TSTP Solution File: MGT039-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT039-2 : TPTP v8.1.0. Released v2.4.0.
% 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 : Unsatisfiable 2.13s 2.30s
% Output : Refutation 2.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT039-2 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % 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 07:33:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.13/2.30
% 2.13/2.30 SPASS V 3.9
% 2.13/2.30 SPASS beiseite: Proof found.
% 2.13/2.30 % SZS status Theorem
% 2.13/2.30 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.13/2.30 SPASS derived 2186 clauses, backtracked 212 clauses, performed 21 splits and kept 1718 clauses.
% 2.13/2.30 SPASS allocated 78860 KBytes.
% 2.13/2.30 SPASS spent 0:00:01.96 on the problem.
% 2.13/2.30 0:00:00.04 for the input.
% 2.13/2.30 0:00:00.00 for the FLOTTER CNF translation.
% 2.13/2.30 0:00:00.06 for inferences.
% 2.13/2.30 0:00:00.02 for the backtracking.
% 2.13/2.30 0:00:01.81 for the reduction.
% 2.13/2.30
% 2.13/2.30
% 2.13/2.30 Here is a proof with depth 15, length 183 :
% 2.13/2.30 % SZS output start Refutation
% 2.13/2.30 1[0:Inp] environment(u) || greater(growth_rate(v,w),growth_rate(x,w)) subpopulations(x,v,u,w)* -> selection_favors(v,x,w).
% 2.13/2.30 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)*.
% 2.13/2.30 3[0:Inp] observational_period(u) || propagation_strategy(first_movers) propagation_strategy(efficient_producers) -> environment(sk1(u)) selection_favors(efficient_producers,first_movers,u)*.
% 2.13/2.30 4[0:Inp] observational_period(u) || propagation_strategy(first_movers) propagation_strategy(efficient_producers) -> in_environment(u,sk1(u))* selection_favors(efficient_producers,first_movers,u)*.
% 2.13/2.30 5[0:Inp] observational_period(u) || propagation_strategy(first_movers) propagation_strategy(efficient_producers) selection_favors(efficient_producers,first_movers,end_time(sk1(u)))* -> selection_favors(efficient_producers,first_movers,u).
% 2.13/2.30 6[0:Inp] environment(u) slow_change(v) observational_period(v) || in_environment(v,u) -> in_environment(u,sk2(u,v))*.
% 2.13/2.30 7[0:Inp] environment(u) slow_change(v) observational_period(v) || in_environment(v,u) -> greater(sk2(u,v),critical_point(u))*l.
% 2.13/2.30 8[0:Inp] || -> propagation_strategy(first_movers)*.
% 2.13/2.30 9[0:Inp] || -> propagation_strategy(efficient_producers)*.
% 2.13/2.30 10[0:Inp] environment(u) || greater_or_equal(v,start_time(u))*+ greater_or_equal(end_time(u),v)* -> in_environment(u,v).
% 2.13/2.30 11[0:Inp] environment(u) || in_environment(u,v) -> greater_or_equal(end_time(u),v)*.
% 2.13/2.30 12[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)*.
% 2.13/2.30 13[0:Inp] environment(u) || in_environment(u,v)*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 2.13/2.30 14[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(first_movers,u,v)*.
% 2.13/2.30 15[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(efficient_producers,u,v)*.
% 2.13/2.30 16[0:Inp] environment(u) || -> greater_or_equal(critical_point(u),appear(efficient_producers,u))*.
% 2.13/2.30 17[0:Inp] environment(u) || -> greater_or_equal(critical_point(u),start_time(u))*.
% 2.13/2.30 18[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*.
% 2.13/2.30 20[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 2.13/2.30 21[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 2.13/2.30 22[0:Inp] || equal(u,v) -> greater_or_equal(u,v)*.
% 2.13/2.30 24[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)).
