TSTP Solution File: GRA002+3 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n024.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 47.86s 46.92s
% Output : Proof 47.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.00/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n024.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 02:57:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 47.86/46.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.93/46.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 47.93/46.93
% 47.93/46.93 %-----------------------------------------------------
% 47.93/46.93 fof(sequential_pairs_and_triangles, axiom, ! [_71129, _71132, _71135] : (path(_71132, _71135, _71129) & ! [_71156, _71159] : (on_path(_71156, _71129) & on_path(_71159, _71129) & sequential(_71156, _71159) => ? [_71197] : triangle(_71156, _71159, _71197)) => number_of_in(sequential_pairs, _71129) = number_of_in(triangles, _71129)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sequential_pairs_and_triangles)).
% 47.93/46.93 fof(shortest_path_defn, axiom, ! [_71556, _71559, _71562] : (shortest_path(_71556, _71559, _71562) <=> path(_71556, _71559, _71562) & (! _71556) = _71559 & ! [_71604] : (path(_71556, _71559, _71604) => less_or_equal(length_of(_71562), length_of(_71604)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', shortest_path_defn)).
% 47.93/46.93 fof(precedes_defn, axiom, ! [_71878, _71881, _71884] : (path(_71881, _71884, _71878) => ! [_71905, _71908] : (precedes(_71905, _71908, _71878) <= on_path(_71905, _71878) & on_path(_71908, _71878) & (sequential(_71905, _71908) | ? [_71959] : (sequential(_71905, _71959) & precedes(_71959, _71908, _71878))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax', precedes_defn)).
% 47.93/46.93 fof(maximal_path_length, conjecture, complete => ! [_72303, _72306, _72309] : (shortest_path(_72306, _72309, _72303) => less_or_equal(minus(length_of(_72303), n1), number_of_in(triangles, graph))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', maximal_path_length)).
% 47.93/46.93 fof(path_length_sequential_pairs, axiom, ! [_72607, _72610, _72613] : (path(_72607, _72610, _72613) => number_of_in(sequential_pairs, _72613) = minus(length_of(_72613), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', path_length_sequential_pairs)).
% 47.93/46.93 fof(graph_has_them_all, axiom, ! [_72819, _72822] : less_or_equal(number_of_in(_72819, _72822), number_of_in(_72819, graph)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', graph_has_them_all)).
% 47.93/46.93 fof(sequential_is_triangle, lemma, complete => ! [_72972, _72975, _72978, _72981, _72984] : (shortest_path(_72972, _72975, _72984) & precedes(_72978, _72981, _72984) & sequential(_72978, _72981) => ? [_73028] : triangle(_72978, _72981, _73028)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sequential_is_triangle)).
% 47.93/46.93
% 47.93/46.93 cnf(1, plain, [-(28 ^ [_42008, _41912, _41815]), triangle(26 ^ [_42008, _41912, _41815], 27 ^ [_42008, _41912, _41815], _49336)], clausify(sequential_pairs_and_triangles)).
% 47.93/46.93 cnf(2, plain, [-(28 ^ [_42008, _41912, _41815]), -(sequential(26 ^ [_42008, _41912, _41815], 27 ^ [_42008, _41912, _41815]))], clausify(sequential_pairs_and_triangles)).
% 47.93/46.93 cnf(3, plain, [-(28 ^ [_42008, _41912, _41815]), -(on_path(27 ^ [_42008, _41912, _41815], _41815))], clausify(sequential_pairs_and_triangles)).
% 47.93/46.93 cnf(4, plain, [-(28 ^ [_42008, _41912, _41815]), -(on_path(26 ^ [_42008, _41912, _41815], _41815))], clausify(sequential_pairs_and_triangles)).
% 47.93/46.93 cnf(5, plain, [-(21 ^ [_37838, _37757, _37675]), -(path(_37675, _37757, _37838))], clausify(shortest_path_defn)).
% 47.93/46.93 cnf(6, plain, [-(16 ^ [_35593, _35505, _35310, _35213, _35115]), sequential(_35505, _35593)], clausify(precedes_defn)).
% 47.93/46.93 cnf(7, plain, [-(complete)], clausify(maximal_path_length)).
% 47.93/46.93 cnf(8, plain, [-(shortest_path(31 ^ [], 32 ^ [], 30 ^ []))], clausify(maximal_path_length)).
% 47.93/46.93 cnf(9, plain, [less_or_equal(minus(length_of(30 ^ []), n1), number_of_in(triangles, graph))], clausify(maximal_path_length)).
% 47.93/46.93 cnf(10, plain, [-(_17044 = _17044)], theory(equality)).
