============================== Prover9 =============================== Prover9 (32) version March-2007, March 2007. Process 21004 was started by mccune on cleo, Mon Mar 19 17:01:59 2007 The command was "/home/mccune/bin/prover9 -f cs.in DE.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file cs.in op(450,infix,@). op(400,infix_right,*). assign(new_constants,1). assign(max_weight,25). formulas(sos). x * y != x * z | y = z. y * x != z * x | y = z. (x * y) * z = x * y * z. y * x * (x @ y) = x * y. end_of_list. % Reading from file DE.in formulas(sos). (x @ z) * (y @ z) = x * y @ z. end_of_list. formulas(sos). A * B * C * B * A != B * A * C * A * B # answer(E). 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 != x * z | y = z. [assumption]. x * y != z * y | x = z. [assumption]. (x * y) * z = x * y * z. [assumption]. x * y * (y @ x) = y * x. [assumption]. (x @ y) * (z @ y) = x * z @ y. [assumption]. A * B * C * B * A != B * A * C * A * B # answer(E). [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([ A, B, C, *, @ ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). % set(hyper_resolution). % (nonunit Horn with equality) % set(neg_ur_resolution). % (nonunit Horn with equality) % assign(para_lit_limit, 2). % (nonunit Horn with equality) 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 != x * z | y = z. [assumption]. 2 x * y != z * y | x = z. [assumption]. 3 (x * y) * z = x * y * z. [assumption]. 4 x * y * (y @ x) = y * x. [assumption]. 6 x * y @ z = (x @ z) * (y @ z). [copy(5),flip(a)]. 7 A * B * C * B * A != B * A * C * A * B # answer(E). [assumption]. end_of_list. formulas(demodulators). 3 (x * y) * z = x * y * z. [assumption]. 4 x * y * (y @ x) = y * x. [assumption]. 6 x * y @ z = (x @ z) * (y @ z). [copy(5),flip(a)]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=10): 1 x * y != x * z | y = z. [assumption]. given #2 (I,wt=10): 2 x * y != z * y | x = z. [assumption]. given #3 (I,wt=11): 3 (x * y) * z = x * y * z. [assumption]. given #4 (I,wt=11): 4 x * y * (y @ x) = y * x. [assumption]. given #5 (I,wt=13): 6 x * y @ z = (x @ z) * (y @ z). [copy(5),flip(a)]. given #6 (I,wt=19): 7 A * B * C * B * A != B * A * C * A * B # answer(E). [assumption]. given #7 (A,wt=14): 8 x * y * z != x * y * u | z = u. [para(3(a,1),1(a,1)),rewrite(3(4))]. given #8 (F,wt=23): 18 A * B * C * B * A * x != B * A * C * A * B * x # answer(E). [ur(2,b,7,a),rewrite(3(10),3(9),3(8),3(7),3(20),3(19),3(18),3(17))]. given #9 (F,wt=23): 19 x * A * B * C * B * A != x * B * A * C * A * B # answer(E). [ur(1,b,7,a)]. given #10 (F,wt=23): 23 B * A * C * A * B * (A @ B) != A * B * C * A * B # answer(E). [para(4(a,1),18(a,1,2,2,2)),flip(a)]. given #11 (F,wt=23): 24 A * B * C * B * A * (B @ A) != B * A * C * B * A # answer(E). [para(4(a,1),18(a,2,2,2,2))]. given #12 (T,wt=7): 10 x * (x @ x) = x. [hyper(1,a,4,a)]. given #13 (T,wt=10): 25 x * y != x | x @ x = y. [para(10(a,1),1(a,1)),flip(a)]. given #14 (T,wt=10): 26 x * (y @ y) != y | y = x. [para(10(a,1),2(a,1)),flip(a)]. given #15 (T,wt=10): 27 x * (y @ y) != y | x = y. [para(10(a,1),2(a,2))]. given #16 (A,wt=14): 9 x * y * z != u * z | x * y = u. [para(3(a,1),2(a,1))]. given #17 (F,wt=23): 32 B * A * C * A * B * (A @ A) != A * B * C * B * A # answer(E). [para(10(a,1),18(a,1,2,2,2,2)),flip(a)]. given #18 (F,wt=23): 33 A * B * C * B * A * (B @ B) != B * A * C * A * B # answer(E). [para(10(a,1),18(a,2,2,2,2,2))]. given #19 (T,wt=11): 28 x * (x @ x) * y = x * y. [para(10(a,1),3(a,1,1)),flip(a)]. given #20 (T,wt=7): 44 (x @ x) * y = y. [hyper(8,a,28,a)]. given #21 (T,wt=9): 51 x * ((y @ y) @ x) = x. [para(44(a,1),4(a,1,2)),rewrite(44(5))]. given #22 (T,wt=9): 58 (x @ x) @ y = y @ y. [hyper(25,a,51,a),flip(a)]. given #23 (A,wt=14): 11 x * y != z * x | z * (z @ x) = y. [para(4(a,1),1(a,1)),flip(a)]. given #24 (F,wt=25): 67 B * A * C * A * B * ((x @ x) @ A) != A * B * C * B * A # answer(E). [para(51(a,1),18(a,1,2,2,2,2)),flip(a)]. given #25 (F,wt=25): 68 A * B * C * B * A * ((x @ x) @ B) != B * A * C * A * B # answer(E). [para(51(a,1),18(a,2,2,2,2,2))]. given #26 (T,wt=6): 84 x != y | y = x. [para(10(a,1),11(a,2)),rewrite(44(2),52(4),10(3))]. given #27 (T,wt=9): 75 ((x @ x) @ y) * z = z. [para(58(a,2),44(a,1,1))]. given #28 (T,wt=9): 79 x * (x @ x * x) = x. [hyper(11,a,3,a)]. given #29 (T,wt=9): 98 x @ x * x = x @ x. [hyper(25,a,79,a),flip(a)]. given #30 (A,wt=14): 12 x * y * (y @ z) != y * z | z = x. [para(4(a,1),2(a,1)),flip(a)]. given #31 (T,wt=10): 50 x * y != y | z @ z = x. [para(44(a,1),2(a,1)),flip(a)]. NOTE: New constant: x @ x = c_0. [new_symbol(106)]. NOTE: New Function symbol precedence: lex([ A, B, C, c_0, *, @ ]). given #32 (T,wt=5): 108 x @ x = c_0. [new_symbol(106)]. given #33 (T,wt=5): 110 c_0 @ x = c_0. [back_rewrite(105),rewrite(108(1),108(3))]. given #34 (T,wt=5): 115 c_0 * x = x. [back_rewrite(96),rewrite(108(1),110(2),110(2))]. given #35 (A,wt=14): 13 x * y * (y @ z) != y * z | x = z. [para(4(a,1),2(a,2))]. given #36 (T,wt=5): 121 x * c_0 = x. [back_rewrite(76),rewrite(108(1),110(2),110(2))]. given #37 (T,wt=7): 113 x @ x * x = c_0. [back_rewrite(98),rewrite(108(3))]. given #38 (T,wt=7): 125 x * (x @ c_0) = x. [back_rewrite(119),rewrite(121(5))]. given #39 (T,wt=8): 114 x * y != x | c_0 = y. [back_rewrite(97),rewrite(108(3),110(4),110(4))]. given #40 (A,wt=15): 14 x * y * (y @ x) * z = y * x * z. [para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)]. given #41 (T,wt=5): 142 x @ c_0 = c_0. [hyper(114,a,125,a),flip(a)]. given #42 (T,wt=8): 118 x * y != y | c_0 = x. [back_rewrite(89),rewrite(108(3),110(4))]. given #43 (T,wt=10): 101 x * y != y * y | y = x. [para(10(a,1),12(a,1,2))]. given #44 (T,wt=12): 111 x * (x @ y) != x * y | c_0 = y. [back_rewrite(104),rewrite(108(5),110(6))]. given #45 (A,wt=17): 15 x * y * z * (z @ x * y) = z * x * y. [para(4(a,1),3(a,1)),flip(a)]. given #46 (F,wt=25): 169 B * A * C * A * B * (A @ C * B) != A * B * A * C * B # answer(E). [para(15(a,1),18(a,1,2,2)),flip(a)]. given #47 (F,wt=25): 170 A * B * C * B * A * (B @ C * A) != B * A * B * C * A # answer(E). [para(15(a,1),18(a,2,2,2))]. given #48 (T,wt=12): 116 x * y * z != z | x * y = c_0. [back_rewrite(94),rewrite(108(4),110(5)),flip(b)]. given #49 (T,wt=12): 120 x * y != y | x * (x @ y) = c_0. [back_rewrite(85),rewrite(108(3),110(4)),flip(b)]. given #50 (T,wt=12): 124 x * y * z != x * y | c_0 = z. [back_rewrite(66),rewrite(108(5),110(6))]. given #51 (T,wt=12): 180 x @ y != x * y | y * x = c_0. [para(4(a,1),116(a,1)),flip(a)]. given #52 (A,wt=19): 16 x * y * z * (y @ x) * (z @ x) = y * z * x. [para(3(a,1),4(a,1,2)),rewrite(6(2),3(8))]. given #53 (T,wt=12): 189 x * y != y * x | x @ y = c_0. [para(4(a,1),124(a,1)),flip(b)]. given #54 (T,wt=13): 123 (x @ x * y) * (y @ x * y) = c_0. [back_rewrite(72),rewrite(108(1),110(3)),flip(a)]. given #55 (T,wt=13): 163 x * y * (y @ y * x) = y * x. [hyper(1,a,15,a)]. given #56 (T,wt=13): 220 x * (x @ x * y) = x * (x @ y). [hyper(11,a,163,a),flip(a)]. given #57 (A,wt=21): 17 (x @ y) * (z @ y) * ((z @ x) @ y) = (z @ y) * (x @ y). [para(4(a,1),6(a,1,1)),rewrite(6(2),6(7)),flip(a)]. given #58 (T,wt=9): 233 x @ x * y = x @ y. [hyper(1,a,220,a)]. given #59 (T,wt=11): 248 (x @ y * x) * (y @ x) = c_0. [back_rewrite(232),rewrite(233(4))]. given #60 (T,wt=11): 262 (x @ y) * (y @ x * y) = c_0. [back_rewrite(123),rewrite(233(2))]. given #61 (T,wt=9): 317 (x @ y) @ x * y = c_0. [para(4(a,1),262(a,1,2,2)),rewrite(286(3),6(6),233(4),298(8))]. given #62 (A,wt=18): 20 x * y * z * u != x * y * z * v | u = v. [para(3(a,1),8(a,1,2)),rewrite(3(5))]. given #63 (T,wt=11): 313 (x @ y * x) @ (y @ x) = c_0. [para(248(a,1),189(a,1)),rewrite(262(5)),xx(a)]. given #64 (T,wt=11): 314 (x @ y) @ (y @ x * y) = c_0. [para(248(a,1),189(a,2)),rewrite(262(4)),xx(a)]. given #65 (T,wt=11): 323 (x @ y * x) @ y * x = c_0. [para(4(a,1),317(a,1,2)),rewrite(286(3))]. given #66 (T,wt=11): 333 (x @ y) @ x * x * y = c_0. [para(233(a,1),317(a,1,1))]. given #67 (A,wt=18): 21 x * y * z != x * u * y | u * (u @ y) = z. [para(4(a,1),8(a,1,2)),flip(a)]. given #68 (T,wt=10): 377 x * y != x * z | z = y. [para(115(a,1),21(a,1,2)),rewrite(121(3),142(5),121(5))]. given #69 (T,wt=11): 365 (x @ y * x) @ x * y = c_0. [para(323(a,1),233(a,2)),rewrite(357(6))]. given #70 (T,wt=12): 239 x * (x @ y) != x | x @ y = c_0. [para(220(a,1),114(a,1)),rewrite(233(6)),flip(b)]. given #71 (T,wt=12): 252 x @ y * x != c_0 | y @ x = c_0. [back_rewrite(216),rewrite(233(6))]. given #72 (A,wt=14): 22 x * y * z != y * x | y @ x = z. [para(4(a,1),8(a,1)),flip(a)]. given #73 (T,wt=12): 253 x @ y != c_0 | y @ x * y = c_0. [back_rewrite(214),rewrite(233(2))]. given #74 (T,wt=12): 404 x * y != y * x | y @ x = c_0. [para(121(a,1),22(a,1,2))]. given #75 (T,wt=13): 265 (x @ y) * (y @ x * y) * z = z. [back_rewrite(54),rewrite(233(2))]. given #76 (T,wt=9): 436 ((x @ y) @ z) @ z = c_0. [para(265(a,1),317(a,1,2)),rewrite(434(5))]. given #77 (A,wt=18): 38 x * y * z * u != v * u | x * y * z = v. [para(3(a,1),9(a,1,2))]. given #78 (T,wt=9): 459 x @ ((y @ z) @ x) = c_0. [para(436(a,1),248(a,1,2)),rewrite(450(3),233(4),121(5))]. given #79 (T,wt=11): 480 (x @ y) @ ((x @ y) @ z) = c_0. [para(233(a,1),459(a,1,2)),rewrite(6(5),459(7),121(6))]. given #80 (T,wt=13): 276 (x @ y) * ((x @ y) @ y) = x @ y. [para(108(a,1),17(a,1,1)),rewrite(115(6),108(6),121(7))]. given #81 (T,wt=7): 486 (x @ y) @ y = c_0. [hyper(239,a,276,a)]. given #82 (A,wt=18): 39 x * y * z != u * v * z | x * y = u * v. [para(3(a,1),9(a,2))]. given #83 (T,wt=7): 494 x @ (y @ x) = c_0. [hyper(253,a,486,a),rewrite(487(2),233(3))]. given #84 (T,wt=7): 502 x @ (x @ y) = c_0. [back_rewrite(335),rewrite(494(2),115(4))]. given #85 (T,wt=9): 507 x @ (y @ x * y) = c_0. [back_rewrite(396),rewrite(502(3),115(5))]. given #86 (T,wt=11): 487 (x @ y) * y = y * (x @ y). [para(276(a,1),4(a,1,2)),flip(a)]. given #87 (A,wt=18): 40 x * y * (y @ z) != u * y * z | u * z = x. [para(4(a,1),9(a,1,2)),flip(a)]. given #88 (T,wt=10): 576 x * y != z * y | z = x. [para(121(a,1),40(a,2,2)),rewrite(142(2),121(2),121(5))]. given #89 (T,wt=11): 501 (x @ y) @ y * (x @ y) = c_0. [para(486(a,1),233(a,2)),rewrite(487(3))]. given #90 (T,wt=11): 520 x @ (y @ x) * (z @ x) = c_0. [para(6(a,1),494(a,1,2))]. given #91 (T,wt=11): 526 (x @ y) @ x * (x @ y) = c_0. [hyper(253,a,502,a)]. given #92 (A,wt=14): 41 x * (y @ z) != y * z | z * y = x. [para(4(a,1),9(a,1)),flip(a)]. given #93 (T,wt=11): 527 (x @ y) * x = x * (x @ y). [para(502(a,1),4(a,1,2,2)),rewrite(121(3))]. given #94 (T,wt=7): 598 (x @ y) @ x = c_0. [hyper(189,a,527,a)]. given #95 (T,wt=11): 593 x @ (x @ y) * (x @ y) = c_0. [para(526(a,1),248(a,1,2)),rewrite(530(6),6(7),233(5),592(10),121(6),121(6))]. given #96 (T,wt=12): 522 x * (y @ x) != x | y @ x = c_0. [para(494(a,1),111(a,1,2)),rewrite(121(2)),flip(a),flip(b)]. given #97 (A,wt=18): 42 x * y * z * (z @ u) != z * u | x * y = u. [para(4(a,1),9(a,2))]. given #98 (T,wt=13): 286 x @ y * (y @ x) = x @ y * x. [para(4(a,1),233(a,1,2)),flip(a)]. given #99 (T,wt=9): 636 (x @ y * x) @ y = c_0. [para(507(a,1),286(a,1,2,2)),rewrite(121(4),540(9))]. given #100 (T,wt=13): 298 (x @ y * x) * (y @ x) * z = z. [para(248(a,1),3(a,1,1)),rewrite(115(2)),flip(a)]. given #101 (T,wt=13): 318 x * y * (y @ x * y) = y * x. [para(262(a,1),14(a,1,2,2)),rewrite(121(2)),flip(a)]. given #102 (A,wt=20): 80 x * y * z != u * x * y | u * (u @ x * y) = z. [para(3(a,1),11(a,1))]. given #103 (T,wt=9): 688 x @ y * x = x @ y. [hyper(22,a,318,a),flip(a)]. given #104 (T,wt=9): 698 (x @ y) * (y @ x) = c_0. [para(318(a,1),248(a,1,1,2)),rewrite(688(2),6(4),233(2),317(4),121(3),688(3),286(4),688(3))]. given #105 (T,wt=9): 700 (x @ y) @ (y @ x) = c_0. [para(318(a,1),313(a,1,1,2)),rewrite(688(2),6(4),233(2),317(4),121(3),688(3),286(4),688(3))]. given #106 (T,wt=10): 704 x @ y != c_0 | y @ x = c_0. [para(318(a,1),252(a,1,2)),rewrite(688(2),6(4),233(2),317(4),121(3),688(5),286(6),688(5))]. given #107 (A,wt=22): 81 x * y * z != z * u | x * y * (x @ z) * (y @ z) = u. [para(3(a,1),11(a,2)),rewrite(6(7),3(9)),flip(a)]. given #108 (T,wt=11): 706 (x @ y) * (y @ x) * z = z. [para(318(a,1),265(a,1,2,1,2)),rewrite(688(2),286(3),688(2),688(3),6(5),233(3),317(5),121(4))]. given #109 (T,wt=11): 716 (x @ y) @ z = z @ (y @ x). [back_rewrite(686),rewrite(688(4),688(5))]. given #110 (T,wt=11): 721 (x @ y) @ ((y @ x) @ z) = c_0. [back_rewrite(681),rewrite(688(2))]. given #111 (T,wt=11): 730 (x @ y) @ (z @ (y @ x)) = c_0. [back_rewrite(672),rewrite(688(5),716(7),6(7),494(4),6(6),502(4),115(7),115(6))]. given #112 (A,wt=18): 82 x * y != z * y | z * (z @ y) = x * (x @ y). [para(4(a,1),11(a,1))]. given #113 (T,wt=11): 754 (x @ y) @ y * (y @ x) = c_0. [back_rewrite(635),rewrite(688(2))]. given #114 (T,wt=11): 777 x @ y * (y @ x) = x @ y. [back_rewrite(286),rewrite(688(5))]. given #115 (T,wt=11): 800 (x @ y) @ (x @ y * y) = c_0. [back_rewrite(783),rewrite(786(4))]. given #116 (T,wt=11): 812 (x @ y) @ (y @ x * x) = c_0. [back_rewrite(356),rewrite(786(4))]. given #117 (A,wt=22): 99 x * y * z * (y @ u) * (z @ u) != y * z * u | u = x. [para(3(a,1),12(a,1,2)),rewrite(6(2),3(8))]. given #118 (T,wt=12): 741 (x @ y) * z != z | y @ x = c_0. [back_rewrite(660),rewrite(688(5))]. given #119 (T,wt=12): 743 x @ y != z | (y @ x) * z = c_0. [back_rewrite(657),rewrite(688(2))]. given #120 (T,wt=12): 756 x * y != c_0 | y @ x = y * x. [back_rewrite(594),rewrite(688(5))]. given #121 (T,wt=12): 767 x * (y @ z) != x | z @ y = c_0. [back_rewrite(312),rewrite(688(2))]. given #122 (A,wt=22): 126 x * y * z * (y @ u) * (z @ u) != y * z * u | x = u. [para(3(a,1),13(a,1,2)),rewrite(6(2),3(8))]. given #123 (T,wt=12): 768 x @ y != z | z * (y @ x) = c_0. [back_rewrite(310),rewrite(688(4))]. given #124 (T,wt=12): 774 x * (y @ z) != c_0 | z @ y = x. [back_rewrite(297),rewrite(688(6))]. given #125 (T,wt=12): 775 (x @ y) * z != c_0 | y @ x = z. [back_rewrite(296),rewrite(688(2))]. given #126 (T,wt=12): 944 (x @ y) * z != z | x @ y = c_0. [para(706(a,1),741(a,1)),flip(a)]. given #127 (A,wt=18): 143 x * y * z != y * u | x * (x @ y) * z = u. [para(14(a,1),1(a,1))]. given #128 (T,wt=12): 974 c_0 != x | (y @ z) * x = y @ z. [para(706(a,1),775(a,1)),flip(a),flip(b)]. given #129 (T,wt=13): 402 (x @ y) @ (z @ y) = (x @ z) @ y. [hyper(22,a,17,a)]. given #130 (T,wt=7): 1035 (y @ z) @ x = c_0. [para(402(a,2),522(a,1,2)),rewrite(1020(3),121(2)),xx(a)]. given #131 (T,wt=7): 1038 x @ (y @ z) = c_0. [para(402(a,2),698(a,1,1)),rewrite(1020(3),115(4))]. given #132 (A,wt=18): 144 x * y * (y @ z) * u != y * z * u | z = x. [para(14(a,1),2(a,1)),flip(a)]. given #133 (T,wt=11): 1024 (x @ y) * z * (y @ x) = z. [para(402(a,2),487(a,1,1)),rewrite(1020(3),115(2),708(3)),flip(a)]. given #134 (T,wt=10): 1121 x * y != x | y @ x = y. [para(1024(a,1),12(a,1)),flip(a),flip(b)]. given #135 (T,wt=11): 1048 (x @ y) * z = z * (x @ y). [back_rewrite(999),rewrite(1038(4),121(3)),flip(a)]. given #136 (T,wt=11): 1060 x @ (y @ z) * (u @ z) = c_0. [back_rewrite(841),rewrite(1035(3)),flip(a)]. given #137 (A,wt=18): 145 x * y * (y @ z) * u != y * z * u | x = z. [para(14(a,1),2(a,2))]. given #138 (T,wt=12): 1073 x * (y @ z) != x | y @ z = c_0. [back_rewrite(977),rewrite(1038(2),121(2)),flip(a)]. given #139 (T,wt=12): 1134 c_0 != x | x * (y @ z) = y @ z. [para(1024(a,1),775(a,1)),flip(a),flip(b)]. given #140 (T,wt=13): 786 x @ y * z * x = x @ y * z. [para(3(a,1),688(a,1,2))]. given #141 (T,wt=11): 1240 x @ y * z = x @ z * y. [para(14(a,1),786(a,1,2)),rewrite(6(5),1035(4),786(4),115(4),6(6),1035(5),115(6))]. given #142 (A,wt=21): 146 x * y * z * (z @ x * y) * u = z * x * y * u. [para(14(a,1),3(a,1)),rewrite(3(2)),flip(a)]. given #143 (F,wt=25): 1263 A * B * C * B * A * (B @ A * C) != B * A * B * C * A # answer(E). [back_rewrite(170),rewrite(1240(10))]. ============================== PROOF ================================= % Proof 1 at 0.18 (+ 0.00) seconds: E. % Length of proof is 80. % Level of proof is 20. % Maximum clause weight is 25. % Given clauses 143. 1 x * y != x * z | y = z. [assumption]. 2 x * y != z * y | x = z. [assumption]. 3 (x * y) * z = x * y * z. [assumption]. 4 x * y * (y @ x) = y * x. [assumption]. 5 (x @ y) * (z @ y) = x * z @ y. [assumption]. 6 x * y @ z = (x @ z) * (y @ z). [copy(5),flip(a)]. 7 A * B * C * B * A != B * A * C * A * B # answer(E). [assumption]. 8 x * y * z != x * y * u | z = u. [para(3(a,1),1(a,1)),rewrite(3(4))]. 9 x * y * z != u * z | x * y = u. [para(3(a,1),2(a,1))]. 10 x * (x @ x) = x. [hyper(1,a,4,a)]. 11 x * y != z * x | z * (z @ x) = y. [para(4(a,1),1(a,1)),flip(a)]. 12 x * y * (y @ z) != y * z | z = x. [para(4(a,1),2(a,1)),flip(a)]. 14 x * y * (y @ x) * z = y * x * z. [para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)]. 15 x * y * z * (z @ x * y) = z * x * y. [para(4(a,1),3(a,1)),flip(a)]. 17 (x @ y) * (z @ y) * ((z @ x) @ y) = (z @ y) * (x @ y). [para(4(a,1),6(a,1,1)),rewrite(6(2),6(7)),flip(a)]. 