TSTP Solution File: MGT034-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT034-2 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 22:26:19 EDT 2022
% Result : Unsatisfiable 0.46s 0.64s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT034-2 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 08:56:27 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.64
% 0.46/0.64 SPASS V 3.9
% 0.46/0.64 SPASS beiseite: Proof found.
% 0.46/0.64 % SZS status Theorem
% 0.46/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.64 SPASS derived 1108 clauses, backtracked 89 clauses, performed 5 splits and kept 659 clauses.
% 0.46/0.64 SPASS allocated 76784 KBytes.
% 0.46/0.64 SPASS spent 0:00:00.29 on the problem.
% 0.46/0.64 0:00:00.04 for the input.
% 0.46/0.64 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.64 0:00:00.03 for inferences.
% 0.46/0.64 0:00:00.01 for the backtracking.
% 0.46/0.64 0:00:00.18 for the reduction.
% 0.46/0.64
% 0.46/0.64
% 0.46/0.64 Here is a proof with depth 8, length 129 :
% 0.46/0.64 % SZS output start Refutation
% 0.46/0.64 1[0:Inp] environment(u) || greater(growth_rate(v,w),growth_rate(x,w))*+ subpopulations(x,v,u,w)* -> selection_favors(v,x,w).
% 0.46/0.64 2[0:Inp] environment(u) || decreases(difference(disbanding_rate(first_movers,v),disbanding_rate(efficient_producers,v)))*+ subpopulations(first_movers,efficient_producers,u,v)* -> .
% 0.46/0.64 3[0:Inp] environment(u) || in_environment(u,critical_point(u)) -> subpopulations(first_movers,efficient_producers,u,critical_point(u))*.
% 0.46/0.64 4[0:Inp] environment(u) || in_environment(u,appear(efficient_producers,u)) -> subpopulations(first_movers,efficient_producers,u,appear(efficient_producers,u))*.
% 0.46/0.64 5[0:Inp] || decreases(difference(founding_rate(first_movers,u),founding_rate(efficient_producers,u)))* -> decreases(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u))) decreases(difference(disbanding_rate(first_movers,u),disbanding_rate(efficient_producers,u))).
% 0.46/0.64 6[0:Inp] environment(u) || decreases(difference(growth_rate(first_movers,v),growth_rate(efficient_producers,v))) greater(w,v)* in_environment(u,w)* greater_or_equal(v,appear(efficient_producers,u))* greater_or_equal(difference(growth_rate(first_movers,w),growth_rate(efficient_producers,w)),zero)*+ -> greater(difference(growth_rate(first_movers,v),growth_rate(efficient_producers,v)),zero)*.
% 0.46/0.64 7[0:Inp] || greater(zero,difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)))* -> greater(growth_rate(efficient_producers,u),growth_rate(first_movers,u)).
% 0.46/0.64 9[0:Inp] || greater(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)),zero)* -> greater(growth_rate(first_movers,u),growth_rate(efficient_producers,u)).
% 0.46/0.64 14[0:Inp] environment(u) || in_environment(u,critical_point(u))* greater_or_equal(v,appear(efficient_producers,u))*+ greater(critical_point(u),v) -> in_environment(u,v).
% 0.46/0.64 16[0:Inp] environment(u) || subpopulations(first_movers,efficient_producers,u,v) -> subpopulations(efficient_producers,first_movers,u,v)*.
% 0.46/0.64 17[0:Inp] environment(u) || subpopulations(first_movers,efficient_producers,u,v) -> greater_or_equal(v,appear(efficient_producers,u))*.
% 0.46/0.64 18[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 0.46/0.64 19[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 0.46/0.64 20[0:Inp] || equal(u,v) -> greater_or_equal(u,v)*.
% 0.46/0.64 21[0:Inp] environment(u) || subpopulations(first_movers,efficient_producers,u,v)*+ -> greater(zero,difference(growth_rate(first_movers,v),growth_rate(efficient_producers,v))) greater_or_equal(difference(growth_rate(first_movers,v),growth_rate(efficient_producers,v)),zero)*.
% 0.46/0.64 22[0:Inp] environment(u) || equal(v,critical_point(u))* greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))*+ -> .
