> false))
1254. (a <-> ((a <-> b) <-> b))
1255. (a <-> ((b <-> a) <-> b))
1256. ((not true) <-> (a and (not true)))
1257. ((not true) <-> (a and (not a)))
1258. ((not true) <-> ((not true) and a))
1259. ((not true) <-> ((not a) and a))
1260. ((not true) <-> (a <-> (not a)))
1261. ((not true) <-> ((not a) <-> a))
1262. ((not a) <-> (not (true and a)))
1263. ((not a) <-> (not (a and true)))
1264. ((not a) <-> (not (a and a)))
1265. ((not a) <-> (not (false or a)))
1266. ((not a) <-> (not (a or false)))
1267. ((not a) <-> (not (a or a)))
1268. ((not a) <-> (not (true -> a)))
1269. ((not a) <-> (not (true <-> a)))
1270. ((not a) <-> (not (a <-> true)))
1271. ((not a) <-> (a -> (not true)))
1272. ((not a) <-> (a -> (not a)))
1273. ((not a) <-> (a <-> (not true)))
1274. ((not a) <-> ((not true) <-> a))
1275. ((not (not a)) <-> (true and a))
1276. ((not (not a)) <-> (a and true))
1277. ((not (not a)) <-> (a and a))
1278. ((not (not a)) <-> (false or a))
1279. ((not (not a)) <-> (a or false))
1280. ((not (not a)) <-> (a or a))
1281. ((not (not a)) <-> (true -> a))
1282. ((not (not a)) <-> (true <-> a))
1283. ((not (not a)) <-> (a <-> true))
1284. ((true and a) <-> (not (not a)))
1285. ((true and a) <-> (a and a))
1286. ((true and a) <-> (false or a))
1287. ((true and a) <-> (a or false))
1288. ((true and a) <-> (a or a))
1289. ((true and a) <-> (true -> a))
1290. ((true and a) <-> (true <-> a))
1291. ((true and a) <-> (a <-> true))
1292. ((false and a) <-> (false and b))
1293. ((false and a) <-> (b and false))
1294. ((false and a) <-> (false or false))
1295. ((false and a) <-> (true -> false))
1296. ((false and a) <-> (true <-> false))
1297. ((false and a) <-> (false <-> true))
1298. ((a and true) <-> (not (not a)))
1299. ((a and true) <-> (a and a))
1300. ((a and true) <-> (false or a))
1301. ((a and true) <-> (a or false))
1302. ((a and true) <-> (a or a))
1303. ((a and true) <-> (true -> a))
1304. ((a and true) <-> (true <-> a))
1305. ((a and true) <-> (a <-> true))
1306. ((a and false) <-> (false and b))
1307. ((a and false) <-> (b and false))
1308. ((a and false) <-> (false or false))
1309. ((a and false) <-> (true -> false))
1310. ((a and false) <-> (true <-> false))
1311. ((a and false) <-> (false <-> true))
1312. ((a and a) <-> (not (not a)))
1313. ((a and a) <-> (true and a))
1314. ((a and a) <-> (a and true))
1315. ((a and a) <-> (false or a))
1316. ((a and a) <-> (a or false))
1317. ((a and a) <-> (a or a))
1318. ((a and a) <-> (true -> a))
1319. ((a and a) <-> (true <-> a))
1320. ((a and a) <-> (a <-> true))
1321. ((a and b) <-> (b and a))
1322. ((false or false) <-> (false and a))
1323. ((false or false) <-> (a and false))
1324. ((false or a) <-> (not (not a)))
1325. ((false or a) <-> (true and a))
1326. ((false or a) <-> (a and true))
1327. ((false or a) <-> (a and a))
1328. ((false or a) <-> (a or a))
1329. ((false or a) <-> (true -> a))
1330. ((false or a) <-> (true <-> a))
1331. ((false or a) <-> (a <-> true))
1332. ((a or false) <-> (not (not a)))
1333. ((a or false) <-> (true and a))
1334. ((a or false) <-> (a and true))
