TSTP Solution File: MGT026+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n027.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 : Sun Jul 17 22:16:49 EDT 2022
% Result : Theorem 0.46s 1.40s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.33 % Computer : n027.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 : Thu Jun 9 12:54:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/1.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/1.41
% 0.46/1.41 %-----------------------------------------------------
% 0.46/1.41 fof(prove_l8, conjecture, ! [_41665, _41668] : (environment(_41665) & in_environment(_41665, _41668) & greater(_41668, critical_point(_41665)) => selection_favors(efficient_producers, first_movers, _41668)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prove_l8)).
% 0.46/1.41 fof(mp1_high_growth_rates, axiom, ! [_41909, _41912, _41915, _41918] : (environment(_41909) & subpopulations(_41912, _41915, _41909, _41918) & greater(growth_rate(_41915, _41918), growth_rate(_41912, _41918)) => selection_favors(_41915, _41912, _41918)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp1_high_growth_rates)).
% 0.46/1.41 fof(mp2_favour_members, axiom, ! [_42179, _42182, _42185, _42188] : (environment(_42179) & subpopulation(_42182, _42179, _42188) & subpopulation(_42185, _42179, _42188) & greater(cardinality_at_time(_42182, _42188), zero) & cardinality_at_time(_42185, _42188) = zero => selection_favors(_42182, _42185, _42188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp2_favour_members)).
% 0.46/1.41 fof(mp_non_empty_fm_and_ep, axiom, ! [_42501, _42504] : (environment(_42501) & in_environment(_42501, _42504) & greater(cardinality_at_time(first_movers, _42504), zero) & greater(cardinality_at_time(efficient_producers, _42504), zero) => subpopulations(first_movers, efficient_producers, _42501, _42504)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp_non_empty_fm_and_ep)).
% 0.46/1.41 fof(mp_first_movers_exist, axiom, ! [_42770, _42773] : (environment(_42770) & in_environment(_42770, _42773) => greater_or_equal(cardinality_at_time(first_movers, _42773), zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp_first_movers_exist)).
% 0.46/1.41 fof(mp_subpopulations, axiom, ! [_42953, _42956] : (environment(_42953) & in_environment(_42953, _42956) => subpopulation(first_movers, _42953, _42956) & subpopulation(efficient_producers, _42953, _42956)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp_subpopulations)).
% 0.46/1.41 fof(mp_critical_point_after_EP, axiom, ! [_43174] : (environment(_43174) => greater_or_equal(critical_point(_43174), appear(efficient_producers, _43174))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp_critical_point_after_EP)).
% 0.46/1.41 fof(mp_greater_transitivity, axiom, ! [_43327, _43330, _43333] : (greater(_43327, _43330) & greater(_43330, _43333) => greater(_43327, _43333)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp_greater_transitivity)).
% 0.46/1.41 fof(mp_greater_or_equal, axiom, ! [_43512, _43515] : (greater_or_equal(_43512, _43515) <=> greater(_43512, _43515) | _43512 = _43515), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mp_greater_or_equal)).
% 0.46/1.41 fof(t6, hypothesis, ! [_43695, _43698] : (environment(_43695) & in_environment(_43695, _43698) & greater_or_equal(_43698, appear(efficient_producers, _43695)) => greater(cardinality_at_time(efficient_producers, _43698), zero)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t6)).
% 0.46/1.41 fof(d1, hypothesis, ! [_43923, _43926] : (environment(_43923) & _43926 = critical_point(_43923) => ~ greater(growth_rate(efficient_producers, _43926), growth_rate(first_movers, _43926)) & ! [_43977] : (subpopulations(first_movers, efficient_producers, _43923, _43977) & greater(_43977, _43926) => greater(growth_rate(efficient_producers, _43977), growth_rate(first_movers, _43977)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', d1)).
% 0.46/1.41
% 0.46/1.41 cnf(1, plain, [-(environment(1 ^ []))], clausify(prove_l8)).
% 0.46/1.41 cnf(2, plain, [-(in_environment(1 ^ [], 2 ^ []))], clausify(prove_l8)).
