TSTP Solution File: MGT026-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT026-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.17s 0.41s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : MGT026-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 9 08:30:38 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.41
% 0.17/0.41 SPASS V 3.9
% 0.17/0.41 SPASS beiseite: Proof found.
% 0.17/0.41 % SZS status Theorem
% 0.17/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 SPASS derived 119 clauses, backtracked 21 clauses, performed 2 splits and kept 124 clauses.
% 0.17/0.41 SPASS allocated 75794 KBytes.
% 0.17/0.41 SPASS spent 0:00:00.08 on the problem.
% 0.17/0.41 0:00:00.04 for the input.
% 0.17/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.41 0:00:00.00 for inferences.
% 0.17/0.41 0:00:00.00 for the backtracking.
% 0.17/0.41 0:00:00.01 for the reduction.
% 0.17/0.41
% 0.17/0.41
% 0.17/0.41 Here is a proof with depth 4, length 66 :
% 0.17/0.41 % SZS output start Refutation
% 0.17/0.41 1[0:Inp] environment(u) || greater(growth_rate(v,w),growth_rate(x,w)) subpopulations(x,v,u,w)* -> selection_favors(v,x,w).
% 0.17/0.41 2[0:Inp] environment(u) || equal(cardinality_at_time(v,w),zero) greater(cardinality_at_time(x,w),zero)+ subpopulation(v,u,w)* subpopulation(x,u,w)* -> selection_favors(x,v,w)*.
% 0.17/0.41 3[0:Inp] environment(u) || in_environment(u,v) greater(cardinality_at_time(efficient_producers,v),zero) greater(cardinality_at_time(first_movers,v),zero) -> subpopulations(first_movers,efficient_producers,u,v)*.
% 0.17/0.41 4[0:Inp] environment(u) || in_environment(u,v)*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 0.17/0.41 5[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(first_movers,u,v)*.
% 0.17/0.41 6[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(efficient_producers,u,v)*.
% 0.17/0.41 7[0:Inp] environment(u) || -> greater_or_equal(critical_point(u),appear(efficient_producers,u))*.
% 0.17/0.41 8[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*.
% 0.17/0.41 9[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 0.17/0.41 10[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 0.17/0.41 13[0:Inp] environment(u) || greater(v,w)*+ equal(w,critical_point(u))* subpopulations(first_movers,efficient_producers,u,v)* -> greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)).
% 0.17/0.41 14[0:Inp] environment(u) || in_environment(u,v) greater_or_equal(v,appear(efficient_producers,u))* -> greater(cardinality_at_time(efficient_producers,v),zero).
% 0.17/0.41 15[0:Inp] || -> environment(sk1)*.
% 0.17/0.41 16[0:Inp] || -> in_environment(sk1,sk2)*.
% 0.17/0.41 17[0:Inp] || -> greater(sk2,critical_point(sk1))*r.
% 0.17/0.41 18[0:Inp] || selection_favors(efficient_producers,first_movers,sk2)* -> .
% 0.17/0.41 27[0:Res:15.0,6.0] || in_environment(sk1,u) -> subpopulation(efficient_producers,sk1,u)*.
% 0.17/0.41 28[0:Res:15.0,7.0] || -> greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1))*.
% 0.17/0.41 29[0:Res:16.0,3.1] environment(sk1) || greater(cardinality_at_time(first_movers,sk2),zero) greater(cardinality_at_time(efficient_producers,sk2),zero) -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.17/0.41 30[0:Res:16.0,14.1] environment(sk1) || greater_or_equal(sk2,appear(efficient_producers,sk1))* -> greater(cardinality_at_time(efficient_producers,sk2),zero).
% 0.17/0.41 31[0:Res:16.0,4.1] environment(sk1) || -> greater_or_equal(cardinality_at_time(first_movers,sk2),zero)*.
% 0.17/0.41 32[0:Res:16.0,5.1] environment(sk1) || -> subpopulation(first_movers,sk1,sk2)*.
