TSTP Solution File: MGT028+1 by Zenon---0.7.1
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% File : Zenon---0.7.1
% Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 22:31:02 EDT 2022
% Result : Theorem 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT028+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n018.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 09:37:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.18/0.50 (* PROOF-FOUND *)
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 (* BEGIN-PROOF *)
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 Theorem prove_l10 : (forall E : zenon_U, (((environment E)/\(stable E))->(exists T2 : zenon_U, ((greater T2 (appear (efficient_producers) E))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater_or_equal T T2))->(greater (zero) (growth_rate (first_movers) T)))))))).
% 0.18/0.50 Proof.
% 0.18/0.50 assert (zenon_L1_ : forall (zenon_TT_f : zenon_U), ((greater (growth_rate (efficient_producers) zenon_TT_f) (zero))/\(greater (zero) (growth_rate (first_movers) zenon_TT_f))) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_f))) -> False).
% 0.18/0.50 do 1 intro. intros zenon_H3 zenon_H4.
% 0.18/0.50 apply (zenon_and_s _ _ zenon_H3). zenon_intro zenon_H7. zenon_intro zenon_H6.
% 0.18/0.50 exact (zenon_H4 zenon_H6).
% 0.18/0.50 (* end of lemma zenon_L1_ *)
% 0.18/0.50 apply NNPP. intro zenon_G.
% 0.18/0.50 apply (zenon_notallex_s (fun E : zenon_U => (((environment E)/\(stable E))->(exists T2 : zenon_U, ((greater T2 (appear (efficient_producers) E))/\(forall T : zenon_U, (((subpopulations (first_movers) (efficient_producers) E T)/\(greater_or_equal T T2))->(greater (zero) (growth_rate (first_movers) T)))))))) zenon_G); [ zenon_intro zenon_H8; idtac ].
% 0.18/0.50 elim zenon_H8. zenon_intro zenon_TE_j. zenon_intro zenon_Ha.
% 0.18/0.50 apply (zenon_notimply_s _ _ zenon_Ha). zenon_intro zenon_Hc. zenon_intro zenon_Hb.
% 0.18/0.50 apply (zenon_and_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd.
% 0.18/0.50 generalize (l11 zenon_TE_j). zenon_intro zenon_Hf.
% 0.18/0.50 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 0.18/0.50 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ].
% 0.18/0.50 exact (zenon_H13 zenon_He).
% 0.18/0.50 exact (zenon_H12 zenon_Hd).
% 0.18/0.50 elim zenon_H10. zenon_intro zenon_TTo_u. zenon_intro zenon_H15.
% 0.18/0.50 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.18/0.50 generalize (mp_first_movers_negative_growth zenon_TE_j). zenon_intro zenon_H18.
% 0.18/0.50 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 0.18/0.50 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H13 | zenon_intro zenon_H1b ].
% 0.18/0.50 exact (zenon_H13 zenon_He).
% 0.18/0.50 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H12 | zenon_intro zenon_H1c ].
% 0.18/0.50 exact (zenon_H12 zenon_Hd).
% 0.18/0.50 apply zenon_H1c. exists zenon_TTo_u. apply NNPP. zenon_intro zenon_H1d.
% 0.18/0.50 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.18/0.50 exact (zenon_H1f zenon_H17).
% 0.18/0.50 apply (zenon_notallex_s (fun T : zenon_U => (((subpopulations (first_movers) (efficient_producers) zenon_TE_j T)/\(greater_or_equal T zenon_TTo_u))->(greater (zero) (growth_rate (first_movers) T)))) zenon_H1e); [ zenon_intro zenon_H20; idtac ].
% 0.18/0.50 elim zenon_H20. zenon_intro zenon_TT_f. zenon_intro zenon_H21.
% 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H22. zenon_intro zenon_H4.
% 0.18/0.50 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.18/0.50 generalize (zenon_H16 zenon_TT_f). zenon_intro zenon_H25.
% 0.18/0.50 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_H3 ].
% 0.18/0.50 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.18/0.50 exact (zenon_H28 zenon_H24).
% 0.18/0.50 exact (zenon_H27 zenon_H23).
% 0.18/0.50 apply (zenon_L1_ zenon_TT_f); trivial.
% 0.18/0.50 exact (zenon_Hb zenon_H19).
% 0.18/0.50 Qed.
% 0.18/0.50 % SZS output end Proof
% 0.18/0.50 (* END-PROOF *)
% 0.18/0.50 nodes searched: 144
% 0.18/0.50 max branch formulas: 134
% 0.18/0.50 proof nodes created: 42
% 0.18/0.50 formulas created: 892
% 0.18/0.50
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