%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS189+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 03:39:43 EDT 2022 % Result : Theorem 1.29s 1.46s % Output : Proof 1.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : KRS189+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n020.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 18:04:06 EDT 2022 % 0.12/0.33 % CPUTime : % 1.29/1.46 (* PROOF-FOUND *) % 1.29/1.46 % SZS status Theorem % 1.29/1.46 (* BEGIN-PROOF *) % 1.29/1.46 % SZS output start Proof % 1.29/1.46 Theorem isa_eth_thm : (isa (eth) (thm)). % 1.29/1.46 Proof. % 1.29/1.46 assert (zenon_L1_ : forall (zenon_TC_bm : zenon_U) (zenon_TAx_bn : zenon_U), (~((exists I2 : zenon_U, (model I2 zenon_TAx_bn))/\(forall I2 : zenon_U, ((model I2 zenon_TAx_bn)<->(model I2 zenon_TC_bm))))) -> (status zenon_TAx_bn zenon_TC_bm (eth)) -> (forall C : zenon_U, (((exists I2 : zenon_U, (model I2 zenon_TAx_bn))/\((exists I2 : zenon_U, (~(model I2 zenon_TAx_bn)))/\(forall I2 : zenon_U, ((model I2 zenon_TAx_bn)<->(model I2 C)))))<->(status zenon_TAx_bn C (eth)))) -> (exists I2 : zenon_U, (model I2 zenon_TAx_bn)) -> False). % 1.29/1.46 do 2 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25. % 1.29/1.46 apply (zenon_notand_s _ _ zenon_H22); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 1.29/1.46 exact (zenon_H29 zenon_H25). % 1.29/1.46 generalize (zenon_H24 zenon_TC_bm). zenon_intro zenon_H2a. % 1.29/1.46 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2d; zenon_intro zenon_H2c | zenon_intro zenon_H2b; zenon_intro zenon_H23 ]. % 1.29/1.46 exact (zenon_H2c zenon_H23). % 1.29/1.46 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H25. zenon_intro zenon_H2e. % 1.29/1.46 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 1.29/1.46 exact (zenon_H28 zenon_H2f). % 1.29/1.46 (* end of lemma zenon_L1_ *) % 1.29/1.46 assert (zenon_L2_ : forall (zenon_TI1_ca : zenon_U) (zenon_TC_bm : zenon_U) (zenon_TAx_bn : zenon_U), ((exists I2 : zenon_U, (model I2 zenon_TAx_bn))/\(forall I2 : zenon_U, ((model I2 zenon_TAx_bn)<->(model I2 zenon_TC_bm)))) -> (~(model zenon_TI1_ca zenon_TC_bm)) -> (model zenon_TI1_ca zenon_TAx_bn) -> False). % 1.29/1.46 do 3 intro. intros zenon_H31 zenon_H32 zenon_H33. % 1.29/1.46 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H25. zenon_intro zenon_H2f. % 1.29/1.46 generalize (zenon_H2f zenon_TI1_ca). zenon_intro zenon_H35. % 1.29/1.46 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H37; zenon_intro zenon_H32 | zenon_intro zenon_H33; zenon_intro zenon_H36 ]. % 1.29/1.46 exact (zenon_H37 zenon_H33). % 1.29/1.46 exact (zenon_H32 zenon_H36). % 1.29/1.46 (* end of lemma zenon_L2_ *) % 1.29/1.46 assert (zenon_L3_ : forall (zenon_TI1_ca : zenon_U) (zenon_TC_bm : zenon_U) (zenon_TAx_bn : zenon_U), (forall C : zenon_U, (((exists I2 : zenon_U, (model I2 zenon_TAx_bn))/\(forall I2 : zenon_U, ((model I2 zenon_TAx_bn)<->(model I2 C))))<->(status zenon_TAx_bn C (eqv)))) -> (status zenon_TAx_bn zenon_TC_bm (eth)) -> (forall C : zenon_U, (((exists I2 : zenon_U, (model I2 zenon_TAx_bn))/\((exists I2 : zenon_U, (~(model I2 zenon_TAx_bn)))/\(forall I2 : zenon_U, ((model I2 zenon_TAx_bn)<->(model I2 C)))))<->(status zenon_TAx_bn C (eth)))) -> (exists I2 : zenon_U, (model I2 zenon_TAx_bn)) -> (~(model zenon_TI1_ca zenon_TC_bm)) -> (model zenon_TI1_ca zenon_TAx_bn) -> False). % 1.29/1.46 do 3 intro. intros zenon_H38 zenon_H23 zenon_H24 zenon_H25 zenon_H32 zenon_H33. % 1.29/1.46 generalize (zenon_H38 zenon_TC_bm). zenon_intro zenon_H39. % 1.29/1.46 