% 0.17/0.41 35[0:Res:2.5,18.0] environment(u) || equal(cardinality_at_time(first_movers,sk2),zero) greater(cardinality_at_time(efficient_producers,sk2),zero) subpopulation(first_movers,u,sk2) subpopulation(efficient_producers,u,sk2)* -> .
% 0.17/0.41 36[0:MRR:32.0,15.0] || -> subpopulation(first_movers,sk1,sk2)*.
% 0.17/0.41 38[0:MRR:31.0,15.0] || -> greater_or_equal(cardinality_at_time(first_movers,sk2),zero)*.
% 0.17/0.41 39[0:MRR:30.0,15.0] || greater_or_equal(sk2,appear(efficient_producers,sk1))* -> greater(cardinality_at_time(efficient_producers,sk2),zero).
% 0.17/0.41 40[0:MRR:29.0,15.0] || greater(cardinality_at_time(efficient_producers,sk2),zero) greater(cardinality_at_time(first_movers,sk2),zero) -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.17/0.41 42[0:Res:38.0,9.0] || -> equal(cardinality_at_time(first_movers,sk2),zero) greater(cardinality_at_time(first_movers,sk2),zero)*l.
% 0.17/0.41 44[0:Res:28.0,9.0] || -> equal(appear(efficient_producers,sk1),critical_point(sk1)) greater(critical_point(sk1),appear(efficient_producers,sk1))*r.
% 0.17/0.41 45[0:Res:7.1,9.0] environment(u) || -> equal(appear(efficient_producers,u),critical_point(u)) greater(critical_point(u),appear(efficient_producers,u))*r.
% 0.17/0.41 48[1:Spt:42.0] || -> equal(cardinality_at_time(first_movers,sk2),zero)**.
% 0.17/0.41 51[1:Rew:48.0,35.1] environment(u) || equal(zero,zero) greater(cardinality_at_time(efficient_producers,sk2),zero) subpopulation(first_movers,u,sk2) subpopulation(efficient_producers,u,sk2)* -> .
% 0.17/0.41 52[1:Obv:51.1] environment(u) || greater(cardinality_at_time(efficient_producers,sk2),zero) subpopulation(first_movers,u,sk2) subpopulation(efficient_producers,u,sk2)* -> .
% 0.17/0.41 56[0:Res:10.1,39.0] || greater(sk2,appear(efficient_producers,sk1))*r -> greater(cardinality_at_time(efficient_producers,sk2),zero).
% 0.17/0.41 58[2:Spt:44.0] || -> equal(appear(efficient_producers,sk1),critical_point(sk1))**.
% 0.17/0.41 63[2:Rew:58.0,56.0] || greater(sk2,critical_point(sk1)) -> greater(cardinality_at_time(efficient_producers,sk2),zero)*l.
% 0.17/0.41 64[2:MRR:63.0,17.0] || -> greater(cardinality_at_time(efficient_producers,sk2),zero)*l.
% 0.17/0.41 66[2:MRR:52.1,64.0] environment(u) || subpopulation(first_movers,u,sk2) subpopulation(efficient_producers,u,sk2)* -> .
% 0.17/0.41 76[2:Res:27.1,66.2] environment(sk1) || in_environment(sk1,sk2) subpopulation(first_movers,sk1,sk2)* -> .
% 0.17/0.41 80[2:SSi:76.0,15.0] || in_environment(sk1,sk2) subpopulation(first_movers,sk1,sk2)* -> .
% 0.17/0.41 81[2:MRR:80.0,80.1,16.0,36.0] || -> .
% 0.17/0.41 84[2:Spt:81.0,44.0,58.0] || equal(appear(efficient_producers,sk1),critical_point(sk1))** -> .
% 0.17/0.41 85[2:Spt:81.0,44.1] || -> greater(critical_point(sk1),appear(efficient_producers,sk1))*r.
% 0.17/0.41 98[2:NCh:8.2,8.1,56.0,85.0] || greater(sk2,critical_point(sk1)) -> greater(cardinality_at_time(efficient_producers,sk2),zero)*l.
