%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 06:38:02 EDT 2022 % Result : Theorem 15.27s 15.50s % Output : Proof 15.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET695+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.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 00:27:55 EDT 2022 % 0.13/0.34 % CPUTime : % 15.27/15.50 (* PROOF-FOUND *) % 15.27/15.50 % SZS status Theorem % 15.27/15.50 (* BEGIN-PROOF *) % 15.27/15.50 % SZS output start Proof % 15.27/15.50 Theorem thI24 : (forall A : zenon_U, (forall B : zenon_U, (forall E : zenon_U, (((subset A E)/\(subset B E))->((subset A B)<->(subset (difference E B) (difference E A))))))). % 15.27/15.50 Proof. % 15.27/15.50 assert (zenon_L1_ : forall (zenon_TX_p : zenon_U) (zenon_TE_q : zenon_U) (zenon_TA_r : zenon_U), (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TE_q))) -> (member zenon_TX_p zenon_TA_r) -> (~(member zenon_TX_p zenon_TE_q)) -> False). % 15.27/15.50 do 3 intro. intros zenon_Hc zenon_Hd zenon_He. % 15.27/15.50 generalize (zenon_Hc zenon_TX_p). zenon_intro zenon_H12. % 15.27/15.50 apply (zenon_imply_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 15.27/15.50 exact (zenon_H14 zenon_Hd). % 15.27/15.50 exact (zenon_He zenon_H13). % 15.27/15.50 (* end of lemma zenon_L1_ *) % 15.27/15.50 assert (zenon_L2_ : forall (zenon_TA_r : zenon_U) (zenon_TB_z : zenon_U) (zenon_TE_q : zenon_U) (zenon_TX_p : zenon_U), (~(~(member zenon_TX_p zenon_TE_q))) -> (forall X : zenon_U, ((member X (difference zenon_TE_q zenon_TB_z))->(member X (difference zenon_TE_q zenon_TA_r)))) -> (forall A : zenon_U, (forall E : zenon_U, ((member zenon_TX_p (difference E A))<->((member zenon_TX_p E)/\(~(member zenon_TX_p A)))))) -> (~(member zenon_TX_p zenon_TB_z)) -> (member zenon_TX_p zenon_TA_r) -> False). % 15.27/15.50 do 4 intro. intros zenon_H15 zenon_H16 zenon_H17 zenon_H18 zenon_Hd. % 15.27/15.50 apply zenon_H15. zenon_intro zenon_H13. % 15.27/15.50 generalize (zenon_H17 zenon_TA_r). zenon_intro zenon_H1a. % 15.27/15.50 generalize (zenon_H1a zenon_TE_q). zenon_intro zenon_H1b. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H1d; zenon_intro zenon_H1c ]. % 15.27/15.50 generalize (zenon_H16 zenon_TX_p). zenon_intro zenon_H20. % 15.27/15.50 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H21 | zenon_intro zenon_H1d ]. % 15.27/15.50 generalize (zenon_H17 zenon_TB_z). zenon_intro zenon_H22. % 15.27/15.50 generalize (zenon_H22 zenon_TE_q). zenon_intro zenon_H23. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H21; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ]. % 15.27/15.50 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_He | zenon_intro zenon_H27 ]. % 15.27/15.50 exact (zenon_He zenon_H13). % 15.27/15.50 exact (zenon_H27 zenon_H18). % 15.27/15.50 exact (zenon_H21 zenon_H25). % 15.27/15.50 exact (zenon_H1f zenon_H1d). % 15.27/15.50 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H13. zenon_intro zenon_H14. % 15.27/15.50 exact (zenon_H14 zenon_Hd). % 15.27/15.50 (* end of lemma zenon_L2_ *) % 15.27/15.50 assert (zenon_L3_ : forall (zenon_TE_q : zenon_U) (zenon_TB_z : zenon_U) (zenon_TX_br : zenon_U), (forall E : zenon_U, ((member zenon_TX_br (difference E zenon_TB_z))<->((member zenon_TX_br E)/\(~(member zenon_TX_br zenon_TB_z))))) -> (member zenon_TX_br (difference zenon_TE_q zenon_TB_z)) -> (~(member zenon_TX_br zenon_TE_q)) -> False). % 15.27/15.50 do 3 intro. intros zenon_H28 zenon_H29 zenon_H2a. % 15.27/15.50 generalize (zenon_H28 zenon_TE_q). zenon_intro zenon_H2c. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H29; zenon_intro zenon_H2d ]. % 15.27/15.50 exact (zenon_H2f zenon_H29). % 15.27/15.50 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H31. zenon_intro zenon_H30. % 15.27/15.50 exact (zenon_H2a zenon_H31). % 15.27/15.50 (* end of lemma zenon_L3_ *) % 15.27/15.50 assert (zenon_L4_ : forall (zenon_TB_z : zenon_U) (zenon_TE_q : zenon_U) (zenon_TX_br : zenon_U), (forall A : zenon_U, (forall E : zenon_U, ((member zenon_TX_br (difference E A))<->((member zenon_TX_br E)/\(~(member zenon_TX_br A)))))) -> (~(member zenon_TX_br zenon_TE_q)) -> (member zenon_TX_br (difference zenon_TE_q zenon_TB_z)) -> False). % 15.27/15.50 do 3 intro. intros zenon_H32 zenon_H2a zenon_H29. % 15.27/15.50 generalize (zenon_H32 zenon_TB_z). zenon_intro zenon_H28. % 15.27/15.50 apply (zenon_L3_ zenon_TE_q zenon_TB_z zenon_TX_br); trivial. % 15.27/15.50 (* end of lemma zenon_L4_ *) % 15.27/15.50 assert (zenon_L5_ : forall (zenon_TX_br : zenon_U) (zenon_TB_z : zenon_U) (zenon_TA_r : zenon_U), (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TB_z))) -> (member zenon_TX_br zenon_TA_r) -> (~(member zenon_TX_br zenon_TB_z)) -> False). % 15.27/15.50 do 3 intro. intros zenon_H33 zenon_H34 zenon_H30. % 15.27/15.50 generalize (zenon_H33 zenon_TX_br). zenon_intro zenon_H35. % 15.27/15.50 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 15.27/15.50 exact (zenon_H37 zenon_H34). % 15.27/15.50 exact (zenon_H30 zenon_H36). % 15.27/15.50 (* end of lemma zenon_L5_ *) % 15.27/15.50 assert (zenon_L6_ : forall (zenon_TE_q : zenon_U) (zenon_TB_z : zenon_U) (zenon_TX_br : zenon_U), (forall E : zenon_U, ((member zenon_TX_br (difference E zenon_TB_z))<->((member zenon_TX_br E)/\(~(member zenon_TX_br zenon_TB_z))))) -> (member zenon_TX_br (difference zenon_TE_q zenon_TB_z)) -> (member zenon_TX_br zenon_TB_z) -> False). % 15.27/15.50 do 3 intro. intros zenon_H28 zenon_H29 zenon_H36. % 15.27/15.50 generalize (zenon_H28 zenon_TE_q). zenon_intro zenon_H2c. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H29; zenon_intro zenon_H2d ]. % 15.27/15.50 exact (zenon_H2f zenon_H29). % 15.27/15.50 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H31. zenon_intro zenon_H30. % 15.27/15.50 exact (zenon_H30 zenon_H36). % 15.27/15.50 (* end of lemma zenon_L6_ *) % 15.27/15.50 assert (zenon_L7_ : forall (zenon_TE_q : zenon_U) (zenon_TB_z : zenon_U) (zenon_TX_br : zenon_U), (~(~(member zenon_TX_br zenon_TB_z))) -> (member zenon_TX_br (difference zenon_TE_q zenon_TB_z)) -> (forall E : zenon_U, ((member zenon_TX_br (difference E zenon_TB_z))<->((member zenon_TX_br E)/\(~(member zenon_TX_br zenon_TB_z))))) -> False). % 15.27/15.50 do 3 intro. intros zenon_H38 zenon_H29 zenon_H28. % 15.27/15.50 apply zenon_H38. zenon_intro zenon_H36. % 15.27/15.50 apply (zenon_L6_ zenon_TE_q zenon_TB_z zenon_TX_br); trivial. % 15.27/15.50 (* end of lemma zenon_L7_ *) % 15.27/15.50 assert (zenon_L8_ : forall (zenon_TB_z : zenon_U) (zenon_TE_q : zenon_U) (zenon_TA_r : zenon_U) (zenon_TX_br : zenon_U), (~(~(member zenon_TX_br zenon_TA_r))) -> (member zenon_TX_br (difference zenon_TE_q zenon_TB_z)) -> (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TB_z))) -> (forall A : zenon_U, (forall E : zenon_U, ((member zenon_TX_br (difference E A))<->((member zenon_TX_br E)/\(~(member zenon_TX_br A)))))) -> False). % 15.27/15.50 do 4 intro. intros zenon_H39 zenon_H29 zenon_H33 zenon_H32. % 15.27/15.50 apply zenon_H39. zenon_intro zenon_H34. % 15.27/15.50 generalize (zenon_H32 zenon_TB_z). zenon_intro zenon_H28. % 15.27/15.50 generalize (zenon_H28 zenon_TB_z). zenon_intro zenon_H3a. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H3e; zenon_intro zenon_H3d | zenon_intro zenon_H3c; zenon_intro zenon_H3b ]. % 15.27/15.50 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H30 | zenon_intro zenon_H38 ]. % 15.27/15.50 apply (zenon_L5_ zenon_TX_br zenon_TB_z zenon_TA_r); trivial. % 15.27/15.50 apply (zenon_L7_ zenon_TE_q zenon_TB_z zenon_TX_br); trivial. % 15.27/15.50 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H36. zenon_intro zenon_H30. % 15.27/15.50 exact (zenon_H30 zenon_H36). % 15.27/15.50 (* end of lemma zenon_L8_ *) % 15.27/15.50 apply NNPP. intro zenon_G. % 15.27/15.50 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall E : zenon_U, (((subset A E)/\(subset B E))->((subset A B)<->(subset (difference E B) (difference E A))))))) zenon_G); [ zenon_intro zenon_H3f; idtac ]. % 15.27/15.50 elim zenon_H3f. zenon_intro zenon_TA_r. zenon_intro zenon_H40. % 15.27/15.50 apply (zenon_notallex_s (fun B : zenon_U => (forall E : zenon_U, (((subset zenon_TA_r E)/\(subset B E))->((subset zenon_TA_r B)<->(subset (difference E B) (difference E zenon_TA_r)))))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 15.27/15.50 elim zenon_H41. zenon_intro zenon_TB_z. zenon_intro zenon_H42. % 15.27/15.50 apply (zenon_notallex_s (fun E : zenon_U => (((subset zenon_TA_r E)/\(subset zenon_TB_z E))->((subset zenon_TA_r zenon_TB_z)<->(subset (difference E zenon_TB_z) (difference E zenon_TA_r))))) zenon_H42); [ zenon_intro zenon_H43; idtac ]. % 15.27/15.50 elim zenon_H43. zenon_intro zenon_TE_q. zenon_intro zenon_H44. % 15.27/15.50 apply (zenon_notimply_s _ _ zenon_H44). zenon_intro zenon_H46. zenon_intro zenon_H45. % 15.27/15.50 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 15.27/15.50 generalize (subset zenon_TA_r). zenon_intro zenon_H49. % 15.27/15.50 generalize (zenon_H49 zenon_TE_q). zenon_intro zenon_H4a. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4c; zenon_intro zenon_H4b | zenon_intro zenon_H48; zenon_intro zenon_Hc ]. % 15.27/15.50 exact (zenon_H4c zenon_H48). % 15.27/15.50 apply (zenon_notequiv_s _ _ zenon_H45); [ zenon_intro zenon_H50; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ]. % 15.27/15.50 generalize (subset zenon_TA_r). zenon_intro zenon_H49. % 15.27/15.50 generalize (zenon_H49 zenon_TB_z). zenon_intro zenon_H51. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H50; zenon_intro zenon_H52 | zenon_intro zenon_H4e; zenon_intro zenon_H33 ]. % 15.27/15.50 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_r)->(member X zenon_TB_z))) zenon_H52); [ zenon_intro zenon_H53; idtac ]. % 15.27/15.50 elim zenon_H53. zenon_intro zenon_TX_p. zenon_intro zenon_H54. % 15.27/15.50 apply (zenon_notimply_s _ _ zenon_H54). zenon_intro zenon_Hd. zenon_intro zenon_H18. % 15.27/15.50 generalize (subset (difference zenon_TE_q zenon_TB_z)). zenon_intro zenon_H55. % 15.27/15.50 generalize (zenon_H55 (difference zenon_TE_q zenon_TA_r)). zenon_intro zenon_H56. