%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS203+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 03:39:45 EDT 2022 % Result : Theorem 87.79s 87.99s % Output : Proof 87.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS203+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n024.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 11:45:04 EDT 2022 % 0.12/0.33 % CPUTime : % 87.79/87.99 (* PROOF-FOUND *) % 87.79/87.99 % SZS status Theorem % 87.79/87.99 (* BEGIN-PROOF *) % 87.79/87.99 % SZS output start Proof % 87.79/87.99 Theorem nota_sat_thm : (nota (sat) (thm)). % 87.79/87.99 Proof. % 87.79/87.99 assert (zenon_L1_ : forall (zenon_TI3_bl : zenon_U) (zenon_TF_bm : zenon_U), (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(model zenon_TI3_bl zenon_TF_bm)) -> False). % 87.79/87.99 do 2 intro. intros zenon_H23 zenon_H24. % 87.79/87.99 apply zenon_H23. exists zenon_TI3_bl. apply NNPP. zenon_intro zenon_H27. % 87.79/87.99 exact (zenon_H27 zenon_H24). % 87.79/87.99 (* end of lemma zenon_L1_ *) % 87.79/87.99 assert (zenon_L2_ : forall (zenon_TC_bq : zenon_U) (zenon_TF_bm : zenon_U), (~(~(status zenon_TF_bm zenon_TC_bq (thm)))) -> (~(status zenon_TF_bm zenon_TC_bq (thm))) -> False). % 87.79/87.99 do 2 intro. intros zenon_H28 zenon_H29. % 87.79/87.99 exact (zenon_H28 zenon_H29). % 87.79/87.99 (* end of lemma zenon_L2_ *) % 87.79/87.99 assert (zenon_L3_ : forall (zenon_TI1_bu : zenon_U) (zenon_TC_bq : zenon_U) (zenon_TAx_bv : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI1_bu zenon_TAx_bv) -> (~(model zenon_TI1_bu zenon_TC_bq)) -> False). % 87.79/87.99 do 3 intro. intros zenon_H2b zenon_H2c zenon_H2d. % 87.79/87.99 generalize (zenon_H2b zenon_TI1_bu). zenon_intro zenon_H30. % 87.79/87.99 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 87.79/87.99 exact (zenon_H32 zenon_H2c). % 87.79/87.99 exact (zenon_H2d zenon_H31). % 87.79/87.99 (* end of lemma zenon_L3_ *) % 87.79/87.99 assert (zenon_L4_ : forall (zenon_TI3_bl : zenon_U) (zenon_TF_bm : zenon_U), (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI3_bl zenon_TF_bm)) -> False). % 87.79/87.99 do 2 intro. intros zenon_H33 zenon_H24. % 87.79/87.99 generalize (zenon_H33 zenon_TI3_bl). zenon_intro zenon_H34. % 87.79/87.99 exact (zenon_H24 zenon_H34). % 87.79/87.99 (* end of lemma zenon_L4_ *) % 87.79/87.99 assert (zenon_L5_ : forall (zenon_TI3_bl : zenon_U) (zenon_TI1_bu : zenon_U) (zenon_TAx_bv : zenon_U) (zenon_TC_bq : zenon_U) (zenon_TF_bm : zenon_U), (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 C)))<->(status zenon_TF_bm C (thm)))) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (sat))/\(~(status Ax C (thm))))))) -> (~(exists I3 : zenon_U, ((model I3 zenon_TC_bq)/\(~(model I3 zenon_TF_bm))))) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI1_bu zenon_TAx_bv) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI3_bl zenon_TAx_bv)) -> False). % 87.79/87.99 do 5 intro. intros zenon_H35 zenon_H36 zenon_H37 zenon_H2b zenon_H2c zenon_H33 zenon_H38. % 87.79/87.99 generalize (zenon_H35 zenon_TAx_bv). zenon_intro zenon_H39. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3d; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H3a ]. % 87.79/87.99 apply zenon_H36. exists zenon_TF_bm. apply NNPP. zenon_intro zenon_H3e. % 87.79/87.99 apply zenon_H3e. exists zenon_TAx_bv. apply NNPP. zenon_intro zenon_H3f. