TSTP Solution File: MGT036+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : MGT036+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n022.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 0.60s 0.81s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : MGT036+2 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 12:17:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.81 (* PROOF-FOUND *)
% 0.60/0.81 % SZS status Theorem
% 0.60/0.81 (* BEGIN-PROOF *)
% 0.60/0.81 % SZS output start Proof
% 0.60/0.81 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))))).
% 0.60/0.81 Proof.
% 0.60/0.81 assert (zenon_L1_ : forall (zenon_TT_n : zenon_U) (zenon_TE_o : zenon_U), (forall T : zenon_U, (((environment zenon_TE_o)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_o T))->(subpopulations (efficient_producers) (first_movers) zenon_TE_o T))) -> (environment zenon_TE_o) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_o zenon_TT_n) -> (~(subpopulations (efficient_producers) (first_movers) zenon_TE_o zenon_TT_n)) -> False).
% 0.60/0.81 do 2 intro. intros zenon_H9 zenon_Ha zenon_Hb zenon_Hc.
% 0.60/0.81 generalize (zenon_H9 zenon_TT_n). zenon_intro zenon_Hf.
% 0.60/0.81 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 0.60/0.81 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ].
% 0.60/0.81 exact (zenon_H13 zenon_Ha).
% 0.60/0.81 exact (zenon_H12 zenon_Hb).
% 0.60/0.81 exact (zenon_Hc zenon_H10).
% 0.60/0.81 (* end of lemma zenon_L1_ *)
% 0.60/0.81 assert (zenon_L2_ : forall (zenon_TT_n : zenon_U) (zenon_TE_o : zenon_U), (~(subpopulations (efficient_producers) (first_movers) zenon_TE_o zenon_TT_n)) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_o zenon_TT_n) -> (environment zenon_TE_o) -> False).
% 0.60/0.81 do 2 intro. intros zenon_Hc zenon_Hb zenon_Ha.
% 0.60/0.81 generalize (mp_symmetry_of_subpopulations zenon_TE_o). zenon_intro zenon_H14.
% 0.60/0.81 generalize (zenon_H14 (first_movers)). zenon_intro zenon_H15.
% 0.60/0.81 generalize (zenon_H15 (efficient_producers)). zenon_intro zenon_H9.
% 0.60/0.81 apply (zenon_L1_ zenon_TT_n zenon_TE_o); trivial.
% 0.60/0.81 (* end of lemma zenon_L2_ *)
% 0.60/0.81 assert (zenon_L3_ : forall (zenon_TT_n : zenon_U), (((greater_or_equal (growth_rate (first_movers) zenon_TT_n) (zero))/\(greater (zero) (growth_rate (efficient_producers) zenon_TT_n)))<->(outcompetes (first_movers) (efficient_producers) zenon_TT_n)) -> (~(greater_or_equal (growth_rate (first_movers) zenon_TT_n) (zero))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_n) -> False).
% 0.60/0.81 do 1 intro. intros zenon_H16 zenon_H17 zenon_H18.
% 0.60/0.81 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 0.60/0.81 exact (zenon_H1a zenon_H18).
% 0.60/0.81 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.60/0.81 exact (zenon_H17 zenon_H1d).
% 0.60/0.81 (* end of lemma zenon_L3_ *)
% 0.60/0.81 assert (zenon_L4_ : forall (zenon_TE_o : zenon_U) (zenon_TT_n : zenon_U), (~(((environment zenon_E)/\(subpopulations (first_movers) zenon_E zenon_E zenon_TT_n))->(greater_or_equal (growth_rate (first_movers) zenon_TT_n) (zero)))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_n) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_o zenon_TT_n) -> (environment zenon_TE_o) -> False).
% 0.60/0.81 do 2 intro. intros zenon_H1e zenon_H18 zenon_Hb zenon_Ha.
% 0.60/0.81 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H1f. zenon_intro zenon_H17.
% 0.60/0.81 generalize (d2 zenon_TE_o). zenon_intro zenon_H20.
% 0.60/0.81 generalize (zenon_H20 (efficient_producers)). zenon_intro zenon_H21.
% 0.60/0.81 generalize (zenon_H21 (first_movers)). zenon_intro zenon_H22.
% 0.60/0.81 generalize (zenon_H22 zenon_TT_n). zenon_intro zenon_H23.
% 0.60/0.81 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H24 | zenon_intro zenon_H16 ].
