TSTP Solution File: MGT036+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 22:31:05 EDT 2022
% Result : Theorem 0.43s 0.62s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 09:59:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.62 (* PROOF-FOUND *)
% 0.43/0.62 % SZS status Theorem
% 0.43/0.62 (* BEGIN-PROOF *)
% 0.43/0.62 % SZS output start Proof
% 0.43/0.62 Theorem prove_t5 : (forall E : zenon_U, (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(~(outcompetes (first_movers) (efficient_producers) T))))).
% 0.43/0.62 Proof.
% 0.43/0.62 assert (zenon_L1_ : forall (zenon_TT_m : zenon_U) (zenon_TE_n : zenon_U), (~(subpopulations (efficient_producers) (first_movers) zenon_TE_n zenon_TT_m)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_n zenon_TT_m) -> (environment zenon_TE_n) -> False).
% 0.43/0.62 do 2 intro. intros zenon_H9 zenon_Ha zenon_Hb.
% 0.43/0.62 generalize (mp_symmetry_of_FM_and_EP zenon_TE_n). zenon_intro zenon_He.
% 0.43/0.62 generalize (zenon_He zenon_TT_m). zenon_intro zenon_Hf.
% 0.43/0.62 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ].
% 0.43/0.62 exact (zenon_H13 zenon_Hb).
% 0.43/0.62 exact (zenon_H12 zenon_Ha).
% 0.43/0.62 exact (zenon_H9 zenon_H10).
% 0.43/0.62 (* end of lemma zenon_L1_ *)
% 0.43/0.62 assert (zenon_L2_ : forall (zenon_TT_m : zenon_U), (((greater_or_equal (growth_rate (first_movers) zenon_TT_m) (zero))/\(greater (zero) (growth_rate (efficient_producers) zenon_TT_m)))<->(outcompetes (first_movers) (efficient_producers) zenon_TT_m)) -> (~(greater_or_equal (growth_rate (first_movers) zenon_TT_m) (zero))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_m) -> False).
% 0.43/0.62 do 1 intro. intros zenon_H14 zenon_H15 zenon_H16.
% 0.43/0.62 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ].
% 0.43/0.62 exact (zenon_H18 zenon_H16).
% 0.43/0.62 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 0.43/0.62 exact (zenon_H15 zenon_H1b).
% 0.43/0.62 (* end of lemma zenon_L2_ *)
% 0.43/0.62 assert (zenon_L3_ : forall (zenon_TT_m : zenon_U) (zenon_TE_n : zenon_U), (forall S1 : zenon_U, (forall S2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_n)/\((in_environment zenon_TE_n T)/\((~(greater (zero) (growth_rate S1 T)))/\(greater (resilience S2) (resilience S1)))))->(~(greater (zero) (growth_rate S2 T))))))) -> (environment zenon_TE_n) -> (in_environment zenon_TE_n zenon_TT_m) -> (~(greater (zero) (growth_rate (first_movers) zenon_TT_m))) -> (greater (zero) (growth_rate (efficient_producers) zenon_TT_m)) -> False).
% 0.43/0.62 do 2 intro. intros zenon_H1c zenon_Hb zenon_H1d zenon_H1e zenon_H1a.
% 0.43/0.62 generalize (zenon_H1c (first_movers)). zenon_intro zenon_H1f.
% 0.43/0.62 generalize (zenon_H1f (efficient_producers)). zenon_intro zenon_H20.
% 0.43/0.62 generalize (zenon_H20 zenon_TT_m). zenon_intro zenon_H21.
% 0.43/0.62 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H13 | zenon_intro zenon_H24 ].
% 0.43/0.62 exact (zenon_H13 zenon_Hb).
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ].
% 0.43/0.62 exact (zenon_H26 zenon_H1d).
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.43/0.62 exact (zenon_H28 zenon_H1e).
% 0.43/0.62 exact (zenon_H27 a2).
% 0.43/0.62 exact (zenon_H22 zenon_H1a).
% 0.43/0.62 (* end of lemma zenon_L3_ *)
% 0.43/0.62 assert (zenon_L4_ : forall (zenon_TT_m : zenon_U), (((greater_or_equal (growth_rate (first_movers) zenon_TT_m) (zero))/\(greater (zero) (growth_rate (efficient_producers) zenon_TT_m)))<->(outcompetes (first_movers) (efficient_producers) zenon_TT_m)) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_m))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_m) -> False).
% 0.43/0.62 do 1 intro. intros zenon_H14 zenon_H22 zenon_H16.
% 0.43/0.62 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ].
% 0.43/0.62 exact (zenon_H18 zenon_H16).
% 0.43/0.62 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 0.43/0.62 exact (zenon_H22 zenon_H1a).
% 0.43/0.62 (* end of lemma zenon_L4_ *)
% 0.43/0.62 assert (zenon_L5_ : forall (zenon_TT_m : zenon_U) (zenon_TE_n : zenon_U), (forall S1 : zenon_U, (forall S2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_n)/\(subpopulations S1 S2 zenon_TE_n T))->(((greater_or_equal (growth_rate S2 T) (zero))/\(greater (zero) (growth_rate S1 T)))<->(outcompetes S2 S1 T)))))) -> (environment zenon_TE_n) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_n zenon_TT_m) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_m))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_m) -> False).
