============================== Prover9 ===============================
Prover9 (32) version August-2006A, August 2006.
Process 11370 was started by mccune on cleo.thornwood,
Sat Aug 12 21:00:08 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).

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 NE.in


formulas(sos).
(x @ y) * z = z * (x @ y).
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 = z * (x @ 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].
5 (x @ y) * z = z * (x @ y).  [assumption].
6 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].
5 (x @ y) * z = z * (x @ y).  [assumption].
        % (lex-dep)
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=11): 5 (x @ y) * z = z * (x @ y).  [assumption].

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

given #7 (F,wt=23): 23 A * B * C * B * A * x != B * A * C * A * B * x # answer(E).  [ur(2,b,6,a),rewrite(3(10),3(9),3(8),3(7),3(20),3(19),3(18),3(17))].

given #8 (F,wt=23): 24 x * A * B * C * B * A != x * B * A * C * A * B # answer(E).  [ur(1,b,6,a)].

given #9 (T,wt=7): 9 x * (x @ x) = x.  [hyper(1,a,4,a)].

given #10 (T,wt=10): 27 x * y != x | x @ x = y.  [para(9(a,1),1(a,1)),flip(a)].

given #11 (A,wt=14): 7 x * y * z != x * y * u | z = u.  [para(3(a,1),1(a,1)),rewrite(3(4))].

given #12 (F,wt=23): 25 B * A * C * A * B * (A @ B) != A * B * C * A * B # answer(E).  [para(4(a,1),23(a,1,2,2,2)),flip(a)].

given #13 (F,wt=23): 26 A * B * C * B * A * (B @ A) != B * A * C * B * A # answer(E).  [para(4(a,1),23(a,2,2,2,2))].

given #14 (T,wt=10): 28 x * (y @ y) != y | y = x.  [para(9(a,1),2(a,1)),flip(a)].

given #15 (T,wt=10): 29 x * (y @ y) != y | x = y.  [para(9(a,1),2(a,2))].

given #16 (A,wt=14): 8 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(9(a,1),23(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(9(a,1),23(a,2,2,2,2,2))].

given #19 (T,wt=10): 49 (x @ x) * y != x | x = y.  [para(5(a,2),28(a,1))].

given #20 (T,wt=10): 50 (x @ x) * y != x | y = x.  [para(5(a,2),29(a,1))].

given #21 (A,wt=14): 10 x * y != z * x | z * (z @ x) = y.  [para(4(a,1),1(a,1)),flip(a)].

given #22 (F,wt=9): 64 x * (x @ (y @ z)) = x.  [hyper(10,a,5,a)].

given #23 (F,wt=25): 81 B * A * C * A * B * (A @ (x @ y)) != A * B * C * B * A # answer(E).  [para(64(a,1),23(a,1,2,2,2,2)),flip(a)].

given #24 (T,wt=9): 65 x * (x @ x * x) = x.  [hyper(10,a,3,a)].

given #25 (T,wt=9): 75 x @ (y @ z) = x @ x.  [hyper(27,a,64,a),flip(a)].

given #26 (A,wt=14): 11 x * y * (y @ z) != y * z | z = x.  [para(4(a,1),2(a,1)),flip(a)].

given #27 (F,wt=25): 82 A * B * C * B * A * (B @ (x @ y)) != B * A * C * A * B # answer(E).  [para(64(a,1),23(a,2,2,2,2,2))].

given #28 (F,wt=9): 89 x @ x * x = x @ x.  [hyper(27,a,65,a),flip(a)].

given #29 (T,wt=10): 98 x * y != y * y | y = x.  [para(9(a,1),11(a,1,2))].

given #30 (T,wt=10): 99 x * y != y | y @ y = x.  [para(9(a,1),11(a,2)),rewrite(64(3))].

given #31 (A,wt=14): 12 x * y * (y @ z) != y * z | x = z.  [para(4(a,1),2(a,2))].

given #32 (F,wt=11): 30 x * (x @ x) * y = x * y.  [para(9(a,1),3(a,1,1)),flip(a)].

given #33 (F,wt=6): 111 x != y | y = x.  [para(30(a,1),49(a,1)),rewrite(107(2),107(5))].

given #34 (T,wt=7): 107 (x @ x) * y = y.  [hyper(7,a,30,a)].

