TSTP Solution File: MGT036+2 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT036+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n019.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 22:27:00 EDT 2022
% Result : Theorem 0.51s 0.72s
% Output : Proof 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : MGT036+2 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n019.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 12:19:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.51/0.72 % SZS status Theorem
% 0.51/0.72 (* PROOF-FOUND *)
% 0.51/0.72 (* BEGIN-PROOF *)
% 0.51/0.72 % SZS output start Proof
% 0.51/0.72 1. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.51/0.72 2. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.51/0.72 3. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.51/0.72 4. (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### Extension/test/mp_symmetry_of_subpopulationsctrp 2 3
% 0.51/0.72 5. (outcompetes (first_movers) (efficient_producers) T_1) (-. (outcompetes (first_movers) (efficient_producers) T_1)) ### Axiom
% 0.51/0.72 6. (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) ### Axiom
% 0.51/0.72 7. ((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) ### And 6
% 0.51/0.72 8. (((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) <=> (outcompetes (first_movers) (efficient_producers) T_1)) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (outcompetes (first_movers) (efficient_producers) T_1) ### Equiv 5 7
% 0.51/0.72 9. (((environment T_0) /\ (subpopulations (efficient_producers) (first_movers) T_0 T_1)) => (((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) <=> (outcompetes (first_movers) (efficient_producers) T_1))) (outcompetes (first_movers) (efficient_producers) T_1) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 1 4 8
% 0.51/0.72 10. (All T, (((environment T_0) /\ (subpopulations (efficient_producers) (first_movers) T_0 T)) => (((greater_or_equal (growth_rate (first_movers) T) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T))) <=> (outcompetes (first_movers) (efficient_producers) T)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (outcompetes (first_movers) (efficient_producers) T_1) ### All 9
% 0.51/0.72 11. (All S2, (All T, (((environment T_0) /\ (subpopulations (efficient_producers) S2 T_0 T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T))) <=> (outcompetes S2 (efficient_producers) T))))) (outcompetes (first_movers) (efficient_producers) T_1) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 10
% 0.51/0.72 12. (All S1, (All S2, (All T, (((environment T_0) /\ (subpopulations S1 S2 T_0 T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T)))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (outcompetes (first_movers) (efficient_producers) T_1) ### All 11
% 0.51/0.72 13. (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 12
% 0.51/0.72 14. (-. (((environment zenon_X2) /\ (subpopulations (first_movers) zenon_X3 zenon_X2 T_1)) => (greater_or_equal (growth_rate (first_movers) T_1) (zero)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) ### ConjTree 13
% 0.51/0.72 15. (environment zenon_X2) (-. (environment zenon_X2)) ### Axiom
% 0.51/0.72 16. (environment zenon_X2) (-. (environment zenon_X2)) ### Axiom
% 0.51/0.72 17. (environment zenon_X2) (-. (environment zenon_X2)) ### Axiom
% 0.51/0.72 18. (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (-. (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1)) ### Axiom
% 0.51/0.72 19. (-. (subpopulations (first_movers) (efficient_producers) zenon_X2 T_1)) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### Extension/test/mp_symmetry_of_subpopulationsctrp 17 18
% 0.51/0.72 20. (-. (in_environment zenon_X2 T_1)) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### Extension/test/mp_time_point_occurctrp 16 19
% 0.51/0.72 21. (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (zero) (growth_rate (first_movers) T_1)) ### Axiom
% 0.51/0.72 22. (greater (resilience (efficient_producers)) (resilience (first_movers))) (-. (greater (resilience (efficient_producers)) (resilience (first_movers)))) ### Axiom
% 0.51/0.72 23. (greater (zero) (growth_rate (efficient_producers) T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### Axiom
% 0.51/0.72 24. (((environment zenon_X2) /\ ((in_environment zenon_X2 T_1) /\ ((-. (greater (zero) (growth_rate (first_movers) T_1))) /\ (greater (resilience (efficient_producers)) (resilience (first_movers)))))) => (-. (greater (zero) (growth_rate (efficient_producers) T_1)))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### DisjTree 15 20 21 22 23
