%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS202+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n028.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 165.40s 165.61s % Output : Proof 165.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.14 % Problem : KRS202+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.12/0.14 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n028.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Tue Jun 7 06:54:29 EDT 2022 % 0.14/0.36 % CPUTime : % 165.40/165.61 (* PROOF-FOUND *) % 165.40/165.61 % SZS status Theorem % 165.40/165.61 (* BEGIN-PROOF *) % 165.40/165.61 % SZS output start Proof % 165.40/165.61 Theorem nota_esa_thm : (nota (esa) (thm)). % 165.40/165.61 Proof. % 165.40/165.61 assert (zenon_L1_ : forall (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (~(~(status zenon_TF_bm zenon_TC_bl (thm)))) -> (~(status zenon_TF_bm zenon_TC_bl (thm))) -> False). % 165.40/165.61 do 2 intro. intros zenon_H23 zenon_H24. % 165.40/165.61 exact (zenon_H23 zenon_H24). % 165.40/165.61 (* end of lemma zenon_L1_ *) % 165.40/165.61 assert (zenon_L2_ : forall (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (~(status zenon_TF_bm zenon_TC_bl (thm))) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> False). % 165.40/165.61 do 2 intro. intros zenon_H27 zenon_H24 zenon_H28 zenon_H29. % 165.40/165.61 apply zenon_H27. exists zenon_TF_bm. apply NNPP. zenon_intro zenon_H2a. % 165.40/165.61 apply zenon_H2a. exists zenon_TC_bl. apply NNPP. zenon_intro zenon_H2b. % 165.40/165.61 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2c | zenon_intro zenon_H23 ]. % 165.40/165.61 generalize (esa zenon_TF_bm). zenon_intro zenon_H2d. % 165.40/165.61 generalize (zenon_H2d zenon_TC_bl). zenon_intro zenon_H2e. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H31; zenon_intro zenon_H2c | zenon_intro zenon_H30; zenon_intro zenon_H2f ]. % 165.40/165.61 apply (zenon_notequiv_s _ _ zenon_H31); [ zenon_intro zenon_H33; zenon_intro zenon_H28 | zenon_intro zenon_H29; zenon_intro zenon_H32 ]. % 165.40/165.61 exact (zenon_H33 zenon_H29). % 165.40/165.61 exact (zenon_H32 zenon_H28). % 165.40/165.61 exact (zenon_H2c zenon_H2f). % 165.40/165.61 exact (zenon_H23 zenon_H24). % 165.40/165.61 (* end of lemma zenon_L2_ *) % 165.40/165.61 assert (zenon_L3_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U), (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(model zenon_TI4_cc zenon_TF_bm)) -> False). % 165.40/165.61 do 2 intro. intros zenon_H34 zenon_H35. % 165.40/165.61 apply zenon_H34. exists zenon_TI4_cc. apply NNPP. zenon_intro zenon_H37. % 165.40/165.61 exact (zenon_H37 zenon_H35). % 165.40/165.61 (* end of lemma zenon_L3_ *) % 165.40/165.61 assert (zenon_L4_ : forall (zenon_TI4_cc : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 zenon_TC_bl))) -> (model zenon_TI4_cc zenon_TF_bm) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False). % 165.40/165.61 do 3 intro. intros zenon_H38 zenon_H39 zenon_H3a. % 165.40/165.61 generalize (zenon_H38 zenon_TI4_cc). zenon_intro zenon_H3b. % 165.40/165.61 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H35 | zenon_intro zenon_H3c ]. % 165.40/165.61 exact (zenon_H35 zenon_H39). % 165.40/165.61 exact (zenon_H3a zenon_H3c). % 165.40/165.61 (* end of lemma zenon_L4_ *) % 165.40/165.61 assert (zenon_L5_ : forall (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TI4_cc : zenon_U), (forall F : zenon_U, (~((model zenon_TI4_cc F)<->(model zenon_TI4_cc (not F))))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 