TSTP Solution File: NUN076+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUN076+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:10:31 EDT 2022
% Result : Theorem 1.95s 2.20s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of clauses : 28 ( 20 unt; 0 nHn; 9 RR)
% Number of literals : 48 ( 0 equ; 21 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 47 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( id(A,dollar_c1)
| ~ r1(A) ),
file('NUN076+1.p',unknown),
[] ).
cnf(4,axiom,
( r2(A,B)
| ~ id(B,dollar_f1(A)) ),
file('NUN076+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ id(A,B)
| id(B,A) ),
file('NUN076+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ id(A,B)
| id(A,C)
| ~ id(B,C) ),
file('NUN076+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ id(A,B)
| ~ r1(B)
| r1(A) ),
file('NUN076+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ id(A,B)
| ~ id(C,D)
| ~ r2(A,C)
| r2(B,D) ),
file('NUN076+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ id(A,B)
| ~ id(C,D)
| ~ id(E,F)
| ~ r3(B,D,F)
| r3(A,C,E) ),
file('NUN076+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ id(A,B)
| ~ r4(C,D,A)
| ~ r2(E,C)
| ~ r1(F)
| ~ r2(F,E)
| ~ id(G,B)
| ~ r3(D,H,G) ),
file('NUN076+1.p',unknown),
[] ).
cnf(44,axiom,
id(A,A),
file('NUN076+1.p',unknown),
[] ).
cnf(55,axiom,
id(dollar_f13(A),A),
file('NUN076+1.p',unknown),
[] ).
cnf(56,axiom,
r1(dollar_f12(A)),
file('NUN076+1.p',unknown),
[] ).
cnf(57,axiom,
r3(A,dollar_f12(A),dollar_f13(A)),
file('NUN076+1.p',unknown),
[] ).
cnf(58,axiom,
r1(dollar_f14(A)),
file('NUN076+1.p',unknown),
[] ).
cnf(59,axiom,
r4(A,dollar_f14(A),dollar_f16(A)),
file('NUN076+1.p',unknown),
[] ).
cnf(60,axiom,
id(dollar_f16(A),dollar_f15(A)),
file('NUN076+1.p',unknown),
[] ).
cnf(61,axiom,
r1(dollar_f15(A)),
file('NUN076+1.p',unknown),
[] ).
cnf(68,plain,
r2(A,dollar_f1(A)),
inference(hyper,[status(thm)],[44,4]),
[iquote('hyper,44,4')] ).
cnf(70,plain,
id(dollar_f12(A),dollar_c1),
inference(hyper,[status(thm)],[56,1]),
[iquote('hyper,56,1')] ).
cnf(71,plain,
id(dollar_f14(A),dollar_c1),
inference(hyper,[status(thm)],[58,1]),
[iquote('hyper,58,1')] ).
cnf(72,plain,
id(dollar_f15(A),dollar_c1),
inference(hyper,[status(thm)],[61,1]),
[iquote('hyper,61,1')] ).
cnf(80,plain,
id(A,dollar_f13(A)),
inference(hyper,[status(thm)],[55,9]),
[iquote('hyper,55,9')] ).
cnf(89,plain,
r2(A,dollar_f1(dollar_f13(A))),
inference(hyper,[status(thm)],[68,13,55,44]),
[iquote('hyper,68,13,55,44')] ).
cnf(95,plain,
id(dollar_c1,dollar_f12(A)),
inference(hyper,[status(thm)],[70,9]),
[iquote('hyper,70,9')] ).
cnf(271,plain,
r1(dollar_f16(A)),
inference(hyper,[status(thm)],[60,12,61]),
[iquote('hyper,60,12,61')] ).
cnf(274,plain,
id(dollar_f16(A),dollar_c1),
inference(hyper,[status(thm)],[60,10,72]),
[iquote('hyper,60,10,72')] ).
cnf(623,plain,
r1(dollar_f13(dollar_f16(A))),
inference(hyper,[status(thm)],[271,12,55]),
[iquote('hyper,271,12,55')] ).
cnf(3499,plain,
r3(A,dollar_c1,A),
inference(hyper,[status(thm)],[57,16,44,95,80]),
[iquote('hyper,57,16,44,95,80')] ).
cnf(3943,plain,
$false,
inference(hyper,[status(thm)],[59,21,274,89,623,89,71,3499]),
[iquote('hyper,59,21,274,89,623,89,71,3499')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUN076+1 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 02:52:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox on n027.cluster.edu,
% 1.75/1.96 Wed Jul 27 02:52:36 2022
% 1.75/1.96 The command was "./otter". The process ID is 30024.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 exists Y24 all X19 (id(X19,Y24)&r1(X19)| -r1(X19)& -id(X19,Y24)).
