%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS217+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 : Sun Jul 17 03:39:47 EDT 2022 % Result : Theorem 77.54s 77.73s % Output : Proof 77.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : KRS217+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n025.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 7 11:19:33 EDT 2022 % 0.12/0.33 % CPUTime : % 77.54/77.73 (* PROOF-FOUND *) % 77.54/77.73 % SZS status Theorem % 77.54/77.73 (* BEGIN-PROOF *) % 77.54/77.73 % SZS output start Proof % 77.54/77.73 Theorem nota_noc_thm : (nota (noc) (thm)). % 77.54/77.73 Proof. % 77.54/77.73 assert (zenon_L1_ : forall (zenon_TI1_bl : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TF_bn : zenon_U), (~(exists I1 : zenon_U, ((model I1 zenon_TF_bn)/\(model I1 zenon_TAx_bm)))) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> (model zenon_TI1_bl zenon_TAx_bm) -> False). % 77.54/77.73 do 3 intro. intros zenon_H22 zenon_H23 zenon_H24. % 77.54/77.73 apply zenon_H22. exists zenon_TI1_bl. apply NNPP. zenon_intro zenon_H28. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 77.54/77.73 generalize (zenon_H23 zenon_TI1_bl). zenon_intro zenon_H2b. % 77.54/77.73 exact (zenon_H2a zenon_H2b). % 77.54/77.73 exact (zenon_H29 zenon_H24). % 77.54/77.73 (* end of lemma zenon_L1_ *) % 77.54/77.73 assert (zenon_L2_ : forall (zenon_TI4_bu : zenon_U) (zenon_TF_bn : zenon_U), (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bn)))) -> (~(model zenon_TI4_bu zenon_TF_bn)) -> False). % 77.54/77.73 do 2 intro. intros zenon_H2c zenon_H2d. % 77.54/77.73 apply zenon_H2c. exists zenon_TI4_bu. apply NNPP. zenon_intro zenon_H2f. % 77.54/77.73 exact (zenon_H2f zenon_H2d). % 77.54/77.73 (* end of lemma zenon_L2_ *) % 77.54/77.73 assert (zenon_L3_ : forall (zenon_TAx_bm : zenon_U) (zenon_TF_bn : zenon_U), (~(~(status zenon_TF_bn zenon_TAx_bm (thm)))) -> (~(status zenon_TF_bn zenon_TAx_bm (thm))) -> False). % 77.54/77.73 do 2 intro. intros zenon_H30 zenon_H31. % 77.54/77.73 exact (zenon_H30 zenon_H31). % 77.54/77.73 (* end of lemma zenon_L3_ *) % 77.54/77.73 assert (zenon_L4_ : forall (zenon_TI1_bl : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TAx_bm : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (model zenon_TI1_bl zenon_TAx_bm) -> (~(model zenon_TI1_bl zenon_TC_ca)) -> False). % 77.54/77.73 do 3 intro. intros zenon_H32 zenon_H24 zenon_H33. % 77.54/77.73 generalize (zenon_H32 zenon_TI1_bl). zenon_intro zenon_H35. % 77.54/77.73 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H29 | zenon_intro zenon_H36 ]. % 77.54/77.73 exact (zenon_H29 zenon_H24). % 77.54/77.73 exact (zenon_H33 zenon_H36). % 77.54/77.73 (* end of lemma zenon_L4_ *) % 77.54/77.73 assert (zenon_L5_ : forall (zenon_TI1_bl : zenon_U) (zenon_TI3_cg : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TC_ca : zenon_U), (~((exists I1 : zenon_U, ((model I1 zenon_TC_ca)/\(model I1 zenon_TAx_bm)))/\(exists I1 : zenon_U, ((model I1 zenon_TC_ca)/\(model I1 (not zenon_TAx_bm)))))) -> (model zenon_TI3_cg (not zenon_TAx_bm)) -> (model zenon_TI3_cg zenon_TC_ca) -> (model zenon_TI1_bl zenon_TAx_bm) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> False). % 77.54/77.73 do 4 intro. intros zenon_H37 zenon_H38 zenon_H39 zenon_H24 zenon_H32. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 77.54/77.73 apply zenon_H3c. exists zenon_TI1_bl. apply NNPP. zenon_intro zenon_H3d. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H33 | zenon_intro zenon_H29 ]. % 77.54/77.73 apply (zenon_L4_ zenon_TI1_bl zenon_TC_ca zenon_TAx_bm); trivial. % 77.54/77.73 exact (zenon_H29 zenon_H24). % 77.54/77.73 apply zenon_H3b. exists zenon_TI3_cg. apply NNPP. zenon_intro zenon_H3e. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 77.54/77.73 exact (zenon_H40 zenon_H39). % 77.54/77.73 exact (zenon_H3f zenon_H38). % 77.54/77.73 (* end of lemma zenon_L5_ *) % 77.54/77.73 assert (zenon_L6_ : forall (zenon_TI1_cq : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TF_bn : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TF_bn)->(model I1 zenon_TAx_bm))) -> (model zenon_TI1_cq zenon_TF_bn) -> (~(model zenon_TI1_cq zenon_TAx_bm)) -> False). % 77.54/77.73 do 3 intro. intros zenon_H41 zenon_H42 zenon_H43. % 77.54/77.73 generalize (zenon_H41 zenon_TI1_cq). zenon_intro zenon_H45. % 77.54/77.73 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 77.54/77.73 exact (zenon_H47 zenon_H42). % 77.54/77.73 exact (zenon_H43 zenon_H46). % 77.54/77.73 (* end of lemma zenon_L6_ *) % 77.54/77.73 assert (zenon_L7_ : forall (zenon_TAx_bm : zenon_U) (zenon_TF_bn : zenon_U) (zenon_TI1_cq : zenon_U), (forall F : zenon_U, ((model zenon_TI1_cq F)<->(~(model zenon_TI1_cq (not F))))) -> (forall I1 : zenon_U, ((model I1 zenon_TF_bn)->(model I1 zenon_TAx_bm))) -> (model zenon_TI1_cq zenon_TF_bn) -> (model zenon_TI1_cq (not zenon_TAx_bm)) -> False). % 77.54/77.73 do 3 intro. intros zenon_H48 zenon_H41 zenon_H42 zenon_H49. % 77.54/77.73 generalize (zenon_H48 zenon_TAx_bm). zenon_intro zenon_H4a. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H43; zenon_intro zenon_H4c | zenon_intro zenon_H46; zenon_intro zenon_H4b ]. % 77.54/77.73 apply (zenon_L6_ zenon_TI1_cq zenon_TAx_bm zenon_TF_bn); trivial. % 77.54/77.73 exact (zenon_H4b zenon_H49). % 77.54/77.73 (* end of lemma zenon_L7_ *) % 77.54/77.73 assert (zenon_L8_ : forall (zenon_TI3_cg : zenon_U) (zenon_TI1_bl : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TF_bn : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TF_bn)->(model I1 zenon_TAx_bm))) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (model zenon_TI1_bl zenon_TAx_bm) -> (model zenon_TI3_cg zenon_TC_ca) -> (model zenon_TI3_cg (not zenon_TAx_bm)) -> False). % 77.54/77.73 do 5 intro. intros zenon_H41 zenon_H23 zenon_H32 zenon_H24 zenon_H39 zenon_H38. % 77.54/77.73 generalize (noc zenon_TC_ca). zenon_intro zenon_H4d. % 77.54/77.73 generalize (zenon_H4d zenon_TAx_bm). zenon_intro zenon_H4e. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H4e); [ zenon_intro zenon_H37; zenon_intro zenon_H51 | zenon_intro zenon_H50; zenon_intro zenon_H4f ]. % 77.54/77.73 apply (zenon_L5_ zenon_TI1_bl zenon_TI3_cg zenon_TAx_bm zenon_TC_ca); trivial. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H53. zenon_intro zenon_H52. % 77.54/77.73 elim zenon_H52. zenon_intro zenon_TI1_cq. zenon_intro zenon_H54. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H55. zenon_intro zenon_H49. % 77.54/77.73 generalize (not zenon_TI1_cq). zenon_intro zenon_H48. % 77.54/77.73 generalize (zenon_H48 zenon_TF_bn). zenon_intro zenon_H56. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H47; zenon_intro zenon_H58 | zenon_intro zenon_H42; zenon_intro zenon_H57 ]. % 77.54/77.73 generalize (zenon_H23 zenon_TI1_cq). zenon_intro zenon_H42. % 77.54/77.73 exact (zenon_H47 zenon_H42). % 77.54/77.73 apply (zenon_L7_ zenon_TAx_bm zenon_TF_bn zenon_TI1_cq); trivial. % 77.54/77.73 (* end of lemma zenon_L8_ *) % 77.54/77.73 assert (zenon_L9_ : forall (zenon_TF_bn : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TI1_bl : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TI3_cg : zenon_U), (forall F : zenon_U, ((model zenon_TI3_cg F)<->(~(model zenon_TI3_cg (not F))))) -> (model zenon_TI3_cg zenon_TC_ca) -> (model zenon_TI1_bl zenon_TAx_bm) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> (forall I1 : zenon_U, ((model I1 zenon_TF_bn)->(model I1 zenon_TAx_bm))) -> (~(model zenon_TI3_cg zenon_TAx_bm)) -> False). % 77.54/77.73 do 5 intro. intros zenon_H59 zenon_H39 zenon_H24 zenon_H32 zenon_H23 zenon_H41 zenon_H5a. % 77.54/77.73 generalize (zenon_H59 zenon_TAx_bm). zenon_intro zenon_H5b. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H5a; zenon_intro zenon_H5d | zenon_intro zenon_H5c; zenon_intro zenon_H3f ]. % 77.54/77.73 apply zenon_H5d. zenon_intro zenon_H38. % 77.54/77.73 apply (zenon_L8_ zenon_TI3_cg zenon_TI1_bl zenon_TC_ca zenon_TAx_bm zenon_TF_bn); trivial. % 77.54/77.73 exact (zenon_H5a zenon_H5c). % 77.54/77.73 (* end of lemma zenon_L9_ *) % 77.54/77.73 assert (zenon_L10_ : forall (zenon_TI1_bl : zenon_U) (zenon_TF_bn : zenon_U) (zenon_TI4_bu : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TI3_cg : zenon_U), (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (noc))/\(~(status Ax C (thm))))))) -> (~(model zenon_TI3_cg zenon_TAx_bm)) -> (model zenon_TI3_cg zenon_TC_ca) -> (forall F : zenon_U, ((model zenon_TI3_cg F)<->(~(model zenon_TI3_cg (not F))))) -> (~(model zenon_TI4_bu zenon_TC_ca)) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bn)))) -> (forall F : zenon_U, (~((model zenon_TI4_bu F)<->(model zenon_TI4_bu (not F))))) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (model zenon_TI1_bl zenon_TAx_bm) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TF_bn)->(model I1 C)))<->(status zenon_TF_bn C (thm)))) -> False). % 77.54/77.73 do 6 intro. intros zenon_H5e zenon_H5a zenon_H39 zenon_H59 zenon_H5f zenon_H2c zenon_H60 zenon_H32 zenon_H24 zenon_H23 zenon_H61. % 77.54/77.73 apply zenon_H5e. exists zenon_TF_bn. apply NNPP. zenon_intro zenon_H62. % 77.54/77.73 generalize (zenon_H61 zenon_TAx_bm). zenon_intro zenon_H63. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H65; zenon_intro zenon_H31 | zenon_intro zenon_H41; zenon_intro zenon_H64 ]. % 77.54/77.73 apply zenon_H62. exists zenon_TAx_bm. apply NNPP. zenon_intro zenon_H66. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H30 ]. % 77.54/77.73 generalize (noc zenon_TF_bn). zenon_intro zenon_H68. % 77.54/77.73 generalize (zenon_H68 zenon_TAx_bm). zenon_intro zenon_H69. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H69); [ zenon_intro zenon_H6c; zenon_intro zenon_H67 | zenon_intro zenon_H6b; zenon_intro zenon_H6a ]. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H22 | zenon_intro zenon_H6d ]. % 77.54/77.73 apply (zenon_L1_ zenon_TI1_bl zenon_TAx_bm zenon_TF_bn); trivial. % 77.54/77.73 generalize (zenon_H32 zenon_TI4_bu). zenon_intro zenon_H6e. % 77.54/77.73 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H70 | zenon_intro zenon_H6f ]. % 77.54/77.73 generalize (zenon_H60 zenon_TAx_bm). zenon_intro zenon_H71. % 77.54/77.73 apply (zenon_notequiv_s _ _ zenon_H71); [ zenon_intro zenon_H70; zenon_intro zenon_H74 | zenon_intro zenon_H73; zenon_intro zenon_H72 ]. % 77.54/77.73 apply zenon_H6d. exists zenon_TI4_bu. apply NNPP. zenon_intro zenon_H75. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H2d | zenon_intro zenon_H72 ]. % 77.54/77.73 apply (zenon_L2_ zenon_TI4_bu zenon_TF_bn); trivial. % 77.54/77.73 exact (zenon_H72 zenon_H74). % 77.54/77.73 exact (zenon_H70 zenon_H73). % 77.54/77.73 exact (zenon_H5f zenon_H6f). % 77.54/77.73 exact (zenon_H67 zenon_H6a). % 77.54/77.73 exact (zenon_H30 zenon_H31). % 77.54/77.73 apply (zenon_L9_ zenon_TF_bn zenon_TAx_bm zenon_TI1_bl zenon_TC_ca zenon_TI3_cg); trivial. % 77.54/77.73 (* end of lemma zenon_L10_ *) % 77.54/77.73 assert (zenon_L11_ : forall (zenon_TI1_bl : zenon_U) (zenon_TF_bn : zenon_U) (zenon_TI4_bu : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TI3_cg : zenon_U), (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (noc))/\(~(status Ax C (thm))))))) -> (~(model zenon_TI3_cg zenon_TAx_bm)) -> (model zenon_TI3_cg zenon_TC_ca) -> (forall F : zenon_U, ((model zenon_TI3_cg F)<->(~(model zenon_TI3_cg (not F))))) -> (~(model zenon_TI4_bu zenon_TC_ca)) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bn)))) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (model zenon_TI1_bl zenon_TAx_bm) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> False). % 77.54/77.73 do 6 intro. intros zenon_H5e zenon_H5a zenon_H39 zenon_H59 zenon_H5f zenon_H2c zenon_H32 zenon_H24 zenon_H23. % 77.54/77.73 generalize (thm zenon_TF_bn). zenon_intro zenon_H61. % 77.54/77.73 generalize (completeness zenon_TI4_bu). zenon_intro zenon_H60. % 77.54/77.73 apply (zenon_L10_ zenon_TI1_bl zenon_TF_bn zenon_TI4_bu zenon_TC_ca zenon_TAx_bm zenon_TI3_cg); trivial. % 77.54/77.73 (* end of lemma zenon_L11_ *) % 77.54/77.73 assert (zenon_L12_ : forall (zenon_TF_bn : zenon_U), (exists I4 : zenon_U, (~(model I4 zenon_TF_bn))) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> False). % 77.54/77.73 do 1 intro. intros zenon_H76 zenon_H23. % 77.54/77.73 elim zenon_H76. zenon_intro zenon_TI4_ep. zenon_intro zenon_H78. % 77.54/77.73 generalize (zenon_H23 zenon_TI4_ep). zenon_intro zenon_H79. % 77.54/77.73 exact (zenon_H78 zenon_H79). % 77.54/77.73 (* end of lemma zenon_L12_ *) % 77.54/77.73 assert (zenon_L13_ : forall (zenon_TF_bn : zenon_U), (~(forall I : zenon_U, (model I zenon_TF_bn))) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> False). % 77.54/77.73 do 1 intro. intros zenon_H7a zenon_H23. % 77.54/77.73 exact (zenon_H7a zenon_H23). % 77.54/77.73 (* end of lemma zenon_L13_ *) % 77.54/77.73 assert (zenon_L14_ : forall (zenon_TF_bn : zenon_U), ((exists I1 : zenon_U, (model I1 zenon_TF_bn))/\((exists I4 : zenon_U, (~(model I4 zenon_TF_bn)))/\(forall I : zenon_U, (model I zenon_TF_bn)))) -> False). % 77.54/77.73 do 1 intro. intros zenon_H7b. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H7d. zenon_intro zenon_H7c. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H76. zenon_intro zenon_H23. % 77.54/77.73 apply (zenon_L12_ zenon_TF_bn); trivial. % 77.54/77.73 (* end of lemma zenon_L14_ *) % 77.54/77.73 assert (zenon_L15_ : forall (zenon_TI1_bl : zenon_U) (zenon_TI4_bu : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TI3_cg : zenon_U) (zenon_TF_bn : zenon_U), (exists I1 : zenon_U, (model I1 zenon_TF_bn)) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (noc))/\(~(status Ax C (thm))))))) -> (~(model zenon_TI3_cg zenon_TAx_bm)) -> (model zenon_TI3_cg zenon_TC_ca) -> (~(model zenon_TI4_bu zenon_TC_ca)) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (model zenon_TI1_bl zenon_TAx_bm) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> (forall C : zenon_U, (((exists I1 : zenon_U, (model I1 zenon_TF_bn))/\((exists I4 : zenon_U, (~(model I4 zenon_TF_bn)))/\(forall I2 : zenon_U, (model I2 C))))<->(status zenon_TF_bn C (wtc)))) -> False). % 77.54/77.73 do 6 intro. intros zenon_H7d zenon_H5e zenon_H5a zenon_H39 zenon_H5f zenon_H32 zenon_H24 zenon_H23 zenon_H7e. % 77.54/77.73 generalize (not zenon_TI3_cg). zenon_intro zenon_H59. % 77.54/77.73 generalize (zenon_H7e zenon_TF_bn). zenon_intro zenon_H7f. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H7f); [ zenon_intro zenon_H82; zenon_intro zenon_H81 | zenon_intro zenon_H7b; zenon_intro zenon_H80 ]. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 77.54/77.73 exact (zenon_H84 zenon_H7d). % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H2c | zenon_intro zenon_H7a ]. % 77.54/77.73 apply (zenon_L11_ zenon_TI1_bl zenon_TF_bn zenon_TI4_bu zenon_TC_ca zenon_TAx_bm zenon_TI3_cg); trivial. % 77.54/77.73 exact (zenon_H7a zenon_H23). % 77.54/77.73 apply (zenon_L14_ zenon_TF_bn); trivial. % 77.54/77.73 (* end of lemma zenon_L15_ *) % 77.54/77.73 assert (zenon_L16_ : forall (zenon_TF_bn : zenon_U), (exists I1 : zenon_U, ((model I1 zenon_TF_bn)/\(model I1 zenon_TF_bn))) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bn))) -> False). % 77.54/77.73 do 1 intro. intros zenon_H85 zenon_H84. % 77.54/77.73 elim zenon_H85. zenon_intro zenon_TI1_fe. zenon_intro zenon_H87. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H88. zenon_intro zenon_H88. % 77.54/77.73 apply zenon_H84. exists zenon_TI1_fe. apply NNPP. zenon_intro zenon_H89. % 77.54/77.73 exact (zenon_H89 zenon_H88). % 77.54/77.73 (* end of lemma zenon_L16_ *) % 77.54/77.73 assert (zenon_L17_ : forall (zenon_TI3_cg : zenon_U) (zenon_TI1_bl : zenon_U) (zenon_TC_ca : zenon_U) (zenon_TAx_bm : zenon_U) (zenon_TF_bn : zenon_U), (~(exists I1 : zenon_U, (model I1 zenon_TF_bn))) -> (forall I : zenon_U, (model I zenon_TF_bn)) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bm)->(model I1 zenon_TC_ca))) -> (model zenon_TI1_bl zenon_TAx_bm) -> (model zenon_TI3_cg zenon_TC_ca) -> (~(model zenon_TI3_cg zenon_TAx_bm)) -> False). % 77.54/77.73 do 5 intro. intros zenon_H84 zenon_H23 zenon_H32 zenon_H24 zenon_H39 zenon_H5a. % 77.54/77.73 generalize (not zenon_TI3_cg). zenon_intro zenon_H59. % 77.54/77.73 generalize (thm zenon_TF_bn). zenon_intro zenon_H61. % 77.54/77.73 generalize (zenon_H59 zenon_TAx_bm). zenon_intro zenon_H5b. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H5a; zenon_intro zenon_H5d | zenon_intro zenon_H5c; zenon_intro zenon_H3f ]. % 77.54/77.73 apply zenon_H5d. zenon_intro zenon_H38. % 77.54/77.73 generalize (sat zenon_TF_bn). zenon_intro zenon_H8a. % 77.54/77.73 generalize (zenon_H61 zenon_TAx_bm). zenon_intro zenon_H63. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H65; zenon_intro zenon_H31 | zenon_intro zenon_H41; zenon_intro zenon_H64 ]. % 77.54/77.73 apply (zenon_notallex_s (fun I1 : zenon_U => ((model I1 zenon_TF_bn)->(model I1 zenon_TAx_bm))) zenon_H65); [ zenon_intro zenon_H8b; idtac ]. % 77.54/77.73 elim zenon_H8b. zenon_intro zenon_TI1_fk. zenon_intro zenon_H8d. % 77.54/77.73 apply (zenon_notimply_s _ _ zenon_H8d). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 77.54/77.73 generalize (zenon_H8a zenon_TF_bn). zenon_intro zenon_H90. % 77.54/77.73 apply (zenon_equiv_s _ _ zenon_H90); [ zenon_intro zenon_H93; zenon_intro zenon_H92 | zenon_intro zenon_H85; zenon_intro zenon_H91 ]. % 77.54/77.73 apply zenon_H93. exists zenon_TI1_fk. apply NNPP. zenon_intro zenon_H94. % 77.54/77.73 apply (zenon_notand_s _ _ zenon_H94); [ zenon_intro zenon_H95 | zenon_intro zenon_H95 ]. % 77.54/77.73 exact (zenon_H95 zenon_H8f). % 77.54/77.73 exact (zenon_H95 zenon_H8f). % 77.54/77.73 apply (zenon_L16_ zenon_TF_bn); trivial. % 77.54/77.73 apply (zenon_L8_ zenon_TI3_cg zenon_TI1_bl zenon_TC_ca zenon_TAx_bm zenon_TF_bn); trivial. % 77.54/77.73 exact (zenon_H5a zenon_H5c). % 77.54/77.73 (* end of lemma zenon_L17_ *) % 77.54/77.73 apply NNPP. intro zenon_G. % 77.54/77.73 elim tautology. zenon_intro zenon_TF_bn. zenon_intro zenon_H23. % 77.54/77.73 elim mixed_pair. zenon_intro zenon_TAx_bm. zenon_intro zenon_H96. % 77.54/77.73 elim zenon_H96. zenon_intro zenon_TC_ca. zenon_intro zenon_H97. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H97). zenon_intro zenon_H99. zenon_intro zenon_H98. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H98). zenon_intro zenon_H32. zenon_intro zenon_H9a. % 77.54/77.73 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 77.54/77.73 elim zenon_H99. zenon_intro zenon_TI1_bl. zenon_intro zenon_H24. % 77.54/77.74 elim zenon_H9c. zenon_intro zenon_TI3_cg. zenon_intro zenon_H9d. % 77.54/77.74 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H5a. zenon_intro zenon_H39. % 77.54/77.74 elim zenon_H9b. zenon_intro zenon_TI4_bu. zenon_intro zenon_H5f. % 77.54/77.74 generalize (nota (noc)). zenon_intro zenon_H9e. % 77.54/77.74 generalize (zenon_H9e (thm)). zenon_intro zenon_H9f. % 77.54/77.74 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_H5e; zenon_intro zenon_G | zenon_intro zenon_Ha1; zenon_intro zenon_Ha0 ]. % 77.54/77.74 generalize (wtc zenon_TF_bn). zenon_intro zenon_H7e. % 77.54/77.74 generalize (cax zenon_TF_bn). zenon_intro zenon_H0. % 77.54/77.74 generalize (zenon_H0 zenon_E). zenon_intro zenon_Ha2. % 77.54/77.74 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha5; zenon_intro zenon_Ha4 | zenon_intro zenon_H84; zenon_intro zenon_Ha3 ]. % 77.54/77.74 apply zenon_Ha5. zenon_intro zenon_H7d. % 77.54/77.74 apply (zenon_L15_ zenon_TI1_bl zenon_TI4_bu zenon_TC_ca zenon_TAx_bm zenon_TI3_cg zenon_TF_bn); trivial. % 77.54/77.74 apply (zenon_L17_ zenon_TI3_cg zenon_TI1_bl zenon_TC_ca zenon_TAx_bm zenon_TF_bn); trivial. % 77.54/77.74 exact (zenon_G zenon_Ha0). % 77.54/77.74 Qed. % 77.54/77.74 % SZS output end Proof % 77.54/77.74 (* END-PROOF *) % 77.54/77.74 nodes searched: 4199611 % 77.54/77.74 max branch formulas: 16535 % 77.54/77.74 proof nodes created: 187657 % 77.54/77.74 formulas created: 11327886 % 77.54/77.74 %------------------------------------------------------------------------------