%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU155+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 15:59:47 EDT 2022 % Result : Theorem 13.90s 14.13s % Output : Proof 13.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SEU155+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n028.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 : Mon Jun 20 12:03:46 EDT 2022 % 0.12/0.33 % CPUTime : % 13.90/14.13 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 13.90/14.13 (* PROOF-FOUND *) % 13.90/14.13 % SZS status Theorem % 13.90/14.13 (* BEGIN-PROOF *) % 13.90/14.13 % SZS output start Proof % 13.90/14.13 Theorem l50_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((in A B)->(subset A (union B))))). % 13.90/14.13 Proof. % 13.90/14.13 assert (zenon_L1_ : forall (zenon_TA_j : zenon_U) (zenon_TB_k : zenon_U) (zenon_TC_l : zenon_U), (~(exists D : zenon_U, ((in zenon_TC_l D)/\(in D zenon_TB_k)))) -> (in zenon_TC_l zenon_TA_j) -> (in zenon_TA_j zenon_TB_k) -> False). % 13.90/14.13 do 3 intro. intros zenon_H6 zenon_H7 zenon_H8. % 13.90/14.13 apply zenon_H6. exists zenon_TA_j. apply NNPP. zenon_intro zenon_Hc. % 13.90/14.13 apply (zenon_notand_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 13.90/14.13 exact (zenon_He zenon_H7). % 13.90/14.13 exact (zenon_Hd zenon_H8). % 13.90/14.13 (* end of lemma zenon_L1_ *) % 13.90/14.13 apply NNPP. intro zenon_G. % 13.90/14.13 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((in A B)->(subset A (union B))))) zenon_G); [ zenon_intro zenon_Hf; idtac ]. % 13.90/14.13 elim zenon_Hf. zenon_intro zenon_TA_j. zenon_intro zenon_H10. % 13.90/14.13 apply (zenon_notallex_s (fun B : zenon_U => ((in zenon_TA_j B)->(subset zenon_TA_j (union B)))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 13.90/14.13 elim zenon_H11. zenon_intro zenon_TB_k. zenon_intro zenon_H12. % 13.90/14.13 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H8. zenon_intro zenon_H13. % 13.90/14.13 generalize (d3_tarski zenon_TA_j). zenon_intro zenon_H14. % 13.90/14.13 generalize (zenon_H14 (union zenon_TB_k)). zenon_intro zenon_H15. % 13.90/14.13 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_H13; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 13.90/14.13 apply (zenon_notallex_s (fun C : zenon_U => ((in C zenon_TA_j)->(in C (union zenon_TB_k)))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 13.90/14.13 elim zenon_H19. zenon_intro zenon_TC_l. zenon_intro zenon_H1a. % 13.90/14.13 apply (zenon_notimply_s _ _ zenon_H1a). zenon_intro zenon_H7. zenon_intro zenon_H1b. % 13.90/14.13 generalize (d4_tarski zenon_TB_k). zenon_intro zenon_H1c. % 13.90/14.13 generalize (zenon_H1c (union zenon_TB_k)). zenon_intro zenon_H1d. % 13.90/14.13 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 13.90/14.13 apply zenon_H21. apply refl_equal. % 13.90/14.13 generalize (zenon_H1e zenon_TC_l). zenon_intro zenon_H22. % 13.90/14.13 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H1b; zenon_intro zenon_H6 | zenon_intro zenon_H24; zenon_intro zenon_H23 ]. % 13.90/14.13 apply (zenon_L1_ zenon_TA_j zenon_TB_k zenon_TC_l); trivial. % 13.90/14.13 exact (zenon_H1b zenon_H24). % 13.90/14.13 exact (zenon_H13 zenon_H17). % 13.90/14.13 Qed. % 13.90/14.13 % SZS output end Proof % 13.90/14.13 (* END-PROOF *) % 13.90/14.13 nodes searched: 371871 % 13.90/14.13 max branch formulas: 9106 % 13.90/14.13 proof nodes created: 25630 % 13.90/14.13 formulas created: 1453324 % 13.90/14.13 %------------------------------------------------------------------------------