TSTP Solution File: MGT026+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Theorem 0.18s 0.44s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.09/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 12:37:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44
% 0.18/0.44 SPASS V 3.9
% 0.18/0.44 SPASS beiseite: Proof found.
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 SPASS derived 96 clauses, backtracked 21 clauses, performed 2 splits and kept 102 clauses.
% 0.18/0.44 SPASS allocated 97731 KBytes.
% 0.18/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.18/0.44 0:00:00.04 for the input.
% 0.18/0.44 0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.44 0:00:00.00 for inferences.
% 0.18/0.44 0:00:00.00 for the backtracking.
% 0.18/0.44 0:00:00.01 for the reduction.
% 0.18/0.44
% 0.18/0.44
% 0.18/0.44 Here is a proof with depth 4, length 65 :
% 0.18/0.44 % SZS output start Refutation
% 0.18/0.44 1[0:Inp] || -> environment(skc3)*.
% 0.18/0.44 2[0:Inp] || -> in_environment(skc3,skc2)*.
% 0.18/0.44 3[0:Inp] || -> greater(skc2,critical_point(skc3))*r.
% 0.18/0.44 4[0:Inp] || selection_favors(efficient_producers,first_movers,skc2)* -> .
% 0.18/0.44 5[0:Inp] || greater(u,v) -> greater_or_equal(u,v)*.
% 0.18/0.44 7[0:Inp] environment(u) || -> greater_or_equal(critical_point(u),appear(efficient_producers,u))*.
% 0.18/0.44 8[0:Inp] || greater_or_equal(u,v)* -> equal(u,v) greater(u,v).
% 0.18/0.44 9[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(first_movers,u,v)*.
% 0.18/0.44 10[0:Inp] environment(u) || in_environment(u,v) -> subpopulation(efficient_producers,u,v)*.
% 0.18/0.44 11[0:Inp] || greater(u,v)* greater(v,w)* -> greater(u,w)*.
% 0.18/0.44 12[0:Inp] environment(u) || in_environment(u,v)*+ -> greater_or_equal(cardinality_at_time(first_movers,v),zero)*.
% 0.18/0.44 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).
% 0.18/0.44 15[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)).
% 0.18/0.44 16[0:Inp] environment(u) || greater(growth_rate(v,w),growth_rate(x,w)) subpopulations(x,v,u,w)* -> selection_favors(v,x,w).
% 0.18/0.44 17[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)*.
% 0.18/0.44 18[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)*.
% 0.18/0.44 27[0:Res:1.0,10.0] || in_environment(skc3,u) -> subpopulation(efficient_producers,skc3,u)*.
% 0.18/0.44 28[0:Res:1.0,7.0] || -> greater_or_equal(critical_point(skc3),appear(efficient_producers,skc3))*.
% 0.18/0.44 29[0:Res:2.0,17.1] environment(skc3) || greater(cardinality_at_time(efficient_producers,skc2),zero) greater(cardinality_at_time(first_movers,skc2),zero) -> subpopulations(first_movers,efficient_producers,skc3,skc2)*.
% 0.18/0.44 30[0:Res:2.0,14.1] environment(skc3) || greater_or_equal(skc2,appear(efficient_producers,skc3))* -> greater(cardinality_at_time(efficient_producers,skc2),zero).
% 0.18/0.44 31[0:Res:2.0,12.1] environment(skc3) || -> greater_or_equal(cardinality_at_time(first_movers,skc2),zero)*.
% 0.18/0.44 32[0:Res:2.0,9.1] environment(skc3) || -> subpopulation(first_movers,skc3,skc2)*.
% 0.18/0.44 35[0:Res:18.5,4.0] environment(u) || equal(cardinality_at_time(first_movers,skc2),zero) greater(cardinality_at_time(efficient_producers,skc2),zero) subpopulation(first_movers,u,skc2) subpopulation(efficient_producers,u,skc2)* -> .
% 0.18/0.44 36[0:MRR:32.0,1.0] || -> subpopulation(first_movers,skc3,skc2)*.