% 1.75/1.96 all X11 exists Y21 all X12 (id(X12,Y21)&r2(X11,X12)| -r2(X11,X12)& -id(X12,Y21)).
% 1.75/1.96 all X13 X14 exists Y22 all X15 (id(X15,Y22)&r3(X13,X14,X15)| -r3(X13,X14,X15)& -id(X15,Y22)).
% 1.75/1.96 all X16 X17 exists Y23 all X18 (id(X18,Y23)&r4(X16,X17,X18)| -r4(X16,X17,X18)& -id(X18,Y23)).
% 1.75/1.96 all X20 id(X20,X20).
% 1.75/1.96 all X21 X22 (-id(X21,X22)|id(X22,X21)).
% 1.75/1.96 all X23 X24 X25 (-id(X23,X24)|id(X23,X25)| -id(X24,X25)).
% 1.75/1.96 all X26 X27 (-id(X26,X27)| -r1(X26)& -r1(X27)|r1(X26)&r1(X27)).
% 1.75/1.96 all X28 X29 X30 X31 (-id(X28,X30)| -id(X29,X31)| -r2(X28,X29)& -r2(X30,X31)|r2(X28,X29)&r2(X30,X31)).
% 1.75/1.96 all X32 X33 X34 X35 X36 X37 (-id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X32,X33,X34)& -r3(X35,X36,X37)|r3(X32,X33,X34)&r3(X35,X36,X37)).
% 1.75/1.96 all X38 X39 X40 X41 X42 X43 (-id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X38,X39,X40)& -r4(X41,X42,X43)|r4(X38,X39,X40)&r4(X41,X42,X43)).
% 1.75/1.96 all X1 X8 exists Y4 ((exists Y5 (id(Y5,Y4)& (exists Y15 (r2(X8,Y15)&r3(X1,Y15,Y5)))))& (exists Y7 (r2(Y7,Y4)&r3(X1,X8,Y7)))).
% 1.75/1.96 all X2 X9 exists Y2 ((exists Y3 (id(Y3,Y2)& (exists Y14 (r2(X9,Y14)&r4(X2,Y14,Y3)))))& (exists Y6 (r3(Y6,X2,Y2)&r4(X2,X9,Y6)))).
% 1.75/1.96 all X3 X10 ((all Y12 ((all Y13 (-id(Y13,Y12)| -r2(X3,Y13)))| -r2(X10,Y12)))|id(X3,X10)).
% 1.75/1.96 all X4 exists Y9 (id(Y9,X4)& (exists Y16 (r1(Y16)&r3(X4,Y16,Y9)))).
% 1.75/1.96 all X5 exists Y8 ((exists Y17 (r1(Y17)&r4(X5,Y17,Y8)))& (exists Y18 (id(Y8,Y18)&r1(Y18)))).
% 1.75/1.96 all X6 ((exists Y19 (id(X6,Y19)&r1(Y19)))| (exists Y1 Y11 (id(X6,Y11)&r2(Y1,Y11)))).
% 1.75/1.96 all X7 Y10 ((all Y20 (-id(Y20,Y10)| -r1(Y20)))| -r2(X7,Y10)).
% 1.75/1.96 -(exists Y1 Y2 Y3 ((exists Y4 (id(Y4,Y1)& (exists Y6 (r4(Y6,Y2,Y4)& (exists Y7 (r2(Y7,Y6)& (exists Y8 (r1(Y8)&r2(Y8,Y7)))))))))& (exists Y5 (id(Y5,Y1)&r3(Y2,Y3,Y5))))).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 -------> usable clausifies to:
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] id(X19,$c1)| -r1(X19).
