TSTP Solution File: SEU181+2 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SEU181+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n005.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 : Tue Jul 19 12:00:47 EDT 2022
% Result : Theorem 98.84s 95.72s
% Output : Proof 98.93s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU181+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n005.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 : Sun Jun 19 07:49:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 98.84/95.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.84/95.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.93/95.73
% 98.93/95.73 %-----------------------------------------------------
% 98.93/95.73 fof(t37_relat_1, conjecture, ! [_210353] : (relation(_210353) => relation_rng(_210353) = relation_dom(relation_inverse(_210353)) & relation_dom(_210353) = relation_rng(relation_inverse(_210353))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t37_relat_1)).
% 98.93/95.73 fof(d4_relat_1, axiom, ! [_210681] : (relation(_210681) => ! [_210696] : (_210696 = relation_dom(_210681) <=> ! [_210714] : (in(_210714, _210696) <=> ? [_210732] : in(ordered_pair(_210714, _210732), _210681)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d4_relat_1)).
% 98.93/95.73 fof(d5_relat_1, axiom, ! [_211014] : (relation(_211014) => ! [_211029] : (_211029 = relation_rng(_211014) <=> ! [_211047] : (in(_211047, _211029) <=> ? [_211065] : in(ordered_pair(_211065, _211047), _211014)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d5_relat_1)).
% 98.93/95.73 fof(d7_relat_1, axiom, ! [_211337] : (relation(_211337) => ! [_211352] : (relation(_211352) => (_211352 = relation_inverse(_211337) <=> ! [_211377, _211380] : (in(ordered_pair(_211377, _211380), _211352) <=> in(ordered_pair(_211380, _211377), _211337))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d7_relat_1)).
% 98.93/95.73 fof(dt_k4_relat_1, axiom, ! [_211665] : (relation(_211665) => relation(relation_inverse(_211665))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dt_k4_relat_1)).
% 98.93/95.73 fof(involutiveness_k4_relat_1, axiom, ! [_211812] : (relation(_211812) => relation_inverse(relation_inverse(_211812)) = _211812), file('/export/starexec/sandbox/benchmark/theBenchmark.p', involutiveness_k4_relat_1)).
% 98.93/95.73 fof(t20_relat_1, lemma, ! [_212006, _212009, _212012] : (relation(_212012) => in(ordered_pair(_212006, _212009), _212012) => in(_212006, relation_dom(_212012)) & in(_212009, relation_rng(_212012))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t20_relat_1)).
% 98.93/95.73
% 98.93/95.73 cnf(1, plain, [-(relation(45 ^ []))], clausify(t37_relat_1)).
% 98.93/95.73 cnf(2, plain, [relation_rng(45 ^ []) = relation_dom(relation_inverse(45 ^ [])), relation_dom(45 ^ []) = relation_rng(relation_inverse(45 ^ []))], clausify(t37_relat_1)).
% 98.93/95.73 cnf(3, plain, [-(_65784 = _65784)], theory(equality)).
% 98.93/95.73 cnf(4, plain, [_65937 = _65982, -(_65982 = _65937)], theory(equality)).
% 98.93/95.73 cnf(5, plain, [relation(_90780), _90889 = relation_dom(_90780), in(_91029, _90889), -(in(ordered_pair(_91029, 19 ^ [_91029, _90889, _90780]), _90780))], clausify(d4_relat_1)).
% 98.93/95.73 cnf(6, plain, [relation(_90780), -(_90889 = relation_dom(_90780)), in(20 ^ [_90889, _90780], _90889), in(ordered_pair(20 ^ [_90889, _90780], _152744), _90780)], clausify(d4_relat_1)).
% 98.93/95.73 cnf(7, plain, [relation(_90780), -(_90889 = relation_dom(_90780)), -(in(20 ^ [_90889, _90780], _90889)), -(in(ordered_pair(20 ^ [_90889, _90780], 21 ^ [_90889, _90780]), _90780))], clausify(d4_relat_1)).
% 98.93/95.73 cnf(8, plain, [relation(_92986), _93095 = relation_rng(_92986), in(_93235, _93095), -(in(ordered_pair(26 ^ [_93235, _93095, _92986], _93235), _92986))], clausify(d5_relat_1)).