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 87.79/87.99 generalize (sat zenon_TF_bm). zenon_intro zenon_H42. % 87.79/87.99 generalize (zenon_H42 zenon_TAx_bv). zenon_intro zenon_H43. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H46; zenon_intro zenon_H41 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 87.79/87.99 apply zenon_H46. exists zenon_TI1_bu. apply NNPP. zenon_intro zenon_H47. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H32 ]. % 87.79/87.99 apply zenon_H37. exists zenon_TI1_bu. apply NNPP. zenon_intro zenon_H49. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 87.79/87.99 apply (zenon_L3_ zenon_TI1_bu zenon_TC_bq zenon_TAx_bv); trivial. % 87.79/87.99 exact (zenon_H4a zenon_H48). % 87.79/87.99 exact (zenon_H32 zenon_H2c). % 87.79/87.99 exact (zenon_H41 zenon_H44). % 87.79/87.99 exact (zenon_H40 zenon_H3c). % 87.79/87.99 generalize (zenon_H3b zenon_TI3_bl). zenon_intro zenon_H4b. % 87.79/87.99 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H24 | zenon_intro zenon_H4c ]. % 87.79/87.99 apply (zenon_L4_ zenon_TI3_bl zenon_TF_bm); trivial. % 87.79/87.99 exact (zenon_H38 zenon_H4c). % 87.79/87.99 (* end of lemma zenon_L5_ *) % 87.79/87.99 assert (zenon_L6_ : forall (zenon_TI3_da : zenon_U) (zenon_TF_bm : zenon_U), (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(model zenon_TI3_da zenon_TF_bm)) -> False). % 87.79/87.99 do 2 intro. intros zenon_H23 zenon_H4d. % 87.79/87.99 apply zenon_H23. exists zenon_TI3_da. apply NNPP. zenon_intro zenon_H4f. % 87.79/87.99 exact (zenon_H4f zenon_H4d). % 87.79/87.99 (* end of lemma zenon_L6_ *) % 87.79/87.99 assert (zenon_L7_ : forall (zenon_TF_bm : zenon_U) (zenon_TC_bq : zenon_U), (exists I3 : zenon_U, ((model I3 zenon_TC_bq)/\(~(model I3 zenon_TF_bm)))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> False). % 87.79/87.99 do 2 intro. intros zenon_H50 zenon_H23. % 87.79/87.99 elim zenon_H50. zenon_intro zenon_TI3_da. zenon_intro zenon_H51. % 87.79/87.99 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H52. zenon_intro zenon_H4d. % 87.79/87.99 apply (zenon_L6_ zenon_TI3_da zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L7_ *) % 87.79/87.99 assert (zenon_L8_ : forall (zenon_TC_bq : zenon_U) (zenon_TF_bm : zenon_U), ((exists I1 : zenon_U, (model I1 zenon_TF_bm))/\((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 zenon_TC_bq)))/\((exists I3 : zenon_U, ((model I3 zenon_TC_bq)/\(~(model I3 zenon_TF_bm))))/\(exists I4 : zenon_U, (~(model I4 zenon_TC_bq)))))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> False). % 87.79/87.99 do 2 intro. intros zenon_H53 zenon_H23. % 87.79/87.99 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H55. zenon_intro zenon_H54. % 87.79/87.99 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H57. zenon_intro zenon_H56. % 87.79/87.99 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H50. zenon_intro zenon_H58. % 87.79/87.99 apply (zenon_L7_ zenon_TF_bm zenon_TC_bq); trivial. % 87.79/87.99 (* end of lemma zenon_L8_ *) % 87.79/87.99 assert (zenon_L9_ : forall (zenon_TI1_bu : zenon_U) (zenon_TAx_bv : zenon_U) (zenon_TI3_bl : zenon_U) (zenon_TC_bq : zenon_U) (zenon_TF_bm : zenon_U), (forall C : zenon_U, (((exists I1 : zenon_U, (model I1 zenon_TF_bm))/\((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 C)))/\((exists I3 : zenon_U, ((model I3 C)/\(~(model I3 zenon_TF_bm))))/\(exists I4 : zenon_U, (~(model I4 C))))))<->(status zenon_TF_bm C (wth)))) -> (exists I4 : zenon_U, (~(model I4 zenon_TC_bq))) -> (~(model zenon_TI3_bl zenon_TAx_bv)) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (model zenon_TI1_bu zenon_TAx_bv) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI3_bl zenon_TC_bq) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (sat))/\(~(status Ax C (thm))))))) -> (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 C)))<->(status zenon_TF_bm C (thm)))) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> False). % 87.79/87.99 do 5 intro. intros zenon_H59 zenon_H58 zenon_H38 zenon_H33 zenon_H2c zenon_H2b zenon_H5a zenon_H23 zenon_H36 zenon_H35 zenon_H55. % 87.79/87.99 generalize (zenon_H59 zenon_TC_bq). zenon_intro zenon_H5b. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H5e; zenon_intro zenon_H5d | zenon_intro zenon_H53; zenon_intro zenon_H5c ]. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 87.79/87.99 exact (zenon_H60 zenon_H55). % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H62 | zenon_intro zenon_H61 ]. % 87.79/87.99 generalize (zenon_H35 zenon_TC_bq). zenon_intro zenon_H63. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H62; zenon_intro zenon_H29 | zenon_intro zenon_H57; zenon_intro zenon_H64 ]. % 87.79/87.99 apply zenon_H36. exists zenon_TF_bm. apply NNPP. zenon_intro zenon_H3e. % 87.79/87.99 apply zenon_H3e. exists zenon_TC_bq. apply NNPP. zenon_intro zenon_H65. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H66 | zenon_intro zenon_H28 ]. % 87.79/87.99 generalize (sat zenon_TF_bm). zenon_intro zenon_H42. % 87.79/87.99 generalize (zenon_H42 zenon_TC_bq). zenon_intro zenon_H67. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H6a; zenon_intro zenon_H66 | zenon_intro zenon_H69; zenon_intro zenon_H68 ]. % 87.79/87.99 apply zenon_H6a. exists zenon_TI3_bl. apply NNPP. zenon_intro zenon_H6b. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H24 | zenon_intro zenon_H6c ]. % 87.79/87.99 apply (zenon_L1_ zenon_TI3_bl zenon_TF_bm); trivial. % 87.79/87.99 exact (zenon_H6c zenon_H5a). % 87.79/87.99 exact (zenon_H66 zenon_H68). % 87.79/87.99 exact (zenon_H28 zenon_H29). % 87.79/87.99 exact (zenon_H62 zenon_H57). % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H37 | zenon_intro zenon_H6d ]. % 87.79/87.99 apply (zenon_L5_ zenon_TI3_bl zenon_TI1_bu zenon_TAx_bv zenon_TC_bq zenon_TF_bm); trivial. % 87.79/87.99 exact (zenon_H6d zenon_H58). % 87.79/87.99 apply (zenon_L8_ zenon_TC_bq zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L9_ *) % 87.79/87.99 assert (zenon_L10_ : forall (zenon_TI1_bu : zenon_U) (zenon_TAx_bv : zenon_U) (zenon_TC_bq : zenon_U) (zenon_TI3_bl : zenon_U) (zenon_TF_bm : zenon_U), (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (sat))/\(~(status Ax C (thm))))))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (model zenon_TI3_bl zenon_TC_bq) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI1_bu zenon_TAx_bv) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI3_bl zenon_TAx_bv)) -> (exists I4 : zenon_U, (~(model I4 zenon_TC_bq))) -> (forall C : zenon_U, (((exists I1 : zenon_U, (model I1 zenon_TF_bm))/\((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 C)))/\((exists I3 : zenon_U, ((model I3 C)/\(~(model I3 