TSTP Solution File: MGT039+2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT039+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 22:26:23 EDT 2022
% Result : Theorem 5.95s 6.11s
% Output : Refutation 6.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT039+2 : TPTP v8.1.0. Released v2.0.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 12:17:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.95/6.11
% 5.95/6.11 SPASS V 3.9
% 5.95/6.11 SPASS beiseite: Proof found.
% 5.95/6.11 % SZS status Theorem
% 5.95/6.11 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.95/6.11 SPASS derived 5009 clauses, backtracked 711 clauses, performed 64 splits and kept 3886 clauses.
% 5.95/6.11 SPASS allocated 103880 KBytes.
% 5.95/6.11 SPASS spent 0:00:05.77 on the problem.
% 5.95/6.11 0:00:00.03 for the input.
% 5.95/6.11 0:00:00.03 for the FLOTTER CNF translation.
% 5.95/6.11 0:00:00.12 for inferences.
% 5.95/6.11 0:00:00.07 for the backtracking.
% 5.95/6.11 0:00:05.45 for the reduction.
% 5.95/6.11
% 5.95/6.11
% 5.95/6.11 Here is a proof with depth 14, length 196 :
% 5.95/6.11 % SZS output start Refutation
% 5.95/6.11 1[0:Inp] || -> observational_period(skc1)*.
% 5.95/6.11 2[0:Inp] || -> slow_change(skc1)*.
% 5.95/6.11 3[0:Inp] || -> propagation_strategy(first_movers)*.
% 5.95/6.11 4[0:Inp] || -> propagation_strategy(efficient_producers)*.
% 5.95/6.11 5[0:Inp] || -> environment(skf2(u))*.
% 5.95/6.11 6[0:Inp] || selection_favors(efficient_producers,first_movers,skc1)* -> .
% 5.95/6.11 7[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 5.95/6.11 8[0:Inp] || equal(u,v) -> greater_or_equal(u,v)*.
% 5.95/6.11 9[0:Inp] environment(u) || -> greater_or_equal(critical_point(u),start_time(u))*.
% 5.95/6.11 10[0:Inp] environment(u) || -> greater_or_equal(critical_point(u),appear(efficient_producers,u))*.
% 5.95/6.11 11[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 5.95/6.11 12[0:Inp] environment(u) || in_environment(u,v) -> greater_or_equal(end_time(u),v)*.
% 5.95/6.11 13[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(first_movers,u,v)*.
% 5.95/6.11 14[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(efficient_producers,u,v)*.
% 5.95/6.11 15[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*.
% 5.95/6.11 16[0:Inp] environment(u) || in_environment(u,v)*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 5.95/6.11 18[0:Inp] environment(u) || greater_or_equal(v,start_time(u))*+ greater_or_equal(end_time(u),v)* -> in_environment(u,v).
% 5.95/6.11 20[0:Inp] observational_period(u) || propagation_strategy(efficient_producers) propagation_strategy(first_movers) -> in_environment(u,skf2(u))* selection_favors(efficient_producers,first_movers,u)*.
% 5.95/6.11 21[0:Inp] environment(u) slow_change(v) observational_period(v) || in_environment(v,u)*+ -> in_environment(u,skf3(u))*.
% 5.95/6.11 22[0:Inp] environment(u) slow_change(v) observational_period(v) || in_environment(v,u)* -> greater(skf3(u),critical_point(u)).
% 5.95/6.11 23[0:Inp] environment(u) || in_environment(u,v) greater_or_equal(v,appear(efficient_producers,u))* -> greater(cardinality_at_time(efficient_producers,v),zero).
% 5.95/6.11 24[0:Inp] observational_period(u) || selection_favors(efficient_producers,first_movers,end_time(skf2(u)))* propagation_strategy(efficient_producers) propagation_strategy(first_movers) -> selection_favors(efficient_producers,first_movers,u).
% 5.95/6.11 25[0:Inp] environment(u) || greater(v,critical_point(u)) subpopulations(first_movers,efficient_producers,u,v)* -> greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)).
% 5.95/6.11 26[0:Inp] environment(u) || greater(growth_rate(v,w),growth_rate(x,w)) subpopulations(x,v,u,w)* -> selection_favors(v,x,w).
% 5.95/6.11 27[0:Inp] environment(u) || in_environment(u,v) greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero) -> subpopulations(first_movers,efficient_producers,u,v)*.
