TSTP Solution File: COL130+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL130+1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:48:19 EDT 2022
% Result : Unknown 2.54s 2.74s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL130+1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 02:22:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/2.03 ----- Otter 3.3f, August 2004 -----
% 1.81/2.03 The process was started by sandbox on n003.cluster.edu,
% 1.81/2.03 Wed Jul 27 02:22:56 2022
% 1.81/2.03 The command was "./otter". The process ID is 17942.
% 1.81/2.03
% 1.81/2.03 set(prolog_style_variables).
% 1.81/2.03 set(auto).
% 1.81/2.03 dependent: set(auto1).
% 1.81/2.03 dependent: set(process_input).
% 1.81/2.03 dependent: clear(print_kept).
% 1.81/2.03 dependent: clear(print_new_demod).
% 1.81/2.03 dependent: clear(print_back_demod).
% 1.81/2.03 dependent: clear(print_back_sub).
% 1.81/2.03 dependent: set(control_memory).
% 1.81/2.03 dependent: assign(max_mem, 12000).
% 1.81/2.03 dependent: assign(pick_given_ratio, 4).
% 1.81/2.03 dependent: assign(stats_level, 1).
% 1.81/2.03 dependent: assign(max_seconds, 10800).
% 1.81/2.03 clear(print_given).
% 1.81/2.03
% 1.81/2.03 formula_list(usable).
% 1.81/2.03 all A (A=A).
% 1.81/2.03 all X Y (a(a(k,X),Y)=X).
% 1.81/2.03 all X Y Z (a(a(a(s,X),Y),Z)=a(a(X,Z),a(Y,Z))).
% 1.81/2.03 -(all X0 X1 X2 X3 ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(a(a(X3,X7),X7),X4),X5),a(a(k,X1),X1)),a(s,a(X6,X2))),k),k),s)=a(a(a(X5,a(s,a(a(a(X2,k),X4),X1))),k),a(a(a(s,s),X3),X2))))-> ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(X3,X5),X4),X7),X5),a(a(a(a(s,k),X1),s),X4)),s),k)=a(a(a(X5,a(s,s)),a(X1,s)),s)))-> ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(a(X2,X6),X5),X7),X6),a(a(a(a(X5,s),X5),k),X1)),a(a(k,a(a(a(s,a(a(a(a(a(X4,k),X7),s),X1),k)),X5),X6)),a(X4,k))),k),k)=a(a(a(a(X4,a(a(k,a(s,a(a(a(X2,s),X0),k))),X7)),a(a(a(k,a(a(k,a(a(k,X3),s)),X5)),a(a(a(a(s,k),k),s),s)),X4)),a(X3,a(X5,k))),a(X0,X3))))-> ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(a(X2,X7),X4),X7),X7),a(X0,X6)),X0),a(s,a(a(a(s,X2),X6),X3))),a(X0,k))=a(a(a(X7,a(X1,a(s,X1))),a(a(a(a(a(a(a(a(X2,a(k,X3)),a(a(s,s),X2)),X7),X0),k),X2),X0),s)),a(s,a(a(a(a(a(s,X1),X1),s),s),s)))))-> ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(a(X1,X6),X7),X5),X5),a(a(a(a(X6,a(a(a(a(a(s,a(a(a(a(k,k),X6),X3),X3)),a(s,k)),s),k),X2)),a(a(a(s,s),k),k)),a(a(s,X2),X7)),a(a(X7,X6),X3))),a(a(a(a(a(a(s,X2),X2),s),s),X7),s)),a(X0,a(X1,k))),a(s,a(a(s,k),k)))=a(k,a(a(a(X2,a(X4,a(a(a(X6,a(a(k,X7),s)),s),s))),a(k,a(a(a(s,X6),k),X3))),a(a(a(X5,s),k),k)))))-> ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(a(X1,X4),X6),X7),X5),a(a(s,a(k,k)),a(a(a(k,k),X1),k))),X5),s),k)=a(a(a(a(X4,a(a(s,s),a(a(k,X1),X5))),a(X7,a(a(s,X4),s))),X7),s)))-> ((all X4 X5 X6 X7 (a(a(a(a(a(a(a(a(a(X0,X6),X4),X4),X4),a(a(s,a(a(k,X3),a(a(a(s,X4),s),k))),X1)),k),s),a(a(s,a(X5,X5)),X4)),X0)=a(a(s,a(a(k,a(a(a(k,a(X4,a(a(a(X5,X2),s),s))),a(X3,k)),a(X5,X7))),a(s,a(X2,k)))),a(a(a(k,a(a(a(a(k,a(X2,a(a(a(a(X5,s),X2),X7),X5))),a(a(s,s),X5)),X1),s)),a(s,a(a(s,k),k))),X0))))-> -(all X4 X5 X6 X7 (a(a(a(a(a(a(a(X0,X4),X5),X4),X5),a(s,X1)),X3),a(X4,a(a(X2,k),X3)))=a(a(a(a(X5,a(X1,s)),k),s),a(a(a(a(s,a(s,X1)),s),X7),s)))))))))))).
% 1.81/2.03 end_of_list.
% 1.81/2.03
% 1.81/2.03 -------> usable clausifies to:
% 1.81/2.03
% 1.81/2.03 list(usable).
% 1.81/2.03 0 [] A=A.
% 1.81/2.03 0 [] a(a(k,X),Y)=X.
% 1.81/2.03 0 [] a(a(a(s,X),Y),Z)=a(a(X,Z),a(Y,Z)).
% 1.81/2.03 0 [] a(a(a(a(a(a(a(a(a($c1,X7),X7),X4),X5),a(a(k,$c3),$c3)),a(s,a(X6,$c2))),k),k),s)=a(a(a(X5,a(s,a(a(a($c2,k),X4),$c3))),k),a(a(a(s,s),$c1),$c2)).
% 1.81/2.03 0 [] a(a(a(a(a(a(a($c1,X9),X8),X11),X9),a(a(a(a(s,k),$c3),s),X8)),s),k)=a(a(a(X9,a(s,s)),a($c3,s)),s).
% 1.81/2.03 0 [] a(a(a(a(a(a(a(a($c2,X14),X13),X15),X14),a(a(a(a(X13,s),X13),k),$c3)),a(a(k,a(a(a(s,a(a(a(a(a(X12,k),X15),s),$c3),k)),X13),X14)),a(X12,k))),k),k)=a(a(a(a(X12,a(a(k,a(s,a(a(a($c2,s),$c4),k))),X15)),a(a(a(k,a(a(k,a(a(k,$c1),s)),X13)),a(a(a(a(s,k),k),s),s)),X12)),a($c1,a(X13,k))),a($c4,$c1)).
% 1.81/2.03 0 [] a(a(a(a(a(a(a(a($c2,X19),X16),X19),X19),a($c4,X18)),$c4),a(s,a(a(a(s,$c2),X18),$c1))),a($c4,k))=a(a(a(X19,a($c3,a(s,$c3))),a(a(a(a(a(a(a(a($c2,a(k,$c1)),a(a(s,s),$c2)),X19),$c4),k),$c2),$c4),s)),a(s,a(a(a(a(a(s,$c3),$c3),s),s),s))).
% 1.81/2.03 0 [] a(a(a(a(a(a(a(a($c3,X22),X23),X21),X21),a(a(a(a(X22,a(a(a(a(a(s,a(a(a(a(k,k),X22),$c1),$c1)),a(s,k)),s),k),$c2)),a(a(a(s,s),k),k)),a(a(s,$c2),X23)),a(a(X23,X22),$c1))),a(a(a(a(a(a(s,$c2),$c2),s),s),X23),s)),a($c4,a($c3,k))),a(s,a(a(s,k),k)))=a(k,a(a(a($c2,a(X20,a(a(a(X22,a(a(k,X23),s)),s),s))),a(k,a(a(a(s,X22),k),$c1))),a(a(a(X21,s),k),k))).