zenon_TC_bl))) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False). % 165.40/165.61 do 3 intro. intros zenon_H3d zenon_H34 zenon_H38 zenon_H3a. % 165.40/165.61 generalize (zenon_H3d zenon_TF_bm). zenon_intro zenon_H3e. % 165.40/165.61 apply (zenon_notequiv_s _ _ zenon_H3e); [ zenon_intro zenon_H35; zenon_intro zenon_H40 | zenon_intro zenon_H39; zenon_intro zenon_H3f ]. % 165.40/165.61 apply (zenon_L3_ zenon_TI4_cc zenon_TF_bm); trivial. % 165.40/165.61 apply (zenon_L4_ zenon_TI4_cc zenon_TC_bl zenon_TF_bm); trivial. % 165.40/165.61 (* end of lemma zenon_L5_ *) % 165.40/165.61 assert (zenon_L6_ : forall (zenon_TI4_cc : zenon_U) (zenon_TC_bl : 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 (esa))/\(~(status Ax C (thm))))))) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> (forall F : zenon_U, (~((model zenon_TI4_cc F)<->(model zenon_TI4_cc (not F))))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False). % 165.40/165.61 do 3 intro. intros zenon_H41 zenon_H27 zenon_H28 zenon_H29 zenon_H3d zenon_H34 zenon_H3a. % 165.40/165.61 generalize (zenon_H41 zenon_TC_bl). zenon_intro zenon_H42. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H44; zenon_intro zenon_H24 | zenon_intro zenon_H38; zenon_intro zenon_H43 ]. % 165.40/165.61 apply (zenon_L2_ zenon_TC_bl zenon_TF_bm); trivial. % 165.40/165.61 apply (zenon_L5_ zenon_TC_bl zenon_TF_bm zenon_TI4_cc); trivial. % 165.40/165.61 (* end of lemma zenon_L6_ *) % 165.40/165.61 assert (zenon_L7_ : 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). % 165.40/165.61 do 1 intro. intros zenon_H45 zenon_H46. % 165.40/165.61 elim zenon_H45. zenon_intro zenon_TI4_ct. zenon_intro zenon_H48. % 165.40/165.61 generalize (zenon_H46 zenon_TI4_ct). zenon_intro zenon_H49. % 165.40/165.61 exact (zenon_H48 zenon_H49). % 165.40/165.61 (* end of lemma zenon_L7_ *) % 165.40/165.61 assert (zenon_L8_ : forall (zenon_TF_bm : zenon_U), (~(forall I : zenon_U, (model I zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> False). % 165.40/165.61 do 1 intro. intros zenon_H4a zenon_H46. % 165.40/165.61 exact (zenon_H4a zenon_H46). % 165.40/165.61 (* end of lemma zenon_L8_ *) % 165.40/165.61 assert (zenon_L9_ : forall (zenon_TC_bl : zenon_U) (zenon_TI4_cc : 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)))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> False). % 165.40/165.61 do 3 intro. intros zenon_H4b zenon_H46 zenon_H3a zenon_H28 zenon_H27 zenon_H29. % 165.40/165.61 generalize (thm zenon_TF_bm). zenon_intro zenon_H41. % 165.40/165.61 generalize (completeness zenon_TI4_cc). zenon_intro zenon_H3d. % 165.40/165.61 generalize (zenon_H4b zenon_TF_bm). zenon_intro zenon_H4c. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H50; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ]. % 165.40/165.61 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H33 | zenon_intro zenon_H51 ]. % 165.40/165.61 exact (zenon_H33 zenon_H29). % 165.40/165.61 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 165.40/165.61 apply (zenon_L6_ zenon_TI4_cc zenon_TC_bl zenon_TF_bm); trivial. % 165.40/165.61 exact (zenon_H4a zenon_H46). % 165.40/165.61 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H29. zenon_intro zenon_H52. % 165.40/165.61 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H45. zenon_intro zenon_H46. % 165.40/165.61 apply (zenon_L7_ zenon_TF_bm); trivial. % 165.40/165.61 (* end of lemma zenon_L9_ *) % 165.40/165.61 assert (zenon_L10_ : forall (zenon_TI1_dg : zenon_U) (zenon_TF_bm : zenon_U), (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI1_dg