% 2.13/2.30 25[0:Inp] environment(u) || in_environment(u,v) greater_or_equal(v,appear(efficient_producers,u))* -> greater(cardinality_at_time(efficient_producers,v),zero).
% 2.13/2.30 26[0:Inp] || -> observational_period(sk3)*.
% 2.13/2.30 27[0:Inp] || -> slow_change(sk3)*.
% 2.13/2.30 28[0:Inp] || selection_favors(efficient_producers,first_movers,sk3)* -> .
% 2.13/2.30 29[0:MRR:3.1,3.2,8.0,9.0] observational_period(u) || -> environment(sk1(u)) selection_favors(efficient_producers,first_movers,u)*.
% 2.13/2.30 30[0:MRR:4.1,4.2,8.0,9.0] observational_period(u) || -> in_environment(u,sk1(u))* selection_favors(efficient_producers,first_movers,u)*.
% 2.13/2.30 31[0:MRR:5.1,5.2,8.0,9.0] observational_period(u) || selection_favors(efficient_producers,first_movers,end_time(sk1(u)))* -> selection_favors(efficient_producers,first_movers,u).
% 2.13/2.30 33[0:Res:27.0,6.1] observational_period(sk3) environment(u) || in_environment(sk3,u) -> in_environment(u,sk2(u,sk3))*.
% 2.13/2.30 34[0:Res:26.0,7.0] slow_change(sk3) environment(u) || in_environment(sk3,u) -> greater(sk2(u,sk3),critical_point(u))*l.
% 2.13/2.30 39[0:Res:31.2,28.0] observational_period(sk3) || selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))* -> .
% 2.13/2.30 40[0:Res:30.2,28.0] observational_period(sk3) || -> in_environment(sk3,sk1(sk3))*.
% 2.13/2.30 41[0:Res:29.2,28.0] observational_period(sk3) || -> environment(sk1(sk3))*.
% 2.13/2.30 44[0:MRR:41.0,26.0] || -> environment(sk1(sk3))*.
% 2.13/2.30 45[0:MRR:40.0,26.0] || -> in_environment(sk3,sk1(sk3))*.
% 2.13/2.30 46[0:MRR:39.0,26.0] || selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))* -> .
% 2.13/2.30 47[0:MRR:33.0,26.0] environment(u) || in_environment(sk3,u) -> in_environment(u,sk2(u,sk3))*.
% 2.13/2.30 48[0:MRR:34.0,27.0] environment(u) || in_environment(sk3,u) -> greater(sk2(u,sk3),critical_point(u))*l.
% 2.13/2.30 59[0:Res:11.2,20.0] environment(u) || in_environment(u,v)* -> equal(end_time(u),v) greater(end_time(u),v).
% 2.13/2.30 60[0:Res:17.1,20.0] environment(u) || -> equal(start_time(u),critical_point(u)) greater(critical_point(u),start_time(u))*r.
% 2.13/2.30 61[0:Res:16.1,20.0] environment(u) || -> equal(appear(efficient_producers,u),critical_point(u)) greater(critical_point(u),appear(efficient_producers,u))*r.
% 2.13/2.30 63[0:Res:21.1,10.1] environment(u) || greater(v,start_time(u)) greater_or_equal(end_time(u),v)* -> in_environment(u,v).
% 2.13/2.30 64[0:Res:22.1,10.1] environment(u) || equal(v,start_time(u)) greater_or_equal(end_time(u),v)* -> in_environment(u,v).
% 2.13/2.30 65[0:Res:11.2,10.1] 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)).
% 2.13/2.30 66[0:Res:17.1,10.1] environment(u) environment(u) || greater_or_equal(end_time(u),critical_point(u))* -> in_environment(u,critical_point(u)).
% 2.13/2.30 67[0:Obv:66.0] environment(u) || greater_or_equal(end_time(u),critical_point(u))* -> in_environment(u,critical_point(u)).
% 2.13/2.30 68[0:Res:21.1,67.1] environment(u) || greater(end_time(u),critical_point(u)) -> in_environment(u,critical_point(u))*.