% 0.51/0.72 25. (All T, (((environment zenon_X2) /\ ((in_environment zenon_X2 T) /\ ((-. (greater (zero) (growth_rate (first_movers) T))) /\ (greater (resilience (efficient_producers)) (resilience (first_movers)))))) => (-. (greater (zero) (growth_rate (efficient_producers) T))))) (environment zenon_X2) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### All 24
% 0.51/0.72 26. (All S2, (All T, (((environment zenon_X2) /\ ((in_environment zenon_X2 T) /\ ((-. (greater (zero) (growth_rate (first_movers) T))) /\ (greater (resilience S2) (resilience (first_movers)))))) => (-. (greater (zero) (growth_rate S2 T)))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### All 25
% 0.51/0.72 27. (All S1, (All S2, (All T, (((environment zenon_X2) /\ ((in_environment zenon_X2 T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T))))))) (environment zenon_X2) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (-. (greater (zero) (growth_rate (first_movers) T_1))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### All 26
% 0.51/0.72 28. (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (-. (greater (zero) (growth_rate (first_movers) T_1))) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### All 27
% 0.51/0.72 29. ((((environment zenon_X2) /\ (subpopulations (first_movers) zenon_X3 zenon_X2 T_1)) => (greater_or_equal (growth_rate (first_movers) T_1) (zero))) <=> (-. (greater (zero) (growth_rate (first_movers) T_1)))) (environment zenon_X2) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (greater (resilience (efficient_producers)) (resilience (first_movers))) (greater (zero) (growth_rate (efficient_producers) T_1)) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### Equiv 14 28
% 0.51/0.72 30. (All T, ((((environment zenon_X2) /\ (subpopulations (first_movers) zenon_X3 zenon_X2 T)) => (greater_or_equal (growth_rate (first_movers) T) (zero))) <=> (-. (greater (zero) (growth_rate (first_movers) T))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### All 29
% 0.51/0.72 31. (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (first_movers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (first_movers) T) (zero))) <=> (-. (greater (zero) (growth_rate (first_movers) T)))))) (environment zenon_X2) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (greater (resilience (efficient_producers)) (resilience (first_movers))) (greater (zero) (growth_rate (efficient_producers) T_1)) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 30
% 0.51/0.72 32. (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1) (environment zenon_X2) ### All 31
% 0.51/0.72 33. (-. (((environment zenon_X2) /\ (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1)) => (greater_or_equal (growth_rate (efficient_producers) T_1) (zero)))) (environment zenon_X2) (greater (resilience (efficient_producers)) (resilience (first_movers))) (greater (zero) (growth_rate (efficient_producers) T_1)) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) ### ConjTree 32
% 0.51/0.72 34. (greater (zero) (growth_rate (efficient_producers) T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### Axiom
% 0.51/0.72 35. ((((environment zenon_X2) /\ (subpopulations (efficient_producers) (first_movers) zenon_X2 T_1)) => (greater_or_equal (growth_rate (efficient_producers) T_1) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T_1)))) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (environment zenon_X2) ### Equiv 33 34
% 0.51/0.72 36. (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) (first_movers) zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T))))) (environment zenon_X2) (greater (resilience (efficient_producers)) (resilience (first_movers))) (greater (zero) (growth_rate (efficient_producers) T_1)) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) ### All 35
% 0.51/0.72 37. (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T)))))) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater (resilience (efficient_producers)) (resilience (first_movers))) (environment zenon_X2) ### All 36
% 0.51/0.73 38. (-. (-. (greater (zero) (growth_rate (efficient_producers) T_1)))) (environment zenon_X2) (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T)))))) ### NotNot 37
% 0.51/0.73 39. (-. (((environment zenon_X2) /\ (subpopulations (efficient_producers) zenon_X4 zenon_X2 T_1)) => (greater_or_equal (growth_rate (efficient_producers) T_1) (zero)))) (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T)))))) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (-. (-. (greater (zero) (growth_rate (efficient_producers) T_1)))) ### ConjTree 38
% 0.51/0.73 40. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.51/0.73 41. (outcompetes (first_movers) (efficient_producers) T_1) (-. (outcompetes (first_movers) (efficient_producers) T_1)) ### Axiom
