%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 06:34:32 EDT 2022 % Result : Theorem 6.75s 6.98s % Output : Proof 6.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET162+4 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n018.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 : Mon Jul 11 10:21:43 EDT 2022 % 0.12/0.34 % CPUTime : % 6.75/6.98 (* PROOF-FOUND *) % 6.75/6.98 % SZS status Theorem % 6.75/6.98 (* BEGIN-PROOF *) % 6.75/6.98 % SZS output start Proof % 6.75/6.98 Theorem thI18 : (forall A : zenon_U, (equal_set (union A (empty_set)) A)). % 6.75/6.98 Proof. % 6.75/6.98 assert (zenon_L1_ : forall (zenon_TA_q : zenon_U) (zenon_TX_r : zenon_U), (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_r (union A B))<->((member zenon_TX_r A)\/(member zenon_TX_r B))))) -> (~(member zenon_TX_r zenon_TA_q)) -> (~(member zenon_TX_r (empty_set))) -> (member zenon_TX_r (union zenon_TA_q (empty_set))) -> False). % 6.75/6.98 do 2 intro. intros zenon_Hc zenon_Hd zenon_He zenon_Hf. % 6.75/6.98 generalize (zenon_Hc zenon_TA_q). zenon_intro zenon_H12. % 6.75/6.98 generalize (zenon_H12 (empty_set)). zenon_intro zenon_H13. % 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H16; zenon_intro zenon_H15 | zenon_intro zenon_Hf; zenon_intro zenon_H14 ]. % 6.75/6.98 exact (zenon_H16 zenon_Hf). % 6.75/6.98 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 6.75/6.98 exact (zenon_Hd zenon_H18). % 6.75/6.98 exact (zenon_He zenon_H17). % 6.75/6.98 (* end of lemma zenon_L1_ *) % 6.75/6.98 assert (zenon_L2_ : forall (zenon_TX_r : zenon_U), (member zenon_TX_r (empty_set)) -> False). % 6.75/6.98 do 1 intro. intros zenon_H17. % 6.75/6.98 generalize (empty_set zenon_TX_r). zenon_intro zenon_He. % 6.75/6.98 exact (zenon_He zenon_H17). % 6.75/6.98 (* end of lemma zenon_L2_ *) % 6.75/6.98 apply NNPP. intro zenon_G. % 6.75/6.98 apply (zenon_notallex_s (fun A : zenon_U => (equal_set (union A (empty_set)) A)) zenon_G); [ zenon_intro zenon_H19; idtac ]. % 6.75/6.98 elim zenon_H19. zenon_intro zenon_TA_q. zenon_intro zenon_H1a. % 6.75/6.98 generalize (equal_set (union zenon_TA_q (empty_set))). zenon_intro zenon_H1b. % 6.75/6.98 generalize (zenon_H1b zenon_TA_q). zenon_intro zenon_H1c. % 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1a; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ]. % 6.75/6.98 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 6.75/6.98 generalize (subset (union zenon_TA_q (empty_set))). zenon_intro zenon_H22. % 6.75/6.98 generalize (zenon_H22 zenon_TA_q). zenon_intro zenon_H23. % 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H21; zenon_intro zenon_H26 | zenon_intro zenon_H25; zenon_intro zenon_H24 ]. % 6.75/6.98 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TA_q (empty_set)))->(member X zenon_TA_q))) zenon_H26); [ zenon_intro zenon_H27; idtac ]. % 6.75/6.98 elim zenon_H27. zenon_intro zenon_TX_r. zenon_intro zenon_H28. % 6.75/6.98 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_Hf. zenon_intro zenon_Hd. % 6.75/6.98 generalize (difference zenon_TX_r). zenon_intro zenon_H29. % 6.75/6.98 generalize (union zenon_TX_r). zenon_intro zenon_Hc. % 6.75/6.98 generalize (zenon_H29 zenon_TA_q). zenon_intro zenon_H2a. % 6.75/6.98 generalize (zenon_H2a (empty_set)). zenon_intro zenon_H2b. % 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H2c ]. % 6.75/6.98 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_He | zenon_intro zenon_H30 ]. % 6.75/6.98 apply (zenon_L1_ zenon_TA_q zenon_TX_r); trivial. % 6.75/6.98 exact (zenon_H30 zenon_Hd). % 6.75/6.98 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H17. zenon_intro zenon_Hd. % 6.75/6.98 apply (zenon_L2_ zenon_TX_r); trivial. % 6.75/6.98 exact (zenon_H21 zenon_H25). % 6.75/6.98 generalize (subset zenon_TA_q). zenon_intro zenon_H31. % 6.75/6.98 generalize (zenon_H31 (union zenon_TA_q (empty_set))). zenon_intro zenon_H32. % 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H20; zenon_intro zenon_H35 | zenon_intro zenon_H34; zenon_intro zenon_H33 ]. % 6.75/6.98 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_q)->(member X (union zenon_TA_q (empty_set))))) zenon_H35); [ zenon_intro zenon_H36; idtac ]. % 6.75/6.98 elim zenon_H36. zenon_intro zenon_TX_cd. zenon_intro zenon_H38. % 6.75/6.98 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_H3a. zenon_intro zenon_H39. % 6.75/6.98 generalize (union zenon_TX_cd). zenon_intro zenon_H3b. % 6.75/6.98 generalize (zenon_H3b zenon_TA_q). zenon_intro zenon_H3c. % 6.75/6.98 generalize (zenon_H3c (empty_set)). zenon_intro zenon_H3d. % 6.75/6.98 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H39; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3e ]. % 6.75/6.98 apply (zenon_notor_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41. % 6.75/6.98 exact (zenon_H42 zenon_H3a). % 6.75/6.98 exact (zenon_H39 zenon_H3f). % 6.75/6.98 exact (zenon_H20 zenon_H34). % 6.82/6.98 exact (zenon_H1a zenon_H1e). % 6.82/6.98 Qed. % 6.82/6.98 % SZS output end Proof % 6.82/6.98 (* END-PROOF *) % 6.82/6.98 nodes searched: 305162 % 6.82/6.98 max branch formulas: 34613 % 6.82/6.98 proof nodes created: 7041 % 6.82/6.98 formulas created: 1404913 % 6.82/6.98 %------------------------------------------------------------------------------