% 2.13/2.30 77[0:Res:21.1,64.2] environment(u) || greater(end_time(u),v) equal(v,start_time(u)) -> in_environment(u,v)*.
% 2.13/2.30 86[0:Res:21.1,25.2] environment(u) || greater(v,appear(efficient_producers,u))*+ in_environment(u,v)* -> greater(cardinality_at_time(efficient_producers,v),zero)*l.
% 2.13/2.30 101[0:Res:47.2,59.1] environment(u) environment(u) || in_environment(sk3,u) -> equal(sk2(u,sk3),end_time(u)) greater(end_time(u),sk2(u,sk3))*r.
% 2.13/2.30 105[0:Obv:101.0] environment(u) || in_environment(sk3,u) -> equal(sk2(u,sk3),end_time(u)) greater(end_time(u),sk2(u,sk3))*r.
% 2.13/2.30 109[0:Res:22.1,63.2] environment(u) || equal(end_time(u),v) greater(v,start_time(u)) -> in_environment(u,v)*.
% 2.13/2.30 121[0:Res:77.3,13.1] environment(u) environment(u) || greater(end_time(u),v)* equal(v,start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 2.13/2.30 123[0:Obv:121.0] environment(u) || greater(end_time(u),v)*+ equal(v,start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 2.13/2.30 126[0:Res:109.3,13.1] environment(u) environment(u) || equal(end_time(u),v) greater(v,start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 2.13/2.30 128[0:Obv:126.0] environment(u) || equal(end_time(u),v) greater(v,start_time(u))*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 2.13/2.30 131[0:Res:22.1,65.3] environment(u) environment(v) || equal(end_time(v),end_time(u))+ in_environment(u,start_time(v))* -> in_environment(v,end_time(u))*.
% 2.13/2.30 135[0:EqR:131.2] environment(u) environment(u) || in_environment(u,start_time(u))* -> in_environment(u,end_time(u)).
% 2.13/2.30 136[0:Obv:135.0] environment(u) || in_environment(u,start_time(u))* -> in_environment(u,end_time(u)).
% 2.13/2.30 138[0:Res:77.3,136.1] environment(u) environment(u) || greater(end_time(u),start_time(u)) equal(start_time(u),start_time(u)) -> in_environment(u,end_time(u))*.
% 2.13/2.30 141[0:Obv:138.3] environment(u) || greater(end_time(u),start_time(u)) -> in_environment(u,end_time(u))*.
% 2.13/2.30 150[0:Res:12.4,1.2] environment(u) environment(u) || in_environment(u,v)* greater(cardinality_at_time(efficient_producers,v),zero) greater(cardinality_at_time(first_movers,v),zero) greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v)) -> selection_favors(efficient_producers,first_movers,v)*.
% 2.13/2.30 151[0:Obv:150.0] environment(u) || in_environment(u,v)* greater(cardinality_at_time(efficient_producers,v),zero) greater(cardinality_at_time(first_movers,v),zero) greater(growth_rate(efficient_producers,v),growth_rate(first_movers,v))+ -> selection_favors(efficient_producers,first_movers,v)*.
% 2.13/2.30 161[0:NCh:18.2,18.1,123.1,60.2] environment(u) environment(v) || greater(end_time(u),critical_point(v))+ equal(start_time(v),start_time(u))* -> greater_or_equal(cardinality_at_time(first_movers,start_time(v)),zero)* equal(start_time(v),critical_point(v)).
% 2.13/2.30 176[0:NCh:18.2,18.1,128.2,60.2] 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))**.
% 2.13/2.30 180[0:Obv:176.0] 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))**.
% 2.13/2.30 184[0:OCh:18.1,18.0,105.3,48.2] environment(u) environment(u) || in_environment(sk3,u) in_environment(sk3,u) -> equal(sk2(u,sk3),end_time(u))** greater(end_time(u),critical_point(u)).
