TSTP Solution File: MGT024-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT024-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:26:15 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT024-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 09:26:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 48 clauses, backtracked 27 clauses, performed 3 splits and kept 84 clauses.
% 0.18/0.40 SPASS allocated 75676 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 3, length 76 :
% 0.18/0.40 % SZS output start Refutation
% 0.18/0.40 1[0:Inp] environment(u) || subpopulations(first_movers,efficient_producers,u,v)* -> in_environment(u,v).
% 0.18/0.40 2[0:Inp] environment(u) || subpopulations(first_movers,efficient_producers,u,v) -> greater(number_of_organizations(u,v),zero)*.
% 0.18/0.40 3[0:Inp] environment(u) || greater_or_equal(v,equilibrium(u)) greater(equilibrium(u),v)* -> .
% 0.18/0.40 5[0:Inp] environment(u) || in_environment(u,v) greater(number_of_organizations(u,v),zero)* -> constant(resources(u,v)) greater(equilibrium(u),v).
% 0.18/0.40 7[0:Inp] environment(u) || constant(resources(u,v))* in_environment(u,v) -> constant(number_of_organizations(u,v)).
% 0.18/0.40 9[0:Inp] environment(u) || constant(number_of_organizations(u,v)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(first_movers,v)) greater(growth_rate(first_movers,v),zero)* equal(growth_rate(first_movers,v),zero).
% 0.18/0.40 10[0:Inp] environment(u) || constant(number_of_organizations(u,v)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(efficient_producers,v)) greater(growth_rate(efficient_producers,v),zero)* equal(growth_rate(first_movers,v),zero).
% 0.18/0.40 12[0:Inp] environment(u) || constant(number_of_organizations(u,v)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(growth_rate(efficient_producers,v),zero)* greater(growth_rate(first_movers,v),zero) equal(growth_rate(efficient_producers,v),zero).
% 0.18/0.40 13[0:Inp] environment(u) || constant(number_of_organizations(u,v)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(first_movers,v)) greater(growth_rate(first_movers,v),zero)* equal(growth_rate(efficient_producers,v),zero).
% 0.18/0.40 14[0:Inp] environment(u) || constant(number_of_organizations(u,v)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(efficient_producers,v)) greater(growth_rate(efficient_producers,v),zero)* equal(growth_rate(efficient_producers,v),zero).
% 0.18/0.40 15[0:Inp] environment(u) || constant(number_of_organizations(u,v)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(zero,growth_rate(first_movers,v)) greater(zero,growth_rate(efficient_producers,v))* equal(growth_rate(efficient_producers,v),zero).
% 0.18/0.40 16[0:Inp] || -> environment(sk1)*.
% 0.18/0.40 17[0:Inp] || -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.18/0.40 18[0:Inp] || -> greater_or_equal(sk2,equilibrium(sk1))*.
% 0.18/0.40 19[0:Inp] || equal(growth_rate(efficient_producers,sk2),zero)** equal(growth_rate(first_movers,sk2),zero) -> .
% 0.18/0.40 20[0:Inp] || greater(zero,growth_rate(efficient_producers,sk2)) greater(growth_rate(first_movers,sk2),zero)* -> .
% 0.18/0.40 21[0:Inp] || greater(zero,growth_rate(first_movers,sk2)) greater(growth_rate(efficient_producers,sk2),zero)* -> .
% 0.18/0.40 31[0:Res:16.0,5.0] || in_environment(sk1,u) greater(number_of_organizations(sk1,u),zero)* -> constant(resources(sk1,u)) greater(equilibrium(sk1),u).
% 0.18/0.40 33[0:Res:16.0,7.0] || constant(resources(sk1,u))* in_environment(sk1,u) -> constant(number_of_organizations(sk1,u)).
% 0.18/0.40 37[0:Res:18.0,3.1] environment(sk1) || greater(equilibrium(sk1),sk2)* -> .
% 0.18/0.40 38[0:Res:17.0,15.1] environment(sk1) || constant(number_of_organizations(sk1,sk2)) -> equal(growth_rate(efficient_producers,sk2),zero) greater(zero,growth_rate(efficient_producers,sk2))* greater(zero,growth_rate(first_movers,sk2)).
% 0.18/0.40 39[0:Res:17.0,14.1] environment(sk1) || constant(number_of_organizations(sk1,sk2)) -> equal(growth_rate(efficient_producers,sk2),zero) greater(zero,growth_rate(efficient_producers,sk2)) greater(growth_rate(efficient_producers,sk2),zero)*.
% 0.18/0.40 40[0:Res:17.0,13.1] environment(sk1) || constant(number_of_organizations(sk1,sk2)) -> equal(growth_rate(efficient_producers,sk2),zero) greater(growth_rate(first_movers,sk2),zero)* greater(zero,growth_rate(first_movers,sk2)).
