%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 06:39:23 EDT 2022 % Result : Theorem 0.18s 0.50s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET880+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n028.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 04:06:12 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.50 (* PROOF-FOUND *) % 0.18/0.50 % SZS status Theorem % 0.18/0.50 (* BEGIN-PROOF *) % 0.18/0.50 % SZS output start Proof % 0.18/0.50 Theorem t21_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (((set_difference (singleton A) (singleton B)) = (empty_set))->(A = B)))). % 0.18/0.50 Proof. % 0.18/0.50 assert (zenon_L1_ : forall (zenon_TB_j : zenon_U) (zenon_TA_k : zenon_U), ((set_difference (singleton zenon_TA_k) (singleton zenon_TB_j)) = (empty_set)) -> (~(in zenon_TA_k (singleton zenon_TB_j))) -> False). % 0.18/0.50 do 2 intro. intros zenon_H7 zenon_H8. % 0.18/0.50 generalize (l36_zfmisc_1 zenon_TA_k). zenon_intro zenon_Hb. % 0.18/0.50 generalize (zenon_Hb (singleton zenon_TB_j)). zenon_intro zenon_Hc. % 0.18/0.50 apply (zenon_equiv_s _ _ zenon_Hc); [ zenon_intro zenon_He; zenon_intro zenon_H8 | zenon_intro zenon_H7; zenon_intro zenon_Hd ]. % 0.18/0.50 exact (zenon_He zenon_H7). % 0.18/0.50 exact (zenon_H8 zenon_Hd). % 0.18/0.50 (* end of lemma zenon_L1_ *) % 0.18/0.50 apply NNPP. intro zenon_G. % 0.18/0.50 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((set_difference (singleton A) (singleton B)) = (empty_set))->(A = B)))) zenon_G); [ zenon_intro zenon_Hf; idtac ]. % 0.18/0.50 elim zenon_Hf. zenon_intro zenon_TA_k. zenon_intro zenon_H10. % 0.18/0.50 apply (zenon_notallex_s (fun B : zenon_U => (((set_difference (singleton zenon_TA_k) (singleton B)) = (empty_set))->(zenon_TA_k = B))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 0.18/0.50 elim zenon_H11. zenon_intro zenon_TB_j. zenon_intro zenon_H12. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H7. zenon_intro zenon_H13. % 0.18/0.50 generalize (d1_tarski zenon_TB_j). zenon_intro zenon_H14. % 0.18/0.50 generalize (zenon_H14 (singleton zenon_TB_j)). zenon_intro zenon_H15. % 0.18/0.50 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.18/0.50 apply zenon_H19. apply refl_equal. % 0.18/0.50 generalize (zenon_H16 zenon_TA_k). zenon_intro zenon_H1a. % 0.18/0.50 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H8; zenon_intro zenon_H13 | zenon_intro zenon_Hd; zenon_intro zenon_H1b ]. % 0.18/0.50 apply (zenon_L1_ zenon_TB_j zenon_TA_k); trivial. % 0.18/0.50 exact (zenon_H13 zenon_H1b). % 0.18/0.50 Qed. % 0.18/0.50 % SZS output end Proof % 0.18/0.50 (* END-PROOF *) % 0.18/0.50 nodes searched: 260 % 0.18/0.50 max branch formulas: 93 % 0.18/0.50 proof nodes created: 57 % 0.18/0.50 formulas created: 963 % 0.18/0.50 %------------------------------------------------------------------------------