% 2.13/2.30 188[0:Obv:184.2] environment(u) || in_environment(sk3,u) -> equal(sk2(u,sk3),end_time(u))** greater(end_time(u),critical_point(u)).
% 2.13/2.30 213[0:SpR:188.2,48.2] environment(u) environment(u) || in_environment(sk3,u)* in_environment(sk3,u)* -> greater(end_time(u),critical_point(u)) greater(end_time(u),critical_point(u)).
% 2.13/2.30 222[0:Obv:213.4] environment(u) || in_environment(sk3,u)* -> greater(end_time(u),critical_point(u)).
% 2.13/2.30 226[0:Res:45.0,222.1] environment(sk1(sk3)) || -> greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r.
% 2.13/2.30 236[0:SSi:226.0,44.0] || -> greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r.
% 2.13/2.30 238[0:Res:236.0,24.1] environment(u) || equal(critical_point(sk1(sk3)),critical_point(u)) subpopulations(first_movers,efficient_producers,u,end_time(sk1(sk3)))* -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 252[0:NCh:18.2,18.1,86.1,61.2] 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))**.
% 2.13/2.30 256[0:Obv:252.0] 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))**.
% 2.13/2.30 439[0:Res:236.0,180.2] environment(sk1(sk3)) || equal(end_time(sk1(sk3)),end_time(sk1(sk3))) -> greater_or_equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)* equal(start_time(sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 458[0:Obv:439.1] environment(sk1(sk3)) || -> greater_or_equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)* equal(start_time(sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 459[0:SSi:458.0,44.0] || -> greater_or_equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)* equal(start_time(sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 464[0:Res:459.0,20.0] || -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3))) equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.30 651[0:Res:236.0,256.1] environment(sk1(sk3)) || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero) equal(appear(efficient_producers,sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 681[0:NCh:18.2,18.1,256.1,236.0] environment(sk1(sk3)) || equal(u,end_time(sk1(sk3))) in_environment(sk1(sk3),u)* -> greater(cardinality_at_time(efficient_producers,u),zero) equal(appear(efficient_producers,sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 682[0:SSi:651.0,44.0] || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero) equal(appear(efficient_producers,sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 683[0:SSi:681.0,44.0] || equal(u,end_time(sk1(sk3)))+ in_environment(sk1(sk3),u)* -> greater(cardinality_at_time(efficient_producers,u),zero) equal(appear(efficient_producers,sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 708[1:Spt:682.1] || -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.30 709[1:Res:708.0,2.2] environment(u) || equal(cardinality_at_time(v,end_time(sk1(sk3))),zero)+ subpopulation(v,u,end_time(sk1(sk3)))* subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> selection_favors(efficient_producers,v,end_time(sk1(sk3)))*.
% 2.13/2.30 995[0:Res:12.4,238.2] environment(u) environment(u) || in_environment(u,end_time(sk1(sk3)))* greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) equal(critical_point(sk1(sk3)),critical_point(u)) -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 996[0:Obv:995.0] environment(u) || in_environment(u,end_time(sk1(sk3)))* greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) equal(critical_point(sk1(sk3)),critical_point(u)) -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 997[1:MRR:996.2,708.0] environment(u) || in_environment(u,end_time(sk1(sk3)))* greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*l equal(critical_point(sk1(sk3)),critical_point(u)) -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 1144[0:Res:236.0,161.2] environment(sk1(sk3)) environment(sk1(sk3)) || equal(start_time(sk1(sk3)),start_time(sk1(sk3))) -> greater_or_equal(cardinality_at_time(first_movers,start_time(sk1(sk3))),zero)* equal(start_time(sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 1147[0:Obv:1144.2] environment(sk1(sk3)) || -> greater_or_equal(cardinality_at_time(first_movers,start_time(sk1(sk3))),zero)* equal(start_time(sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 1148[0:SSi:1147.0,44.0] || -> greater_or_equal(cardinality_at_time(first_movers,start_time(sk1(sk3))),zero)* equal(start_time(sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 1149[2:Spt:1148.1] || -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 1202[2:SpL:1149.0,10.1] environment(sk1(sk3)) || greater_or_equal(u,critical_point(sk1(sk3)))* greater_or_equal(end_time(sk1(sk3)),u)* -> in_environment(sk1(sk3),u).