% 0.46/1.41 cnf(3, plain, [-(greater(2 ^ [], critical_point(1 ^ [])))], clausify(prove_l8)).
% 0.46/1.41 cnf(4, plain, [selection_favors(efficient_producers, first_movers, 2 ^ [])], clausify(prove_l8)).
% 0.46/1.41 cnf(5, plain, [-(selection_favors(_18393, _18319, _18466)), environment(_18244), subpopulations(_18319, _18393, _18244, _18466), greater(growth_rate(_18393, _18466), growth_rate(_18319, _18466))], clausify(mp1_high_growth_rates)).
% 0.46/1.41 cnf(6, plain, [-(selection_favors(_19181, _19267, _19352)), environment(_19094), subpopulation(_19181, _19094, _19352), subpopulation(_19267, _19094, _19352), greater(cardinality_at_time(_19181, _19352), zero), cardinality_at_time(_19267, _19352) = zero], clausify(mp2_favour_members)).
% 0.46/1.41 cnf(7, plain, [-(subpopulations(first_movers, efficient_producers, _20140, _20210)), environment(_20140), in_environment(_20140, _20210), greater(cardinality_at_time(first_movers, _20210), zero), greater(cardinality_at_time(efficient_producers, _20210), zero)], clausify(mp_non_empty_fm_and_ep)).
% 0.46/1.41 cnf(8, plain, [-(greater_or_equal(cardinality_at_time(first_movers, _20908), zero)), environment(_20855), in_environment(_20855, _20908)], clausify(mp_first_movers_exist)).
% 0.46/1.41 cnf(9, plain, [-(subpopulation(first_movers, _21271, _21329)), environment(_21271), in_environment(_21271, _21329)], clausify(mp_subpopulations)).
% 0.46/1.41 cnf(10, plain, [-(subpopulation(efficient_producers, _21271, _21329)), environment(_21271), in_environment(_21271, _21329)], clausify(mp_subpopulations)).
% 0.46/1.41 cnf(11, plain, [environment(_21814), -(greater_or_equal(critical_point(_21814), appear(efficient_producers, _21814)))], clausify(mp_critical_point_after_EP)).
% 0.46/1.41 cnf(12, plain, [-(greater(_22104, _22215)), greater(_22104, _22160), greater(_22160, _22215)], clausify(mp_greater_transitivity)).
% 0.46/1.41 cnf(13, plain, [-(greater_or_equal(_22571, _22622)), greater(_22571, _22622)], clausify(mp_greater_or_equal)).
% 0.46/1.41 cnf(14, plain, [greater_or_equal(_22571, _22622), -(greater(_22571, _22622)), -(_22571 = _22622)], clausify(mp_greater_or_equal)).
% 0.46/1.41 cnf(15, plain, [-(greater(cardinality_at_time(efficient_producers, _24025), zero)), environment(_23963), in_environment(_23963, _24025), greater_or_equal(_24025, appear(efficient_producers, _23963))], clausify(t6)).
% 0.46/1.41 cnf(16, plain, [_23058 = critical_point(_22967), environment(_22967), -(greater(growth_rate(efficient_producers, _23425), growth_rate(first_movers, _23425))), subpopulations(first_movers, efficient_producers, _22967, _23425), greater(_23425, _23058)], clausify(d1)).
% 0.46/1.41 cnf(17, plain, [-(_9224 = _9224)], theory(equality)).
% 0.46/1.41 cnf(18, plain, [-(greater(_10528, _10659)), greater(_10461, _10594), _10461 = _10528, _10594 = _10659], theory(equality)).
% 0.46/1.41
% 0.46/1.41 cnf('1',plain,[selection_favors(efficient_producers, first_movers, 2 ^ [])],start(4)).
% 0.46/1.41 cnf('1.1',plain,[-(selection_favors(efficient_producers, first_movers, 2 ^ [])), environment(1 ^ []), subpopulation(efficient_producers, 1 ^ [], 2 ^ []), subpopulation(first_movers, 1 ^ [], 2 ^ []), greater(cardinality_at_time(efficient_producers, 2 ^ []), zero), cardinality_at_time(first_movers, 2 ^ []) = zero],extension(6,bind([[_19094, _19181, _19267, _19352], [1 ^ [], efficient_producers, first_movers, 2 ^ []]]))).
