%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 06:34:50 EDT 2022 % Result : Theorem 0.55s 0.71s % Output : Proof 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET199+3 : TPTP v8.1.0. Released v2.2.0. % 0.00/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n025.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 02:09:31 EDT 2022 % 0.12/0.34 % CPUTime : % 0.55/0.71 (* PROOF-FOUND *) % 0.55/0.71 % SZS status Theorem % 0.55/0.71 (* BEGIN-PROOF *) % 0.55/0.71 % SZS output start Proof % 0.55/0.71 Theorem prove_intersection_of_subsets : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset B D))->(subset B (intersection C D)))))). % 0.55/0.71 Proof. % 0.55/0.71 assert (zenon_L1_ : forall (zenon_TD_j : zenon_U) (zenon_TC_k : zenon_U) (zenon_TD_l : zenon_U), (~(member zenon_TD_l (intersection zenon_TC_k zenon_TD_j))) -> (member zenon_TD_l (intersection zenon_TD_j zenon_TC_k)) -> ((intersection zenon_TD_j zenon_TC_k) = (intersection zenon_TC_k zenon_TD_j)) -> False). % 0.55/0.71 do 3 intro. intros zenon_H6 zenon_H7 zenon_H8. % 0.55/0.71 cut ((member zenon_TD_l (intersection zenon_TD_j zenon_TC_k)) = (member zenon_TD_l (intersection zenon_TC_k zenon_TD_j))). % 0.55/0.71 intro zenon_D_pnotp. % 0.55/0.71 apply zenon_H6. % 0.55/0.71 rewrite <- zenon_D_pnotp. % 0.55/0.71 exact zenon_H7. % 0.55/0.71 cut (((intersection zenon_TD_j zenon_TC_k) = (intersection zenon_TC_k zenon_TD_j))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.55/0.71 cut ((zenon_TD_l = zenon_TD_l)); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 0.55/0.71 congruence. % 0.55/0.71 apply zenon_Hd. apply refl_equal. % 0.55/0.71 exact (zenon_Hc zenon_H8). % 0.55/0.71 (* end of lemma zenon_L1_ *) % 0.55/0.71 apply NNPP. intro zenon_G. % 0.55/0.71 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset B D))->(subset B (intersection C D)))))) zenon_G); [ zenon_intro zenon_He; idtac ]. % 0.55/0.71 elim zenon_He. zenon_intro zenon_TB_p. zenon_intro zenon_H10. % 0.55/0.71 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_p C)/\(subset zenon_TB_p D))->(subset zenon_TB_p (intersection C D))))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 0.55/0.71 elim zenon_H11. zenon_intro zenon_TC_k. zenon_intro zenon_H12. % 0.55/0.71 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_p zenon_TC_k)/\(subset zenon_TB_p D))->(subset zenon_TB_p (intersection zenon_TC_k D)))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 0.55/0.71 elim zenon_H13. zenon_intro zenon_TD_j. zenon_intro zenon_H14. % 0.55/0.71 apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.55/0.71 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.55/0.71 generalize (subset_defn zenon_TB_p). zenon_intro zenon_H19. % 0.55/0.71 generalize (zenon_H19 zenon_TC_k). zenon_intro zenon_H1a. % 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H1d; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H1b ]. % 0.55/0.71 exact (zenon_H1d zenon_H18). % 0.55/0.71 generalize (subset_defn zenon_TB_p). zenon_intro zenon_H19. % 0.55/0.71 generalize (zenon_H19 zenon_TD_j). zenon_intro zenon_H1e. % 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H17; zenon_intro zenon_H1f ]. % 0.55/0.71 exact (zenon_H21 zenon_H17). % 0.55/0.71 generalize (subset_defn zenon_TB_p). zenon_intro zenon_H19. % 0.55/0.71 generalize (zenon_H19 (intersection zenon_TC_k zenon_TD_j)). zenon_intro zenon_H22. % 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H15; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H23 ]. % 0.55/0.71 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_p)->(member D (intersection zenon_TC_k zenon_TD_j)))) zenon_H25); [ zenon_intro zenon_H26; idtac ]. % 0.55/0.71 elim zenon_H26. zenon_intro zenon_TD_l. zenon_intro zenon_H27. % 0.55/0.71 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H28. zenon_intro zenon_H6. % 0.55/0.71 generalize (commutativity_of_intersection zenon_TD_j). zenon_intro zenon_H29. % 0.55/0.71 generalize (zenon_H29 zenon_TC_k). zenon_intro zenon_H8. % 0.55/0.71 generalize (intersection_defn zenon_TD_j). zenon_intro zenon_H2a. % 0.55/0.71 generalize (zenon_H2a zenon_TC_k). zenon_intro zenon_H2b. % 0.55/0.71 generalize (zenon_H2b zenon_TD_l). zenon_intro zenon_H2c. % 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H7; zenon_intro zenon_H2d ]. % 0.55/0.71 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.55/0.71 generalize (zenon_H1f zenon_TD_l). zenon_intro zenon_H32. % 0.55/0.71 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.55/0.71 exact (zenon_H34 zenon_H28). % 0.55/0.71 exact (zenon_H31 zenon_H33). % 0.55/0.71 generalize (zenon_H1b zenon_TD_l). zenon_intro zenon_H35. % 0.55/0.71 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H34 | zenon_intro zenon_H36 ]. % 0.55/0.71 exact (zenon_H34 zenon_H28). % 0.55/0.71 exact (zenon_H30 zenon_H36). % 0.55/0.71 apply (zenon_L1_ zenon_TD_j zenon_TC_k zenon_TD_l); trivial. % 0.55/0.71 exact (zenon_H15 zenon_H24). % 0.55/0.71 Qed. % 0.55/0.71 % SZS output end Proof % 0.55/0.71 (* END-PROOF *) % 0.55/0.71 nodes searched: 7493 % 0.55/0.71 max branch formulas: 1010 % 0.55/0.71 proof nodes created: 508 % 0.55/0.71 formulas created: 13798 % 0.55/0.71 %------------------------------------------------------------------------------