% 5.95/6.11 28[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)*.
% 5.95/6.11 29[0:MRR:20.1,20.2,4.0,3.0] observational_period(u) || -> in_environment(u,skf2(u))* selection_favors(efficient_producers,first_movers,u)*.
% 5.95/6.11 30[0:MRR:24.2,24.3,4.0,3.0] observational_period(u) || selection_favors(efficient_producers,first_movers,end_time(skf2(u)))* -> selection_favors(efficient_producers,first_movers,u).
% 5.95/6.11 33[0:Res:1.0,22.0] slow_change(skc1) environment(u) || in_environment(skc1,u)* -> greater(skf3(u),critical_point(u)).
% 5.95/6.11 37[0:Res:30.2,6.0] observational_period(skc1) || selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))* -> .
% 5.95/6.11 38[0:Res:29.2,6.0] observational_period(skc1) || -> in_environment(skc1,skf2(skc1))*.
% 5.95/6.11 41[0:MRR:38.0,1.0] || -> in_environment(skc1,skf2(skc1))*.
% 5.95/6.11 42[0:MRR:37.0,1.0] || selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))* -> .
% 5.95/6.11 44[0:MRR:33.0,2.0] environment(u) || in_environment(skc1,u)* -> greater(skf3(u),critical_point(u)).
% 5.95/6.11 52[0:Res:12.2,11.0] environment(u) || in_environment(u,v)* -> equal(end_time(u),v) greater(end_time(u),v).
% 5.95/6.11 53[0:Res:9.1,11.0] environment(u) || -> equal(start_time(u),critical_point(u)) greater(critical_point(u),start_time(u))*r.
% 5.95/6.11 54[0:Res:10.1,11.0] environment(u) || -> equal(appear(efficient_producers,u),critical_point(u)) greater(critical_point(u),appear(efficient_producers,u))*r.
% 5.95/6.11 57[0:Res:7.1,18.1] environment(u) || greater(v,start_time(u)) greater_or_equal(end_time(u),v)* -> in_environment(u,v).
% 5.95/6.11 58[0:Res:8.1,18.1] environment(u) || equal(v,start_time(u)) greater_or_equal(end_time(u),v)* -> in_environment(u,v).
% 5.95/6.11 59[0:Res:12.2,18.1] environment(u) environment(v) || in_environment(u,start_time(v)) greater_or_equal(end_time(v),end_time(u))* -> in_environment(v,end_time(u)).
% 5.95/6.11 62[0:Res:41.0,21.3] environment(skf2(skc1)) slow_change(skc1) observational_period(skc1) || -> in_environment(skf2(skc1),skf3(skf2(skc1)))*.
% 5.95/6.11 63[0:Res:29.1,21.3] observational_period(u) environment(skf2(u)) slow_change(u) observational_period(u) || -> selection_favors(efficient_producers,first_movers,u) in_environment(skf2(u),skf3(skf2(u)))*.
% 5.95/6.11 65[0:SSi:62.2,62.1,62.0,2.0,1.0,2.0,1.0,5.0,2.0,1.0] || -> in_environment(skf2(skc1),skf3(skf2(skc1)))*.
% 5.95/6.11 66[0:Obv:63.0] environment(skf2(u)) slow_change(u) observational_period(u) || -> selection_favors(efficient_producers,first_movers,u) in_environment(skf2(u),skf3(skf2(u)))*.
% 5.95/6.11 67[0:SSi:66.0,5.0] slow_change(u) observational_period(u) || -> selection_favors(efficient_producers,first_movers,u) in_environment(skf2(u),skf3(skf2(u)))*.
% 5.95/6.11 69[0:Res:65.0,16.1] environment(skf2(skc1)) || -> greater_or_equal(cardinality_at_time(first_movers,skf3(skf2(skc1))),zero)*.
% 5.95/6.11 70[0:SSi:69.0,5.0,2.0,1.0] || -> greater_or_equal(cardinality_at_time(first_movers,skf3(skf2(skc1))),zero)*.
% 5.95/6.11 71[0:Res:70.0,11.0] || -> equal(cardinality_at_time(first_movers,skf3(skf2(skc1))),zero) greater(cardinality_at_time(first_movers,skf3(skf2(skc1))),zero)*l.
% 5.95/6.11 82[0:Res:7.1,58.2] environment(u) || greater(end_time(u),v) equal(v,start_time(u)) -> in_environment(u,v)*.
