TSTP Solution File: GRP124-6.004 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP124-6.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:56:09 EDT 2022
% Result : Unsatisfiable 1.68s 1.91s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of clauses : 57 ( 22 unt; 29 nHn; 55 RR)
% Number of literals : 125 ( 0 equ; 24 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ e_qualish(e_1,e_2),
file('GRP124-6.004.p',unknown),
[] ).
cnf(2,axiom,
~ e_qualish(e_1,e_3),
file('GRP124-6.004.p',unknown),
[] ).
cnf(3,axiom,
~ e_qualish(e_1,e_4),
file('GRP124-6.004.p',unknown),
[] ).
cnf(4,axiom,
~ e_qualish(e_2,e_1),
file('GRP124-6.004.p',unknown),
[] ).
cnf(5,axiom,
~ e_qualish(e_2,e_3),
file('GRP124-6.004.p',unknown),
[] ).
cnf(6,axiom,
~ e_qualish(e_2,e_4),
file('GRP124-6.004.p',unknown),
[] ).
cnf(7,axiom,
~ e_qualish(e_3,e_1),
file('GRP124-6.004.p',unknown),
[] ).
cnf(8,axiom,
~ e_qualish(e_3,e_2),
file('GRP124-6.004.p',unknown),
[] ).
cnf(13,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3)
| product1(A,B,e_4) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(15,axiom,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| e_qualish(B,D) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(16,axiom,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| e_qualish(A,D) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(17,axiom,
( ~ group_element(A)
| ~ group_element(B)
| product2(A,B,e_1)
| product2(A,B,e_2)
| product2(A,B,e_3)
| product2(A,B,e_4) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(18,axiom,
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| e_qualish(C,D) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(19,axiom,
( ~ product2(A,B,C)
| ~ product2(A,D,C)
| e_qualish(B,D) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(20,axiom,
( ~ product2(A,B,C)
| ~ product2(D,B,C)
| e_qualish(A,D) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(21,axiom,
( ~ product1(A,B,C)
| ~ product1(C,A,D)
| product2(D,B,A) ),
file('GRP124-6.004.p',unknown),
[] ).
cnf(31,axiom,
group_element(e_1),
file('GRP124-6.004.p',unknown),
[] ).
cnf(32,axiom,
group_element(e_2),
file('GRP124-6.004.p',unknown),
[] ).
cnf(33,axiom,
group_element(e_3),
file('GRP124-6.004.p',unknown),
[] ).
cnf(35,axiom,
product1(A,A,A),
file('GRP124-6.004.p',unknown),
[] ).
cnf(36,axiom,
product2(A,A,A),
file('GRP124-6.004.p',unknown),
[] ).
cnf(39,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[32,13,31]),
[iquote('hyper,32,13,31')] ).
cnf(40,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_4) ),
inference(hyper,[status(thm)],[32,13,31]),
[iquote('hyper,32,13,31')] ).
cnf(41,plain,
( product2(e_2,e_3,e_1)
| product2(e_2,e_3,e_2)
| product2(e_2,e_3,e_3)
| product2(e_2,e_3,e_4) ),
inference(hyper,[status(thm)],[33,17,32]),
[iquote('hyper,33,17,32')] ).
cnf(42,plain,
( product2(e_1,e_3,e_1)
| product2(e_1,e_3,e_2)
| product2(e_1,e_3,e_3)
| product2(e_1,e_3,e_4) ),
inference(hyper,[status(thm)],[33,17,31]),
[iquote('hyper,33,17,31')] ).
cnf(45,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_4) ),
inference(hyper,[status(thm)],[33,13,32]),
[iquote('hyper,33,13,32')] ).
cnf(46,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_4) ),
inference(hyper,[status(thm)],[33,13,31]),
[iquote('hyper,33,13,31')] ).
cnf(69,plain,
( product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[39,15,35]),1]),
[iquote('hyper,39,15,35,unit_del,1')] ).
cnf(71,plain,
( product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[69,16,35]),4]),
[iquote('hyper,69,16,35,unit_del,4')] ).
cnf(72,plain,
( product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[40,16,35]),1]),
[iquote('hyper,40,16,35,unit_del,1')] ).
cnf(76,plain,
( product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[72,15,35]),4]),
[iquote('hyper,72,15,35,unit_del,4')] ).
cnf(77,plain,
( product2(e_2,e_3,e_1)
| product2(e_2,e_3,e_3)
| product2(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[41,19,36]),5]),
[iquote('hyper,41,19,36,unit_del,5')] ).
cnf(80,plain,
( product2(e_1,e_3,e_2)
| product2(e_1,e_3,e_3)
| product2(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[42,19,36]),2]),
[iquote('hyper,42,19,36,unit_del,2')] ).
