TSTP Solution File: GRA004+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : GRA004+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 07:19:05 EDT 2022
% Result : Theorem 184.17s 177.67s
% Output : Proof 184.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRA004+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.13 % Command : leancop_casc.sh %s %d
% 0.12/0.34 % Computer : n017.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 : 600
% 0.12/0.34 % DateTime : Tue May 31 03:02:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 184.17/177.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 184.17/177.67 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 184.17/177.68
% 184.17/177.68 %-----------------------------------------------------
% 184.17/177.68 fof(shortest_path_properties_lemma, conjecture, ! [_95880, _95883, _95886, _95889, _95892] : (shortest_path(_95880, _95883, _95892) & precedes(_95886, _95889, _95892) => ~ ? [_95928] : (tail_of(_95928) = tail_of(_95886) & head_of(_95928) = head_of(_95889)) & (! head_of(_95889)) = tail_of(_95886) & (! head_of(_95889)) = head_of(_95886)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', shortest_path_properties_lemma)).
% 184.17/177.68 fof(shortest_path_defn, axiom, ! [_96357, _96360, _96363] : (shortest_path(_96357, _96360, _96363) <=> path(_96357, _96360, _96363) & (! _96357) = _96360 & ! [_96405] : (path(_96357, _96360, _96405) => less_or_equal(length_of(_96363), length_of(_96405)))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', shortest_path_defn)).
% 184.17/177.68 fof(shortest_path_properties, axiom, ! [_96682, _96685, _96688, _96691, _96694] : (shortest_path(_96682, _96685, _96694) & precedes(_96688, _96691, _96694) => ~ ? [_96730] : (tail_of(_96730) = tail_of(_96688) & head_of(_96730) = head_of(_96691)) & ~ precedes(_96691, _96688, _96694)), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', shortest_path_properties)).
% 184.17/177.68 fof(on_path_properties, axiom, ! [_97054, _97057, _97060, _97063] : (path(_97054, _97057, _97060) & on_path(_97063, _97060) => edge(_97063) & in_path(head_of(_97063), _97060) & in_path(tail_of(_97063), _97060)), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', on_path_properties)).
% 184.17/177.68 fof(precedes_properties, axiom, ! [_97344, _97347, _97350] : (path(_97347, _97350, _97344) => ! [_97371, _97374] : (precedes(_97371, _97374, _97344) => on_path(_97371, _97344) & on_path(_97374, _97344) & (sequential(_97371, _97374) <~> ? [_97425] : (sequential(_97371, _97425) & precedes(_97425, _97374, _97344))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', precedes_properties)).
% 184.17/177.68 fof(precedes_defn, axiom, ! [_97767, _97770, _97773] : (path(_97770, _97773, _97767) => ! [_97794, _97797] : (precedes(_97794, _97797, _97767) <= on_path(_97794, _97767) & on_path(_97797, _97767) & (sequential(_97794, _97797) | ? [_97848] : (sequential(_97794, _97848) & precedes(_97848, _97797, _97767))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', precedes_defn)).
% 184.17/177.68 fof(sequential_defn, axiom, ! [_98157, _98160] : (sequential(_98157, _98160) <=> edge(_98157) & edge(_98160) & (! _98157) = _98160 & head_of(_98157) = tail_of(_98160)), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax', sequential_defn)).
% 184.17/177.68
% 184.17/177.68 cnf(1, plain, [15 ^ [], -(head_of(12 ^ []) = tail_of(11 ^ [])), -(head_of(12 ^ []) = head_of(11 ^ []))], clausify(shortest_path_properties_lemma)).
% 184.17/177.68 cnf(2, plain, [_17042 = _17087, -(_17087 = _17042)], theory(equality)).
% 184.17/177.68 cnf(3, plain, [-(shortest_path(_22757, _22924, _23087)), shortest_path(_22672, _22841, _23006), _22672 = _22757, _22841 = _22924, _23006 = _23087], theory(equality)).
% 184.17/177.68 cnf(4, plain, [-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))], clausify(shortest_path_properties_lemma)).
% 184.17/177.68 cnf(5, plain, [-(precedes(_21108, _21275, _21438)), precedes(_21023, _21192, _21357), _21023 = _21108, _21192 = _21275, _21357 = _21438], theory(equality)).