NOTE: New constant: x @ x = c_0.  [new_symbol(116)].
NOTE: New Function symbol precedence:  lex([ A, B, C, c_0, *, @ ]).

given #35 (T,wt=5): 128 x @ x = c_0.  [new_symbol(116)].

given #36 (A,wt=15): 13 x * y * (y @ x) * z = y * x * z.  [para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].

given #37 (F,wt=5): 130 x * c_0 = x.  [back_rewrite(92),rewrite(124(3),128(1)),flip(a)].

given #38 (F,wt=5): 138 c_0 * x = x.  [back_rewrite(107),rewrite(128(1))].

given #39 (T,wt=7): 136 x * (c_0 @ x) = x.  [back_rewrite(119),rewrite(128(1))].

given #40 (T,wt=7): 142 x @ x * x = c_0.  [back_rewrite(89),rewrite(128(3))].

given #41 (A,wt=17): 14 x * y * z * (z @ x * y) = z * x * y.  [para(4(a,1),3(a,1)),flip(a)].

given #42 (F,wt=23): 170 B * A * C * A * B * (c_0 @ A) != A * B * C * B * A # answer(E).  [para(136(a,1),23(a,1,2,2,2,2)),flip(a)].

given #43 (F,wt=23): 171 A * B * C * B * A * (c_0 @ B) != B * A * C * A * B # answer(E).  [para(136(a,1),23(a,2,2,2,2,2))].

given #44 (T,wt=7): 144 x @ (y @ z) = c_0.  [back_rewrite(75),rewrite(128(3))].

given #45 (T,wt=5): 194 x @ c_0 = c_0.  [para(128(a,1),144(a,1,2))].

given #46 (A,wt=17): 15 x * y * z * (y * z @ x) = y * z * x.  [para(3(a,1),4(a,1,2)),rewrite(3(7))].

given #47 (F,wt=25): 186 B * A * C * A * B * (A @ C * B) != A * B * A * C * B # answer(E).  [para(14(a,1),23(a,1,2,2)),flip(a)].

given #48 (F,wt=25): 187 A * B * C * B * A * (B @ C * A) != B * A * B * C * A # answer(E).  [para(14(a,1),23(a,2,2,2))].

given #49 (T,wt=8): 137 x * y != y | c_0 = x.  [back_rewrite(118),rewrite(128(3))].

given #50 (T,wt=8): 148 x * y != x | c_0 = y.  [back_rewrite(27),rewrite(128(3))].

given #51 (A,wt=14): 16 (x @ y) * z != u * (x @ y) | u = z.  [para(5(a,1),1(a,1)),flip(a)].

given #52 (F,wt=25): 199 B * A * C * A * B * (B * A @ C) != A * B * B * A * C # answer(E).  [para(15(a,1),23(a,1,2,2)),flip(a)].

given #53 (F,wt=25): 200 A * B * C * B * A * (A * B @ C) != B * A * A * B * C # answer(E).  [para(15(a,1),23(a,2,2,2))].

given #54 (T,wt=5): 215 c_0 @ x = c_0.  [hyper(148,a,136,a),flip(a)].

given #55 (T,wt=9): 195 x * (x * x @ x) = x.  [hyper(7,a,15,a)].

given #56 (A,wt=14): 17 (x @ y) * z != z * u | x @ y = u.  [para(5(a,2),1(a,1))].

given #57 (F,wt=7): 220 x * x @ x = c_0.  [hyper(148,a,195,a),flip(a)].

given #58 (F,wt=12): 132 x * (x @ y) != x * y | c_0 = y.  [back_rewrite(126),rewrite(128(5))].

