============================== Prover9 =============================== Prover9 (32) version August-2006A, August 2006. Process 11363 was started by mccune on cleo.thornwood, Sat Aug 12 21:00:03 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). formulas(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 formulas(sos). x * y * z * y * x = y * x * z * x * y. end_of_list. formulas(sos). (A @ B) * C != C * (A @ B) # answer(N). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). (x * y) * z = x * y * z. [assumption]. e * x = x. [assumption]. x' * x = e. [assumption]. x @ y = x' * y' * x * y. [assumption]. x * y * z * y * x = y * x * z * x * y. [assumption]. (A @ B) * C != C * (A @ B) # answer(N). [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= 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: formulas(usable). end_of_list. formulas(sos). 1 (x * y) * z = x * y * z. [assumption]. 2 e * x = x. [assumption]. 3 x' * x = e. [assumption]. 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. 6 x * y * z * y * x = y * x * z * x * y. [assumption]. 7 (A @ B) * C != C * (A @ B) # answer(N). [assumption]. end_of_list. formulas(demodulators). 1 (x * y) * z = x * y * z. [assumption]. 2 e * x = x. [assumption]. 3 x' * x = e. [assumption]. 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=11): 1 (x * y) * z = x * y * z. [assumption]. given #2 (I,wt=5): 2 e * x = x. [assumption]. given #3 (I,wt=6): 3 x' * x = e. [assumption]. given #4 (I,wt=13): 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. given #5 (I,wt=19): 6 x * y * z * y * x = y * x * z * x * y. [assumption]. given #6 (I,wt=11): 7 (A @ B) * C != C * (A @ B) # answer(N). [assumption]. given #7 (F,wt=5): 11 e @ x = e. [para(2(a,1),5(a,1,2,2)),rewrite(3(4),3(4)),flip(a)]. given #8 (F,wt=6): 12 x' @ x = e. [para(3(a,1),5(a,1,2,2)),rewrite(8(6)),flip(a)]. given #9 (T,wt=8): 8 x' * x * y = y. [para(3(a,1),1(a,1,1)),rewrite(2(2)),flip(a)]. given #10 (T,wt=5): 26 x @ x = e. [para(8(a,1),5(a,1,2)),rewrite(3(2)),flip(a)]. given #11 (A,wt=17): 9 x' * y' * x * y * z = (x @ y) * z. [para(5(a,1),1(a,1,1)),rewrite(1(7),1(6)),flip(a)]. given #12 (F,wt=17): 51 A' * B' * A * B * C != C * (A @ B) # answer(N). [para(9(a,2),7(a,1))]. given #13 (F,wt=5): 35 x * e = x. [back_rewrite(24),rewrite(32(4))]. given #14 (T,wt=4): 57 e' = e. [para(35(a,1),3(a,1))]. given #15 (T,wt=5): 58 x @ e = e. [para(35(a,1),5(a,1,2,2)),rewrite(57(3),2(3),3(2)),flip(a)]. given #16 (A,wt=19): 10 (x * y)' * z' * x * y * z = x * y @ z. [para(1(a,1),5(a,1,2,2))]. given #17 (F,wt=7): 69 x * x @ x = e. [para(10(a,1),10(a,1,2)),rewrite(3(2),57(2),2(4),3(4),11(5))]. given #18 (F,wt=9): 32 x'' * y = x * y. [para(8(a,1),8(a,1,2))]. given #19 (T,wt=5): 83 x'' = x. [para(32(a,1),35(a,1)),rewrite(35(2)),flip(a)]. given #20 (T,wt=6): 74 x * x' = e. [para(32(a,1),3(a,1))]. given #21 (A,wt=23): 14 x * y * z * y * x * u = y * x * z * x * y * u. [para(6(a,1),1(a,1,1)),rewrite(1(5),1(4),1(3),1(2),1(9),1(8),1(7))]. given #22 (F,wt=6): 85 x @ x' = e. [para(83(a,1),12(a,1,1))]. given #23 (F,wt=8): 79 x * x' * y = y. [para(32(a,1),8(a,1))]. given #24 (T,wt=10): 86 x * y * (x * y)' = e. [para(74(a,1),1(a,1)),flip(a)]. given #25 (T,wt=9): 118 x * (y * x)' = y'. [para(86(a,1),8(a,1,2)),rewrite(35(3)),flip(a)]. given #26 (A,wt=23): 15 x * y * z * u * z * y = x * z * y * u * y * z. [para(6(a,1),1(a,2,2)),rewrite(1(5))]. given #27 (F,wt=8): 132 (x @ y)' = y @ x. [para(9(a,2),118(a,1,2,1)),rewrite(131(7),131(5),131(3),131(2),1(5),83(7),1(6),1(5),83(8),1(7),1(6),1(5),5(6),79(4)),flip(a)]. given #28 (F,wt=9): 141 (x @ y) * (y @ x) = e. [back_rewrite(120),rewrite(131(8),131(6),131(4),131(3),1(6),83(8),1(7),1(6),83(9),1(8),1(7),1(6),5(7),79(5))]. given #29 (T,wt=9): 147 x * y @ x = y @ x. [back_rewrite(65),rewrite(131(2),1(5),5(5)),flip(a)]. given #30 (T,wt=9): 174 (x @ y) @ (y @ x) = e. [para(132(a,1),12(a,1,1))]. given #31 (A,wt=23): 16 x * y * z * u * y * x = y * x * z * u * x * y. [para(1(a,1),6(a,1,2,2)),rewrite(1(8))]. given #32 (F,wt=9): 188 x @ x * y = x @ y. [para(147(a,1),132(a,1,1)),rewrite(132(2)),flip(a)]. given #33 (F,wt=10): 131 (x * y)' = y' * x'. [para(118(a,1),8(a,1,2)),flip(a)]. given #34 (T,wt=10): 160 x * y @ y' = y @ x. [back_rewrite(89),rewrite(147(5))]. given #35 (T,wt=10): 186 x' * y @ x = y @ x. [para(79(a,1),147(a,1,1)),flip(a)]. given #36 (A,wt=15): 18 x * y * y * x = y * x * x * y. [para(2(a,1),6(a,1,2,2)),rewrite(2(6))]. given #37 (F,wt=10): 210 x @ x' * y = x @ y. [para(79(a,1),188(a,1,2)),flip(a)]. given #38 (F,wt=10): 221 x' @ y * x = y @ x. [para(160(a,1),132(a,1,1)),rewrite(132(2)),flip(a)]. given #39 (T,wt=11): 154 x' @ x * y = x' @ y. [back_rewrite(34),rewrite(131(2),1(4),77(5)),flip(a)]. given #40 (T,wt=11): 161 x * y * (y @ x) = y * x. [back_rewrite(71),rewrite(147(2))]. given #41 (A,wt=21): 28 x * y * x' * z * y = y * z * x * y * x'. [para(8(a,1),6(a,1,2,2,2)),rewrite(1(5),1(10),1(12),8(13))]. given #42 (F,wt=11): 162 x * y' @ y = y' @ x. [back_rewrite(70),rewrite(147(6))]. given #43 (F,wt=11): 175 (x @ y) * (y @ x) * z = z. [para(132(a,1),8(a,1,1))]. given #44 (T,wt=11): 182 x * y @ x' = y @ x'. [para(8(a,1),147(a,1,1)),flip(a)]. given #45 (T,wt=11): 216 x' * y' @ y * x = e. [para(131(a,1),12(a,1,1))]. given #46 (A,wt=16): 29 x * y * x' * y * x = y * x * y. [para(8(a,1),6(a,1,2,2)),flip(a)]. given #47 (F,wt=11): 217 x * y @ y' * x' = e. [para(131(a,1),85(a,1,2))]. given #48 (F,wt=11): 235 (x @ y) * y * x = x * y. [para(18(a,1),9(a,1,2,2)),rewrite(8(6),8(4)),flip(a)]. given #49 (T,wt=9): 359 (x @ y) @ y * x = e. [para(235(a,1),5(a,1,2,2)),rewrite(132(2),131(3),1(6),5(6),141(3)),flip(a)]. given #50 (T,wt=7): 399 (x @ y) @ x = e. [para(79(a,1),359(a,1,2)),rewrite(186(3))]. given #51 (A,wt=18): 30 x' * y * x * y * x' = y * x' * y. [para(8(a,1),6(a,1,2)),flip(a)]. given #52 (F,wt=7): 417 x @ (x @ y) = e. [para(399(a,1),132(a,1,1)),rewrite(57(2)),flip(a)]. given #53 (F,wt=8): 419 (x @ y) @ y' = e. [para(221(a,1),399(a,1,1))]. given #54 (T,wt=8): 457 (x @ y) @ x' = e. [para(417(a,1),160(a,2)),rewrite(420(2),182(4))]. given #55 (T,wt=7): 478 (x @ y) @ y = e. [para(221(a,1),457(a,1,1)),rewrite(83(3))]. given #56 (A,wt=20): 31 x' * y * x * z * x * y = y * z * y * x. [para(6(a,1),8(a,1,2))]. given #57 (F,wt=7): 486 x @ (y @ x) = e. [para(478(a,1),132(a,1,1)),rewrite(57(2)),flip(a)]. given #58 (F,wt=8): 459 x' @ (y @ x) = e. [para(221(a,1),417(a,1,2))]. given #59 (T,wt=8): 460 (x' @ y) @ x = e. [para(417(a,1),162(a,2)),rewrite(420(4),186(5))]. given #60 (T,wt=8): 466 (x @ y') @ y = e. [para(83(a,1),419(a,1,2))]. given #61 (A,wt=12): 33 x' * y * x = y * (y @ x). [back_rewrite(27),rewrite(32(4)),flip(a)]. given #62 (F,wt=8): 473 x' @ (x @ y) = e. [para(457(a,1),132(a,1,1)),rewrite(57(2)),flip(a)]. given #63 (F,wt=8): 481 x @ y' = y @ x. [back_rewrite(361),rewrite(473(3),2(4))]. given #64 (T,wt=8): 516 x @ (x' @ y) = e. [para(162(a,1),486(a,1,2))]. given #65 (T,wt=8): 519 x @ (y @ x') = e. [para(83(a,1),459(a,1,1))]. given #66 (A,wt=21): 39 x * y' * z' * y * z * u = x * (y @ z) * u. [para(9(a,1),1(a,2,2)),rewrite(1(7))]. given #67 (F,wt=12): 578 (B @ A') * C != C * (A @ B) # answer(N). [para(481(a,2),7(a,1,1))]. given #68 (F,wt=12): 579 C * (B @ A') != (A @ B) * C # answer(N). [para(481(a,2),7(a,2,2)),flip(a)]. given #69 (T,wt=8): 570 x' @ y = y @ x. [para(460(a,1),33(a,2,2)),rewrite(48(4),8(4),35(5)),flip(a)]. given #70 (T,wt=9): 373 (x @ y) @ x * y = e. [para(235(a,1),188(a,1,2)),rewrite(359(6))]. given #71 (A,wt=22): 46 x' * y * x * (y @ z) = (x @ y') * z' * y * z. [para(5(a,1),9(a,1,2,2,2)),rewrite(32(6))]. given #72 (F,wt=13): 651 (B @ A') * C != C * (B @ A') # answer(N). [para(481(a,2),578(a,2,2))]. given #73 (F,wt=17): 650 B' * A * B * A' * C != C * (A @ B) # answer(N). [para(9(a,2),578(a,1)),rewrite(83(5))]. given #74 (T,wt=9): 402 x * y @ y * x = e. [para(359(a,1),147(a,2)),rewrite(1(3),161(3))]. given #75 (T,wt=9): 427 x @ y * x = x @ y. [back_rewrite(163),rewrite(420(3),8(4)),flip(a)]. given #76 (A,wt=12): 48 (x' @ y) * x = x * (y @ x). [para(5(a,1),9(a,1,2)),rewrite(32(4)),flip(a)]. given #77 (F,wt=18): 582 A' * B' * A * B * C != C * (B @ A') # answer(N). [para(481(a,2),51(a,2,2))]. given #78 (F,wt=18): 717 B' * A * B * A' * C != C * (B @ A') # answer(N). [para(9(a,2),651(a,1)),rewrite(83(5))]. given #79 (T,wt=9): 586 x' @ y' = x @ y. [para(481(a,2),147(a,1)),rewrite(131(2),255(4))]. given #80 (T,wt=9): 592 x * y @ y = x @ y. [para(481(a,2),221(a,1)),rewrite(83(3))]. given #81 (A,wt=15): 49 (x @ y) * z * y * x = z * x * y. [para(6(a,1),9(a,1,2,2)),rewrite(8(7),8(5)),flip(a)]. given #82 (F,wt=21): 841 A' * B' * (B @ C) * A * C * B != C * (A @ B) # answer(N). [para(49(a,2),51(a,1,2,2))]. given #83 (F,wt=21): 901 (A @ B * A' * C) * A' * C * A != C * (A @ B) # answer(N). [para(49(a,2),650(a,1)),rewrite(1(18),1(17),8(19))]. given #84 (T,wt=9): 594 x' @ y = x @ y'. [para(481(a,2),162(a,1)),rewrite(131(3),83(2),188(3)),flip(a)]. given #85 (T,wt=10): 412 x' * y * x @ y = e. [back_rewrite(225),rewrite(399(6))]. given #86 (A,wt=13): 50 x' * y = (y @ x) * y * x'. [para(6(a,1),9(a,1,2)),rewrite(8(6),8(5))]. given #87 (F,wt=20): 919 (A @ B * A' * C) * C * (C @ A) != C * (A @ B) # answer(N). [para(33(a,1),901(a,1,2))]. given #88 (F,wt=20): 922 (C @ A) * (A @ B * A' * C) * C != C * (A @ B) # answer(N). [para(49(a,2),901(a,1)),rewrite(221(6),1(17),74(16),35(14))]. given #89 (T,wt=10): 418 (x @ y) @ y' * x = e. [para(186(a,1),399(a,1,1))]. given #90 (T,wt=10): 421 (x @ y') @ y * x = e. [para(182(a,1),399(a,1,1))]. given #91 (A,wt=16): 52 x' * y * x * z = y * (y @ x) * z. [para(9(a,1),8(a,1,2)),rewrite(32(5)),flip(a)]. given #92 (F,wt=21): 1007 B' * A * B * (C @ A) * C * A' != C * (A @ B) # answer(N). [para(50(a,1),650(a,1,2,2,2))]. given #93 (F,wt=20): 1191 A * (A @ B) * (C @ A) * C * A' != C * (A @ B) # answer(N). [para(52(a,1),1007(a,1))]. given #94 (T,wt=10): 422 x @ y' * x * y = e. [back_rewrite(244),rewrite(417(6))]. given #95 (T,wt=10): 461 x * y @ (y @ x') = e. [para(182(a,1),417(a,1,2))]. given #96 (A,wt=17): 54 x' * y * x * z = (x @ y') * y * z. [para(8(a,1),9(a,1,2,2,2)),rewrite(32(5))]. given #97 (F,wt=17): 1250 A' * (B @ A') * A * C != C * (A @ B) # answer(N). [para(54(a,1),51(a,1,2))]. given #98 (F,wt=18): 1300 A' * (B @ A') * A * C != C * (B @ A') # answer(N). [para(54(a,1),582(a,1,2))]. given #99 (T,wt=10): 471 (x @ y) * (x @ y') = e. [para(457(a,1),5(a,2)),rewrite(132(2),83(3),390(5))]. given #100 (T,wt=10): 477 (x @ y) @ x' * y = e. [para(186(a,1),457(a,1,1)),rewrite(131(4),83(4))]. given #101 (A,wt=16): 56 (x' @ y) * x * z = x * (y @ x) * z. [para(9(a,1),9(a,1,2)),rewrite(32(5)),flip(a)]. given #102 (F,wt=20): 1504 A * (A @ B) * C * (C @ A) * A' != C * (A @ B) # answer(N). [back_rewrite(1191),rewrite(1430(12))]. given #103 (F,wt=20): 1535 (C @ A) * (A @ B * C * A') * C != C * (A @ B) # answer(N). [back_rewrite(1027),rewrite(1489(16))]. given #104 (T,wt=10): 487 (x' @ y) @ x * y = e. [para(154(a,1),478(a,1,1))]. given #105 (T,wt=10): 515 x * y @ (x' @ y) = e. [para(154(a,1),486(a,1,2))]. given #106 (A,wt=18): 63 x' * y * z * x = y * z * (y * z @ x). [para(10(a,1),8(a,1,2)),rewrite(32(6),1(4)),flip(a)]. given #107 (F,wt=18): 1541 (C @ A) * (B * C @ A') * C != C * (A @ B) # answer(N). [para(481(a,2),1535(a,1,2,1)),rewrite(811(12))]. given #108 (F,wt=17): 1652 (C @ A) * (A @ B * C) * C != C * (A @ B) # answer(N). [para(481(a,1),1541(a,1,2,1))]. given #109 (T,wt=10): 523 (x @ y') * (x @ y) = e. [para(460(a,1),5(a,2)),rewrite(132(3),48(6),8(6))]. given #110 (T,wt=10): 584 (x @ y) * (x' @ y) = e. [para(481(a,1),141(a,1,1))]. given #111 (A,wt=21): 68 x' * y' * x * y * z @ u = (x @ y) * z @ u. [para(9(a,2),10(a,2,1)),rewrite(10(9)),flip(a)]. given #112 (F,wt=18): 1657 (A' @ C) * (A @ B * C) * C != C * (A @ B) # answer(N). [para(481(a,2),1652(a,1,1)),rewrite(594(4,R))]. given #113 (F,wt=18): 1658 C * (B @ A') != (C @ A) * (A @ B * C) * C # answer(N). [para(481(a,2),1652(a,2,2)),flip(a)]. given #114 (T,wt=10): 585 (x' @ y) * (x @ y) = e. [para(481(a,1),141(a,1,2))]. given #115 (T,wt=10): 587 (x @ y) @ (x' @ y) = e. [para(481(a,1),174(a,1,1))]. given #116 (A,wt=14): 76 x' * y * x * y' = x @ y'. [para(32(a,1),5(a,1,2))]. given #117 (F,wt=19): 1543 (C @ A) * (C' * B' @ A) * C != C * (A @ B) # answer(N). [para(570(a,2),1535(a,1,2,1)),rewrite(131(10),131(8),83(6),1(10),147(12))]. given #118 (F,wt=19): 1653 (A' @ C) * (B * C @ A') * C != C * (A @ B) # answer(N). [para(481(a,2),1541(a,1,1)),rewrite(594(4,R))]. given #119 (T,wt=10): 588 (x @ y) @ (y @ x') = e. [para(481(a,1),174(a,1,2)),rewrite(583(4))]. given #120 (T,wt=10): 589 (x @ y) @ (y' @ x) = e. [para(481(a,2),174(a,1,1)),rewrite(583(4))]. given #121 (A,wt=14): 77 x * y' * x' * y = x' @ y. [para(32(a,1),5(a,1))]. given #122 (F,wt=19): 1655 (C @ A) * (B * C @ A') * C != C * (B @ A') # answer(N). [para(481(a,2),1541(a,2,2))]. given #123 (F,wt=19): 1761 (A' @ C) * (A @ B * C) * C != C * (B @ A') # answer(N). [para(481(a,2),1657(a,2,2))]. given #124 (T,wt=10): 590 (x @ y) @ (x @ y') = e. [para(481(a,2),174(a,1,2))]. given #125 (T,wt=10): 601 (x @ y') @ x * y = e. [para(481(a,2),359(a,1,1))]. given #126 (A,wt=18): 81 x' * y * x * y' * z = (x @ y') * z. [para(32(a,1),9(a,1,2))]. given #127 (F,wt=20): 1536 (A @ B * C * A') * C * (C @ A) != C * (A @ B) # answer(N). [back_rewrite(1021),rewrite(1489(13))]. given #128 (F,wt=18): 1933 (B * C @ A') * C * (C @ A) != C * (A @ B) # answer(N). [para(481(a,2),1536(a,1,1)),rewrite(811(9))]. given #129 (T,wt=10): 657 (x @ y) @ x * y' = e. [para(570(a,1),359(a,1,1))]. given #130 (T,wt=10): 681 (x @ y) @ y * x' = e. [para(481(a,1),373(a,1,1))]. given #131 (A,wt=18): 82 (x' @ y) * z = x * y' * x' * y * z. [para(32(a,1),9(a,1)),flip(a)]. given #132 (F,wt=17): 1939 (A @ B * C) * C * (C @ A) != C * (A @ B) # answer(N). [para(481(a,1),1933(a,1,1))]. given #133 (F,wt=18): 2065 (A @ B * C) * A' * C * A != C * (A @ B) # answer(N). [para(33(a,2),1939(a,1,2))]. given #134 (T,wt=10): 684 (x' @ y) @ y * x = e. [para(570(a,2),373(a,1,1))]. given #135 (T,wt=10): 722 x @ y * x * y' = e. [para(8(a,1),402(a,1,1)),rewrite(1(3))]. given #136 (A,wt=14): 87 x' * y' * x = (x @ y) * y'. [para(74(a,1),9(a,1,2,2,2)),rewrite(35(4))]. given #137 (F,wt=18): 2066 (A @ B * C) * C * (A' @ C) != C * (A @ B) # answer(N). [para(481(a,2),1939(a,1,2,2)),rewrite(594(10,R))]. given #138 (F,wt=18): 2067 C * (B @ A') != (A @ B * C) * C * (C @ A) # answer(N). [para(481(a,2),1939(a,2,2)),flip(a)]. given #139 (T,wt=10): 723 x * y * x' @ y = e. [para(8(a,1),402(a,1,2)),rewrite(1(3))]. given #140 (T,wt=10): 1222 x * y @ (x @ y') = e. [para(461(a,1),186(a,2)),rewrite(132(3),656(4))]. given #141 (A,wt=19): 90 x * y * y * x * z = y * x * x * y * z. [para(2(a,1),14(a,1,2,2)),rewrite(2(8))]. given #142 (F,wt=19): 1936 (C' * B' @ A) * C * (C @ A) != C * (A @ B) # answer(N). [para(570(a,2),1536(a,1,1)),rewrite(131(7),131(5),83(3),1(7),147(9))]. given #143 (F,wt=19): 1938 A' * (B * C @ A') * C * A != C * (A @ B) # answer(N). [para(33(a,2),1933(a,1,2)),rewrite(1389(13))]. given #144 (T,wt=10): 1235 x * y @ (y' @ x) = e. [para(594(a,2),461(a,1,2))]. given #145 (T,wt=11): 255 x @ y * x' = y @ x'. [para(83(a,1),221(a,1,1))]. given #146 (A,wt=22): 91 x' * y * z * y = y * x' * z * x' * y * x. [para(3(a,1),14(a,1,2,2,2,2)),rewrite(35(3))]. given #147 (F,wt=19): 1941 (B * C @ A') * C * (A' @ C) != C * (A @ B) # answer(N). [para(481(a,2),1933(a,1,2,2)),rewrite(594(11,R))]. given #148 (F,wt=19): 1942 (B * C @ A') * C * (C @ A) != C * (B @ A') # answer(N). [para(481(a,2),1933(a,2,2))]. given #149 (T,wt=11): 323 x * y' @ y * x' = e. [para(83(a,1),216(a,1,1,1))]. given #150 (T,wt=11): 324 x' * y @ y' * x = e. [para(83(a,1),216(a,1,1,2))]. given #151 (A,wt=19): 94 x' * y' * z * (y @ x) = y' * x' * z. [para(5(a,1),14(a,1,2,2,2)),rewrite(8(12),3(10),35(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. 1 (x * y) * z = x * y * z. [assumption]. 2 e * x = x. [assumption]. 3 x' * x = e. [assumption]. 4 x @ y = x' * y' * x * y. [assumption]. 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. 6 x * y * z * y * x = y * x * z * x * y. [assumption]. 7 (A @ B) * C != C * (A @ B) # answer(N). [assumption]. 8 x' * x * y = y. [para(3(a,1),1(a,1,1)),rewrite(2(2)),flip(a)]. 9 x' * y' * x * y * z = (x @ y) * z. [para(5(a,1),1(a,1,1)),rewrite(1(7),1(6)),flip(a)]. 10 (x * y)' * z' * x * y * z = x * y @ z. [para(1(a,1),5(a,1,2,2))]. 14 x * y * z * y * x * u = y * x * z * x * y * u. [para(6(a,1),1(a,1,1)),rewrite(1(5),1(4),1(3),1(2),1(9),1(8),1(7))]. 18 x * y * y * x = y * x * x * y. [para(2(a,1),6(a,1,2,2)),rewrite(2(6))]. 20 x * y * (x * y)' * y * x = y * x * e. [para(3(a,1),6(a,1,2,2)),flip(a)]. 24 x'' * e = x. [para(3(a,1),8(a,1,2))]. 32 x'' * y = x * y. [para(8(a,1),8(a,1,2))]. 35 x * e = x. [back_rewrite(24),rewrite(32(4))]. 37 x * y * (x * y)' * y * x = y * x. [back_rewrite(20),rewrite(35(8))]. 57 e' = e. [para(35(a,1),3(a,1))]. 65 (x * y)' * y * x = x * y @ x. [para(8(a,1),10(a,1,2))]. 71 x * y * (x * y @ x) = y * x. [back_rewrite(37),rewrite(65(4))]. 74 x * x' = e. [para(32(a,1),3(a,1))]. 76 x' * y * x * y' = x @ y'. [para(32(a,1),5(a,1,2))]. 