% 1.81/2.03 0 [] a(a(a(a(a(a(a(a($c3,X24),X26),X27),X25),a(a(s,a(k,k)),a(a(a(k,k),$c3),k))),X25),s),k)=a(a(a(a(X24,a(a(s,s),a(a(k,$c3),X25))),a(X27,a(a(s,X24),s))),X27),s).
% 1.81/2.03 0 [] a(a(a(a(a(a(a(a(a($c4,X30),X28),X28),X28),a(a(s,a(a(k,$c1),a(a(a(s,X28),s),k))),$c3)),k),s),a(a(s,a(X29,X29)),X28)),$c4)=a(a(s,a(a(k,a(a(a(k,a(X28,a(a(a(X29,$c2),s),s))),a($c1,k)),a(X29,X31))),a(s,a($c2,k)))),a(a(a(k,a(a(a(a(k,a($c2,a(a(a(a(X29,s),$c2),X31),X29))),a(a(s,s),X29)),$c3),s)),a(s,a(a(s,k),k))),$c4)).
% 1.81/2.03 0 [] a(a(a(a(a(a(a($c4,X32),X33),X32),X33),a(s,$c3)),$c1),a(X32,a(a($c2,k),$c1)))=a(a(a(a(X33,a($c3,s)),k),s),a(a(a(a(s,a(s,$c3)),s),X35),s)).
% 1.81/2.03 end_of_list.
% 1.81/2.03
% 1.81/2.03 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.81/2.03
% 1.81/2.03 All clauses are units, and equality is present; the
% 1.81/2.03 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.81/2.03
% 1.81/2.03 dependent: set(knuth_bendix).
% 1.81/2.03 dependent: set(anl_eq).
% 1.81/2.03 dependent: set(para_from).
% 1.81/2.03 dependent: set(para_into).
% 1.81/2.03 dependent: clear(para_from_right).
% 1.81/2.03 dependent: clear(para_into_right).
% 1.81/2.03 dependent: set(para_from_vars).
% 1.81/2.03 dependent: set(eq_units_both_ways).
% 1.81/2.03 dependent: set(dynamic_demod_all).
% 1.81/2.03 dependent: set(dynamic_demod).
% 1.81/2.03 dependent: set(order_eq).
% 1.81/2.03 dependent: set(back_demod).
% 1.81/2.03 dependent: set(lrpo).
% 1.81/2.03
% 1.81/2.03 There is no negative clause, so all clause lists will
% 1.81/2.03 be printed at the end of the search.
% 1.81/2.03
% 1.81/2.03 dependent: set(print_lists_at_end).
% 1.81/2.03
% 1.81/2.03 ------------> process usable:
% 1.81/2.03
% 1.81/2.03 ------------> process sos:
% 1.81/2.03 ** KEPT (pick-wt=3): 1 [] A=A.
% 1.81/2.03 ** KEPT (pick-wt=7): 2 [] a(a(k,A),B)=A.
% 1.81/2.03 ---> New Demodulator: 3 [new_demod,2] a(a(k,A),B)=A.
% 1.81/2.03 ** KEPT (pick-wt=15): 4 [] a(a(a(s,A),B),C)=a(a(A,C),a(B,C)).
% 1.81/2.03 ** KEPT (pick-wt=45): 6 [copy,5,demod,3] a(a(a(a(a(a(a(a(a($c1,A),A),B),C),$c3),a(s,a(D,$c2))),k),k),s)=a(a(a(C,a(s,a(a(a($c2,k),B),$c3))),k),a(a(a(s,s),$c1),$c2)).
