============================== Prover9 ===============================
Prover9 (32) version June-2006C, June 2006.
Process 13135 was started by mccune on cleo.thornwood,
Mon Jun 19 16:41:46 2006
The command was "/home/mccune/bin/prover9 -f cs.in NE.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).

clauses(sos).
x * y != x * z | y = z.
x * y != z * y | x = z.
(x * y) * z = x * y * z.
x * y * (y @ x) = y * x.
end_of_list.

% Reading from file NE.in


clauses(sos).
(x @ y) * z = z * (x @ y).
end_of_list.

clauses(sos).
A * B * C * B * A != B * A * C * A * B # answer(E).
end_of_list.

============================== end of input ==========================

============================== PROCESS INITIAL CLAUSES ===============

% Clauses before input processing:

clauses(usable).
end_of_list.

clauses(sos).
1 x * y != x * z | y = z.  [input].
2 x * y != z * y | x = z.  [input].
3 (x * y) * z = x * y * z.  [input].
4 x * y * (y @ x) = y * x.  [input].
5 (x @ y) * z = z * (x @ y).  [input].
6 A * B * C * B * A != B * A * C * A * B # answer(E).  [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([ A, B, C, *, @ ]).
After inverse_order: Function symbol precedence:  lex([ A, B, C, *, @ ]).
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:

clauses(usable).
end_of_list.

clauses(sos).
7 x * y != x * z | y = z.  [input].
8 x * y != z * y | x = z.  [input].
9 (x * y) * z = x * y * z.  [input].
10 x * y * (y @ x) = y * x.  [input].
11 (x @ y) * z = z * (x @ y).  [input].
12 A * B * C * B * A != B * A * C * A * B # answer(E).  [input].
end_of_list.

clauses(demodulators).
9 (x * y) * z = x * y * z.  [input].
10 x * y * (y @ x) = y * x.  [input].
11 (x @ y) * z = z * (x @ y).  [input].
        % (lex-dep)
end_of_list.

clauses(denials).
end_of_list.

============================== end of clauses for search =============

============================== SEARCH ================================

% Starting search at 0.00 seconds.

given #1 (I,wt=10): 7 x * y != x * z | y = z.  [input].

given #2 (I,wt=10): 8 x * y != z * y | x = z.  [input].

given #3 (I,wt=11): 9 (x * y) * z = x * y * z.  [input].

given #4 (I,wt=11): 10 x * y * (y @ x) = y * x.  [input].

given #5 (I,wt=11): 11 (x @ y) * z = z * (x @ y).  [input].

given #6 (I,wt=19): 12 A * B * C * B * A != B * A * C * A * B # answer(E).  [input].

given #7 (F,wt=23): 29 A * B * C * B * A * x != B * A * C * A * B * x # answer(E).  [ur(8,b,12,a),demod(9(10),9(9),9(8),9(7),9(20),9(19),9(18),9(17))].

given #8 (F,wt=23): 30 x * A * B * C * B * A != x * B * A * C * A * B # answer(E).  [ur(7,b,12,a)].

given #9 (T,wt=7): 15 x * (x @ x) = x.  [hyper(7,a,10,a)].

given #10 (T,wt=10): 33 x * y != x | x @ x = y.  [para(15(a,1),7(a,1)),flip(a)].

given #11 (A,wt=14): 13 x * y * z != x * y * u | z = u.  [para(9(a,1),7(a,1)),demod(9(4))].

given #12 (F,wt=23): 31 B * A * C * A * B * (A @ B) != A * B * C * A * B # answer(E).  [para(10(a,1),29(a,1,2,2,2)),flip(a)].

given #13 (F,wt=23): 32 A * B * C * B * A * (B @ A) != B * A * C * B * A # answer(E).  [para(10(a,1),29(a,2,2,2,2))].

given #14 (T,wt=10): 34 x * (y @ y) != y | y = x.  [para(15(a,1),8(a,1)),flip(a)].

given #15 (T,wt=10): 35 x * (y @ y) != y | x = y.  [para(15(a,1),8(a,2))].

given #16 (A,wt=14): 14 x * y * z != u * z | x * y = u.  [para(9(a,1),8(a,1))].

given #17 (F,wt=23): 38 B * A * C * A * B * (A @ A) != A * B * C * B * A # answer(E).  [para(15(a,1),29(a,1,2,2,2,2)),flip(a)].

given #18 (F,wt=23): 39 A * B * C * B * A * (B @ B) != B * A * C * A * B # answer(E).  [para(15(a,1),29(a,2,2,2,2,2))].