cnf(83,plain,
( product2(e_2,e_3,e_1)
| product2(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[77,20,36]),8]),
[iquote('hyper,77,20,36,unit_del,8')] ).
cnf(86,plain,
( product2(e_1,e_3,e_2)
| product2(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[80,20,36]),7]),
[iquote('hyper,80,20,36,unit_del,7')] ).
cnf(93,plain,
( product2(e_1,e_3,e_2)
| product2(e_2,e_3,e_1) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[86,20,83]),4]),
[iquote('hyper,86,20,83,unit_del,4')] ).
cnf(115,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[45,15,35]),5]),
[iquote('hyper,45,15,35,unit_del,5')] ).
cnf(120,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[115,16,35]),8]),
[iquote('hyper,115,16,35,unit_del,8')] ).
cnf(123,plain,
( product1(e_2,e_3,e_4)
| product2(e_3,e_3,e_2)
| product1(e_1,e_2,e_4) ),
inference(hyper,[status(thm)],[120,21,71]),
[iquote('hyper,120,21,71')] ).
cnf(124,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[120,15,76]),2]),
[iquote('hyper,120,15,76,unit_del,2')] ).
cnf(127,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[46,15,35]),2]),
[iquote('hyper,46,15,35,unit_del,2')] ).
cnf(144,plain,
( product1(e_2,e_3,e_4)
| product1(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[123,18,36]),8]),
[iquote('hyper,123,18,36,unit_del,8')] ).
cnf(145,plain,
( product1(e_1,e_2,e_4)
| product1(e_2,e_1,e_3) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[144,15,76]),2]),
[iquote('hyper,144,15,76,unit_del,2')] ).
cnf(200,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[127,16,35]),7]),
[iquote('hyper,127,16,35,unit_del,7')] ).
cnf(210,plain,
( product1(e_1,e_3,e_2)
| product1(e_1,e_2,e_4) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[200,16,144]),4]),
[iquote('hyper,200,16,144,unit_del,4')] ).
cnf(215,plain,
( product1(e_1,e_2,e_4)
| product2(e_3,e_3,e_1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[210,21,145])]),
[iquote('hyper,210,21,145,factor_simp')] ).
cnf(216,plain,
product1(e_1,e_3,e_2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[210,15,200]),8])]),
[iquote('hyper,210,15,200,unit_del,8,factor_simp')] ).
cnf(227,plain,
( product2(e_3,e_3,e_1)
| product1(e_2,e_3,e_1) ),
inference(hyper,[status(thm)],[216,21,124]),
[iquote('hyper,216,21,124')] ).
cnf(228,plain,
( product2(e_4,e_3,e_1)
| product1(e_2,e_1,e_3) ),
inference(hyper,[status(thm)],[216,21,76]),
[iquote('hyper,216,21,76')] ).
cnf(236,plain,
product1(e_1,e_2,e_4),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[215,18,36]),7]),
[iquote('hyper,215,18,36,unit_del,7')] ).
cnf(243,plain,
product1(e_2,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[227,18,36]),7]),
[iquote('hyper,227,18,36,unit_del,7')] ).
cnf(254,plain,
product2(e_4,e_3,e_2),
inference(hyper,[status(thm)],[243,21,236]),
[iquote('hyper,243,21,236')] ).
cnf(256,plain,
product2(e_2,e_3,e_1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[254,20,93]),3]),
[iquote('hyper,254,20,93,unit_del,3')] ).
cnf(264,plain,
product1(e_2,e_1,e_3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[228,20,256]),6]),
[iquote('hyper,228,20,256,unit_del,6')] ).
cnf(265,plain,
product2(e_3,e_3,e_1),
inference(hyper,[status(thm)],[264,21,216]),
[iquote('hyper,264,21,216')] ).
cnf(266,plain,
e_qualish(e_2,e_3),
inference(hyper,[status(thm)],[265,20,256]),
[iquote('hyper,265,20,256')] ).
cnf(267,plain,
$false,
inference(binary,[status(thm)],[266,5]),
[iquote('binary,266.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP124-6.004 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 04:31:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.91 ----- Otter 3.3f, August 2004 -----
% 1.68/1.91 The process was started by sandbox on n017.cluster.edu,
% 1.68/1.91 Wed Jul 27 04:31:03 2022
% 1.68/1.91 The command was "./otter". The process ID is 18224.
% 1.68/1.91
% 1.68/1.91 set(prolog_style_variables).
% 1.68/1.91 set(auto).
% 1.68/1.91 dependent: set(auto1).
% 1.68/1.91 dependent: set(process_input).
