%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 06:59:59 EDT 2022 % Result : Theorem 0.42s 0.59s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO112+1 : TPTP v8.1.0. Released v2.4.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n026.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jun 17 23:43:09 EDT 2022 % 0.12/0.34 % CPUTime : % 0.42/0.59 (* PROOF-FOUND *) % 0.42/0.59 % SZS status Theorem % 0.42/0.59 (* BEGIN-PROOF *) % 0.42/0.59 % SZS output start Proof % 0.42/0.59 Theorem theorem_3_8_2 : (forall C : zenon_U, (forall P : zenon_U, (forall Q : zenon_U, (forall R : zenon_U, ((between_c C P Q R)->(between_c C R Q P)))))). % 0.42/0.59 Proof. % 0.42/0.59 apply NNPP. intro zenon_G. % 0.42/0.59 apply (zenon_notallex_s (fun C : zenon_U => (forall P : zenon_U, (forall Q : zenon_U, (forall R : zenon_U, ((between_c C P Q R)->(between_c C R Q P)))))) zenon_G); [ zenon_intro zenon_H12; idtac ]. % 0.42/0.59 elim zenon_H12. zenon_intro zenon_TC_t. zenon_intro zenon_H14. % 0.42/0.59 apply (zenon_notallex_s (fun P : zenon_U => (forall Q : zenon_U, (forall R : zenon_U, ((between_c zenon_TC_t P Q R)->(between_c zenon_TC_t R Q P))))) zenon_H14); [ zenon_intro zenon_H15; idtac ]. % 0.42/0.59 elim zenon_H15. zenon_intro zenon_TP_w. zenon_intro zenon_H17. % 0.42/0.59 apply (zenon_notallex_s (fun Q : zenon_U => (forall R : zenon_U, ((between_c zenon_TC_t zenon_TP_w Q R)->(between_c zenon_TC_t R Q zenon_TP_w)))) zenon_H17); [ zenon_intro zenon_H18; idtac ]. % 0.42/0.59 elim zenon_H18. zenon_intro zenon_TQ_z. zenon_intro zenon_H1a. % 0.42/0.59 apply (zenon_notallex_s (fun R : zenon_U => ((between_c zenon_TC_t zenon_TP_w zenon_TQ_z R)->(between_c zenon_TC_t R zenon_TQ_z zenon_TP_w))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.42/0.59 elim zenon_H1b. zenon_intro zenon_TR_bc. zenon_intro zenon_H1d. % 0.42/0.59 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.42/0.59 generalize (between_c_defn zenon_TC_t). zenon_intro zenon_H20. % 0.42/0.59 generalize (zenon_H20 zenon_TP_w). zenon_intro zenon_H21. % 0.42/0.59 generalize (zenon_H21 zenon_TQ_z). zenon_intro zenon_H22. % 0.42/0.59 generalize (zenon_H22 zenon_TR_bc). zenon_intro zenon_H23. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H1f; zenon_intro zenon_H24 ]. % 0.42/0.59 exact (zenon_H26 zenon_H1f). % 0.42/0.59 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.42/0.59 elim zenon_H27. zenon_intro zenon_TCpp_bp. zenon_intro zenon_H2a. % 0.42/0.59 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.42/0.59 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.42/0.59 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.42/0.59 generalize (part_of_defn zenon_TC_t). zenon_intro zenon_H31. % 0.42/0.59 generalize (zenon_H31 zenon_TCpp_bp). zenon_intro zenon_H32. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2c; zenon_intro zenon_H33 ]. % 0.42/0.59 exact (zenon_H35 zenon_H2c). % 0.42/0.59 generalize (end_point_defn zenon_TP_w). zenon_intro zenon_H36. % 0.42/0.59 generalize (zenon_H36 zenon_TCpp_bp). zenon_intro zenon_H37. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H2e; zenon_intro zenon_H38 ]. % 0.42/0.59 exact (zenon_H3a zenon_H2e). % 0.42/0.59 generalize (end_point_defn zenon_TR_bc). zenon_intro zenon_H3b. % 0.42/0.59 generalize (zenon_H3b zenon_TCpp_bp). zenon_intro zenon_H3c. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H30; zenon_intro zenon_H3d ]. % 0.42/0.59 exact (zenon_H3f zenon_H30). % 0.42/0.59 generalize (inner_point_defn zenon_TQ_z). zenon_intro zenon_H40. % 0.42/0.59 generalize (zenon_H40 zenon_TCpp_bp). zenon_intro zenon_H41. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H2f; zenon_intro zenon_H42 ]. % 0.42/0.59 exact (zenon_H44 zenon_H2f). % 0.42/0.59 generalize (between_c_defn zenon_TC_t). zenon_intro zenon_H20. % 0.42/0.59 generalize (zenon_H20 zenon_TR_bc). zenon_intro zenon_H45. % 0.42/0.59 generalize (zenon_H45 zenon_TQ_z). zenon_intro zenon_H46. % 0.42/0.59 generalize (zenon_H46 zenon_TP_w). zenon_intro zenon_H47. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H1e; zenon_intro zenon_H4a | zenon_intro zenon_H49; zenon_intro zenon_H48 ]. % 0.42/0.59 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.42/0.59 apply zenon_H4c. zenon_intro zenon_H4d. % 0.42/0.59 apply zenon_H28. apply sym_equal. exact zenon_H4d. % 0.42/0.59 apply zenon_H4b. exists zenon_TCpp_bp. apply NNPP. zenon_intro zenon_H4e. % 0.42/0.59 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H35 | zenon_intro zenon_H4f ]. % 0.42/0.59 generalize (part_of_defn zenon_TC_t). zenon_intro zenon_H31. % 0.42/0.59 generalize (zenon_H31 zenon_TCpp_bp). zenon_intro zenon_H32. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2c; zenon_intro zenon_H33 ]. % 0.42/0.59 exact (zenon_H34 zenon_H33). % 0.42/0.59 exact (zenon_H35 zenon_H2c). % 0.42/0.59 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H3f | zenon_intro zenon_H50 ]. % 0.42/0.59 generalize (end_point_defn zenon_TR_bc). zenon_intro zenon_H3b. % 0.42/0.59 generalize (zenon_H3b zenon_TCpp_bp). zenon_intro zenon_H3c. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H30; zenon_intro zenon_H3d ]. % 0.42/0.59 exact (zenon_H3e zenon_H3d). % 0.42/0.59 exact (zenon_H3f zenon_H30). % 0.42/0.59 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H3a | zenon_intro zenon_H44 ]. % 0.42/0.59 generalize (end_point_defn zenon_TP_w). zenon_intro zenon_H36. % 0.42/0.59 generalize (zenon_H36 zenon_TCpp_bp). zenon_intro zenon_H37. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H2e; zenon_intro zenon_H38 ]. % 0.42/0.59 exact (zenon_H39 zenon_H38). % 0.42/0.59 exact (zenon_H3a zenon_H2e). % 0.42/0.59 generalize (inner_point_defn zenon_TQ_z). zenon_intro zenon_H40. % 0.42/0.59 generalize (zenon_H40 zenon_TCpp_bp). zenon_intro zenon_H41. % 0.42/0.59 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H2f; zenon_intro zenon_H42 ]. % 0.42/0.59 exact (zenon_H43 zenon_H42). % 0.42/0.59 exact (zenon_H44 zenon_H2f). % 0.42/0.59 exact (zenon_H1e zenon_H49). % 0.42/0.59 Qed. % 0.42/0.59 % SZS output end Proof % 0.42/0.59 (* END-PROOF *) % 0.42/0.59 nodes searched: 2740 % 0.42/0.59 max branch formulas: 1491 % 0.42/0.59 proof nodes created: 117 % 0.42/0.59 formulas created: 23110 % 0.42/0.59 %------------------------------------------------------------------------------