given #19 (T,wt=10): 55 (x @ x) * y != x | x = y.  [para(11(a,2),34(a,1))].

given #20 (T,wt=10): 56 (x @ x) * y != x | y = x.  [para(11(a,2),35(a,1))].

given #21 (A,wt=14): 16 x * y != z * x | z * (z @ x) = y.  [para(10(a,1),7(a,1)),flip(a)].

given #22 (F,wt=9): 70 x * (x @ (y @ z)) = x.  [hyper(16,a,11,a)].

given #23 (F,wt=25): 87 B * A * C * A * B * (A @ (x @ y)) != A * B * C * B * A # answer(E).  [para(70(a,1),29(a,1,2,2,2,2)),flip(a)].

given #24 (T,wt=9): 71 x * (x @ x * x) = x.  [hyper(16,a,9,a)].

given #25 (T,wt=9): 81 x @ (y @ z) = x @ x.  [hyper(33,a,70,a),flip(a)].

given #26 (A,wt=14): 17 x * y * (y @ z) != y * z | z = x.  [para(10(a,1),8(a,1)),flip(a)].

given #27 (F,wt=25): 88 A * B * C * B * A * (B @ (x @ y)) != B * A * C * A * B # answer(E).  [para(70(a,1),29(a,2,2,2,2,2))].

given #28 (F,wt=9): 95 x @ x * x = x @ x.  [hyper(33,a,71,a),flip(a)].

given #29 (T,wt=10): 104 x * y != y * y | y = x.  [para(15(a,1),17(a,1,2))].

given #30 (T,wt=10): 105 x * y != y | y @ y = x.  [para(15(a,1),17(a,2)),demod(70(3))].

given #31 (A,wt=14): 18 x * y * (y @ z) != y * z | x = z.  [para(10(a,1),8(a,2))].

given #32 (F,wt=11): 36 x * (x @ x) * y = x * y.  [para(15(a,1),9(a,1,1)),flip(a)].

given #33 (F,wt=6): 117 x != y | y = x.  [para(36(a,1),55(a,1)),demod(113(2),113(5))].

given #34 (T,wt=7): 113 (x @ x) * y = y.  [hyper(13,a,36,a)].

NOTE: New constant: 0 x @ x = c_0.  [new_symbol(122)].
NOTE: New Function symbol precedence:  lex([ A, B, C, c_0, *, @ ]).

given #35 (T,wt=5): 134 x @ x = c_0.  [new_symbol(122)].

given #36 (A,wt=15): 19 x * y * (y @ x) * z = y * x * z.  [para(10(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)].

given #37 (F,wt=5): 136 x * c_0 = x.  [back_demod(98),demod(130(3),134(1)),flip(a)].

given #38 (F,wt=5): 144 c_0 * x = x.  [back_demod(113),demod(134(1))].

given #39 (T,wt=7): 142 x * (c_0 @ x) = x.  [back_demod(125),demod(134(1))].

given #40 (T,wt=7): 148 x @ x * x = c_0.  [back_demod(95),demod(134(3))].

given #41 (A,wt=17): 20 x * y * z * (z @ x * y) = z * x * y.  [para(10(a,1),9(a,1)),flip(a)].

given #42 (F,wt=23): 176 B * A * C * A * B * (c_0 @ A) != A * B * C * B * A # answer(E).  [para(142(a,1),29(a,1,2,2,2,2)),flip(a)].

given #43 (F,wt=23): 177 A * B * C * B * A * (c_0 @ B) != B * A * C * A * B # answer(E).  [para(142(a,1),29(a,2,2,2,2,2))].

given #44 (T,wt=7): 150 x @ (y @ z) = c_0.  [back_demod(81),demod(134(3))].

given #45 (T,wt=5): 200 x @ c_0 = c_0.  [para(134(a,1),150(a,1,2))].

given #46 (A,wt=17): 21 x * y * z * (y * z @ x) = y * z * x.  [para(9(a,1),10(a,1,2)),demod(9(7))].

given #47 (F,wt=25): 192 B * A * C * A * B * (A @ C * B) != A * B * A * C * B # answer(E).  [para(20(a,1),29(a,1,2,2)),flip(a)].

given #48 (F,wt=25): 193 A * B * C * B * A * (B @ C * A) != B * A * B * C * A # answer(E).  [para(20(a,1),29(a,2,2,2))].

given #49 (T,wt=8): 143 x * y != y | c_0 = x.  [back_demod(124),demod(134(3))].