% 184.17/177.68 cnf(6, plain, [shortest_path(_37520, _37602, _37683), -(path(_37520, _37602, _37683))], clausify(shortest_path_defn)).
% 184.17/177.68 cnf(7, plain, [precedes(_38630, _38726, _38821), shortest_path(_38435, _38533, _38821), tail_of(_39147) = tail_of(_38630), head_of(_39147) = head_of(_38726)], clausify(shortest_path_properties)).
% 184.17/177.68 cnf(8, plain, [-(_17321 = _17432), _17321 = _17377, _17377 = _17432], theory(equality)).
% 184.17/177.68 cnf(9, plain, [-(edge(_32794)), path(_32566, _32643, _32719), on_path(_32794, _32719)], clausify(on_path_properties)).
% 184.17/177.68 cnf(10, plain, [-(15 ^ []), -(head_of(14 ^ []) = head_of(12 ^ []))], clausify(shortest_path_properties_lemma)).
% 184.17/177.68 cnf(11, plain, [path(_36327, _36426, _36227), precedes(_36623, _36713, _36227), -(on_path(_36623, _36227))], clausify(precedes_properties)).
% 184.17/177.68 cnf(12, plain, [-(15 ^ []), -(tail_of(14 ^ []) = tail_of(11 ^ []))], clausify(shortest_path_properties_lemma)).
% 184.17/177.68 cnf(13, plain, [_27711 = _27760, -(tail_of(_27711) = tail_of(_27760))], theory(equality)).
% 184.17/177.68 cnf(14, plain, [path(_35058, _35155, _34960), -(precedes(_35350, _35438, _34960)), on_path(_35350, _34960), on_path(_35438, _34960), sequential(_35350, _35438)], clausify(precedes_defn)).
% 184.17/177.68 cnf(15, plain, [-(sequential(_34378, _34445)), edge(_34378), edge(_34445), -(_34378 = _34445), head_of(_34378) = tail_of(_34445)], clausify(sequential_defn)).
% 184.17/177.68 cnf(16, plain, [path(_36327, _36426, _36227), precedes(_36623, _36713, _36227), -(on_path(_36713, _36227))], clausify(precedes_properties)).
% 184.17/177.68 cnf(17, plain, [-(precedes(11 ^ [], 12 ^ [], 13 ^ []))], clausify(shortest_path_properties_lemma)).
% 184.17/177.68 cnf(18, plain, [precedes(_38630, _38726, _38821), shortest_path(_38435, _38533, _38821), precedes(_38726, _38630, _38821)], clausify(shortest_path_properties)).
% 184.17/177.68 cnf(19, plain, [-(_16889 = _16889)], theory(equality)).
% 184.17/177.68
% 184.17/177.68 cnf('1',plain,[15 ^ [], -(head_of(12 ^ []) = tail_of(11 ^ [])), -(head_of(12 ^ []) = head_of(11 ^ []))],start(1)).
% 184.17/177.68 cnf('1.1',plain,[-(15 ^ []), -(head_of(14 ^ []) = head_of(12 ^ []))],extension(10)).
% 184.17/177.68 cnf('1.1.1',plain,[head_of(14 ^ []) = head_of(12 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ []), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), tail_of(14 ^ []) = tail_of(11 ^ [])],extension(7,bind([[_38726, _38435, _38533, _38821, _39147, _38630], [12 ^ [], 9 ^ [], 10 ^ [], 13 ^ [], 14 ^ [], 11 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.1',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ [])), precedes(11 ^ [], 12 ^ [], 13 ^ []), 11 ^ [] = 11 ^ [], 12 ^ [] = 12 ^ [], 13 ^ [] = 13 ^ []],extension(5,bind([[_21023, _21108, _21192, _21275, _21357, _21438], [11 ^ [], 11 ^ [], 12 ^ [], 12 ^ [], 13 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.1.1',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.1.1.1.2',plain,[-(11 ^ [] = 11 ^ [])],extension(19,bind([[_16889], [11 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.1.3',plain,[-(12 ^ [] = 12 ^ [])],extension(19,bind([[_16889], [12 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(19,bind([[_16889], [13 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.2',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(3,bind([[_22672, _22757, _22841, _22924, _23006, _23087], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.2.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.1.1.2.2',plain,[-(9 ^ [] = 9 ^ [])],extension(19,bind([[_16889], [9 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.2.3',plain,[-(10 ^ [] = 10 ^ [])],extension(19,bind([[_16889], [10 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.2.4',plain,[-(13 ^ [] = 13 ^ [])],extension(19,bind([[_16889], [13 ^ []]]))).