% 0.18/0.44 38[0:MRR:31.0,1.0] || -> greater_or_equal(cardinality_at_time(first_movers,skc2),zero)*.
% 0.18/0.44 39[0:MRR:30.0,1.0] || greater_or_equal(skc2,appear(efficient_producers,skc3))* -> greater(cardinality_at_time(efficient_producers,skc2),zero).
% 0.18/0.44 40[0:MRR:29.0,1.0] || greater(cardinality_at_time(first_movers,skc2),zero) greater(cardinality_at_time(efficient_producers,skc2),zero) -> subpopulations(first_movers,efficient_producers,skc3,skc2)*.
% 0.18/0.44 42[0:Res:38.0,8.0] || -> equal(cardinality_at_time(first_movers,skc2),zero) greater(cardinality_at_time(first_movers,skc2),zero)*l.
% 0.18/0.44 44[0:Res:28.0,8.0] || -> equal(appear(efficient_producers,skc3),critical_point(skc3)) greater(critical_point(skc3),appear(efficient_producers,skc3))*r.
% 0.18/0.44 45[0:Res:7.1,8.0] environment(u) || -> equal(appear(efficient_producers,u),critical_point(u)) greater(critical_point(u),appear(efficient_producers,u))*r.
% 0.18/0.44 48[1:Spt:42.0] || -> equal(cardinality_at_time(first_movers,skc2),zero)**.
% 0.18/0.44 51[1:Rew:48.0,35.1] environment(u) || equal(zero,zero) greater(cardinality_at_time(efficient_producers,skc2),zero) subpopulation(first_movers,u,skc2) subpopulation(efficient_producers,u,skc2)* -> .
% 0.18/0.44 52[1:Obv:51.1] environment(u) || greater(cardinality_at_time(efficient_producers,skc2),zero) subpopulation(first_movers,u,skc2) subpopulation(efficient_producers,u,skc2)* -> .
% 0.18/0.44 56[0:Res:5.1,39.0] || greater(skc2,appear(efficient_producers,skc3))*r -> greater(cardinality_at_time(efficient_producers,skc2),zero).
% 0.18/0.44 64[2:Spt:44.0] || -> equal(appear(efficient_producers,skc3),critical_point(skc3))**.
% 0.18/0.44 69[2:Rew:64.0,56.0] || greater(skc2,critical_point(skc3)) -> greater(cardinality_at_time(efficient_producers,skc2),zero)*l.
% 0.18/0.44 70[2:MRR:69.0,3.0] || -> greater(cardinality_at_time(efficient_producers,skc2),zero)*l.
% 0.18/0.44 72[2:MRR:52.1,70.0] environment(u) || subpopulation(first_movers,u,skc2) subpopulation(efficient_producers,u,skc2)* -> .
% 0.18/0.44 78[2:Res:27.1,72.2] environment(skc3) || in_environment(skc3,skc2) subpopulation(first_movers,skc3,skc2)* -> .
% 0.18/0.44 82[2:SSi:78.0,1.0] || in_environment(skc3,skc2) subpopulation(first_movers,skc3,skc2)* -> .
% 0.18/0.44 83[2:MRR:82.0,82.1,2.0,36.0] || -> .
% 0.18/0.44 86[2:Spt:83.0,44.0,64.0] || equal(appear(efficient_producers,skc3),critical_point(skc3))** -> .
% 0.18/0.44 87[2:Spt:83.0,44.1] || -> greater(critical_point(skc3),appear(efficient_producers,skc3))*r.
% 0.18/0.44 102[2:NCh:11.2,11.1,56.0,87.0] || greater(skc2,critical_point(skc3)) -> greater(cardinality_at_time(efficient_producers,skc2),zero)*l.
% 0.18/0.44 104[0:NCh:11.2,11.1,56.0,45.2] environment(skc3) || greater(skc2,critical_point(skc3)) -> greater(cardinality_at_time(efficient_producers,skc2),zero) equal(appear(efficient_producers,skc3),critical_point(skc3))**.
