TSTP Solution File: MGT028-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 22:26:16 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : MGT028-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 9 11:08:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 62 clauses, backtracked 21 clauses, performed 4 splits and kept 76 clauses.
% 0.21/0.43 SPASS allocated 75710 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.43 0:00:00.04 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.01 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 7, length 80 :
% 0.21/0.43 % SZS output start Refutation
% 0.21/0.43 1[0:Inp] stable(u) environment(u) || in_environment(u,v) -> greater(sk2(u),appear(efficient_producers,u)) subpopulations(first_movers,efficient_producers,u,sk1(v,u))*.
% 0.21/0.43 2[0:Inp] stable(u) environment(u) || in_environment(u,v)+ -> greater(sk2(u),appear(efficient_producers,u))* greater_or_equal(sk1(v,u),v)*.
% 0.21/0.43 3[0:Inp] stable(u) environment(u) || in_environment(u,v) greater_or_equal(w,sk2(u)) subpopulations(first_movers,efficient_producers,u,w)* -> greater(zero,growth_rate(first_movers,w))* subpopulations(first_movers,efficient_producers,u,sk1(v,u))*.
% 0.21/0.43 4[0:Inp] stable(u) environment(u) || in_environment(u,v) greater_or_equal(w,sk2(u)) subpopulations(first_movers,efficient_producers,u,w)*+ -> greater(zero,growth_rate(first_movers,w))* greater_or_equal(sk1(v,u),v)*.
% 0.21/0.43 5[0:Inp] stable(u) environment(u) || in_environment(u,v) greater(zero,growth_rate(first_movers,sk1(v,u)))*+ -> greater(sk2(u),appear(efficient_producers,u))*.
% 0.21/0.43 6[0:Inp] stable(u) environment(u) || in_environment(u,v) greater_or_equal(w,sk2(u)) greater(zero,growth_rate(first_movers,sk1(v,u)))* subpopulations(first_movers,efficient_producers,u,w)* -> greater(zero,growth_rate(first_movers,w))*.
% 0.21/0.43 7[0:Inp] stable(u) environment(u) || -> in_environment(u,sk3(u))*.
% 0.21/0.43 9[0:Inp] stable(u) environment(u) || greater_or_equal(v,sk3(u)) subpopulations(first_movers,efficient_producers,u,v)*+ -> greater(zero,growth_rate(first_movers,v))*.
% 0.21/0.43 10[0:Inp] || -> environment(sk4)*.
% 0.21/0.43 11[0:Inp] || -> stable(sk4)*.
% 0.21/0.43 12[0:Inp] || greater(u,appear(efficient_producers,sk4)) -> subpopulations(first_movers,efficient_producers,sk4,sk5(u))*.
% 0.21/0.43 13[0:Inp] || greater(u,appear(efficient_producers,sk4))*+ -> greater_or_equal(sk5(u),u)*.
% 0.21/0.43 14[0:Inp] || greater(u,appear(efficient_producers,sk4)) greater(zero,growth_rate(first_movers,sk5(u)))* -> .
% 0.21/0.43 20[0:Res:11.0,9.1] environment(sk4) || subpopulations(first_movers,efficient_producers,sk4,u) greater_or_equal(u,sk3(sk4)) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 22[0:Res:11.0,2.1] environment(sk4) || in_environment(sk4,u) -> greater_or_equal(sk1(u,sk4),u)* greater(sk2(sk4),appear(efficient_producers,sk4))*.
% 0.21/0.43 23[0:Res:11.0,7.1] environment(sk4) || -> in_environment(sk4,sk3(sk4))*.
% 0.21/0.43 24[0:Res:10.0,6.0] stable(sk4) || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* subpopulations(first_movers,efficient_producers,sk4,v) greater_or_equal(v,sk2(sk4)) -> greater(zero,growth_rate(first_movers,v))*.
% 0.21/0.43 25[0:Res:10.0,3.0] stable(sk4) || in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) greater_or_equal(v,sk2(sk4)) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* greater(zero,growth_rate(first_movers,v))*.
% 0.21/0.43 26[0:Res:10.0,4.0] stable(sk4) || in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) greater_or_equal(v,sk2(sk4)) -> greater_or_equal(sk1(u,sk4),u)* greater(zero,growth_rate(first_movers,v))*.
% 0.21/0.43 27[0:Res:10.0,5.0] stable(sk4) || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> greater(sk2(sk4),appear(efficient_producers,sk4)).
% 0.21/0.43 28[0:Res:10.0,1.0] stable(sk4) || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* greater(sk2(sk4),appear(efficient_producers,sk4)).