% 184.17/177.68 cnf('1.1.1.3',plain,[-(tail_of(14 ^ []) = tail_of(11 ^ [])), tail_of(14 ^ []) = tail_of(11 ^ []), tail_of(11 ^ []) = tail_of(11 ^ [])],extension(8,bind([[_17321, _17377, _17432], [tail_of(14 ^ []), tail_of(11 ^ []), tail_of(11 ^ [])]]))).
% 184.17/177.68 cnf('1.1.1.3.1',plain,[-(tail_of(14 ^ []) = tail_of(11 ^ [])), -(15 ^ [])],extension(12)).
% 184.17/177.68 cnf('1.1.1.3.1.1',plain,[15 ^ []],reduction('1')).
% 184.17/177.68 cnf('1.1.1.3.2',plain,[-(tail_of(11 ^ []) = tail_of(11 ^ []))],extension(19,bind([[_16889], [tail_of(11 ^ [])]]))).
% 184.17/177.68 cnf('1.2',plain,[head_of(12 ^ []) = tail_of(11 ^ []), -(sequential(12 ^ [], 11 ^ [])), edge(12 ^ []), edge(11 ^ []), -(12 ^ [] = 11 ^ [])],extension(15,bind([[_34378, _34445], [12 ^ [], 11 ^ []]]))).
% 184.17/177.68 cnf('1.2.1',plain,[sequential(12 ^ [], 11 ^ []), path(9 ^ [], 10 ^ [], 13 ^ []), -(precedes(12 ^ [], 11 ^ [], 13 ^ [])), on_path(12 ^ [], 13 ^ []), on_path(11 ^ [], 13 ^ [])],extension(14,bind([[_35058, _35155, _35350, _35438, _34960], [9 ^ [], 10 ^ [], 12 ^ [], 11 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.1.2',plain,[precedes(12 ^ [], 11 ^ [], 13 ^ []), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(18,bind([[_38435, _38533, _38726, _38630, _38821], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.2.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.1.2.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.2.1.3',plain,[-(on_path(12 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(16,bind([[_36327, _36426, _36623, _36713, _36227], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.3.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.3.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.1.3.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.2.1.4',plain,[-(on_path(11 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(11,bind([[_36327, _36426, _36623, _36713, _36227], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.4.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.1.4.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.1.4.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.2.2',plain,[-(edge(12 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), on_path(12 ^ [], 13 ^ [])],extension(9,bind([[_32566, _32643, _32794, _32719], [9 ^ [], 10 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.2.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.2.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.2.2',plain,[-(on_path(12 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(16,bind([[_36327, _36426, _36623, _36713, _36227], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.2.2.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.2.2.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.2.2.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.2.3',plain,[-(edge(11 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), on_path(11 ^ [], 13 ^ [])],extension(9,bind([[_32566, _32643, _32794, _32719], [9 ^ [], 10 ^ [], 11 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.3.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.3.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.3.2',plain,[-(on_path(11 ^ [], 13 ^ [])), path(9 ^ [], 10 ^ [], 13 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ [])],extension(11,bind([[_36327, _36426, _36623, _36713, _36227], [9 ^ [], 10 ^ [], 11 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.3.2.1',plain,[-(path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ [])],extension(6,bind([[_37520, _37602, _37683], [9 ^ [], 10 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.3.2.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.3.2.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.2.4',plain,[12 ^ [] = 11 ^ [], -(11 ^ [] = 12 ^ [])],extension(2,bind([[_17087, _17042], [11 ^ [], 12 ^ []]]))).
% 184.17/177.68 cnf('1.2.4.1',plain,[11 ^ [] = 12 ^ [], -(precedes(12 ^ [], 12 ^ [], 13 ^ [])), precedes(11 ^ [], 12 ^ [], 13 ^ []), 12 ^ [] = 12 ^ [], 13 ^ [] = 13 ^ []],extension(5,bind([[_21108, _21023, _21192, _21275, _21357, _21438], [12 ^ [], 11 ^ [], 12 ^ [], 12 ^ [], 13 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.4.1.1',plain,[precedes(12 ^ [], 12 ^ [], 13 ^ []), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), precedes(12 ^ [], 12 ^ [], 13 ^ [])],extension(18,bind([[_38435, _38533, _38726, _38630, _38821], [9 ^ [], 10 ^ [], 12 ^ [], 12 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.2.4.1.1.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.2.4.1.1.2',plain,[-(precedes(12 ^ [], 12 ^ [], 13 ^ []))],reduction('1.2.4.1')).
