%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO184+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 07:00:30 EDT 2022 % Result : Theorem 0.18s 0.49s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO184+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.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 : Sat Jun 18 02:26:38 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.49 (* PROOF-FOUND *) % 0.18/0.49 % SZS status Theorem % 0.18/0.49 (* BEGIN-PROOF *) % 0.18/0.49 % SZS output start Proof % 0.18/0.49 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)))))))). % 0.18/0.49 Proof. % 0.18/0.49 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TY_s : zenon_U), (apart_point_and_line zenon_TY_s (line_connecting zenon_TX_r zenon_TY_s)) -> (distinct_points zenon_TX_r zenon_TY_s) -> False). % 0.18/0.49 do 2 intro. intros zenon_Hf zenon_H10. % 0.18/0.49 generalize (ci2 zenon_TX_r). zenon_intro zenon_H13. % 0.18/0.49 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14. % 0.18/0.49 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.18/0.49 exact (zenon_H16 zenon_H10). % 0.18/0.49 exact (zenon_H15 zenon_Hf). % 0.18/0.49 (* end of lemma zenon_L1_ *) % 0.18/0.49 apply NNPP. intro zenon_G. % 0.18/0.49 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 ]. % 0.18/0.49 elim zenon_H17. zenon_intro zenon_TX_r. zenon_intro zenon_H18. % 0.18/0.49 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_r Y)/\((convergent_lines U V)/\((~(apart_point_and_line zenon_TX_r U))/\(~(apart_point_and_line Y U)))))->(~(distinct_lines U (line_connecting zenon_TX_r Y))))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.18/0.49 elim zenon_H19. zenon_intro zenon_TY_s. zenon_intro zenon_H1a. % 0.18/0.49 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_r zenon_TY_s)/\((convergent_lines U V)/\((~(apart_point_and_line zenon_TX_r U))/\(~(apart_point_and_line zenon_TY_s U)))))->(~(distinct_lines U (line_connecting zenon_TX_r zenon_TY_s)))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.18/0.49 elim zenon_H1b. zenon_intro zenon_TU_bc. zenon_intro zenon_H1d. % 0.18/0.49 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_r zenon_TY_s)/\((convergent_lines zenon_TU_bc V)/\((~(apart_point_and_line zenon_TX_r zenon_TU_bc))/\(~(apart_point_and_line zenon_TY_s zenon_TU_bc)))))->(~(distinct_lines zenon_TU_bc (line_connecting zenon_TX_r zenon_TY_s))))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ]. % 0.18/0.49 elim zenon_H1e. zenon_intro zenon_TV_bf. zenon_intro zenon_H20. % 0.18/0.49 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.18/0.49 apply zenon_H21. zenon_intro zenon_H23. % 0.18/0.49 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H10. zenon_intro zenon_H24. % 0.18/0.49 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.18/0.49 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.18/0.49 generalize (cu1 zenon_TX_r). zenon_intro zenon_H29. % 0.18/0.49 generalize (zenon_H29 zenon_TY_s). zenon_intro zenon_H2a. % 0.18/0.49 generalize (zenon_H2a zenon_TU_bc). zenon_intro zenon_H2b. % 0.18/0.49 generalize (zenon_H2b (line_connecting zenon_TX_r zenon_TY_s)). zenon_intro zenon_H2c. % 0.18/0.49 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.18/0.49 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H16 | zenon_intro zenon_H2f ]. % 0.18/0.49 exact (zenon_H16 zenon_H10). % 0.18/0.49 exact (zenon_H2f zenon_H23). % 0.18/0.49 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.18/0.49 exact (zenon_H28 zenon_H31). % 0.18/0.49 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.18/0.49 generalize (ci1 zenon_TX_r). zenon_intro zenon_H34. % 0.18/0.49 generalize (zenon_H34 zenon_TY_s). zenon_intro zenon_H35. % 0.18/0.49 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H16 | zenon_intro zenon_H36 ]. % 0.18/0.49 exact (zenon_H16 zenon_H10). % 0.18/0.49 exact (zenon_H36 zenon_H33). % 0.18/0.49 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H37 | zenon_intro zenon_Hf ]. % 0.18/0.49 exact (zenon_H27 zenon_H37). % 0.18/0.49 apply (zenon_L1_ zenon_TX_r zenon_TY_s); trivial. % 0.18/0.49 Qed. % 0.18/0.49 % SZS output end Proof % 0.18/0.49 (* END-PROOF *) % 0.18/0.49 nodes searched: 219 % 0.18/0.49 max branch formulas: 183 % 0.18/0.49 proof nodes created: 33 % 0.18/0.49 formulas created: 1325 % 0.18/0.49 %------------------------------------------------------------------------------