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H22; zenon_intro zenon_H3b | zenon_intro zenon_H31; zenon_intro zenon_H3a ]. % 1.29/1.46 apply (zenon_L1_ zenon_TC_bm zenon_TAx_bn); trivial. % 1.29/1.46 apply (zenon_L2_ zenon_TI1_ca zenon_TC_bm zenon_TAx_bn); trivial. % 1.29/1.46 (* end of lemma zenon_L3_ *) % 1.29/1.46 assert (zenon_L4_ : forall (zenon_TC_bm : zenon_U) (zenon_TAx_bn : zenon_U) (zenon_TI1_ca : zenon_U), (model zenon_TI1_ca zenon_TAx_bn) -> (~(model zenon_TI1_ca zenon_TC_bm)) -> (exists I2 : zenon_U, (model I2 zenon_TAx_bn)) -> (status zenon_TAx_bn zenon_TC_bm (eth)) -> (forall C : zenon_U, (((exists I2 : zenon_U, (model I2 zenon_TAx_bn))/\(forall I2 : zenon_U, ((model I2 zenon_TAx_bn)<->(model I2 C))))<->(status zenon_TAx_bn C (eqv)))) -> False). % 1.29/1.46 do 3 intro. intros zenon_H33 zenon_H32 zenon_H25 zenon_H23 zenon_H38. % 1.29/1.46 generalize (eth zenon_TAx_bn). zenon_intro zenon_H24. % 1.29/1.46 apply (zenon_L3_ zenon_TI1_ca zenon_TC_bm zenon_TAx_bn); trivial. % 1.29/1.46 (* end of lemma zenon_L4_ *) % 1.29/1.46 apply NNPP. intro zenon_G. % 1.29/1.46 generalize (isa (eth)). zenon_intro zenon_H3c. % 1.29/1.46 generalize (zenon_H3c (thm)). zenon_intro zenon_H3d. % 1.29/1.46 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H40; zenon_intro zenon_G | zenon_intro zenon_H3f; zenon_intro zenon_H3e ]. % 1.29/1.46 apply (zenon_notallex_s (fun Ax : zenon_U => (forall C : zenon_U, ((status Ax C (eth))->(status Ax C (thm))))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 1.29/1.46 elim zenon_H41. zenon_intro zenon_TAx_bn. zenon_intro zenon_H42. % 1.29/1.46 apply (zenon_notallex_s (fun C : zenon_U => ((status zenon_TAx_bn C (eth))->(status zenon_TAx_bn C (thm)))) zenon_H42); [ zenon_intro zenon_H43; idtac ]. % 1.29/1.46 elim zenon_H43. zenon_intro zenon_TC_bm. zenon_intro zenon_H44. % 1.29/1.46 apply (zenon_notimply_s _ _ zenon_H44). zenon_intro zenon_H23. zenon_intro zenon_H45. % 1.29/1.46 generalize (thm zenon_TAx_bn). zenon_intro zenon_H46. % 1.29/1.46 generalize (zenon_H46 zenon_TC_bm). zenon_intro zenon_H47. % 1.29/1.46 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H4a; zenon_intro zenon_H45 | zenon_intro zenon_H49; zenon_intro zenon_H48 ]. % 1.29/1.46 apply (zenon_notallex_s (fun I1 : zenon_U => ((model I1 zenon_TAx_bn)->(model I1 zenon_TC_bm))) zenon_H4a); [ zenon_intro zenon_H4b; idtac ]. % 1.29/1.46 elim zenon_H4b. zenon_intro zenon_TI1_ca. zenon_intro zenon_H4c. % 1.29/1.46 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H33. zenon_intro zenon_H32. % 1.29/1.46 generalize (eqv zenon_TAx_bn). zenon_intro zenon_H38. % 1.29/1.46 generalize (cax zenon_TAx_bn). zenon_intro zenon_H0. % 1.29/1.46 generalize (zenon_H0 zenon_E). zenon_intro zenon_H4d. % 1.29/1.46 apply (zenon_equiv_s _ _ zenon_H4d); [ zenon_intro zenon_H50; zenon_intro zenon_H4f | zenon_intro zenon_H29; zenon_intro zenon_H4e ]. % 1.29/1.46 apply zenon_H50. zenon_intro zenon_H25. % 1.29/1.46 apply (zenon_L4_ zenon_TC_bm zenon_TAx_bn zenon_TI1_ca); trivial. % 1.29/1.46 apply zenon_H29. exists zenon_TI1_ca. apply NNPP. zenon_intro zenon_H37. % 1.29/1.46 exact (zenon_H37 zenon_H33). % 1.29/1.46 exact (zenon_H45 zenon_H48). % 1.29/1.46 exact (zenon_G zenon_H3e). % 1.29/1.46 Qed. % 1.29/1.46 % SZS output end Proof % 1.29/1.46 (* END-PROOF *) % 1.29/1.46 nodes searched: 63856 % 1.29/1.46 max branch formulas: 4439 % 1.29/1.46 proof nodes created: 4156 % 1.29/1.46 formulas created: 191945 % 1.29/1.46 %------------------------------------------------------------------------------