%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 16:01:12 EDT 2022 % Result : Theorem 1.38s 1.55s % Output : Proof 1.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Mon Jun 20 06:32:24 EDT 2022 % 0.20/0.34 % CPUTime : % 1.38/1.55 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 1.38/1.55 (* PROOF-FOUND *) % 1.38/1.55 % SZS status Theorem % 1.38/1.55 (* BEGIN-PROOF *) % 1.38/1.55 % SZS output start Proof % 1.38/1.55 Theorem l40_tops_1 : (forall A : zenon_U, (((~(empty_carrier A))/\(one_sorted_str A))->(forall B : zenon_U, ((element B (powerset (the_carrier A)))->(forall C : zenon_U, ((element C (the_carrier A))->((in C (subset_complement (the_carrier A) B))<->(~(in C B))))))))). % 1.38/1.55 Proof. % 1.38/1.55 assert (zenon_L1_ : forall (zenon_TA_bq : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset (the_carrier zenon_TA_bq) (empty_set))) -> ((the_carrier zenon_TA_bq) = (empty_set)) -> False). % 1.38/1.55 do 1 intro. intros zenon_H27 zenon_H28 zenon_H29. % 1.38/1.55 generalize (zenon_H27 (the_carrier zenon_TA_bq)). zenon_intro zenon_H2b. % 1.38/1.55 cut ((subset (the_carrier zenon_TA_bq) (the_carrier zenon_TA_bq)) = (subset (the_carrier zenon_TA_bq) (empty_set))). % 1.38/1.55 intro zenon_D_pnotp. % 1.38/1.55 apply zenon_H28. % 1.38/1.55 rewrite <- zenon_D_pnotp. % 1.38/1.55 exact zenon_H2b. % 1.38/1.55 cut (((the_carrier zenon_TA_bq) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 1.38/1.55 cut (((the_carrier zenon_TA_bq) = (the_carrier zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 1.38/1.55 congruence. % 1.38/1.55 apply zenon_H2d. apply refl_equal. % 1.38/1.55 exact (zenon_H2c zenon_H29). % 1.38/1.55 (* end of lemma zenon_L1_ *) % 1.38/1.55 assert (zenon_L2_ : forall (zenon_TA_bq : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(element (the_carrier zenon_TA_bq) (powerset (empty_set)))) -> ((the_carrier zenon_TA_bq) = (empty_set)) -> False). % 1.38/1.55 do 1 intro. intros zenon_H27 zenon_H2e zenon_H29. % 1.38/1.55 generalize (t3_subset (the_carrier zenon_TA_bq)). zenon_intro zenon_H2f. % 1.38/1.55 generalize (zenon_H2f (empty_set)). zenon_intro zenon_H30. % 1.38/1.55 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H2e; zenon_intro zenon_H28 | zenon_intro zenon_H32; zenon_intro zenon_H31 ]. % 1.38/1.55 apply (zenon_L1_ zenon_TA_bq); trivial. % 1.38/1.55 exact (zenon_H2e zenon_H32). % 1.38/1.55 (* end of lemma zenon_L2_ *) % 1.38/1.55 assert (zenon_L3_ : forall (zenon_TC_ce : zenon_U) (zenon_TB_cf : zenon_U) (zenon_TA_bq : zenon_U), (forall B : zenon_U, ((element B (powerset (the_carrier zenon_TA_bq)))->(forall C : zenon_U, ((element C (the_carrier zenon_TA_bq))->((~(in C B))->(in C (subset_complement (the_carrier zenon_TA_bq) B))))))) -> (element zenon_TB_cf (powerset (the_carrier zenon_TA_bq))) -> (element zenon_TC_ce (the_carrier zenon_TA_bq)) -> (~(in zenon_TC_ce zenon_TB_cf)) -> (~(in zenon_TC_ce (subset_complement (the_carrier zenon_TA_bq) zenon_TB_cf))) -> False). % 1.38/1.55 do 3 intro. intros zenon_H33 zenon_H34 zenon_H35 zenon_H36 zenon_H37. % 1.38/1.55 generalize (zenon_H33 zenon_TB_cf). zenon_intro zenon_H3a. % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 1.38/1.55 exact (zenon_H3c zenon_H34). % 1.38/1.55 generalize (zenon_H3b zenon_TC_ce). zenon_intro zenon_H3d. % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 1.38/1.55 exact (zenon_H3f zenon_H35). % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 1.38/1.55 exact (zenon_H41 zenon_H36). % 1.38/1.55 exact (zenon_H37 zenon_H40). % 1.38/1.55 (* end of lemma zenon_L3_ *) % 1.38/1.55 apply NNPP. intro zenon_G. % 1.38/1.55 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H27 | zenon_intro zenon_H42 ]. % 1.38/1.55 apply (zenon_and_s _ _ fc6_membered). zenon_intro zenon_H44. zenon_intro zenon_H43. % 1.38/1.55 apply (zenon_notallex_s (fun A : zenon_U => (((~(empty_carrier A))/\(one_sorted_str A))->(forall B : zenon_U, ((element B (powerset (the_carrier A)))->(forall C : zenon_U, ((element