%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 : Tue Jul 19 16:00:42 EDT 2022 % Result : Theorem 0.36s 0.52s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SEU264+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n017.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sun Jun 19 16:19:13 EDT 2022 % 0.12/0.32 % CPUTime : % 0.36/0.52 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.36/0.52 (* PROOF-FOUND *) % 0.36/0.52 % SZS status Theorem % 0.36/0.52 (* BEGIN-PROOF *) % 0.36/0.52 % SZS output start Proof % 0.36/0.52 Theorem t16_relset_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((relation_of2_as_subset D C A)->((subset A B)->(relation_of2_as_subset D C B))))))). % 0.36/0.52 Proof. % 0.36/0.52 assert (zenon_L1_ : forall (zenon_TA_p : zenon_U) (zenon_TC_q : zenon_U) (zenon_TD_r : zenon_U), (relation_of2 zenon_TD_r zenon_TC_q zenon_TA_p) -> (~(relation_of2_as_subset zenon_TD_r zenon_TC_q zenon_TA_p)) -> False). % 0.36/0.52 do 3 intro. intros zenon_Hd zenon_He. % 0.36/0.52 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12. % 0.36/0.52 generalize (zenon_H12 zenon_TA_p). zenon_intro zenon_H13. % 0.36/0.52 generalize (zenon_H13 zenon_TD_r). zenon_intro zenon_H14. % 0.36/0.52 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_He; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_Hd ]. % 0.36/0.52 exact (zenon_H16 zenon_Hd). % 0.36/0.52 exact (zenon_He zenon_H15). % 0.36/0.52 (* end of lemma zenon_L1_ *) % 0.36/0.52 assert (zenon_L2_ : forall (zenon_TB_z : zenon_U) (zenon_TC_q : zenon_U) (zenon_TD_r : zenon_U), (relation_of2_as_subset zenon_TD_r zenon_TC_q zenon_TB_z) -> (~(relation_of2 zenon_TD_r zenon_TC_q zenon_TB_z)) -> False). % 0.36/0.53 do 3 intro. intros zenon_H17 zenon_H18. % 0.36/0.53 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12. % 0.36/0.53 generalize (zenon_H12 zenon_TB_z). zenon_intro zenon_H1a. % 0.36/0.53 generalize (zenon_H1a zenon_TD_r). zenon_intro zenon_H1b. % 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H1c ]. % 0.36/0.53 exact (zenon_H1d zenon_H17). % 0.36/0.53 exact (zenon_H18 zenon_H1c). % 0.36/0.53 (* end of lemma zenon_L2_ *) % 0.36/0.53 apply NNPP. intro zenon_G. % 0.36/0.53 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((subset x y)->((subset y z)->(subset x z))))))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.36/0.53 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((relation_of2_as_subset D C A)->((subset A B)->(relation_of2_as_subset D C B))))))) zenon_G); [ zenon_intro zenon_H20; idtac ]. % 0.36/0.53 elim zenon_H20. zenon_intro zenon_TA_p. zenon_intro zenon_H21. % 0.36/0.53 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((relation_of2_as_subset D C zenon_TA_p)->((subset zenon_TA_p B)->(relation_of2_as_subset D C B)))))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.36/0.53 elim zenon_H22. zenon_intro zenon_TB_z. zenon_intro zenon_H23. % 0.36/0.53 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((relation_of2_as_subset D C zenon_TA_p)->((subset zenon_TA_p zenon_TB_z)->(relation_of2_as_subset D C zenon_TB_z))))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 0.36/0.53 elim zenon_H24. zenon_intro zenon_TC_q. zenon_intro zenon_H25. % 0.36/0.53 apply (zenon_notallex_s (fun D : zenon_U => ((relation_of2_as_subset D zenon_TC_q zenon_TA_p)->((subset zenon_TA_p zenon_TB_z)->(relation_of2_as_subset D zenon_TC_q zenon_TB_z)))) zenon_H25); [ zenon_intro zenon_H26; idtac ]. % 0.36/0.53 elim zenon_H26. zenon_intro zenon_TD_r. zenon_intro zenon_H27. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H15. zenon_intro zenon_H28. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H29. zenon_intro zenon_H1d. % 0.36/0.53 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12. % 0.36/0.53 generalize (zenon_H12 zenon_TA_p). zenon_intro zenon_H13. % 0.36/0.53 generalize (zenon_H13 zenon_TD_r). zenon_intro zenon_H14. % 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_He; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_Hd ]. % 0.36/0.53 exact (zenon_He zenon_H15). % 0.36/0.53 generalize (redefinition_m2_relset_1 zenon_TC_q). zenon_intro zenon_H12. % 0.36/0.53 generalize (zenon_H12 zenon_TB_z). zenon_intro zenon_H1a. % 0.36/0.53 generalize (zenon_H1a zenon_TD_r). zenon_intro zenon_H1b. % 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1d; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H1c ]. % 0.36/0.53 generalize (t14_relset_1 zenon_TA_p). zenon_intro zenon_H2a. % 0.36/0.53 generalize (zenon_H2a zenon_TB_z). zenon_intro zenon_H2b. % 0.36/0.53 generalize (zenon_H2b zenon_TC_q). zenon_intro zenon_H2c. % 0.36/0.53 generalize (zenon_H2c zenon_TD_r). zenon_intro zenon_H2d. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_He | zenon_intro zenon_H2e ]. % 0.36/0.53 apply (zenon_L1_ zenon_TA_p zenon_TC_q zenon_TD_r); trivial. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2f | zenon_intro zenon_H17 ]. % 0.36/0.53 elim (classic ((~((relation_rng zenon_TD_r) = zenon_TA_p))/\(~(subset (relation_rng zenon_TD_r) zenon_TA_p)))); [ zenon_intro zenon_H30 | zenon_intro zenon_H31 ]. % 0.36/0.53 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.36/0.53 generalize (t12_relset_1 zenon_TC_q). zenon_intro zenon_H34. % 0.36/0.53 generalize (zenon_H34 zenon_TA_p). zenon_intro zenon_H35. % 0.36/0.53 generalize (zenon_H35 zenon_TD_r). zenon_intro zenon_H36. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_He | zenon_intro zenon_H37 ]. % 0.36/0.53 apply (zenon_L1_ zenon_TA_p zenon_TC_q zenon_TD_r); trivial. % 0.36/0.53 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.36/0.53 exact (zenon_H32 zenon_H38). % 0.36/0.53 cut ((subset zenon_TA_p zenon_TB_z) = (subset (relation_rng zenon_TD_r) zenon_TB_z)). % 0.36/0.53 intro zenon_D_pnotp. % 0.36/0.53 apply zenon_H2f. % 0.36/0.53 rewrite <- zenon_D_pnotp. % 0.36/0.53 exact zenon_H29. % 0.36/0.53 cut ((zenon_TB_z = zenon_TB_z)); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 0.36/0.53 cut ((zenon_TA_p = (relation_rng zenon_TD_r))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 0.36/0.53 congruence. % 0.36/0.53 apply (zenon_notand_s _ _ zenon_H31); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.36/0.53 apply zenon_H3d. zenon_intro zenon_H3e. % 0.36/0.53 elim (classic ((relation_rng zenon_TD_r) = (relation_rng zenon_TD_r))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 0.36/0.53 cut (((relation_rng zenon_TD_r) = (relation_rng zenon_TD_r)) = (zenon_TA_p = (relation_rng zenon_TD_r))). % 0.36/0.53 intro zenon_D_pnotp. % 0.36/0.53 apply zenon_H3b. % 0.36/0.53 rewrite <- zenon_D_pnotp. % 0.36/0.53 exact zenon_H3f. % 0.36/0.53 cut (((relation_rng zenon_TD_r) = (relation_rng zenon_TD_r))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 0.36/0.53 cut (((relation_rng zenon_TD_r) = zenon_TA_p)); [idtac | apply NNPP; zenon_intro zenon_H33]. % 0.36/0.53 congruence. % 0.36/0.53 exact (zenon_H33 zenon_H3e). % 0.36/0.53 apply zenon_H40. apply refl_equal. % 0.36/0.53 apply zenon_H40. apply refl_equal. % 0.36/0.53 apply zenon_H3c. zenon_intro zenon_H38. % 0.36/0.53 generalize (zenon_H1e (relation_rng zenon_TD_r)). zenon_intro zenon_H41. % 0.36/0.53 generalize (zenon_H41 zenon_TA_p). zenon_intro zenon_H42. % 0.36/0.53 generalize (zenon_H42 zenon_TB_z). zenon_intro zenon_H43. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H32 | zenon_intro zenon_H44 ]. % 0.36/0.53 exact (zenon_H32 zenon_H38). % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.36/0.53 exact (zenon_H46 zenon_H29). % 0.36/0.53 exact (zenon_H2f zenon_H45). % 0.36/0.53 apply zenon_H3a. apply refl_equal. % 0.36/0.53 apply (zenon_L2_ zenon_TB_z zenon_TC_q zenon_TD_r); trivial. % 0.36/0.53 exact (zenon_H1d zenon_H17). % 0.36/0.53 apply zenon_H1f. zenon_intro zenon_Tx_ct. apply NNPP. zenon_intro zenon_H48. % 0.36/0.53 apply zenon_H48. zenon_intro zenon_Ty_cv. apply NNPP. zenon_intro zenon_H4a. % 0.36/0.53 apply zenon_H4a. zenon_intro zenon_Tz_cx. apply NNPP. zenon_intro zenon_H4c. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.36/0.53 generalize (t1_xboole_1 zenon_Tx_ct). zenon_intro zenon_H51. % 0.36/0.53 generalize (zenon_H51 zenon_Ty_cv). zenon_intro zenon_H52. % 0.36/0.53 generalize (zenon_H52 zenon_Tz_cx). zenon_intro zenon_H53. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.36/0.53 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.36/0.53 exact (zenon_H57 zenon_H4e). % 0.36/0.53 exact (zenon_H56 zenon_H50). % 0.36/0.53 exact (zenon_H4f zenon_H54). % 0.36/0.53 Qed. % 0.36/0.53 % SZS output end Proof % 0.36/0.53 (* END-PROOF *) % 0.36/0.53 nodes searched: 1481 % 0.36/0.53 max branch formulas: 457 % 0.36/0.53 proof nodes created: 136 % 0.36/0.53 formulas created: 3413 % 0.36/0.53 %------------------------------------------------------------------------------