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H4d; zenon_intro zenon_H57 | zenon_intro zenon_H4f; zenon_intro zenon_H16 ]. % 15.27/15.50 exact (zenon_H4d zenon_H4f). % 15.27/15.50 generalize (difference zenon_TX_p). zenon_intro zenon_H17. % 15.27/15.50 generalize (zenon_H17 zenon_TE_q). zenon_intro zenon_H58. % 15.27/15.50 generalize (zenon_H58 zenon_TE_q). zenon_intro zenon_H59. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5d; zenon_intro zenon_H5c | zenon_intro zenon_H5b; zenon_intro zenon_H5a ]. % 15.27/15.50 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_He | zenon_intro zenon_H15 ]. % 15.27/15.50 apply (zenon_L1_ zenon_TX_p zenon_TE_q zenon_TA_r); trivial. % 15.27/15.50 apply (zenon_L2_ zenon_TA_r zenon_TB_z zenon_TE_q zenon_TX_p); trivial. % 15.27/15.50 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H13. zenon_intro zenon_He. % 15.27/15.50 exact (zenon_He zenon_H13). % 15.27/15.50 exact (zenon_H50 zenon_H4e). % 15.27/15.50 generalize (subset zenon_TA_r). zenon_intro zenon_H49. % 15.27/15.50 generalize (zenon_H49 zenon_TB_z). zenon_intro zenon_H51. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H50; zenon_intro zenon_H52 | zenon_intro zenon_H4e; zenon_intro zenon_H33 ]. % 15.27/15.50 exact (zenon_H50 zenon_H4e). % 15.27/15.50 generalize (subset (difference zenon_TE_q zenon_TB_z)). zenon_intro zenon_H55. % 15.27/15.50 generalize (zenon_H55 (difference zenon_TE_q zenon_TA_r)). zenon_intro zenon_H56. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H4d; zenon_intro zenon_H57 | zenon_intro zenon_H4f; zenon_intro zenon_H16 ]. % 15.27/15.50 apply (zenon_notallex_s (fun X : zenon_U => ((member X (difference zenon_TE_q zenon_TB_z))->(member X (difference zenon_TE_q zenon_TA_r)))) zenon_H57); [ zenon_intro zenon_H5e; idtac ]. % 15.27/15.50 elim zenon_H5e. zenon_intro zenon_TX_br. zenon_intro zenon_H5f. % 15.27/15.50 apply (zenon_notimply_s _ _ zenon_H5f). zenon_intro zenon_H29. zenon_intro zenon_H60. % 15.27/15.50 generalize (difference zenon_TX_br). zenon_intro zenon_H32. % 15.27/15.50 generalize (zenon_H32 zenon_TA_r). zenon_intro zenon_H61. % 15.27/15.50 generalize (zenon_H61 zenon_TE_q). zenon_intro zenon_H62. % 15.27/15.50 apply (zenon_equiv_s _ _ zenon_H62); [ zenon_intro zenon_H60; zenon_intro zenon_H65 | zenon_intro zenon_H64; zenon_intro zenon_H63 ]. % 15.27/15.50 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H2a | zenon_intro zenon_H39 ]. % 15.27/15.50 apply (zenon_L4_ zenon_TB_z zenon_TE_q zenon_TX_br); trivial. % 15.27/15.50 apply (zenon_L8_ zenon_TB_z zenon_TE_q zenon_TA_r zenon_TX_br); trivial. % 15.27/15.50 exact (zenon_H60 zenon_H64). % 15.27/15.50 exact (zenon_H4d zenon_H4f). % 15.27/15.50 Qed. % 15.27/15.50 % SZS output end Proof % 15.27/15.50 (* END-PROOF *) % 15.27/15.50 nodes searched: 711377 % 15.27/15.50 max branch formulas: 33136 % 15.27/15.50 proof nodes created: 11950 % 15.27/15.50 formulas created: 2983718 % 15.27/15.50 %------------------------------------------------------------------------------