% 1.75/1.96 0 [] r1(X19)| -id(X19,$c1).
% 1.75/1.96 0 [] id(X12,$f1(X11))| -r2(X11,X12).
% 1.75/1.96 0 [] r2(X11,X12)| -id(X12,$f1(X11)).
% 1.75/1.96 0 [] id(X15,$f2(X13,X14))| -r3(X13,X14,X15).
% 1.75/1.96 0 [] r3(X13,X14,X15)| -id(X15,$f2(X13,X14)).
% 1.75/1.96 0 [] id(X18,$f3(X16,X17))| -r4(X16,X17,X18).
% 1.75/1.96 0 [] r4(X16,X17,X18)| -id(X18,$f3(X16,X17)).
% 1.75/1.96 0 [] id(X20,X20).
% 1.75/1.96 0 [] -id(X21,X22)|id(X22,X21).
% 1.75/1.96 0 [] -id(X23,X24)|id(X23,X25)| -id(X24,X25).
% 1.75/1.96 0 [] -id(X26,X27)| -r1(X26)|r1(X27).
% 1.75/1.96 0 [] -id(X26,X27)| -r1(X27)|r1(X26).
% 1.75/1.96 0 [] -id(X28,X30)| -id(X29,X31)| -r2(X28,X29)|r2(X30,X31).
% 1.75/1.96 0 [] -id(X28,X30)| -id(X29,X31)| -r2(X30,X31)|r2(X28,X29).
% 1.75/1.96 0 [] -id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X32,X33,X34)|r3(X35,X36,X37).
% 1.75/1.97 0 [] -id(X32,X35)| -id(X33,X36)| -id(X34,X37)| -r3(X35,X36,X37)|r3(X32,X33,X34).
% 1.75/1.97 0 [] -id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X38,X39,X40)|r4(X41,X42,X43).
% 1.75/1.97 0 [] -id(X38,X41)| -id(X39,X42)| -id(X40,X43)| -r4(X41,X42,X43)|r4(X38,X39,X40).
% 1.75/1.97 0 [] id($f5(X1,X8),$f7(X1,X8)).
% 1.75/1.97 0 [] r2(X8,$f4(X1,X8)).
% 1.75/1.97 0 [] r3(X1,$f4(X1,X8),$f5(X1,X8)).
% 1.75/1.97 0 [] r2($f6(X1,X8),$f7(X1,X8)).
% 1.75/1.97 0 [] r3(X1,X8,$f6(X1,X8)).
% 1.75/1.97 0 [] id($f9(X2,X9),$f11(X2,X9)).
% 1.75/1.97 0 [] r2(X9,$f8(X2,X9)).
% 1.75/1.97 0 [] r4(X2,$f8(X2,X9),$f9(X2,X9)).
% 1.75/1.97 0 [] r3($f10(X2,X9),X2,$f11(X2,X9)).
% 1.75/1.97 0 [] r4(X2,X9,$f10(X2,X9)).
% 1.75/1.97 0 [] -id(Y13,Y12)| -r2(X3,Y13)| -r2(X10,Y12)|id(X3,X10).
% 1.75/1.97 0 [] id($f13(X4),X4).
% 1.75/1.97 0 [] r1($f12(X4)).
% 1.75/1.97 0 [] r3(X4,$f12(X4),$f13(X4)).
% 1.75/1.97 0 [] r1($f14(X5)).
% 1.75/1.97 0 [] r4(X5,$f14(X5),$f16(X5)).
% 1.75/1.97 0 [] id($f16(X5),$f15(X5)).
% 1.75/1.97 0 [] r1($f15(X5)).
% 1.75/1.97 0 [] id(X6,$f17(X6))|id(X6,$f18(X6)).
% 1.75/1.97 0 [] id(X6,$f17(X6))|r2($f19(X6),$f18(X6)).
% 1.75/1.97 0 [] r1($f17(X6))|id(X6,$f18(X6)).
% 1.75/1.97 0 [] r1($f17(X6))|r2($f19(X6),$f18(X6)).
% 1.75/1.97 0 [] -id(Y20,Y10)| -r1(Y20)| -r2(X7,Y10).