given #59 (T,wt=12): 135 x * y * z != z | x * y = c_0.  [back_rewrite(122),rewrite(128(4)),flip(b)].

given #60 (T,wt=12): 140 x * (y @ z) != x | y @ z = c_0.  [back_rewrite(104),rewrite(128(5))].

given #61 (A,wt=14): 18 (x @ y) * z != u * (x @ y) | z = u.  [para(5(a,1),1(a,2))].

given #62 (F,wt=12): 145 x * y * z != x * y | c_0 = z.  [back_rewrite(46),rewrite(128(5))].

given #63 (F,wt=12): 146 (x @ y) * z != z | x @ y = c_0.  [back_rewrite(37),rewrite(128(5))].

given #64 (T,wt=12): 147 x * y != y | x * (x @ y) = c_0.  [back_rewrite(35),rewrite(128(3)),flip(b)].

given #65 (T,wt=12): 231 x @ y != x * y | y * x = c_0.  [para(4(a,1),135(a,1)),flip(a)].

given #66 (A,wt=14): 19 x * (y @ z) != u * x | y @ z = u.  [para(5(a,1),2(a,1))].

given #67 (F,wt=12): 244 x * y != y * x | x @ y = c_0.  [para(4(a,1),145(a,1)),flip(b)].

given #68 (F,wt=7): 265 (x @ y) @ z = c_0.  [hyper(244,a,5,a)].

given #69 (T,wt=13): 67 x * y * (x * y @ x) = y * x.  [hyper(10,a,3,a(flip)),rewrite(3(4))].

given #70 (T,wt=13): 141 x * y @ x * y * x * y = c_0.  [back_rewrite(101),rewrite(128(8))].

given #71 (A,wt=15): 20 (x @ y) * z * u = z * (x @ y) * u.  [para(5(a,1),3(a,1,1)),rewrite(3(3)),flip(a)].

given #72 (F,wt=25): 278 B * A * C * A * B * (B * A @ B) != A * B * C * A * B # answer(E).  [para(67(a,1),23(a,1,2,2,2)),flip(a)].

given #73 (F,wt=25): 279 A * B * C * B * A * (A * B @ A) != B * A * C * B * A # answer(E).  [para(67(a,1),23(a,2,2,2,2))].

given #74 (T,wt=13): 178 x * y * (y @ y * x) = y * x.  [hyper(1,a,14,a)].

given #75 (T,wt=13): 226 x * y * x * y @ x * y = c_0.  [para(3(a,1),220(a,1,1))].

given #76 (A,wt=15): 21 (x @ y) * z * u = z * u * (x @ y).  [para(5(a,2),3(a,1))].

given #77 (F,wt=25): 361 B * A * C * A * B * (A @ A * B) != A * B * C * A * B # answer(E).  [para(178(a,1),23(a,1,2,2,2)),flip(a)].

given #78 (F,wt=25): 362 A * B * C * B * A * (B @ B * A) != B * A * C * B * A # answer(E).  [para(178(a,1),23(a,2,2,2,2))].

given #79 (T,wt=13): 272 x * (y * x @ y) = x * (x @ y).  [hyper(10,a,67,a),flip(a)].

given #80 (T,wt=9): 438 x * y @ x = y @ x.  [hyper(1,a,272,a)].

given #81 (A,wt=15): 22 x * (y @ z) * u = x * u * (y @ z).  [para(5(a,1),3(a,2,2)),rewrite(3(3))].

given #82 (F,wt=9): 445 (x @ y) * z @ z = c_0.  [para(5(a,2),438(a,1,1)),rewrite(265(5))].

given #83 (F,wt=13): 357 x * (x @ x * y) = x * (x @ y).  [hyper(10,a,178,a),flip(a)].

given #84 (T,wt=9): 515 x @ x * y = x @ y.  [hyper(1,a,357,a)].

given #85 (T,wt=9): 530 x @ (y @ z) * x = c_0.  [para(5(a,2),515(a,1,2)),rewrite(144(5))].

