%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET027+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 : Tue Jul 19 06:32:44 EDT 2022 % Result : Theorem 0.68s 0.91s % Output : Proof 0.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET027+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n011.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jul 10 20:04:26 EDT 2022 % 0.13/0.33 % CPUTime : % 0.68/0.91 (* PROOF-FOUND *) % 0.68/0.91 % SZS status Theorem % 0.68/0.91 (* BEGIN-PROOF *) % 0.68/0.91 % SZS output start Proof % 0.68/0.91 Theorem transitivity : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((subclass X Y)/\(subclass Y Z))->(subclass X Z))))). % 0.68/0.91 Proof. % 0.68/0.91 apply NNPP. intro zenon_G. % 0.68/0.91 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((subclass X Y)/\(subclass Y Z))->(subclass X Z))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 0.68/0.91 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e. % 0.68/0.91 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((subclass zenon_TX_bt Y)/\(subclass Y Z))->(subclass zenon_TX_bt Z)))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ]. % 0.68/0.91 elim zenon_H2f. zenon_intro zenon_TY_bw. zenon_intro zenon_H31. % 0.68/0.91 apply (zenon_notallex_s (fun Z : zenon_U => (((subclass zenon_TX_bt zenon_TY_bw)/\(subclass zenon_TY_bw Z))->(subclass zenon_TX_bt Z))) zenon_H31); [ zenon_intro zenon_H32; idtac ]. % 0.68/0.91 elim zenon_H32. zenon_intro zenon_TZ_bz. zenon_intro zenon_H34. % 0.68/0.91 apply (zenon_notimply_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.68/0.91 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 0.68/0.91 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H39. % 0.68/0.91 generalize (zenon_H39 zenon_TY_bw). zenon_intro zenon_H3a. % 0.68/0.91 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H3d; zenon_intro zenon_H3c | zenon_intro zenon_H38; zenon_intro zenon_H3b ]. % 0.68/0.91 exact (zenon_H3d zenon_H38). % 0.68/0.91 generalize (subclass_defn zenon_TY_bw). zenon_intro zenon_H3e. % 0.68/0.91 generalize (zenon_H3e zenon_TZ_bz). zenon_intro zenon_H3f. % 0.68/0.91 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H42; zenon_intro zenon_H41 | zenon_intro zenon_H37; zenon_intro zenon_H40 ]. % 0.68/0.91 exact (zenon_H42 zenon_H37). % 0.68/0.91 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H39. % 0.68/0.91 generalize (zenon_H39 zenon_TZ_bz). zenon_intro zenon_H43. % 0.68/0.91 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H35; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 0.68/0.91 apply (zenon_notallex_s (fun U : zenon_U => ((member U zenon_TX_bt)->(member U zenon_TZ_bz))) zenon_H46); [ zenon_intro zenon_H47; idtac ]. % 0.68/0.91 elim zenon_H47. zenon_intro zenon_TU_cu. zenon_intro zenon_H49. % 0.68/0.91 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 0.68/0.91 generalize (zenon_H40 zenon_TU_cu). zenon_intro zenon_H4c. % 0.68/0.91 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.68/0.91 generalize (zenon_H3b zenon_TU_cu). zenon_intro zenon_H4f. % 0.68/0.91 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.68/0.91 exact (zenon_H51 zenon_H4b). % 0.68/0.91 exact (zenon_H4e zenon_H50). % 0.68/0.91 exact (zenon_H4a zenon_H4d). % 0.68/0.91 exact (zenon_H35 zenon_H45). % 0.68/0.91 Qed. % 0.68/0.91 % SZS output end Proof % 0.68/0.91 (* END-PROOF *) % 0.68/0.91 nodes searched: 15287 % 0.68/0.91 max branch formulas: 3605 % 0.68/0.91 proof nodes created: 1605 % 0.68/0.91 formulas created: 66726 % 0.68/0.91 %------------------------------------------------------------------------------