% 0.46/0.64 24[0:Inp] environment(u) || greater_or_equal(v,w)* greater_or_equal(w,x)* subpopulations(first_movers,efficient_producers,u,v)*+ subpopulations(first_movers,efficient_producers,u,x)* -> subpopulations(first_movers,efficient_producers,u,w)*.
% 0.46/0.64 25[0:Inp] environment(u) || subpopulations(first_movers,efficient_producers,u,v)*+ -> decreases(difference(founding_rate(first_movers,v),founding_rate(efficient_producers,v)))*.
% 0.46/0.64 26[0:Inp] || -> environment(sk1)*.
% 0.46/0.64 27[0:Inp] || -> in_environment(sk1,critical_point(sk1))*.
% 0.46/0.64 28[0:Inp] || -> greater_or_equal(sk2,appear(efficient_producers,sk1))*.
% 0.46/0.64 29[0:Inp] || -> greater(critical_point(sk1),sk2)*.
% 0.46/0.64 30[0:Inp] || selection_favors(first_movers,efficient_producers,sk2)* -> .
% 0.46/0.64 38[0:Res:26.0,1.0] || greater(growth_rate(u,v),growth_rate(w,v))* subpopulations(w,u,sk1,v) -> selection_favors(u,w,v).
% 0.46/0.64 41[0:Res:26.0,4.0] || in_environment(sk1,appear(efficient_producers,sk1)) -> subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))*.
% 0.46/0.64 42[0:Res:26.0,22.0] || equal(u,critical_point(sk1)) greater(growth_rate(efficient_producers,u),growth_rate(first_movers,u))* -> .
% 0.46/0.64 45[0:Res:26.0,17.0] || subpopulations(first_movers,efficient_producers,sk1,u) -> greater_or_equal(u,appear(efficient_producers,sk1))*.
% 0.46/0.64 48[0:Res:29.0,19.0] || -> greater_or_equal(critical_point(sk1),sk2)*.
% 0.46/0.64 52[0:Res:27.0,14.1] environment(sk1) || greater_or_equal(u,appear(efficient_producers,sk1))* greater(critical_point(sk1),u) -> in_environment(sk1,u).
% 0.46/0.64 53[0:Res:27.0,3.1] environment(sk1) || -> subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))*.
% 0.46/0.64 59[0:Res:28.0,14.2] environment(sk1) || in_environment(sk1,critical_point(sk1))* greater(critical_point(sk1),sk2) -> in_environment(sk1,sk2).
% 0.46/0.64 60[0:Res:28.0,6.3] environment(sk1) || in_environment(sk1,u) greater_or_equal(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)),zero)* greater(u,sk2) decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.64 61[0:Res:28.0,18.0] || -> greater(sk2,appear(efficient_producers,sk1))* equal(appear(efficient_producers,sk1),sk2).
% 0.46/0.64 62[0:Res:28.0,24.3] environment(u) || greater_or_equal(v,sk2) subpopulations(first_movers,efficient_producers,u,v)* subpopulations(first_movers,efficient_producers,u,appear(efficient_producers,sk1))*+ -> subpopulations(first_movers,efficient_producers,u,sk2).
% 0.46/0.64 66[0:MRR:53.0,26.0] || -> subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))*.
% 0.46/0.64 67[0:MRR:59.0,59.1,59.2,26.0,27.0,29.0] || -> in_environment(sk1,sk2)*.
% 0.46/0.64 68[0:MRR:52.0,26.0] || greater_or_equal(u,appear(efficient_producers,sk1))* greater(critical_point(sk1),u) -> in_environment(sk1,u).
% 0.46/0.64 71[0:MRR:60.0,26.0] || decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) greater(u,sk2) in_environment(sk1,u) greater_or_equal(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)),zero)* -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.64 72[1:Spt:61.1] || -> equal(appear(efficient_producers,sk1),sk2)**.
% 0.46/0.64 81[1:Rew:72.0,41.0] || in_environment(sk1,sk2) -> subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))*.
% 0.46/0.64 82[1:Rew:72.0,81.1] || in_environment(sk1,sk2) -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.64 83[1:MRR:82.0,67.0] || -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.64 129[1:Res:83.0,25.1] environment(sk1) || -> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))*.
