%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 : Sat Jul 16 07:00:23 EDT 2022 % Result : Theorem 0.35s 0.54s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n021.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 : Sat Jun 18 13:25:16 EDT 2022 % 0.13/0.34 % CPUTime : % 0.35/0.54 (* PROOF-FOUND *) % 0.35/0.54 % SZS status Theorem % 0.35/0.54 (* BEGIN-PROOF *) % 0.35/0.54 % SZS output start Proof % 0.35/0.54 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((apart_point_and_line X U)\/(apart_point_and_line Y U))))->(distinct_lines U (line_connecting X Y))))))). % 0.35/0.54 Proof. % 0.35/0.54 assert (zenon_L1_ : forall (zenon_TY_p : zenon_U) (zenon_TX_q : zenon_U), ((distinct_points zenon_TX_q zenon_TX_q)/\(distinct_points zenon_TX_q zenon_TY_p)) -> (~(distinct_points zenon_TX_q zenon_TX_q)) -> False). % 0.35/0.54 do 2 intro. intros zenon_Hd zenon_He. % 0.35/0.54 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.35/0.54 exact (zenon_He zenon_H12). % 0.35/0.54 (* end of lemma zenon_L1_ *) % 0.35/0.54 assert (zenon_L2_ : forall (zenon_TX_q : zenon_U) (zenon_TY_p : zenon_U), ((distinct_points zenon_TY_p zenon_TX_q)/\(distinct_points zenon_TY_p zenon_TY_p)) -> (~(distinct_points zenon_TY_p zenon_TY_p)) -> False). % 0.35/0.54 do 2 intro. intros zenon_H13 zenon_H14. % 0.35/0.54 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.35/0.54 exact (zenon_H14 zenon_H15). % 0.35/0.54 (* end of lemma zenon_L2_ *) % 0.35/0.54 apply NNPP. intro zenon_G. % 0.35/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((apart_point_and_line X U)\/(apart_point_and_line Y U))))->(distinct_lines U (line_connecting X Y))))))) zenon_G); [ zenon_intro zenon_H17; idtac ]. % 0.35/0.54 elim zenon_H17. zenon_intro zenon_TX_q. zenon_intro zenon_H18. % 0.35/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_q Y)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_q U)\/(apart_point_and_line Y U))))->(distinct_lines U (line_connecting zenon_TX_q Y)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.35/0.54 elim zenon_H19. zenon_intro zenon_TY_p. zenon_intro zenon_H1a. % 0.35/0.54 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_q zenon_TY_p)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_q U)\/(apart_point_and_line zenon_TY_p U))))->(distinct_lines U (line_connecting zenon_TX_q zenon_TY_p))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.35/0.54 elim zenon_H1b. zenon_intro zenon_TU_bc. zenon_intro zenon_H1d. % 0.35/0.54 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_q zenon_TY_p)/\((convergent_lines zenon_TU_bc V)/\((apart_point_and_line zenon_TX_q zenon_TU_bc)\/(apart_point_and_line zenon_TY_p zenon_TU_bc))))->(distinct_lines zenon_TU_bc (line_connecting zenon_TX_q zenon_TY_p)))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ]. % 0.35/0.54 elim zenon_H1e. zenon_intro zenon_TV_bf. zenon_intro zenon_H20. % 0.35/0.54 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.35/0.54 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H11. zenon_intro zenon_H23. % 0.35/0.54 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.35/0.54 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.35/0.54 generalize (ceq2 zenon_TX_q). zenon_intro zenon_H28. % 0.35/0.54 generalize (zenon_H28 zenon_TU_bc). zenon_intro zenon_H29. % 0.35/0.54 generalize (con1 zenon_TX_q). zenon_intro zenon_H2a. % 0.35/0.54 generalize (zenon_H2a zenon_TY_p). zenon_intro zenon_H2b. % 0.35/0.54 generalize (apart1 zenon_TX_q). zenon_intro zenon_He. % 0.35/0.54 generalize (zenon_H2b zenon_TX_q). zenon_intro zenon_H2c. % 0.35/0.54 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.35/0.54 exact (zenon_H2e zenon_H11). % 0.35/0.54 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_Hd ]. % 0.35/0.54 generalize (zenon_H29 (line_connecting zenon_TX_q zenon_TY_p)). zenon_intro zenon_H30. % 0.35/0.54 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.35/0.54 exact (zenon_H32 zenon_H27). % 0.35/0.54 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.35/0.54 exact (zenon_H21 zenon_H34). % 0.35/0.54 exact (zenon_H2f zenon_H33). % 0.35/0.54 apply (zenon_L1_ zenon_TY_p zenon_TX_q); trivial. % 0.35/0.54 generalize (apart1 zenon_TY_p). zenon_intro zenon_H14. % 0.35/0.54 generalize (ceq2 zenon_TY_p). zenon_intro zenon_H35. % 0.35/0.54 generalize (zenon_H35 zenon_TU_bc). zenon_intro zenon_H36. % 0.38/0.54 generalize (con1 zenon_TX_q). zenon_intro zenon_H2a. % 0.38/0.54 generalize (zenon_H2a zenon_TY_p). zenon_intro zenon_H2b. % 0.38/0.54 generalize (zenon_H2b zenon_TY_p). zenon_intro zenon_H37. % 0.38/0.54 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H2e | zenon_intro zenon_H38 ]. % 0.38/0.54 exact (zenon_H2e zenon_H11). % 0.38/0.54 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H39 | zenon_intro zenon_H13 ]. % 0.38/0.54 generalize (zenon_H36 (line_connecting zenon_TX_q zenon_TY_p)). zenon_intro zenon_H3a. % 0.38/0.54 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.38/0.54 exact (zenon_H3c zenon_H26). % 0.38/0.54 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H34 | zenon_intro zenon_H3d ]. % 0.38/0.54 exact (zenon_H21 zenon_H34). % 0.38/0.54 exact (zenon_H39 zenon_H3d). % 0.38/0.54 apply (zenon_L2_ zenon_TX_q zenon_TY_p); trivial. % 0.38/0.54 Qed. % 0.38/0.54 % SZS output end Proof % 0.38/0.54 (* END-PROOF *) % 0.38/0.54 nodes searched: 1427 % 0.38/0.54 max branch formulas: 486 % 0.38/0.54 proof nodes created: 159 % 0.38/0.54 formulas created: 5437 % 0.38/0.54 %------------------------------------------------------------------------------