zenon_TF_bm)) -> False). % 165.40/165.61 do 2 intro. intros zenon_H46 zenon_H53. % 165.40/165.61 generalize (zenon_H46 zenon_TI1_dg). zenon_intro zenon_H55. % 165.40/165.61 exact (zenon_H53 zenon_H55). % 165.40/165.61 (* end of lemma zenon_L10_ *) % 165.40/165.61 assert (zenon_L11_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TAx_dk : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)/\(model I1 zenon_TF_bm))) -> (~(model zenon_TI4_cc zenon_TAx_dk)) -> False). % 165.40/165.61 do 3 intro. intros zenon_H56 zenon_H57. % 165.40/165.61 generalize (zenon_H56 zenon_TI4_cc). zenon_intro zenon_H59. % 165.40/165.61 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5a. zenon_intro zenon_H39. % 165.40/165.61 exact (zenon_H57 zenon_H5a). % 165.40/165.61 (* end of lemma zenon_L11_ *) % 165.40/165.61 assert (zenon_L12_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TAx_dk : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)->(model I1 zenon_TC_bl))) -> (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TAx_dk)/\(model I1 C)))<->(status zenon_TAx_dk C (tau)))) -> (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))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False). % 165.40/165.61 do 4 intro. intros zenon_H5b zenon_H5c zenon_H41 zenon_H33 zenon_H46 zenon_H3a. % 165.40/165.61 generalize (zenon_H5b zenon_TI4_cc). zenon_intro zenon_H5d. % 165.40/165.61 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H57 | zenon_intro zenon_H3c ]. % 165.40/165.61 generalize (zenon_H5c zenon_TF_bm). zenon_intro zenon_H5e. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H61; zenon_intro zenon_H60 | zenon_intro zenon_H56; zenon_intro zenon_H5f ]. % 165.40/165.61 apply (zenon_notallex_s (fun I1 : zenon_U => ((model I1 zenon_TAx_dk)/\(model I1 zenon_TF_bm))) zenon_H61); [ zenon_intro zenon_H62; idtac ]. % 165.40/165.61 elim zenon_H62. zenon_intro zenon_TI1_dg. zenon_intro zenon_H63. % 165.40/165.61 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H64 | zenon_intro zenon_H53 ]. % 165.40/165.61 generalize (zenon_H41 zenon_TAx_dk). zenon_intro zenon_H65. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H69; zenon_intro zenon_H68 | zenon_intro zenon_H67; zenon_intro zenon_H66 ]. % 165.40/165.61 apply (zenon_notallex_s (fun I1 : zenon_U => ((model I1 zenon_TF_bm)->(model I1 zenon_TAx_dk))) zenon_H69); [ zenon_intro zenon_H6a; idtac ]. % 165.40/165.61 elim zenon_H6a. zenon_intro zenon_TI1_ed. zenon_intro zenon_H6c. % 165.40/165.61 apply (zenon_notimply_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 165.40/165.61 apply zenon_H33. exists zenon_TI1_ed. apply NNPP. zenon_intro zenon_H6f. % 165.40/165.61 exact (zenon_H6f zenon_H6e). % 165.40/165.61 generalize (zenon_H67 zenon_TI1_dg). zenon_intro zenon_H70. % 165.40/165.61 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H53 | zenon_intro zenon_H71 ]. % 165.40/165.61 apply (zenon_L10_ zenon_TI1_dg zenon_TF_bm); trivial. % 165.40/165.61 exact (zenon_H64 zenon_H71). % 165.40/165.61 apply (zenon_L10_ zenon_TI1_dg zenon_TF_bm); trivial. % 165.40/165.61 apply (zenon_L11_ zenon_TI4_cc zenon_TF_bm zenon_TAx_dk); trivial. % 165.40/165.61 exact (zenon_H3a zenon_H3c). % 165.40/165.61 (* end of lemma zenon_L12_ *) % 165.40/165.61 assert (zenon_L13_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TAx_dk : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)->(model I1 zenon_TC_bl))) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False). % 165.40/165.61 do 4 intro. intros zenon_H5b zenon_H33 zenon_H46 zenon_H3a. % 165.40/165.61 generalize (thm zenon_TF_bm). zenon_intro