% 0.17/0.41 100[0:NCh:8.2,8.1,56.0,45.2] environment(sk1) || greater(sk2,critical_point(sk1)) -> greater(cardinality_at_time(efficient_producers,sk2),zero) equal(appear(efficient_producers,sk1),critical_point(sk1))**.
% 0.17/0.41 102[2:MRR:98.0,17.0] || -> greater(cardinality_at_time(efficient_producers,sk2),zero)*l.
% 0.17/0.41 103[2:MRR:52.1,102.0] environment(u) || subpopulation(first_movers,u,sk2) subpopulation(efficient_producers,u,sk2)* -> .
% 0.17/0.41 123[2:Res:27.1,103.2] environment(sk1) || in_environment(sk1,sk2) subpopulation(first_movers,sk1,sk2)* -> .
% 0.17/0.41 127[2:SSi:123.0,15.0] || in_environment(sk1,sk2) subpopulation(first_movers,sk1,sk2)* -> .
% 0.17/0.41 128[2:MRR:127.0,127.1,16.0,36.0] || -> .
% 0.17/0.41 131[1:Spt:128.0,42.0,48.0] || equal(cardinality_at_time(first_movers,sk2),zero)** -> .
% 0.17/0.41 132[1:Spt:128.0,42.1] || -> greater(cardinality_at_time(first_movers,sk2),zero)*l.
% 0.17/0.41 134[1:MRR:40.1,132.0] || greater(cardinality_at_time(efficient_producers,sk2),zero) -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.17/0.41 135[0:SSi:100.0,15.0] || greater(sk2,critical_point(sk1)) -> greater(cardinality_at_time(efficient_producers,sk2),zero) equal(appear(efficient_producers,sk1),critical_point(sk1))**.
% 0.17/0.41 136[0:MRR:135.0,17.0] || -> greater(cardinality_at_time(efficient_producers,sk2),zero) equal(appear(efficient_producers,sk1),critical_point(sk1))**.
% 0.17/0.41 139[0:Rew:136.1,56.0] || greater(sk2,critical_point(sk1)) -> greater(cardinality_at_time(efficient_producers,sk2),zero)*l.
% 0.17/0.41 140[0:MRR:139.0,17.0] || -> greater(cardinality_at_time(efficient_producers,sk2),zero)*l.
% 0.17/0.41 141[1:MRR:134.0,140.0] || -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.17/0.41 147[1:Res:141.0,1.2] environment(sk1) || greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) -> selection_favors(efficient_producers,first_movers,sk2)*.
% 0.17/0.41 148[1:SSi:147.0,15.0] || greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) -> selection_favors(efficient_producers,first_movers,sk2)*.
% 0.17/0.41 149[1:MRR:148.1,18.0] || greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))*l -> .
% 0.17/0.41 150[0:Res:17.0,13.1] environment(u) || equal(critical_point(sk1),critical_point(u)) subpopulations(first_movers,efficient_producers,u,sk2)* -> greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)).
% 0.17/0.41 168[1:MRR:150.3,149.0] environment(u) || equal(critical_point(sk1),critical_point(u)) subpopulations(first_movers,efficient_producers,u,sk2)* -> .
% 0.17/0.41 178[1:Res:141.0,168.2] environment(sk1) || equal(critical_point(sk1),critical_point(sk1))* -> .
% 0.17/0.41 179[1:Obv:178.1] environment(sk1) || -> .
% 0.17/0.41 180[1:SSi:179.0,15.0] || -> .
% 0.17/0.41 % SZS output end Refutation
% 0.17/0.41 Formulae used in the proof : mp1_high_growth_rates_28 mp2_favour_members_29 mp_non_empty_fm_and_ep_30 mp_first_movers_exist_31 mp_subpopulations_32 mp_subpopulations_33 mp_critical_point_after_EP_34 mp_greater_transitivity_35 mp_greater_or_equal_36 mp_greater_or_equal_37 d1_40 t6_41 prove_l8_42 prove_l8_43 prove_l8_44 prove_l8_45
% 0.17/0.41
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