% 2.13/2.30 1206[2:SpL:1149.0,136.1] environment(sk1(sk3)) || in_environment(sk1(sk3),critical_point(sk1(sk3)))* -> in_environment(sk1(sk3),end_time(sk1(sk3))).
% 2.13/2.30 1211[2:SSi:1206.0,44.0] || in_environment(sk1(sk3),critical_point(sk1(sk3)))* -> in_environment(sk1(sk3),end_time(sk1(sk3))).
% 2.13/2.30 1212[2:SSi:1202.0,44.0] || greater_or_equal(u,critical_point(sk1(sk3)))*+ greater_or_equal(end_time(sk1(sk3)),u)* -> in_environment(sk1(sk3),u).
% 2.13/2.30 1222[2:Res:68.2,1211.0] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> in_environment(sk1(sk3),end_time(sk1(sk3)))*.
% 2.13/2.30 1225[2:SSi:1222.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> in_environment(sk1(sk3),end_time(sk1(sk3)))*.
% 2.13/2.30 1226[2:MRR:1225.0,236.0] || -> in_environment(sk1(sk3),end_time(sk1(sk3)))*.
% 2.13/2.30 1228[2:Res:1226.0,13.1] environment(sk1(sk3)) || -> greater_or_equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*.
% 2.13/2.30 1232[2:SSi:1228.0,44.0] || -> greater_or_equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*.
% 2.13/2.30 1234[2:Res:1232.0,20.0] || -> equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.30 1235[2:Res:21.1,1212.0] || greater(u,critical_point(sk1(sk3))) greater_or_equal(end_time(sk1(sk3)),u)* -> in_environment(sk1(sk3),u).
% 2.13/2.30 1303[3:Spt:1234.0] || -> equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)**.
% 2.13/2.30 1318[3:SpL:1303.0,709.1] environment(u) || equal(zero,zero) subpopulation(first_movers,u,end_time(sk1(sk3))) subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))*.
% 2.13/2.30 1321[3:Obv:1318.1] environment(u) || subpopulation(first_movers,u,end_time(sk1(sk3))) subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))*.
% 2.13/2.30 1322[3:MRR:1321.3,46.0] environment(u) || subpopulation(first_movers,u,end_time(sk1(sk3))) subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1326[3:Res:15.2,1322.2] environment(u) environment(u) || in_environment(u,end_time(sk1(sk3))) subpopulation(first_movers,u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1327[3:Obv:1326.0] environment(u) || in_environment(u,end_time(sk1(sk3))) subpopulation(first_movers,u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1328[3:MRR:1327.2,14.2] environment(u) || in_environment(u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1335[3:Res:141.2,1328.1] environment(sk1(sk3)) environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 1347[3:Obv:1335.0] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 1348[3:Rew:1149.0,1347.1] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.30 1349[3:SSi:1348.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.30 1350[3:MRR:1349.0,236.0] || -> .
% 2.13/2.30 1364[3:Spt:1350.0,1234.0,1303.0] || equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)** -> .
% 2.13/2.30 1365[3:Spt:1350.0,1234.1] || -> greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.30 1366[3:MRR:997.2,1365.0] environment(u) || in_environment(u,end_time(sk1(sk3)))* equal(critical_point(sk1(sk3)),critical_point(u))+ -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))*l.
% 2.13/2.30 1417[2:Res:22.1,1235.1] || equal(end_time(sk1(sk3)),u) greater(u,critical_point(sk1(sk3))) -> in_environment(sk1(sk3),u)*.