% 0.18/0.40 41[0:Res:17.0,12.1] environment(sk1) || constant(number_of_organizations(sk1,sk2)) -> equal(growth_rate(efficient_producers,sk2),zero) greater(growth_rate(first_movers,sk2),zero) greater(growth_rate(efficient_producers,sk2),zero)*.
% 0.18/0.40 43[0:Res:17.0,10.1] environment(sk1) || constant(number_of_organizations(sk1,sk2)) -> equal(growth_rate(first_movers,sk2),zero) greater(zero,growth_rate(efficient_producers,sk2)) greater(growth_rate(efficient_producers,sk2),zero)*.
% 0.18/0.40 44[0:Res:17.0,9.1] environment(sk1) || constant(number_of_organizations(sk1,sk2)) -> equal(growth_rate(first_movers,sk2),zero) greater(growth_rate(first_movers,sk2),zero)* greater(zero,growth_rate(first_movers,sk2)).
% 0.18/0.40 46[0:Res:17.0,2.1] environment(sk1) || -> greater(number_of_organizations(sk1,sk2),zero)*.
% 0.18/0.40 47[0:Res:17.0,1.1] environment(sk1) || -> in_environment(sk1,sk2)*.
% 0.18/0.40 48[0:MRR:47.0,16.0] || -> in_environment(sk1,sk2)*.
% 0.18/0.40 49[0:MRR:37.0,16.0] || greater(equilibrium(sk1),sk2)* -> .
% 0.18/0.40 50[0:MRR:46.0,16.0] || -> greater(number_of_organizations(sk1,sk2),zero)*.
% 0.18/0.40 52[0:MRR:44.0,16.0] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(first_movers,sk2)) greater(growth_rate(first_movers,sk2),zero)* equal(growth_rate(first_movers,sk2),zero).
% 0.18/0.40 53[0:MRR:43.0,16.0] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(efficient_producers,sk2)) greater(growth_rate(efficient_producers,sk2),zero)* equal(growth_rate(first_movers,sk2),zero).
% 0.18/0.40 55[0:MRR:41.0,16.0] || constant(number_of_organizations(sk1,sk2)) -> greater(growth_rate(efficient_producers,sk2),zero)* greater(growth_rate(first_movers,sk2),zero) equal(growth_rate(efficient_producers,sk2),zero).
% 0.18/0.40 56[0:MRR:40.0,16.0] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(first_movers,sk2)) greater(growth_rate(first_movers,sk2),zero)* equal(growth_rate(efficient_producers,sk2),zero).
% 0.18/0.40 57[0:MRR:39.0,16.0] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(efficient_producers,sk2)) greater(growth_rate(efficient_producers,sk2),zero)* equal(growth_rate(efficient_producers,sk2),zero).
% 0.18/0.40 58[0:MRR:38.0,16.0] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(first_movers,sk2)) greater(zero,growth_rate(efficient_producers,sk2))* equal(growth_rate(efficient_producers,sk2),zero).
% 0.18/0.40 59[1:Spt:55.3] || -> equal(growth_rate(efficient_producers,sk2),zero)**.
% 0.18/0.40 61[1:Rew:59.0,53.2] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(efficient_producers,sk2))* greater(zero,zero) equal(growth_rate(first_movers,sk2),zero).
% 0.18/0.40 62[1:Rew:59.0,21.1] || greater(zero,growth_rate(first_movers,sk2))* greater(zero,zero) -> .
% 0.18/0.40 64[1:Rew:59.0,20.0] || greater(zero,zero) greater(growth_rate(first_movers,sk2),zero)* -> .
% 0.18/0.40 65[1:Rew:59.0,19.0] || equal(zero,zero) equal(growth_rate(first_movers,sk2),zero)** -> .
% 0.18/0.40 66[1:Obv:65.0] || equal(growth_rate(first_movers,sk2),zero)** -> .
% 0.18/0.40 67[1:MRR:52.3,66.0] || constant(number_of_organizations(sk1,sk2)) -> greater(zero,growth_rate(first_movers,sk2)) greater(growth_rate(first_movers,sk2),zero)*.
% 0.18/0.40 69[1:Rew:59.0,61.1] || constant(number_of_organizations(sk1,sk2))* -> greater(zero,zero) greater(zero,zero) equal(growth_rate(first_movers,sk2),zero).
% 0.18/0.40 70[1:Obv:69.1] || constant(number_of_organizations(sk1,sk2))* -> greater(zero,zero) equal(growth_rate(first_movers,sk2),zero).
% 0.18/0.40 71[1:MRR:70.2,66.0] || constant(number_of_organizations(sk1,sk2))* -> greater(zero,zero).
