%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 06:37:35 EDT 2022 % Result : Theorem 0.70s 0.88s % Output : Proof 0.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SET632+3 : TPTP v8.1.0. Released v2.2.0. % 0.04/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n012.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 13:15:13 EDT 2022 % 0.12/0.33 % CPUTime : % 0.70/0.88 (* PROOF-FOUND *) % 0.70/0.88 % SZS status Theorem % 0.70/0.88 (* BEGIN-PROOF *) % 0.70/0.88 % SZS output start Proof % 0.70/0.88 Theorem prove_th114 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\((subset B D)/\(disjoint C D)))->(B = (empty_set)))))). % 0.70/0.88 Proof. % 0.70/0.88 assert (zenon_L1_ : forall (zenon_TD_m : zenon_U) (zenon_TD_n : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TD_n))) -> (member zenon_TD_m zenon_TB_o) -> (~(member zenon_TD_m zenon_TD_n)) -> False). % 0.70/0.88 do 3 intro. intros zenon_H9 zenon_Ha zenon_Hb. % 0.70/0.88 generalize (zenon_H9 zenon_TD_m). zenon_intro zenon_Hf. % 0.70/0.88 apply (zenon_imply_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.70/0.88 exact (zenon_H11 zenon_Ha). % 0.70/0.88 exact (zenon_Hb zenon_H10). % 0.70/0.88 (* end of lemma zenon_L1_ *) % 0.70/0.88 assert (zenon_L2_ : forall (zenon_TB_o : zenon_U), (~(subset (empty_set) zenon_TB_o)) -> False). % 0.70/0.88 do 1 intro. intros zenon_H12. % 0.70/0.88 generalize (subset_defn (empty_set)). zenon_intro zenon_H13. % 0.70/0.88 generalize (zenon_H13 zenon_TB_o). zenon_intro zenon_H14. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H12; zenon_intro zenon_H17 | zenon_intro zenon_H16; zenon_intro zenon_H15 ]. % 0.70/0.88 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D zenon_TB_o))) zenon_H17); [ zenon_intro zenon_H18; idtac ]. % 0.70/0.88 elim zenon_H18. zenon_intro zenon_TD_z. zenon_intro zenon_H1a. % 0.70/0.88 apply (zenon_notimply_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.70/0.88 generalize (empty_set_defn zenon_TD_z). zenon_intro zenon_H1d. % 0.70/0.88 exact (zenon_H1d zenon_H1c). % 0.70/0.88 exact (zenon_H12 zenon_H16). % 0.70/0.88 (* end of lemma zenon_L2_ *) % 0.70/0.88 apply NNPP. intro zenon_G. % 0.70/0.88 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\((subset B D)/\(disjoint C D)))->(B = (empty_set)))))) zenon_G); [ zenon_intro zenon_H1e; idtac ]. % 0.70/0.88 elim zenon_H1e. zenon_intro zenon_TB_o. zenon_intro zenon_H1f. % 0.70/0.88 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_o C)/\((subset zenon_TB_o D)/\(disjoint C D)))->(zenon_TB_o = (empty_set))))) zenon_H1f); [ zenon_intro zenon_H20; idtac ]. % 0.70/0.88 elim zenon_H20. zenon_intro zenon_TC_bh. zenon_intro zenon_H22. % 0.70/0.88 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_o zenon_TC_bh)/\((subset zenon_TB_o D)/\(disjoint zenon_TC_bh D)))->(zenon_TB_o = (empty_set)))) zenon_H22); [ zenon_intro zenon_H23; idtac ]. % 0.70/0.88 elim zenon_H23. zenon_intro zenon_TD_n. zenon_intro zenon_H24. % 0.70/0.88 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.70/0.88 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.70/0.88 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.70/0.88 generalize (subset_defn zenon_TB_o). zenon_intro zenon_H2b. % 0.70/0.88 generalize (zenon_H2b zenon_TC_bh). zenon_intro zenon_H2c. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H28; zenon_intro zenon_H2d ]. % 0.70/0.88 exact (zenon_H2f zenon_H28). % 0.70/0.88 generalize (subset_defn zenon_TB_o). zenon_intro zenon_H2b. % 0.70/0.88 generalize (zenon_H2b zenon_TD_n). zenon_intro zenon_H30. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H32; zenon_intro zenon_H31 | zenon_intro zenon_H2a; zenon_intro zenon_H9 ]. % 0.70/0.88 exact (zenon_H32 zenon_H2a). % 0.70/0.88 generalize (disjoint_defn zenon_TC_bh). zenon_intro zenon_H33. % 0.70/0.88 generalize (zenon_H33 zenon_TD_n). zenon_intro zenon_H34. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H29; zenon_intro zenon_H35 ]. % 0.70/0.88 exact (zenon_H37 zenon_H29). % 0.70/0.88 generalize (intersect_defn zenon_TC_bh). zenon_intro zenon_H38. % 0.70/0.88 generalize (zenon_H38 zenon_TD_n). zenon_intro zenon_H39. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H35; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H3a ]. % 0.70/0.88 generalize (equal_defn zenon_TB_o). zenon_intro zenon_H3d. % 0.70/0.88 generalize (zenon_H3d (empty_set)). zenon_intro zenon_H3e. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H25; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ]. % 0.70/0.88 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H42 | zenon_intro zenon_H12 ]. % 0.70/0.88 generalize (subset_defn zenon_TB_o). zenon_intro zenon_H2b. % 0.70/0.88 generalize (zenon_H2b (empty_set)). zenon_intro zenon_H43. % 0.70/0.88 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H42; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 0.70/0.88 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_o)->(member D (empty_set)))) zenon_H46); [ zenon_intro zenon_H47; idtac ]. % 0.70/0.88 elim zenon_H47. zenon_intro zenon_TD_m. zenon_intro zenon_H48. % 0.70/0.88 apply (zenon_notimply_s _ _ zenon_H48). zenon_intro zenon_Ha. zenon_intro zenon_H49. % 0.70/0.88 generalize (zenon_H2d zenon_TD_m). zenon_intro zenon_H4a. % 0.70/0.88 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H11 | zenon_intro zenon_H4b ]. % 0.70/0.88 exact (zenon_H11 zenon_Ha). % 0.70/0.88 apply zenon_H3c. exists zenon_TD_m. apply NNPP. zenon_intro zenon_H4c. % 0.70/0.88 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H4d | zenon_intro zenon_Hb ]. % 0.70/0.88 exact (zenon_H4d zenon_H4b). % 0.70/0.88 apply (zenon_L1_ zenon_TD_m zenon_TD_n zenon_TB_o); trivial. % 0.70/0.88 exact (zenon_H42 zenon_H45). % 0.70/0.88 apply (zenon_L2_ zenon_TB_o); trivial. % 0.70/0.88 exact (zenon_H25 zenon_H40). % 0.70/0.88 exact (zenon_H35 zenon_H3b). % 0.70/0.88 Qed. % 0.70/0.88 % SZS output end Proof % 0.70/0.88 (* END-PROOF *) % 0.70/0.88 nodes searched: 17161 % 0.70/0.88 max branch formulas: 1380 % 0.70/0.88 proof nodes created: 1683 % 0.70/0.88 formulas created: 33614 % 0.70/0.88 %------------------------------------------------------------------------------