% 2.13/2.30 1821[3:EqR:1366.2] environment(sk1(sk3)) || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 1822[3:SSi:1821.0,44.0] || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 1823[3:MRR:1822.0,1226.0] || -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))*l.
% 2.13/2.30 1826[3:Res:1823.0,151.4] environment(u) || in_environment(u,end_time(sk1(sk3)))* greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero) greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) -> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))*.
% 2.13/2.30 1856[3:MRR:1826.2,1826.3,1826.4,708.0,1365.0,46.0] environment(u) || in_environment(u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1867[3:Res:1417.2,1856.1] environment(sk1(sk3)) || equal(end_time(sk1(sk3)),end_time(sk1(sk3))) greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.30 1882[3:Obv:1867.1] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.30 1883[3:SSi:1882.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.30 1884[3:MRR:1883.0,236.0] || -> .
% 2.13/2.30 1900[2:Spt:1884.0,1148.1,1149.0] || equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))** -> .
% 2.13/2.30 1901[2:Spt:1884.0,1148.0] || -> greater_or_equal(cardinality_at_time(first_movers,start_time(sk1(sk3))),zero)*.
% 2.13/2.30 1903[2:MRR:464.0,1900.0] || -> equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.30 1942[3:Spt:1903.0] || -> equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)**.
% 2.13/2.30 1957[3:SpL:1942.0,709.1] environment(u) || equal(zero,zero) subpopulation(first_movers,u,end_time(sk1(sk3))) subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))*.
% 2.13/2.30 1960[3:Obv:1957.1] environment(u) || subpopulation(first_movers,u,end_time(sk1(sk3))) subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))*.
% 2.13/2.30 1961[3:MRR:1960.3,46.0] environment(u) || subpopulation(first_movers,u,end_time(sk1(sk3))) subpopulation(efficient_producers,u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1963[3:Res:15.2,1961.2] environment(u) environment(u) || in_environment(u,end_time(sk1(sk3))) subpopulation(first_movers,u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1964[3:Obv:1963.0] environment(u) || in_environment(u,end_time(sk1(sk3))) subpopulation(first_movers,u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1965[3:MRR:1964.2,14.2] environment(u) || in_environment(u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 1972[3:Res:141.2,1965.1] environment(sk1(sk3)) environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 1979[3:Obv:1972.0] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 1980[3:SSi:1979.0,44.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 2001[3:NCh:18.2,18.1,1980.0,60.2] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 2005[3:SSi:2001.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 2006[3:MRR:2005.0,2005.1,236.0,1900.0] || -> .
% 2.13/2.30 2007[3:Spt:2006.0,1903.0,1942.0] || equal(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)** -> .
% 2.13/2.30 2008[3:Spt:2006.0,1903.1] || -> greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.30 2020[3:MRR:997.2,2008.0] environment(u) || in_environment(u,end_time(sk1(sk3)))* equal(critical_point(sk1(sk3)),critical_point(u))+ -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))*l.
% 2.13/2.30 2190[3:EqR:2020.2] environment(sk1(sk3)) || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 2191[3:SSi:2190.0,44.0] || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3)))).
% 2.13/2.30 2198[3:Res:141.2,2191.0] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))*l.
% 2.13/2.30 2203[3:SSi:2198.0,44.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) -> greater(growth_rate(efficient_producers,end_time(sk1(sk3))),growth_rate(first_movers,end_time(sk1(sk3))))*l.
% 2.13/2.30 2303[3:Res:2203.1,151.4] environment(u) || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) in_environment(u,end_time(sk1(sk3)))* greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero) greater(cardinality_at_time(first_movers,end_time(sk1(sk3))),zero) -> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))*.
% 2.13/2.30 2333[3:MRR:2303.3,2303.4,2303.5,708.0,2008.0,46.0] environment(u) || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) in_environment(u,end_time(sk1(sk3)))* -> .
