%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN053+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 13:49:08 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 % 0.11/0.12 % Problem : SYN053+1 : TPTP v8.1.0. Released v2.0.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n015.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Mon Jul 11 13:11:39 EDT 2022 % 0.12/0.34 % 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 pel23 : ((forall X : zenon_U, ((p)\/(big_f X)))<->((p)\/(forall X1 : zenon_U, (big_f X1)))). % 0.19/0.50 Proof. % 0.19/0.50 assert (zenon_L1_ : (~(p)) -> (p) -> False). % 0.19/0.50 do 0 intro. intros zenon_H1 zenon_H2. % 0.19/0.50 exact (zenon_H1 zenon_H2). % 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_H4; zenon_intro zenon_H3 ]. % 0.19/0.50 apply (zenon_notallex_s (fun X : zenon_U => ((p)\/(big_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_notor_s _ _ zenon_H9). zenon_intro zenon_H1. zenon_intro zenon_Ha. % 0.19/0.50 apply (zenon_or_s _ _ zenon_H5); [ zenon_intro zenon_H2 | zenon_intro zenon_Hb ]. % 0.19/0.50 exact (zenon_H1 zenon_H2). % 0.19/0.50 generalize (zenon_Hb zenon_TX_i). zenon_intro zenon_Hc. % 0.19/0.50 exact (zenon_Ha zenon_Hc). % 0.19/0.50 apply (zenon_notor_s _ _ zenon_H3). zenon_intro zenon_H1. zenon_intro zenon_Hd. % 0.19/0.50 apply (zenon_notallex_s (fun X1 : zenon_U => (big_f X1)) zenon_Hd); [ zenon_intro zenon_He; idtac ]. % 0.19/0.50 elim zenon_He. zenon_intro zenon_TX1_p. zenon_intro zenon_H10. % 0.19/0.50 generalize (zenon_H4 zenon_TX1_p). zenon_intro zenon_H11. % 0.19/0.50 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H2 | zenon_intro zenon_H12 ]. % 0.19/0.50 exact (zenon_H1 zenon_H2). % 0.19/0.50 exact (zenon_H10 zenon_H12). % 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: 19 % 0.19/0.50 max branch formulas: 12 % 0.19/0.50 proof nodes created: 12 % 0.19/0.50 formulas created: 109 % 0.19/0.50 %------------------------------------------------------------------------------