TSTP Solution File: COM003+3 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : COM003+3 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n031.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 : Fri May 19 10:14:31 EDT 2023
% Result : Theorem 0.43s 1.39s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COM003+3 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.13 % Command : nanocop.sh %s %d
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri May 19 03:37:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.43/1.39
% 0.43/1.39 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.43/1.39 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.43/1.39 %-----------------------------------------------------
% 0.43/1.39 ncf(matrix, plain, [(123 ^ _71051) ^ [] : [-(algorithm(121 ^ []))], (125 ^ _71051) ^ [_75277] : [program(_75277), 128 ^ _71051 : [(129 ^ _71051) ^ [_75388] : [-(decides(121 ^ [], _75277, _75388))]]], (2 ^ _71051) ^ [] : [3 ^ _71051 : [(4 ^ _71051) ^ [_71180] : [algorithm(_71180), 8 ^ _71051 : [(9 ^ _71051) ^ [] : [-(program(7 ^ [_71180]))], (12 ^ _71051) ^ [] : [decides(_71180, 7 ^ [_71180], 10 ^ [_71180])]]]], 14 ^ _71051 : [(15 ^ _71051) ^ [] : [-(program(13 ^ []))], (17 ^ _71051) ^ [_71655] : [program(_71655), 20 ^ _71051 : [(21 ^ _71051) ^ [_71766] : [-(decides(13 ^ [], _71655, _71766))]]]]], (23 ^ _71051) ^ [_71875] : [program(_71875), 29 ^ _71051 : [(30 ^ _71051) ^ [] : [-(program(28 ^ [_71875]))], (33 ^ _71051) ^ [] : [decides(_71875, 28 ^ [_71875], 31 ^ [_71875])]], 34 ^ _71051 : [(35 ^ _71051) ^ [_72365, _72367] : [42 ^ _71051 : [(43 ^ _71051) ^ [] : [-(halts3(_71875, _72367, _72365))], (45 ^ _71051) ^ [] : [-(outputs(_71875, good))]], program(_72367), halts2(_72367, _72365)], (47 ^ _71051) ^ [_72705, _72707] : [54 ^ _71051 : [(55 ^ _71051) ^ [] : [-(halts3(_71875, _72707, _72705))], (57 ^ _71051) ^ [] : [-(outputs(_71875, bad))]], program(_72707), -(halts2(_72707, _72705))]]], (59 ^ _71051) ^ [_73071] : [program(_73071), 68 ^ _71051 : [(69 ^ _71051) ^ [] : [-(program(64 ^ [_73071]))], (71 ^ _71051) ^ [] : [-(halts2(64 ^ [_73071], 65 ^ [_73071]))], (73 ^ _71051) ^ [] : [halts3(_73071, 64 ^ [_73071], 65 ^ [_73071]), outputs(_73071, good)]], 78 ^ _71051 : [(79 ^ _71051) ^ [] : [-(program(64 ^ [_73071]))], (81 ^ _71051) ^ [] : [halts2(64 ^ [_73071], 65 ^ [_73071])], (83 ^ _71051) ^ [] : [halts3(_73071, 64 ^ [_73071], 65 ^ [_73071]), outputs(_73071, bad)]], 89 ^ _71051 : [(90 ^ _71051) ^ [] : [-(program(88 ^ [_73071]))], (92 ^ _71051) ^ [_74345] : [halts2(88 ^ [_73071], _74345), program(_74345), halts3(_73071, _74345, _74345), outputs(_73071, good)], (106 ^ _71051) ^ [_74698] : [117 ^ _71051 : [(118 ^ _71051) ^ [] : [-(halts2(88 ^ [_73071], _74698))], (120 ^ _71051) ^ [] : [-(outputs(88 ^ [_73071], bad))]], program(_74698), halts3(_73071, _74698, _74698), outputs(_73071, bad)]]]], input).