% 98.93/95.73 cnf(9, plain, [relation(_92986), -(_93095 = relation_rng(_92986)), in(27 ^ [_93095, _92986], _93095), in(ordered_pair(_153606, 27 ^ [_93095, _92986]), _92986)], clausify(d5_relat_1)).
% 98.93/95.73 cnf(10, plain, [relation(_92986), -(_93095 = relation_rng(_92986)), -(in(27 ^ [_93095, _92986], _93095)), -(in(ordered_pair(28 ^ [_93095, _92986], 27 ^ [_93095, _92986]), _92986))], clausify(d5_relat_1)).
% 98.93/95.73 cnf(11, plain, [relation(_94758), relation(_94875), _94875 = relation_inverse(_94758), in(ordered_pair(_95061, _95120), _94875), -(in(ordered_pair(_95120, _95061), _94758))], clausify(d7_relat_1)).
% 98.93/95.73 cnf(12, plain, [relation(_99520), -(relation(relation_inverse(_99520)))], clausify(dt_k4_relat_1)).
% 98.93/95.73 cnf(13, plain, [relation(_105713), -(relation_inverse(relation_inverse(_105713)) = _105713)], clausify(involutiveness_k4_relat_1)).
% 98.93/95.73 cnf(14, plain, [relation(_121158), in(ordered_pair(_121023, _121091), _121158), -(in(_121023, relation_dom(_121158)))], clausify(t20_relat_1)).
% 98.93/95.73 cnf(15, plain, [relation(_121158), in(ordered_pair(_121023, _121091), _121158), -(in(_121091, relation_rng(_121158)))], clausify(t20_relat_1)).
% 98.93/95.73
% 98.93/95.73 cnf('1',plain,[relation_rng(45 ^ []) = relation_dom(relation_inverse(45 ^ [])), relation_dom(45 ^ []) = relation_rng(relation_inverse(45 ^ []))],start(2)).
% 98.93/95.73 cnf('1.1',plain,[-(relation_rng(45 ^ []) = relation_dom(relation_inverse(45 ^ []))), relation(relation_inverse(45 ^ [])), in(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ [])), in(ordered_pair(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 26 ^ [20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []), 45 ^ []]), relation_inverse(45 ^ []))],extension(6,bind([[_90889, _152744, _90780], [relation_rng(45 ^ []), 26 ^ [20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []), 45 ^ []], relation_inverse(45 ^ [])]]))).
% 98.93/95.73 cnf('1.1.1',plain,[-(relation(relation_inverse(45 ^ []))), relation(45 ^ [])],extension(12,bind([[_99520], [45 ^ []]]))).
% 98.93/95.73 cnf('1.1.1.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.1.2',plain,[-(in(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []))), relation(relation_inverse(45 ^ [])), -(relation_rng(45 ^ []) = relation_dom(relation_inverse(45 ^ []))), -(in(ordered_pair(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 21 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])]), relation_inverse(45 ^ [])))],extension(7,bind([[_90889, _90780], [relation_rng(45 ^ []), relation_inverse(45 ^ [])]]))).
% 98.93/95.73 cnf('1.1.2.1',plain,[-(relation(relation_inverse(45 ^ [])))],lemmata('1.1')).
% 98.93/95.73 cnf('1.1.2.2',plain,[relation_rng(45 ^ []) = relation_dom(relation_inverse(45 ^ []))],reduction('1')).
% 98.93/95.73 cnf('1.1.2.3',plain,[in(ordered_pair(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 21 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])]), relation_inverse(45 ^ [])), relation(45 ^ []), relation(relation_inverse(45 ^ [])), relation_inverse(45 ^ []) = relation_inverse(45 ^ []), -(in(ordered_pair(21 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])]), 45 ^ []))],extension(11,bind([[_94875, _95120, _95061, _94758], [relation_inverse(45 ^ []), 21 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 45 ^ []]]))).
% 98.93/95.73 cnf('1.1.2.3.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.1.2.3.2',plain,[-(relation(relation_inverse(45 ^ [])))],lemmata('1.1.2')).