given #50 (T,wt=8): 154 x * y != x | c_0 = y.  [back_demod(33),demod(134(3))].

given #51 (A,wt=14): 22 (x @ y) * z != u * (x @ y) | u = z.  [para(11(a,1),7(a,1)),flip(a)].

given #52 (F,wt=25): 205 B * A * C * A * B * (B * A @ C) != A * B * B * A * C # answer(E).  [para(21(a,1),29(a,1,2,2)),flip(a)].

given #53 (F,wt=25): 206 A * B * C * B * A * (A * B @ C) != B * A * A * B * C # answer(E).  [para(21(a,1),29(a,2,2,2))].

given #54 (T,wt=5): 221 c_0 @ x = c_0.  [hyper(154,a,142,a),flip(a)].

given #55 (T,wt=9): 201 x * (x * x @ x) = x.  [hyper(13,a,21,a)].

given #56 (A,wt=14): 23 (x @ y) * z != z * u | x @ y = u.  [para(11(a,2),7(a,1))].

given #57 (F,wt=7): 226 x * x @ x = c_0.  [hyper(154,a,201,a),flip(a)].

given #58 (F,wt=12): 138 x * (x @ y) != x * y | c_0 = y.  [back_demod(132),demod(134(5))].

given #59 (T,wt=12): 141 x * y * z != z | x * y = c_0.  [back_demod(128),demod(134(4)),flip(b)].

given #60 (T,wt=12): 146 x * (y @ z) != x | y @ z = c_0.  [back_demod(110),demod(134(5))].

given #61 (A,wt=14): 24 (x @ y) * z != u * (x @ y) | z = u.  [para(11(a,1),7(a,2))].

given #62 (F,wt=12): 151 x * y * z != x * y | c_0 = z.  [back_demod(52),demod(134(5))].

given #63 (F,wt=12): 152 (x @ y) * z != z | x @ y = c_0.  [back_demod(43),demod(134(5))].

given #64 (T,wt=12): 153 x * y != y | x * (x @ y) = c_0.  [back_demod(41),demod(134(3)),flip(b)].

given #65 (T,wt=12): 237 x @ y != x * y | y * x = c_0.  [para(10(a,1),141(a,1)),flip(a)].

given #66 (A,wt=14): 25 x * (y @ z) != u * x | y @ z = u.  [para(11(a,1),8(a,1))].

given #67 (F,wt=12): 250 x * y != y * x | x @ y = c_0.  [para(10(a,1),151(a,1)),flip(b)].

given #68 (F,wt=7): 271 (x @ y) @ z = c_0.  [hyper(250,a,11,a)].

given #69 (T,wt=13): 73 x * y * (x * y @ x) = y * x.  [hyper(16,a,9,a(flip)),demod(9(4))].

given #70 (T,wt=13): 147 x * y @ x * y * x * y = c_0.  [back_demod(107),demod(134(8))].

given #71 (A,wt=15): 26 (x @ y) * z * u = z * (x @ y) * u.  [para(11(a,1),9(a,1,1)),demod(9(3)),flip(a)].

given #72 (F,wt=25): 284 B * A * C * A * B * (B * A @ B) != A * B * C * A * B # answer(E).  [para(73(a,1),29(a,1,2,2,2)),flip(a)].

given #73 (F,wt=25): 285 A * B * C * B * A * (A * B @ A) != B * A * C * B * A # answer(E).  [para(73(a,1),29(a,2,2,2,2))].

given #74 (T,wt=13): 184 x * y * (y @ y * x) = y * x.  [hyper(7,a,20,a)].

given #75 (T,wt=13): 232 x * y * x * y @ x * y = c_0.  [para(9(a,1),226(a,1,1))].

given #76 (A,wt=15): 27 (x @ y) * z * u = z * u * (x @ y).  [para(11(a,2),9(a,1))].

given #77 (F,wt=25): 367 B * A * C * A * B * (A @ A * B) != A * B * C * A * B # answer(E).  [para(184(a,1),29(a,1,2,2,2)),flip(a)].

given #78 (F,wt=25): 368 A * B * C * B * A * (B @ B * A) != B * A * C * B * A # answer(E).  [para(184(a,1),29(a,2,2,2,2))].

given #79 (T,wt=13): 278 x * (y * x @ y) = x * (x @ y).  [hyper(16,a,73,a),flip(a)].

given #80 (T,wt=9): 444 x * y @ x = y @ x.  [hyper(7,a,278,a)].