given #86 (A,wt=18): 38 x * y * z * u != x * y * z * v | u = v.  [para(3(a,1),7(a,1,2)),rewrite(3(5))].

given #87 (F,wt=13): 444 x * (x @ y) @ y = x * y @ y.  [para(4(a,1),438(a,1,1)),flip(a)].

given #88 (F,wt=13): 454 (x @ y) * z @ z * (x @ y) = c_0.  [back_rewrite(377),rewrite(443(8))].

given #89 (T,wt=13): 455 x * (y @ z) @ (y @ z) * x = c_0.  [back_rewrite(375),rewrite(443(8))].

given #90 (T,wt=13): 509 x * (y @ z) * u @ x * u = c_0.  [para(13(a,1),445(a,1,1)),rewrite(144(5),138(5))].

given #91 (A,wt=18): 39 x * y * z != x * u * y | u * (u @ y) = z.  [para(4(a,1),7(a,1,2)),flip(a)].

given #92 (F,wt=10): 613 x * y != x * z | z = y.  [para(130(a,1),39(a,2,2)),rewrite(138(2),194(5),130(5))].

given #93 (F,wt=13): 529 x @ y * (y @ x) = x @ y * x.  [para(4(a,1),515(a,1,2)),flip(a)].

given #94 (T,wt=13): 539 x * y @ x * (z @ u) * y = c_0.  [para(13(a,1),530(a,1,2)),rewrite(144(2),138(2))].

given #95 (T,wt=14): 40 x * y * z != y * x | y @ x = z.  [para(4(a,1),7(a,1)),flip(a)].

given #96 (A,wt=18): 41 x * (y @ z) * u != x * v * (y @ z) | v = u.  [para(5(a,1),7(a,1,2)),flip(a)].

given #97 (F,wt=12): 651 x * y != y * x | y @ x = c_0.  [para(130(a,1),40(a,1,2))].

given #98 (F,wt=14): 54 x * (y @ z) != y * z | z * y = x.  [para(4(a,1),8(a,1)),flip(a)].

given #99 (T,wt=14): 72 x * (y @ z) != u * (y @ z) | u = x.  [para(5(a,1),10(a,1)),rewrite(64(8))].

given #100 (T,wt=14): 401 (x @ y) * z * x != x * y | y = z.  [para(21(a,2),11(a,1))].

given #101 (A,wt=18): 42 (x @ y) * z * u != z * v * (x @ y) | v = u.  [para(5(a,1),7(a,1)),rewrite(3(3)),flip(a)].

given #102 (F,wt=14): 402 (x @ y) * z * x != x * y | z = y.  [para(21(a,2),12(a,1))].

given #103 (F,wt=14): 446 x * y * z != z * y * z | z = x.  [para(438(a,1),11(a,1,2,2)),rewrite(3(3),4(3),3(4))].

given #104 (T,wt=14): 606 x * (y @ x) * z != y * x | y = z.  [para(4(a,1),39(a,2)),rewrite(144(7),130(7))].

given #105 (T,wt=12): 710 x * (y @ x) != y * x | c_0 = y.  [para(4(a,1),606(a,1)),rewrite(5(2),265(6)),flip(b)].

given #106 (A,wt=18): 43 x * (y @ z) * u != x * u * v | y @ z = v.  [para(5(a,2),7(a,1,2))].

given #107 (F,wt=14): 621 x * y * z != x * y * u | u = z.  [para(3(a,1),613(a,1)),rewrite(3(4))].

given #108 (F,wt=14): 678 (x @ y) * z != x * y | y * x = z.  [para(5(a,2),54(a,1))].

given #109 (T,wt=14): 679 x * (y @ z) != u | (y @ z) * x = u.  [para(144(a,1),54(a,1,2)),rewrite(130(2)),flip(a)].

given #110 (T,wt=14): 680 (x @ y) * z != u | z * (x @ y) = u.  [para(265(a,1),54(a,1,2)),rewrite(130(2)),flip(a)].