% 5.95/6.11 88[0:Res:7.1,23.2] environment(u) || greater(v,appear(efficient_producers,u))*+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 5.95/6.11 93[0:Res:41.0,44.1] environment(skf2(skc1)) || -> greater(skf3(skf2(skc1)),critical_point(skf2(skc1)))*l.
% 5.95/6.11 97[0:SSi:93.0,5.0,2.0,1.0] || -> greater(skf3(skf2(skc1)),critical_point(skf2(skc1)))*l.
% 5.95/6.11 135[0:Res:65.0,52.1] environment(skf2(skc1)) || -> equal(skf3(skf2(skc1)),end_time(skf2(skc1))) greater(end_time(skf2(skc1)),skf3(skf2(skc1)))*r.
% 5.95/6.11 137[0:SSi:135.0,5.0,2.0,1.0] || -> equal(skf3(skf2(skc1)),end_time(skf2(skc1))) greater(end_time(skf2(skc1)),skf3(skf2(skc1)))*r.
% 5.95/6.11 140[1:Spt:137.0] || -> equal(skf3(skf2(skc1)),end_time(skf2(skc1)))**.
% 5.95/6.11 141[1:Rew:140.0,65.0] || -> in_environment(skf2(skc1),end_time(skf2(skc1)))*.
% 5.95/6.11 143[1:Rew:140.0,71.0] || -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(cardinality_at_time(first_movers,skf3(skf2(skc1))),zero)*l.
% 5.95/6.11 144[1:Rew:140.0,97.0] || -> greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r.
% 5.95/6.11 147[1:Rew:140.0,143.1] || -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 158[0:Res:27.4,26.2] environment(u) environment(u) || in_environment(u,v)* greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero) greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) -> selection_favors(efficient_producers,first_movers,v)*.
% 5.95/6.11 159[0:Res:27.4,25.2] environment(u) environment(u) || in_environment(u,v)* greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero)*l greater(v,critical_point(u)) -> greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)).
% 5.95/6.11 160[0:Obv:158.0] environment(u) || in_environment(u,v)* greater(cardinality_at_time(first_movers,v),zero) greater(cardinality_at_time(efficient_producers,v),zero) greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))+ -> selection_favors(efficient_producers,first_movers,v)*.
% 5.95/6.11 161[0:Obv:159.0] environment(u) || in_environment(u,v)* greater(cardinality_at_time(first_movers,v),zero)+ greater(cardinality_at_time(efficient_producers,v),zero)*l greater(v,critical_point(u)) -> greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)).
% 5.95/6.11 163[0:Res:8.1,57.2] environment(u) || equal(end_time(u),v) greater(v,start_time(u)) -> in_environment(u,v)*.
% 5.95/6.11 171[0:Res:82.3,16.1] environment(u) environment(u) || greater(end_time(u),v)* equal(v,start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 5.95/6.11 173[0:Obv:171.0] environment(u) || greater(end_time(u),v)*+ equal(v,start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 5.95/6.11 179[0:Res:163.3,16.1] environment(u) environment(u) || equal(end_time(u),v) greater(v,start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 5.95/6.11 181[0:Obv:179.0] environment(u) || equal(end_time(u),v) greater(v,start_time(u))*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 5.95/6.11 192[0:Res:8.1,59.3] environment(u) environment(v) || equal(end_time(v),end_time(u))+ in_environment(u,start_time(v))* -> in_environment(v,end_time(u))*.
% 5.95/6.11 196[0:EqR:192.2] environment(u) environment(u) || in_environment(u,start_time(u))* -> in_environment(u,end_time(u)).
% 5.95/6.11 197[0:Obv:196.0] environment(u) || in_environment(u,start_time(u))* -> in_environment(u,end_time(u)).
% 5.95/6.11 199[0:Res:82.3,197.1] environment(u) environment(u) || greater(end_time(u),start_time(u)) equal(start_time(u),start_time(u)) -> in_environment(u,end_time(u))*.
% 5.95/6.11 202[0:Obv:199.3] environment(u) || greater(end_time(u),start_time(u)) -> in_environment(u,end_time(u))*.
% 5.95/6.11 216[0:Res:202.2,16.1] environment(u) environment(u) || greater(end_time(u),start_time(u)) -> greater_or_equal(cardinality_at_time(first_movers,end_time(u)),zero)*.