% 0.46/1.41 cnf('1.1.1',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.2',plain,[-(subpopulation(efficient_producers, 1 ^ [], 2 ^ [])), environment(1 ^ []), in_environment(1 ^ [], 2 ^ [])],extension(10,bind([[_21271, _21329], [1 ^ [], 2 ^ []]]))).
% 0.46/1.41 cnf('1.1.2.1',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.2.2',plain,[-(in_environment(1 ^ [], 2 ^ []))],extension(2)).
% 0.46/1.41 cnf('1.1.3',plain,[-(subpopulation(first_movers, 1 ^ [], 2 ^ [])), environment(1 ^ []), in_environment(1 ^ [], 2 ^ [])],extension(9,bind([[_21271, _21329], [1 ^ [], 2 ^ []]]))).
% 0.46/1.41 cnf('1.1.3.1',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.3.2',plain,[-(in_environment(1 ^ [], 2 ^ []))],extension(2)).
% 0.46/1.41 cnf('1.1.4',plain,[-(greater(cardinality_at_time(efficient_producers, 2 ^ []), zero)), environment(1 ^ []), in_environment(1 ^ [], 2 ^ []), greater_or_equal(2 ^ [], appear(efficient_producers, 1 ^ []))],extension(15,bind([[_24025, _23963], [2 ^ [], 1 ^ []]]))).
% 0.46/1.41 cnf('1.1.4.1',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.4.2',plain,[-(in_environment(1 ^ [], 2 ^ []))],extension(2)).
% 0.46/1.41 cnf('1.1.4.3',plain,[-(greater_or_equal(2 ^ [], appear(efficient_producers, 1 ^ []))), greater(2 ^ [], appear(efficient_producers, 1 ^ []))],extension(13,bind([[_22571, _22622], [2 ^ [], appear(efficient_producers, 1 ^ [])]]))).
% 0.46/1.41 cnf('1.1.4.3.1',plain,[-(greater(2 ^ [], appear(efficient_producers, 1 ^ []))), greater(2 ^ [], critical_point(1 ^ [])), 2 ^ [] = 2 ^ [], critical_point(1 ^ []) = appear(efficient_producers, 1 ^ [])],extension(18,bind([[_10461, _10528, _10594, _10659], [2 ^ [], 2 ^ [], critical_point(1 ^ []), appear(efficient_producers, 1 ^ [])]]))).
% 0.46/1.41 cnf('1.1.4.3.1.1',plain,[-(greater(2 ^ [], critical_point(1 ^ [])))],extension(3)).
% 0.46/1.41 cnf('1.1.4.3.1.2',plain,[-(2 ^ [] = 2 ^ [])],extension(17,bind([[_9224], [2 ^ []]]))).
% 0.46/1.41 cnf('1.1.4.3.1.3',plain,[-(critical_point(1 ^ []) = appear(efficient_producers, 1 ^ [])), greater_or_equal(critical_point(1 ^ []), appear(efficient_producers, 1 ^ [])), -(greater(critical_point(1 ^ []), appear(efficient_producers, 1 ^ [])))],extension(14,bind([[_22571, _22622], [critical_point(1 ^ []), appear(efficient_producers, 1 ^ [])]]))).
% 0.46/1.41 cnf('1.1.4.3.1.3.1',plain,[-(greater_or_equal(critical_point(1 ^ []), appear(efficient_producers, 1 ^ []))), environment(1 ^ [])],extension(11,bind([[_21814], [1 ^ []]]))).
% 0.46/1.41 cnf('1.1.4.3.1.3.1.1',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.4.3.1.3.2',plain,[greater(critical_point(1 ^ []), appear(efficient_producers, 1 ^ [])), -(greater(2 ^ [], appear(efficient_producers, 1 ^ []))), greater(2 ^ [], critical_point(1 ^ []))],extension(12,bind([[_22215, _22104, _22160], [appear(efficient_producers, 1 ^ []), 2 ^ [], critical_point(1 ^ [])]]))).