% 1.81/2.03 ---> New Demodulator: 7 [new_demod,6] a(a(a(a(a(a(a(a(a($c1,A),A),B),C),$c3),a(s,a(D,$c2))),k),k),s)=a(a(a(C,a(s,a(a(a($c2,k),B),$c3))),k),a(a(a(s,s),$c1),$c2)).
% 1.81/2.03 ** KEPT (pick-wt=35): 8 [] a(a(a(a(a(a(a($c1,A),B),C),A),a(a(a(a(s,k),$c3),s),B)),s),k)=a(a(a(A,a(s,s)),a($c3,s)),s).
% 1.81/2.03 ---> New Demodulator: 9 [new_demod,8] a(a(a(a(a(a(a($c1,A),B),C),A),a(a(a(a(s,k),$c3),s),B)),s),k)=a(a(a(A,a(s,s)),a($c3,s)),s).
% 1.81/2.03 ** KEPT (pick-wt=67): 11 [copy,10,demod,3,3,3,3,3] a(a(a(a(a(a(a(a($c2,A),B),C),A),a(a(a(a(B,s),B),k),$c3)),a(a(a(s,a(a(a(a(a(D,k),C),s),$c3),k)),B),A)),k),k)=a(a(a(a(D,a(s,a(a(a($c2,s),$c4),k))),a($c1,D)),a($c1,a(B,k))),a($c4,$c1)).
% 1.81/2.03 ---> New Demodulator: 12 [new_demod,11] a(a(a(a(a(a(a(a($c2,A),B),C),A),a(a(a(a(B,s),B),k),$c3)),a(a(a(s,a(a(a(a(a(D,k),C),s),$c3),k)),B),A)),k),k)=a(a(a(a(D,a(s,a(a(a($c2,s),$c4),k))),a($c1,D)),a($c1,a(B,k))),a($c4,$c1)).
% 1.81/2.03 ** KEPT (pick-wt=75): 13 [] a(a(a(a(a(a(a(a($c2,A),B),A),A),a($c4,C)),$c4),a(s,a(a(a(s,$c2),C),$c1))),a($c4,k))=a(a(a(A,a($c3,a(s,$c3))),a(a(a(a(a(a(a(a($c2,a(k,$c1)),a(a(s,s),$c2)),A),$c4),k),$c2),$c4),s)),a(s,a(a(a(a(a(s,$c3),$c3),s),s),s))).
% 1.81/2.03 ** KEPT (pick-wt=105): 15 [copy,14,demod,3,3,3] a(a(a(a(a(a(a(a($c3,A),B),C),C),a(a(a(a(A,a(a(a(a(a(s,$c1),a(s,k)),s),k),$c2)),a(a(a(s,s),k),k)),a(a(s,$c2),B)),a(a(B,A),$c1))),a(a(a(a(a(a(s,$c2),$c2),s),s),B),s)),a($c4,a($c3,k))),a(s,a(a(s,k),k)))=a(k,a(a(a($c2,a(D,a(a(a(A,B),s),s))),a(k,a(a(a(s,A),k),$c1))),a(a(a(C,s),k),k))).
% 1.81/2.03 ** KEPT (pick-wt=45): 17 [copy,16,demod,3,3] a(a(a(a(a(a(a(a($c3,A),B),C),D),a(a(s,a(k,k)),a(k,k))),D),s),k)=a(a(a(a(A,a(a(s,s),$c3)),a(C,a(a(s,A),s))),C),s).
% 1.81/2.03 ---> New Demodulator: 18 [new_demod,17] a(a(a(a(a(a(a(a($c3,A),B),C),D),a(a(s,a(k,k)),a(k,k))),D),s),k)=a(a(a(a(A,a(a(s,s),$c3)),a(C,a(a(s,A),s))),C),s).
% 1.81/2.03 ** KEPT (pick-wt=63): 20 [copy,19,demod,3,3,3,3,3] a(a(a(a(a(a(a(a(a($c4,A),B),B),B),a(a(s,$c1),$c3)),k),s),a(a(s,a(C,C)),B)),$c4)=a(a(s,a(a(B,a(a(a(C,$c2),s),s)),a(C,D))),a(a(a(a($c2,a(a(a(a(C,s),$c2),D),C)),$c3),s),$c4)).