1335. ((a or false) <-> (a and a))
1336. ((a or false) <-> (a or a))
1337. ((a or false) <-> (true -> a))
1338. ((a or false) <-> (true <-> a))
1339. ((a or false) <-> (a <-> true))
1340. ((a or a) <-> (not (not a)))
1341. ((a or a) <-> (true and a))
1342. ((a or a) <-> (a and true))
1343. ((a or a) <-> (a and a))
1344. ((a or a) <-> (false or a))
1345. ((a or a) <-> (a or false))
1346. ((a or a) <-> (true -> a))
1347. ((a or a) <-> (true <-> a))
1348. ((a or a) <-> (a <-> true))
1349. ((a or b) <-> (b or a))
1350. ((true -> false) <-> (false and a))
1351. ((true -> false) <-> (a and false))
1352. ((true -> a) <-> (not (not a)))
1353. ((true -> a) <-> (true and a))
1354. ((true -> a) <-> (a and true))
1355. ((true -> a) <-> (a and a))
1356. ((true -> a) <-> (false or a))
1357. ((true -> a) <-> (a or false))
1358. ((true -> a) <-> (a or a))
1359. ((true -> a) <-> (true <-> a))
1360. ((true -> a) <-> (a <-> true))
1361. ((a -> false) <-> (false <-> a))
1362. ((a -> false) <-> (a <-> false))
1363. ((true <-> false) <-> (false and a))
1364. ((true <-> false) <-> (a and false))
1365. ((true <-> a) <-> (not (not a)))
1366. ((true <-> a) <-> (true and a))
1367. ((true <-> a) <-> (a and true))
1368. ((true <-> a) <-> (a and a))
1369. ((true <-> a) <-> (false or a))
1370. ((true <-> a) <-> (a or false))
1371. ((true <-> a) <-> (a or a))
1372. ((true <-> a) <-> (true -> a))
1373. ((false <-> true) <-> (false and a))
1374. ((false <-> true) <-> (a and false))
1375. ((false <-> a) <-> (a -> false))
1376. ((a <-> true) <-> (not (not a)))
1377. ((a <-> true) <-> (true and a))
1378. ((a <-> true) <-> (a and true))
1379. ((a <-> true) <-> (a and a))
1380. ((a <-> true) <-> (false or a))
1381. ((a <-> true) <-> (a or false))
1382. ((a <-> true) <-> (a or a))
1383. ((a <-> true) <-> (true -> a))
1384. ((a <-> false) <-> (a -> false))
1385. ((a <-> b) <-> (b <-> a))
1386. ((not (true and a)) <-> (not a))
1387. ((not (a and true)) <-> (not a))
1388. ((not (a and a)) <-> (not a))
1389. ((not (false or a)) <-> (not a))
1390. ((not (a or false)) <-> (not a))
1391. ((not (a or a)) <-> (not a))
1392. ((not (true -> a)) <-> (not a))
1393. ((not (true <-> a)) <-> (not a))
1394. ((not (a <-> true)) <-> (not a))
1395. ((a and (not true)) <-> (not true))
1396. ((a and (not a)) <-> (not true))
1397. (((not true) and a) <-> (not true))
1398. (((not a) and a) <-> (not true))
1399. ((a -> (not true)) <-> (not a))
1400. ((a -> (not a)) <-> (not a))
1401. ((a <-> (not true)) <-> (not a))
1402. ((a <-> (not a)) <-> (not true))
1403. (((not true) <-> a) <-> (not a))
1404. (((not a) <-> a) <-> (not true))
1405. ((not (not (not (not a)))) <-> a)
1406. ((not (not (true and a))) <-> a)
1407. ((not (not (a and true))) <-> a)
1408. ((not (not (a and a))) <-> a)
1409. ((not (not (false or a))) <-> a)
1410. ((not (not (a or false))) <-> a)
1411. ((not (not (a or a))) <-> a)
1412. ((not (not (true -> a))) <-> a)
1413. ((not (not (true <-> a))) <-> a)
1414. ((not (not (a <-> true))) <-> a)
1415. ((not (true and (not a))) <-> a)
1416. ((not ((not a) and true)) <-> a)
1417. ((not (false or (not a))) <-> a)
