%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:24:21 AM UTC 2026 % Result : Theorem 0.13s 0.44s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT036+3 : TPTP v9.3.0. Released v2.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.34 % Computer : n004.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.34 % CPULimit : 300 % 0.09/0.34 % WCLimit : 300 % 0.09/0.34 % DateTime : Mon Sep 7 12:42:00 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.44 (* PROOF-FOUND *) % 0.13/0.44 % SZS status Theorem % 0.13/0.44 (* BEGIN-PROOF *) % 0.13/0.44 % SZS output start Proof % 0.13/0.44 Theorem prove_t5_star : (exists E : zenon_U, (exists T : zenon_U, ((environment E)/\((subpopulations (first_movers) (efficient_producers) E T)/\(outcompetes (first_movers) (efficient_producers) T))))). % 0.13/0.44 Proof. % 0.13/0.44 apply NNPP. intro zenon_G. % 0.13/0.44 elim a13_star. zenon_intro zenon_TE_e. zenon_intro zenon_H5. % 0.13/0.44 elim zenon_H5. zenon_intro zenon_TT_g. zenon_intro zenon_H7. % 0.13/0.44 apply (zenon_and_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.13/0.44 apply (zenon_and_s _ _ zenon_H8). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.13/0.44 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.13/0.44 generalize (d2 zenon_TE_e). zenon_intro zenon_He. % 0.13/0.44 apply zenon_G. exists zenon_TE_e. apply NNPP. zenon_intro zenon_Hf. % 0.13/0.44 generalize (zenon_He (efficient_producers)). zenon_intro zenon_H10. % 0.13/0.44 generalize (zenon_H10 (first_movers)). zenon_intro zenon_H11. % 0.13/0.44 generalize (zenon_H11 zenon_TT_g). zenon_intro zenon_H12. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 0.13/0.45 apply (zenon_notand_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.13/0.45 exact (zenon_H16 zenon_H9). % 0.13/0.45 generalize (mp_symmetry_of_subpopulations zenon_TE_e). zenon_intro zenon_H17. % 0.13/0.45 generalize (zenon_H17 (first_movers)). zenon_intro zenon_H18. % 0.13/0.45 generalize (zenon_H18 (efficient_producers)). zenon_intro zenon_H19. % 0.13/0.45 generalize (zenon_H19 zenon_TT_g). zenon_intro zenon_H1a. % 0.13/0.45 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.13/0.45 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H16 | zenon_intro zenon_H1d ]. % 0.13/0.45 exact (zenon_H16 zenon_H9). % 0.13/0.45 exact (zenon_H1d zenon_Hb). % 0.13/0.45 exact (zenon_H15 zenon_H1b). % 0.13/0.45 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H20; zenon_intro zenon_H1f | zenon_intro zenon_Ha; zenon_intro zenon_H1e ]. % 0.13/0.45 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.13/0.45 exact (zenon_H22 zenon_Hd). % 0.13/0.45 exact (zenon_H21 zenon_Hc). % 0.13/0.45 apply zenon_Hf. exists zenon_TT_g. apply NNPP. zenon_intro zenon_H23. % 0.13/0.45 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H16 | zenon_intro zenon_H24 ]. % 0.13/0.45 exact (zenon_H16 zenon_H9). % 0.13/0.45 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H1d | zenon_intro zenon_H1f ]. % 0.13/0.45 exact (zenon_H1d zenon_Hb). % 0.13/0.45 exact (zenon_H1f zenon_H1e). % 0.13/0.45 Qed. % 0.13/0.45 % SZS output end Proof % 0.13/0.45 (* END-PROOF *) % 0.13/0.45 nodes searched: 674 % 0.13/0.45 max branch formulas: 388 % 0.13/0.45 proof nodes created: 60 % 0.13/0.45 formulas created: 2450 % 0.13/0.45 %------------------------------------------------------------------------------