% 5.95/6.11 217[0:Obv:216.0] environment(u) || greater(end_time(u),start_time(u)) -> greater_or_equal(cardinality_at_time(first_movers,end_time(u)),zero)*.
% 5.95/6.11 244[0:NCh:15.2,15.1,173.1,54.2] environment(u) environment(v) || greater(end_time(u),critical_point(v))+ equal(appear(efficient_producers,v),start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,appear(efficient_producers,v)),zero)* equal(appear(efficient_producers,v),critical_point(v)).
% 5.95/6.11 253[0:NCh:15.2,15.1,88.1,54.2] environment(u) environment(u) || greater(v,critical_point(u)) in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l equal(appear(efficient_producers,u),critical_point(u))**.
% 5.95/6.11 257[0:Obv:253.0] environment(u) || greater(v,critical_point(u))+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l equal(appear(efficient_producers,u),critical_point(u))**.
% 5.95/6.11 262[1:NCh:15.2,15.0,181.2,147.1] environment(u) || equal(end_time(u),cardinality_at_time(first_movers,end_time(skf2(skc1))))*+ equal(start_time(u),zero)** -> greater_or_equal(cardinality_at_time(first_movers,cardinality_at_time(first_movers,end_time(skf2(skc1)))),zero)* equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero).
% 5.95/6.11 263[0:NCh:15.2,15.1,181.2,53.2] environment(u) environment(u) || equal(end_time(u),v) greater(v,critical_point(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)* equal(start_time(u),critical_point(u))**.
% 5.95/6.11 267[0:Obv:263.0] environment(u) || equal(end_time(u),v) greater(v,critical_point(u))*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)* equal(start_time(u),critical_point(u))**.
% 5.95/6.11 422[1:Res:147.1,161.2] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l greater(end_time(skf2(skc1)),critical_point(u)) -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 5.95/6.11 580[1:Res:144.0,257.1] environment(skf2(skc1)) || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero) equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 607[1:SSi:580.0,5.0,2.0,1.0] || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero) equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 608[1:MRR:607.0,141.0] || -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 611[2:Spt:608.0] || -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 612[2:MRR:422.2,611.0] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(end_time(skf2(skc1)),critical_point(u)) -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)** greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 5.95/6.11 613[2:Res:611.0,28.2] environment(u) || equal(cardinality_at_time(v,end_time(skf2(skc1))),zero)+ subpopulation(v,u,end_time(skf2(skc1)))* subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> selection_favors(efficient_producers,v,end_time(skf2(skc1)))*.
% 5.95/6.11 903[3:Spt:262.4] || -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)**.
% 5.95/6.11 917[3:SpL:903.0,613.1] environment(u) || equal(zero,zero) subpopulation(first_movers,u,end_time(skf2(skc1))) subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))*.
% 5.95/6.11 920[3:Obv:917.1] environment(u) || subpopulation(first_movers,u,end_time(skf2(skc1))) subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))*.
% 5.95/6.11 921[3:MRR:920.3,42.0] environment(u) || subpopulation(first_movers,u,end_time(skf2(skc1))) subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 923[3:Res:14.2,921.2] environment(u) environment(u) || in_environment(u,end_time(skf2(skc1))) subpopulation(first_movers,u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 924[3:Obv:923.0] environment(u) || in_environment(u,end_time(skf2(skc1))) subpopulation(first_movers,u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 925[3:MRR:924.2,13.2] environment(u) || in_environment(u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 934[3:Res:141.0,925.1] environment(skf2(skc1)) || -> .
% 5.95/6.11 937[3:SSi:934.0,5.0,2.0,1.0] || -> .
% 5.95/6.11 953[3:Spt:937.0,262.4,903.0] || equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)** -> .
% 5.95/6.11 954[3:Spt:937.0,262.0,262.1,262.2,262.3] environment(u) || equal(end_time(u),cardinality_at_time(first_movers,end_time(skf2(skc1))))*+ equal(start_time(u),zero)** -> greater_or_equal(cardinality_at_time(first_movers,cardinality_at_time(first_movers,end_time(skf2(skc1)))),zero)*.
% 5.95/6.11 955[3:MRR:147.0,953.0] || -> greater(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 966[3:MRR:612.3,953.0] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(end_time(skf2(skc1)),critical_point(u))+ -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1))))*l.