% 0.60/0.81 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H13 | zenon_intro zenon_Hc ].
% 0.60/0.81 exact (zenon_H13 zenon_Ha).
% 0.60/0.81 apply (zenon_L2_ zenon_TT_n zenon_TE_o); trivial.
% 0.60/0.81 apply (zenon_L3_ zenon_TT_n); trivial.
% 0.60/0.81 (* end of lemma zenon_L4_ *)
% 0.60/0.81 assert (zenon_L5_ : forall (zenon_TT_n : zenon_U) (zenon_TE_o : zenon_U), (forall T : zenon_U, ((((environment zenon_E)/\(subpopulations (first_movers) zenon_E zenon_E T))->(greater_or_equal (growth_rate (first_movers) T) (zero)))<->(~(greater (zero) (growth_rate (first_movers) T))))) -> (environment zenon_TE_o) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_o zenon_TT_n) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_n) -> (forall S1 : zenon_U, (forall S2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_o)/\((in_environment zenon_TE_o T)/\((~(greater (zero) (growth_rate S1 T)))/\(greater (resilience S2) (resilience S1)))))->(~(greater (zero) (growth_rate S2 T))))))) -> (in_environment zenon_TE_o zenon_TT_n) -> (greater (zero) (growth_rate (efficient_producers) zenon_TT_n)) -> False).
% 0.60/0.81 do 2 intro. intros zenon_H25 zenon_Ha zenon_Hb zenon_H18 zenon_H26 zenon_H27 zenon_H1c.
% 0.60/0.81 generalize (zenon_H25 zenon_TT_n). zenon_intro zenon_H28.
% 0.60/0.81 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H1e; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ].
% 0.60/0.81 apply (zenon_L4_ zenon_TE_o zenon_TT_n); trivial.
% 0.60/0.81 generalize (zenon_H26 (first_movers)). zenon_intro zenon_H2c.
% 0.60/0.81 generalize (zenon_H2c (efficient_producers)). zenon_intro zenon_H2d.
% 0.60/0.81 generalize (zenon_H2d zenon_TT_n). zenon_intro zenon_H2e.
% 0.60/0.81 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.60/0.81 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H13 | zenon_intro zenon_H31 ].
% 0.60/0.81 exact (zenon_H13 zenon_Ha).
% 0.60/0.81 apply (zenon_notand_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.60/0.81 exact (zenon_H33 zenon_H27).
% 0.60/0.81 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H2b | zenon_intro zenon_H34 ].
% 0.60/0.81 exact (zenon_H2b zenon_H29).
% 0.60/0.81 exact (zenon_H34 a2).
% 0.60/0.81 exact (zenon_H2f zenon_H1c).
% 0.60/0.81 (* end of lemma zenon_L5_ *)
% 0.60/0.81 assert (zenon_L6_ : forall (zenon_TT_n : zenon_U), (((greater_or_equal (growth_rate (first_movers) zenon_TT_n) (zero))/\(greater (zero) (growth_rate (efficient_producers) zenon_TT_n)))<->(outcompetes (first_movers) (efficient_producers) zenon_TT_n)) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_n))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_n) -> False).
% 0.60/0.81 do 1 intro. intros zenon_H16 zenon_H2f zenon_H18.
% 0.60/0.81 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ].
% 0.60/0.81 exact (zenon_H1a zenon_H18).
% 0.60/0.81 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.60/0.81 exact (zenon_H2f zenon_H1c).
% 0.60/0.81 (* end of lemma zenon_L6_ *)
% 0.60/0.81 assert (zenon_L7_ : forall (zenon_TT_n : zenon_U) (zenon_TE_o : zenon_U), (forall S1 : zenon_U, (forall S2 : zenon_U, (forall T : zenon_U, (((environment zenon_TE_o)/\(subpopulations S1 S2 zenon_TE_o T))->(((greater_or_equal (growth_rate S2 T) (zero))/\(greater (zero) (growth_rate S1 T)))<->(outcompetes S2 S1 T)))))) -> (environment zenon_TE_o) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_o zenon_TT_n) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_n))) -> (outcompetes (first_movers) (efficient_producers) zenon_TT_n) -> False).
% 0.60/0.81 do 2 intro. intros zenon_H20 zenon_Ha zenon_Hb zenon_H2f zenon_H18.
% 0.60/0.81 generalize (zenon_H20 (efficient_producers)). zenon_intro zenon_H21.
