TSTP Solution File: MGT036+3 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : MGT036+3 : 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 22:27:01 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : MGT036+3 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.33 % Computer : n019.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 07:40:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 (* PROOF-FOUND *)
% 0.19/0.43 (* BEGIN-PROOF *)
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 1. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.43 2. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.43 3. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.19/0.43 4. (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (efficient_producers) (first_movers) T_0 T_1) ### Axiom
% 0.19/0.43 5. (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T_1)) => (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 2 3 4
% 0.19/0.43 6. (All T, (((environment T_0) /\ (subpopulations (first_movers) (efficient_producers) T_0 T)) => (subpopulations (efficient_producers) (first_movers) T_0 T))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) ### All 5
% 0.19/0.43 7. (All S2, (All T, (((environment T_0) /\ (subpopulations (first_movers) S2 T_0 T)) => (subpopulations S2 (first_movers) T_0 T)))) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 6
% 0.19/0.43 8. (All S1, (All S2, (All T, (((environment T_0) /\ (subpopulations S1 S2 T_0 T)) => (subpopulations S2 S1 T_0 T))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) ### All 7
% 0.19/0.43 9. (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (-. (subpopulations (efficient_producers) (first_movers) T_0 T_1)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### All 8
% 0.19/0.43 10. (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (-. (greater_or_equal (growth_rate (first_movers) T_1) (zero))) ### Axiom
% 0.19/0.43 11. (greater (zero) (growth_rate (efficient_producers) T_1)) (-. (greater (zero) (growth_rate (efficient_producers) T_1))) ### Axiom
% 0.19/0.43 12. (-. ((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)) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) ### NotAnd 10 11
% 0.19/0.43 13. (environment T_0) (-. (environment T_0)) ### Axiom
% 0.19/0.43 14. (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (subpopulations (first_movers) (efficient_producers) T_0 T_1)) ### Axiom
% 0.19/0.43 15. (outcompetes (first_movers) (efficient_producers) T_1) (-. (outcompetes (first_movers) (efficient_producers) T_1)) ### Axiom
% 0.19/0.43 16. (-. ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ (outcompetes (first_movers) (efficient_producers) T_1)))) (outcompetes (first_movers) (efficient_producers) T_1) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) ### DisjTree 13 14 15
% 0.19/0.43 17. (-. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (outcompetes (first_movers) (efficient_producers) T))))) (environment T_0) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (outcompetes (first_movers) (efficient_producers) T_1) ### NotExists 16
% 0.19/0.43 18. (((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)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (environment T_0) (-. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (outcompetes (first_movers) (efficient_producers) T))))) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (greater (zero) (growth_rate (efficient_producers) T_1)) ### Equiv 12 17
% 0.19/0.43 19. (((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))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (-. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (outcompetes (first_movers) (efficient_producers) T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (environment T_0) ### DisjTree 1 9 18
% 0.19/0.43 20. (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) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (outcompetes (first_movers) (efficient_producers) T))))) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (greater (zero) (growth_rate (efficient_producers) T_1)) ### All 19
% 0.19/0.43 21. (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))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (-. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (outcompetes (first_movers) (efficient_producers) T))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (environment T_0) ### All 20
% 0.19/0.43 22. (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) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (-. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ (outcompetes (first_movers) (efficient_producers) T))))) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (greater (zero) (growth_rate (efficient_producers) T_1)) ### All 21
% 0.19/0.43 23. (-. (Ex E, (Ex T, ((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (outcompetes (first_movers) (efficient_producers) T)))))) (greater (zero) (growth_rate (efficient_producers) T_1)) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (environment T_0) (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)))))) ### NotExists 22
% 0.19/0.43 24. (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))))))) (environment T_0) (All E, (All S1, (All S2, (All T, (((environment E) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (subpopulations (first_movers) (efficient_producers) T_0 T_1) (greater_or_equal (growth_rate (first_movers) T_1) (zero)) (greater (zero) (growth_rate (efficient_producers) T_1)) (-. (Ex E, (Ex T, ((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (outcompetes (first_movers) (efficient_producers) T)))))) ### All 23
% 0.19/0.43 25. ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T_1) /\ ((greater_or_equal (growth_rate (first_movers) T_1) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T_1))))) (-. (Ex E, (Ex 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)) => (subpopulations S2 S1 E 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))))))) ### ConjTree 24
% 0.19/0.43 26. (Ex T, ((environment T_0) /\ ((subpopulations (first_movers) (efficient_producers) T_0 T) /\ ((greater_or_equal (growth_rate (first_movers) T) (zero)) /\ (greater (zero) (growth_rate (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) /\ (subpopulations S1 S2 E T)) => (subpopulations S2 S1 E T)))))) (-. (Ex E, (Ex T, ((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ (outcompetes (first_movers) (efficient_producers) T)))))) ### Exists 25
% 0.19/0.43 27. (Ex E, (Ex T, ((environment E) /\ ((subpopulations (first_movers) (efficient_producers) E T) /\ ((greater_or_equal (growth_rate (first_movers) T) (zero)) /\ (greater (zero) (growth_rate (efficient_producers) T))))))) (-. (Ex E, (Ex 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)) => (subpopulations S2 S1 E 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))))))) ### Exists 26
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 (* END-PROOF *)
%------------------------------------------------------------------------------