zenon_TF_bm))))/\(exists I4 : zenon_U, (~(model I4 C))))))<->(status zenon_TF_bm C (wth)))) -> False). % 87.79/87.99 do 5 intro. intros zenon_H55 zenon_H36 zenon_H23 zenon_H5a zenon_H2b zenon_H2c zenon_H33 zenon_H38 zenon_H58 zenon_H59. % 87.79/87.99 generalize (thm zenon_TF_bm). zenon_intro zenon_H35. % 87.79/87.99 apply (zenon_L9_ zenon_TI1_bu zenon_TAx_bv zenon_TI3_bl zenon_TC_bq zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L10_ *) % 87.79/87.99 assert (zenon_L11_ : forall (zenon_TI1_ej : zenon_U) (zenon_TAx_ek : zenon_U) (zenon_TF_bm : zenon_U), ((exists I1 : zenon_U, ((model I1 zenon_TF_bm)/\(model I1 zenon_TAx_ek)))<->(status zenon_TF_bm zenon_TAx_ek (sat))) -> (~(status zenon_TF_bm zenon_TAx_ek (sat))) -> (model zenon_TI1_ej zenon_TAx_ek) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> False). % 87.79/87.99 do 3 intro. intros zenon_H6e zenon_H6f zenon_H70 zenon_H33. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H6e); [ zenon_intro zenon_H75; zenon_intro zenon_H6f | zenon_intro zenon_H74; zenon_intro zenon_H73 ]. % 87.79/87.99 apply zenon_H75. exists zenon_TI1_ej. apply NNPP. zenon_intro zenon_H76. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H76); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 87.79/87.99 generalize (zenon_H33 zenon_TI1_ej). zenon_intro zenon_H79. % 87.79/87.99 exact (zenon_H78 zenon_H79). % 87.79/87.99 exact (zenon_H77 zenon_H70). % 87.79/87.99 exact (zenon_H6f zenon_H73). % 87.79/87.99 (* end of lemma zenon_L11_ *) % 87.79/87.99 assert (zenon_L12_ : forall (zenon_TI1_eu : zenon_U) (zenon_TF_bm : zenon_U), (~(exists I1 : zenon_U, ((model I1 zenon_TF_bm)/\(model I1 zenon_TF_bm)))) -> (model zenon_TI1_eu zenon_TF_bm) -> False). % 87.79/87.99 do 2 intro. intros zenon_H7a zenon_H7b. % 87.79/87.99 apply zenon_H7a. exists zenon_TI1_eu. apply NNPP. zenon_intro zenon_H7d. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H7d); [ zenon_intro zenon_H7e | zenon_intro zenon_H7e ]. % 87.79/87.99 exact (zenon_H7e zenon_H7b). % 87.79/87.99 exact (zenon_H7e zenon_H7b). % 87.79/87.99 (* end of lemma zenon_L12_ *) % 87.79/87.99 assert (zenon_L13_ : forall (zenon_TF_bm : zenon_U), (exists I1 : zenon_U, ((model I1 zenon_TF_bm)/\(model I1 zenon_TF_bm))) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> False). % 87.79/87.99 do 1 intro. intros zenon_H7f zenon_H60. % 87.79/87.99 elim zenon_H7f. zenon_intro zenon_TI1_ey. zenon_intro zenon_H81. % 87.79/87.99 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H82. zenon_intro zenon_H82. % 87.79/87.99 apply zenon_H60. exists zenon_TI1_ey. apply NNPP. zenon_intro zenon_H83. % 87.79/87.99 exact (zenon_H83 zenon_H82). % 87.79/87.99 (* end of lemma zenon_L13_ *) % 87.79/87.99 assert (zenon_L14_ : forall (zenon_TAx_ek : zenon_U) (zenon_TI1_ej : zenon_U) (zenon_TF_bm : zenon_U), (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (model zenon_TI1_ej zenon_TAx_ek) -> False). % 87.79/87.99 do 3 intro. intros zenon_H60 zenon_H33 zenon_H70. % 87.79/87.99 generalize (sat zenon_TF_bm). zenon_intro zenon_H42. % 87.79/87.99 generalize (zenon_H42 zenon_TAx_ek). zenon_intro zenon_H6e. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H6e); [ zenon_intro zenon_H75; zenon_intro zenon_H6f | zenon_intro zenon_H74; zenon_intro zenon_H73 ]. % 87.79/87.99 apply (zenon_L11_ zenon_TI1_ej zenon_TAx_ek zenon_TF_bm); trivial. % 87.79/87.99 elim zenon_H74. zenon_intro zenon_TI1_eu. zenon_intro zenon_H84. % 87.79/87.99 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H7b. zenon_intro zenon_H85. % 87.79/87.99 generalize (zenon_H42 zenon_TF_bm). zenon_intro zenon_H86. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H86); [ zenon_intro zenon_H7a; zenon_intro zenon_H88 | zenon_intro zenon_H7f; zenon_intro zenon_H87 ]. % 87.79/87.99 apply (zenon_L12_ zenon_TI1_eu zenon_TF_bm); trivial. % 87.79/87.99 apply (zenon_L13_ zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L14_ *) % 87.79/87.99 assert (zenon_L15_ : forall (zenon_TF_bm : zenon_U) (zenon_TAx_ek : zenon_U), (exists I1 : zenon_U, (model I1 zenon_TAx_ek)) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> False). % 87.79/87.99 do 2 intro. intros zenon_H89 zenon_H33 zenon_H60. % 87.79/87.99 elim zenon_H89. zenon_intro zenon_TI1_ej. zenon_intro zenon_H70. % 87.79/87.99 apply (zenon_L14_ zenon_TAx_ek zenon_TI1_ej zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L15_ *) % 87.79/87.99 assert (zenon_L16_ : forall (zenon_TF_bm : zenon_U) (zenon_TAx_ek : zenon_U), (~(~(exists I1 : zenon_U, (model I1 zenon_TAx_ek)))) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> False). % 87.79/87.99 do 2 intro. intros zenon_H8a zenon_H60 zenon_H33. % 87.79/87.99 apply zenon_H8a. zenon_intro zenon_H89. % 87.79/87.99 apply (zenon_L15_ zenon_TF_bm zenon_TAx_ek); trivial. % 87.79/87.99 (* end of lemma zenon_L16_ *) % 87.79/87.99 assert (zenon_L17_ : forall (zenon_TI1_fl : zenon_U) (zenon_TAx_ek : zenon_U), (~(exists I1 : zenon_U, (model I1 zenon_TAx_ek))) -> (model zenon_TI1_fl zenon_TAx_ek) -> False). % 87.79/87.99 do 2 intro. intros zenon_H8b zenon_H8c. % 87.79/87.99 apply zenon_H8b. exists zenon_TI1_fl. apply NNPP. zenon_intro zenon_H8e. % 87.79/87.99 exact (zenon_H8e zenon_H8c). % 87.79/87.99 (* end of lemma zenon_L17_ *) % 87.79/87.99 assert (zenon_L18_ : forall (zenon_TF_bm : zenon_U) (zenon_TAx_ek : zenon_U) (zenon_TI1_fl : zenon_U), (model zenon_TI1_fl zenon_TAx_ek) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> False). % 87.79/87.99 do 3 intro. intros zenon_H8c zenon_H33 zenon_H60. % 87.79/87.99 generalize (cax zenon_TAx_ek). zenon_intro zenon_H0. % 87.79/87.99 generalize (zenon_H0 zenon_E). zenon_intro zenon_H8f. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H8f); [ zenon_intro zenon_H8a; zenon_intro zenon_H91 | zenon_intro zenon_H8b; zenon_intro zenon_H90 ]. % 87.79/87.99 apply (zenon_L16_ zenon_TF_bm zenon_TAx_ek); trivial. % 87.79/87.99 apply (zenon_L17_ zenon_TI1_fl zenon_TAx_ek); trivial. % 87.79/87.99 (* end of lemma zenon_L18_ *) % 87.79/87.99 assert (zenon_L19_ : forall (zenon_TAx_ek : zenon_U) (zenon_TI1_fl : zenon_U) (zenon_TI1_bu : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TAx_bv : zenon_U) (zenon_TI3_bl : zenon_U) (zenon_TC_bq : zenon_U), (exists I4 : zenon_U, (~(model I4 zenon_TC_bq))) -> (~(model zenon_TI3_bl zenon_TAx_bv)) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (model zenon_TI1_bu zenon_TAx_bv) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI3_bl zenon_TC_bq) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (sat))/\(~(status Ax C (thm))))))) -> (model zenon_TI1_fl zenon_TAx_ek) -> False). % 87.79/87.99 do 7 intro. intros zenon_H58 zenon_H38 zenon_H33 zenon_H2c zenon_H2b zenon_H5a zenon_H23 zenon_H36 zenon_H8c. % 87.79/87.99 generalize (wth zenon_TF_bm). zenon_intro zenon_H59. % 87.79/87.99 generalize (cax zenon_TF_bm). zenon_intro zenon_H1. % 87.79/87.99 generalize (zenon_H1 zenon_E). zenon_intro zenon_H92. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H92); [ zenon_intro zenon_H95; zenon_intro zenon_H94 | zenon_intro zenon_H60; zenon_intro zenon_H93 ]. % 87.79/87.99 apply zenon_H95. zenon_intro zenon_H55. % 87.79/87.99 apply (zenon_L10_ zenon_TI1_bu zenon_TAx_bv zenon_TC_bq zenon_TI3_bl zenon_TF_bm); trivial. % 87.79/87.99 apply (zenon_L18_ zenon_TF_bm zenon_TAx_ek zenon_TI1_fl); trivial. % 87.79/87.99 (* end of lemma zenon_L19_ *) % 87.79/87.99 assert (zenon_L20_ : forall (zenon_TF_bm : zenon_U), (exists I4 : zenon_U, (~(model I4 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> False). % 87.79/87.99 do 1 intro. intros zenon_H96 zenon_H33. % 87.79/87.99 elim zenon_H96. zenon_intro zenon_TI4_fv. zenon_intro zenon_H98. % 87.79/87.99 generalize (zenon_H33 zenon_TI4_fv). zenon_intro zenon_H99. % 87.79/87.99 exact (zenon_H98 zenon_H99). % 87.79/87.99 (* end of lemma zenon_L20_ *) % 87.79/87.99 assert (zenon_L21_ : forall (zenon_TI1_bu : zenon_U) (zenon_TAx_bv : zenon_U) (zenon_TC_bq : zenon_U) (zenon_TI3_bl : zenon_U) (zenon_TAx_ek : zenon_U) (zenon_TI1_fl : zenon_U) (zenon_TF_bm : zenon_U), (forall C : zenon_U, (((exists I1 : zenon_U, (model I1 zenon_TF_bm))/\((exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))/\(forall I2 : zenon_U, (model I2 C))))<->(status zenon_TF_bm C (wtc)))) -> (model zenon_TI1_fl zenon_TAx_ek) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (sat))/\(~(status Ax C (thm))))))) -> (model zenon_TI3_bl zenon_TC_bq) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI1_bu zenon_TAx_bv) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI3_bl zenon_TAx_bv)) -> (exists I4 : zenon_U, (~(model I4 zenon_TC_bq))) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> False). % 87.79/87.99 do 7 intro. intros zenon_H9a zenon_H8c zenon_H36 zenon_H5a zenon_H2b zenon_H2c zenon_H33 zenon_H38 zenon_H58 zenon_H55. % 87.79/87.99 generalize (zenon_H9a zenon_TF_bm). zenon_intro zenon_H9b. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H9b); [ zenon_intro zenon_H9f; zenon_intro zenon_H9e | zenon_intro zenon_H9d; zenon_intro zenon_H9c ]. % 87.79/87.99 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_H60 | zenon_intro zenon_Ha0 ]. % 87.79/87.99 exact (zenon_H60 zenon_H55). % 87.79/87.99 apply (zenon_notand_s _ _ zenon_Ha0); [ zenon_intro zenon_H23 | zenon_intro zenon_Ha1 ]. % 87.79/87.99 apply (zenon_L19_ zenon_TAx_ek zenon_TI1_fl zenon_TI1_bu zenon_TF_bm zenon_TAx_bv zenon_TI3_bl zenon_TC_bq); trivial. % 87.79/87.99 exact (zenon_Ha1 zenon_H33). % 87.79/87.99 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H55. zenon_intro zenon_Ha2. % 87.79/87.99 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_H96. zenon_intro zenon_H33. % 87.79/87.99 apply (zenon_L20_ zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L21_ *) % 87.79/87.99 assert (zenon_L22_ : forall (zenon_TAx_ek : zenon_U) (zenon_TI1_fl : zenon_U) (zenon_TI1_bu : zenon_U) (zenon_TAx_bv : zenon_U) (zenon_TI3_bl : zenon_U) (zenon_TC_bq : zenon_U) (zenon_TF_bm : zenon_U), (~(~(exists I1 : zenon_U, (model I1 zenon_TF_bm)))) -> (exists I4 : zenon_U, (~(model I4 