% 1.81/2.03 ** KEPT (pick-wt=45): 21 [] a(a(a(a(a(a(a($c4,A),B),A),B),a(s,$c3)),$c1),a(A,a(a($c2,k),$c1)))=a(a(a(a(B,a($c3,s)),k),s),a(a(a(a(s,a(s,$c3)),s),C),s)).
% 1.81/2.03 Following clause subsumed by 1 during input processing: 0 [copy,1,flip.1] A=A.
% 1.81/2.03 >>>> Starting back demodulation with 3.
% 1.81/2.03 ** KEPT (pick-wt=15): 22 [copy,4,flip.1] a(a(A,B),a(C,B))=a(a(a(s,A),C),B).
% 1.81/2.03 >>>> Starting back demodulation with 7.
% 1.81/2.03 >>>> Starting back demodulation with 9.
% 1.81/2.03 >>>> Starting back demodulation with 12.
% 1.81/2.03 ** KEPT (pick-wt=75): 23 [copy,13,flip.1] a(a(a(A,a($c3,a(s,$c3))),a(a(a(a(a(a(a(a($c2,a(k,$c1)),a(a(s,s),$c2)),A),$c4),k),$c2),$c4),s)),a(s,a(a(a(a(a(s,$c3),$c3),s),s),s)))=a(a(a(a(a(a(a(a($c2,A),B),A),A),a($c4,C)),$c4),a(s,a(a(a(s,$c2),C),$c1))),a($c4,k)).
% 2.54/2.74 ** KEPT (pick-wt=105): 24 [copy,15,flip.1] a(k,a(a(a($c2,a(A,a(a(a(B,C),s),s))),a(k,a(a(a(s,B),k),$c1))),a(a(a(D,s),k),k)))=a(a(a(a(a(a(a(a($c3,B),C),D),D),a(a(a(a(B,a(a(a(a(a(s,$c1),a(s,k)),s),k),$c2)),a(a(a(s,s),k),k)),a(a(s,$c2),C)),a(a(C,B),$c1))),a(a(a(a(a(a(s,$c2),$c2),s),s),C),s)),a($c4,a($c3,k))),a(s,a(a(s,k),k))).
% 2.54/2.74 >>>> Starting back demodulation with 18.
% 2.54/2.74 ** KEPT (pick-wt=63): 25 [copy,20,flip.1] a(a(s,a(a(A,a(a(a(B,$c2),s),s)),a(B,C))),a(a(a(a($c2,a(a(a(a(B,s),$c2),C),B)),$c3),s),$c4))=a(a(a(a(a(a(a(a(a($c4,D),A),A),A),a(a(s,$c1),$c3)),k),s),a(a(s,a(B,B)),A)),$c4).
% 2.54/2.74 ** KEPT (pick-wt=45): 26 [copy,21,flip.1] a(a(a(a(A,a($c3,s)),k),s),a(a(a(a(s,a(s,$c3)),s),B),s))=a(a(a(a(a(a(a($c4,C),A),C),A),a(s,$c3)),$c1),a(C,a(a($c2,k),$c1))).
% 2.54/2.74 Following clause subsumed by 4 during input processing: 0 [copy,22,flip.1] a(a(a(s,A),B),C)=a(a(A,C),a(B,C)).
% 2.54/2.74 Following clause subsumed by 13 during input processing: 0 [copy,23,flip.1] a(a(a(a(a(a(a(a($c2,A),B),A),A),a($c4,C)),$c4),a(s,a(a(a(s,$c2),C),$c1))),a($c4,k))=a(a(a(A,a($c3,a(s,$c3))),a(a(a(a(a(a(a(a($c2,a(k,$c1)),a(a(s,s),$c2)),A),$c4),k),$c2),$c4),s)),a(s,a(a(a(a(a(s,$c3),$c3),s),s),s))).
