%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN052+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 13:49:07 EDT 2022 % Result : Theorem 0.18s 0.47s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : SYN052+1 : TPTP v8.1.0. Released v2.0.0. % 0.06/0.12 % 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 15:32:21 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.47 (* PROOF-FOUND *) % 0.18/0.47 % SZS status Theorem % 0.18/0.47 (* BEGIN-PROOF *) % 0.18/0.47 % SZS output start Proof % 0.18/0.47 Theorem pel22 : ((forall X : zenon_U, ((p)<->(big_f X)))->((p)<->(forall X1 : zenon_U, (big_f X1)))). % 0.18/0.47 Proof. % 0.18/0.47 assert (zenon_L1_ : (~(p)) -> (p) -> False). % 0.18/0.47 do 0 intro. intros zenon_H2 zenon_H3. % 0.18/0.47 exact (zenon_H2 zenon_H3). % 0.18/0.47 (* end of lemma zenon_L1_ *) % 0.18/0.47 apply NNPP. intro zenon_G. % 0.18/0.47 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H5. zenon_intro zenon_H4. % 0.18/0.47 apply (zenon_notequiv_s _ _ zenon_H4); [ zenon_intro zenon_H2; zenon_intro zenon_H0 | zenon_intro zenon_H3; zenon_intro zenon_H6 ]. % 0.18/0.47 generalize (zenon_H0 zenon_E). zenon_intro zenon_H7. % 0.18/0.47 generalize (zenon_H5 zenon_E). zenon_intro zenon_H8. % 0.18/0.47 apply (zenon_equiv_s _ _ zenon_H8); [ zenon_intro zenon_H2; zenon_intro zenon_H9 | zenon_intro zenon_H3; zenon_intro zenon_H7 ]. % 0.18/0.47 exact (zenon_H9 zenon_H7). % 0.18/0.47 exact (zenon_H2 zenon_H3). % 0.18/0.47 apply (zenon_notallex_s (fun X1 : zenon_U => (big_f X1)) zenon_H6); [ zenon_intro zenon_Ha; idtac ]. % 0.18/0.47 elim zenon_Ha. zenon_intro zenon_TX1_l. zenon_intro zenon_Hc. % 0.18/0.47 generalize (zenon_H5 zenon_TX1_l). zenon_intro zenon_Hd. % 0.18/0.47 apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_H2; zenon_intro zenon_Hc | zenon_intro zenon_H3; zenon_intro zenon_He ]. % 0.18/0.47 exact (zenon_H2 zenon_H3). % 0.18/0.47 exact (zenon_Hc zenon_He). % 0.18/0.47 Qed. % 0.18/0.47 % SZS output end Proof % 0.18/0.47 (* END-PROOF *) % 0.18/0.47 nodes searched: 18 % 0.18/0.47 max branch formulas: 12 % 0.18/0.47 proof nodes created: 11 % 0.18/0.47 formulas created: 108 % 0.18/0.47 %------------------------------------------------------------------------------