% 0.51/0.73 42. (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Axiom
% 0.51/0.73 43. ((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### And 42
% 0.51/0.73 44. (((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) <=> (outcompetes (first_movers) (efficient_producers) T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (outcompetes (first_movers) (efficient_producers) T_1) ### Equiv 41 43
% 0.51/0.73 45. (((environment T_0) /\ (subpopulations (efficient_producers) (first_movers) T_0 T_1)) => (((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))) <=> (outcompetes (first_movers) (efficient_producers) T_1))) (outcompetes (first_movers) (efficient_producers) T_1) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 40 4 44
% 0.51/0.73 46. (All T, (((environment T_0) /\ (subpopulations (efficient_producers) (first_movers) T_0 T)) => (((greater_or_equal (growth_rate (first_movers) T) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T))) <=> (outcompetes (first_movers) (efficient_producers) T)))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (outcompetes (first_movers) (efficient_producers) T_1) ### All 45
% 0.51/0.73 47. (All S2, (All T, (((environment T_0) /\ (subpopulations (efficient_producers) S2 T_0 T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T))) <=> (outcompetes S2 (efficient_producers) T))))) (outcompetes (first_movers) (efficient_producers) T_1) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 46
% 0.51/0.73 48. (All S1, (All S2, (All T, (((environment T_0) /\ (subpopulations S1 S2 T_0 T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T)))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (outcompetes (first_movers) (efficient_producers) T_1) ### All 47
% 0.51/0.73 49. (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 48
% 0.51/0.73 50. ((((environment zenon_X2) /\ (subpopulations (efficient_producers) zenon_X4 zenon_X2 T_1)) => (greater_or_equal (growth_rate (efficient_producers) T_1) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T_1)))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T)))))) ### Equiv 39 49
% 0.51/0.73 51. (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) zenon_X4 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T))))) (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T)))))) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) ### All 50
% 0.51/0.73 52. (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations (efficient_producers) S2 zenon_X2 T)) => (greater_or_equal (growth_rate (efficient_producers) T) (zero))) <=> (-. (greater (zero) (growth_rate (efficient_producers) T)))))) ### All 51
% 0.51/0.73 53. (All S1, (All S2, (All T, ((((environment zenon_X2) /\ (subpopulations S1 S2 zenon_X2 T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T))))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) ### All 52
% 0.51/0.73 54. (All E, (All S1, (All S2, (All T, ((((environment E) /\ (subpopulations S1 S2 E T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 53
% 0.51/0.73 55. (-. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (-. (outcompetes (first_movers) (efficient_producers) T_1)))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, ((((environment E) /\ (subpopulations S1 S2 E T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T)))))))) ### ConjTree 54
% 0.51/0.73 56. (-. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (-. (outcompetes (first_movers) (efficient_producers) T))))) (All E, (All S1, (All S2, (All T, ((((environment E) /\ (subpopulations S1 S2 E T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) ### NotAllEx 55
% 0.51/0.73 57. (-. (All E, (All T, (((environment E) /\ (subpopulations (first_movers) (efficient_producers) E T)) => (-. (outcompetes (first_movers) (efficient_producers) T)))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (((greater_or_equal (growth_rate S2 T) (zero)) /\ (greater (zero) (growth_rate S1 T))) <=> (outcompetes S2 S1 T))))))) (All E, (All S1, (All S2, (All T, (((environment E) /\ ((in_environment E T) /\ ((-. (greater (zero) (growth_rate S1 T))) /\ (greater (resilience S2) (resilience S1))))) => (-. (greater (zero) (growth_rate S2 T)))))))) (greater (resilience (efficient_producers)) (resilience (first_movers))) (All E, (All S1, (All S2, (All T, ((((environment E) /\ (subpopulations S1 S2 E T)) => (greater_or_equal (growth_rate S1 T) (zero))) <=> (-. (greater (zero) (growth_rate S1 T)))))))) ### NotAllEx 56
% 0.51/0.73 % SZS output end Proof
% 0.51/0.73 (* END-PROOF *)
%------------------------------------------------------------------------------