% 0.21/0.43 33[0:MRR:23.0,10.0] || -> in_environment(sk4,sk3(sk4))*.
% 0.21/0.43 34[0:MRR:22.0,10.0] || in_environment(sk4,u)+ -> greater(sk2(sk4),appear(efficient_producers,sk4))* greater_or_equal(sk1(u,sk4),u)*.
% 0.21/0.43 35[0:MRR:20.0,10.0] || greater_or_equal(u,sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 37[0:MRR:28.0,11.0] || in_environment(sk4,u) -> greater(sk2(sk4),appear(efficient_producers,sk4)) subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*.
% 0.21/0.43 38[0:MRR:27.0,11.0] || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> greater(sk2(sk4),appear(efficient_producers,sk4)).
% 0.21/0.43 39[0:MRR:26.0,11.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,v) subpopulations(first_movers,efficient_producers,sk4,u)+ -> greater(zero,growth_rate(first_movers,u))* greater_or_equal(sk1(v,sk4),v)*.
% 0.21/0.43 40[0:MRR:25.0,11.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,v) subpopulations(first_movers,efficient_producers,sk4,u)+ -> greater(zero,growth_rate(first_movers,u))* subpopulations(first_movers,efficient_producers,sk4,sk1(v,sk4))*.
% 0.21/0.43 41[0:MRR:24.0,11.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,v) greater(zero,growth_rate(first_movers,sk1(v,sk4)))*+ subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 44[1:Spt:39.0,39.2,39.3] || greater_or_equal(u,sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 45[2:Spt:34.1] || -> greater(sk2(sk4),appear(efficient_producers,sk4))*.
% 0.21/0.43 46[2:Res:45.0,13.0] || -> greater_or_equal(sk5(sk2(sk4)),sk2(sk4))*.
% 0.21/0.43 47[1:Res:44.2,14.1] || greater_or_equal(sk5(u),sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk5(u))* greater(u,appear(efficient_producers,sk4)) -> .
% 0.21/0.43 48[1:MRR:47.1,12.1] || greater_or_equal(sk5(u),sk2(sk4))* greater(u,appear(efficient_producers,sk4)) -> .
% 0.21/0.43 49[2:Res:46.0,48.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> .
% 0.21/0.43 50[2:MRR:49.0,45.0] || -> .
% 0.21/0.43 51[2:Spt:50.0,34.1,45.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> .
% 0.21/0.43 52[2:Spt:50.0,34.0,34.2] || in_environment(sk4,u) -> greater_or_equal(sk1(u,sk4),u)*.
% 0.21/0.43 53[2:MRR:37.1,51.0] || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*.
% 0.21/0.43 54[2:MRR:38.2,51.0] || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> .
% 0.21/0.43 65[2:Res:35.2,54.1] || greater_or_equal(sk1(u,sk4),sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* in_environment(sk4,u) -> .
% 0.21/0.43 67[2:MRR:65.1,53.1] || greater_or_equal(sk1(u,sk4),sk3(sk4))* in_environment(sk4,u) -> .
% 0.21/0.43 68[2:Res:52.1,67.0] || in_environment(sk4,sk3(sk4))* in_environment(sk4,sk3(sk4))* -> .
% 0.21/0.43 71[2:Obv:68.0] || in_environment(sk4,sk3(sk4))* -> .
% 0.21/0.43 72[2:MRR:71.0,33.0] || -> .
% 0.21/0.43 73[1:Spt:72.0,39.1,39.4] || in_environment(sk4,u) -> greater_or_equal(sk1(u,sk4),u)*.
% 0.21/0.43 74[2:Spt:40.0,40.2,40.3] || greater_or_equal(u,sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 75[2:Res:74.2,14.1] || greater_or_equal(sk5(u),sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk5(u))* greater(u,appear(efficient_producers,sk4)) -> .
% 0.21/0.43 76[2:MRR:75.1,12.1] || greater_or_equal(sk5(u),sk2(sk4))* greater(u,appear(efficient_producers,sk4)) -> .
% 0.21/0.43 77[3:Spt:37.1] || -> greater(sk2(sk4),appear(efficient_producers,sk4))*.
% 0.21/0.43 78[3:Res:77.0,13.0] || -> greater_or_equal(sk5(sk2(sk4)),sk2(sk4))*.
% 0.21/0.43 80[3:Res:78.0,76.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> .
% 0.21/0.43 81[3:MRR:80.0,77.0] || -> .
% 0.21/0.43 82[3:Spt:81.0,37.1,77.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> .
% 0.21/0.43 83[3:Spt:81.0,37.0,37.2] || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*.