79 x * x' * y = y. [para(32(a,1),8(a,1))]. 83 x'' = x. [para(32(a,1),35(a,1)),rewrite(35(2)),flip(a)]. 86 x * y * (x * y)' = e. [para(74(a,1),1(a,1)),flip(a)]. 89 x * y @ y' = x * y @ x. [para(74(a,1),10(a,1,2,2,2)),rewrite(83(4),35(4),65(4)),flip(a)]. 94 x' * y' * z * (y @ x) = y' * x' * z. [para(5(a,1),14(a,1,2,2,2)),rewrite(8(12),3(10),35(10))]. 118 x * (y * x)' = y'. [para(86(a,1),8(a,1,2)),rewrite(35(3)),flip(a)]. 120 (x @ y) * z * (x' * y' * x * y * z)' = e. [para(9(a,2),86(a,1,2,2,1))]. 131 (x * y)' = y' * x'. [para(118(a,1),8(a,1,2)),flip(a)]. 132 (x @ y)' = y @ x. [para(9(a,2),118(a,1,2,1)),rewrite(131(7),131(5),131(3),131(2),1(5),83(7),1(6),1(5),83(8),1(7),1(6),1(5),5(6),79(4)),flip(a)]. 141 (x @ y) * (y @ x) = e. [back_rewrite(120),rewrite(131(8),131(6),131(4),131(3),1(6),83(8),1(7),1(6),83(9),1(8),1(7),1(6),5(7),79(5))]. 147 x * y @ x = y @ x. [back_rewrite(65),rewrite(131(2),1(5),5(5)),flip(a)]. 160 x * y @ y' = y @ x. [back_rewrite(89),rewrite(147(5))]. 161 x * y * (y @ x) = y * x. [back_rewrite(71),rewrite(147(2))]. 182 x * y @ x' = y @ x'. [para(8(a,1),147(a,1,1)),flip(a)]. 186 x' * y @ x = y @ x. [para(79(a,1),147(a,1,1)),flip(a)]. 188 x @ x * y = x @ y. [para(147(a,1),132(a,1,1)),rewrite(132(2)),flip(a)]. 205 x' @ y' * x * y = x' @ (x @ y). [para(5(a,1),188(a,1,2)),flip(a)]. 221 x' @ y * x = y @ x. [para(160(a,1),132(a,1,1)),rewrite(132(2)),flip(a)]. 235 (x @ y) * y * x = x * y. [para(18(a,1),9(a,1,2,2)),rewrite(8(6),8(4)),flip(a)]. 255 x @ y * x' = y @ x'. [para(83(a,1),221(a,1,1))]. 359 (x @ y) @ y * x = e. [para(235(a,1),5(a,1,2,2)),rewrite(132(2),131(3),1(6),5(6),141(3)),flip(a)]. 361 (x' @ (x @ y)) * (y @ x') = x @ y. [para(5(a,1),235(a,2)),rewrite(205(5),1(8),1(7),76(8))]. 399 (x @ y) @ x = e. [para(79(a,1),359(a,1,2)),rewrite(186(3))]. 417 x @ (x @ y) = e. [para(399(a,1),132(a,1,1)),rewrite(57(2)),flip(a)]. 420 (x @ y) * x = x * (x @ y). [para(399(a,1),161(a,1,2,2)),rewrite(35(3)),flip(a)]. 457 (x @ y) @ x' = e. [para(417(a,1),160(a,2)),rewrite(420(2),182(4))]. 473 x' @ (x @ y) = e. [para(457(a,1),132(a,1,1)),rewrite(57(2)),flip(a)]. 481 x @ y' = y @ x. [back_rewrite(361),rewrite(473(3),2(4))]. 578 (B @ A') * C != C * (A @ B) # answer(N). [para(481(a,2),7(a,1,1))]. 586 x' @ y' = x @ y. [para(481(a,2),147(a,1)),rewrite(131(2),255(4))]. 651 (B @ A') * C != C * (B @ A') # answer(N). [para(481(a,2),578(a,2,2))]. 2411 (x @ y) * z = z * (x @ y). [para(94(a,2),9(a,1,2,2)),rewrite(83(2),83(2),79(7),79(5),586(5)),flip(a)]. 2412 $F # answer(N). [resolve(2411,a,651,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=151. Generated=14623. Kept=2410. proofs=1. Usable=130. Sos=1803. Demods=1161. 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=244632. 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 11363 exit (max_proofs) Sat Aug 12 21:00:03 2006