%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0. % 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 : Thu Jul 21 21:38:08 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 % 0.06/0.12 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0. % 0.06/0.12 % 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 May 29 04:47:48 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 kelley_5_19a : (forall X1 : zenon_U, (forall A1 : zenon_U, ((a_locally_compact_top_space (the_product_top_space_over X1 A1))->(forall A : zenon_U, (a_locally_compact_top_space (apply X1 A)))))). % 0.18/0.50 Proof. % 0.18/0.50 apply NNPP. intro zenon_G. % 0.18/0.50 apply (zenon_notallex_s (fun X1 : zenon_U => (forall A1 : zenon_U, ((a_locally_compact_top_space (the_product_top_space_over X1 A1))->(forall A : zenon_U, (a_locally_compact_top_space (apply X1 A)))))) zenon_G); [ zenon_intro zenon_H4; idtac ]. % 0.18/0.50 elim zenon_H4. zenon_intro zenon_TX1_f. zenon_intro zenon_H6. % 0.18/0.50 apply (zenon_notallex_s (fun A1 : zenon_U => ((a_locally_compact_top_space (the_product_top_space_over zenon_TX1_f A1))->(forall A : zenon_U, (a_locally_compact_top_space (apply zenon_TX1_f A))))) zenon_H6); [ zenon_intro zenon_H7; idtac ]. % 0.18/0.50 elim zenon_H7. zenon_intro zenon_TA1_i. zenon_intro zenon_H9. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.18/0.50 apply (zenon_notallex_s (fun A : zenon_U => (a_locally_compact_top_space (apply zenon_TX1_f A))) zenon_Ha); [ zenon_intro zenon_Hc; idtac ]. % 0.18/0.50 elim zenon_Hc. zenon_intro zenon_TA_n. zenon_intro zenon_He. % 0.18/0.50 generalize (kelley_p90a zenon_TA_n). zenon_intro zenon_Hf. % 0.18/0.50 generalize (zenon_Hf zenon_TX1_f). zenon_intro zenon_H10. % 0.18/0.50 generalize (zenon_H10 zenon_TA1_i). zenon_intro zenon_H11. % 0.18/0.50 generalize (kelley_p_147e (the_projection_function zenon_TA_n zenon_TX1_f zenon_TA1_i)). zenon_intro zenon_H12. % 0.18/0.50 generalize (zenon_H12 (the_product_top_space_over zenon_TX1_f zenon_TA1_i)). zenon_intro zenon_H13. % 0.18/0.50 generalize (zenon_H13 (apply zenon_TX1_f zenon_TA_n)). zenon_intro zenon_H14. % 0.18/0.50 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.18/0.50 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.18/0.50 generalize (kelley_3_2 zenon_TA_n). zenon_intro zenon_H19. % 0.18/0.50 generalize (zenon_H19 zenon_TX1_f). zenon_intro zenon_H1a. % 0.18/0.50 generalize (zenon_H1a zenon_TA1_i). zenon_intro zenon_H1b. % 0.18/0.50 generalize (zenon_H1b zenon_TX1_f). zenon_intro zenon_H1c. % 0.18/0.50 exact (zenon_H18 zenon_H1c). % 0.18/0.50 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.18/0.50 exact (zenon_H1e zenon_H11). % 0.18/0.50 exact (zenon_H1d zenon_Hb). % 0.18/0.50 exact (zenon_He zenon_H15). % 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: 133 % 0.18/0.50 max branch formulas: 111 % 0.18/0.50 proof nodes created: 38 % 0.18/0.50 formulas created: 849 % 0.18/0.50 %------------------------------------------------------------------------------