% 0.43/1.39 ncf('1',plain,[program(13 ^ []), 73 : halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []]), 73 : outputs(13 ^ [], good), 81 : halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []]), 92 : halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []]), 92 : program(88 ^ [13 ^ []]), 92 : halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]), 92 : outputs(13 ^ [], good)],start(59 ^ 0,bind([[_73071, _74345], [13 ^ [], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.1',plain,[-(program(13 ^ [])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 1,bind([[_71180], [121 ^ []]]))).
% 0.43/1.39 ncf('1.1.1',plain,[-(algorithm(121 ^ []))],extension(123 ^ 4)).
% 0.43/1.39 ncf('1.1.2',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 6,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.1.2.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 9)).
% 0.43/1.39 ncf('1.2',plain,[-(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])), 35 : program(64 ^ [13 ^ []]), 35 : halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []]), 35 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 3,bind([[_71875, _72365, _72367], [13 ^ [], 65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.2.1',plain,[-(program(64 ^ [13 ^ []]))],extension(69 ^ 6)).
% 0.43/1.39 ncf('1.2.2',plain,[-(halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []])), 55 : -(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])), 55 : program(64 ^ [13 ^ []])],extension(47 ^ 6,bind([[_72705, _72707], [65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.2.2.1',plain,[halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])],reduction('1')).
% 0.43/1.39 ncf('1.2.2.2',plain,[-(program(64 ^ [13 ^ []]))],lemmata('[1].x')).
% 0.43/1.39 ncf('1.2.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.2.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 6,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.2.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 11)).
% 0.43/1.39 ncf('1.2.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.2.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 11,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.2.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 14)).
% 0.43/1.39 ncf('1.3',plain,[-(outputs(13 ^ [], good)), 35 : program(7 ^ [121 ^ []]), 35 : halts2(7 ^ [121 ^ []], 7 ^ [121 ^ []]), 35 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 3,bind([[_71875, _72365, _72367], [13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.3.1',plain,[-(program(7 ^ [121 ^ []])), 4 : algorithm(121 ^ []), 15 : -(program(13 ^ []))],extension(2 ^ 6,bind([[_71180], [121 ^ []]]))).
% 0.43/1.39 ncf('1.3.1.1',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.3.1.2',plain,[program(13 ^ []), 118 : -(halts2(88 ^ [13 ^ []], 13 ^ [])), 118 : halts3(13 ^ [], 13 ^ [], 13 ^ []), 118 : outputs(13 ^ [], bad), 106 : program(13 ^ []), 69 : -(program(64 ^ [13 ^ []])), 79 : -(program(64 ^ [13 ^ []]))],extension(59 ^ 9,bind([[_73071, _74698], [13 ^ [], 13 ^ []]]))).
% 0.43/1.39 ncf('1.3.1.2.1',plain,[halts2(88 ^ [13 ^ []], 13 ^ []), 45 : -(outputs(13 ^ [], good)), 45 : program(88 ^ [13 ^ []])],extension(35 ^ 14,bind([[_72365, _72367], [13 ^ [], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.1.2.1.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.1.2.1.2',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 15)).
% 0.43/1.39 ncf('1.3.1.2.2',plain,[-(halts3(13 ^ [], 13 ^ [], 13 ^ [])), program(13 ^ []), halts2(13 ^ [], 13 ^ [])],extension(35 ^ 12,bind([[_72365, _72367], [13 ^ [], 13 ^ []]]))).
% 0.43/1.39 ncf('1.3.1.2.2.1',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.3.1.2.2.2',plain,[-(halts2(13 ^ [], 13 ^ [])), 55 : -(halts3(13 ^ [], 13 ^ [], 13 ^ [])), 55 : program(13 ^ [])],extension(47 ^ 13,bind([[_72705, _72707], [13 ^ [], 13 ^ []]]))).
% 0.43/1.39 ncf('1.3.1.2.2.2.1',plain,[halts3(13 ^ [], 13 ^ [], 13 ^ [])],reduction('1.3.1.2')).
% 0.43/1.39 ncf('1.3.1.2.2.2.2',plain,[-(program(13 ^ []))],lemmata('[2, 1, 3, 1].x')).