18 A * B * C * B * A * x != B * A * C * A * B * x # answer(E). [ur(2,b,7,a),rewrite(3(10),3(9),3(8),3(7),3(20),3(19),3(18),3(17))]. 22 x * y * z != y * x | y @ x = z. [para(4(a,1),8(a,1)),flip(a)]. 25 x * y != x | x @ x = y. [para(10(a,1),1(a,1)),flip(a)]. 28 x * (x @ x) * y = x * y. [para(10(a,1),3(a,1,1)),flip(a)]. 41 x * (y @ z) != y * z | z * y = x. [para(4(a,1),9(a,1)),flip(a)]. 44 (x @ x) * y = y. [hyper(8,a,28,a)]. 50 x * y != y | z @ z = x. [para(44(a,1),2(a,1)),flip(a)]. 51 x * ((y @ y) @ x) = x. [para(44(a,1),4(a,1,2)),rewrite(44(5))]. 54 (x @ x * y) * (y @ x * y) * z = z. [para(6(a,1),44(a,1,1)),rewrite(3(6))]. 58 (x @ x) @ y = y @ y. [hyper(25,a,51,a),flip(a)]. 72 (x @ x) @ y * z = (y @ y * z) * (z @ y * z). [para(58(a,2),6(a,1))]. 75 ((x @ x) @ y) * z = z. [para(58(a,2),44(a,1,1))]. 76 x * (((y @ y) @ z) @ x) = x. [para(58(a,2),51(a,1,2,1))]. 88 x * (x @ ((y @ y) @ z)) = x * ((y @ y) @ z). [hyper(11,a,75,a)]. 96 (((x @ x) @ y) @ z) * u = u. [para(58(a,2),75(a,1,1,1))]. 97 x * y != x | ((z @ z) @ u) @ x = y. [para(75(a,1),11(a,2)),rewrite(75(8))]. 104 x * (x @ y) != x * y | (z @ z) @ u = y. [para(75(a,1),12(a,1)),flip(b)]. 105 (x @ x) @ y = z @ z. [hyper(50,a,75,a),flip(a)]. 106 x @ x = y @ y. [hyper(50,a,44,a)]. 108 x @ x = c_0. [new_symbol(106)]. 110 c_0 @ x = c_0. [back_rewrite(105),rewrite(108(1),108(3))]. 111 x * (x @ y) != x * y | c_0 = y. [back_rewrite(104),rewrite(108(5),110(6))]. 114 x * y != x | c_0 = y. [back_rewrite(97),rewrite(108(3),110(4),110(4))]. 115 c_0 * x = x. [back_rewrite(96),rewrite(108(1),110(2),110(2))]. 119 x * (x @ c_0) = x * c_0. [back_rewrite(88),rewrite(108(1),110(2),108(4),110(5))]. 121 x * c_0 = x. [back_rewrite(76),rewrite(108(1),110(2),110(2))]. 123 (x @ x * y) * (y @ x * y) = c_0. [back_rewrite(72),rewrite(108(1),110(3)),flip(a)]. 125 x * (x @ c_0) = x. [back_rewrite(119),rewrite(121(5))]. 142 x @ c_0 = c_0. [hyper(114,a,125,a),flip(a)]. 163 x * y * (y @ y * x) = y * x. [hyper(1,a,15,a)]. 170 A * B * C * B * A * (B @ C * A) != B * A * B * C * A # answer(E). [para(15(a,1),18(a,2,2,2))]. 214 x @ x * y != c_0 | y @ x * y = c_0. [para(123(a,1),114(a,1)),flip(a),flip(b)]. 220 x * (x @ x * y) = x * (x @ y). [hyper(11,a,163,a),flip(a)]. 232 (x @ y * x) * (y @ y * x) = c_0. [para(123(a,1),163(a,1,2,2,2)),rewrite(142(8),121(6),123(10))]. 233 x @ x * y = x @ y. [hyper(1,a,220,a)]. 239 x * (x @ y) != x | x @ y = c_0. [para(220(a,1),114(a,1)),rewrite(233(6)),flip(b)]. 248 (x @ y * x) * (y @ x) = c_0. [back_rewrite(232),rewrite(233(4))]. 253 x @ y != c_0 | y @ x * y = c_0. [back_rewrite(214),rewrite(233(2))]. 262 (x @ y) * (y @ x * y) = c_0. [back_rewrite(123),rewrite(233(2))]. 265 (x @ y) * (y @ x * y) * z = z. [back_rewrite(54),rewrite(233(2))]. 276 (x @ y) * ((x @ y) @ y) = x @ y. [para(108(a,1),17(a,1,1)),rewrite(115(6),108(6),121(7))]. 