% 0.18/0.40 74[2:Spt:62.1] || greater(zero,zero)* -> .
% 0.18/0.40 75[2:MRR:71.1,74.0] || constant(number_of_organizations(sk1,sk2))* -> .
% 0.18/0.40 77[0:Res:50.0,31.1] || in_environment(sk1,sk2) -> constant(resources(sk1,sk2))* greater(equilibrium(sk1),sk2).
% 0.18/0.40 80[0:MRR:77.0,77.2,48.0,49.0] || -> constant(resources(sk1,sk2))*.
% 0.18/0.40 82[0:Res:80.0,33.0] || in_environment(sk1,sk2) -> constant(number_of_organizations(sk1,sk2))*.
% 0.18/0.40 83[0:Res:80.0,7.1] environment(sk1) || in_environment(sk1,sk2) -> constant(number_of_organizations(sk1,sk2))*.
% 0.18/0.40 85[0:SSi:83.0,16.0] || in_environment(sk1,sk2) -> constant(number_of_organizations(sk1,sk2))*.
% 0.18/0.41 86[2:MRR:85.0,85.1,48.0,75.0] || -> .
% 0.18/0.41 87[2:Spt:86.0,62.1,74.0] || -> greater(zero,zero)*.
% 0.18/0.41 88[2:Spt:86.0,62.0] || greater(zero,growth_rate(first_movers,sk2))* -> .
% 0.18/0.41 89[0:MRR:82.0,48.0] || -> constant(number_of_organizations(sk1,sk2))*.
% 0.18/0.41 90[2:MRR:64.0,87.0] || greater(growth_rate(first_movers,sk2),zero)* -> .
% 0.18/0.41 91[2:MRR:67.0,67.1,67.2,89.0,88.0,90.0] || -> .
% 0.18/0.41 92[1:Spt:91.0,55.3,59.0] || equal(growth_rate(efficient_producers,sk2),zero)** -> .
% 0.18/0.41 93[1:Spt:91.0,55.0,55.1,55.2] || constant(number_of_organizations(sk1,sk2)) -> greater(growth_rate(efficient_producers,sk2),zero)* greater(growth_rate(first_movers,sk2),zero).
% 0.18/0.41 94[1:MRR:93.0,89.0] || -> greater(growth_rate(efficient_producers,sk2),zero)* greater(growth_rate(first_movers,sk2),zero).
% 0.18/0.41 98[1:MRR:56.0,56.3,89.0,92.0] || -> greater(zero,growth_rate(first_movers,sk2)) greater(growth_rate(first_movers,sk2),zero)*.
% 0.18/0.41 99[1:MRR:57.0,57.3,89.0,92.0] || -> greater(zero,growth_rate(efficient_producers,sk2)) greater(growth_rate(efficient_producers,sk2),zero)*.
% 0.18/0.41 100[1:MRR:58.0,58.3,89.0,92.0] || -> greater(zero,growth_rate(first_movers,sk2)) greater(zero,growth_rate(efficient_producers,sk2))*.
% 0.18/0.41 101[2:Spt:20.0] || greater(zero,growth_rate(efficient_producers,sk2))* -> .
% 0.18/0.41 102[2:MRR:99.0,101.0] || -> greater(growth_rate(efficient_producers,sk2),zero)*.
% 0.18/0.41 103[2:MRR:100.1,101.0] || -> greater(zero,growth_rate(first_movers,sk2))*.
% 0.18/0.41 104[2:MRR:21.1,102.0] || greater(zero,growth_rate(first_movers,sk2))* -> .
% 0.18/0.41 105[2:MRR:104.0,103.0] || -> .
% 0.18/0.41 106[2:Spt:105.0,20.0,101.0] || -> greater(zero,growth_rate(efficient_producers,sk2))*.
% 0.18/0.41 107[2:Spt:105.0,20.1] || greater(growth_rate(first_movers,sk2),zero)* -> .
% 0.18/0.41 108[2:MRR:94.1,107.0] || -> greater(growth_rate(efficient_producers,sk2),zero)*.
% 0.18/0.41 109[2:MRR:98.1,107.0] || -> greater(zero,growth_rate(first_movers,sk2))*.
% 0.18/0.41 110[2:MRR:21.0,21.1,109.0,108.0] || -> .
% 0.18/0.41 % SZS output end Refutation
% 0.18/0.41 Formulae used in the proof : mp_time_point_occur_24 mp_positive_number_of_organizations_25 mp_equilibrium_26 a3_28 a6_30 l7_32 l7_33 l7_35 l7_36 l7_37 l7_38 prove_l6_39 prove_l6_40 prove_l6_41 prove_l6_42 prove_l6_43 prove_l6_44
% 0.18/0.41
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