1418. ((not ((not a) or false)) <-> a)
1419. ((not (true -> (not a))) <-> a)
1420. ((not (a -> (not true))) <-> a)
1421. ((not (a -> (not a))) <-> a)
1422. ((not (true <-> (not a))) <-> a)
1423. ((not (a <-> (not true))) <-> a)
1424. ((not ((not true) <-> a)) <-> a)
1425. ((not ((not a) <-> true)) <-> a)
1426. ((true and (not (not a))) <-> a)
1427. ((true and (true and a)) <-> a)
1428. ((true and (a and true)) <-> a)
1429. ((true and (a and a)) <-> a)
1430. ((true and (false or a)) <-> a)
1431. ((true and (a or false)) <-> a)
1432. ((true and (a or a)) <-> a)
1433. ((true and (true -> a)) <-> a)
1434. ((true and (true <-> a)) <-> a)
1435. ((true and (a <-> true)) <-> a)
1436. ((a and (not (not a))) <-> a)
1437. ((a and (true and a)) <-> a)
1438. ((a and (false and b)) <-> false)
1439. ((a and (a and true)) <-> a)
1440. ((a and (a and a)) <-> a)
1441. ((a and (b and false)) <-> false)
1442. ((a and (false or false)) <-> false)
1443. ((a and (a or b)) <-> a)
1444. ((a and (b or a)) <-> a)
1445. ((a and (true -> false)) <-> false)
1446. ((a and (a -> false)) <-> false)
1447. ((a and (b -> a)) <-> a)
1448. ((a and (true <-> false)) <-> false)
1449. ((a and (true <-> a)) <-> a)
1450. ((a and (false <-> true)) <-> false)
1451. ((a and (false <-> a)) <-> false)
1452. ((a and (a <-> true)) <-> a)
1453. ((a and (a <-> false)) <-> false)
1454. (((not (not a)) and true) <-> a)
1455. (((not (not a)) and a) <-> a)
1456. (((true and a) and true) <-> a)
1457. (((true and a) and a) <-> a)
1458. (((false and a) and b) <-> false)
1459. (((a and true) and true) <-> a)
1460. (((a and true) and a) <-> a)
1461. (((a and false) and b) <-> false)
1462. (((a and a) and true) <-> a)
1463. (((a and a) and a) <-> a)
1464. (((false or false) and a) <-> false)
1465. (((false or a) and true) <-> a)
1466. (((a or false) and true) <-> a)
1467. (((a or a) and true) <-> a)
1468. (((a or b) and a) <-> a)
1469. (((a or b) and b) <-> b)
1470. (((true -> false) and a) <-> false)
1471. (((true -> a) and true) <-> a)
1472. (((a -> false) and a) <-> false)
1473. (((a -> b) and b) <-> b)
1474. (((true <-> false) and a) <-> false)
1475. (((true <-> a) and true) <-> a)
1476. (((true <-> a) and a) <-> a)
1477. (((false <-> true) and a) <-> false)
1478. (((false <-> a) and a) <-> false)
1479. (((a <-> true) and true) <-> a)
1480. (((a <-> true) and a) <-> a)
1481. (((a <-> false) and a) <-> false)
1482. ((false or (not (not a))) <-> a)
1483. ((false or (true and a)) <-> a)
1484. ((false or (a and true)) <-> a)
1485. ((false or (a and a)) <-> a)
1486. ((false or (false or a)) <-> a)
1487. ((false or (a or false)) <-> a)
1488. ((false or (a or a)) <-> a)
1489. ((false or (true -> a)) <-> a)
1490. ((false or (true <-> a)) <-> a)
1491. ((false or (a <-> true)) <-> a)
1492. ((a or (not (not a))) <-> a)
1493. ((a or (false and b)) <-> a)
1494. ((a or (a and b)) <-> a)
1495. ((a or (b and false)) <-> a)
1496. ((a or (b and a)) <-> a)
1497. ((a or (false or false)) <-> a)
1498. ((a or (false or a)) <-> a)
1499. ((a or (a or false)) <-> a)
1500. ((a or (a or a)) <-> a)
1501. ((a or (true -> false)) <-> a)