286 x @ y * (y @ x) = x @ y * x. [para(4(a,1),233(a,1,2)),flip(a)]. 298 (x @ y * x) * (y @ x) * z = z. [para(248(a,1),3(a,1,1)),rewrite(115(2)),flip(a)]. 317 (x @ y) @ x * y = c_0. [para(4(a,1),262(a,1,2,2)),rewrite(286(3),6(6),233(4),298(8))]. 318 x * y * (y @ x * y) = y * x. [para(262(a,1),14(a,1,2,2)),rewrite(121(2)),flip(a)]. 402 (x @ y) @ (z @ y) = (x @ z) @ y. [hyper(22,a,17,a)]. 486 (x @ y) @ y = c_0. [hyper(239,a,276,a)]. 487 (x @ y) * y = y * (x @ y). [para(276(a,1),4(a,1,2)),flip(a)]. 494 x @ (y @ x) = c_0. [hyper(253,a,486,a),rewrite(487(2),233(3))]. 522 x * (y @ x) != x | y @ x = c_0. [para(494(a,1),111(a,1,2)),rewrite(121(2)),flip(a),flip(b)]. 688 x @ y * x = x @ y. [hyper(22,a,318,a),flip(a)]. 698 (x @ y) * (y @ x) = c_0. [para(318(a,1),248(a,1,1,2)),rewrite(688(2),6(4),233(2),317(4),121(3),688(3),286(4),688(3))]. 706 (x @ y) * (y @ x) * z = z. [para(318(a,1),265(a,1,2,1,2)),rewrite(688(2),286(3),688(2),688(3),6(5),233(3),317(5),121(4))]. 708 x * ((y @ z) @ x) = (y @ z) * x * (z @ y). [para(265(a,1),318(a,1,2,2,2)),rewrite(688(3),688(5),6(6),108(6),121(7),3(6),706(7),688(5),3(7))]. 786 x @ y * z * x = x @ y * z. [para(3(a,1),688(a,1,2))]. 999 x * (y @ z) * ((y @ x) @ (z @ x)) = (y @ z) * x. [para(402(a,2),4(a,1,2,2))]. 1020 (x @ y) @ (z @ y) = c_0. [para(494(a,1),402(a,1,2)),rewrite(142(4)),flip(a)]. 1024 (x @ y) * z * (y @ x) = z. [para(402(a,2),487(a,1,1)),rewrite(1020(3),115(2),708(3)),flip(a)]. 1035 (y @ z) @ x = c_0. [para(402(a,2),522(a,1,2)),rewrite(1020(3),121(2)),xx(a)]. 1038 x @ (y @ z) = c_0. [para(402(a,2),698(a,1,1)),rewrite(1020(3),115(4))]. 1048 (x @ y) * z = z * (x @ y). [back_rewrite(999),rewrite(1038(4),121(3)),flip(a)]. 1117 (x @ y * z) * u * (y @ x) * (z @ x) = u. [para(6(a,1),1024(a,1,2,2))]. 1240 x @ y * z = x @ z * y. [para(14(a,1),786(a,1,2)),rewrite(6(5),1035(4),786(4),115(4),6(6),1035(5),115(6))]. 1263 A * B * C * B * A * (B @ A * C) != B * A * B * C * A # answer(E). [back_rewrite(170),rewrite(1240(10))]. 1331 $F # answer(E). [ur(41,b,1263,a(flip)),rewrite(6(24),6(25),108(21),6(24),1048(26,R),115(27),3(27),3(26),3(25),3(24),3(23),1117(22),4(10),3(18),3(17),3(16)),xx(a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=143. Generated=7940. Kept=1329. proofs=1. Usable=74. Sos=394. Demods=76. Limbo=0, Disabled=867. Hints=0. Weight_deleted=1179. Literals_deleted=0. Forward_subsumed=5431. Back_subsumed=221. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=475 (3 lex), Back_demodulated=640. Back_unit_deleted=0. Demod_attempts=108330. Demod_rewrites=18593. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=47168. Nonunit_bsub_feature_tests=13577. Megabytes=0.88. User_CPU=0.18, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 21004 exit (max_proofs) Mon Mar 19 17:01:59 2007