%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 06:24:26 AM UTC 2026 % Result : Theorem 13.54s 13.88s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n013.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 13:53:20 UTC 2026 % 0.09/0.36 % CPUTime : % 13.54/13.88 (* PROOF-FOUND *) % 13.54/13.88 % SZS status Theorem % 13.54/13.88 (* BEGIN-PROOF *) % 13.54/13.88 % SZS output start Proof % 13.54/13.88 Theorem unknown_sound_compatible : (exists V : zenon_U, ((leq (ninf) V)/\((leq V (nsup))/\(completion_compatible V (ninf) (nsup))))). % 13.54/13.88 Proof. % 13.54/13.88 assert (zenon_L1_ : (~((ninf) = (ninf))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H28. % 13.54/13.88 apply zenon_H28. apply refl_equal. % 13.54/13.88 (* end of lemma zenon_L1_ *) % 13.54/13.88 assert (zenon_L2_ : (~((n0) = (n0))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H29. % 13.54/13.88 apply zenon_H29. apply refl_equal. % 13.54/13.88 (* end of lemma zenon_L2_ *) % 13.54/13.88 assert (zenon_L3_ : (~(leq (ninf) (ninf))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H2a. % 13.54/13.88 generalize (leq_def (ninf)). zenon_intro zenon_H2b. % 13.54/13.88 generalize (zenon_H2b (ninf)). zenon_intro zenon_H2c. % 13.54/13.88 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2a; zenon_intro zenon_H2f | zenon_intro zenon_H2e; zenon_intro zenon_H2d ]. % 13.54/13.88 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H30. zenon_intro zenon_H28. % 13.54/13.88 apply zenon_H28. apply refl_equal. % 13.54/13.88 exact (zenon_H2a zenon_H2e). % 13.54/13.88 (* end of lemma zenon_L3_ *) % 13.54/13.88 assert (zenon_L4_ : (~((nsup) = (nsup))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H31. % 13.54/13.88 apply zenon_H31. apply refl_equal. % 13.54/13.88 (* end of lemma zenon_L4_ *) % 13.54/13.88 assert (zenon_L5_ : (less (ninf) (nsup)) -> (~(leq (ninf) (nsup))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H32 zenon_H33. % 13.54/13.88 generalize (leq_def (ninf)). zenon_intro zenon_H2b. % 13.54/13.88 generalize (zenon_H2b (nsup)). zenon_intro zenon_H34. % 13.54/13.88 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H33; zenon_intro zenon_H37 | zenon_intro zenon_H36; zenon_intro zenon_H35 ]. % 13.54/13.88 apply (zenon_notor_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 13.54/13.88 exact (zenon_H39 zenon_H32). % 13.54/13.88 exact (zenon_H33 zenon_H36). % 13.54/13.88 (* end of lemma zenon_L5_ *) % 13.54/13.88 assert (zenon_L6_ : (~((nsup) = (ninf))) -> (~(completion_compatible (ninf) (ninf) (nsup))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H3a zenon_H3b. % 13.54/13.88 generalize (h_inf_lb (nsup)). zenon_intro zenon_H36. % 13.54/13.88 generalize (leq_def (ninf)). zenon_intro zenon_H2b. % 13.54/13.88 generalize (zenon_H2b (nsup)). zenon_intro zenon_H34. % 13.54/13.88 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H33; zenon_intro zenon_H37 | zenon_intro zenon_H36; zenon_intro zenon_H35 ]. % 13.54/13.88 exact (zenon_H33 zenon_H36). % 13.54/13.88 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H32 | zenon_intro zenon_H3c ]. % 13.54/13.88 generalize (completion_compat (ninf)). zenon_intro zenon_H3d. % 13.54/13.88 generalize (zenon_H3d (ninf)). zenon_intro zenon_H3e. % 13.54/13.88 generalize (zenon_H3e (nsup)). zenon_intro zenon_H3f. % 13.54/13.88 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 13.54/13.88 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 13.54/13.88 apply (zenon_L3_); trivial. % 13.54/13.88 apply (zenon_L5_); trivial. % 13.54/13.88 exact (zenon_H3b zenon_H40). % 13.54/13.88 apply zenon_H3a. apply sym_equal. exact zenon_H3c. % 13.54/13.88 (* end of lemma zenon_L6_ *) % 13.54/13.88 assert (zenon_L7_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less x y)->((less y z)->(less x z)))))) -> (~(less (ninf) (ninf))) -> (~(exists V : zenon_U, ((leq (ninf) V)/\((leq V (nsup))/\(completion_compatible V (ninf) (nsup)))))) -> False). % 13.54/13.88 do 0 intro. intros zenon_H42 zenon_H30 zenon_G. % 13.54/13.88 elim (classic (less (n0) (ninf))); [ zenon_intro zenon_H43 | zenon_intro zenon_H44 ]. % 13.54/13.88 generalize (zenon_H42 (ninf)). zenon_intro zenon_H45. % 13.54/13.88 generalize (zenon_H45 (n0)). zenon_intro zenon_H46. % 13.54/13.88 generalize (zenon_H46 (ninf)). zenon_intro zenon_H47. % 13.54/13.88 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 13.54/13.88 exact (zenon_H49 h_inf_0). % 13.54/13.88 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H44 | zenon_intro zenon_H4a ]. % 13.54/13.88 exact (zenon_H44 zenon_H43). % 13.54/13.88 exact (zenon_H30 zenon_H4a). % 13.54/13.88 elim (classic ((nsup) = (ninf))); [ zenon_intro zenon_H4b | zenon_intro zenon_H3a ]. % 13.54/13.88 cut ((less (n0) (nsup)) = (less (n0) (ninf))). % 13.54/13.88 intro zenon_D_pnotp. % 13.54/13.88 apply zenon_H44. % 13.54/13.88 rewrite <- zenon_D_pnotp. % 13.54/13.88 exact h_0_sup. % 13.54/13.88 cut (((nsup) = (ninf))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 13.54/13.88 cut (((n0) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 13.54/13.88 congruence. % 13.54/13.88 apply zenon_H29. apply refl_equal. % 13.54/13.88 exact (zenon_H3a zenon_H4b). % 13.54/13.88 apply zenon_G. exists (ninf). apply NNPP. zenon_intro zenon_H4c. % 13.54/13.88 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H2a | zenon_intro zenon_H4d ]. % 0.14/13.90 apply (zenon_L3_); trivial. % 0.14/13.90 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H33 | zenon_intro zenon_H3b ]. % 0.14/13.90 generalize (leq_def (ninf)). zenon_intro zenon_H2b. % 0.14/13.90 generalize (zenon_H2b (nsup)). zenon_intro zenon_H34. % 0.14/13.90 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H33; zenon_intro zenon_H37 | zenon_intro zenon_H36; zenon_intro zenon_H35 ]. % 0.14/13.90 apply (zenon_notor_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.14/13.90 elim (classic ((~((ninf) = (n0)))/\(~(less (ninf) (n0))))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ]. % 0.14/13.90 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H49. % 0.14/13.90 exact (zenon_H49 h_inf_0). % 0.14/13.90 cut ((less (n0) (nsup)) = (less (ninf) (nsup))). % 0.14/13.90 intro zenon_D_pnotp. % 0.14/13.90 apply zenon_H39. % 0.14/13.90 rewrite <- zenon_D_pnotp. % 0.14/13.90 exact h_0_sup. % 0.14/13.90 cut (((nsup) = (nsup))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 0.14/13.90 cut (((n0) = (ninf))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 0.14/13.90 congruence. % 0.14/13.90 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.14/13.90 apply zenon_H53. zenon_intro zenon_H54. % 0.14/13.90 elim (classic ((ninf) = (ninf))); [ zenon_intro zenon_H55 | zenon_intro zenon_H28 ]. % 0.14/13.90 cut (((ninf) = (ninf)) = ((n0) = (ninf))). % 0.14/13.90 intro zenon_D_pnotp. % 0.14/13.90 apply zenon_H51. % 0.14/13.90 rewrite <- zenon_D_pnotp. % 0.14/13.90 exact zenon_H55. % 0.14/13.90 cut (((ninf) = (ninf))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 0.14/13.90 cut (((ninf) = (n0))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 0.14/13.90 congruence. % 0.14/13.90 exact (zenon_H50 zenon_H54). % 0.14/13.90 apply zenon_H28. apply refl_equal. % 0.14/13.90 apply zenon_H28. apply refl_equal. % 0.14/13.90 apply zenon_H52. zenon_intro h_inf_0. % 0.14/13.90 generalize (zenon_H42 (ninf)). zenon_intro zenon_H45. % 0.14/13.90 generalize (zenon_H45 (n0)). zenon_intro zenon_H46. % 0.14/13.90 generalize (zenon_H46 (nsup)). zenon_intro zenon_H56. % 0.14/13.90 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H49 | zenon_intro zenon_H57 ]. % 0.14/13.90 exact (zenon_H49 h_inf_0). % 0.14/13.90 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H32 ]. % 0.14/13.90 exact (zenon_H58 h_0_sup). % 0.14/13.90 exact (zenon_H39 zenon_H32). % 0.14/13.90 apply zenon_H31. apply refl_equal. % 0.14/13.90 exact (zenon_H33 zenon_H36). % 0.14/13.90 apply (zenon_L6_); trivial. % 0.14/13.90 (* end of lemma zenon_L7_ *) % 0.14/13.90 apply NNPP. intro zenon_G. % 0.14/13.90 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_H42 | zenon_intro zenon_H59 ]. % 0.14/13.90 generalize (irreflexive (ninf)). zenon_intro zenon_H30. % 0.14/13.90 apply (zenon_L7_); trivial. % 0.14/13.90 apply zenon_H59. zenon_intro zenon_Tx_dm. apply NNPP. zenon_intro zenon_H5b. % 0.14/13.90 apply zenon_H5b. zenon_intro zenon_Ty_do. apply NNPP. zenon_intro zenon_H5d. % 0.14/13.90 apply zenon_H5d. zenon_intro zenon_Tz_dq. apply NNPP. zenon_intro zenon_H5f. % 0.14/13.90 apply (zenon_notimply_s _ _ zenon_H5f). zenon_intro zenon_H61. zenon_intro zenon_H60. % 0.14/13.90 apply (zenon_notimply_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 0.14/13.90 generalize (transitive zenon_Tx_dm). zenon_intro zenon_H64. % 0.14/13.90 generalize (zenon_H64 zenon_Ty_do). zenon_intro zenon_H65. % 0.14/13.90 generalize (zenon_H65 zenon_Tz_dq). zenon_intro zenon_H66. % 0.14/13.90 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.14/13.90 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 0.14/13.90 exact (zenon_H6a zenon_H61). % 0.14/13.90 exact (zenon_H69 zenon_H63). % 0.14/13.90 exact (zenon_H62 zenon_H67). % 0.14/13.90 Qed. % 0.14/13.90 % SZS output end Proof % 0.14/13.90 (* END-PROOF *) % 0.14/13.90 nodes searched: 603476 % 0.14/13.90 max branch formulas: 11319 % 0.14/13.90 proof nodes created: 6136 % 0.14/13.90 formulas created: 316648 % 0.14/13.90 %------------------------------------------------------------------------------