% 0.43/1.39 ncf('1.3.1.2.3',plain,[-(outputs(13 ^ [], bad)), program(13 ^ []), -(halts2(13 ^ [], _22301))],extension(47 ^ 12,bind([[_72705, _72707], [_22301, 13 ^ []]]))).
% 0.43/1.39 ncf('1.3.1.2.3.1',plain,[-(program(13 ^ []))],reduction('1.3.1')).
% 0.43/1.39 ncf('1.3.1.2.3.2',plain,[halts2(13 ^ [], _22301), 45 : -(outputs(13 ^ [], good)), 45 : program(13 ^ [])],extension(35 ^ 13,bind([[_72365, _72367], [_22301, 13 ^ []]]))).
% 0.43/1.39 ncf('1.3.1.2.3.2.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.1.2.3.2.2',plain,[-(program(13 ^ []))],lemmata('[2, 1, 3, 1].x')).
% 0.43/1.39 ncf('1.3.1.2.4',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.3.1.2.5',plain,[program(64 ^ [13 ^ []]), 45 : -(outputs(13 ^ [], good)), 45 : halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []])],extension(35 ^ 12,bind([[_72365, _72367], [65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.1.2.5.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.1.2.5.2',plain,[-(halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []]))],extension(71 ^ 13)).
% 0.43/1.39 ncf('1.3.1.2.6',plain,[program(64 ^ [13 ^ []]), 57 : -(outputs(13 ^ [], bad)), 57 : -(halts2(64 ^ [13 ^ []], _24638))],extension(47 ^ 12,bind([[_72705, _72707], [_24638, 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.1.2.6.1',plain,[outputs(13 ^ [], bad), halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])],extension(83 ^ 15)).
% 0.43/1.39 ncf('1.3.1.2.6.1.1',plain,[-(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []]))],lemmata('x')).
% 0.43/1.39 ncf('1.3.1.2.6.2',plain,[halts2(64 ^ [13 ^ []], _24638), 45 : -(outputs(13 ^ [], good)), 45 : program(64 ^ [13 ^ []])],extension(35 ^ 13,bind([[_72365, _72367], [_24638, 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.1.2.6.2.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.1.2.6.2.2',plain,[-(program(64 ^ [13 ^ []]))],reduction('1.3.1.2')).
% 0.43/1.39 ncf('1.3.2',plain,[-(halts2(7 ^ [121 ^ []], 7 ^ [121 ^ []])), 55 : -(halts3(13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []])), 55 : program(7 ^ [121 ^ []]), 47 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 6,bind([[_71875, _72705, _72707], [13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.1',plain,[halts3(13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []]), 118 : -(halts2(88 ^ [13 ^ []], 7 ^ [121 ^ []])), 118 : program(7 ^ [121 ^ []]), 118 : outputs(13 ^ [], bad), 106 : program(13 ^ []), 69 : -(program(64 ^ [13 ^ []])), 79 : -(program(64 ^ [13 ^ []]))],extension(59 ^ 11,bind([[_73071, _74698], [13 ^ [], 7 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.1.1',plain,[halts2(88 ^ [13 ^ []], 7 ^ [121 ^ []]), 45 : -(outputs(13 ^ [], good)), 45 : program(88 ^ [13 ^ []])],extension(35 ^ 16,bind([[_72365, _72367], [7 ^ [121 ^ []], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.1.1.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.2.1.1.2',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 17)).
% 0.43/1.39 ncf('1.3.2.1.2',plain,[-(program(7 ^ [121 ^ []]))],lemmata('[1].x')).
% 0.43/1.39 ncf('1.3.2.1.3',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 14)).
% 0.43/1.39 ncf('1.3.2.1.4',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.3.2.1.5',plain,[program(64 ^ [13 ^ []]), 45 : -(outputs(13 ^ [], good)), 45 : halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []])],extension(35 ^ 14,bind([[_72365, _72367], [65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.1.5.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.2.1.5.2',plain,[-(halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []]))],extension(71 ^ 15)).
% 0.43/1.39 ncf('1.3.2.1.6',plain,[program(64 ^ [13 ^ []]), 57 : -(outputs(13 ^ [], bad)), 57 : -(halts2(64 ^ [13 ^ []], _30686))],extension(47 ^ 14,bind([[_72705, _72707], [_30686, 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.1.6.1',plain,[outputs(13 ^ [], bad), halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])],extension(83 ^ 17)).
