%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 07:00:24 EDT 2022 % Result : Theorem 1.60s 1.77s % Output : Proof 1.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO176+1 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n019.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 11:02:54 EDT 2022 % 0.13/0.34 % CPUTime : % 1.60/1.77 (* PROOF-FOUND *) % 1.60/1.77 % SZS status Theorem % 1.60/1.77 (* BEGIN-PROOF *) % 1.60/1.77 % SZS output start Proof % 1.60/1.77 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 X V))))->(distinct_points X (intersection_point U V))))))). % 1.60/1.77 Proof. % 1.60/1.77 assert (zenon_L1_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_t Y)->(~(apart_point_and_line (intersection_point zenon_TU_t Y) zenon_TU_t)))) -> (convergent_lines zenon_TU_t zenon_TV_s) -> (apart_point_and_line (intersection_point zenon_TU_t zenon_TV_s) zenon_TU_t) -> False). % 1.60/1.77 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11. % 1.60/1.77 generalize (zenon_Hf zenon_TV_s). zenon_intro zenon_H14. % 1.60/1.77 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 1.60/1.77 exact (zenon_H16 zenon_H10). % 1.60/1.77 exact (zenon_H15 zenon_H11). % 1.60/1.77 (* end of lemma zenon_L1_ *) % 1.60/1.77 assert (zenon_L2_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U) (zenon_TX_bb : zenon_U), (forall Z : zenon_U, ((apart_point_and_line zenon_TX_bb zenon_TU_t)->((distinct_points zenon_TX_bb Z)\/(apart_point_and_line Z zenon_TU_t)))) -> (apart_point_and_line zenon_TX_bb zenon_TU_t) -> (~(distinct_points zenon_TX_bb (intersection_point zenon_TU_t zenon_TV_s))) -> (~(distinct_lines zenon_TU_t zenon_TU_t)) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_t Y)->(~(apart_point_and_line (intersection_point zenon_TU_t Y) zenon_TU_t)))) -> (convergent_lines zenon_TU_t zenon_TV_s) -> False). % 1.60/1.77 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19 zenon_H1a zenon_Hf zenon_H10. % 1.60/1.77 generalize (ceq2 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H1c. % 1.60/1.77 generalize (zenon_H1c zenon_TU_t). zenon_intro zenon_H1d. % 1.60/1.77 generalize (zenon_H1d zenon_TU_t). zenon_intro zenon_H1e. % 1.60/1.77 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H15 | zenon_intro zenon_H1f ]. % 1.60/1.77 generalize (zenon_H17 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H20. % 1.60/1.77 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 1.60/1.77 exact (zenon_H22 zenon_H18). % 1.60/1.77 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H11 ]. % 1.60/1.77 exact (zenon_H19 zenon_H23). % 1.60/1.77 exact (zenon_H15 zenon_H11). % 1.60/1.77 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H11 ]. % 1.60/1.77 exact (zenon_H1a zenon_H24). % 1.60/1.77 apply (zenon_L1_ zenon_TV_s zenon_TU_t); trivial. % 1.60/1.77 (* end of lemma zenon_L2_ *) % 1.60/1.77 assert (zenon_L3_ : forall (zenon_TV_s : zenon_U) (zenon_TU_t : zenon_U), (apart_point_and_line (intersection_point zenon_TU_t zenon_TV_s) zenon_TV_s) -> (convergent_lines zenon_TU_t zenon_TV_s) -> False). % 1.60/1.77 do 2 intro. intros zenon_H25 zenon_H10. % 1.60/1.77 generalize (ci4 zenon_TU_t). zenon_intro zenon_H26. % 1.60/1.77 generalize (zenon_H26 zenon_TV_s). zenon_intro zenon_H27. % 1.60/1.77 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H16 | zenon_intro zenon_H28 ]. % 1.60/1.77 exact (zenon_H16 zenon_H10). % 1.60/1.77 exact (zenon_H28 zenon_H25). % 1.60/1.77 (* end of lemma zenon_L3_ *) % 1.60/1.77 apply NNPP. intro