%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN398+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 13:51:51 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 : SYN398+1 : TPTP v8.1.0. Released v2.0.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.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 : Mon Jul 11 20:14:52 EDT 2022 % 0.12/0.33 % 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 kalish215 : ((forall X : zenon_U, ((p)/\(f X)))<->((p)/\(forall Y : zenon_U, (f Y)))). % 0.19/0.50 Proof. % 0.19/0.50 assert (zenon_L1_ : (~(p)) -> (p) -> False). % 0.19/0.50 do 0 intro. intros zenon_H2 zenon_H3. % 0.19/0.50 exact (zenon_H2 zenon_H3). % 0.19/0.50 (* end of lemma zenon_L1_ *) % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H6; zenon_intro zenon_H5 | zenon_intro zenon_H0; zenon_intro zenon_H4 ]. % 0.19/0.50 apply (zenon_notallex_s (fun X : zenon_U => ((p)/\(f X))) zenon_H6); [ zenon_intro zenon_H7; idtac ]. % 0.19/0.50 elim zenon_H7. zenon_intro zenon_TX_i. zenon_intro zenon_H9. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H5). zenon_intro zenon_H3. zenon_intro zenon_Ha. % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H9); [ zenon_intro zenon_H2 | zenon_intro zenon_Hb ]. % 0.19/0.50 exact (zenon_H2 zenon_H3). % 0.19/0.50 generalize (zenon_Ha zenon_TX_i). zenon_intro zenon_Hc. % 0.19/0.50 exact (zenon_Hb zenon_Hc). % 0.19/0.50 apply (zenon_notand_s _ _ zenon_H4); [ zenon_intro zenon_H2 | zenon_intro zenon_Hd ]. % 0.19/0.50 generalize (zenon_H0 zenon_E). zenon_intro zenon_He. % 0.19/0.50 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H3. zenon_intro zenon_Hf. % 0.19/0.50 exact (zenon_H2 zenon_H3). % 0.19/0.50 apply (zenon_notallex_s (fun Y : zenon_U => (f Y)) zenon_Hd); [ zenon_intro zenon_H10; idtac ]. % 0.19/0.50 elim zenon_H10. zenon_intro zenon_TY_r. zenon_intro zenon_H12. % 0.19/0.50 generalize (zenon_H0 zenon_TY_r). zenon_intro zenon_H13. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H3. zenon_intro zenon_H14. % 0.19/0.50 exact (zenon_H12 zenon_H14). % 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: 21 % 0.19/0.50 max branch formulas: 12 % 0.19/0.50 proof nodes created: 14 % 0.19/0.50 formulas created: 113 % 0.19/0.50 %------------------------------------------------------------------------------