% 47.93/46.93 cnf(11, plain, [_17197 = _17242, -(_17242 = _17197)], theory(equality)).
% 47.93/46.93 cnf(12, plain, [-(_17476 = _17587), _17476 = _17532, _17532 = _17587], theory(equality)).
% 47.93/46.93 cnf(13, plain, [-(less_or_equal(_18972, _19103)), less_or_equal(_18905, _19038), _18905 = _18972, _19038 = _19103], theory(equality)).
% 47.93/46.93 cnf(14, plain, [path(_41283, _41342, _41400), -(number_of_in(sequential_pairs, _41400) = minus(length_of(_41400), n1))], clausify(path_length_sequential_pairs)).
% 47.93/46.93 cnf(15, plain, [-(number_of_in(sequential_pairs, _41815) = number_of_in(triangles, _41815)), path(_41912, _42008, _41815), 28 ^ [_42008, _41912, _41815]], clausify(sequential_pairs_and_triangles)).
% 47.93/46.93 cnf(16, plain, [-(less_or_equal(number_of_in(_43007, _43052), number_of_in(_43007, graph)))], clausify(graph_has_them_all)).
% 47.93/46.93 cnf(17, plain, [complete, -(triangle(_43488, _43566, 29 ^ [_43643, _43566, _43488, _43409, _43329])), shortest_path(_43329, _43409, _43643), precedes(_43488, _43566, _43643), sequential(_43488, _43566)], clausify(sequential_is_triangle)).
% 47.93/46.93 cnf(18, plain, [path(_35213, _35310, _35115), -(precedes(_35505, _35593, _35115)), on_path(_35505, _35115), on_path(_35593, _35115), 16 ^ [_35593, _35505, _35310, _35213, _35115]], clausify(precedes_defn)).
% 47.93/46.93 cnf(19, plain, [shortest_path(_37675, _37757, _37838), 21 ^ [_37838, _37757, _37675]], clausify(shortest_path_defn)).
% 47.93/46.93
% 47.93/46.93 cnf('1',plain,[-(shortest_path(31 ^ [], 32 ^ [], 30 ^ []))],start(8)).
% 47.93/46.93 cnf('1.1',plain,[shortest_path(31 ^ [], 32 ^ [], 30 ^ []), 21 ^ [30 ^ [], 32 ^ [], 31 ^ []]],extension(19,bind([[_37838, _37757, _37675], [30 ^ [], 32 ^ [], 31 ^ []]]))).
% 47.93/46.93 cnf('1.1.1',plain,[-(21 ^ [30 ^ [], 32 ^ [], 31 ^ []]), -(path(31 ^ [], 32 ^ [], 30 ^ []))],extension(5,bind([[_37675, _37757, _37838], [31 ^ [], 32 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1',plain,[path(31 ^ [], 32 ^ [], 30 ^ []), -(number_of_in(sequential_pairs, 30 ^ []) = number_of_in(triangles, 30 ^ [])), 28 ^ [32 ^ [], 31 ^ [], 30 ^ []]],extension(15,bind([[_42008, _41912, _41815], [32 ^ [], 31 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.1',plain,[number_of_in(sequential_pairs, 30 ^ []) = number_of_in(triangles, 30 ^ []), -(number_of_in(triangles, 30 ^ []) = number_of_in(sequential_pairs, 30 ^ []))],extension(11,bind([[_17242, _17197], [number_of_in(triangles, 30 ^ []), number_of_in(sequential_pairs, 30 ^ [])]]))).
% 47.93/46.93 cnf('1.1.1.1.1.1',plain,[number_of_in(triangles, 30 ^ []) = number_of_in(sequential_pairs, 30 ^ []), -(number_of_in(triangles, 30 ^ []) = minus(length_of(30 ^ []), n1)), number_of_in(sequential_pairs, 30 ^ []) = minus(length_of(30 ^ []), n1)],extension(12,bind([[_17476, _17532, _17587], [number_of_in(triangles, 30 ^ []), number_of_in(sequential_pairs, 30 ^ []), minus(length_of(30 ^ []), n1)]]))).
% 47.93/46.93 cnf('1.1.1.1.1.1.1',plain,[number_of_in(triangles, 30 ^ []) = minus(length_of(30 ^ []), n1), -(less_or_equal(minus(length_of(30 ^ []), n1), number_of_in(triangles, graph))), less_or_equal(number_of_in(triangles, 30 ^ []), number_of_in(triangles, graph)), number_of_in(triangles, graph) = number_of_in(triangles, graph)],extension(13,bind([[_18972, _18905, _19038, _19103], [minus(length_of(30 ^ []), n1), number_of_in(triangles, 30 ^ []), number_of_in(triangles, graph), number_of_in(triangles, graph)]]))).