% 0.46/1.41 cnf('1.1.4.3.1.3.2.1',plain,[greater(2 ^ [], appear(efficient_producers, 1 ^ []))],reduction('1.1.4.3')).
% 0.46/1.41 cnf('1.1.4.3.1.3.2.2',plain,[-(greater(2 ^ [], critical_point(1 ^ [])))],extension(3)).
% 0.46/1.41 cnf('1.1.5',plain,[-(cardinality_at_time(first_movers, 2 ^ []) = zero), greater_or_equal(cardinality_at_time(first_movers, 2 ^ []), zero), -(greater(cardinality_at_time(first_movers, 2 ^ []), zero))],extension(14,bind([[_22571, _22622], [cardinality_at_time(first_movers, 2 ^ []), zero]]))).
% 0.46/1.41 cnf('1.1.5.1',plain,[-(greater_or_equal(cardinality_at_time(first_movers, 2 ^ []), zero)), environment(1 ^ []), in_environment(1 ^ [], 2 ^ [])],extension(8,bind([[_20855, _20908], [1 ^ [], 2 ^ []]]))).
% 0.46/1.41 cnf('1.1.5.1.1',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.5.1.2',plain,[-(in_environment(1 ^ [], 2 ^ []))],extension(2)).
% 0.46/1.41 cnf('1.1.5.2',plain,[greater(cardinality_at_time(first_movers, 2 ^ []), zero), -(subpopulations(first_movers, efficient_producers, 1 ^ [], 2 ^ [])), environment(1 ^ []), in_environment(1 ^ [], 2 ^ []), greater(cardinality_at_time(efficient_producers, 2 ^ []), zero)],extension(7,bind([[_20140, _20210], [1 ^ [], 2 ^ []]]))).
% 0.46/1.41 cnf('1.1.5.2.1',plain,[subpopulations(first_movers, efficient_producers, 1 ^ [], 2 ^ []), -(selection_favors(efficient_producers, first_movers, 2 ^ [])), environment(1 ^ []), greater(growth_rate(efficient_producers, 2 ^ []), growth_rate(first_movers, 2 ^ []))],extension(5,bind([[_18244, _18393, _18319, _18466], [1 ^ [], efficient_producers, first_movers, 2 ^ []]]))).
% 0.46/1.41 cnf('1.1.5.2.1.1',plain,[selection_favors(efficient_producers, first_movers, 2 ^ [])],extension(4)).
% 0.46/1.41 cnf('1.1.5.2.1.2',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.5.2.1.3',plain,[-(greater(growth_rate(efficient_producers, 2 ^ []), growth_rate(first_movers, 2 ^ []))), critical_point(1 ^ []) = critical_point(1 ^ []), environment(1 ^ []), subpopulations(first_movers, efficient_producers, 1 ^ [], 2 ^ []), greater(2 ^ [], critical_point(1 ^ []))],extension(16,bind([[_22967, _23425, _23058], [1 ^ [], 2 ^ [], critical_point(1 ^ [])]]))).
% 0.46/1.41 cnf('1.1.5.2.1.3.1',plain,[-(critical_point(1 ^ []) = critical_point(1 ^ []))],extension(17,bind([[_9224], [critical_point(1 ^ [])]]))).
% 0.46/1.41 cnf('1.1.5.2.1.3.2',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.5.2.1.3.3',plain,[-(subpopulations(first_movers, efficient_producers, 1 ^ [], 2 ^ []))],reduction('1.1.5.2')).
% 0.46/1.41 cnf('1.1.5.2.1.3.4',plain,[-(greater(2 ^ [], critical_point(1 ^ [])))],extension(3)).
% 0.46/1.41 cnf('1.1.5.2.2',plain,[-(environment(1 ^ []))],extension(1)).
% 0.46/1.41 cnf('1.1.5.2.3',plain,[-(in_environment(1 ^ [], 2 ^ []))],extension(2)).
% 0.46/1.41 cnf('1.1.5.2.4',plain,[-(greater(cardinality_at_time(efficient_producers, 2 ^ []), zero))],lemmata('1.1')).
% 0.46/1.41 %-----------------------------------------------------
% 0.46/1.41
% 0.46/1.41 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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