given #111 (A,wt=18): 44 x * (y @ z) * u != x * v * (y @ z) | u = v.  [para(5(a,1),7(a,2,2))].

given #112 (F,wt=14): 698 (x @ y) * y * z != x * y | x = z.  [para(4(a,1),42(a,2))].

given #113 (F,wt=14): 709 x * y * (z @ x) != z * x | z = y.  [para(4(a,1),606(a,1,2)),rewrite(144(7),130(7))].

given #114 (T,wt=14): 758 x * (y @ x) * z != y * x | z = y.  [para(4(a,1),44(a,2))].

given #115 (T,wt=14): 784 x * y * (z @ x) != z * x | y = z.  [para(4(a,1),758(a,1,2)),rewrite(144(7),130(7))].

given #116 (A,wt=18): 45 (x @ y) * z * u != z * v * (x @ y) | u = v.  [para(5(a,1),7(a,2)),rewrite(3(6))].

given #117 (F,wt=14): 786 (x @ y) * y * z != x * y | z = x.  [para(13(a,1),758(a,1)),rewrite(265(7),138(7))].

given #118 (F,wt=15): 154 x * y * z * (y @ x) = y * x * z.  [para(4(a,1),13(a,1,2,2)),rewrite(144(6),130(6))].

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

% Proof 1 at 0.14 (+ 0.00) seconds: E.
% Length of proof is 25.
% Level of proof is 8.
% Maximum clause weight is 19.
% Given clauses 118.

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 = z * (x @ y).  [assumption].
6 A * B * C * B * A != B * A * C * A * B # answer(E).  [assumption].
7 x * y * z != x * y * u | z = u.  [para(3(a,1),1(a,1)),rewrite(3(4))].
9 x * (x @ x) = x.  [hyper(1,a,4,a)].
10 x * y != z * x | z * (z @ x) = y.  [para(4(a,1),1(a,1)),flip(a)].
11 x * y * (y @ z) != y * z | z = x.  [para(4(a,1),2(a,1)),flip(a)].
13 x * y * (y @ x) * z = y * x * z.  [para(4(a,1),3(a,1,1)),rewrite(3(2),3(5)),flip(a)].
27 x * y != x | x @ x = y.  [para(9(a,1),1(a,1)),flip(a)].
30 x * (x @ x) * y = x * y.  [para(9(a,1),3(a,1,1)),flip(a)].
64 x * (x @ (y @ z)) = x.  [hyper(10,a,5,a)].
75 x @ (y @ z) = x @ x.  [hyper(27,a,64,a),flip(a)].
92 (x @ (y @ z)) * u = u * (x @ x).  [para(75(a,2),5(a,1,1))].
99 x * y != y | y @ y = x.  [para(9(a,1),11(a,2)),rewrite(64(3))].
107 (x @ x) * y = y.  [hyper(7,a,30,a)].
116 x @ x = y @ y.  [hyper(99,a,107,a)].
124 (x @ (y @ z)) * u = u.  [para(75(a,2),107(a,1,1))].
128 x @ x = c_0.  [new_symbol(116)].
130 x * c_0 = x.  [back_rewrite(92),rewrite(124(3),128(1)),flip(a)].
144 x @ (y @ z) = c_0.  [back_rewrite(75),rewrite(128(3))].
154 x * y * z * (y @ x) = y * x * z.  [para(4(a,1),13(a,1,2,2)),rewrite(144(6),130(6))].
808 $F # answer(E).  [para(154(a,2),6(a,1)),rewrite(3(11),3(10),4(10)),xx(a)].

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

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

Given=118. Generated=5533. Kept=807. proofs=1.
Usable=85. Sos=546. Demods=164. 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=85620. 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=0.00, Wall_clock=0.

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

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

THEOREM PROVED

Exiting with 1 proof.

Process 11370 exit (max_proofs) Sat Aug 12 21:00:08 2006