% 0.43/1.39 ncf('1.3.2.1.6.1.1',plain,[-(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []]))],lemmata('x')).
% 0.43/1.39 ncf('1.3.2.1.6.2',plain,[halts2(64 ^ [13 ^ []], _30686), 45 : -(outputs(13 ^ [], good)), 45 : program(64 ^ [13 ^ []])],extension(35 ^ 15,bind([[_72365, _72367], [_30686, 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.1.6.2.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.3.2.1.6.2.2',plain,[-(program(64 ^ [13 ^ []]))],reduction('1.3.2.1')).
% 0.43/1.39 ncf('1.3.2.2',plain,[-(program(7 ^ [121 ^ []]))],lemmata('[1].x')).
% 0.43/1.39 ncf('1.3.2.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.3.2.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 9,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.3.2.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 14)).
% 0.43/1.39 ncf('1.3.2.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 12)).
% 0.43/1.39 ncf('1.3.2.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 14,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.3.2.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 17)).
% 0.43/1.39 ncf('1.3.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.3.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 6,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.3.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 11)).
% 0.43/1.39 ncf('1.3.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.3.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 11,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.3.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 14)).
% 0.43/1.39 ncf('1.4',plain,[-(halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []])), 55 : -(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])), 55 : program(64 ^ [13 ^ []]), 47 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 3,bind([[_71875, _72705, _72707], [13 ^ [], 65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.4.1',plain,[halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []]), outputs(13 ^ [], bad)],extension(83 ^ 8)).
% 0.43/1.39 ncf('1.4.1.1',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 9)).
% 0.43/1.39 ncf('1.4.2',plain,[-(program(64 ^ [13 ^ []]))],extension(79 ^ 6)).
% 0.43/1.39 ncf('1.4.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.4.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 6,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.4.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 11)).
% 0.43/1.39 ncf('1.4.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.4.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 11,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.4.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 14)).
% 0.43/1.39 ncf('1.5',plain,[-(halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []])), 55 : -(halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []])), 55 : program(88 ^ [13 ^ []]), 47 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 3,bind([[_71875, _72705, _72707], [13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1',plain,[halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]), 92 : halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []]), 92 : program(88 ^ [13 ^ []]), 92 : outputs(13 ^ [], good), 92 : program(13 ^ []), 69 : -(program(64 ^ [13 ^ []])), 79 : -(program(64 ^ [13 ^ []]))],extension(59 ^ 8,bind([[_73071, _74345], [13 ^ [], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.1',plain,[-(halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []])), 55 : -(halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []])), 55 : program(88 ^ [13 ^ []])],extension(47 ^ 11,bind([[_72705, _72707], [88 ^ [13 ^ []], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.1.1',plain,[halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]), 118 : -(halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []])), 118 : program(88 ^ [13 ^ []]), 118 : outputs(13 ^ [], bad)],extension(106 ^ 14,bind([[_74698], [88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.1.1.1',plain,[halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []])],reduction('1.5.1')).
% 0.43/1.39 ncf('1.5.1.1.1.2',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 15)).
% 0.43/1.39 ncf('1.5.1.1.1.3',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 15)).
% 0.43/1.39 ncf('1.5.1.1.2',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 12)).
% 0.43/1.39 ncf('1.5.1.2',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 11)).
% 0.43/1.39 ncf('1.5.1.3',plain,[-(outputs(13 ^ [], good)), program(88 ^ [13 ^ []]), halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []])],extension(35 ^ 11,bind([[_72365, _72367], [88 ^ [13 ^ []], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.3.1',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 12)).
% 0.43/1.39 ncf('1.5.1.3.2',plain,[-(halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []])), program(88 ^ [13 ^ []]), halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]), outputs(13 ^ [], bad)],extension(106 ^ 12,bind([[_74698], [88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.3.2.1',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 13)).