% 0.46/0.64 133[1:SSi:129.0,26.0] || -> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))*.
% 0.46/0.64 184[1:Res:133.0,5.0] || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*.
% 0.46/0.64 190[1:Res:184.1,2.1] environment(u) || subpopulations(first_movers,efficient_producers,u,sk2)*+ -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.64 191[1:Res:83.0,190.1] environment(sk1) || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.64 192[1:SSi:191.0,26.0] || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.64 193[1:MRR:71.0,192.0] || greater(u,sk2) in_environment(sk1,u) greater_or_equal(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)),zero)* -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.64 210[0:Res:66.0,21.1] environment(sk1) || -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)*.
% 0.46/0.64 214[0:SSi:210.0,26.0] || -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)*.
% 0.46/0.64 227[0:Res:66.0,24.3] environment(sk1) || greater_or_equal(critical_point(sk1),u) greater_or_equal(u,v)* subpopulations(first_movers,efficient_producers,sk1,v)* -> subpopulations(first_movers,efficient_producers,sk1,u)*.
% 0.46/0.64 231[0:SSi:227.0,26.0] || greater_or_equal(critical_point(sk1),u) greater_or_equal(u,v)* subpopulations(first_movers,efficient_producers,sk1,v)*+ -> subpopulations(first_movers,efficient_producers,sk1,u)*.
% 0.46/0.64 327[0:Res:4.2,231.2] environment(sk1) || in_environment(sk1,appear(efficient_producers,sk1)) greater_or_equal(critical_point(sk1),u) greater_or_equal(u,appear(efficient_producers,sk1))* -> subpopulations(first_movers,efficient_producers,sk1,u).
% 0.46/0.64 461[1:Res:214.1,193.2] || greater(critical_point(sk1),sk2) in_environment(sk1,critical_point(sk1)) -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))* greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.64 463[1:MRR:461.0,461.1,29.0,27.0] || -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))* greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.64 464[2:Spt:463.0] || -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))*.
% 0.46/0.64 466[2:Res:464.0,7.0] || -> greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))*.
% 0.46/0.64 469[2:Res:466.0,42.1] || equal(critical_point(sk1),critical_point(sk1))* -> .
% 0.46/0.64 474[2:Obv:469.0] || -> .
% 0.46/0.64 476[2:Spt:474.0,463.0,464.0] || greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))* -> .
% 0.46/0.64 477[2:Spt:474.0,463.1] || -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)*.
% 0.46/0.64 484[2:Res:477.0,9.0] || -> greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))*.
% 0.46/0.64 489[2:Res:484.0,38.0] || subpopulations(efficient_producers,first_movers,sk1,sk2)* -> selection_favors(first_movers,efficient_producers,sk2).
% 0.46/0.64 491[2:MRR:489.1,30.0] || subpopulations(efficient_producers,first_movers,sk1,sk2)* -> .
% 0.46/0.64 493[2:Res:16.2,491.0] environment(sk1) || subpopulations(first_movers,efficient_producers,sk1,sk2)* -> .
% 0.46/0.64 495[2:SSi:493.0,26.0] || subpopulations(first_movers,efficient_producers,sk1,sk2)* -> .
% 0.46/0.64 496[2:MRR:495.0,83.0] || -> .
% 0.46/0.64 497[1:Spt:496.0,61.1,72.0] || equal(appear(efficient_producers,sk1),sk2)** -> .
% 0.46/0.64 498[1:Spt:496.0,61.0] || -> greater(sk2,appear(efficient_producers,sk1))*.
% 0.46/0.64 499[0:SSi:327.0,26.0] || in_environment(sk1,appear(efficient_producers,sk1)) greater_or_equal(critical_point(sk1),u) greater_or_equal(u,appear(efficient_producers,sk1))* -> subpopulations(first_movers,efficient_producers,sk1,u).
% 0.46/0.64 508[0:Res:45.1,18.0] || subpopulations(first_movers,efficient_producers,sk1,u) -> equal(u,appear(efficient_producers,sk1)) greater(u,appear(efficient_producers,sk1))*.
