%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO170+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 07:00:20 EDT 2022 % Result : Theorem 0.20s 0.50s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO170+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n013.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 08:11:29 EDT 2022 % 0.13/0.35 % CPUTime : % 0.20/0.50 (* PROOF-FOUND *) % 0.20/0.50 % SZS status Theorem % 0.20/0.50 (* BEGIN-PROOF *) % 0.20/0.50 % SZS output start Proof % 0.20/0.50 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((~(apart_point_and_line X Z))/\(~(apart_point_and_line Y Z))))->(~(distinct_lines Z (line_connecting X Y))))))). % 0.20/0.50 Proof. % 0.20/0.50 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). % 0.20/0.50 do 2 intro. intros zenon_Hf zenon_H10. % 0.20/0.50 generalize (ci2 zenon_TX_r). zenon_intro zenon_H13. % 0.20/0.50 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14. % 0.20/0.50 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.20/0.50 exact (zenon_H16 zenon_H10). % 0.20/0.50 exact (zenon_H15 zenon_Hf). % 0.20/0.50 (* end of lemma zenon_L1_ *) % 0.20/0.50 apply NNPP. intro zenon_G. % 0.20/0.50 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((~(apart_point_and_line X Z))/\(~(apart_point_and_line Y Z))))->(~(distinct_lines Z (line_connecting X Y))))))) zenon_G); [ zenon_intro zenon_H17; idtac ]. % 0.20/0.50 elim zenon_H17. zenon_intro zenon_TX_r. zenon_intro zenon_H18. % 0.20/0.50 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_r Y)/\((~(apart_point_and_line zenon_TX_r Z))/\(~(apart_point_and_line Y Z))))->(~(distinct_lines Z (line_connecting zenon_TX_r Y)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.20/0.50 elim zenon_H19. zenon_intro zenon_TY_s. zenon_intro zenon_H1a. % 0.20/0.50 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_r zenon_TY_s)/\((~(apart_point_and_line zenon_TX_r Z))/\(~(apart_point_and_line zenon_TY_s Z))))->(~(distinct_lines Z (line_connecting zenon_TX_r zenon_TY_s))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.20/0.50 elim zenon_H1b. zenon_intro zenon_TZ_bc. zenon_intro zenon_H1d. % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.20/0.50 apply zenon_H1e. zenon_intro zenon_H20. % 0.20/0.50 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H10. zenon_intro zenon_H21. % 0.20/0.50 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.20/0.50 generalize (cu1 zenon_TX_r). zenon_intro zenon_H24. % 0.20/0.50 generalize (zenon_H24 zenon_TY_s). zenon_intro zenon_H25. % 0.20/0.50 generalize (zenon_H25 zenon_TZ_bc). zenon_intro zenon_H26. % 0.20/0.50 generalize (zenon_H26 (line_connecting zenon_TX_r zenon_TY_s)). zenon_intro zenon_H27. % 0.20/0.50 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.50 apply (zenon_notand_s _ _ zenon_H29); [ zenon_intro zenon_H16 | zenon_intro zenon_H2a ]. % 0.20/0.50 exact (zenon_H16 zenon_H10). % 0.20/0.50 exact (zenon_H2a zenon_H20). % 0.20/0.50 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.20/0.50 exact (zenon_H23 zenon_H2c). % 0.20/0.50 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.20/0.50 generalize (ci1 zenon_TX_r). zenon_intro zenon_H2f. % 0.20/0.50 generalize (zenon_H2f zenon_TY_s). zenon_intro zenon_H30. % 0.20/0.50 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H16 | zenon_intro zenon_H31 ]. % 0.20/0.50 exact (zenon_H16 zenon_H10). % 0.20/0.50 exact (zenon_H31 zenon_H2e). % 0.20/0.50 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_Hf ]. % 0.20/0.50 exact (zenon_H22 zenon_H32). % 0.20/0.50 apply (zenon_L1_ zenon_TX_r zenon_TY_s); trivial. % 0.20/0.50 Qed. % 0.20/0.50 % SZS output end Proof % 0.20/0.50 (* END-PROOF *) % 0.20/0.50 nodes searched: 184 % 0.20/0.50 max branch formulas: 151 % 0.20/0.50 proof nodes created: 30 % 0.20/0.50 formulas created: 1123 % 0.20/0.50 %------------------------------------------------------------------------------