% 0.43/1.39 ncf('1.5.1.3.2.2',plain,[-(halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]))],reduction('1.5')).
% 0.43/1.39 ncf('1.5.1.3.2.3',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 13)).
% 0.43/1.39 ncf('1.5.1.4',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.5.1.5',plain,[program(64 ^ [13 ^ []]), 43 : -(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])), 43 : halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []])],extension(35 ^ 11,bind([[_72365, _72367], [65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.5.1',plain,[halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []]), outputs(13 ^ [], good)],extension(73 ^ 14)).
% 0.43/1.39 ncf('1.5.1.5.1.1',plain,[-(outputs(13 ^ [], good))],extension(45 ^ 15)).
% 0.43/1.39 ncf('1.5.1.5.2',plain,[-(halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []]))],extension(71 ^ 12)).
% 0.43/1.39 ncf('1.5.1.6',plain,[program(64 ^ [13 ^ []]), 55 : -(halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []])), 55 : -(halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []]))],extension(47 ^ 11,bind([[_72705, _72707], [65 ^ [13 ^ []], 64 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.5.1.6.1',plain,[halts3(13 ^ [], 64 ^ [13 ^ []], 65 ^ [13 ^ []]), outputs(13 ^ [], bad)],extension(83 ^ 14)).
% 0.43/1.39 ncf('1.5.1.6.1.1',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 15)).
% 0.43/1.39 ncf('1.5.1.6.2',plain,[halts2(64 ^ [13 ^ []], 65 ^ [13 ^ []])],extension(81 ^ 12)).
% 0.43/1.39 ncf('1.5.2',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 6)).
% 0.43/1.39 ncf('1.5.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.5.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 6,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.5.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 11)).
% 0.43/1.39 ncf('1.5.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.5.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 11,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.5.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 14)).
% 0.43/1.39 ncf('1.6',plain,[-(program(88 ^ [13 ^ []]))],extension(90 ^ 3)).
% 0.43/1.39 ncf('1.7',plain,[-(halts3(13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []])), 35 : program(88 ^ [13 ^ []]), 35 : halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []]), 35 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 3,bind([[_71875, _72365, _72367], [13 ^ [], 88 ^ [13 ^ []], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.7.1',plain,[-(program(88 ^ [13 ^ []]))],lemmata('x')).
% 0.43/1.39 ncf('1.7.2',plain,[-(halts2(88 ^ [13 ^ []], 88 ^ [13 ^ []]))],lemmata('x')).
% 0.43/1.39 ncf('1.7.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.7.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 6,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.7.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 11)).
% 0.43/1.39 ncf('1.7.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.7.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 11,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.7.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 14)).
% 0.43/1.39 ncf('1.8',plain,[-(outputs(13 ^ [], good)), 35 : program(7 ^ [121 ^ []]), 35 : halts2(7 ^ [121 ^ []], 7 ^ [121 ^ []]), 35 : program(13 ^ []), 30 : -(program(28 ^ [13 ^ []]))],extension(23 ^ 3,bind([[_71875, _72365, _72367], [13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.8.1',plain,[-(program(7 ^ [121 ^ []])), 4 : algorithm(121 ^ []), 15 : -(program(13 ^ []))],extension(2 ^ 6,bind([[_71180], [121 ^ []]]))).
% 0.43/1.39 ncf('1.8.1.1',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.8.1.2',plain,[program(13 ^ []), 55 : -(halts3(13 ^ [], 13 ^ [], 13 ^ [])), 55 : -(halts2(13 ^ [], 13 ^ []))],extension(47 ^ 9,bind([[_72705, _72707], [13 ^ [], 13 ^ []]]))).
% 0.43/1.39 ncf('1.8.1.2.1',plain,[halts3(13 ^ [], 13 ^ [], 13 ^ []), 118 : -(halts2(88 ^ [13 ^ []], 13 ^ [])), 118 : program(13 ^ []), 118 : outputs(13 ^ [], bad)],extension(106 ^ 12,bind([[_74698], [13 ^ []]]))).