% 1.68/1.91 dependent: clear(print_kept).
% 1.68/1.91 dependent: clear(print_new_demod).
% 1.68/1.91 dependent: clear(print_back_demod).
% 1.68/1.91 dependent: clear(print_back_sub).
% 1.68/1.91 dependent: set(control_memory).
% 1.68/1.91 dependent: assign(max_mem, 12000).
% 1.68/1.91 dependent: assign(pick_given_ratio, 4).
% 1.68/1.91 dependent: assign(stats_level, 1).
% 1.68/1.91 dependent: assign(max_seconds, 10800).
% 1.68/1.91 clear(print_given).
% 1.68/1.91
% 1.68/1.91 list(usable).
% 1.68/1.91 0 [] group_element(e_1).
% 1.68/1.91 0 [] group_element(e_2).
% 1.68/1.91 0 [] group_element(e_3).
% 1.68/1.91 0 [] group_element(e_4).
% 1.68/1.91 0 [] -e_qualish(e_1,e_2).
% 1.68/1.91 0 [] -e_qualish(e_1,e_3).
% 1.68/1.91 0 [] -e_qualish(e_1,e_4).
% 1.68/1.91 0 [] -e_qualish(e_2,e_1).
% 1.68/1.91 0 [] -e_qualish(e_2,e_3).
% 1.68/1.91 0 [] -e_qualish(e_2,e_4).
% 1.68/1.91 0 [] -e_qualish(e_3,e_1).
% 1.68/1.91 0 [] -e_qualish(e_3,e_2).
% 1.68/1.91 0 [] -e_qualish(e_3,e_4).
% 1.68/1.91 0 [] -e_qualish(e_4,e_1).
% 1.68/1.91 0 [] -e_qualish(e_4,e_2).
% 1.68/1.91 0 [] -e_qualish(e_4,e_3).
% 1.68/1.91 0 [] -group_element(X)| -group_element(Y)|product1(X,Y,e_1)|product1(X,Y,e_2)|product1(X,Y,e_3)|product1(X,Y,e_4).
% 1.68/1.91 0 [] -product1(X,Y,W)| -product1(X,Y,Z)|e_qualish(W,Z).
% 1.68/1.91 0 [] -product1(X,W,Y)| -product1(X,Z,Y)|e_qualish(W,Z).
% 1.68/1.91 0 [] -product1(W,Y,X)| -product1(Z,Y,X)|e_qualish(W,Z).
% 1.68/1.91 0 [] product1(X,X,X).
% 1.68/1.91 0 [] -group_element(X)| -group_element(Y)|product2(X,Y,e_1)|product2(X,Y,e_2)|product2(X,Y,e_3)|product2(X,Y,e_4).
% 1.68/1.91 0 [] -product2(X,Y,W)| -product2(X,Y,Z)|e_qualish(W,Z).
% 1.68/1.91 0 [] -product2(X,W,Y)| -product2(X,Z,Y)|e_qualish(W,Z).
% 1.68/1.91 0 [] -product2(W,Y,X)| -product2(Z,Y,X)|e_qualish(W,Z).
% 1.68/1.91 0 [] product2(X,X,X).
% 1.68/1.91 0 [] -product1(X,Y,Z1)| -product1(Z1,X,Z2)|product2(Z2,Y,X).
% 1.68/1.91 end_of_list.
% 1.68/1.91
% 1.68/1.91 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.68/1.91
% 1.68/1.91 This is a non-Horn set without equality. The strategy will
% 1.68/1.91 be ordered hyper_res, unit deletion, and factoring, with
% 1.68/1.91 satellites in sos and with nuclei in usable.
% 1.68/1.91
% 1.68/1.91 dependent: set(hyper_res).
% 1.68/1.91 dependent: set(factor).
% 1.68/1.91 dependent: set(unit_deletion).
% 1.68/1.91
% 1.68/1.91 ------------> process usable:
% 1.68/1.91 ** KEPT (pick-wt=3): 1 [] -e_qualish(e_1,e_2).
% 1.68/1.91 ** KEPT (pick-wt=3): 2 [] -e_qualish(e_1,e_3).
% 1.68/1.91 ** KEPT (pick-wt=3): 3 [] -e_qualish(e_1,e_4).
% 1.68/1.91 ** KEPT (pick-wt=3): 4 [] -e_qualish(e_2,e_1).
% 1.68/1.91 ** KEPT (pick-wt=3): 5 [] -e_qualish(e_2,e_3).
% 1.68/1.91 ** KEPT (pick-wt=3): 6 [] -e_qualish(e_2,e_4).
% 1.68/1.91 ** KEPT (pick-wt=3): 7 [] -e_qualish(e_3,e_1).
