TSTP Solution File: GRA003+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% 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 : 600s
% DateTime : Sat Jul 16 07:19:04 EDT 2022
% Result : Theorem 1.78s 2.43s
% Output : Proof 1.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : leancop_casc.sh %s %d
% 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 : 600
% 0.12/0.33 % DateTime : Tue May 31 01:51:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.78/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.78/2.44 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.78/2.44
% 1.78/2.44 %-----------------------------------------------------
% 1.78/2.44 fof(vertices_and_edges, conjecture, ! [_78933, _78936, _78939, _78942, _78945] : (shortest_path(_78933, _78936, _78945) & precedes(_78939, _78942, _78945) => vertex(_78933) & vertex(_78936) & (! _78933) = _78936 & edge(_78939) & edge(_78942) & (! _78939) = _78942 & path(_78933, _78936, _78945)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vertices_and_edges)).
% 1.78/2.44 fof(path_properties, axiom, ! [_79406, _79409, _79412] : (path(_79406, _79409, _79412) => vertex(_79406) & vertex(_79409) & ? [_79447] : (edge(_79447) & _79406 = tail_of(_79447) & (_79409 = head_of(_79447) & _79412 = path_cons(_79447, empty) <~> ? [_79495] : (path(head_of(_79447), _79409, _79495) & _79412 = path_cons(_79447, _79495))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', path_properties)).
% 1.78/2.44 fof(on_path_properties, axiom, ! [_79874, _79877, _79880, _79883] : (path(_79874, _79877, _79880) & on_path(_79883, _79880) => edge(_79883) & in_path(head_of(_79883), _79880) & in_path(tail_of(_79883), _79880)), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', on_path_properties)).
% 1.78/2.44 fof(precedes_properties, axiom, ! [_80156, _80159, _80162] : (path(_80159, _80162, _80156) => ! [_80183, _80186] : (precedes(_80183, _80186, _80156) => on_path(_80183, _80156) & on_path(_80186, _80156) & (sequential(_80183, _80186) <~> ? [_80237] : (sequential(_80183, _80237) & precedes(_80237, _80186, _80156))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', precedes_properties)).
% 1.78/2.44 fof(shortest_path_properties, axiom, ! [_80561, _80564, _80567, _80570, _80573] : (shortest_path(_80561, _80564, _80573) & precedes(_80567, _80570, _80573) => ~ ? [_80609] : (tail_of(_80609) = tail_of(_80567) & head_of(_80609) = head_of(_80570)) & ~ precedes(_80570, _80567, _80573)), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', shortest_path_properties)).
% 1.78/2.44 fof(shortest_path_defn, axiom, ! [_80917, _80920, _80923] : (shortest_path(_80917, _80920, _80923) <=> path(_80917, _80920, _80923) & (! _80917) = _80920 & ! [_80965] : (path(_80917, _80920, _80965) => less_or_equal(length_of(_80923), length_of(_80965)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', shortest_path_defn)).
% 1.78/2.44
% 1.78/2.44 cnf(1, plain, [-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))], clausify(vertices_and_edges)).
% 1.78/2.44 cnf(2, plain, [-(precedes(11 ^ [], 12 ^ [], 13 ^ []))], clausify(vertices_and_edges)).
% 1.78/2.44 cnf(3, plain, [vertex(9 ^ []), vertex(10 ^ []), -(9 ^ [] = 10 ^ []), edge(11 ^ []), edge(12 ^ []), -(11 ^ [] = 12 ^ []), path(9 ^ [], 10 ^ [], 13 ^ [])], clausify(vertices_and_edges)).
% 1.78/2.44 cnf(4, plain, [_25167 = _25216, -(head_of(_25167) = head_of(_25216))], theory(equality)).
% 1.78/2.44 cnf(5, plain, [-(_16865 = _16865)], theory(equality)).
% 1.78/2.44 cnf(6, plain, [-(path(_20059, _20226, _20389)), path(_19974, _20143, _20308), _19974 = _20059, _20143 = _20226, _20308 = _20389], theory(equality)).
% 1.78/2.44 cnf(7, plain, [path(_31126, _31241, _31355), -(vertex(_31126))], clausify(path_properties)).
% 1.78/2.44 cnf(8, plain, [path(_31126, _31241, _31355), -(vertex(_31241))], clausify(path_properties)).
% 1.78/2.44 cnf(9, plain, [-(edge(_32770)), path(_32542, _32619, _32695), on_path(_32770, _32695)], clausify(on_path_properties)).
% 1.78/2.44 cnf(10, plain, [path(_36303, _36402, _36203), precedes(_36599, _36689, _36203), -(on_path(_36599, _36203))], clausify(precedes_properties)).
% 1.78/2.44 cnf(11, plain, [path(_36303, _36402, _36203), precedes(_36599, _36689, _36203), -(on_path(_36689, _36203))], clausify(precedes_properties)).
% 1.78/2.44 cnf(12, plain, [precedes(_38606, _38702, _38797), shortest_path(_38411, _38509, _38797), tail_of(_39123) = tail_of(_38606), head_of(_39123) = head_of(_38702)], clausify(shortest_path_properties)).