% 0.46/0.64 522[0:Res:20.1,68.0] || equal(u,appear(efficient_producers,sk1)) greater(critical_point(sk1),u)* -> in_environment(sk1,u).
% 0.46/0.64 551[0:Res:508.2,522.1] || subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))* equal(appear(efficient_producers,sk1),appear(efficient_producers,sk1)) -> equal(appear(efficient_producers,sk1),critical_point(sk1)) in_environment(sk1,appear(efficient_producers,sk1)).
% 0.46/0.64 558[0:Obv:551.1] || subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))* -> equal(appear(efficient_producers,sk1),critical_point(sk1)) in_environment(sk1,appear(efficient_producers,sk1)).
% 0.46/0.64 559[0:MRR:558.0,66.0] || -> equal(appear(efficient_producers,sk1),critical_point(sk1)) in_environment(sk1,appear(efficient_producers,sk1))*.
% 0.46/0.64 564[2:Spt:559.0] || -> equal(appear(efficient_producers,sk1),critical_point(sk1))**.
% 0.46/0.64 587[2:Rew:564.0,62.3] environment(u) || greater_or_equal(v,sk2) subpopulations(first_movers,efficient_producers,u,v)* subpopulations(first_movers,efficient_producers,u,critical_point(sk1))*+ -> subpopulations(first_movers,efficient_producers,u,sk2).
% 0.46/0.64 659[2:Res:66.0,587.3] environment(sk1) || greater_or_equal(u,sk2) subpopulations(first_movers,efficient_producers,sk1,u)* -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.64 662[2:SSi:659.0,26.0] || greater_or_equal(u,sk2) subpopulations(first_movers,efficient_producers,sk1,u)*+ -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.64 665[2:Res:66.0,662.1] || greater_or_equal(critical_point(sk1),sk2) -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.64 669[2:MRR:665.0,48.0] || -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.64 680[2:Res:669.0,25.1] environment(sk1) || -> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))*.
% 0.46/0.64 681[2:SSi:680.0,26.0] || -> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))*.
% 0.46/0.64 683[2:Res:681.0,5.0] || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*.
% 0.46/0.64 729[2:Res:683.1,2.1] environment(u) || subpopulations(first_movers,efficient_producers,u,sk2)*+ -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.64 753[2:Res:669.0,729.1] environment(sk1) || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.64 754[2:SSi:753.0,26.0] || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.64 755[2:MRR:71.0,754.0] || greater(u,sk2) in_environment(sk1,u) greater_or_equal(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)),zero)* -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.64 1017[3:Spt:214.0] || -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))*.
% 0.46/0.64 1020[3:Res:1017.0,7.0] || -> greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))*.
% 0.46/0.64 1024[3:Res:1020.0,42.1] || equal(critical_point(sk1),critical_point(sk1))* -> .
% 0.46/0.64 1029[3:Obv:1024.0] || -> .
% 0.46/0.64 1031[3:Spt:1029.0,214.0,1017.0] || greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))* -> .
% 0.46/0.64 1032[3:Spt:1029.0,214.1] || -> greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)*.
% 0.46/0.64 1045[3:Res:1032.0,755.2] || greater(critical_point(sk1),sk2) in_environment(sk1,critical_point(sk1)) -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)*.
% 0.46/0.64 1046[3:MRR:1045.0,1045.1,29.0,27.0] || -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)*.
% 0.46/0.64 1050[3:Res:1046.0,9.0] || -> greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))*.
% 0.46/0.64 1058[3:Res:1050.0,38.0] || subpopulations(efficient_producers,first_movers,sk1,sk2)* -> selection_favors(first_movers,efficient_producers,sk2).
% 0.46/0.64 1060[3:MRR:1058.1,30.0] || subpopulations(efficient_producers,first_movers,sk1,sk2)* -> .
% 0.46/0.64 1063[3:Res:16.2,1060.0] environment(sk1) || subpopulations(first_movers,efficient_producers,sk1,sk2)* -> .
% 0.46/0.64 1065[3:SSi:1063.0,26.0] || subpopulations(first_movers,efficient_producers,sk1,sk2)* -> .
% 0.46/0.64 1066[3:MRR:1065.0,669.0] || -> .