% 2.13/2.30 2381[3:Res:141.2,2333.2] environment(sk1(sk3)) environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 2387[3:Obv:2381.2] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 2388[3:SSi:2387.0,44.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.30 2397[3:NCh:18.2,18.1,2388.0,60.2] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 2401[3:SSi:2397.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.30 2402[3:MRR:2401.0,2401.1,236.0,1900.0] || -> .
% 2.13/2.30 2403[1:Spt:2402.0,682.1,708.0] || greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l -> .
% 2.13/2.30 2404[1:Spt:2402.0,682.0,682.2] || in_environment(sk1(sk3),end_time(sk1(sk3)))* -> equal(appear(efficient_producers,sk1(sk3)),critical_point(sk1(sk3))).
% 2.13/2.30 2612[2:Spt:683.0,683.1,683.2] || equal(u,end_time(sk1(sk3))) in_environment(sk1(sk3),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 2.13/2.30 2624[2:Res:141.2,2612.1] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) equal(end_time(sk1(sk3)),end_time(sk1(sk3))) -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.33 2636[2:Obv:2624.2] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.33 2637[2:SSi:2636.0,44.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.33 2638[2:MRR:2637.1,2403.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.33 2676[2:NCh:18.2,18.1,2638.0,60.2] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2679[2:SSi:2676.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2680[2:MRR:2679.0,236.0] || -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2684[2:Rew:2680.0,2638.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.33 2714[2:MRR:2684.0,236.0] || -> .
% 2.13/2.33 2733[2:Spt:2714.0,683.3] || -> equal(appear(efficient_producers,sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2745[2:SpL:2733.0,86.1] environment(sk1(sk3)) || greater(u,critical_point(sk1(sk3))) in_environment(sk1(sk3),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 2.13/2.33 2761[2:SSi:2745.0,44.0] || greater(u,critical_point(sk1(sk3))) in_environment(sk1(sk3),u)* -> greater(cardinality_at_time(efficient_producers,u),zero).
% 2.13/2.33 2905[2:Res:141.2,2761.1] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.33 2914[2:SSi:2905.0,44.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3))) greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> greater(cardinality_at_time(efficient_producers,end_time(sk1(sk3))),zero)*l.
% 2.13/2.33 2915[2:MRR:2914.1,2914.2,236.0,2403.0] || greater(end_time(sk1(sk3)),start_time(sk1(sk3)))*r -> .
% 2.13/2.33 2927[2:NCh:18.2,18.1,2915.0,60.2] environment(sk1(sk3)) || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2929[2:SSi:2927.0,44.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3))) -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2930[2:MRR:2929.0,236.0] || -> equal(start_time(sk1(sk3)),critical_point(sk1(sk3)))**.
% 2.13/2.33 2933[2:Rew:2930.0,2915.0] || greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))*r -> .
% 2.13/2.33 2950[2:MRR:2933.0,236.0] || -> .
% 2.13/2.33 % SZS output end Refutation
% 2.13/2.33 Formulae used in the proof : mp1_high_growth_rates_33 mp2_favour_members_34 mp3_favoured_trategy_35 mp3_favoured_trategy_36 mp3_favoured_trategy_37 mp4_critical_point_38 mp4_critical_point_39 mp_organizational_sets1_40 mp_organizational_sets2_41 mp_time_in_environment_42 mp_environment_end_point_43 mp_contains_FM_and_EP_44 mp_first_movers_exist_45 mp_subpopulations_46 mp_subpopulations_47 mp_critical_point_after_EP_48 mp_time_of_critical_point_49 mp_greater_transitivity_50 mp_greater_or_equal_52 mp_greater_or_equal_53 mp_greater_or_equal_54 d1_56 t6_57 prove_t8_58 prove_t8_59 prove_t8_60
% 2.13/2.33
%------------------------------------------------------------------------------