% 0.21/0.43 85[3:MRR:38.2,82.0] || in_environment(sk4,u) greater(zero,growth_rate(first_movers,sk1(u,sk4)))* -> .
% 0.21/0.43 89[3:Res:83.1,9.3] stable(sk4) environment(sk4) || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*.
% 0.21/0.43 90[3:SSi:89.1,89.0,11.0,10.0,11.0,10.0] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*.
% 0.21/0.43 91[3:MRR:90.2,85.1] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4))* -> .
% 0.21/0.43 92[3:Res:73.1,91.1] || in_environment(sk4,sk3(sk4))* in_environment(sk4,sk3(sk4))* -> .
% 0.21/0.43 95[3:Obv:92.0] || in_environment(sk4,sk3(sk4))* -> .
% 0.21/0.43 96[3:MRR:95.0,33.0] || -> .
% 0.21/0.43 97[2:Spt:96.0,40.1,40.4] || in_environment(sk4,u) -> subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))*.
% 0.21/0.43 98[2:Res:97.1,9.3] stable(sk4) environment(sk4) || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*.
% 0.21/0.43 101[2:SSi:98.1,98.0,11.0,10.0,11.0,10.0] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4)) -> greater(zero,growth_rate(first_movers,sk1(u,sk4)))*.
% 0.21/0.43 102[0:Res:35.2,38.1] || greater_or_equal(sk1(u,sk4),sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk1(u,sk4))* in_environment(sk4,u) -> greater(sk2(sk4),appear(efficient_producers,sk4)).
% 0.21/0.43 103[2:MRR:102.1,97.1] || greater_or_equal(sk1(u,sk4),sk3(sk4))* in_environment(sk4,u) -> greater(sk2(sk4),appear(efficient_producers,sk4)).
% 0.21/0.43 109[2:Res:73.1,103.0] || in_environment(sk4,sk3(sk4)) in_environment(sk4,sk3(sk4)) -> greater(sk2(sk4),appear(efficient_producers,sk4))*.
% 0.21/0.43 111[2:Obv:109.0] || in_environment(sk4,sk3(sk4)) -> greater(sk2(sk4),appear(efficient_producers,sk4))*.
% 0.21/0.43 112[2:MRR:111.0,33.0] || -> greater(sk2(sk4),appear(efficient_producers,sk4))*.
% 0.21/0.43 114[2:Res:112.0,13.0] || -> greater_or_equal(sk5(sk2(sk4)),sk2(sk4))*.
% 0.21/0.43 127[2:Res:101.2,41.2] || in_environment(sk4,u) greater_or_equal(sk1(u,sk4),sk3(sk4))* greater_or_equal(v,sk2(sk4)) in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) -> greater(zero,growth_rate(first_movers,v))*.
% 0.21/0.43 128[2:Obv:127.0] || greater_or_equal(sk1(u,sk4),sk3(sk4))*+ greater_or_equal(v,sk2(sk4)) in_environment(sk4,u) subpopulations(first_movers,efficient_producers,sk4,v) -> greater(zero,growth_rate(first_movers,v))*.
% 0.21/0.43 129[2:Res:73.1,128.0] || in_environment(sk4,sk3(sk4)) greater_or_equal(u,sk2(sk4)) in_environment(sk4,sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 130[2:Obv:129.0] || greater_or_equal(u,sk2(sk4)) in_environment(sk4,sk3(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 131[2:MRR:130.1,33.0] || greater_or_equal(u,sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,u) -> greater(zero,growth_rate(first_movers,u))*.
% 0.21/0.43 132[2:Res:131.2,14.1] || greater_or_equal(sk5(u),sk2(sk4)) subpopulations(first_movers,efficient_producers,sk4,sk5(u))* greater(u,appear(efficient_producers,sk4)) -> .
% 0.21/0.43 133[2:MRR:132.1,12.1] || greater_or_equal(sk5(u),sk2(sk4))* greater(u,appear(efficient_producers,sk4)) -> .
% 0.21/0.43 134[2:Res:114.0,133.0] || greater(sk2(sk4),appear(efficient_producers,sk4))* -> .
% 0.21/0.43 135[2:MRR:134.0,112.0] || -> .
% 0.21/0.43 % SZS output end Refutation
% 0.21/0.43 Formulae used in the proof : mp_first_movers_negative_growth_1 mp_first_movers_negative_growth_2 mp_first_movers_negative_growth_3 mp_first_movers_negative_growth_4 mp_first_movers_negative_growth_5 mp_first_movers_negative_growth_6 l11_7 l11_9 prove_l10_10 prove_l10_11 prove_l10_12 prove_l10_13 prove_l10_14
% 0.21/0.43
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