% 0.43/1.39 ncf('1.8.1.2.1.1',plain,[halts2(88 ^ [13 ^ []], 13 ^ []), 45 : -(outputs(13 ^ [], good)), 45 : program(88 ^ [13 ^ []])],extension(35 ^ 15,bind([[_72365, _72367], [13 ^ [], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.8.1.2.1.1.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.8.1.2.1.1.2',plain,[-(program(88 ^ [13 ^ []]))],lemmata('x')).
% 0.43/1.39 ncf('1.8.1.2.1.2',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.8.1.2.1.3',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 13)).
% 0.43/1.39 ncf('1.8.1.2.2',plain,[halts2(13 ^ [], 13 ^ []), 45 : -(outputs(13 ^ [], good)), 45 : program(13 ^ [])],extension(35 ^ 10,bind([[_72365, _72367], [13 ^ [], 13 ^ []]]))).
% 0.43/1.39 ncf('1.8.1.2.2.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.8.1.2.2.2',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.8.2',plain,[-(halts2(7 ^ [121 ^ []], 7 ^ [121 ^ []])), 55 : -(halts3(13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []])), 55 : program(7 ^ [121 ^ []])],extension(47 ^ 6,bind([[_72705, _72707], [7 ^ [121 ^ []], 7 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.8.2.1',plain,[halts3(13 ^ [], 7 ^ [121 ^ []], 7 ^ [121 ^ []]), 118 : -(halts2(88 ^ [13 ^ []], 7 ^ [121 ^ []])), 118 : program(7 ^ [121 ^ []]), 118 : outputs(13 ^ [], bad)],extension(106 ^ 9,bind([[_74698], [7 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.8.2.1.1',plain,[halts2(88 ^ [13 ^ []], 7 ^ [121 ^ []]), 45 : -(outputs(13 ^ [], good)), 45 : program(88 ^ [13 ^ []])],extension(35 ^ 12,bind([[_72365, _72367], [7 ^ [121 ^ []], 88 ^ [13 ^ []]]]))).
% 0.43/1.39 ncf('1.8.2.1.1.1',plain,[outputs(13 ^ [], good)],reduction('1')).
% 0.43/1.39 ncf('1.8.2.1.1.2',plain,[-(program(88 ^ [13 ^ []]))],lemmata('x')).
% 0.43/1.39 ncf('1.8.2.1.2',plain,[-(program(7 ^ [121 ^ []]))],lemmata('[1].x')).
% 0.43/1.39 ncf('1.8.2.1.3',plain,[-(outputs(13 ^ [], bad))],extension(57 ^ 10)).
% 0.43/1.39 ncf('1.8.2.2',plain,[-(program(7 ^ [121 ^ []]))],lemmata('[1].x')).
% 0.43/1.39 ncf('1.8.3',plain,[-(program(13 ^ []))],lemmata('x')).
% 0.43/1.39 ncf('1.8.4',plain,[program(28 ^ [13 ^ []]), 21 : -(decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])), 4 : algorithm(121 ^ []), 9 : -(program(7 ^ [121 ^ []]))],extension(2 ^ 6,bind([[_71655, _71766, _71180], [28 ^ [13 ^ []], 31 ^ [13 ^ []], 121 ^ []]]))).
% 0.43/1.39 ncf('1.8.4.1',plain,[decides(13 ^ [], 28 ^ [13 ^ []], 31 ^ [13 ^ []])],extension(33 ^ 11)).
% 0.43/1.39 ncf('1.8.4.2',plain,[-(algorithm(121 ^ []))],extension(123 ^ 9)).
% 0.43/1.39 ncf('1.8.4.3',plain,[program(7 ^ [121 ^ []]), 129 : -(decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []]))],extension(125 ^ 11,bind([[_75277, _75388], [7 ^ [121 ^ []], 10 ^ [121 ^ []]]]))).
% 0.43/1.39 ncf('1.8.4.3.1',plain,[decides(121 ^ [], 7 ^ [121 ^ []], 10 ^ [121 ^ []])],extension(12 ^ 14)).
% 0.43/1.39 %-----------------------------------------------------
% 0.43/1.39 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------