============================== Prover9 =============================== Prover9 (32) version June-2006C, June 2006. Process 13128 was started by mccune on cleo.thornwood, Mon Jun 19 16:41:41 2006 The command was "/home/mccune/bin/prover9 -f gt.in EN.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file gt.in op(450,infix,@). op(400,infix_right,*). assign(eq_defs,fold). assign(max_weight,25). clauses(sos). (x * y) * z = x * y * z. e * x = x. x ' * x = e. x @ y = x ' * y ' * x * y. end_of_list. % Reading from file EN.in clauses(sos). x * y * z * y * x = y * x * z * x * y. end_of_list. clauses(sos). (A @ B) * C != C * (A @ B) # answer(N). end_of_list. ============================== end of input ========================== ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: clauses(usable). end_of_list. clauses(sos). 1 (x * y) * z = x * y * z. [input]. 2 e * x = x. [input]. 3 x ' * x = e. [input]. 4 x @ y = x ' * y ' * x * y. [input]. 5 x * y * z * y * x = y * x * z * x * y. [input]. 6 (A @ B) * C != C * (A @ B) # answer(N). [input]. end_of_list. clauses(demodulators). end_of_list. Predicate elimination: (none). Auto_denials: no changes. Term ordering decisions: Relation symbol precedence: lex([ = ]). Function symbol precedence: lex([ e, A, B, C, *, @, ' ]). After inverse_order: Function symbol precedence: lex([ e, A, B, C, *, ', @ ]). Folding symbols: @/2. After fold_eq: Function symbol precedence: lex([ e, A, B, C, @, *, ' ]). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). Auto_process settings: no changes. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: clauses(usable). end_of_list. clauses(sos). 7 (x * y) * z = x * y * z. [input]. 8 e * x = x. [input]. 9 x ' * x = e. [input]. 10 x ' * y ' * x * y = x @ y. [copy(4),flip(a)]. 11 x * y * z * y * x = y * x * z * x * y. [input]. 12 (A @ B) * C != C * (A @ B) # answer(N). [input]. end_of_list. clauses(demodulators). 7 (x * y) * z = x * y * z. [input]. 8 e * x = x. [input]. 9 x ' * x = e. [input]. 10 x ' * y ' * x * y = x @ y. [copy(4),flip(a)]. end_of_list. clauses(denials). end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=11): 7 (x * y) * z = x * y * z. [input]. given #2 (I,wt=5): 8 e * x = x. [input]. given #3 (I,wt=6): 9 x ' * x = e. [input]. given #4 (I,wt=13): 10 x ' * y ' * x * y = x @ y. [copy(4),flip(a)]. given #5 (I,wt=19): 11 x * y * z * y * x = y * x * z * x * y. [input]. given #6 (I,wt=11): 12 (A @ B) * C != C * (A @ B) # answer(N). [input]. given #7 (F,wt=5): 16 e @ x = e. [para(8(a,1),10(a,1,2,2)),demod(9(4),9(4)),flip(a)]. given #8 (F,wt=6): 17 x ' @ x = e. [para(9(a,1),10(a,1,2,2)),demod(13(6)),flip(a)]. given #9 (T,wt=8): 