% 0.60/0.81 generalize (zenon_H21 (first_movers)). zenon_intro zenon_H22.
% 0.60/0.81 generalize (zenon_H22 zenon_TT_n). zenon_intro zenon_H23.
% 0.60/0.81 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H24 | zenon_intro zenon_H16 ].
% 0.60/0.81 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H13 | zenon_intro zenon_Hc ].
% 0.60/0.81 exact (zenon_H13 zenon_Ha).
% 0.60/0.81 apply (zenon_L2_ zenon_TT_n zenon_TE_o); trivial.
% 0.60/0.81 apply (zenon_L6_ zenon_TT_n); trivial.
% 0.60/0.81 (* end of lemma zenon_L7_ *)
% 0.60/0.81 assert (zenon_L8_ : forall (zenon_TE_o : zenon_U) (zenon_TT_n : zenon_U), (outcompetes (first_movers) (efficient_producers) zenon_TT_n) -> (~(greater (zero) (growth_rate (efficient_producers) zenon_TT_n))) -> (subpopulations (first_movers) (efficient_producers) zenon_TE_o zenon_TT_n) -> (environment zenon_TE_o) -> False).
% 0.60/0.81 do 2 intro. intros zenon_H18 zenon_H2f zenon_Hb zenon_Ha.
% 0.60/0.81 generalize (d2 zenon_TE_o). zenon_intro zenon_H20.
% 0.60/0.81 apply (zenon_L7_ zenon_TT_n zenon_TE_o); trivial.
% 0.60/0.81 (* end of lemma zenon_L8_ *)
% 0.60/0.81 apply NNPP. intro zenon_G.
% 0.60/0.81 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_H35; idtac ].
% 0.60/0.81 elim zenon_H35. zenon_intro zenon_TE_o. zenon_intro zenon_H36.
% 0.60/0.82 apply (zenon_notallex_s (fun T : zenon_U => (((environment zenon_TE_o)/\(subpopulations (first_movers) (efficient_producers) zenon_TE_o T))->(~(outcompetes (first_movers) (efficient_producers) T)))) zenon_H36); [ zenon_intro zenon_H37; idtac ].
% 0.60/0.82 elim zenon_H37. zenon_intro zenon_TT_n. zenon_intro zenon_H38.
% 0.60/0.82 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_H3a. zenon_intro zenon_H39.
% 0.60/0.82 apply zenon_H39. zenon_intro zenon_H18.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_Ha. zenon_intro zenon_Hb.
% 0.60/0.82 generalize (mp_growth_rate_relationships zenon_E). zenon_intro zenon_H3b.
% 0.60/0.82 generalize (mp_time_point_occur zenon_TE_o). zenon_intro zenon_H3c.
% 0.60/0.82 generalize (zenon_H3c zenon_TT_n). zenon_intro zenon_H3d.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H11 | zenon_intro zenon_H27 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H11); [ zenon_intro zenon_H13 | zenon_intro zenon_H12 ].
% 0.60/0.82 exact (zenon_H13 zenon_Ha).
% 0.60/0.82 exact (zenon_H12 zenon_Hb).
% 0.60/0.82 generalize (a13 zenon_TE_o). zenon_intro zenon_H26.
% 0.60/0.82 generalize (zenon_H3b (efficient_producers)). zenon_intro zenon_H3e.
% 0.60/0.82 generalize (zenon_H3e zenon_E). zenon_intro zenon_H3f.
% 0.60/0.82 generalize (zenon_H3b (first_movers)). zenon_intro zenon_H40.
% 0.60/0.82 generalize (zenon_H40 zenon_E). zenon_intro zenon_H25.
% 0.60/0.82 generalize (zenon_H3f zenon_TT_n). zenon_intro zenon_H41.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H42; zenon_intro zenon_H2f ].
% 0.60/0.82 apply zenon_H43. zenon_intro zenon_H1c.
% 0.60/0.82 apply (zenon_L5_ zenon_TT_n zenon_TE_o); trivial.
% 0.60/0.82 apply (zenon_L8_ zenon_TE_o zenon_TT_n); trivial.
% 0.60/0.82 Qed.
% 0.60/0.82 % SZS output end Proof
% 0.60/0.82 (* END-PROOF *)
% 0.60/0.82 nodes searched: 20795
% 0.60/0.82 max branch formulas: 2797
% 0.60/0.82 proof nodes created: 672
% 0.60/0.82 formulas created: 64605
% 0.60/0.82
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