given #81 (A,wt=15): 28 x * (y @ z) * u = x * u * (y @ z).  [para(11(a,1),9(a,2,2)),demod(9(3))].

given #82 (F,wt=9): 451 (x @ y) * z @ z = c_0.  [para(11(a,2),444(a,1,1)),demod(271(5))].

given #83 (F,wt=13): 363 x * (x @ x * y) = x * (x @ y).  [hyper(16,a,184,a),flip(a)].

given #84 (T,wt=9): 521 x @ x * y = x @ y.  [hyper(7,a,363,a)].

given #85 (T,wt=9): 536 x @ (y @ z) * x = c_0.  [para(11(a,2),521(a,1,2)),demod(150(5))].

given #86 (A,wt=18): 44 x * y * z * u != x * y * z * v | u = v.  [para(9(a,1),13(a,1,2)),demod(9(5))].

given #87 (F,wt=13): 450 x * (x @ y) @ y = x * y @ y.  [para(10(a,1),444(a,1,1)),flip(a)].

given #88 (F,wt=13): 460 (x @ y) * z @ z * (x @ y) = c_0.  [back_demod(383),demod(449(8))].

given #89 (T,wt=13): 461 x * (y @ z) @ (y @ z) * x = c_0.  [back_demod(381),demod(449(8))].

given #90 (T,wt=13): 515 x * (y @ z) * u @ x * u = c_0.  [para(19(a,1),451(a,1,1)),demod(150(5),144(5))].

given #91 (A,wt=18): 45 x * y * z != x * u * y | u * (u @ y) = z.  [para(10(a,1),13(a,1,2)),flip(a)].

given #92 (F,wt=10): 619 x * y != x * z | z = y.  [para(136(a,1),45(a,2,2)),demod(144(2),200(5),136(5))].

given #93 (F,wt=13): 535 x @ y * (y @ x) = x @ y * x.  [para(10(a,1),521(a,1,2)),flip(a)].

given #94 (T,wt=13): 545 x * y @ x * (z @ u) * y = c_0.  [para(19(a,1),536(a,1,2)),demod(150(2),144(2))].

given #95 (T,wt=14): 46 x * y * z != y * x | y @ x = z.  [para(10(a,1),13(a,1)),flip(a)].

given #96 (A,wt=18): 47 x * (y @ z) * u != x * v * (y @ z) | v = u.  [para(11(a,1),13(a,1,2)),flip(a)].

given #97 (F,wt=12): 657 x * y != y * x | y @ x = c_0.  [para(136(a,1),46(a,1,2))].

given #98 (F,wt=14): 60 x * (y @ z) != y * z | z * y = x.  [para(10(a,1),14(a,1)),flip(a)].

given #99 (T,wt=14): 78 x * (y @ z) != u * (y @ z) | u = x.  [para(11(a,1),16(a,1)),demod(70(8))].

given #100 (T,wt=14): 407 (x @ y) * z * x != x * y | y = z.  [para(27(a,2),17(a,1))].

given #101 (A,wt=18): 48 (x @ y) * z * u != z * v * (x @ y) | v = u.  [para(11(a,1),13(a,1)),demod(9(3)),flip(a)].

given #102 (F,wt=14): 408 (x @ y) * z * x != x * y | z = y.  [para(27(a,2),18(a,1))].

given #103 (F,wt=14): 452 x * y * z != z * y * z | z = x.  [para(444(a,1),17(a,1,2,2)),demod(9(3),10(3),9(4))].

given #104 (T,wt=14): 612 x * (y @ x) * z != y * x | y = z.  [para(10(a,1),45(a,2)),demod(150(7),136(7))].

given #105 (T,wt=12): 716 x * (y @ x) != y * x | c_0 = y.  [para(10(a,1),612(a,1)),demod(11(2),271(6)),flip(b)].

given #106 (A,wt=18): 49 x * (y @ z) * u != x * u * v | y @ z = v.  [para(11(a,2),13(a,1,2))].

given #107 (F,wt=14): 627 x * y * z != x * y * u | u = z.  [para(9(a,1),619(a,1)),demod(9(4))].

given #108 (F,wt=14): 684 (x @ y) * z != x * y | y * x = z.  [para(11(a,2),60(a,1))].

given #109 (T,wt=14): 685 x * (y @ z) != u | (y @ z) * x = u.  [para(150(a,1),60(a,1,2)),demod(136(2)),flip(a)].