13 x ' * x * y = y. [para(9(a,1),7(a,1,1)),demod(8(2)),flip(a)]. given #10 (T,wt=5): 31 x @ x = e. [para(13(a,1),10(a,1,2)),demod(9(2)),flip(a)]. given #11 (A,wt=17): 14 x ' * y ' * x * y * z = (x @ y) * z. [para(10(a,1),7(a,1,1)),demod(7(7),7(6)),flip(a)]. given #12 (F,wt=17): 56 A ' * B ' * A * B * C != C * (A @ B) # answer(N). [para(14(a,2),12(a,1))]. given #13 (F,wt=5): 40 x * e = x. [back_demod(29),demod(37(4))]. given #14 (T,wt=4): 62 e ' = e. [para(40(a,1),9(a,1))]. given #15 (T,wt=5): 63 x @ e = e. [para(40(a,1),10(a,1,2,2)),demod(62(3),8(3),9(2)),flip(a)]. given #16 (A,wt=19): 15 (x * y) ' * z ' * x * y * z = x * y @ z. [para(7(a,1),10(a,1,2,2))]. given #17 (F,wt=7): 74 x * x @ x = e. [para(15(a,1),15(a,1,2)),demod(9(2),62(2),8(4),9(4),16(5))]. given #18 (F,wt=9): 37 x ' ' * y = x * y. [para(13(a,1),13(a,1,2))]. given #19 (T,wt=5): 88 x ' ' = x. [para(37(a,1),40(a,1)),demod(40(2)),flip(a)]. given #20 (T,wt=6): 79 x * x ' = e. [para(37(a,1),9(a,1))]. given #21 (A,wt=23): 19 x * y * z * y * x * u = y * x * z * x * y * u. [para(11(a,1),7(a,1,1)),demod(7(5),7(4),7(3),7(2),7(9),7(8),7(7))]. given #22 (F,wt=6): 90 x @ x ' = e. [para(88(a,1),17(a,1,1))]. given #23 (F,wt=8): 84 x * x ' * y = y. [para(37(a,1),13(a,1))]. given #24 (T,wt=10): 91 x * y * (x * y) ' = e. [para(79(a,1),7(a,1)),flip(a)]. given #25 (T,wt=9): 123 x * (y * x) ' = y '. [para(91(a,1),13(a,1,2)),demod(40(3)),flip(a)]. given #26 (A,wt=23): 20 x * y * z * u * z * y = x * z * y * u * y * z. [para(11(a,1),7(a,2,2)),demod(7(5))]. given #27 (F,wt=8): 137 (x @ y) ' = y @ x. [para(14(a,2),123(a,1,2,1)),demod(136(7),136(5),136(3),136(2),7(5),88(7),7(6),7(5),88(8),7(7),7(6),7(5),10(6),84(4)),flip(a)]. given #28 (F,wt=9): 146 (x @ y) * (y @ x) = e. [back_demod(125),demod(136(8),136(6),136(4),136(3),7(6),88(8),7(7),7(6),88(9),7(8),7(7),7(6),10(7),84(5))]. given #29 (T,wt=9): 152 x * y @ x = y @ x. [back_demod(70),demod(136(2),7(5),10(5)),flip(a)]. given #30 (T,wt=9): 179 (x @ y) @ (y @ x) = e. [para(137(a,1),17(a,1,1))]. given #31 (A,wt=23): 21 x * y * z * u * y * x = y * x * z * u * x * y. [para(7(a,1),11(a,1,2,2)),demod(7(8))]. given #32 (F,wt=9): 193 x @ x * y = x @ y. [para(152(a,1),137(a,1,1)),demod(137(2)),flip(a)]. given #33 (F,wt=10): 136 (x * y) ' = y ' * x '. [para(123(a,1),13(a,1,2)),flip(a)]. given #34 (T,wt=10): 165 x * y @ y ' = y @ x. [back_demod(94),demod(152(5))]. given #35 (T,wt=10): 191 x ' * y @ x = y @ x. [para(84(a,1),152(a,1,1)),flip(a)]. given #36 (A,wt=15): 23 x * y * y * x = y * x * x * y. [para(8(a,1),11(a,1,2,2)),demod(8(6))]. given #37 (F,wt=10): 215 x @ x ' * y = x @ y. [para(84(a,1),193(a,1,2)),flip(a)]. given #38 (F,wt=10): 226 x ' @ y * x = y @ x. [para(165(a,1),137(a,1,1)),demod(137(2)),flip(a)]. given #39 (T,wt=11): 159 x ' @ x * y = x ' @ y. [back_demod(39),demod(136(2),7(4),82(5)),flip(a)]. given #40 (T,wt=11): 166 x * y * (y @ x) = y * x. [back_demod(76),demod(152(2))]. given #41 (A,wt=21): 33 x * y * x ' * z * y = y * z * x * y * x '. [para(13(a,1),11(a,1,2,2,2)),demod(7(5),7(10),7(12),13(13))]. given #42 (F,wt=11): 167 x * y ' @ y = y ' @ x. [back_demod(75),demod(152(6))]. given #43 (F,wt=11): 180 (x @ y) * (y @ x) * z = z. [para(137(a,1),13(a,1,1))]. given #44 (T,wt=11): 187 x * y @ x ' = y @ x '. [para(13(a,1),152(a,1,1)),flip(a)]. given #45 (T,wt=11): 221 x ' * y ' @ y * x = e. [para(136(a,1),17(a,1,1))]. given #46 (A,wt=16): 34 x * y * x ' * y * x = y * x * y. [para(13(a,1),11(a,1,2,2)),flip(a)]. given #47 (F,wt=11): 222 x * y @ y ' * x ' = e. [para(136(a,1),90(a,1,2))]. given #48 (F,wt=11): 240 (x @ y) * y * x = x * y. [para(23(a,1),14(a,1,2,2)),demod(13(6),13(4)),flip(a)]. given #49 (T,wt=9): 364 (x @ y) @ y * x = e. [para(240(a,1),10(a,1,2,2)),demod(137(2),136(3),7(6),10(6),146(3)),flip(a)]. given #50 (T,wt=7): 404 (x @ y) @ x = e. [para(84(a,1),364(a,1,2)),demod(191(3))]. given #51 (A,wt=18): 35 x ' * y * x * y * x ' = y * x ' * y. [para(13(a,1),11(a,1,2)),flip(a)]. given #52 (F,wt=7): 422 x @ (x @ y) = e. [para(404(a,1),137(a,1,1)),demod(62(2)),flip(a)]. given #53 (F,wt=8): 424 (x @ y) @ y ' = e. [para(226(a,1),404(a,1,1))]. given #54 (T,wt=8): 462 (x @ y) @ x ' = e. [para(422(a,1),165(a,2)),demod(425(2),187(4))]. given #55 (T,wt=7): 483 (x @ y) @ y = e. [para(226(a,1),462(a,1,1)),demod(88(3))]. given #56 (A,wt=20): 36 x ' * y * x * z * x * y = y * z * y * x. [para(11(a,1),13(a,1,2))]. given #57 (F,wt=7): 491 x @ (y @ x) = e. [para(483(a,1),137(a,1,1)),demod(62(2)),flip(a)]. given #58 (F,wt=8): 464 x ' @ (y @ x) = e. [para(226(a,1),422(a,1,2))]. given #59 (T,wt=8): 465 (x ' @ y) @ x = e. [para(422(a,1),167(a,2)),demod(425(4),191(5))]. given #60 (T,wt=8): 471 (x @ y ') @ y = e. [para(88(a,1),424(a,1,2))]. given #61 (A,wt=12): 38 x ' * y * x = y * (y @ x). [back_demod(32),demod(37(4)),flip(a)]. given #62 (F,wt=8): 478 x ' @ (x @ y) = e. [para(462(a,1),137(a,1,1)),demod(62(2)),flip(a)]. given #63 (F,wt=8): 486 x @ y ' = y @ x. [back_demod(366),demod(478(3),8(4))]. given #64 (T,wt=8): 521 x @ (x ' @ y) = e. [para(167(a,1),491(a,1,2))]. given #65 (T,wt=8): 524 x @ (y @ x ') = e. [para(88(a,1),464(a,1,1))]. given #66 (A,wt=21): 44 x * y ' * z ' * y * z * u = x * (y @ z) * u. [para(14(a,1),7(a,2,2)),demod(7(7))]. given #67 (F,wt=12): 583 (B @ A ') * C != C * (A @ B) # answer(N). [para(486(a,2),12(a,1,1))]. given #68 (F,wt=12): 584 C * (B @ A ') != (A @ B) * C # answer(N). [para(486(a,2),12(a,2,2)),flip(a)]. given #69 (T,wt=8): 575 x ' @ y = y @ x. [para(465(a,1),38(a,2,2)),demod(53(4),13(4),40(5)),flip(a)]. given #70 (T,wt=9): 378 (x @ y) @ x * y = e. [para(240(a,1),193(a,1,2)),demod(364(6))]. given #71 (A,wt=22): 51 x ' * y * x * (y @ z) = (x @ y ') * z ' * y * z. [para(10(a,1),14(a,1,2,2,2)),demod(37(6))]. given #72 (F,wt=13): 656 (B @ A ') * C != C * (B @ A ') # answer(N). [para(486(a,2),583(a,2,2))]. given #73 (F,wt=17): 655 B ' * A * B * A ' * C != C * (A @ B) # answer(N). [para(14(a,2),583(a,1)),demod(88(5))]. given #74 (T,wt=9): 407 x * y @ y * x = e. [para(364(a,1),152(a,2)),demod(7(3),166(3))]. given #75 (T,wt=9): 432 x @ y * x = x @ y. [back_demod(168),demod(425(3),13(4)),flip(a)]. given #76 (A,wt=12): 53 (x ' @ y) * x = x * (y @ x). [para(10(a,1),14(a,1,2)),demod(37(4)),flip(a)]. given #77 (F,wt=18): 587 A ' * B ' * A * B * C != C * (B @ A ') # answer(N). [para(486(a,2),56(a,2,2))]. given #78 (F,wt=18): 722 B ' * A * B * A ' * C != C * (B @ A ') # answer(N). [para(14(a,2),656(a,1)),demod(88(5))]. given #79 (T,wt=9): 591 x ' @ y ' = x @ y. [para(486(a,2),152(a,1)),demod(136(2),260(4))]. given #80 (T,wt=9): 597 x * y @ y = x @ y. [para(486(a,2),226(a,1)),demod(88(3))]. given #81 (A,wt=15): 54 (x @ y) * z * y * x = z * x * y. [para(11(a,1),14(a,1,2,2)),demod(13(7),13(5)),flip(a)]. given #82 (F,wt=21): 846 A ' * B ' * (B @ C) * A * C * B != C * (A @ B) # answer(N). [para(54(a,2),56(a,1,2,2))]. given #83 (F,wt=21): 906 (A @ B * A ' * C) * A ' * C * A != C * (A @ B) # answer(N). [para(54(a,2),655(a,1)),demod(7(18),7(17),13(19))]. given #84 (T,wt=9): 599 x ' @ y = x @ y '. [para(486(a,2),167(a,1)),demod(136(3),88(2),193(3)),flip(a)]. given #85 (T,wt=10): 417 x ' * y * x @ y = e. [back_demod(230),demod(404(6))]. given #86 (A,wt=13): 55 x ' * y = (y @ x) * y * x '. [para(11(a,1),14(a,1,2)),demod(13(6),13(5))]. given #87 (F,wt=20): 924 (A @ B * A ' * C) * C * (C @ A) != C * (A @ B) # answer(N). [para(38(a,1),906(a,1,2))]. given #88 (F,wt=20): 927 (C @ A) * (A @ B * A ' * C) * C != C * (A @ B) # answer(N). [para(54(a,2),906(a,1)),demod(226(6),7(17),79(16),40(14))]. given #89 (T,wt=10): 423 (x @ y) @ y ' * x = e. [para(191(a,1),404(a,1,1))]. given #90 (T,wt=10): 426 (x @ y ') @ y * x = e. [para(187(a,1),404(a,1,1))]. given #91 (A,wt=16): 57 x ' * y * x * z = y * (y @ x) * z. [para(14(a,1),13(a,1,2)),demod(37(5)),flip(a)]. given #92 (F,wt=21): 1012 B ' * A * B * (C @ A) * C * A ' != C * (A @ B) # answer(N). [para(55(a,1),655(a,1,2,2,2))]. given #93 (F,wt=20): 1196 A * (A @ B) * (C @ A) * C * A ' != C * (A @ B) # answer(N). [para(57(a,1),1012(a,1))]. given #94 (T,wt=10): 427 x @ y ' * x * y = e. [back_demod(249),demod(422(6))]. given #95 (T,wt=10): 466 x * y @ (y @ x ') = e. [para(187(a,1),422(a,1,2))]. given #96 (A,wt=17): 59 x ' * y * x * z = (x @ y ') * y * z. [para(13(a,1),14(a,1,2,2,2)),demod(37(5))]. given #97 (F,wt=17): 1255 A ' * (B @ A ') * A * C != C * (A @ B) # answer(N). [para(59(a,1),56(a,1,2))]. given #98 (F,wt=18): 1305 A ' * (B @ A ') * A * C != C * (B @ A ') # answer(N). [para(59(a,1),587(a,1,2))]. given #99 (T,wt=10): 476 (x @ y) * (x @ y ') = e. [para(462(a,1),10(a,2)),demod(137(2),88(3),395(5))]. given #100 (T,wt=10): 482 (x @ y) @ x ' * y = e. [para(191(a,1),462(a,1,1)),demod(136(4),88(4))]. given #101 (A,wt=16): 61 (x ' @ y) * x * z = x * (y @ x) * z. [para(14(a,1),14(a,1,2)),demod(37(5)),flip(a)]. given #102 (F,wt=20): 1509 A * (A @ B) * C * (C @ A) * A ' != C * (A @ B) # answer(N). [back_demod(1196),demod(1435(12))]. given #103 (F,wt=20): 1540 (C @ A) * (A @ B * C * A ') * C != C * (A @ B) # answer(N). [back_demod(1032),demod(1494(16))]. given #104 (T,wt=10): 492 (x ' @ y) @ x * y = e. [para(159(a,1),483(a,1,1))]. given #105 (T,wt=10): 520 x * y @ (x ' @ y) = e. [para(159(a,1),491(a,1,2))]. given #106 (A,wt=18): 68 x ' * y * z * x = y * z * (y * z @ x). [para(15(a,1),13(a,1,2)),demod(37(6),7(4)),flip(a)]. given #107 (F,wt=18): 1546 (C @ A) * (B * C @ A ') * C != C * (A @ B) # answer(N). [para(486(a,2),1540(a,1,2,1)),demod(816(12))]. given #108 (F,wt=17): 1657 (C @ A) * (A @ B * C) * C != C * (A @ B) # answer(N). [para(486(a,1),1546(a,1,2,1))]. given #109 (T,wt=10): 528 (x @ y ') * (x @ y) = e. [para(465(a,1),10(a,2)),demod(137(3),53(6),13(6))]. given #110 (T,wt=10): 589 (x @ y) * (x ' @ y) = e. [para(486(a,1),146(a,1,1))]. given #111 (A,wt=21): 73 x ' * y ' * x * y * z @ u = (x @ y) * z @ u. [para(14(a,2),15(a,2,1)),demod(15(9)),flip(a)]. given #112 (F,wt=18): 1662 (A ' @ C) * (A @ B * C) * C != C * (A @ B) # answer(N). [para(486(a,2),1657(a,1,1)),demod(599(4,R))]. given #113 (F,wt=18): 1663 C * (B @ A ') != (C @ A) * (A @ B * C) * C # answer(N). [para(486(a,2),1657(a,2,2)),flip(a)]. given #114 (T,wt=10): 590 (x ' @ y) * (x @ y) = e. [para(486(a,1),146(a,1,2))]. given #115 (T,wt=10): 592 (x @ y) @ (x ' @ y) = e. [para(486(a,1),179(a,1,1))]. given #116 (A,wt=14): 81 x ' * y * x * y ' = x @ y '. [para(37(a,1),10(a,1,2))]. given #117 (F,wt=19): 1548 (C @ A) * (C ' * B ' @ A) * C != C * (A @ B) # answer(N). [para(575(a,2),1540(a,1,2,1)),demod(136(10),136(8),88(6),7(10),152(12))]. given #118 (F,wt=19): 1658 (A ' @ C) * (B * C @ A ') * C != C * (A @ B) # answer(N). [para(486(a,2),1546(a,1,1)),demod(599(4,R))]. given #119 (T,wt=10): 593 (x @ y) @ (y @ x ') = e. [para(486(a,1),179(a,1,2)),demod(588(4))]. given #120 (T,wt=10): 594 (x @ y) @ (y ' @ x) = e. [para(486(a,2),179(a,1,1)),demod(588(4))]. given #121 (A,wt=14): 82 x * y ' * x ' * y = x ' @ y. [para(37(a,1),10(a,1))]. given #122 (F,wt=19): 1660 (C @ A) * (B * C @ A ') * C != C * (B @ A ') # answer(N). [para(486(a,2),1546(a,2,2))]. given #123 (F,wt=19): 1766 (A ' @ C) * (A @ B * C) * C != C * (B @ A ') # answer(N). [para(486(a,2),1662(a,2,2))]. given #124 (T,wt=10): 595 (x @ y) @ (x @ y ') = e. [para(486(a,2),179(a,1,2))]. given #125 (T,wt=10): 606 (x @ y ') @ x * y = e. [para(486(a,2),364(a,1,1))]. given #126 (A,wt=18): 86 x ' * y * x * y ' * z = (x @ y ') * z. [para(37(a,1),14(a,1,2))]. given #127 (F,wt=20): 1541 (A @ B * C * A ') * C * (C @ A) != C * (A @ B) # answer(N). [back_demod(1026),demod(1494(13))]. given #128 (F,wt=18): 1938 (B * C @ A ') * C * (C @ A) != C * (A @ B) # answer(N). [para(486(a,2),1541(a,1,1)),demod(816(9))]. given #129 (T,wt=10): 662 (x @ y) @ x * y ' = e. [para(575(a,1),364(a,1,1))]. given #130 (T,wt=10): 686 (x @ y) @ y * x ' = e. [para(486(a,1),378(a,1,1))]. given #131 (A,wt=18): 87 (x ' @ y) * z = x * y ' * x ' * y * z. [para(37(a,1),14(a,1)),flip(a)]. given #132 (F,wt=17): 1944 (A @ B * C) * C * (C @ A) != C * (A @ B) # answer(N). [para(486(a,1),1938(a,1,1))]. given #133 (F,wt=18): 2070 (A @ B * C) * A ' * C * A != C * (A @ B) # answer(N). [para(38(a,2),1944(a,1,2))]. given #134 (T,wt=10): 689 (x ' @ y) @ y * x = e. [para(575(a,2),378(a,1,1))]. given #135 (T,wt=10): 727 x @ y * x * y ' = e. [para(13(a,1),407(a,1,1)),demod(7(3))]. given #136 (A,wt=14): 92 x ' * y ' * x = (x @ y) * y '. [para(79(a,1),14(a,1,2,2,2)),demod(40(4))]. given #137 (F,wt=18): 2071 (A @ B * C) * C * (A ' @ C) != C * (A @ B) # answer(N). [para(486(a,2),1944(a,1,2,2)),demod(599(10,R))]. given #138 (F,wt=18): 2072 C * (B @ A ') != (A @ B * C) * C * (C @ A) # answer(N). [para(486(a,2),1944(a,2,2)),flip(a)]. given #139 (T,wt=10): 728 x * y * x ' @ y = e. [para(13(a,1),407(a,1,2)),demod(7(3))]. given #140 (T,wt=10): 1227 x * y @ (x @ y ') = e. [para(466(a,1),191(a,2)),demod(137(3),661(4))]. given #141 (A,wt=19): 95 x * y * y * x * z = y * x * x * y * z. [para(8(a,1),19(a,1,2,2)),demod(8(8))]. given #142 (F,wt=19): 1941 (C ' * B ' @ A) * C * (C @ A) != C * (A @ B) # answer(N). [para(575(a,2),1541(a,1,1)),demod(136(7),136(5),88(3),7(7),152(9))]. given #143 (F,wt=19): 1943 A ' * (B * C @ A ') * C * A != C * (A @ B) # answer(N). [para(38(a,2),1938(a,1,2)),demod(1394(13))]. given #144 (T,wt=10): 1240 x * y @ (y ' @ x) = e. [para(599(a,2),466(a,1,2))]. given #145 (T,wt=11): 260 x @ y * x ' = y @ x '. [para(88(a,1),226(a,1,1))]. given #146 (A,wt=22): 96 x ' * y * z * y = y * x ' * z * x ' * y * x. [para(9(a,1),19(a,1,2,2,2,2)),demod(40(3))]. given #147 (F,wt=19): 1946 (B * C @ A ') * C * (A ' @ C) != C * (A @ B) # answer(N). [para(486(a,2),1938(a,1,2,2)),demod(599(11,R))]. given #148 (F,wt=19): 1947 (B * C @ A ') * C * (C @ A) != C * (B @ A ') # answer(N). [para(486(a,2),1938(a,2,2))]. given #149 (T,wt=11): 328 x * y ' @ y * x ' = e. [para(88(a,1),221(a,1,1,1))]. given #150 (T,wt=11): 329 x ' * y @ y ' * x = e. [para(88(a,1),221(a,1,1,2))]. given #151 (A,wt=19): 99 x ' * y ' * z * (y @ x) = y ' * x ' * z. [para(10(a,1),19(a,1,2,2,2)),demod(13(12),9(10),40(10))]. ============================== PROOF ================================= % Proof 1 at 0.37 (+ 0.01) seconds: N. % Length of proof is 55. % Level of proof is 16. % Maximum clause weight is 23. % Given clauses 151. 4 x @ y = x ' * y ' * x * y. [input]. 7 (x * y) * z = x * y * z. [input]. 8 e * x = x. [input]. 9 x ' * x = e. [input]. 10 x ' * y ' * x * y = x @ y. [copy(4),flip(a)]. 11 x * y * z * y * x = y * x * z * x * y. [input]. 12 (A @ B) * C != C * (A @ B) # answer(N). [input]. 13 x ' * x * y = y. [para(9(a,1),7(a,1,1)),demod(8(2)),flip(a)]. 14 x ' * y ' * x * y * z = (x @ y) * z. [para(10(a,1),7(a,1,1)),demod(7(7),7(6)),flip(a)]. 15 (x * y) ' * z ' * x * y * z = x * y @ z. [para(7(a,1),10(a,1,2,2))]. 19 x * y * z * y * x * u = y * x * z * x * y * u. [para(11(a,1),7(a,1,1)),demod(7(5),7(4),7(3),7(2),7(9),7(8),7(7))]. 23 x * y * y * x = y * x * x * y. [para(8(a,1),11(a,1,2,2)),demod(8(6))]. 25 x * y * (x * y) ' * y * x = y * x * e. [para(9(a,1),11(a,1,2,2)),flip(a)]. 29 x ' ' * e = x. [para(9(a,1),13(a,1,2))]. 37 x ' ' * y = x * y. [para(13(a,1),13(a,1,2))]. 40 x * e = x. [back_demod(29),demod(37(4))]. 42 x * y * (x * y) ' * y * x = y * x. [back_demod(25),demod(40(8))]. 62 e ' = e. [para(40(a,1),9(a,1))]. 70 (x * y) ' * y * x = x * y @ x. [para(13(a,1),15(a,1,2))]. 76 x * y * (x * y @ x) = y * x. [back_demod(42),demod(70(4))]. 79 x * x ' = e. [para(37(a,1),9(a,1))]. 81 x ' * y * x * y ' = x @ y '. [para(37(a,1),10(a,1,2))]. 84 x * x ' * y = y. [para(37(a,1),13(a,1))]. 88 x ' ' = x. [para(37(a,1),40(a,1)),demod(40(2)),flip(a)]. 91 x * y * (x * y) ' = e. [para(79(a,1),7(a,1)),flip(a)]. 94 x * y @ y ' = x * y @ x. [para(79(a,1),15(a,1,2,2,2)),demod(88(4),40(4),70(4)),flip(a)]. 99 x ' * y ' * z * (y @ x) = y ' * x ' * z. [para(10(a,1),19(a,1,2,2,2)),demod(13(12),9(10),40(10))]. 123 x * (y * x) ' = y '. [para(91(a,1),13(a,1,2)),demod(40(3)),flip(a)]. 125 (x @ y) * z * (x ' * y ' * x * y * z) ' = e. [para(14(a,2),91(a,1,2,2,1))]. 