% 5.95/6.11 2344[3:Res:144.0,966.2] environment(skf2(skc1)) || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 5.95/6.11 2347[3:SSi:2344.0,5.0,2.0,1.0] || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 5.95/6.11 2348[3:MRR:2347.0,141.0] || -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1))))*l.
% 5.95/6.11 2350[3:Res:2348.0,160.4] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero) -> selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))*.
% 5.95/6.11 2381[3:MRR:2350.2,2350.3,2350.4,955.0,611.0,42.0] environment(u) || in_environment(u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 2391[3:Res:141.0,2381.1] environment(skf2(skc1)) || -> .
% 5.95/6.11 2398[3:SSi:2391.0,5.0,2.0,1.0] || -> .
% 5.95/6.11 2426[2:Spt:2398.0,608.0,611.0] || greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l -> .
% 5.95/6.11 2427[2:Spt:2398.0,608.1] || -> equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1)))**.
% 5.95/6.11 2450[2:SpL:2427.0,88.1] environment(skf2(skc1)) || greater(u,critical_point(skf2(skc1))) in_environment(skf2(skc1),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 5.95/6.11 2461[2:SSi:2450.0,5.0,2.0,1.0] || greater(u,critical_point(skf2(skc1))) in_environment(skf2(skc1),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 5.95/6.11 2586[2:Res:67.3,2461.1] slow_change(skc1) observational_period(skc1) || greater(skf3(skf2(skc1)),critical_point(skf2(skc1))) -> selection_favors(efficient_producers,first_movers,skc1) greater(cardinality_at_time(efficient_producers,skf3(skf2(skc1))),zero)*l.
% 5.95/6.11 2594[2:Rew:140.0,2586.4,140.0,2586.2] slow_change(skc1) observational_period(skc1) || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> selection_favors(efficient_producers,first_movers,skc1) greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 2595[2:SSi:2594.1,2594.0,2.0,1.0,2.0,1.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> selection_favors(efficient_producers,first_movers,skc1) greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 2596[2:MRR:2595.0,2595.1,2595.2,144.0,6.0,2426.0] || -> .
% 5.95/6.11 2610[1:Spt:2596.0,137.0,140.0] || equal(skf3(skf2(skc1)),end_time(skf2(skc1)))** -> .
% 5.95/6.11 2611[1:Spt:2596.0,137.1] || -> greater(end_time(skf2(skc1)),skf3(skf2(skc1)))*r.
% 5.95/6.11 2640[1:OCh:15.1,15.0,97.0,2611.0] || -> greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r.
% 5.95/6.11 2675[1:Res:2640.0,257.1] environment(skf2(skc1)) || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero) equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 2676[1:Res:2640.0,267.2] environment(skf2(skc1)) || equal(end_time(skf2(skc1)),end_time(skf2(skc1))) -> greater_or_equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)* equal(start_time(skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 2707[1:Obv:2676.1] environment(skf2(skc1)) || -> greater_or_equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)* equal(start_time(skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 2708[1:SSi:2707.0,5.0,2.0,1.0] || -> greater_or_equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)* equal(start_time(skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 2713[1:SSi:2675.0,5.0,2.0,1.0] || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero) equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 2758[2:Spt:2708.0] || -> greater_or_equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)*.
% 5.95/6.11 2759[2:Res:2758.0,11.0] || -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 2801[2:Res:2759.1,161.2] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l greater(end_time(skf2(skc1)),critical_point(u)) -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 5.95/6.11 2830[2:NCh:15.2,15.0,2759.1,181.2] environment(u) || equal(end_time(u),cardinality_at_time(first_movers,end_time(skf2(skc1))))*+ equal(start_time(u),zero)** -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater_or_equal(cardinality_at_time(first_movers,cardinality_at_time(first_movers,end_time(skf2(skc1)))),zero)*.
% 5.95/6.11 2906[3:Spt:2713.1] || -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 2907[3:MRR:2801.2,2906.0] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(end_time(skf2(skc1)),critical_point(u)) -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)** greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 5.95/6.11 2908[3:Res:2906.0,28.2] environment(u) || equal(cardinality_at_time(v,end_time(skf2(skc1))),zero)+ subpopulation(v,u,end_time(skf2(skc1)))* subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> selection_favors(efficient_producers,v,end_time(skf2(skc1)))*.
