%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT059+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 06:24:24 AM UTC 2026 % Result : Theorem 0.45s 0.73s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT059+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n003.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 13:34:09 UTC 2026 % 0.08/0.35 % CPUTime : % 0.45/0.73 (* PROOF-FOUND *) % 0.45/0.73 % SZS status Theorem % 0.45/0.73 (* BEGIN-PROOF *) % 0.45/0.73 % SZS output start Proof % 0.45/0.73 Theorem assumption_2 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((has_immunity X T0)/\(has_immunity X T)))->((hazard_of_mortality X T0) = (hazard_of_mortality X T)))))). % 0.45/0.73 Proof. % 0.45/0.73 apply NNPP. intro zenon_G. % 0.45/0.73 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\((has_immunity X T0)/\(has_immunity X T)))->((hazard_of_mortality X T0) = (hazard_of_mortality X T)))))) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 0.45/0.73 elim zenon_H8. zenon_intro zenon_TX_j. zenon_intro zenon_Ha. % 0.45/0.73 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_j)/\((has_immunity zenon_TX_j T0)/\(has_immunity zenon_TX_j T)))->((hazard_of_mortality zenon_TX_j T0) = (hazard_of_mortality zenon_TX_j T))))) zenon_Ha); [ zenon_intro zenon_Hb; idtac ]. % 0.45/0.73 elim zenon_Hb. zenon_intro zenon_TT0_m. zenon_intro zenon_Hd. % 0.45/0.73 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_j)/\((has_immunity zenon_TX_j zenon_TT0_m)/\(has_immunity zenon_TX_j T)))->((hazard_of_mortality zenon_TX_j zenon_TT0_m) = (hazard_of_mortality zenon_TX_j T)))) zenon_Hd); [ zenon_intro zenon_He; idtac ]. % 0.45/0.73 elim zenon_He. zenon_intro zenon_TT_p. zenon_intro zenon_H10. % 0.45/0.73 apply (zenon_notimply_s _ _ zenon_H10). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.45/0.73 apply (zenon_and_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.45/0.73 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.45/0.73 generalize (assumption_17 zenon_TX_j). zenon_intro zenon_H17. % 0.45/0.73 generalize (zenon_H17 zenon_TT_p). zenon_intro zenon_H18. % 0.45/0.73 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 0.45/0.73 exact (zenon_H1a zenon_H14). % 0.45/0.73 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.45/0.73 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.45/0.73 exact (zenon_H1e zenon_H15). % 0.45/0.73 generalize (zenon_H17 zenon_TT0_m). zenon_intro zenon_H1f. % 0.45/0.73 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H1a | zenon_intro zenon_H20 ]. % 0.45/0.73 exact (zenon_H1a zenon_H14). % 0.45/0.73 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.45/0.73 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.45/0.73 exact (zenon_H24 zenon_H16). % 0.45/0.73 elim (classic ((hazard_of_mortality zenon_TX_j zenon_TT_p) = (hazard_of_mortality zenon_TX_j zenon_TT_p))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 0.45/0.73 cut (((hazard_of_mortality zenon_TX_j zenon_TT_p) = (hazard_of_mortality zenon_TX_j zenon_TT_p)) = ((hazard_of_mortality zenon_TX_j zenon_TT0_m) = (hazard_of_mortality zenon_TX_j zenon_TT_p))). % 0.45/0.73 intro zenon_D_pnotp. % 0.45/0.73 apply zenon_H11. % 0.45/0.73 rewrite <- zenon_D_pnotp. % 0.45/0.73 exact zenon_H25. % 0.45/0.73 cut (((hazard_of_mortality zenon_TX_j zenon_TT_p) = (hazard_of_mortality zenon_TX_j zenon_TT_p))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 0.45/0.73 cut (((hazard_of_mortality zenon_TX_j zenon_TT_p) = (hazard_of_mortality zenon_TX_j zenon_TT0_m))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 0.45/0.73 congruence. % 0.45/0.73 cut (((hazard_of_mortality zenon_TX_j zenon_TT_p) = (very_low)) = ((hazard_of_mortality zenon_TX_j zenon_TT_p) = (hazard_of_mortality zenon_TX_j zenon_TT0_m))). % 0.45/0.73 intro zenon_D_pnotp. % 0.45/0.73 apply zenon_H27. % 0.45/0.73 rewrite <- zenon_D_pnotp. % 0.45/0.73 exact zenon_H1d. % 0.45/0.73 cut (((very_low) = (hazard_of_mortality zenon_TX_j zenon_TT0_m))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 0.45/0.73 cut (((hazard_of_mortality zenon_TX_j zenon_TT_p) = (hazard_of_mortality zenon_TX_j zenon_TT_p))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 0.45/0.73 congruence. % 0.45/0.73 apply zenon_H26. apply refl_equal. % 0.45/0.73 apply zenon_H28. apply sym_equal. exact zenon_H23. % 0.45/0.73 apply zenon_H26. apply refl_equal. % 0.45/0.73 apply zenon_H26. apply refl_equal. % 0.45/0.73 Qed. % 0.45/0.73 % SZS output end Proof % 0.45/0.73 (* END-PROOF *) % 0.45/0.73 nodes searched: 14887 % 0.45/0.73 max branch formulas: 648 % 0.45/0.73 proof nodes created: 446 % 0.45/0.73 formulas created: 7086 % 0.45/0.73 %------------------------------------------------------------------------------