%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT103+1 : TPTP v9.3.1. Bugfixed v9.3.1. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n031.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 06:24:29 AM UTC 2026 % Result : Unsatisfiable 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 : MGT103+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n031.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 14:42:11 UTC 2026 % 0.08/0.35 % CPUTime : % 0.13/0.44 (* PROOF-FOUND *) % 0.13/0.44 % SZS status Unsatisfiable % 0.13/0.44 (* BEGIN-PROOF *) % 0.13/0.44 % SZS output start Proof % 0.13/0.44 Theorem zenon_thm : False. % 0.13/0.44 Proof. % 0.13/0.44 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less x y)->((less y z)->(less x z))))))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 0.13/0.44 apply (zenon_and_s _ _ contradiction). zenon_intro zenon_H24. zenon_intro ord_v600_v800. % 0.13/0.44 generalize (irreflexive (v800)). zenon_intro zenon_H25. % 0.13/0.44 elim (classic ((~((v800) = (v600)))/\(~(less (v800) (v600))))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 0.13/0.44 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.13/0.44 exact (zenon_H28 zenon_H24). % 0.13/0.44 cut ((less (v600) (v800)) = (less (v800) (v800))). % 0.13/0.44 intro zenon_D_pnotp. % 0.13/0.44 apply zenon_H25. % 0.13/0.44 rewrite <- zenon_D_pnotp. % 0.13/0.44 exact ord_v600_v800. % 0.13/0.44 cut (((v800) = (v800))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.13/0.44 cut (((v600) = (v800))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.13/0.44 congruence. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.13/0.44 apply zenon_H2d. zenon_intro zenon_H2e. % 0.13/0.44 elim (classic ((v800) = (v800))); [ zenon_intro zenon_H2f | zenon_intro zenon_H2a ]. % 0.13/0.44 cut (((v800) = (v800)) = ((v600) = (v800))). % 0.13/0.44 intro zenon_D_pnotp. % 0.13/0.44 apply zenon_H2b. % 0.13/0.44 rewrite <- zenon_D_pnotp. % 0.13/0.44 exact zenon_H2f. % 0.13/0.44 cut (((v800) = (v800))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.13/0.44 cut (((v800) = (v600))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 0.13/0.44 congruence. % 0.13/0.44 exact (zenon_H29 zenon_H2e). % 0.13/0.44 apply zenon_H2a. apply refl_equal. % 0.13/0.44 apply zenon_H2a. apply refl_equal. % 0.13/0.44 apply zenon_H2c. zenon_intro zenon_H24. % 0.13/0.44 generalize (zenon_H22 (v800)). zenon_intro zenon_H30. % 0.13/0.44 generalize (zenon_H30 (v600)). zenon_intro zenon_H31. % 0.13/0.44 generalize (zenon_H31 (v800)). zenon_intro zenon_H32. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H28 | zenon_intro zenon_H33 ]. % 0.13/0.44 exact (zenon_H28 zenon_H24). % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.13/0.44 exact (zenon_H35 ord_v600_v800). % 0.13/0.44 exact (zenon_H25 zenon_H34). % 0.13/0.44 apply zenon_H2a. apply refl_equal. % 0.13/0.44 apply zenon_H23. zenon_intro zenon_Tx_cc. apply NNPP. zenon_intro zenon_H37. % 0.13/0.44 apply zenon_H37. zenon_intro zenon_Ty_ce. apply NNPP. zenon_intro zenon_H39. % 0.13/0.44 apply zenon_H39. zenon_intro zenon_Tz_cg. apply NNPP. zenon_intro zenon_H3b. % 0.13/0.44 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.13/0.44 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.13/0.44 generalize (transitive zenon_Tx_cc). zenon_intro zenon_H40. % 0.13/0.44 generalize (zenon_H40 zenon_Ty_ce). zenon_intro zenon_H41. % 0.13/0.44 generalize (zenon_H41 zenon_Tz_cg). zenon_intro zenon_H42. % 0.13/0.44 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.13/0.44 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.13/0.44 exact (zenon_H46 zenon_H3d). % 0.13/0.44 exact (zenon_H45 zenon_H3f). % 0.13/0.44 exact (zenon_H3e zenon_H43). % 0.13/0.44 Qed. % 0.13/0.44 % SZS output end Proof % 0.13/0.44 (* END-PROOF *) % 0.13/0.44 nodes searched: 120 % 0.13/0.44 max branch formulas: 112 % 0.13/0.44 proof nodes created: 8 % 0.13/0.44 formulas created: 1181 % 0.13/0.44 %------------------------------------------------------------------------------