zenon_G. % 1.60/1.77 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 X V))))->(distinct_points X (intersection_point U V))))))) zenon_G); [ zenon_intro zenon_H29; idtac ]. % 1.60/1.77 elim zenon_H29. zenon_intro zenon_TX_bb. zenon_intro zenon_H2a. % 1.60/1.77 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bb Y)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_bb U)\/(apart_point_and_line zenon_TX_bb V))))->(distinct_points zenon_TX_bb (intersection_point U V)))))) zenon_H2a); [ zenon_intro zenon_H2b; idtac ]. % 1.60/1.77 elim zenon_H2b. zenon_intro zenon_TY_bs. zenon_intro zenon_H2d. % 1.60/1.77 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bb zenon_TY_bs)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_bb U)\/(apart_point_and_line zenon_TX_bb V))))->(distinct_points zenon_TX_bb (intersection_point U V))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 1.60/1.77 elim zenon_H2e. zenon_intro zenon_TU_t. zenon_intro zenon_H2f. % 1.60/1.77 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bb zenon_TY_bs)/\((convergent_lines zenon_TU_t V)/\((apart_point_and_line zenon_TX_bb zenon_TU_t)\/(apart_point_and_line zenon_TX_bb V))))->(distinct_points zenon_TX_bb (intersection_point zenon_TU_t V)))) zenon_H2f); [ zenon_intro zenon_H30; idtac ]. % 1.60/1.77 elim zenon_H30. zenon_intro zenon_TV_s. zenon_intro zenon_H31. % 1.60/1.77 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H32. zenon_intro zenon_H19. % 1.60/1.77 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33. % 1.60/1.77 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H10. zenon_intro zenon_H35. % 1.60/1.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H18 | zenon_intro zenon_H36 ]. % 1.60/1.77 generalize (ci3 zenon_TU_t). zenon_intro zenon_Hf. % 1.60/1.77 generalize (apart2 zenon_TU_t). zenon_intro zenon_H1a. % 1.60/1.77 generalize (ceq1 zenon_TX_bb). zenon_intro zenon_H37. % 1.60/1.77 generalize (zenon_H37 zenon_TU_t). zenon_intro zenon_H17. % 1.60/1.77 apply (zenon_L2_ zenon_TV_s zenon_TU_t zenon_TX_bb); trivial. % 1.60/1.77 generalize (ceq1 zenon_TX_bb). zenon_intro zenon_H37. % 1.60/1.77 generalize (zenon_H37 zenon_TV_s). zenon_intro zenon_H38. % 1.60/1.77 generalize (apart2 zenon_TV_s). zenon_intro zenon_H39. % 1.60/1.77 generalize (ceq2 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H1c. % 1.60/1.77 generalize (zenon_H1c zenon_TV_s). zenon_intro zenon_H3a. % 1.60/1.77 generalize (zenon_H3a zenon_TV_s). zenon_intro zenon_H3b. % 1.60/1.77 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H28 | zenon_intro zenon_H3c ]. % 1.60/1.77 generalize (zenon_H38 (intersection_point zenon_TU_t zenon_TV_s)). zenon_intro zenon_H3d. % 1.60/1.77 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 1.60/1.77 exact (zenon_H3f zenon_H36). % 1.60/1.77 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H23 | zenon_intro zenon_H25 ]. % 1.60/1.77 exact (zenon_H19 zenon_H23). % 1.60/1.77 exact (zenon_H28 zenon_H25). % 1.60/1.77 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H40 | zenon_intro zenon_H25 ]. % 1.60/1.77 exact (zenon_H39 zenon_H40). % 1.60/1.77 apply (zenon_L3_ zenon_TV_s zenon_TU_t); trivial. % 1.60/1.77 Qed. % 1.60/1.77 % SZS output end Proof % 1.60/1.77 (* END-PROOF *) % 1.60/1.77 nodes searched: 118289 % 1.60/1.77 max branch formulas: 5693 % 1.60/1.77 proof nodes created: 3013 % 1.60/1.77 formulas created: 253236 % 1.60/1.77 %------------------------------------------------------------------------------