% 0.18/0.44 106[2:MRR:102.0,3.0] || -> greater(cardinality_at_time(efficient_producers,skc2),zero)*l.
% 0.18/0.44 107[2:MRR:52.1,106.0] environment(u) || subpopulation(first_movers,u,skc2) subpopulation(efficient_producers,u,skc2)* -> .
% 0.18/0.44 127[2:Res:27.1,107.2] environment(skc3) || in_environment(skc3,skc2) subpopulation(first_movers,skc3,skc2)* -> .
% 0.18/0.44 131[2:SSi:127.0,1.0] || in_environment(skc3,skc2) subpopulation(first_movers,skc3,skc2)* -> .
% 0.18/0.44 132[2:MRR:131.0,131.1,2.0,36.0] || -> .
% 0.18/0.44 135[1:Spt:132.0,42.0,48.0] || equal(cardinality_at_time(first_movers,skc2),zero)** -> .
% 0.18/0.44 136[1:Spt:132.0,42.1] || -> greater(cardinality_at_time(first_movers,skc2),zero)*l.
% 0.18/0.44 138[1:MRR:40.0,136.0] || greater(cardinality_at_time(efficient_producers,skc2),zero) -> subpopulations(first_movers,efficient_producers,skc3,skc2)*.
% 0.18/0.44 139[0:SSi:104.0,1.0] || greater(skc2,critical_point(skc3)) -> greater(cardinality_at_time(efficient_producers,skc2),zero) equal(appear(efficient_producers,skc3),critical_point(skc3))**.
% 0.18/0.44 140[0:MRR:139.0,3.0] || -> greater(cardinality_at_time(efficient_producers,skc2),zero) equal(appear(efficient_producers,skc3),critical_point(skc3))**.
% 0.18/0.44 143[0:Rew:140.1,56.0] || greater(skc2,critical_point(skc3)) -> greater(cardinality_at_time(efficient_producers,skc2),zero)*l.
% 0.18/0.44 144[0:MRR:143.0,3.0] || -> greater(cardinality_at_time(efficient_producers,skc2),zero)*l.
% 0.18/0.44 145[1:MRR:138.0,144.0] || -> subpopulations(first_movers,efficient_producers,skc3,skc2)*.
% 0.18/0.44 151[1:Res:145.0,16.2] environment(skc3) || greater(growth_rate(efficient_producers,skc2),growth_rate(first_movers,skc2)) -> selection_favors(efficient_producers,first_movers,skc2)*.
% 0.18/0.44 152[1:Res:145.0,15.2] environment(skc3) || greater(skc2,critical_point(skc3)) -> greater(growth_rate(efficient_producers,skc2),growth_rate(first_movers,skc2))*l.
% 0.18/0.44 153[1:SSi:151.0,1.0] || greater(growth_rate(efficient_producers,skc2),growth_rate(first_movers,skc2)) -> selection_favors(efficient_producers,first_movers,skc2)*.
% 0.18/0.44 154[1:MRR:153.1,4.0] || greater(growth_rate(efficient_producers,skc2),growth_rate(first_movers,skc2))*l -> .
% 0.18/0.44 155[1:SSi:152.0,1.0] || greater(skc2,critical_point(skc3)) -> greater(growth_rate(efficient_producers,skc2),growth_rate(first_movers,skc2))*l.
% 0.18/0.44 156[1:MRR:155.0,3.0] || -> greater(growth_rate(efficient_producers,skc2),growth_rate(first_movers,skc2))*l.
% 0.18/0.44 157[1:MRR:156.0,154.0] || -> .
% 0.18/0.45 % SZS output end Refutation
% 0.18/0.45 Formulae used in the proof : prove_l8 mp_greater_or_equal mp_critical_point_after_EP mp_subpopulations mp_greater_transitivity mp_first_movers_exist t6 d1 mp1_high_growth_rates mp_non_empty_fm_and_ep mp2_favour_members
% 0.18/0.45
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