%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : COM003+2 : TPTP v8.1.2. Bugfixed v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n004.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 0.41s 1.38s
% Output   : Proof 0.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM003+2 : TPTP v8.1.2. Bugfixed v2.2.0.
% 0.07/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n004.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri May 19 03:19:24 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.41/1.38  
% 0.41/1.38  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 0.41/1.38  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.41/1.38  %-----------------------------------------------------
% 0.41/1.38  ncf(matrix, plain, [(262 ^ _38387) ^ [] : [-(algorithm_program_decides(260 ^ []))], (12 ^ _38387) ^ [_38842] : [14 ^ _38387 : [(15 ^ _38387) ^ [] : [-(program(13 ^ [_38842]))], (18 ^ _38387) ^ [] : [decides(_38842, 13 ^ [_38842], 16 ^ [_38842])]], -(program_decides(_38842))], (2 ^ _38387) ^ [_38515] : [program_decides(_38515), 5 ^ _38387 : [(6 ^ _38387) ^ [_38651] : [program(_38651), 9 ^ _38387 : [(10 ^ _38387) ^ [_38768] : [-(decides(_38515, _38651, _38768))]]]]], (22 ^ _38387) ^ [_39258] : [program_program_decides(_39258), 25 ^ _38387 : [(26 ^ _38387) ^ [] : [-(program(_39258))], (28 ^ _38387) ^ [] : [-(program_decides(_39258))]]], (30 ^ _38387) ^ [_39481] : [-(program_program_decides(_39481)), program(_39481), program_decides(_39481)], (40 ^ _38387) ^ [_39781] : [algorithm_program_decides(_39781), 43 ^ _38387 : [(44 ^ _38387) ^ [] : [-(algorithm(_39781))], (46 ^ _38387) ^ [] : [-(program_decides(_39781))]]], (48 ^ _38387) ^ [_40004] : [-(algorithm_program_decides(_40004)), algorithm(_40004), program_decides(_40004)], (58 ^ _38387) ^ [_40318, _40320] : [program_halts2(_40320, _40318), 61 ^ _38387 : [(62 ^ _38387) ^ [] : [-(program(_40320))], (64 ^ _38387) ^ [] : [-(halts2(_40320, _40318))]]], (66 ^ _38387) ^ [_40553, _40555] : [-(program_halts2(_40555, _40553)), program(_40555), halts2(_40555, _40553)], (76 ^ _38387) ^ [_40909, _40911, _40913, _40915] : [halts3_outputs(_40915, _40913, _40911, _40909), 79 ^ _38387 : [(80 ^ _38387) ^ [] : [-(halts3(_40915, _40913, _40911))], (82 ^ _38387) ^ [] : [-(outputs(_40915, _40909))]]], (84 ^ _38387) ^ [_41168, _41170, _41172, _41174] : [-(halts3_outputs(_41174, _41172, _41170, _41168)), halts3(_41174, _41172, _41170), outputs(_41174, _41168)], (94 ^ _38387) ^ [_41524, _41526] : [program_not_halts2(_41526, _41524), 97 ^ _38387 : [(98 ^ _38387) ^ [] : [-(program(_41526))], (100 ^ _38387) ^ [] : [halts2(_41526, _41524)]]], (102 ^ _38387) ^ [_41760, _41762] : [-(program_not_halts2(_41762, _41760)), program(_41762), -(halts2(_41762, _41760))], (112 ^ _38387) ^ [_42105, _42107, _42109] : [halts2_outputs(_42109, _42107, _42105), 115 ^ _38387 : [(116 ^ _38387) ^ [] : [-(halts2(_42109, _42107))], (118 ^ _38387) ^ [] : [-(outputs(_42109, _42105))]]], (120 ^ _38387) ^ [_42352, _42354, _42356] : [-(halts2_outputs(_42356, _42354, _42352)), halts2(_42356, _42354), outputs(_42356, _42352)], (140 ^ _38387) ^ [_43001, _43003, _43005, _43007] : [141 ^ _38387 : [(142 ^ _38387) ^ [] : [-(program_halts2(_43005, _43003))], (144 ^ _38387) ^ [] : [halts3_outputs(_43007, _43005, _43003, _43001)]], -(program_halts2_halts3_outputs(_43007, _43005, _43003, _43001))], (130 ^ _38387) ^ [_42722, _42724, _42726, _42728] : [program_halts2_halts3_outputs(_42728, _42726, _42724, _42722), program_halts2(_42726, _42724), -(halts3_outputs(_42728, _42726, _42724, _42722))], (158 ^ _38387) ^ [_43648, _43650, _43652, _43654] : [159 ^ _38387 : [(160 ^ _38387) ^ [] : [-(program_not_halts2(_43652, _43650))], (162 ^ _38387) ^ [] : [halts3_outputs(_43654, _43652, _43650, _43648)]], -(program_not_halts2_halts3_outputs(_43654, _43652, _43650, _43648))], (148 ^ _38387) ^ [_43369, _43371, _43373, _43375] : [program_not_halts2_halts3_outputs(_43375, _43373, _43371, _43369), program_not_halts2(_43373, _43371), -(halts3_outputs(_43375, _43373, _43371, _43369))], (176 ^ _38387) ^ [_44267, _44269, _44271] : [177 ^ _38387 : [(178 ^ _38387) ^ [] : [-(program_halts2(_44269, _44269))], (180 ^ _38387) ^ [] : [halts2_outputs(_44271, _44269, _44267)]], -(program_halts2_halts2_outputs(_44271, _44269, _44267))], (166 ^ _38387) ^ [_44002, _44004, _44006] : [program_halts2_halts2_outputs(_44006, _44004, _44002), program_halts2(_44004, _44004), -(halts2_outputs(_44006, _44004, _44002))], (194 ^ _38387) ^ [_44874, _44876, _44878] : [195 ^ _38387 : [(196 ^ _38387) ^ [] : [-(program_not_halts2(_44876, _44876))], (198 ^ _38387) ^ [] : [halts2_outputs(_44878, _44876, _44874)]], -(program_not_halts2_halts2_outputs(_44878, _44876, _44874))], (184 ^ _38387) ^ [_44609, _44611, _44613] : [program_not_halts2_halts2_outputs(_44613, _44611, _44609), program_not_halts2(_44611, _44611), -(halts2_outputs(_44613, _44611, _44609))], (202 ^ _38387) ^ [] : [203 ^ _38387 : [(204 ^ _38387) ^ [_45173] : [algorithm_program_decides(_45173)]], -(program_program_decides(205 ^ []))], (209 ^ _38387) ^ [_45339] : [program_program_decides(_45339), 212 ^ _38387 : [(213 ^ _38387) ^ [_45498, _45500] : [-(program_halts2_halts3_outputs(_45339, _45500, _45498, good))], (215 ^ _38387) ^ [_45548, _45550] : [-(program_not_halts2_halts3_outputs(_45339, _45550, _45548, bad))]]], (217 ^ _38387) ^ [] : [230 ^ _38387 : [(231 ^ _38387) ^ [] : [-(program(229 ^ []))], (233 ^ _38387) ^ [_46133] : [-(program_halts2_halts2_outputs(229 ^ [], _46133, good))], (235 ^ _38387) ^ [_46178] : [-(program_not_halts2_halts2_outputs(229 ^ [], _46178, bad))]], 218 ^ _38387 : [(219 ^ _38387) ^ [_45684] : [program(_45684), program_halts2_halts3_outputs(_45684, 222 ^ [_45684], 222 ^ [_45684], good), program_not_halts2_halts3_outputs(_45684, 222 ^ [_45684], 222 ^ [_45684], bad)]]], (237 ^ _38387) ^ [] : [250 ^ _38387 : [(251 ^ _38387) ^ [] : [-(program(249 ^ []))], (259 ^ _38387) ^ [_46889] : [-(program_not_halts2_halts2_outputs(249 ^ [], _46889, good))], (253 ^ _38387) ^ [_46747] : [program_halts2(_46747, _46747), halts2(249 ^ [], _46747)]], 238 ^ _38387 : [(239 ^ _38387) ^ [_46292] : [program(_46292), program_halts2_halts2_outputs(_46292, 242 ^ [_46292], good), program_not_halts2_halts2_outputs(_46292, 242 ^ [_46292], bad)]]]], input).
% 0.41/1.38  ncf('1',plain,[253 : program_halts2(249 ^ [], 249 ^ []), 253 : halts2(249 ^ [], 249 ^ []), 239 : program(229 ^ []), 239 : program_halts2_halts2_outputs(229 ^ [], 242 ^ [229 ^ []], good), 239 : program_not_halts2_halts2_outputs(229 ^ [], 242 ^ [229 ^ []], bad)],start(237 ^ 0,bind([[_46747, _46292], [249 ^ [], 229 ^ []]]))).
% 0.41/1.38  ncf('1.1',plain,[-(program_halts2(249 ^ [], 249 ^ [])), program(249 ^ []), halts2(249 ^ [], 249 ^ [])],extension(66 ^ 3,bind([[_40553, _40555], [249 ^ [], 249 ^ []]]))).
% 0.41/1.38  ncf('1.1.1',plain,[-(program(249 ^ []))],extension(251 ^ 4)).
% 0.41/1.38  ncf('1.1.2',plain,[-(halts2(249 ^ [], 249 ^ [])), -(program_not_halts2(249 ^ [], 249 ^ [])), program(249 ^ [])],extension(102 ^ 4,bind([[_41760, _41762], [249 ^ [], 249 ^ []]]))).
% 0.41/1.38  ncf('1.1.2.1',plain,[program_not_halts2(249 ^ [], 249 ^ []), program_not_halts2_halts2_outputs(249 ^ [], 249 ^ [], good), -(halts2_outputs(249 ^ [], 249 ^ [], good))],extension(184 ^ 5,bind([[_44609, _44611, _44613], [good, 249 ^ [], 249 ^ []]]))).
