%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0. % 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 06:32:23 EDT 2022 % Result : Theorem 0.42s 0.59s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.14 % Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0. % 0.13/0.15 % Command : run_zenon %s %d % 0.15/0.36 % Computer : n017.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Sun Jul 10 12:37:48 EDT 2022 % 0.15/0.37 % CPUTime : % 0.42/0.59 (* PROOF-FOUND *) % 0.42/0.59 % SZS status Theorem % 0.42/0.59 (* BEGIN-PROOF *) % 0.42/0.59 % SZS output start Proof % 0.42/0.59 Theorem prove_union_subset : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset D C))->(subset (union B D) C))))). % 0.42/0.59 Proof. % 0.42/0.59 apply NNPP. intro zenon_G. % 0.42/0.59 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset D C))->(subset (union B D) C))))) zenon_G); [ zenon_intro zenon_H6; idtac ]. % 0.42/0.59 elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8. % 0.42/0.59 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_h C)/\(subset D C))->(subset (union zenon_TB_h D) C)))) zenon_H8); [ zenon_intro zenon_H9; idtac ]. % 0.42/0.59 elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb. % 0.42/0.59 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_h zenon_TC_k)/\(subset D zenon_TC_k))->(subset (union zenon_TB_h D) zenon_TC_k))) zenon_Hb); [ zenon_intro zenon_Hc; idtac ]. % 0.42/0.59 elim zenon_Hc. zenon_intro zenon_TD_n. zenon_intro zenon_He. % 0.42/0.59 apply (zenon_notimply_s _ _ zenon_He). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.42/0.59 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.42/0.59 generalize (subset_defn zenon_TB_h). zenon_intro zenon_H13. % 0.42/0.59 generalize (zenon_H13 zenon_TC_k). zenon_intro zenon_H14. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_H12; zenon_intro zenon_H15 ]. % 0.42/0.59 exact (zenon_H17 zenon_H12). % 0.42/0.59 generalize (subset_defn zenon_TD_n). zenon_intro zenon_H18. % 0.42/0.59 generalize (zenon_H18 zenon_TC_k). zenon_intro zenon_H19. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H11; zenon_intro zenon_H1a ]. % 0.42/0.59 exact (zenon_H1c zenon_H11). % 0.42/0.59 generalize (subset_defn (union zenon_TB_h zenon_TD_n)). zenon_intro zenon_H1d. % 0.42/0.59 generalize (zenon_H1d zenon_TC_k). zenon_intro zenon_H1e. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_Hf; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H1f ]. % 0.42/0.59 apply (zenon_notallex_s (fun D : zenon_U => ((member D (union zenon_TB_h zenon_TD_n))->(member D zenon_TC_k))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.42/0.59 elim zenon_H22. zenon_intro zenon_TD_bj. zenon_intro zenon_H24. % 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.42/0.59 generalize (zenon_H15 zenon_TD_bj). zenon_intro zenon_H27. % 0.42/0.59 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.42/0.59 generalize (zenon_H1a zenon_TD_bj). zenon_intro zenon_H2a. % 0.42/0.59 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2b | zenon_intro zenon_H28 ]. % 0.42/0.59 generalize (commutativity_of_union zenon_TD_n). zenon_intro zenon_H2c. % 0.42/0.59 generalize (union_defn zenon_TD_n). zenon_intro zenon_H2d. % 0.42/0.59 generalize (zenon_H2d zenon_TB_h). zenon_intro zenon_H2e. % 0.42/0.59 generalize (zenon_H2c zenon_TB_h). zenon_intro zenon_H2f. % 0.42/0.59 generalize (zenon_H2e zenon_TD_bj). zenon_intro zenon_H30. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H34; zenon_intro zenon_H33 | zenon_intro zenon_H32; zenon_intro zenon_H31 ]. % 0.42/0.59 cut ((member zenon_TD_bj (union zenon_TB_h zenon_TD_n)) = (member zenon_TD_bj (union zenon_TD_n zenon_TB_h))). % 0.42/0.59 intro zenon_D_pnotp. % 0.42/0.59 apply zenon_H34. % 0.42/0.59 rewrite <- zenon_D_pnotp. % 0.42/0.59 exact zenon_H26. % 0.42/0.59 cut (((union zenon_TB_h zenon_TD_n) = (union zenon_TD_n zenon_TB_h))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 0.42/0.59 cut ((zenon_TD_bj = zenon_TD_bj)); [idtac | apply NNPP; zenon_intro zenon_H36]. % 0.42/0.59 congruence. % 0.42/0.59 apply zenon_H36. apply refl_equal. % 0.42/0.59 apply zenon_H35. apply sym_equal. exact zenon_H2f. % 0.42/0.59 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.42/0.59 exact (zenon_H2b zenon_H38). % 0.42/0.59 exact (zenon_H29 zenon_H37). % 0.42/0.59 exact (zenon_H25 zenon_H28). % 0.42/0.59 exact (zenon_H25 zenon_H28). % 0.42/0.59 exact (zenon_Hf zenon_H20). % 0.42/0.59 Qed. % 0.42/0.59 % SZS output end Proof % 0.42/0.59 (* END-PROOF *) % 0.42/0.59 nodes searched: 812 % 0.42/0.59 max branch formulas: 371 % 0.42/0.59 proof nodes created: 84 % 0.42/0.59 formulas created: 3590 % 0.42/0.59 %------------------------------------------------------------------------------