% 47.93/46.93 cnf('1.1.1.1.1.1.1.1',plain,[less_or_equal(minus(length_of(30 ^ []), n1), number_of_in(triangles, graph))],extension(9)).
% 47.93/46.93 cnf('1.1.1.1.1.1.1.2',plain,[-(less_or_equal(number_of_in(triangles, 30 ^ []), number_of_in(triangles, graph)))],extension(16,bind([[_43052, _43007], [30 ^ [], triangles]]))).
% 47.93/46.93 cnf('1.1.1.1.1.1.1.3',plain,[-(number_of_in(triangles, graph) = number_of_in(triangles, graph))],extension(10,bind([[_17044], [number_of_in(triangles, graph)]]))).
% 47.93/46.93 cnf('1.1.1.1.1.1.2',plain,[-(number_of_in(sequential_pairs, 30 ^ []) = minus(length_of(30 ^ []), n1)), path(31 ^ [], 32 ^ [], 30 ^ [])],extension(14,bind([[_41283, _41342, _41400], [31 ^ [], 32 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.1.1.2.1',plain,[-(path(31 ^ [], 32 ^ [], 30 ^ []))],reduction('1.1.1')).
% 47.93/46.93 cnf('1.1.1.1.2',plain,[-(28 ^ [32 ^ [], 31 ^ [], 30 ^ []]), -(sequential(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []]))],extension(2,bind([[_42008, _41912, _41815], [32 ^ [], 31 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1',plain,[sequential(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []]), complete, -(triangle(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 29 ^ [30 ^ [], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 32 ^ [], 31 ^ []])), shortest_path(31 ^ [], 32 ^ [], 30 ^ []), precedes(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ [])],extension(17,bind([[_43329, _43409, _43488, _43566, _43643], [31 ^ [], 32 ^ [], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1.1',plain,[-(complete)],extension(7)).
% 47.93/46.93 cnf('1.1.1.1.2.1.2',plain,[triangle(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 29 ^ [30 ^ [], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 32 ^ [], 31 ^ []]), -(28 ^ [32 ^ [], 31 ^ [], 30 ^ []])],extension(1,bind([[_49336, _42008, _41912, _41815], [29 ^ [30 ^ [], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 32 ^ [], 31 ^ []], 32 ^ [], 31 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1.2.1',plain,[28 ^ [32 ^ [], 31 ^ [], 30 ^ []]],reduction('1.1.1.1')).
% 47.93/46.93 cnf('1.1.1.1.2.1.3',plain,[-(shortest_path(31 ^ [], 32 ^ [], 30 ^ []))],extension(8)).
% 47.93/46.93 cnf('1.1.1.1.2.1.4',plain,[-(precedes(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ [])), path(31 ^ [], 32 ^ [], 30 ^ []), on_path(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ []), on_path(27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ []), 16 ^ [27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 32 ^ [], 31 ^ [], 30 ^ []]],extension(18,bind([[_35593, _35505, _35310, _35213, _35115], [27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 32 ^ [], 31 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.1',plain,[-(path(31 ^ [], 32 ^ [], 30 ^ []))],reduction('1.1.1')).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.2',plain,[-(on_path(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ [])), -(28 ^ [32 ^ [], 31 ^ [], 30 ^ []])],extension(4,bind([[_42008, _41912, _41815], [32 ^ [], 31 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.2.1',plain,[28 ^ [32 ^ [], 31 ^ [], 30 ^ []]],reduction('1.1.1.1')).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.3',plain,[-(on_path(27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 30 ^ [])), -(28 ^ [32 ^ [], 31 ^ [], 30 ^ []])],extension(3,bind([[_42008, _41912, _41815], [32 ^ [], 31 ^ [], 30 ^ []]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.3.1',plain,[28 ^ [32 ^ [], 31 ^ [], 30 ^ []]],reduction('1.1.1.1')).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.4',plain,[-(16 ^ [27 ^ [32 ^ [], 31 ^ [], 30 ^ []], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 32 ^ [], 31 ^ [], 30 ^ []]), sequential(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []])],extension(6,bind([[_35310, _35213, _35115, _35505, _35593], [32 ^ [], 31 ^ [], 30 ^ [], 26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []]]]))).
% 47.93/46.93 cnf('1.1.1.1.2.1.4.4.1',plain,[-(sequential(26 ^ [32 ^ [], 31 ^ [], 30 ^ []], 27 ^ [32 ^ [], 31 ^ [], 30 ^ []]))],reduction('1.1.1.1.2')).
% 47.93/46.93 %-----------------------------------------------------
% 47.93/46.94
% 47.94/46.94 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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