% 1.78/2.44 cnf(13, plain, [shortest_path(_37496, _37578, _37659), -(path(_37496, _37578, _37659))], clausify(shortest_path_defn)).
% 1.78/2.44 cnf(14, plain, [shortest_path(_37496, _37578, _37659), _37496 = _37578], clausify(shortest_path_defn)).
% 1.78/2.44
% 1.78/2.44 cnf('1',plain,[shortest_path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 10 ^ []],start(14,bind([[_37659, _37496, _37578], [13 ^ [], 9 ^ [], 10 ^ []]]))).
% 1.78/2.44 cnf('1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2',plain,[-(9 ^ [] = 10 ^ []), vertex(9 ^ []), vertex(10 ^ []), edge(11 ^ []), edge(12 ^ []), -(11 ^ [] = 12 ^ []), path(9 ^ [], 10 ^ [], 13 ^ [])],extension(3)).
% 1.78/2.44 cnf('1.2.1',plain,[-(vertex(9 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ [])],extension(7,bind([[_31126, _31241, _31355], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(6,bind([[_19974, _20059, _20143, _20226, _20308, _20389], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.1.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.1.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.1.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(5,bind([[_16865], [9 ^ []]]))).
% 1.78/2.44 cnf('1.2.1.1.3',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_16865], [10 ^ []]]))).
% 1.78/2.44 cnf('1.2.1.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(5,bind([[_16865], [13 ^ []]]))).
% 1.78/2.44 cnf('1.2.2',plain,[-(vertex(10 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ [])],extension(8,bind([[_31126, _31241, _31355], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.2.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(6,bind([[_19974, _20059, _20143, _20226, _20308, _20389], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.2.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.2.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.2.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(5,bind([[_16865], [9 ^ []]]))).
% 1.78/2.44 cnf('1.2.2.1.3',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_16865], [10 ^ []]]))).
% 1.78/2.44 cnf('1.2.2.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(5,bind([[_16865], [13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3',plain,[-(edge(11 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), on_path(11 ^ [], 13 ^ [])],extension(9,bind([[_32542, _32619, _32770, _32695], [9 ^ [], 10 ^ [], 11 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(6,bind([[_19974, _20059, _20143, _20226, _20308, _20389], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.3.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(5,bind([[_16865], [9 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.1.3',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_16865], [10 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(5,bind([[_16865], [13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.2',plain,[-(on_path(11 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(10,bind([[_36303, _36402, _36599, _36689, _36203], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.2.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.3.2.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.3.2.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(2)).
% 1.78/2.44 cnf('1.2.4',plain,[-(edge(12 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), on_path(12 ^ [], 13 ^ [])],extension(9,bind([[_32542, _32619, _32770, _32695], [9 ^ [], 10 ^ [], 12 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(6,bind([[_19974, _20059, _20143, _20226, _20308, _20389], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.4.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(5,bind([[_16865], [9 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.1.3',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_16865], [10 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(5,bind([[_16865], [13 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.2',plain,[-(on_path(12 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(11,bind([[_36303, _36402, _36599, _36689, _36203], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.2.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.4.2.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.4.2.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(2)).
% 1.78/2.44 cnf('1.2.5',plain,[11 ^ [] = 12 ^ [], -(head_of(11 ^ []) = head_of(12 ^ []))],extension(4,bind([[_25167, _25216], [11 ^ [], 12 ^ []]]))).
% 1.78/2.44 cnf('1.2.5.1',plain,[head_of(11 ^ []) = head_of(12 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ []), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), tail_of(11 ^ []) = tail_of(11 ^ [])],extension(12,bind([[_38702, _38411, _38509, _38797, _39123, _38606], [12 ^ [], 9 ^ [], 10 ^ [], 13 ^ [], 11 ^ [], 11 ^ []]]))).
% 1.78/2.44 cnf('1.2.5.1.1',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(2)).
% 1.78/2.44 cnf('1.2.5.1.2',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.5.1.3',plain,[-(tail_of(11 ^ []) = tail_of(11 ^ []))],extension(5,bind([[_16865], [tail_of(11 ^ [])]]))).
% 1.78/2.44 cnf('1.2.6',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(6,bind([[_19974, _20059, _20143, _20226, _20308, _20389], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(6,bind([[_19974, _20059, _20143, _20226, _20308, _20389], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(13,bind([[_37496, _37578, _37659], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(1)).
% 1.78/2.44 cnf('1.2.6.1.2',plain,[-(9 ^ [] = 9 ^ [])],extension(5,bind([[_16865], [9 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.1.3',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_16865], [10 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(5,bind([[_16865], [13 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.2',plain,[-(9 ^ [] = 9 ^ [])],extension(5,bind([[_16865], [9 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.3',plain,[-(10 ^ [] = 10 ^ [])],extension(5,bind([[_16865], [10 ^ []]]))).
% 1.78/2.44 cnf('1.2.6.4',plain,[-(13 ^ [] = 13 ^ [])],extension(5,bind([[_16865], [13 ^ []]]))).
% 1.78/2.44 %-----------------------------------------------------
% 1.78/2.45
% 1.78/2.45 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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