% 98.93/95.73 cnf('1.1.2.3.3',plain,[-(relation_inverse(45 ^ []) = relation_inverse(45 ^ []))],extension(3,bind([[_65784], [relation_inverse(45 ^ [])]]))).
% 98.93/95.73 cnf('1.1.2.3.4',plain,[in(ordered_pair(21 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])]), 45 ^ []), relation(45 ^ []), -(in(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ [])))],extension(15,bind([[_121023, _121091, _121158], [21 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 45 ^ []]]))).
% 98.93/95.73 cnf('1.1.2.3.4.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.1.2.3.4.2',plain,[in(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []))],reduction('1.1')).
% 98.93/95.73 cnf('1.1.3',plain,[-(in(ordered_pair(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 26 ^ [20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []), 45 ^ []]), relation_inverse(45 ^ []))), relation(relation_inverse(45 ^ [])), relation(45 ^ []), 45 ^ [] = relation_inverse(relation_inverse(45 ^ [])), in(ordered_pair(26 ^ [20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []), 45 ^ []], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])]), 45 ^ [])],extension(11,bind([[_94758, _95061, _95120, _94875], [relation_inverse(45 ^ []), 26 ^ [20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []), 45 ^ []], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], 45 ^ []]]))).
% 98.93/95.73 cnf('1.1.3.1',plain,[-(relation(relation_inverse(45 ^ [])))],lemmata('1.1')).
% 98.93/95.73 cnf('1.1.3.2',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.1.3.3',plain,[-(45 ^ [] = relation_inverse(relation_inverse(45 ^ []))), relation_inverse(relation_inverse(45 ^ [])) = 45 ^ []],extension(4,bind([[_65937, _65982], [relation_inverse(relation_inverse(45 ^ [])), 45 ^ []]]))).
% 98.93/95.73 cnf('1.1.3.3.1',plain,[-(relation_inverse(relation_inverse(45 ^ [])) = 45 ^ []), relation(45 ^ [])],extension(13,bind([[_105713], [45 ^ []]]))).
% 98.93/95.73 cnf('1.1.3.3.1.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.1.3.4',plain,[-(in(ordered_pair(26 ^ [20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []), 45 ^ []], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])]), 45 ^ [])), relation(45 ^ []), relation_rng(45 ^ []) = relation_rng(45 ^ []), in(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ []))],extension(8,bind([[_92986, _93235, _93095], [45 ^ [], 20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ [])]]))).
% 98.93/95.73 cnf('1.1.3.4.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.1.3.4.2',plain,[-(relation_rng(45 ^ []) = relation_rng(45 ^ []))],extension(3,bind([[_65784], [relation_rng(45 ^ [])]]))).
% 98.93/95.73 cnf('1.1.3.4.3',plain,[-(in(20 ^ [relation_rng(45 ^ []), relation_inverse(45 ^ [])], relation_rng(45 ^ [])))],lemmata('1.1')).
% 98.93/95.73 cnf('1.2',plain,[-(relation_dom(45 ^ []) = relation_rng(relation_inverse(45 ^ []))), relation(relation_inverse(45 ^ [])), in(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ [])), in(ordered_pair(19 ^ [27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []), 45 ^ []], 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])]), relation_inverse(45 ^ []))],extension(9,bind([[_153606, _93095, _92986], [19 ^ [27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []), 45 ^ []], relation_dom(45 ^ []), relation_inverse(45 ^ [])]]))).
% 98.93/95.73 cnf('1.2.1',plain,[-(relation(relation_inverse(45 ^ []))), relation(45 ^ [])],extension(12,bind([[_99520], [45 ^ []]]))).
% 98.93/95.73 cnf('1.2.1.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.2.2',plain,[-(in(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []))), relation(relation_inverse(45 ^ [])), -(relation_dom(45 ^ []) = relation_rng(relation_inverse(45 ^ []))), -(in(ordered_pair(28 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])]), relation_inverse(45 ^ [])))],extension(10,bind([[_93095, _92986], [relation_dom(45 ^ []), relation_inverse(45 ^ [])]]))).