% 5.95/6.11 3198[4:Spt:2830.3] || -> equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)**.
% 5.95/6.11 3212[4:SpL:3198.0,2908.1] environment(u) || equal(zero,zero) subpopulation(first_movers,u,end_time(skf2(skc1))) subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))*.
% 5.95/6.11 3215[4:Obv:3212.1] environment(u) || subpopulation(first_movers,u,end_time(skf2(skc1))) subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))*.
% 5.95/6.11 3216[4:MRR:3215.3,42.0] environment(u) || subpopulation(first_movers,u,end_time(skf2(skc1))) subpopulation(efficient_producers,u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 3218[4:Res:14.2,3216.2] environment(u) environment(u) || in_environment(u,end_time(skf2(skc1))) subpopulation(first_movers,u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 3219[4:Obv:3218.0] environment(u) || in_environment(u,end_time(skf2(skc1))) subpopulation(first_movers,u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 3220[4:MRR:3219.2,13.2] environment(u) || in_environment(u,end_time(skf2(skc1)))* -> .
% 5.95/6.11 3237[4:Res:202.2,3220.1] environment(skf2(skc1)) environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 5.95/6.11 3244[4:Obv:3237.0] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 5.95/6.11 3245[4:SSi:3244.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 5.95/6.11 3258[4:NCh:15.2,15.1,3245.0,53.2] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 5.95/6.11 3261[4:SSi:3258.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 5.95/6.11 3262[4:MRR:3261.0,2640.0] || -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 5.95/6.11 3272[4:Rew:3262.0,3245.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r -> .
% 5.95/6.11 3367[4:MRR:3272.0,2640.0] || -> .
% 5.95/6.11 3400[4:Spt:3367.0,2830.3,3198.0] || equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)** -> .
% 5.95/6.11 3401[4:Spt:3367.0,2830.0,2830.1,2830.2,2830.4] environment(u) || equal(end_time(u),cardinality_at_time(first_movers,end_time(skf2(skc1))))*+ equal(start_time(u),zero)** -> greater_or_equal(cardinality_at_time(first_movers,cardinality_at_time(first_movers,end_time(skf2(skc1)))),zero)*.
% 5.95/6.11 3402[4:MRR:2759.0,3400.0] || -> greater(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)*l.
% 5.95/6.11 3413[4:MRR:2907.3,3400.0] environment(u) || in_environment(u,end_time(skf2(skc1)))* greater(end_time(skf2(skc1)),critical_point(u))+ -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1))))*l.
% 5.95/6.11 4339[1:Res:2640.0,244.2] environment(skf2(skc1)) environment(skf2(skc1)) || equal(appear(efficient_producers,skf2(skc1)),start_time(skf2(skc1))) -> greater_or_equal(cardinality_at_time(first_movers,appear(efficient_producers,skf2(skc1))),zero)* equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 4342[1:Obv:4339.0] environment(skf2(skc1)) || equal(appear(efficient_producers,skf2(skc1)),start_time(skf2(skc1))) -> greater_or_equal(cardinality_at_time(first_movers,appear(efficient_producers,skf2(skc1))),zero)* equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 5.95/6.11 5244[4:Res:2640.0,3413.2] environment(skf2(skc1)) || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 6.04/6.27 5247[4:SSi:5244.0,5.0,2.0,1.0] || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1)))).
% 6.04/6.27 5338[1:SSi:4342.0,5.0,2.0,1.0] || equal(appear(efficient_producers,skf2(skc1)),start_time(skf2(skc1))) -> greater_or_equal(cardinality_at_time(first_movers,appear(efficient_producers,skf2(skc1))),zero)* equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 6.04/6.27 5450[4:Res:202.2,5247.0] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1))))*l.
% 6.04/6.27 5455[4:SSi:5450.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) -> greater(growth_rate(efficient_producers,end_time(skf2(skc1))),growth_rate(first_movers,end_time(skf2(skc1))))*l.
% 6.04/6.27 5650[4:Res:5455.1,160.4] environment(u) || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) in_environment(u,end_time(skf2(skc1)))* greater(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero) greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero) -> selection_favors(efficient_producers,first_movers,end_time(skf2(skc1)))*.
% 6.04/6.27 5683[4:MRR:5650.3,5650.4,5650.5,3402.0,2906.0,42.0] environment(u) || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) in_environment(u,end_time(skf2(skc1)))* -> .
