%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS215+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 243.84s 244.11s % Output : Proof 243.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS215+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.00/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n022.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 7 17:32:05 EDT 2022 % 0.13/0.33 % CPUTime : % 243.84/244.11 (* PROOF-FOUND *) % 243.84/244.11 % SZS status Theorem % 243.84/244.11 (* BEGIN-PROOF *) % 243.84/244.11 % SZS output start Proof % 243.84/244.11 Theorem nota_csa_thm : (nota (csa) (thm)). % 243.84/244.11 Proof. % 243.84/244.11 assert (zenon_L1_ : forall (zenon_TI2_bk : zenon_U) (zenon_TF_bl : zenon_U), (~(exists I2 : zenon_U, (model I2 zenon_TF_bl))) -> (model zenon_TI2_bk zenon_TF_bl) -> False). % 243.84/244.11 do 2 intro. intros zenon_H22 zenon_H23. % 243.84/244.11 apply zenon_H22. exists zenon_TI2_bk. apply NNPP. zenon_intro zenon_H26. % 243.84/244.11 exact (zenon_H26 zenon_H23). % 243.84/244.11 (* end of lemma zenon_L1_ *) % 243.84/244.11 assert (zenon_L2_ : forall (zenon_TF_bp : zenon_U) (zenon_TF_bl : zenon_U), (~(exists I2 : zenon_U, (model I2 zenon_TF_bl))) -> (forall I : zenon_U, (model I zenon_TF_bp)) -> (~(exists I1 : zenon_U, ((model I1 zenon_TF_bp)/\(model I1 (not zenon_TF_bl))))) -> False). % 243.84/244.11 do 2 intro. intros zenon_H22 zenon_H27 zenon_H28. % 243.84/244.11 generalize (completeness zenon_TI2_bk). zenon_intro zenon_H2a. % 243.84/244.11 generalize (zenon_H2a zenon_TF_bl). zenon_intro zenon_H2b. % 243.84/244.11 apply (zenon_notequiv_s _ _ zenon_H2b); [ zenon_intro zenon_H26; zenon_intro zenon_H2d | zenon_intro zenon_H23; zenon_intro zenon_H2c ]. % 243.84/244.11 apply zenon_H28. exists zenon_TI2_bk. apply NNPP. zenon_intro zenon_H2e. % 243.84/244.11 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H2f | zenon_intro zenon_H2c ]. % 243.84/244.11 generalize (zenon_H27 zenon_TI2_bk). zenon_intro zenon_H30. % 243.84/244.11 exact (zenon_H2f zenon_H30). % 243.84/244.11 exact (zenon_H2c zenon_H2d). % 243.84/244.11 apply (zenon_L1_ zenon_TI2_bk zenon_TF_bl); trivial. % 243.84/244.11 (* end of lemma zenon_L2_ *) % 243.84/244.11 assert (zenon_L3_ : forall (zenon_TF_bl : zenon_U), (exists I1 : zenon_U, ((model I1 zenon_TF_bl)/\(model I1 (not zenon_TF_bl)))) -> (forall I : zenon_U, (~(model I zenon_TF_bl))) -> False). % 243.84/244.11 do 1 intro. intros zenon_H31 zenon_H32. % 243.84/244.11 elim zenon_H31. zenon_intro zenon_TI1_bz. zenon_intro zenon_H34. % 243.84/244.11 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 243.84/244.11 generalize (zenon_H32 zenon_TI1_bz). zenon_intro zenon_H37. % 243.84/244.11 exact (zenon_H37 zenon_H36). % 243.84/244.11 (* end of lemma zenon_L3_ *) % 243.84/244.11 assert (zenon_L4_ : forall (zenon_TF_bp : zenon_U) (zenon_TF_bl : zenon_U), (forall I : zenon_U, (~(model I zenon_TF_bl))) -> (forall I : zenon_U, (model I zenon_TF_bp)) -> (~(exists I2 : zenon_U, (model I2 zenon_TF_bl))) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (csa))/\(~(status Ax C (thm))))))) -> (forall C : zenon_U, ((exists I1 : zenon_U, ((model I1 zenon_TF_bl)/\(model I1 (not C))))<->(status zenon_TF_bl C (csa)))) -> False). % 243.84/244.11 do 2 intro. intros zenon_H32 zenon_H27 zenon_H22 zenon_H38 zenon_H39. % 243.84/244.11 generalize (thm zenon_TF_bp). zenon_intro zenon_H3a. % 243.84/244.11 generalize (zenon_H39 zenon_TF_bl). zenon_intro zenon_H3b. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3e; zenon_intro zenon_H3d | zenon_intro zenon_H31; zenon_intro zenon_H3c ]. % 243.84/244.11 generalize (zenon_H3a zenon_TF_bl). zenon_intro zenon_H3f. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H43; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 243.84/244.11 apply zenon_H38. exists zenon_TF_bp. apply NNPP. zenon_intro zenon_H44. % 243.84/244.11 apply zenon_H44. exists zenon_TF_bl. apply NNPP. zenon_intro zenon_H45. % 243.84/244.11 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 243.84/244.11 generalize (csa zenon_TF_bp). zenon_intro zenon_H48. % 243.84/244.11 generalize (zenon_H48 zenon_TF_bl). zenon_intro zenon_H49. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H28; zenon_intro zenon_H47 | zenon_intro zenon_H4b; zenon_intro zenon_H4a ]. % 243.84/244.11 apply (zenon_L2_ zenon_TF_bp zenon_TF_bl); trivial. % 243.84/244.11 exact (zenon_H47 zenon_H4a). % 243.84/244.11 exact (zenon_H46 zenon_H42). % 243.84/244.11 generalize (csa zenon_TF_bp). zenon_intro zenon_H48. % 243.84/244.11 generalize (zenon_H48 zenon_TF_bl). zenon_intro zenon_H49. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H28; zenon_intro zenon_H47 | zenon_intro zenon_H4b; zenon_intro zenon_H4a ]. % 243.84/244.11 apply (zenon_L2_ zenon_TF_bp zenon_TF_bl); trivial. % 243.84/244.11 elim zenon_H4b. zenon_intro zenon_TI1_cy. zenon_intro zenon_H4d. % 243.84/244.11 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 243.84/244.11 apply zenon_H3e. exists zenon_TI1_cy. apply NNPP. zenon_intro zenon_H50. % 243.84/244.11 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 243.84/244.11 generalize (zenon_H41 zenon_TI1_cy). zenon_intro zenon_H53. % 243.84/244.11 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 243.84/244.11 exact (zenon_H55 zenon_H4f). % 243.84/244.11 exact (zenon_H52 zenon_H54). % 243.84/244.11 exact (zenon_H51 zenon_H4e). % 243.84/244.11 apply (zenon_L3_ zenon_TF_bl); trivial. % 243.84/244.11 (* end of lemma zenon_L4_ *) % 243.84/244.11 assert (zenon_L5_ : forall (zenon_TF_bl : zenon_U), (exists I2 : zenon_U, (model I2 zenon_TF_bl)) -> (forall I : zenon_U, (~(model I zenon_TF_bl))) -> False). % 243.84/244.11 do 1 intro. intros zenon_H56 zenon_H32. % 243.84/244.11 elim zenon_H56. zenon_intro zenon_TI2_dj. zenon_intro zenon_H58. % 243.84/244.11 generalize (zenon_H32 zenon_TI2_dj). zenon_intro zenon_H59. % 243.84/244.11 exact (zenon_H59 zenon_H58). % 243.84/244.11 (* end of lemma zenon_L5_ *) % 243.84/244.11 assert (zenon_L6_ : forall (zenon_TF_bp : zenon_U) (zenon_TF_bl : zenon_U), (~((exists I2 : zenon_U, (model I2 zenon_TF_bl))<->(exists I2 : zenon_U, (model I2 zenon_E)))) -> (forall C : zenon_U, ((exists I1 : zenon_U, ((model I1 zenon_TF_bl)/\(model I1 (not C))))<->(status zenon_TF_bl C (csa)))) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (csa))/\(~(status Ax C (thm))))))) -> (forall I : zenon_U, (model I zenon_TF_bp)) -> (forall I : zenon_U, (~(model I zenon_TF_bl))) -> False). % 243.84/244.11 do 2 intro. intros zenon_H5a zenon_H39 zenon_H38 zenon_H27 zenon_H32. % 243.84/244.11 apply (zenon_notequiv_s _ _ zenon_H5a); [ zenon_intro zenon_H22; zenon_intro zenon_H5c | zenon_intro zenon_H56; zenon_intro zenon_H5b ]. % 243.84/244.11 apply (zenon_L4_ zenon_TF_bp zenon_TF_bl); trivial. % 243.84/244.11 apply (zenon_L5_ zenon_TF_bl); trivial. % 243.84/244.11 (* end of lemma zenon_L6_ *) % 243.84/244.11 apply NNPP. intro zenon_G. % 243.84/244.11 elim tautology. zenon_intro zenon_TF_bp. zenon_intro zenon_H27. % 243.84/244.11 elim contradiction. zenon_intro zenon_TF_bl. zenon_intro zenon_H32. % 243.84/244.11 generalize (nota (csa)). zenon_intro zenon_H5d. % 243.84/244.11 generalize (zenon_H5d (thm)). zenon_intro zenon_H5e. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H38; zenon_intro zenon_G | zenon_intro zenon_H60; zenon_intro zenon_H5f ]. % 243.84/244.11 generalize (csa zenon_TF_bl). zenon_intro zenon_H39. % 243.84/244.11 generalize (esa zenon_TF_bl). zenon_intro zenon_H0. % 243.84/244.11 generalize (zenon_H0 zenon_E). zenon_intro zenon_H61. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5a; zenon_intro zenon_H64 | zenon_intro zenon_H63; zenon_intro zenon_H62 ]. % 243.84/244.11 apply (zenon_L6_ zenon_TF_bp zenon_TF_bl); trivial. % 243.84/244.11 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H22; zenon_intro zenon_H5b | zenon_intro zenon_H56; zenon_intro zenon_H5c ]. % 243.84/244.11 apply (zenon_L4_ zenon_TF_bp zenon_TF_bl); trivial. % 243.84/244.11 apply (zenon_L5_ zenon_TF_bl); trivial. % 243.84/244.11 exact (zenon_G zenon_H5f). % 243.84/244.11 Qed. % 243.84/244.11 % SZS output end Proof % 243.84/244.11 (* END-PROOF *) % 243.84/244.11 nodes searched: 12221090 % 243.84/244.11 max branch formulas: 22309 % 243.84/244.11 proof nodes created: 518603 % 243.84/244.11 formulas created: 30530587 % 243.84/244.11 %------------------------------------------------------------------------------