% 1.75/1.97 0 [] -id(Y4,Y1)| -r4(Y6,Y2,Y4)| -r2(Y7,Y6)| -r1(Y8)| -r2(Y8,Y7)| -id(Y5,Y1)| -r3(Y2,Y3,Y5).
% 1.95/2.20 end_of_list.
% 1.95/2.20
% 1.95/2.20 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=7.
% 1.95/2.20
% 1.95/2.20 This is a non-Horn set without equality. The strategy will
% 1.95/2.20 be ordered hyper_res, unit deletion, and factoring, with
% 1.95/2.20 satellites in sos and with nuclei in usable.
% 1.95/2.20
% 1.95/2.20 dependent: set(hyper_res).
% 1.95/2.20 dependent: set(factor).
% 1.95/2.20 dependent: set(unit_deletion).
% 1.95/2.20
% 1.95/2.20 ------------> process usable:
% 1.95/2.20 ** KEPT (pick-wt=5): 1 [] id(A,$c1)| -r1(A).
% 1.95/2.20 ** KEPT (pick-wt=5): 2 [] r1(A)| -id(A,$c1).
% 1.95/2.20 ** KEPT (pick-wt=7): 3 [] id(A,$f1(B))| -r2(B,A).
% 1.95/2.20 ** KEPT (pick-wt=7): 4 [] r2(A,B)| -id(B,$f1(A)).
% 1.95/2.20 ** KEPT (pick-wt=9): 5 [] id(A,$f2(B,C))| -r3(B,C,A).
% 1.95/2.20 ** KEPT (pick-wt=9): 6 [] r3(A,B,C)| -id(C,$f2(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=9): 7 [] id(A,$f3(B,C))| -r4(B,C,A).
% 1.95/2.20 ** KEPT (pick-wt=9): 8 [] r4(A,B,C)| -id(C,$f3(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=6): 9 [] -id(A,B)|id(B,A).
% 1.95/2.20 ** KEPT (pick-wt=9): 10 [] -id(A,B)|id(A,C)| -id(B,C).
% 1.95/2.20 ** KEPT (pick-wt=7): 11 [] -id(A,B)| -r1(A)|r1(B).
% 1.95/2.20 ** KEPT (pick-wt=7): 12 [] -id(A,B)| -r1(B)|r1(A).
% 1.95/2.20 ** KEPT (pick-wt=12): 13 [] -id(A,B)| -id(C,D)| -r2(A,C)|r2(B,D).
% 1.95/2.20 ** KEPT (pick-wt=12): 14 [] -id(A,B)| -id(C,D)| -r2(B,D)|r2(A,C).
% 1.95/2.20 ** KEPT (pick-wt=17): 15 [] -id(A,B)| -id(C,D)| -id(E,F)| -r3(A,C,E)|r3(B,D,F).
% 1.95/2.20 ** KEPT (pick-wt=17): 16 [] -id(A,B)| -id(C,D)| -id(E,F)| -r3(B,D,F)|r3(A,C,E).
% 1.95/2.20 ** KEPT (pick-wt=17): 17 [] -id(A,B)| -id(C,D)| -id(E,F)| -r4(A,C,E)|r4(B,D,F).
% 1.95/2.20 ** KEPT (pick-wt=17): 18 [] -id(A,B)| -id(C,D)| -id(E,F)| -r4(B,D,F)|r4(A,C,E).
% 1.95/2.20 ** KEPT (pick-wt=12): 19 [] -id(A,B)| -r2(C,A)| -r2(D,B)|id(C,D).
% 1.95/2.20 ** KEPT (pick-wt=8): 20 [] -id(A,B)| -r1(A)| -r2(C,B).
% 1.95/2.20 ** KEPT (pick-wt=22): 21 [] -id(A,B)| -r4(C,D,A)| -r2(E,C)| -r1(F)| -r2(F,E)| -id(G,B)| -r3(D,H,G).
% 1.95/2.20
% 1.95/2.20 ------------> process sos:
% 1.95/2.20 ** KEPT (pick-wt=3): 44 [] id(A,A).
% 1.95/2.20 ** KEPT (pick-wt=7): 45 [] id($f5(A,B),$f7(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=5): 46 [] r2(A,$f4(B,A)).