% 0.46/0.64 1067[2:Spt:1066.0,559.0,564.0] || equal(appear(efficient_producers,sk1),critical_point(sk1))** -> .
% 0.46/0.64 1068[2:Spt:1066.0,559.1] || -> in_environment(sk1,appear(efficient_producers,sk1))*.
% 0.46/0.64 1070[2:MRR:499.0,1068.0] || greater_or_equal(critical_point(sk1),u) greater_or_equal(u,appear(efficient_producers,sk1))* -> subpopulations(first_movers,efficient_producers,sk1,u).
% 0.46/0.65 1140[2:Res:28.0,1070.1] || greater_or_equal(critical_point(sk1),sk2) -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.65 1141[2:MRR:1140.0,48.0] || -> subpopulations(first_movers,efficient_producers,sk1,sk2)*.
% 0.46/0.65 1156[2:Res:1141.0,25.1] environment(sk1) || -> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))*.
% 0.46/0.65 1159[2:SSi:1156.0,26.0] || -> decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2)))*.
% 0.46/0.65 1161[2:Res:1159.0,5.0] || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))) decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))*.
% 0.46/0.65 1185[2:Res:1161.1,2.1] environment(u) || subpopulations(first_movers,efficient_producers,u,sk2)*+ -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.65 1220[2:Res:1141.0,1185.1] environment(sk1) || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.65 1221[2:SSi:1220.0,26.0] || -> decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))*.
% 0.46/0.65 1222[2:MRR:71.0,1221.0] || greater(u,sk2) in_environment(sk1,u) greater_or_equal(difference(growth_rate(first_movers,u),growth_rate(efficient_producers,u)),zero)* -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero).
% 0.46/0.65 1365[3:Spt:214.0] || -> greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))*.
% 0.46/0.65 1368[3:Res:1365.0,7.0] || -> greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))*.
% 0.46/0.65 1372[3:Res:1368.0,42.1] || equal(critical_point(sk1),critical_point(sk1))* -> .
% 0.46/0.65 1377[3:Obv:1372.0] || -> .
% 0.46/0.65 1379[3:Spt:1377.0,214.0,1365.0] || greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))))* -> .
% 0.46/0.65 1380[3:Spt:1377.0,214.1] || -> greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)*.
% 0.46/0.65 1391[3:Res:1380.0,1222.2] || greater(critical_point(sk1),sk2) in_environment(sk1,critical_point(sk1)) -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)*.
% 0.46/0.65 1392[3:MRR:1391.0,1391.1,29.0,27.0] || -> greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)*.
% 0.46/0.65 1396[3:Res:1392.0,9.0] || -> greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))*.
% 0.46/0.65 1403[3:Res:1396.0,38.0] || subpopulations(efficient_producers,first_movers,sk1,sk2)* -> selection_favors(first_movers,efficient_producers,sk2).
% 0.46/0.65 1405[3:MRR:1403.1,30.0] || subpopulations(efficient_producers,first_movers,sk1,sk2)* -> .
% 0.46/0.65 1407[3:Res:16.2,1405.0] environment(sk1) || subpopulations(first_movers,efficient_producers,sk1,sk2)* -> .
% 0.46/0.65 1409[3:SSi:1407.0,26.0] || subpopulations(first_movers,efficient_producers,sk1,sk2)* -> .
% 0.46/0.65 1410[3:MRR:1409.0,1141.0] || -> .
% 0.46/0.65 % SZS output end Refutation
% 0.46/0.65 Formulae used in the proof : mp1_high_growth_rates_33 l3_34 mp_critical_point_means_FM_and_EP_35 mp_FM_and_EP_when_EP_appears_36 mp_difference_between_founding_rates_37 mp_decreasing_function_38 mp_negative_growth_rate_difference_39 mp_positive_growth_rate_difference_41 mp_critical_time_points_46 mp_symmetry_of_subpopulations_48 mp_FM_and_EP_members_EP_appeared_49 mp_greater_or_equal_50 mp_greater_or_equal_51 mp_greater_or_equal_52 mp_relationship_of_growth_rates_53 d1_54 a10_56 a12_57 prove_t3_58 prove_t3_59 prove_t3_60 prove_t3_61 prove_t3_62
% 0.46/0.65
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