%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0. % 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 : Wed Jul 20 23:04:07 EDT 2022 % Result : Theorem 0.48s 0.65s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n026.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 : Tue Jun 14 15:49:06 EDT 2022 % 0.13/0.33 % CPUTime : % 0.48/0.65 Zenon warning: unused variable (X : zenon_U) in ax47 % 0.48/0.65 Zenon warning: unused variable (X : zenon_U) in ax48 % 0.48/0.65 Zenon warning: unused variable (X : zenon_U) in ax49 % 0.48/0.65 Zenon warning: unused variable (X : zenon_U) in ax51 % 0.48/0.65 (* PROOF-FOUND *) % 0.48/0.65 % SZS status Theorem % 0.48/0.65 (* BEGIN-PROOF *) % 0.48/0.65 % SZS output start Proof % 0.48/0.65 Theorem l7_co : (forall U : zenon_U, (forall V : zenon_U, (forall W : zenon_U, ((phi (findmin_cpq_eff (triple U V W)))->(pi_sharp_find_min (i (triple U V W)) (findmin_cpq_res (triple U V W))))))). % 0.48/0.65 Proof. % 0.48/0.65 assert (zenon_L1_ : forall (zenon_TW_cp : zenon_U) (zenon_TV_cq : zenon_U) (zenon_TU_cr : zenon_U), (exists V : zenon_U, ((succ_cpq (findmin_cpq_eff (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp)) V)/\((ok V)/\(check_cpq V)))) -> (~(phi (findmin_cpq_eff (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp)))) -> False). % 0.48/0.65 do 3 intro. intros zenon_H41 zenon_H42. % 0.48/0.65 generalize (ax62 (findmin_cpq_eff (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H46. % 0.48/0.65 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H42; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H41 ]. % 0.48/0.65 exact (zenon_H48 zenon_H41). % 0.48/0.65 exact (zenon_H42 zenon_H47). % 0.48/0.65 (* end of lemma zenon_L1_ *) % 0.48/0.65 apply NNPP. intro zenon_G. % 0.48/0.65 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (forall W : zenon_U, ((phi (findmin_cpq_eff (triple U V W)))->(pi_sharp_find_min (i (triple U V W)) (findmin_cpq_res (triple U V W))))))) zenon_G); [ zenon_intro zenon_H49; idtac ]. % 0.48/0.65 elim zenon_H49. zenon_intro zenon_TU_cr. zenon_intro zenon_H4a. % 0.48/0.65 apply (zenon_notallex_s (fun V : zenon_U => (forall W : zenon_U, ((phi (findmin_cpq_eff (triple zenon_TU_cr V W)))->(pi_sharp_find_min (i (triple zenon_TU_cr V W)) (findmin_cpq_res (triple zenon_TU_cr V W)))))) zenon_H4a); [ zenon_intro zenon_H4b; idtac ]. % 0.48/0.65 elim zenon_H4b. zenon_intro zenon_TV_cq. zenon_intro zenon_H4c. % 0.48/0.65 apply (zenon_notallex_s (fun W : zenon_U => ((phi (findmin_cpq_eff (triple zenon_TU_cr zenon_TV_cq W)))->(pi_sharp_find_min (i (triple zenon_TU_cr zenon_TV_cq W)) (findmin_cpq_res (triple zenon_TU_cr zenon_TV_cq W))))) zenon_H4c); [ zenon_intro zenon_H4d; idtac ]. % 0.48/0.65 elim zenon_H4d. zenon_intro zenon_TW_cp. zenon_intro zenon_H4e. % 0.48/0.65 apply (zenon_notimply_s _ _ zenon_H4e). zenon_intro zenon_H47. zenon_intro zenon_H4f. % 0.48/0.65 generalize (ax62 (findmin_cpq_eff (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H46. % 0.48/0.65 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H42; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H41 ]. % 0.48/0.65 exact (zenon_H42 zenon_H47). % 0.48/0.65 generalize (ax58 (i (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H50. % 0.48/0.65 generalize (zenon_H50 (findmin_cpq_res (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H51. % 0.48/0.65 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H4f; zenon_intro zenon_H54 | zenon_intro zenon_H53; zenon_intro zenon_H52 ]. % 0.48/0.65 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.48/0.65 generalize (l7_l8 zenon_TU_cr). zenon_intro zenon_H57. % 0.48/0.65 generalize (zenon_H57 zenon_TV_cq). zenon_intro zenon_H58. % 0.48/0.65 generalize (zenon_H58 zenon_TW_cp). zenon_intro zenon_H59. % 0.48/0.65 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H42 | zenon_intro zenon_H5a ]. % 0.48/0.65 apply (zenon_L1_ zenon_TW_cp zenon_TV_cq zenon_TU_cr); trivial. % 0.48/0.65 exact (zenon_H56 zenon_H5a). % 0.48/0.65 generalize (ax10 (i (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H5b. % 0.48/0.65 generalize (zenon_H5b (findmin_cpq_res (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H5c. % 0.48/0.65 apply (zenon_equiv_s _ _ zenon_H5c); [ zenon_intro zenon_H55; zenon_intro zenon_H5f | zenon_intro zenon_H5e; zenon_intro zenon_H5d ]. % 0.48/0.65 generalize (l7_lX zenon_TU_cr). zenon_intro zenon_H60. % 0.48/0.65 generalize (zenon_H60 zenon_TV_cq). zenon_intro zenon_H61. % 0.48/0.65 generalize (zenon_H61 zenon_TW_cp). zenon_intro zenon_H62. % 0.48/0.65 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H42 | zenon_intro zenon_H5e ]. % 0.48/0.65 apply (zenon_L1_ zenon_TW_cp zenon_TV_cq zenon_TU_cr); trivial. % 0.48/0.65 generalize (ax10 (i (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H5b. % 0.48/0.65 generalize (zenon_H5b (findmin_cpq_res (triple zenon_TU_cr zenon_TV_cq zenon_TW_cp))). zenon_intro zenon_H5c. % 0.48/0.65 apply (zenon_equiv_s _ _ zenon_H5c); [ zenon_intro zenon_H55; zenon_intro zenon_H5f | zenon_intro zenon_H5e; zenon_intro zenon_H5d ]. % 0.48/0.65 exact (zenon_H55 zenon_H5e). % 0.48/0.65 exact (zenon_H5f zenon_H5d). % 0.48/0.65 exact (zenon_H55 zenon_H5e). % 0.48/0.65 exact (zenon_H4f zenon_H53). % 0.48/0.65 Qed. % 0.48/0.65 % SZS output end Proof % 0.48/0.65 (* END-PROOF *) % 0.48/0.65 nodes searched: 5097 % 0.48/0.65 max branch formulas: 1023 % 0.48/0.65 proof nodes created: 199 % 0.48/0.65 formulas created: 13114 % 0.48/0.65 %------------------------------------------------------------------------------