% 1.95/2.20 ** KEPT (pick-wt=8): 47 [] r3(A,$f4(A,B),$f5(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=7): 48 [] r2($f6(A,B),$f7(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=6): 49 [] r3(A,B,$f6(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=7): 50 [] id($f9(A,B),$f11(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=5): 51 [] r2(A,$f8(B,A)).
% 1.95/2.20 ** KEPT (pick-wt=8): 52 [] r4(A,$f8(A,B),$f9(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=8): 53 [] r3($f10(A,B),A,$f11(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=6): 54 [] r4(A,B,$f10(A,B)).
% 1.95/2.20 ** KEPT (pick-wt=4): 55 [] id($f13(A),A).
% 1.95/2.20 ** KEPT (pick-wt=3): 56 [] r1($f12(A)).
% 1.95/2.20 ** KEPT (pick-wt=6): 57 [] r3(A,$f12(A),$f13(A)).
% 1.95/2.20 ** KEPT (pick-wt=3): 58 [] r1($f14(A)).
% 1.95/2.20 ** KEPT (pick-wt=6): 59 [] r4(A,$f14(A),$f16(A)).
% 1.95/2.20 ** KEPT (pick-wt=5): 60 [] id($f16(A),$f15(A)).
% 1.95/2.20 ** KEPT (pick-wt=3): 61 [] r1($f15(A)).
% 1.95/2.20 ** KEPT (pick-wt=8): 62 [] id(A,$f17(A))|id(A,$f18(A)).
% 1.95/2.20 ** KEPT (pick-wt=9): 63 [] id(A,$f17(A))|r2($f19(A),$f18(A)).
% 1.95/2.20 ** KEPT (pick-wt=7): 64 [] r1($f17(A))|id(A,$f18(A)).
% 1.95/2.20 ** KEPT (pick-wt=8): 65 [] r1($f17(A))|r2($f19(A),$f18(A)).
% 1.95/2.20 44 back subsumes 36.
% 1.95/2.20
% 1.95/2.20 ======= end of input processing =======
% 1.95/2.20
% 1.95/2.20 =========== start of search ===========
% 1.95/2.20
% 1.95/2.20
% 1.95/2.20 Resetting weight limit to 7.
% 1.95/2.20
% 1.95/2.20
% 1.95/2.20 Resetting weight limit to 7.
% 1.95/2.20
% 1.95/2.20 sos_size=3208
% 1.95/2.20
% 1.95/2.20 -------- PROOF --------
% 1.95/2.20
% 1.95/2.20 -----> EMPTY CLAUSE at 0.24 sec ----> 3943 [hyper,59,21,274,89,623,89,71,3499] $F.
% 1.95/2.20
% 1.95/2.20 Length of proof is 11. Level of proof is 3.
% 1.95/2.20
% 1.95/2.20 ---------------- PROOF ----------------
% 1.95/2.20 % SZS status Theorem
% 1.95/2.20 % SZS output start Refutation
% See solution above
% 1.95/2.20 ------------ end of proof -------------
% 1.95/2.20
% 1.95/2.20
% 1.95/2.20 Search stopped by max_proofs option.
% 1.95/2.20
% 1.95/2.20
% 1.95/2.20 Search stopped by max_proofs option.
% 1.95/2.20
% 1.95/2.20 ============ end of search ============
% 1.95/2.20
% 1.95/2.20 -------------- statistics -------------
% 1.95/2.20 clauses given 56
% 1.95/2.20 clauses generated 12198
% 1.95/2.20 clauses kept 3942
% 1.95/2.20 clauses forward subsumed 2933
% 1.95/2.20 clauses back subsumed 235
% 1.95/2.20 Kbytes malloced 4882
% 1.95/2.20
% 1.95/2.20 ----------- times (seconds) -----------
% 1.95/2.20 user CPU time 0.24 (0 hr, 0 min, 0 sec)
% 1.95/2.20 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.20 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.20
% 1.95/2.20 That finishes the proof of the theorem.
% 1.95/2.20
% 1.95/2.20 Process 30024 finished Wed Jul 27 02:52:38 2022
% 1.95/2.20 Otter interrupted
% 1.95/2.20 PROOF FOUND
%------------------------------------------------------------------------------