%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0. % 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 : Thu Jul 21 13:49:31 EDT 2022 % Result : Theorem 0.17s 0.48s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SYN082+1 : TPTP v8.1.0. Released v2.0.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n020.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Mon Jul 11 19:57:27 EDT 2022 % 0.12/0.33 % CPUTime : % 0.17/0.48 (* PROOF-FOUND *) % 0.17/0.48 % SZS status Theorem % 0.17/0.48 (* BEGIN-PROOF *) % 0.17/0.48 % SZS output start Proof % 0.17/0.48 Theorem pel60 : (forall X : zenon_U, ((big_f X (f X))<->(exists Y : zenon_U, ((forall Z : zenon_U, ((big_f Z Y)->(big_f Z (f X))))/\(big_f X Y))))). % 0.17/0.48 Proof. % 0.17/0.48 apply NNPP. intro zenon_G. % 0.17/0.48 apply (zenon_notallex_s (fun X : zenon_U => ((big_f X (f X))<->(exists Y : zenon_U, ((forall Z : zenon_U, ((big_f Z Y)->(big_f Z (f X))))/\(big_f X Y))))) zenon_G); [ zenon_intro zenon_H1; idtac ]. % 0.17/0.48 elim zenon_H1. zenon_intro zenon_TX_c. zenon_intro zenon_H3. % 0.17/0.48 apply (zenon_notequiv_s _ _ zenon_H3); [ zenon_intro zenon_H7; zenon_intro zenon_H6 | zenon_intro zenon_H5; zenon_intro zenon_H4 ]. % 0.17/0.48 elim zenon_H6. zenon_intro zenon_TY_i. zenon_intro zenon_H9. % 0.17/0.48 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.17/0.48 generalize (zenon_Hb zenon_TX_c). zenon_intro zenon_Hc. % 0.17/0.48 apply (zenon_imply_s _ _ zenon_Hc); [ zenon_intro zenon_Hd | zenon_intro zenon_H5 ]. % 0.17/0.48 exact (zenon_Hd zenon_Ha). % 0.17/0.48 exact (zenon_H7 zenon_H5). % 0.17/0.48 apply zenon_H4. exists (f zenon_TX_c). apply NNPP. zenon_intro zenon_He. % 0.17/0.48 apply (zenon_notand_s _ _ zenon_He); [ zenon_intro zenon_Hf | zenon_intro zenon_H7 ]. % 0.17/0.48 apply (zenon_notallex_s (fun Z : zenon_U => ((big_f Z (f zenon_TX_c))->(big_f Z (f zenon_TX_c)))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 0.17/0.48 elim zenon_H10. zenon_intro zenon_TZ_r. zenon_intro zenon_H12. % 0.17/0.48 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.17/0.48 exact (zenon_H13 zenon_H14). % 0.17/0.48 exact (zenon_H7 zenon_H5). % 0.17/0.48 Qed. % 0.17/0.48 % SZS output end Proof % 0.17/0.48 (* END-PROOF *) % 0.17/0.48 nodes searched: 22 % 0.17/0.48 max branch formulas: 14 % 0.17/0.48 proof nodes created: 15 % 0.17/0.48 formulas created: 155 % 0.17/0.48 %------------------------------------------------------------------------------