%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : PHI009+1 : TPTP v8.1.0. Released v7.2.0. % 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 : Mon Jul 18 16:50:13 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : PHI009+1 : TPTP v8.1.0. Released v7.2.0. % 0.07/0.13 % 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 : Thu Jun 2 01:26:07 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem description_theorem_1 : (forall F : zenon_U, ((property F)->((exists Y : zenon_U, ((object Y)/\((exemplifies_property F Y)/\(forall Z : zenon_U, ((object Z)->((exemplifies_property F Z)->(Z = Y)))))))->(exists U : zenon_U, ((object U)/\(is_the U F)))))). % 0.19/0.50 Proof. % 0.19/0.50 assert (zenon_L1_ : forall (zenon_TY_g : zenon_U) (zenon_TF_h : zenon_U), (~(exists Y : zenon_U, ((object Y)/\((exemplifies_property zenon_TF_h Y)/\((forall Z : zenon_U, ((object Z)->((exemplifies_property zenon_TF_h Z)->(Z = Y))))/\(exemplifies_property zenon_TF_h Y)))))) -> (object zenon_TY_g) -> (exemplifies_property zenon_TF_h zenon_TY_g) -> (forall Z : zenon_U, ((object Z)->((exemplifies_property zenon_TF_h Z)->(Z = zenon_TY_g)))) -> False). % 0.19/0.50 do 2 intro. intros zenon_H2 zenon_H3 zenon_H4 zenon_H5. % 0.19/0.50 apply zenon_H2. exists zenon_TY_g. apply NNPP. zenon_intro zenon_H8. % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H8); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ]. % 0.19/0.50 exact (zenon_Ha zenon_H3). % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H9); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 0.19/0.50 exact (zenon_Hc zenon_H4). % 0.19/0.50 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_Hd | zenon_intro zenon_Hc ]. % 0.19/0.50 exact (zenon_Hd zenon_H5). % 0.19/0.50 exact (zenon_Hc zenon_H4). % 0.19/0.50 (* end of lemma zenon_L1_ *) % 0.19/0.50 assert (zenon_L2_ : forall (zenon_TF_h : zenon_U) (zenon_TY_g : zenon_U), (((is_the zenon_TY_g zenon_TF_h)/\(exemplifies_property zenon_TF_h zenon_TY_g))<->(exists Y : zenon_U, ((object Y)/\((exemplifies_property zenon_TF_h Y)/\((forall Z : zenon_U, ((object Z)->((exemplifies_property zenon_TF_h Z)->(Z = Y))))/\(exemplifies_property zenon_TF_h Y)))))) -> (~(is_the zenon_TY_g zenon_TF_h)) -> (exists Y : zenon_U, ((object Y)/\((exemplifies_property zenon_TF_h Y)/\((forall Z : zenon_U, ((object Z)->((exemplifies_property zenon_TF_h Z)->(Z = Y))))/\(exemplifies_property zenon_TF_h Y))))) -> False). % 0.19/0.50 do 2 intro. intros zenon_He zenon_Hf zenon_H10. % 0.19/0.50 apply (zenon_equiv_s _ _ zenon_He); [ zenon_intro zenon_H12; zenon_intro zenon_H2 | zenon_intro zenon_H11; zenon_intro zenon_H10 ]. % 0.19/0.50 exact (zenon_H2 zenon_H10). % 0.19/0.50 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H13. zenon_intro zenon_H4. % 0.19/0.50 exact (zenon_Hf zenon_H13). % 0.19/0.50 (* end of lemma zenon_L2_ *) % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notallex_s (fun F : zenon_U => ((property F)->((exists Y : zenon_U, ((object Y)/\((exemplifies_property F Y)/\(forall Z : zenon_U, ((object Z)->((exemplifies_property F Z)->(Z = Y)))))))->(exists U : zenon_U, ((object U)/\(is_the U F)))))) zenon_G); [ zenon_intro zenon_H14; idtac ]. % 0.19/0.50 elim zenon_H14. zenon_intro zenon_TF_h. zenon_intro zenon_H15. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H16). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.19/0.50 elim zenon_H19. zenon_intro zenon_TY_g. zenon_intro zenon_H1a. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H3. zenon_intro zenon_H1b. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H4. zenon_intro zenon_H5. % 0.19/0.50 generalize (description_axiom_schema_instance zenon_TF_h). zenon_intro zenon_H1c. % 0.19/0.50 apply zenon_H18. exists zenon_TY_g. apply NNPP. zenon_intro zenon_H1d. % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_Ha | zenon_intro zenon_Hf ]. % 0.19/0.50 exact (zenon_Ha zenon_H3). % 0.19/0.50 generalize (zenon_H1c zenon_TF_h). zenon_intro zenon_H1e. % 0.19/0.50 generalize (zenon_H1e zenon_TY_g). zenon_intro zenon_H1f. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H20 | zenon_intro zenon_He ]. % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.19/0.50 exact (zenon_H22 zenon_H17). % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H21); [ zenon_intro zenon_H22 | zenon_intro zenon_Ha ]. % 0.19/0.50 exact (zenon_H22 zenon_H17). % 0.19/0.50 exact (zenon_Ha zenon_H3). % 0.19/0.50 apply (zenon_equiv_s _ _ zenon_He); [ zenon_intro zenon_H12; zenon_intro zenon_H2 | zenon_intro zenon_H11; zenon_intro zenon_H10 ]. % 0.19/0.50 apply (zenon_L1_ zenon_TY_g zenon_TF_h); trivial. % 0.19/0.50 apply (zenon_L2_ zenon_TF_h zenon_TY_g); trivial. % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 225 % 0.19/0.50 max branch formulas: 116 % 0.19/0.50 proof nodes created: 58 % 0.19/0.50 formulas created: 936 % 0.19/0.50 %------------------------------------------------------------------------------