%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 06:37:06 EDT 2022 % Result : Theorem 32.19s 32.46s % Output : Proof 32.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.13 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n024.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 09:53:58 EDT 2022 % 0.13/0.34 % CPUTime : % 32.19/32.46 (* PROOF-FOUND *) % 32.19/32.46 % SZS status Theorem % 32.19/32.46 (* BEGIN-PROOF *) % 32.19/32.46 % SZS output start Proof % 32.19/32.46 Theorem prove_th51 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\((subset B D)/\((intersection C D) = (empty_set))))->(B = (empty_set)))))). % 32.19/32.46 Proof. % 32.19/32.46 assert (zenon_L1_ : forall (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TC_n))) -> (~(subset zenon_TB_o zenon_TC_n)) -> False). % 32.19/32.46 do 2 intro. intros zenon_Hb zenon_Hc. % 32.19/32.46 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf. % 32.19/32.46 generalize (zenon_Hf zenon_TC_n). zenon_intro zenon_H10. % 32.19/32.46 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hc; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_Hb ]. % 32.19/32.46 exact (zenon_H12 zenon_Hb). % 32.19/32.46 exact (zenon_Hc zenon_H11). % 32.19/32.46 (* end of lemma zenon_L1_ *) % 32.19/32.46 assert (zenon_L2_ : forall (zenon_TD_v : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TD_v))) -> (~(subset zenon_TB_o zenon_TD_v)) -> False). % 32.19/32.46 do 2 intro. intros zenon_H13 zenon_H14. % 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf. % 32.19/32.47 generalize (zenon_Hf zenon_TD_v). zenon_intro zenon_H16. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H13 ]. % 32.19/32.47 exact (zenon_H18 zenon_H13). % 32.19/32.47 exact (zenon_H14 zenon_H17). % 32.19/32.47 (* end of lemma zenon_L2_ *) % 32.19/32.47 assert (zenon_L3_ : forall (zenon_TD_bc : zenon_U) (zenon_TD_v : zenon_U) (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D (intersection zenon_TC_n zenon_TD_v)))) -> (member zenon_TD_bc zenon_TB_o) -> (~(member zenon_TD_bc (intersection zenon_TC_n zenon_TD_v))) -> False). % 32.19/32.47 do 4 intro. intros zenon_H19 zenon_H1a zenon_H1b. % 32.19/32.47 generalize (zenon_H19 zenon_TD_bc). zenon_intro zenon_H1d. % 32.19/32.47 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 32.19/32.47 exact (zenon_H1f zenon_H1a). % 32.19/32.47 exact (zenon_H1b zenon_H1e). % 32.19/32.47 (* end of lemma zenon_L3_ *) % 32.19/32.47 assert (zenon_L4_ : forall (zenon_TD_bc : zenon_U) (zenon_TD_v : zenon_U) (zenon_TB_o : zenon_U), (forall D : zenon_U, ((member D zenon_TB_o)->(member D zenon_TD_v))) -> (member zenon_TD_bc zenon_TB_o) -> (~(member zenon_TD_bc zenon_TD_v)) -> False). % 32.19/32.47 do 3 intro. intros zenon_H13 zenon_H1a zenon_H20. % 32.19/32.47 generalize (zenon_H13 zenon_TD_bc). zenon_intro zenon_H21. % 32.19/32.47 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H1f | zenon_intro zenon_H22 ]. % 32.19/32.47 exact (zenon_H1f zenon_H1a). % 32.19/32.47 exact (zenon_H20 zenon_H22). % 32.19/32.47 (* end of lemma zenon_L4_ *) % 32.19/32.47 assert (zenon_L5_ : forall (zenon_TD_v : zenon_U) (zenon_TC_n : zenon_U), (~((intersection (intersection zenon_TC_n zenon_TD_v) zenon_TD_v) = (intersection (empty_set) zenon_TD_v))) -> ((intersection zenon_TC_n