1502. ((a or (true -> a)) <-> a)
1503. ((a or (true <-> false)) <-> a)
1504. ((a or (true <-> a)) <-> a)
1505. ((a or (false <-> true)) <-> a)
1506. ((a or (a <-> true)) <-> a)
1507. (((not true) or (not true)) <-> false)
1508. (((not (not a)) or false) <-> a)
1509. (((not (not a)) or a) <-> a)
1510. (((true and a) or false) <-> a)
1511. (((false and a) or b) <-> b)
1512. (((a and true) or false) <-> a)
1513. (((a and false) or b) <-> b)
1514. (((a and a) or false) <-> a)
1515. (((a and b) or a) <-> a)
1516. (((a and b) or b) <-> b)
1517. (((false or false) or a) <-> a)
1518. (((false or a) or false) <-> a)
1519. (((false or a) or a) <-> a)
1520. (((a or false) or false) <-> a)
1521. (((a or false) or a) <-> a)
1522. (((a or a) or false) <-> a)
1523. (((a or a) or a) <-> a)
1524. (((true -> false) or a) <-> a)
1525. (((true -> a) or false) <-> a)
1526. (((true -> a) or a) <-> a)
1527. (((true <-> false) or a) <-> a)
1528. (((true <-> a) or false) <-> a)
1529. (((true <-> a) or a) <-> a)
1530. (((false <-> true) or a) <-> a)
1531. (((a <-> true) or false) <-> a)
1532. (((a <-> true) or a) <-> a)
1533. ((true -> (not (not a))) <-> a)
1534. ((true -> (true and a)) <-> a)
1535. ((true -> (false and a)) <-> false)
1536. ((true -> (a and true)) <-> a)
1537. ((true -> (a and false)) <-> false)
1538. ((true -> (a and a)) <-> a)
1539. ((true -> (false or a)) <-> a)
1540. ((true -> (a or false)) <-> a)
1541. ((true -> (a or a)) <-> a)
1542. ((true -> (true -> a)) <-> a)
1543. ((true -> (true <-> a)) <-> a)
1544. ((true -> (a <-> true)) <-> a)
1545. (((not a) -> (not true)) <-> a)
1546. (((a -> false) -> false) <-> a)
1547. (((a -> b) -> a) <-> a)
1548. (((false <-> a) -> false) <-> a)
1549. (((false <-> a) -> a) <-> a)
1550. (((a <-> false) -> false) <-> a)
1551. (((a <-> false) -> a) <-> a)
1552. ((true <-> (not (not a))) <-> a)
1553. ((true <-> (true and a)) <-> a)
1554. ((true <-> (false and a)) <-> false)
1555. ((true <-> (a and true)) <-> a)
1556. ((true <-> (a and false)) <-> false)
1557. ((true <-> (a and a)) <-> a)
1558. ((true <-> (false or a)) <-> a)
1559. ((true <-> (a or false)) <-> a)
1560. ((true <-> (a or a)) <-> a)
1561. ((true <-> (true -> a)) <-> a)
1562. ((false <-> (a -> false)) <-> a)
1563. ((a <-> (a -> false)) <-> false)
1564. ((a <-> (a <-> b)) <-> b)
1565. ((a <-> (b <-> a)) <-> b)
1566. (((not true) <-> (not a)) <-> a)
1567. (((not a) <-> (not true)) <-> a)
1568. (((not (not a)) <-> true) <-> a)
1569. (((true and a) <-> true) <-> a)
1570. (((false and a) <-> true) <-> false)
1571. (((a and true) <-> true) <-> a)
1572. (((a and false) <-> true) <-> false)
1573. (((a and a) <-> true) <-> a)
1574. (((false or a) <-> true) <-> a)
1575. (((a or false) <-> true) <-> a)
1576. (((a or a) <-> true) <-> a)
1577. (((true -> a) <-> true) <-> a)
1578. (((a -> false) <-> false) <-> a)
1579. (((a -> false) <-> a) <-> false)
1580. (((a <-> b) <-> a) <-> b)
1581. (((a <-> b) <-> b) <-> a)

Kazimir Majorinc's Blog (currently not in use)

One Hundred Propositional Tautologies (5)

No comments:

Post a Comment

Newlisp Related Blogs

Newlisp Related Sites.