%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 06:40:03 EDT 2022 % Result : Theorem 0.59s 0.78s % Output : Proof 0.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n012.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 11:55:28 EDT 2022 % 0.12/0.33 % CPUTime : % 0.59/0.78 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 0.59/0.78 (* PROOF-FOUND *) % 0.59/0.78 % SZS status Theorem % 0.59/0.78 (* BEGIN-PROOF *) % 0.59/0.78 % SZS output start Proof % 0.59/0.78 Theorem t141_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((~(in A B))->((set_difference (set_union2 B (singleton A)) (singleton A)) = B)))). % 0.59/0.78 Proof. % 0.59/0.78 assert (zenon_L1_ : forall (zenon_TB_m : zenon_U) (zenon_TA_n : zenon_U), (~(~(in zenon_TA_n zenon_TB_m))) -> (~(in zenon_TA_n zenon_TB_m)) -> False). % 0.59/0.78 do 2 intro. intros zenon_Ha zenon_Hb. % 0.59/0.78 exact (zenon_Ha zenon_Hb). % 0.59/0.78 (* end of lemma zenon_L1_ *) % 0.59/0.78 assert (zenon_L2_ : forall (zenon_TA_n : zenon_U) (zenon_TB_m : zenon_U), (~((set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)) = (set_difference zenon_TB_m (singleton zenon_TA_n)))) -> False). % 0.59/0.78 do 2 intro. intros zenon_He. % 0.59/0.78 generalize (t40_xboole_1 zenon_TB_m). zenon_intro zenon_Hf. % 0.59/0.78 generalize (zenon_Hf (singleton zenon_TA_n)). zenon_intro zenon_H10. % 0.59/0.78 exact (zenon_He zenon_H10). % 0.59/0.78 (* end of lemma zenon_L2_ *) % 0.59/0.78 apply NNPP. intro zenon_G. % 0.59/0.78 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((~(in A B))->((set_difference (set_union2 B (singleton A)) (singleton A)) = B)))) zenon_G); [ zenon_intro zenon_H11; idtac ]. % 0.59/0.78 elim zenon_H11. zenon_intro zenon_TA_n. zenon_intro zenon_H12. % 0.59/0.78 apply (zenon_notallex_s (fun B : zenon_U => ((~(in zenon_TA_n B))->((set_difference (set_union2 B (singleton zenon_TA_n)) (singleton zenon_TA_n)) = B))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 0.59/0.78 elim zenon_H13. zenon_intro zenon_TB_m. zenon_intro zenon_H14. % 0.59/0.78 apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_Hb. zenon_intro zenon_H15. % 0.59/0.78 generalize (t65_zfmisc_1 zenon_TB_m). zenon_intro zenon_H16. % 0.59/0.78 generalize (zenon_H16 zenon_TA_n). zenon_intro zenon_H17. % 0.59/0.78 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H19; zenon_intro zenon_Ha | zenon_intro zenon_H18; zenon_intro zenon_Hb ]. % 0.59/0.78 exact (zenon_Ha zenon_Hb). % 0.59/0.78 cut (((set_difference zenon_TB_m (singleton zenon_TA_n)) = zenon_TB_m) = ((set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)) = zenon_TB_m)). % 0.59/0.78 intro zenon_D_pnotp. % 0.59/0.78 apply zenon_H15. % 0.59/0.78 rewrite <- zenon_D_pnotp. % 0.59/0.78 exact zenon_H18. % 0.59/0.78 cut ((zenon_TB_m = zenon_TB_m)); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 0.59/0.78 cut (((set_difference zenon_TB_m (singleton zenon_TA_n)) = (set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.59/0.78 congruence. % 0.59/0.78 elim (classic ((set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)) = (set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)))); [ zenon_intro zenon_H1c | zenon_intro zenon_H1d ]. % 0.59/0.78 cut (((set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)) = (set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n))) = ((set_difference zenon_TB_m (singleton zenon_TA_n)) = (set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)))). % 0.59/0.78 intro zenon_D_pnotp. % 0.59/0.78 apply zenon_H1b. % 0.59/0.78 rewrite <- zenon_D_pnotp. % 0.59/0.78 exact zenon_H1c. % 0.59/0.78 cut (((set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)) = (set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 0.59/0.78 cut (((set_difference (set_union2 zenon_TB_m (singleton zenon_TA_n)) (singleton zenon_TA_n)) = (set_difference zenon_TB_m (singleton zenon_TA_n)))); [idtac | apply NNPP; zenon_intro zenon_He]. % 0.59/0.78 congruence. % 0.59/0.78 apply (zenon_L2_ zenon_TA_n zenon_TB_m); trivial. % 0.59/0.78 apply zenon_H1d. apply refl_equal. % 0.59/0.78 apply zenon_H1d. apply refl_equal. % 0.59/0.78 apply zenon_H1a. apply refl_equal. % 0.59/0.78 Qed. % 0.59/0.78 % SZS output end Proof % 0.59/0.78 (* END-PROOF *) % 0.59/0.78 nodes searched: 2444 % 0.59/0.78 max branch formulas: 452 % 0.59/0.78 proof nodes created: 141 % 0.59/0.78 formulas created: 7461 % 0.59/0.78 %------------------------------------------------------------------------------