%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 06:32:26 EDT 2022 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n029.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 07:28:31 EDT 2022 % 0.13/0.34 % CPUTime : % 0.37/0.57 (* PROOF-FOUND *) % 0.37/0.57 % SZS status Theorem % 0.37/0.57 (* BEGIN-PROOF *) % 0.37/0.57 % SZS output start Proof % 0.37/0.57 Theorem thI07 : (forall A : zenon_U, (forall B : zenon_U, (equal_set (union A B) (union B A)))). % 0.37/0.57 Proof. % 0.37/0.57 assert (zenon_L1_ : forall (zenon_TA_p : zenon_U) (zenon_TB_q : zenon_U) (zenon_TX_r : zenon_U), (forall B : zenon_U, ((member zenon_TX_r (union zenon_TB_q B))<->((member zenon_TX_r zenon_TB_q)\/(member zenon_TX_r B)))) -> (member zenon_TX_r zenon_TA_p) -> (~(member zenon_TX_r (union zenon_TB_q zenon_TA_p))) -> False). % 0.37/0.57 do 3 intro. intros zenon_Hc zenon_Hd zenon_He. % 0.37/0.57 generalize (zenon_Hc zenon_TA_p). zenon_intro zenon_H12. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_He; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ]. % 0.37/0.57 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.37/0.57 exact (zenon_H16 zenon_Hd). % 0.37/0.57 exact (zenon_He zenon_H14). % 0.37/0.57 (* end of lemma zenon_L1_ *) % 0.37/0.57 assert (zenon_L2_ : forall (zenon_TB_q : zenon_U) (zenon_TA_p : zenon_U) (zenon_TX_bb : zenon_U), (forall B : zenon_U, ((member zenon_TX_bb (union zenon_TA_p B))<->((member zenon_TX_bb zenon_TA_p)\/(member zenon_TX_bb B)))) -> (member zenon_TX_bb zenon_TB_q) -> (~(member zenon_TX_bb (union zenon_TA_p zenon_TB_q))) -> False). % 0.37/0.57 do 3 intro. intros zenon_H18 zenon_H19 zenon_H1a. % 0.37/0.57 generalize (zenon_H18 zenon_TB_q). zenon_intro zenon_H1c. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1a; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ]. % 0.37/0.57 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.37/0.57 exact (zenon_H20 zenon_H19). % 0.37/0.57 exact (zenon_H1a zenon_H1e). % 0.37/0.57 (* end of lemma zenon_L2_ *) % 0.37/0.57 apply NNPP. intro zenon_G. % 0.37/0.57 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (equal_set (union A B) (union B A)))) zenon_G); [ zenon_intro zenon_H22; idtac ]. % 0.37/0.57 elim zenon_H22. zenon_intro zenon_TA_p. zenon_intro zenon_H23. % 0.37/0.57 apply (zenon_notallex_s (fun B : zenon_U => (equal_set (union zenon_TA_p B) (union B zenon_TA_p))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 0.37/0.57 elim zenon_H24. zenon_intro zenon_TB_q. zenon_intro zenon_H25. % 0.37/0.57 generalize (equal_set (union zenon_TA_p zenon_TB_q)). zenon_intro zenon_H26. % 0.37/0.57 generalize (zenon_H26 (union zenon_TB_q zenon_TA_p)). zenon_intro zenon_H27. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H27); [ zenon_intro zenon_H25; zenon_intro zenon_H2a | zenon_intro zenon_H29; zenon_intro zenon_H28 ]. % 0.37/0.57 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.37/0.57 generalize (subset (union zenon_TA_p zenon_TB_q)). zenon_intro zenon_H2d. % 0.37/0.57 generalize (zenon_H2d (union zenon_TB_q zenon_TA_p)). zenon_intro zenon_H2e. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H2c; zenon_intro zenon_H31 | zenon_intro zenon_H30; zenon_intro zenon_H2f ]. % 0.37/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TA_p zenon_TB_q))->(member X (union zenon_TB_q zenon_TA_p)))) zenon_H31); [ zenon_intro zenon_H32; idtac ]. % 0.37/0.57 elim zenon_H32. zenon_intro zenon_TX_r. zenon_intro zenon_H33. % 0.37/0.57 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H34. zenon_intro zenon_He. % 0.37/0.57 generalize (union zenon_TX_r). zenon_intro zenon_H35. % 0.37/0.57 generalize (zenon_H35 zenon_TA_p). zenon_intro zenon_H36. % 0.37/0.57 generalize (zenon_H35 zenon_TB_q). zenon_intro zenon_Hc. % 0.37/0.57 generalize (zenon_H36 zenon_TA_p). zenon_intro zenon_H37. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3b; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ]. % 0.37/0.57 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H16. zenon_intro zenon_H16. % 0.37/0.57 generalize (zenon_Hc zenon_TA_p). zenon_intro zenon_H12. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_He; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ]. % 0.37/0.57 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.37/0.57 generalize (zenon_H36 zenon_TB_q). zenon_intro zenon_H3c. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H34; zenon_intro zenon_H3d ]. % 0.37/0.57 exact (zenon_H3f zenon_H34). % 0.37/0.57 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_Hd | zenon_intro zenon_H40 ]. % 0.37/0.57 exact (zenon_H16 zenon_Hd). % 0.37/0.57 exact (zenon_H17 zenon_H40). % 0.37/0.57 exact (zenon_He zenon_H14). % 0.37/0.57 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_Hd | zenon_intro zenon_Hd ]. % 0.37/0.57 apply (zenon_L1_ zenon_TA_p zenon_TB_q zenon_TX_r); trivial. % 0.37/0.57 apply (zenon_L1_ zenon_TA_p zenon_TB_q zenon_TX_r); trivial. % 0.37/0.57 exact (zenon_H2c zenon_H30). % 0.37/0.57 generalize (subset (union zenon_TB_q zenon_TA_p)). zenon_intro zenon_H41. % 0.37/0.57 generalize (zenon_H41 (union zenon_TA_p zenon_TB_q)). zenon_intro zenon_H42. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H2b; zenon_intro zenon_H45 | zenon_intro zenon_H44; zenon_intro zenon_H43 ]. % 0.37/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TB_q zenon_TA_p))->(member X (union zenon_TA_p zenon_TB_q)))) zenon_H45); [ zenon_intro zenon_H46; idtac ]. % 0.37/0.57 elim zenon_H46. zenon_intro zenon_TX_bb. zenon_intro zenon_H47. % 0.37/0.57 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H48. zenon_intro zenon_H1a. % 0.37/0.57 generalize (union zenon_TX_bb). zenon_intro zenon_H49. % 0.37/0.57 generalize (zenon_H49 zenon_TB_q). zenon_intro zenon_H4a. % 0.37/0.57 generalize (zenon_H49 zenon_TA_p). zenon_intro zenon_H18. % 0.37/0.57 generalize (zenon_H4a zenon_TB_q). zenon_intro zenon_H4b. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ]. % 0.37/0.57 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H20. zenon_intro zenon_H20. % 0.37/0.57 generalize (zenon_H18 zenon_TB_q). zenon_intro zenon_H1c. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1a; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ]. % 0.37/0.57 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.37/0.57 generalize (zenon_H4a zenon_TA_p). zenon_intro zenon_H50. % 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H50); [ zenon_intro zenon_H53; zenon_intro zenon_H52 | zenon_intro zenon_H48; zenon_intro zenon_H51 ]. % 0.37/0.57 exact (zenon_H53 zenon_H48). % 0.37/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H19 | zenon_intro zenon_H54 ]. % 0.37/0.57 exact (zenon_H20 zenon_H19). % 0.37/0.57 exact (zenon_H21 zenon_H54). % 0.37/0.57 exact (zenon_H1a zenon_H1e). % 0.37/0.57 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H19 | zenon_intro zenon_H19 ]. % 0.37/0.57 apply (zenon_L2_ zenon_TB_q zenon_TA_p zenon_TX_bb); trivial. % 0.37/0.57 apply (zenon_L2_ zenon_TB_q zenon_TA_p zenon_TX_bb); trivial. % 0.37/0.57 exact (zenon_H2b zenon_H44). % 0.37/0.57 exact (zenon_H25 zenon_H29). % 0.37/0.57 Qed. % 0.37/0.57 % SZS output end Proof % 0.37/0.57 (* END-PROOF *) % 0.37/0.57 nodes searched: 2821 % 0.37/0.57 max branch formulas: 800 % 0.37/0.57 proof nodes created: 153 % 0.37/0.57 formulas created: 16259 % 0.37/0.57 %------------------------------------------------------------------------------