% 0.43/0.62 do 2 intro. intros zenon_H29 zenon_Hb zenon_Ha zenon_H22 zenon_H16.
% 0.43/0.62 generalize (zenon_H29 (efficient_producers)). zenon_intro zenon_H2a.
% 0.43/0.62 generalize (zenon_H2a (first_movers)). zenon_intro zenon_H2b.
% 0.43/0.62 generalize (zenon_H2b zenon_TT_m). zenon_intro zenon_H2c.
% 0.43/0.62 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2d | zenon_intro zenon_H14 ].
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H13 | zenon_intro zenon_H9 ].
% 0.43/0.62 exact (zenon_H13 zenon_Hb).
% 0.43/0.62 apply (zenon_L1_ zenon_TT_m zenon_TE_n); trivial.
% 0.43/0.62 apply (zenon_L4_ zenon_TT_m); trivial.
% 0.43/0.62 (* end of lemma zenon_L5_ *)
% 0.43/0.62 apply NNPP. intro zenon_G.
% 0.43/0.62 apply (zenon_notallex_s (fun E : zenon_U => (forall T : zenon_U, (((environment E)/\(subpopulations (first_movers) (efficient_producers) E T))->(~(outcompetes (first_movers) (efficient_producers) T))))) zenon_G); [ zenon_intro zenon_H2e; idtac ].
% 0.43/0.62 elim zenon_H2e. zenon_intro zenon_TE_n. zenon_intro zenon_H2f.
% 0.43/0.62 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_n)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_n T))->(~(outcompetes (first_movers) (efficient_producers) T)))) zenon_H2f); [ zenon_intro zenon_H30; idtac ].
% 0.43/0.62 elim zenon_H30. zenon_intro zenon_TT_m. zenon_intro zenon_H31.
% 0.43/0.62 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32.
% 0.43/0.62 apply zenon_H32. zenon_intro zenon_H16.
% 0.43/0.62 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_Hb. zenon_intro zenon_Ha.
% 0.43/0.62 generalize (mp_growth_rate_relationships zenon_E). zenon_intro zenon_H34.
% 0.43/0.62 generalize (mp_time_point_occur zenon_TE_n). zenon_intro zenon_H35.
% 0.43/0.62 generalize (zenon_H35 zenon_TT_m). zenon_intro zenon_H36.
% 0.43/0.62 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H11 | zenon_intro zenon_H1d ].
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ].
% 0.43/0.62 exact (zenon_H13 zenon_Hb).
% 0.43/0.62 exact (zenon_H12 zenon_Ha).
% 0.43/0.62 generalize (a12 zenon_TE_n). zenon_intro zenon_H1c.
% 0.43/0.62 generalize (zenon_H34 (first_movers)). zenon_intro zenon_H37.
% 0.43/0.62 generalize (zenon_H37 zenon_E). zenon_intro zenon_H38.
% 0.43/0.62 generalize (zenon_H38 zenon_TT_m). zenon_intro zenon_H39.
% 0.43/0.62 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3b; zenon_intro zenon_H28 | zenon_intro zenon_H3a; zenon_intro zenon_H1e ].
% 0.43/0.62 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3c. zenon_intro zenon_H15.
% 0.43/0.62 generalize (d2 zenon_TE_n). zenon_intro zenon_H29.
% 0.43/0.62 generalize (zenon_H29 (efficient_producers)). zenon_intro zenon_H2a.
% 0.43/0.62 generalize (zenon_H2a (first_movers)). zenon_intro zenon_H2b.
% 0.43/0.62 generalize (zenon_H2b zenon_TT_m). zenon_intro zenon_H2c.
% 0.43/0.62 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2d | zenon_intro zenon_H14 ].
% 0.43/0.62 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H13 | zenon_intro zenon_H9 ].
% 0.43/0.62 exact (zenon_H13 zenon_Hb).
% 0.43/0.62 apply (zenon_L1_ zenon_TT_m zenon_TE_n); trivial.
% 0.43/0.62 apply (zenon_L2_ zenon_TT_m); trivial.
% 0.43/0.62 generalize (d2 zenon_TE_n). zenon_intro zenon_H29.
% 0.43/0.62 generalize (zenon_H34 (efficient_producers)). zenon_intro zenon_H3d.
% 0.43/0.62 generalize (zenon_H3d zenon_E). zenon_intro zenon_H3e.
% 0.43/0.62 generalize (zenon_H3e zenon_TT_m). zenon_intro zenon_H3f.
% 0.43/0.62 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H42; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H22 ].
% 0.43/0.62 apply zenon_H41. zenon_intro zenon_H1a.
% 0.43/0.62 apply (zenon_L3_ zenon_TT_m zenon_TE_n); trivial.
% 0.43/0.62 apply (zenon_L5_ zenon_TT_m zenon_TE_n); trivial.
% 0.43/0.62 Qed.
% 0.43/0.62 % SZS output end Proof
% 0.43/0.62 (* END-PROOF *)
% 0.43/0.62 nodes searched: 7647
% 0.43/0.62 max branch formulas: 1753
% 0.43/0.62 proof nodes created: 270
% 0.43/0.62 formulas created: 28406
% 0.43/0.62
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