given #110 (T,wt=14): 686 (x @ y) * z != u | z * (x @ y) = u.  [para(271(a,1),60(a,1,2)),demod(136(2)),flip(a)].

given #111 (A,wt=18): 50 x * (y @ z) * u != x * v * (y @ z) | u = v.  [para(11(a,1),13(a,2,2))].

given #112 (F,wt=14): 704 (x @ y) * y * z != x * y | x = z.  [para(10(a,1),48(a,2))].

given #113 (F,wt=14): 715 x * y * (z @ x) != z * x | z = y.  [para(10(a,1),612(a,1,2)),demod(150(7),136(7))].

given #114 (T,wt=14): 764 x * (y @ x) * z != y * x | z = y.  [para(10(a,1),50(a,2))].

given #115 (T,wt=14): 790 x * y * (z @ x) != z * x | y = z.  [para(10(a,1),764(a,1,2)),demod(150(7),136(7))].

given #116 (A,wt=18): 51 (x @ y) * z * u != z * v * (x @ y) | u = v.  [para(11(a,1),13(a,2)),demod(9(6))].

given #117 (F,wt=14): 792 (x @ y) * y * z != x * y | z = x.  [para(19(a,1),764(a,1)),demod(271(7),144(7))].

given #118 (F,wt=15): 160 x * y * z * (y @ x) = y * x * z.  [para(10(a,1),19(a,1,2,2)),demod(150(6),136(6))].

============================== PROOF =================================

% Proof 1 at 0.14 (+ 0.01) seconds: E.
% Length of proof is 25.
% Level of proof is 8.
% Maximum clause weight is 19.
% Given clauses 118.

7 x * y != x * z | y = z.  [input].
8 x * y != z * y | x = z.  [input].
9 (x * y) * z = x * y * z.  [input].
10 x * y * (y @ x) = y * x.  [input].
11 (x @ y) * z = z * (x @ y).  [input].
12 A * B * C * B * A != B * A * C * A * B # answer(E).  [input].
13 x * y * z != x * y * u | z = u.  [para(9(a,1),7(a,1)),demod(9(4))].
15 x * (x @ x) = x.  [hyper(7,a,10,a)].
16 x * y != z * x | z * (z @ x) = y.  [para(10(a,1),7(a,1)),flip(a)].
17 x * y * (y @ z) != y * z | z = x.  [para(10(a,1),8(a,1)),flip(a)].
19 x * y * (y @ x) * z = y * x * z.  [para(10(a,1),9(a,1,1)),demod(9(2),9(5)),flip(a)].
33 x * y != x | x @ x = y.  [para(15(a,1),7(a,1)),flip(a)].
36 x * (x @ x) * y = x * y.  [para(15(a,1),9(a,1,1)),flip(a)].
70 x * (x @ (y @ z)) = x.  [hyper(16,a,11,a)].
81 x @ (y @ z) = x @ x.  [hyper(33,a,70,a),flip(a)].
98 (x @ (y @ z)) * u = u * (x @ x).  [para(81(a,2),11(a,1,1))].
105 x * y != y | y @ y = x.  [para(15(a,1),17(a,2)),demod(70(3))].
113 (x @ x) * y = y.  [hyper(13,a,36,a)].
122 x @ x = y @ y.  [hyper(105,a,113,a)].
130 (x @ (y @ z)) * u = u.  [para(81(a,2),113(a,1,1))].
134 x @ x = c_0.  [new_symbol(122)].
136 x * c_0 = x.  [back_demod(98),demod(130(3),134(1)),flip(a)].
150 x @ (y @ z) = c_0.  [back_demod(81),demod(134(3))].
160 x * y * z * (y @ x) = y * x * z.  [para(10(a,1),19(a,1,2,2)),demod(150(6),136(6))].
814 $F # answer(E).  [para(160(a,2),12(a,1)),demod(9(11),9(10),10(10)),xx(a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=118. Generated=5533. Kept=807. proofs=1.
Usable=85. Sos=546. Demods=164. Denials=0. Limbo=14, Disabled=168. Hints=0.
Weight_deleted=1125. Literals_deleted=0.
Forward_subsumed=3600. Back_subsumed=23.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=232 (1 lex), Back_demodulated=139. Back_unit_deleted=0.
Demod_attempts=85591. Demod_rewrites=11548.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=51163. Nonunit_bsub_feature_tests=11149.
Megabytes=0.64.
User_CPU=0.14, System_CPU=0.01, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 13135 exit (max_proofs) Mon Jun 19 16:41:46 2006