% 98.93/95.73 cnf('1.2.2.1',plain,[-(relation(relation_inverse(45 ^ [])))],lemmata('1.2')).
% 98.93/95.73 cnf('1.2.2.2',plain,[relation_dom(45 ^ []) = relation_rng(relation_inverse(45 ^ []))],reduction('1')).
% 98.93/95.73 cnf('1.2.2.3',plain,[in(ordered_pair(28 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])]), relation_inverse(45 ^ [])), relation(45 ^ []), relation(relation_inverse(45 ^ [])), relation_inverse(45 ^ []) = relation_inverse(45 ^ []), -(in(ordered_pair(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 28 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])]), 45 ^ []))],extension(11,bind([[_94875, _95120, _95061, _94758], [relation_inverse(45 ^ []), 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 28 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 45 ^ []]]))).
% 98.93/95.73 cnf('1.2.2.3.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.2.2.3.2',plain,[-(relation(relation_inverse(45 ^ [])))],lemmata('1.2.2')).
% 98.93/95.73 cnf('1.2.2.3.3',plain,[-(relation_inverse(45 ^ []) = relation_inverse(45 ^ []))],extension(3,bind([[_65784], [relation_inverse(45 ^ [])]]))).
% 98.93/95.73 cnf('1.2.2.3.4',plain,[in(ordered_pair(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 28 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])]), 45 ^ []), relation(45 ^ []), -(in(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ [])))],extension(14,bind([[_121091, _121023, _121158], [28 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 45 ^ []]]))).
% 98.93/95.73 cnf('1.2.2.3.4.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.2.2.3.4.2',plain,[in(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []))],reduction('1.2')).
% 98.93/95.73 cnf('1.2.3',plain,[-(in(ordered_pair(19 ^ [27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []), 45 ^ []], 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])]), relation_inverse(45 ^ []))), relation(relation_inverse(45 ^ [])), relation(45 ^ []), 45 ^ [] = relation_inverse(relation_inverse(45 ^ [])), in(ordered_pair(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 19 ^ [27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []), 45 ^ []]), 45 ^ [])],extension(11,bind([[_94758, _95061, _95120, _94875], [relation_inverse(45 ^ []), 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 19 ^ [27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []), 45 ^ []], 45 ^ []]]))).
% 98.93/95.73 cnf('1.2.3.1',plain,[-(relation(relation_inverse(45 ^ [])))],lemmata('1.2')).
% 98.93/95.73 cnf('1.2.3.2',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.2.3.3',plain,[-(45 ^ [] = relation_inverse(relation_inverse(45 ^ []))), relation_inverse(relation_inverse(45 ^ [])) = 45 ^ []],extension(4,bind([[_65937, _65982], [relation_inverse(relation_inverse(45 ^ [])), 45 ^ []]]))).
% 98.93/95.73 cnf('1.2.3.3.1',plain,[-(relation_inverse(relation_inverse(45 ^ [])) = 45 ^ []), relation(45 ^ [])],extension(13,bind([[_105713], [45 ^ []]]))).
% 98.93/95.73 cnf('1.2.3.3.1.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.2.3.4',plain,[-(in(ordered_pair(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], 19 ^ [27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []), 45 ^ []]), 45 ^ [])), relation(45 ^ []), relation_dom(45 ^ []) = relation_dom(45 ^ []), in(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ []))],extension(5,bind([[_90780, _91029, _90889], [45 ^ [], 27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ [])]]))).
% 98.93/95.73 cnf('1.2.3.4.1',plain,[-(relation(45 ^ []))],extension(1)).
% 98.93/95.73 cnf('1.2.3.4.2',plain,[-(relation_dom(45 ^ []) = relation_dom(45 ^ []))],extension(3,bind([[_65784], [relation_dom(45 ^ [])]]))).
% 98.93/95.73 cnf('1.2.3.4.3',plain,[-(in(27 ^ [relation_dom(45 ^ []), relation_inverse(45 ^ [])], relation_dom(45 ^ [])))],lemmata('1.2')).
% 98.93/95.73 %-----------------------------------------------------
% 98.93/95.73
% 98.93/95.74 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------