% 6.04/6.27 5691[4:Res:202.2,5683.2] environment(skf2(skc1)) environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 6.04/6.27 5697[4:Obv:5691.2] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 6.04/6.27 5698[4:SSi:5697.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 6.04/6.27 5713[4:NCh:15.2,15.1,5698.0,53.2] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 5717[4:SSi:5713.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 5720[4:MRR:5717.0,2640.0] || -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 5726[4:Rew:5720.0,5698.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r -> .
% 6.04/6.27 5811[4:MRR:5726.0,2640.0] || -> .
% 6.04/6.27 5823[3:Spt:5811.0,2713.1,2906.0] || greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l -> .
% 6.04/6.27 5824[3:Spt:5811.0,2713.0,2713.2] || in_environment(skf2(skc1),end_time(skf2(skc1)))* -> equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1))).
% 6.04/6.27 5834[3:Res:202.2,5824.0] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) -> equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 5839[3:SSi:5834.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) -> equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6088[4:Spt:5338.2] || -> equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6100[4:SpL:6088.0,88.1] environment(skf2(skc1)) || greater(u,critical_point(skf2(skc1))) in_environment(skf2(skc1),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 6.04/6.27 6116[4:SSi:6100.0,5.0,2.0,1.0] || greater(u,critical_point(skf2(skc1))) in_environment(skf2(skc1),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 6.04/6.27 6209[4:Res:202.2,6116.1] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l.
% 6.04/6.27 6218[4:SSi:6209.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1))) greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> greater(cardinality_at_time(efficient_producers,end_time(skf2(skc1))),zero)*l.
% 6.04/6.27 6219[4:MRR:6218.1,6218.2,2640.0,5823.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 6.04/6.27 6235[4:NCh:15.2,15.1,6219.0,53.2] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6237[4:SSi:6235.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6238[4:MRR:6237.0,2640.0] || -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6243[4:Rew:6238.0,6219.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r -> .
% 6.04/6.27 6281[4:MRR:6243.0,2640.0] || -> .
% 6.04/6.27 6296[4:Spt:6281.0,5338.2,6088.0] || equal(appear(efficient_producers,skf2(skc1)),critical_point(skf2(skc1)))** -> .
% 6.04/6.27 6297[4:Spt:6281.0,5338.0,5338.1] || equal(appear(efficient_producers,skf2(skc1)),start_time(skf2(skc1))) -> greater_or_equal(cardinality_at_time(first_movers,appear(efficient_producers,skf2(skc1))),zero)*.
% 6.04/6.27 6300[4:MRR:5839.1,6296.0] || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 6.04/6.27 6332[4:NCh:15.2,15.1,6300.0,53.2] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6335[4:SSi:6332.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1))) -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6336[4:MRR:6335.0,2640.0] || -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6340[4:Rew:6336.0,6300.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r -> .
% 6.04/6.27 6367[4:MRR:6340.0,2640.0] || -> .
% 6.04/6.27 6377[2:Spt:6367.0,2708.0,2758.0] || greater_or_equal(cardinality_at_time(first_movers,end_time(skf2(skc1))),zero)* -> .
% 6.04/6.27 6378[2:Spt:6367.0,2708.1] || -> equal(start_time(skf2(skc1)),critical_point(skf2(skc1)))**.
% 6.04/6.27 6454[2:Res:217.2,6377.0] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),start_time(skf2(skc1)))*r -> .
% 6.04/6.27 6458[2:Rew:6378.0,6454.1] environment(skf2(skc1)) || greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r -> .
% 6.04/6.27 6459[2:SSi:6458.0,5.0,2.0,1.0] || greater(end_time(skf2(skc1)),critical_point(skf2(skc1)))*r -> .
% 6.04/6.27 6460[2:MRR:6459.0,2640.0] || -> .
% 6.04/6.27 % SZS output end Refutation
% 6.04/6.27 Formulae used in the proof : prove_t8 mp_organizational_sets1 mp_organizational_sets2 mp3_favoured_trategy mp_greater_or_equal mp_time_of_critical_point mp_critical_point_after_EP mp_environment_end_point mp_subpopulations mp_greater_transitivity mp_first_movers_exist mp_time_in_environment mp4_critical_point t6 d1 mp1_high_growth_rates mp_contains_FM_and_EP mp2_favour_members
% 6.04/6.27
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