136 (x * y) ' = y ' * x '. [para(123(a,1),13(a,1,2)),flip(a)]. 137 (x @ y) ' = y @ x. [para(14(a,2),123(a,1,2,1)),demod(136(7),136(5),136(3),136(2),7(5),88(7),7(6),7(5),88(8),7(7),7(6),7(5),10(6),84(4)),flip(a)]. 146 (x @ y) * (y @ x) = e. [back_demod(125),demod(136(8),136(6),136(4),136(3),7(6),88(8),7(7),7(6),88(9),7(8),7(7),7(6),10(7),84(5))]. 152 x * y @ x = y @ x. [back_demod(70),demod(136(2),7(5),10(5)),flip(a)]. 165 x * y @ y ' = y @ x. [back_demod(94),demod(152(5))]. 166 x * y * (y @ x) = y * x. [back_demod(76),demod(152(2))]. 187 x * y @ x ' = y @ x '. [para(13(a,1),152(a,1,1)),flip(a)]. 191 x ' * y @ x = y @ x. [para(84(a,1),152(a,1,1)),flip(a)]. 193 x @ x * y = x @ y. [para(152(a,1),137(a,1,1)),demod(137(2)),flip(a)]. 210 x ' @ y ' * x * y = x ' @ (x @ y). [para(10(a,1),193(a,1,2)),flip(a)]. 226 x ' @ y * x = y @ x. [para(165(a,1),137(a,1,1)),demod(137(2)),flip(a)]. 240 (x @ y) * y * x = x * y. [para(23(a,1),14(a,1,2,2)),demod(13(6),13(4)),flip(a)]. 260 x @ y * x ' = y @ x '. [para(88(a,1),226(a,1,1))]. 364 (x @ y) @ y * x = e. [para(240(a,1),10(a,1,2,2)),demod(137(2),136(3),7(6),10(6),146(3)),flip(a)]. 366 (x ' @ (x @ y)) * (y @ x ') = x @ y. [para(10(a,1),240(a,2)),demod(210(5),7(8),7(7),81(8))]. 404 (x @ y) @ x = e. [para(84(a,1),364(a,1,2)),demod(191(3))]. 422 x @ (x @ y) = e. [para(404(a,1),137(a,1,1)),demod(62(2)),flip(a)]. 425 (x @ y) * x = x * (x @ y). [para(404(a,1),166(a,1,2,2)),demod(40(3)),flip(a)]. 462 (x @ y) @ x ' = e. [para(422(a,1),165(a,2)),demod(425(2),187(4))]. 478 x ' @ (x @ y) = e. [para(462(a,1),137(a,1,1)),demod(62(2)),flip(a)]. 486 x @ y ' = y @ x. [back_demod(366),demod(478(3),8(4))]. 583 (B @ A ') * C != C * (A @ B) # answer(N). [para(486(a,2),12(a,1,1))]. 591 x ' @ y ' = x @ y. [para(486(a,2),152(a,1)),demod(136(2),260(4))]. 656 (B @ A ') * C != C * (B @ A ') # answer(N). [para(486(a,2),583(a,2,2))]. 2416 (x @ y) * z = z * (x @ y). [para(99(a,2),14(a,1,2,2)),demod(88(2),88(2),84(7),84(5),591(5)),flip(a)]. 2417 $F # answer(N). [resolve(2416,a,656,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=151. Generated=14623. Kept=2410. proofs=1. Usable=130. Sos=1803. Demods=1161. Denials=0. Limbo=9, Disabled=473. Hints=0. Weight_deleted=3499. Literals_deleted=0. Forward_subsumed=8714. Back_subsumed=44. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=1459 (2 lex), Back_demodulated=423. Back_unit_deleted=0. Demod_attempts=244598. Demod_rewrites=44267. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. Megabytes=2.05. User_CPU=0.37, System_CPU=0.01, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 13128 exit (max_proofs) Mon Jun 19 16:41:41 2006