% 184.17/177.68 cnf('1.2.4.1.2',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.2.4.1.3',plain,[-(12 ^ [] = 12 ^ []), 12 ^ [] = 11 ^ [], 11 ^ [] = 12 ^ []],extension(8,bind([[_17321, _17377, _17432], [12 ^ [], 11 ^ [], 12 ^ []]]))).
% 184.17/177.68 cnf('1.2.4.1.3.1',plain,[-(12 ^ [] = 11 ^ [])],reduction('1.2')).
% 184.17/177.68 cnf('1.2.4.1.3.2',plain,[-(11 ^ [] = 12 ^ [])],reduction('1.2.4')).
% 184.17/177.68 cnf('1.2.4.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(19,bind([[_16889], [13 ^ []]]))).
% 184.17/177.68 cnf('1.3',plain,[head_of(12 ^ []) = head_of(11 ^ []), -(head_of(11 ^ []) = head_of(12 ^ []))],extension(2,bind([[_17087, _17042], [head_of(11 ^ []), head_of(12 ^ [])]]))).
% 184.17/177.68 cnf('1.3.1',plain,[head_of(11 ^ []) = head_of(12 ^ []), precedes(11 ^ [], 12 ^ [], 13 ^ []), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), tail_of(11 ^ []) = tail_of(11 ^ [])],extension(7,bind([[_38726, _38435, _38533, _38821, _39147, _38630], [12 ^ [], 9 ^ [], 10 ^ [], 13 ^ [], 11 ^ [], 11 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.1',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ [])), precedes(11 ^ [], 12 ^ [], 13 ^ []), 11 ^ [] = 11 ^ [], 12 ^ [] = 12 ^ [], 13 ^ [] = 13 ^ []],extension(5,bind([[_21023, _21108, _21192, _21275, _21357, _21438], [11 ^ [], 11 ^ [], 12 ^ [], 12 ^ [], 13 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.1.1',plain,[-(precedes(11 ^ [], 12 ^ [], 13 ^ []))],extension(17)).
% 184.17/177.68 cnf('1.3.1.1.2',plain,[-(11 ^ [] = 11 ^ [])],extension(19,bind([[_16889], [11 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.1.3',plain,[-(12 ^ [] = 12 ^ [])],extension(19,bind([[_16889], [12 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.1.4',plain,[-(13 ^ [] = 13 ^ [])],extension(19,bind([[_16889], [13 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.2',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ [])), shortest_path(9 ^ [], 10 ^ [], 13 ^ []), 9 ^ [] = 9 ^ [], 10 ^ [] = 10 ^ [], 13 ^ [] = 13 ^ []],extension(3,bind([[_22672, _22757, _22841, _22924, _23006, _23087], [9 ^ [], 9 ^ [], 10 ^ [], 10 ^ [], 13 ^ [], 13 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.2.1',plain,[-(shortest_path(9 ^ [], 10 ^ [], 13 ^ []))],extension(4)).
% 184.17/177.68 cnf('1.3.1.2.2',plain,[-(9 ^ [] = 9 ^ [])],extension(19,bind([[_16889], [9 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.2.3',plain,[-(10 ^ [] = 10 ^ [])],extension(19,bind([[_16889], [10 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.2.4',plain,[-(13 ^ [] = 13 ^ [])],extension(19,bind([[_16889], [13 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.3',plain,[-(tail_of(11 ^ []) = tail_of(11 ^ [])), 11 ^ [] = 11 ^ []],extension(13,bind([[_27711, _27760], [11 ^ [], 11 ^ []]]))).
% 184.17/177.68 cnf('1.3.1.3.1',plain,[-(11 ^ [] = 11 ^ [])],extension(19,bind([[_16889], [11 ^ []]]))).
% 184.17/177.68 %-----------------------------------------------------
% 184.17/177.68
% 184.17/177.68 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------