%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 06:34:43 EDT 2022 % Result : Theorem 0.92s 1.08s % Output : Proof 0.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n005.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 : Sun Jul 10 21:58:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.92/1.08 (* PROOF-FOUND *) % 0.92/1.08 % SZS status Theorem % 0.92/1.08 (* BEGIN-PROOF *) % 0.92/1.08 % SZS output start Proof % 0.92/1.08 Theorem prove_subset_intersection : (forall B : zenon_U, (forall C : zenon_U, ((subset B C)->((intersection B C) = B)))). % 0.92/1.08 Proof. % 0.92/1.08 apply NNPP. intro zenon_G. % 0.92/1.08 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((subset B C)->((intersection B C) = B)))) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 0.92/1.08 elim zenon_H8. zenon_intro zenon_TB_j. zenon_intro zenon_Ha. % 0.92/1.08 apply (zenon_notallex_s (fun C : zenon_U => ((subset zenon_TB_j C)->((intersection zenon_TB_j C) = zenon_TB_j))) zenon_Ha); [ zenon_intro zenon_Hb; idtac ]. % 0.92/1.08 elim zenon_Hb. zenon_intro zenon_TC_m. zenon_intro zenon_Hd. % 0.92/1.08 apply (zenon_notimply_s _ _ zenon_Hd). zenon_intro zenon_Hf. zenon_intro zenon_He. % 0.92/1.08 generalize (subset_defn zenon_TB_j). zenon_intro zenon_H10. % 0.92/1.08 generalize (zenon_H10 zenon_TC_m). zenon_intro zenon_H11. % 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H11); [ zenon_intro zenon_H14; zenon_intro zenon_H13 | zenon_intro zenon_Hf; zenon_intro zenon_H12 ]. % 0.92/1.08 exact (zenon_H14 zenon_Hf). % 0.92/1.08 generalize (commutativity_of_intersection zenon_TC_m). zenon_intro zenon_H15. % 0.92/1.08 generalize (intersection_defn zenon_TC_m). zenon_intro zenon_H16. % 0.92/1.08 generalize (equal_defn zenon_TB_j). zenon_intro zenon_H17. % 0.92/1.08 generalize (zenon_H15 zenon_TB_j). zenon_intro zenon_H18. % 0.92/1.08 generalize (zenon_H16 zenon_TB_j). zenon_intro zenon_H19. % 0.92/1.08 elim (classic (zenon_TB_j = zenon_TB_j)); [ zenon_intro zenon_H1a | zenon_intro zenon_H1b ]. % 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j) = ((intersection zenon_TB_j zenon_TC_m) = zenon_TB_j)). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_He. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H1a. % 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j)); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.92/1.08 cut ((zenon_TB_j = (intersection zenon_TB_j zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 0.92/1.08 congruence. % 0.92/1.08 cut (((intersection zenon_TC_m zenon_TB_j) = (intersection zenon_TB_j zenon_TC_m)) = (zenon_TB_j = (intersection zenon_TB_j zenon_TC_m))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H1c. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H18. % 0.92/1.08 cut (((intersection zenon_TB_j zenon_TC_m) = (intersection zenon_TB_j zenon_TC_m))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 0.92/1.08 cut (((intersection zenon_TC_m zenon_TB_j) = zenon_TB_j)); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 0.92/1.08 congruence. % 0.92/1.08 elim (classic (zenon_TB_j = zenon_TB_j)); [ zenon_intro zenon_H1a | zenon_intro zenon_H1b ]. % 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j) = ((intersection zenon_TC_m zenon_TB_j) = zenon_TB_j)). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H1e. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H1a. % 0.92/1.08 cut ((zenon_TB_j = zenon_TB_j)); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.92/1.08 cut ((zenon_TB_j = (intersection zenon_TC_m zenon_TB_j))); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 0.92/1.08 congruence. % 0.92/1.08 generalize (zenon_H17 (intersection zenon_TC_m zenon_TB_j)). zenon_intro zenon_H20. % 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1f; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.92/1.08 generalize (subset_defn zenon_TB_j). zenon_intro zenon_H10. % 0.92/1.08 generalize (zenon_H10 (intersection zenon_TC_m zenon_TB_j)). zenon_intro zenon_H26. % 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H25; zenon_intro zenon_H29 | zenon_intro zenon_H28; zenon_intro zenon_H27 ]. % 0.92/1.08 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_j)->(member D (intersection zenon_TC_m zenon_TB_j)))) zenon_H29); [ zenon_intro zenon_H2a; idtac ]. % 0.92/1.08 elim zenon_H2a. zenon_intro zenon_TD_br. zenon_intro zenon_H2c. % 0.92/1.08 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.92/1.08 generalize (zenon_H19 zenon_TD_br). zenon_intro zenon_H2f. % 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2d; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.92/1.08 generalize (zenon_H12 zenon_TD_br). zenon_intro zenon_H35. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H33 | zenon_intro zenon_H36 ]. % 0.92/1.08 exact (zenon_H33 zenon_H2e). % 0.92/1.08 exact (zenon_H34 zenon_H36). % 0.92/1.08 exact (zenon_H33 zenon_H2e). % 0.92/1.08 exact (zenon_H2d zenon_H31). % 0.92/1.08 exact (zenon_H25 zenon_H28). % 0.92/1.08 generalize (subset_defn (intersection zenon_TC_m zenon_TB_j)). zenon_intro zenon_H37. % 0.92/1.08 generalize (zenon_H37 zenon_TB_j). zenon_intro zenon_H38. % 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H24; zenon_intro zenon_H3b | zenon_intro zenon_H3a; zenon_intro zenon_H39 ]. % 0.92/1.08 apply (zenon_notallex_s (fun D : zenon_U => ((member D (intersection zenon_TC_m zenon_TB_j))->(member D zenon_TB_j))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ]. % 0.92/1.08 elim zenon_H3c. zenon_intro zenon_TD_cj. zenon_intro zenon_H3e. % 0.92/1.08 apply (zenon_notimply_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.92/1.08 generalize (zenon_H19 zenon_TD_cj). zenon_intro zenon_H41. % 0.92/1.08 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H40; zenon_intro zenon_H42 ]. % 0.92/1.08 exact (zenon_H44 zenon_H40). % 0.92/1.08 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H46. zenon_intro zenon_H45. % 0.92/1.08 exact (zenon_H3f zenon_H45). % 0.92/1.08 exact (zenon_H24 zenon_H3a). % 0.92/1.08 exact (zenon_H1f zenon_H22). % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 apply zenon_H1d. apply refl_equal. % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 Qed. % 0.92/1.08 % SZS output end Proof % 0.92/1.08 (* END-PROOF *) % 0.92/1.08 nodes searched: 18882 % 0.92/1.08 max branch formulas: 1946 % 0.92/1.08 proof nodes created: 1009 % 0.92/1.08 formulas created: 38648 % 0.92/1.08 %------------------------------------------------------------------------------