% 1.68/1.91 ** KEPT (pick-wt=3): 8 [] -e_qualish(e_3,e_2).
% 1.68/1.91 ** KEPT (pick-wt=3): 9 [] -e_qualish(e_3,e_4).
% 1.68/1.91 ** KEPT (pick-wt=3): 10 [] -e_qualish(e_4,e_1).
% 1.68/1.91 ** KEPT (pick-wt=3): 11 [] -e_qualish(e_4,e_2).
% 1.68/1.91 ** KEPT (pick-wt=3): 12 [] -e_qualish(e_4,e_3).
% 1.68/1.91 ** KEPT (pick-wt=20): 13 [] -group_element(A)| -group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)|product1(A,B,e_4).
% 1.68/1.91 ** KEPT (pick-wt=11): 14 [] -product1(A,B,C)| -product1(A,B,D)|e_qualish(C,D).
% 1.68/1.91 ** KEPT (pick-wt=11): 15 [] -product1(A,B,C)| -product1(A,D,C)|e_qualish(B,D).
% 1.68/1.91 ** KEPT (pick-wt=11): 16 [] -product1(A,B,C)| -product1(D,B,C)|e_qualish(A,D).
% 1.68/1.91 ** KEPT (pick-wt=20): 17 [] -group_element(A)| -group_element(B)|product2(A,B,e_1)|product2(A,B,e_2)|product2(A,B,e_3)|product2(A,B,e_4).
% 1.68/1.91 ** KEPT (pick-wt=11): 18 [] -product2(A,B,C)| -product2(A,B,D)|e_qualish(C,D).
% 1.68/1.91 ** KEPT (pick-wt=11): 19 [] -product2(A,B,C)| -product2(A,D,C)|e_qualish(B,D).
% 1.68/1.91 ** KEPT (pick-wt=11): 20 [] -product2(A,B,C)| -product2(D,B,C)|e_qualish(A,D).
% 1.68/1.91 ** KEPT (pick-wt=12): 21 [] -product1(A,B,C)| -product1(C,A,D)|product2(D,B,A).
% 1.68/1.91
% 1.68/1.91 ------------> process sos:
% 1.68/1.91 ** KEPT (pick-wt=2): 31 [] group_element(e_1).
% 1.68/1.91 ** KEPT (pick-wt=2): 32 [] group_element(e_2).
% 1.68/1.91 ** KEPT (pick-wt=2): 33 [] group_element(e_3).
% 1.68/1.91 ** KEPT (pick-wt=2): 34 [] group_element(e_4).
% 1.68/1.91 ** KEPT (pick-wt=4): 35 [] product1(A,A,A).
% 1.68/1.91 ** KEPT (pick-wt=4): 36 [] product2(A,A,A).
% 1.68/1.91 36 back subsumes 30.
% 1.68/1.91
% 1.68/1.91 ======= end of input processing =======
% 1.68/1.91
% 1.68/1.91 =========== start of search ===========
% 1.68/1.91
% 1.68/1.91 -------- PROOF --------
% 1.68/1.91
% 1.68/1.91 ----> UNIT CONFLICT at 0.03 sec ----> 267 [binary,266.1,5.1] $F.
% 1.68/1.91
% 1.68/1.91 Length of proof is 35. Level of proof is 14.
% 1.68/1.91
% 1.68/1.91 ---------------- PROOF ----------------
% 1.68/1.91 % SZS status Unsatisfiable
% 1.68/1.91 % SZS output start Refutation
% See solution above
% 1.68/1.91 ------------ end of proof -------------
% 1.68/1.91
% 1.68/1.91
% 1.68/1.91 Search stopped by max_proofs option.
% 1.68/1.91
% 1.68/1.91
% 1.68/1.91 Search stopped by max_proofs option.
% 1.68/1.91
% 1.68/1.91 ============ end of search ============
% 1.68/1.91
% 1.68/1.91 -------------- statistics -------------
% 1.68/1.91 clauses given 75
% 1.68/1.91 clauses generated 2317
% 1.68/1.91 clauses kept 266
% 1.68/1.91 clauses forward subsumed 2078
% 1.68/1.91 clauses back subsumed 179
% 1.68/1.91 Kbytes malloced 976
% 1.68/1.91
% 1.68/1.91 ----------- times (seconds) -----------
% 1.68/1.91 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.68/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.91
% 1.68/1.91 That finishes the proof of the theorem.
% 1.68/1.91
% 1.68/1.91 Process 18224 finished Wed Jul 27 04:31:04 2022
% 1.76/1.91 Otter interrupted
% 1.76/1.91 PROOF FOUND
%------------------------------------------------------------------------------