zenon_TC_bq))) -> (~(model zenon_TI3_bl zenon_TAx_bv)) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (model zenon_TI1_bu zenon_TAx_bv) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_bv)->(model I1 zenon_TC_bq))) -> (model zenon_TI3_bl zenon_TC_bq) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (sat))/\(~(status Ax C (thm))))))) -> (model zenon_TI1_fl zenon_TAx_ek) -> (forall C : zenon_U, (((exists I1 : zenon_U, (model I1 zenon_TF_bm))/\((exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))/\(forall I2 : zenon_U, (model I2 C))))<->(status zenon_TF_bm C (wtc)))) -> False). % 87.79/87.99 do 7 intro. intros zenon_H95 zenon_H58 zenon_H38 zenon_H33 zenon_H2c zenon_H2b zenon_H5a zenon_H36 zenon_H8c zenon_H9a. % 87.79/87.99 apply zenon_H95. zenon_intro zenon_H55. % 87.79/87.99 apply (zenon_L21_ zenon_TI1_bu zenon_TAx_bv zenon_TC_bq zenon_TI3_bl zenon_TAx_ek zenon_TI1_fl zenon_TF_bm); trivial. % 87.79/87.99 (* end of lemma zenon_L22_ *) % 87.79/87.99 apply NNPP. intro zenon_G. % 87.79/87.99 elim tautology. zenon_intro zenon_TF_bm. zenon_intro zenon_H33. % 87.79/87.99 elim mixed_pair. zenon_intro zenon_TAx_bv. zenon_intro zenon_Ha3. % 87.79/87.99 elim zenon_Ha3. zenon_intro zenon_TC_bq. zenon_intro zenon_Ha4. % 87.79/87.99 apply (zenon_and_s _ _ zenon_Ha4). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 87.79/87.99 apply (zenon_and_s _ _ zenon_Ha5). zenon_intro zenon_H2b. zenon_intro zenon_Ha7. % 87.79/87.99 apply (zenon_and_s _ _ zenon_Ha7). zenon_intro zenon_Ha8. zenon_intro zenon_H58. % 87.79/87.99 elim zenon_Ha6. zenon_intro zenon_TI1_bu. zenon_intro zenon_H2c. % 87.79/87.99 elim zenon_Ha8. zenon_intro zenon_TI3_bl. zenon_intro zenon_Ha9. % 87.79/87.99 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_H38. zenon_intro zenon_H5a. % 87.79/87.99 elim non_thm_spt. zenon_intro zenon_TI1_fl. zenon_intro zenon_Haa. % 87.79/87.99 elim zenon_Haa. zenon_intro zenon_TAx_ek. zenon_intro zenon_Hab. % 87.79/87.99 elim zenon_Hab. zenon_intro zenon_TC_gq. zenon_intro zenon_Had. % 87.79/87.99 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H8c. zenon_intro zenon_Hae. % 87.79/87.99 generalize (nota (sat)). zenon_intro zenon_Haf. % 87.79/87.99 generalize (zenon_Haf (thm)). zenon_intro zenon_Hb0. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_Hb0); [ zenon_intro zenon_H36; zenon_intro zenon_G | zenon_intro zenon_Hb2; zenon_intro zenon_Hb1 ]. % 87.79/87.99 generalize (wtc zenon_TF_bm). zenon_intro zenon_H9a. % 87.79/87.99 generalize (cax zenon_TF_bm). zenon_intro zenon_H1. % 87.79/87.99 generalize (zenon_H1 zenon_E). zenon_intro zenon_H92. % 87.79/87.99 apply (zenon_equiv_s _ _ zenon_H92); [ zenon_intro zenon_H95; zenon_intro zenon_H94 | zenon_intro zenon_H60; zenon_intro zenon_H93 ]. % 87.79/87.99 apply (zenon_L22_ zenon_TAx_ek zenon_TI1_fl zenon_TI1_bu zenon_TAx_bv zenon_TI3_bl zenon_TC_bq zenon_TF_bm); trivial. % 87.79/87.99 apply (zenon_L18_ zenon_TF_bm zenon_TAx_ek zenon_TI1_fl); trivial. % 87.79/87.99 exact (zenon_G zenon_Hb1). % 87.79/87.99 Qed. % 87.79/87.99 % SZS output end Proof % 87.79/87.99 (* END-PROOF *) % 87.79/87.99 nodes searched: 4202579 % 87.79/87.99 max branch formulas: 16448 % 87.79/87.99 proof nodes created: 233304 % 87.79/87.99 formulas created: 10885783 % 87.79/87.99 %------------------------------------------------------------------------------