zenon_TD_v) = (empty_set)) -> False). % 32.19/32.47 do 2 intro. intros zenon_H23 zenon_H24. % 32.19/32.47 cut ((zenon_TD_v = zenon_TD_v)); [idtac | apply NNPP; zenon_intro zenon_H25]. % 32.19/32.47 cut (((intersection zenon_TC_n zenon_TD_v) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 32.19/32.47 congruence. % 32.19/32.47 exact (zenon_H26 zenon_H24). % 32.19/32.47 apply zenon_H25. apply refl_equal. % 32.19/32.47 (* end of lemma zenon_L5_ *) % 32.19/32.47 assert (zenon_L6_ : forall (zenon_TD_v : zenon_U) (zenon_TD_bc : zenon_U), ((member zenon_TD_bc (empty_set))/\(member zenon_TD_bc zenon_TD_v)) -> (~(member zenon_TD_bc (empty_set))) -> False). % 32.19/32.47 do 2 intro. intros zenon_H27 zenon_H28. % 32.19/32.47 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H22. % 32.19/32.47 exact (zenon_H28 zenon_H29). % 32.19/32.47 (* end of lemma zenon_L6_ *) % 32.19/32.47 assert (zenon_L7_ : forall (zenon_TD_bc : zenon_U), (member zenon_TD_bc (empty_set)) -> False). % 32.19/32.47 do 1 intro. intros zenon_H29. % 32.19/32.47 generalize (empty_set_defn zenon_TD_bc). zenon_intro zenon_H28. % 32.19/32.47 exact (zenon_H28 zenon_H29). % 32.19/32.47 (* end of lemma zenon_L7_ *) % 32.19/32.47 apply NNPP. intro zenon_G. % 32.19/32.47 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\((subset B D)/\((intersection C D) = (empty_set))))->(B = (empty_set)))))) zenon_G); [ zenon_intro zenon_H2a; idtac ]. % 32.19/32.47 elim zenon_H2a. zenon_intro zenon_TB_o. zenon_intro zenon_H2b. % 32.19/32.47 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_o C)/\((subset zenon_TB_o D)/\((intersection C D) = (empty_set))))->(zenon_TB_o = (empty_set))))) zenon_H2b); [ zenon_intro zenon_H2c; idtac ]. % 32.19/32.47 elim zenon_H2c. zenon_intro zenon_TC_n. zenon_intro zenon_H2d. % 32.19/32.47 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_o zenon_TC_n)/\((subset zenon_TB_o D)/\((intersection zenon_TC_n D) = (empty_set))))->(zenon_TB_o = (empty_set)))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 32.19/32.47 elim zenon_H2e. zenon_intro zenon_TD_v. zenon_intro zenon_H2f. % 32.19/32.47 apply (zenon_notimply_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 32.19/32.47 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H11. zenon_intro zenon_H32. % 32.19/32.47 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H17. zenon_intro zenon_H24. % 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf. % 32.19/32.47 generalize (zenon_Hf zenon_TC_n). zenon_intro zenon_H10. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_Hc; zenon_intro zenon_H12 | zenon_intro zenon_H11; zenon_intro zenon_Hb ]. % 32.19/32.47 exact (zenon_Hc zenon_H11). % 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf. % 32.19/32.47 generalize (zenon_Hf zenon_TD_v). zenon_intro zenon_H16. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H14; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H13 ]. % 32.19/32.47 exact (zenon_H14 zenon_H17). % 32.19/32.47 generalize (equal_member_defn (empty_set)). zenon_intro zenon_H33. % 32.19/32.47 generalize (zenon_H33 zenon_TB_o). zenon_intro zenon_H34. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H38; zenon_intro zenon_H37 | zenon_intro zenon_H36; zenon_intro zenon_H35 ]. % 32.19/32.47 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))<->(member D zenon_TB_o))) zenon_H37); [ zenon_intro zenon_H39; idtac ]. % 32.19/32.47 elim zenon_H39. zenon_intro zenon_TD_bc. zenon_intro zenon_H3a. % 32.19/32.47 apply (zenon_notequiv_s _ _ zenon_H3a); [ zenon_intro zenon_H28; zenon_intro zenon_H1a | zenon_intro zenon_H29; zenon_intro zenon_H1f ]. % 32.19/32.47 generalize (intersection_of_subsets zenon_TB_o). zenon_intro zenon_H3b. % 32.19/32.47 generalize (intersection_defn (empty_set)). zenon_intro zenon_H3c. % 32.19/32.47 generalize (zenon_H3b zenon_TC_n). zenon_intro zenon_H3d. % 32.19/32.47 generalize (zenon_H3c zenon_TD_v). zenon_intro zenon_H3e. % 32.19/32.47 generalize (zenon_H3e zenon_TD_bc). zenon_intro zenon_H3f. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H42; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H27 ]. % 32.19/32.47 generalize (zenon_H3d zenon_TD_v). zenon_intro zenon_H43. % 32.19/32.47 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 32.19/32.47 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_Hc | zenon_intro zenon_H14 ]. % 32.19/32.47 apply (zenon_L1_ zenon_TC_n zenon_TB_o); trivial. % 32.19/32.47 apply (zenon_L2_ zenon_TD_v zenon_TB_o); trivial. % 32.19/32.47 generalize (subset_defn zenon_TB_o). zenon_intro zenon_Hf. % 32.19/32.47 generalize (zenon_Hf (intersection zenon_TC_n zenon_TD_v)). zenon_intro zenon_H46. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H44; zenon_intro zenon_H19 ]. % 32.19/32.47 exact (zenon_H48 zenon_H44). % 32.19/32.47 generalize (intersection_defn (intersection zenon_TC_n zenon_TD_v)). zenon_intro zenon_H49. % 32.19/32.47 generalize (zenon_H49 zenon_TD_v). zenon_intro zenon_H4a. % 32.19/32.47 generalize (zenon_H4a zenon_TD_bc). zenon_intro zenon_H4b. % 32.19/32.47 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ]. % 32.19/32.47 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H1b | zenon_intro zenon_H20 ]. % 32.19/32.47 apply (zenon_L3_ zenon_TD_bc zenon_TD_v zenon_TC_n zenon_TB_o); trivial. % 32.19/32.47 apply (zenon_L4_ zenon_TD_bc zenon_TD_v zenon_TB_o); trivial. % 32.19/32.47 cut ((member zenon_TD_bc (intersection (intersection zenon_TC_n zenon_TD_v) zenon_TD_v)) = (member zenon_TD_bc (intersection (empty_set) zenon_TD_v))). % 32.19/32.47 intro zenon_D_pnotp. % 32.19/32.47 apply zenon_H42. % 32.19/32.47 rewrite <- zenon_D_pnotp. % 32.19/32.47 exact zenon_H4d. % 32.19/32.47 cut (((intersection (intersection zenon_TC_n zenon_TD_v) zenon_TD_v) = (intersection (empty_set) zenon_TD_v))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 32.19/32.47 cut ((zenon_TD_bc = zenon_TD_bc)); [idtac | apply NNPP; zenon_intro zenon_H50]. % 32.19/32.47 congruence. % 32.19/32.47 apply zenon_H50. apply refl_equal. % 32.29/32.48 apply (zenon_L5_ zenon_TD_v zenon_TC_n); trivial. % 32.29/32.48 apply (zenon_L6_ zenon_TD_v zenon_TD_bc); trivial. % 32.29/32.48 apply (zenon_L7_ zenon_TD_bc); trivial. % 32.29/32.48 apply zenon_H30. apply sym_equal. exact zenon_H36. % 32.29/32.48 Qed. % 32.29/32.48 % SZS output end Proof % 32.29/32.48 (* END-PROOF *) % 32.29/32.48 nodes searched: 1165023 % 32.29/32.48 max branch formulas: 21838 % 32.29/32.48 proof nodes created: 30538 % 32.29/32.48 formulas created: 2167699 % 32.29/32.48 %------------------------------------------------------------------------------