zenon_H41. % 165.40/165.61 generalize (tau zenon_TAx_dk). zenon_intro zenon_H5c. % 165.40/165.61 apply (zenon_L12_ zenon_TI4_cc zenon_TF_bm zenon_TC_bl zenon_TAx_dk); trivial. % 165.40/165.61 (* end of lemma zenon_L13_ *) % 165.40/165.61 assert (zenon_L14_ : forall (zenon_TAx_dk : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TI4_cc : zenon_U) (zenon_TC_bl : zenon_U), (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)->(model I1 zenon_TC_bl))) -> False). % 165.40/165.61 do 4 intro. intros zenon_H27 zenon_H28 zenon_H3a zenon_H46 zenon_H5b. % 165.40/165.61 generalize (wtc zenon_TF_bm). zenon_intro zenon_H4b. % 165.40/165.61 generalize (cax zenon_TF_bm). zenon_intro zenon_H0. % 165.40/165.61 generalize (zenon_H0 zenon_E). zenon_intro zenon_H72. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H75; zenon_intro zenon_H74 | zenon_intro zenon_H33; zenon_intro zenon_H73 ]. % 165.40/165.61 apply zenon_H75. zenon_intro zenon_H29. % 165.40/165.61 apply (zenon_L9_ zenon_TC_bl zenon_TI4_cc zenon_TF_bm); trivial. % 165.40/165.61 apply (zenon_L13_ zenon_TI4_cc zenon_TF_bm zenon_TC_bl zenon_TAx_dk); trivial. % 165.40/165.61 (* end of lemma zenon_L14_ *) % 165.40/165.61 assert (zenon_L15_ : forall (zenon_TI3_ep : zenon_U) (zenon_TC_bl : zenon_U), (~(exists I1 : zenon_U, (model I1 zenon_TC_bl))) -> (model zenon_TI3_ep zenon_TC_bl) -> False). % 165.40/165.61 do 2 intro. intros zenon_H32 zenon_H76. % 165.40/165.61 apply zenon_H32. exists zenon_TI3_ep. apply NNPP. zenon_intro zenon_H78. % 165.40/165.61 exact (zenon_H78 zenon_H76). % 165.40/165.61 (* end of lemma zenon_L15_ *) % 165.40/165.61 apply NNPP. intro zenon_G. % 165.40/165.61 elim tautology. zenon_intro zenon_TF_bm. zenon_intro zenon_H46. % 165.40/165.61 elim mixed_pair. zenon_intro zenon_TAx_dk. zenon_intro zenon_H79. % 165.40/165.61 elim zenon_H79. zenon_intro zenon_TC_bl. zenon_intro zenon_H7a. % 165.40/165.61 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 165.40/165.61 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H5b. zenon_intro zenon_H7d. % 165.40/165.61 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 165.40/165.61 elim zenon_H7f. zenon_intro zenon_TI3_ep. zenon_intro zenon_H80. % 165.40/165.61 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H81. zenon_intro zenon_H76. % 165.40/165.61 elim zenon_H7e. zenon_intro zenon_TI4_cc. zenon_intro zenon_H3a. % 165.40/165.61 generalize (nota (esa)). zenon_intro zenon_H82. % 165.40/165.61 generalize (zenon_H82 (thm)). zenon_intro zenon_H83. % 165.40/165.61 apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H27; zenon_intro zenon_G | zenon_intro zenon_H85; zenon_intro zenon_H84 ]. % 165.40/165.62 generalize (cax zenon_TC_bl). zenon_intro zenon_H1. % 165.40/165.62 generalize (zenon_H1 zenon_E). zenon_intro zenon_H86. % 165.40/165.62 apply (zenon_equiv_s _ _ zenon_H86); [ zenon_intro zenon_H89; zenon_intro zenon_H88 | zenon_intro zenon_H32; zenon_intro zenon_H87 ]. % 165.40/165.62 apply zenon_H89. zenon_intro zenon_H28. % 165.40/165.62 apply (zenon_L14_ zenon_TAx_dk zenon_TF_bm zenon_TI4_cc zenon_TC_bl); trivial. % 165.40/165.62 apply (zenon_L15_ zenon_TI3_ep zenon_TC_bl); trivial. % 165.40/165.62 exact (zenon_G zenon_H84). % 165.40/165.62 Qed. % 165.40/165.62 % SZS output end Proof % 165.40/165.62 (* END-PROOF *) % 165.40/165.62 nodes searched: 7884492 % 165.40/165.62 max branch formulas: 25923 % 165.40/165.62 proof nodes created: 490335 % 165.40/165.62 formulas created: 19112971 % 165.40/165.62 %------------------------------------------------------------------------------