% 0.41/1.38  ncf('1.1.2.1.1',plain,[-(program_not_halts2_halts2_outputs(249 ^ [], 249 ^ [], good))],extension(259 ^ 6,bind([[_46889], [249 ^ []]]))).
% 0.41/1.38  ncf('1.1.2.1.2',plain,[halts2_outputs(249 ^ [], 249 ^ [], good), 116 : -(halts2(249 ^ [], 249 ^ []))],extension(112 ^ 6,bind([[_42105, _42107, _42109], [good, 249 ^ [], 249 ^ []]]))).
% 0.41/1.38  ncf('1.1.2.1.2.1',plain,[halts2(249 ^ [], 249 ^ [])],reduction('1.1')).
% 0.41/1.38  ncf('1.1.2.2',plain,[-(program(249 ^ []))],lemmata('[1].x')).
% 0.41/1.38  ncf('1.2',plain,[-(halts2(249 ^ [], 249 ^ [])), program_halts2(249 ^ [], 249 ^ [])],extension(58 ^ 3,bind([[_40318, _40320], [249 ^ [], 249 ^ []]]))).
% 0.41/1.38  ncf('1.2.1',plain,[-(program_halts2(249 ^ [], 249 ^ []))],lemmata('x')).
% 0.41/1.38  ncf('1.3',plain,[-(program(229 ^ [])), 219 : program(205 ^ []), 219 : program_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], good), 219 : program_not_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], bad)],extension(217 ^ 3,bind([[_45684], [205 ^ []]]))).
% 0.41/1.38  ncf('1.3.1',plain,[-(program(205 ^ [])), program_program_decides(205 ^ [])],extension(22 ^ 6,bind([[_39258], [205 ^ []]]))).
% 0.41/1.38  ncf('1.3.1.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.3.1.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.3.2',plain,[-(program_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], good)), program_program_decides(205 ^ [])],extension(209 ^ 6,bind([[_45339, _45498, _45500], [205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []]]]))).
% 0.41/1.38  ncf('1.3.2.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.3.2.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.3.3',plain,[-(program_not_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], bad)), program_program_decides(205 ^ [])],extension(209 ^ 6,bind([[_45339, _45548, _45550], [205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []]]]))).
% 0.41/1.38  ncf('1.3.3.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.3.3.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.4',plain,[-(program_halts2_halts2_outputs(229 ^ [], 242 ^ [229 ^ []], good)), 219 : program(205 ^ []), 219 : program_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], good), 219 : program_not_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], bad)],extension(217 ^ 3,bind([[_46133, _45684], [242 ^ [229 ^ []], 205 ^ []]]))).
% 0.41/1.38  ncf('1.4.1',plain,[-(program(205 ^ [])), program_program_decides(205 ^ [])],extension(22 ^ 6,bind([[_39258], [205 ^ []]]))).
% 0.41/1.38  ncf('1.4.1.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.4.1.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.4.2',plain,[-(program_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], good)), program_program_decides(205 ^ [])],extension(209 ^ 6,bind([[_45339, _45498, _45500], [205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []]]]))).
% 0.41/1.38  ncf('1.4.2.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.4.2.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.4.3',plain,[-(program_not_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], bad)), program_program_decides(205 ^ [])],extension(209 ^ 6,bind([[_45339, _45548, _45550], [205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []]]]))).
% 0.41/1.38  ncf('1.4.3.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.4.3.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.5',plain,[-(program_not_halts2_halts2_outputs(229 ^ [], 242 ^ [229 ^ []], bad)), 219 : program(205 ^ []), 219 : program_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], good), 219 : program_not_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], bad)],extension(217 ^ 3,bind([[_46178, _45684], [242 ^ [229 ^ []], 205 ^ []]]))).
% 0.41/1.38  ncf('1.5.1',plain,[-(program(205 ^ [])), program_program_decides(205 ^ [])],extension(22 ^ 6,bind([[_39258], [205 ^ []]]))).
% 0.41/1.38  ncf('1.5.1.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.5.1.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.5.2',plain,[-(program_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], good)), program_program_decides(205 ^ [])],extension(209 ^ 6,bind([[_45339, _45498, _45500], [205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []]]]))).
% 0.41/1.38  ncf('1.5.2.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.5.2.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  ncf('1.5.3',plain,[-(program_not_halts2_halts3_outputs(205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []], bad)), program_program_decides(205 ^ [])],extension(209 ^ 6,bind([[_45339, _45548, _45550], [205 ^ [], 222 ^ [205 ^ []], 222 ^ [205 ^ []]]]))).
% 0.41/1.38  ncf('1.5.3.1',plain,[-(program_program_decides(205 ^ [])), 204 : algorithm_program_decides(260 ^ [])],extension(202 ^ 7,bind([[_45173], [260 ^ []]]))).
% 0.41/1.38  ncf('1.5.3.1.1',plain,[-(algorithm_program_decides(260 ^ []))],extension(262 ^ 10)).
% 0.41/1.38  %-----------------------------------------------------
% 0.41/1.38  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------