% 2.54/2.74 Following clause subsumed by 15 during input processing: 0 [copy,24,flip.1] a(a(a(a(a(a(a(a($c3,A),B),C),C),a(a(a(a(A,a(a(a(a(a(s,$c1),a(s,k)),s),k),$c2)),a(a(a(s,s),k),k)),a(a(s,$c2),B)),a(a(B,A),$c1))),a(a(a(a(a(a(s,$c2),$c2),s),s),B),s)),a($c4,a($c3,k))),a(s,a(a(s,k),k)))=a(k,a(a(a($c2,a(D,a(a(a(A,B),s),s))),a(k,a(a(a(s,A),k),$c1))),a(a(a(C,s),k),k))).
% 2.54/2.74 Following clause subsumed by 20 during input processing: 0 [copy,25,flip.1] a(a(a(a(a(a(a(a(a($c4,A),B),B),B),a(a(s,$c1),$c3)),k),s),a(a(s,a(C,C)),B)),$c4)=a(a(s,a(a(B,a(a(a(C,$c2),s),s)),a(C,D))),a(a(a(a($c2,a(a(a(a(C,s),$c2),D),C)),$c3),s),$c4)).
% 2.54/2.74 Following clause subsumed by 21 during input processing: 0 [copy,26,flip.1] a(a(a(a(a(a(a($c4,A),B),A),B),a(s,$c3)),$c1),a(A,a(a($c2,k),$c1)))=a(a(a(a(B,a($c3,s)),k),s),a(a(a(a(s,a(s,$c3)),s),C),s)).
% 2.54/2.74
% 2.54/2.74 ======= end of input processing =======
% 2.54/2.74
% 2.54/2.74 =========== start of search ===========
% 2.54/2.74
% 2.54/2.74
% 2.54/2.74 Resetting weight limit to 17.
% 2.54/2.74
% 2.54/2.74
% 2.54/2.74 Resetting weight limit to 17.
% 2.54/2.74
% 2.54/2.74 sos_size=155
% 2.54/2.74
% 2.54/2.74 Search stopped because sos empty.
% 2.54/2.74
% 2.54/2.74
% 2.54/2.74 Search stopped because sos empty.
% 2.54/2.74
% 2.54/2.74 ============ end of search ============
% 2.54/2.74
% 2.54/2.74 list(usable).
% 2.54/2.74 455 [para_into,454.1.1,454.1.1] A=B.
% 2.54/2.74 end_of_list.
% 2.54/2.74
% 2.54/2.74 list(sos).
% 2.54/2.74 end_of_list.
% 2.54/2.74
% 2.54/2.74 list(demodulators).
% 2.54/2.74 428 [new_demod,427] k=$c4.
% 2.54/2.74 444 [new_demod,443] a($c4,A)=$c4.
% 2.54/2.74 452 [new_demod,451] a(A,$c4)=$c4.
% 2.54/2.74 end_of_list.
% 2.54/2.74
% 2.54/2.74
% 2.54/2.74 -------------- statistics -------------
% 2.54/2.74 clauses given 208
% 2.54/2.74 clauses generated 60867
% 2.54/2.74 clauses kept 284
% 2.54/2.74 clauses forward subsumed 3371
% 2.54/2.74 clauses back subsumed 10
% 2.54/2.74 Kbytes malloced 6835
% 2.54/2.74
% 2.54/2.74 ----------- times (seconds) -----------
% 2.54/2.74 user CPU time 0.71 (0 hr, 0 min, 0 sec)
% 2.54/2.74 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.54/2.74 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.54/2.74
% 2.54/2.74 Process 17942 finished Wed Jul 27 02:22:58 2022
% 2.54/2.74 Otter interrupted
% 2.54/2.74 PROOF NOT FOUND
%------------------------------------------------------------------------------