C (the_carrier A))->((in C (subset_complement (the_carrier A) B))<->(~(in C B))))))))) zenon_G); [ zenon_intro zenon_H45; idtac ]. % 1.38/1.55 elim zenon_H45. zenon_intro zenon_TA_bq. zenon_intro zenon_H46. % 1.38/1.55 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 1.38/1.55 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 1.38/1.55 apply (zenon_notallex_s (fun B : zenon_U => ((element B (powerset (the_carrier zenon_TA_bq)))->(forall C : zenon_U, ((element C (the_carrier zenon_TA_bq))->((in C (subset_complement (the_carrier zenon_TA_bq) B))<->(~(in C B))))))) zenon_H47); [ zenon_intro zenon_H4b; idtac ]. % 1.38/1.55 elim zenon_H4b. zenon_intro zenon_TB_cf. zenon_intro zenon_H4c. % 1.38/1.55 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H34. zenon_intro zenon_H4d. % 1.38/1.55 apply (zenon_notallex_s (fun C : zenon_U => ((element C (the_carrier zenon_TA_bq))->((in C (subset_complement (the_carrier zenon_TA_bq) zenon_TB_cf))<->(~(in C zenon_TB_cf))))) zenon_H4d); [ zenon_intro zenon_H4e; idtac ]. % 1.38/1.55 elim zenon_H4e. zenon_intro zenon_TC_ce. zenon_intro zenon_H4f. % 1.38/1.55 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H35. zenon_intro zenon_H50. % 1.38/1.55 apply (zenon_notequiv_s _ _ zenon_H50); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H40; zenon_intro zenon_H41 ]. % 1.38/1.55 generalize (t2_subset zenon_TC_ce). zenon_intro zenon_H51. % 1.38/1.55 generalize (t5_subset zenon_TC_ce). zenon_intro zenon_H52. % 1.38/1.55 generalize (t50_subset_1 (the_carrier zenon_TA_bq)). zenon_intro zenon_H53. % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H54 | zenon_intro zenon_H33 ]. % 1.38/1.55 apply zenon_H54. zenon_intro zenon_H29. % 1.38/1.55 generalize (fc1_struct_0 zenon_TA_bq). zenon_intro zenon_H55. % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 1.38/1.55 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 1.38/1.55 exact (zenon_H59 zenon_H4a). % 1.38/1.55 exact (zenon_H58 zenon_H49). % 1.38/1.55 generalize (zenon_H51 (the_carrier zenon_TA_bq)). zenon_intro zenon_H5a. % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H3f | zenon_intro zenon_H5b ]. % 1.38/1.55 exact (zenon_H3f zenon_H35). % 1.38/1.55 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 1.38/1.55 exact (zenon_H56 zenon_H5d). % 1.38/1.55 generalize (zenon_H52 (the_carrier zenon_TA_bq)). zenon_intro zenon_H5e. % 1.38/1.55 generalize (zenon_H5e (empty_set)). zenon_intro zenon_H5f. % 1.38/1.55 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 1.38/1.55 exact (zenon_H61 zenon_H5c). % 1.38/1.55 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H2e | zenon_intro zenon_H62 ]. % 1.38/1.55 apply (zenon_L2_ zenon_TA_bq); trivial. % 1.38/1.55 exact (zenon_H62 zenon_H44). % 1.38/1.55 apply (zenon_L3_ zenon_TC_ce zenon_TB_cf zenon_TA_bq); trivial. % 1.38/1.55 apply zenon_H41. zenon_intro zenon_H63. % 1.38/1.55 generalize (t54_subset_1 (the_carrier zenon_TA_bq)). zenon_intro zenon_H64. % 1.38/1.55 generalize (zenon_H64 zenon_TC_ce). zenon_intro zenon_H65. % 1.38/1.55 generalize (zenon_H65 zenon_TB_cf). zenon_intro zenon_H66. % 1.38/1.55 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H3c | zenon_intro zenon_H67 ]. % 1.38/1.55 exact (zenon_H3c zenon_H34). % 1.38/1.55 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 1.38/1.55 exact (zenon_H37 zenon_H40). % 1.38/1.55 exact (zenon_H36 zenon_H63). % 1.38/1.55 apply zenon_H42. zenon_intro zenon_Tx_ea. apply NNPP. zenon_intro zenon_H69. % 1.38/1.55 generalize (reflexivity_r1_tarski zenon_Tx_ea). zenon_intro zenon_H0. % 1.38/1.55 generalize (zenon_H0 zenon_E). zenon_intro zenon_H6a. % 1.38/1.55 exact (zenon_H69 zenon_H6a). % 1.38/1.55 Qed. % 1.38/1.55 % SZS output end Proof % 1.38/1.55 (* END-PROOF *) % 1.38/1.55 nodes searched: 34311 % 1.38/1.55 max branch formulas: 2685 % 1.38/1.55 proof nodes created: 2376 % 1.38/1.55 formulas created: 84365 % 1.38/1.55 %------------------------------------------------------------------------------