%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN967+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 13:56:44 EDT 2022 % Result : Theorem 0.20s 0.50s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN967+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue Jul 12 09:12:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.50 (* PROOF-FOUND *) % 0.20/0.50 % SZS status Theorem % 0.20/0.50 (* BEGIN-PROOF *) % 0.20/0.50 % SZS output start Proof % 0.20/0.50 Theorem prove_this : (forall A : zenon_U, (forall B : zenon_U, ((forall Y : zenon_U, ((q Y)->(p Y)))->(exists X : zenon_U, (((p X)->(p A))/\((q X)->(p B))))))). % 0.20/0.50 Proof. % 0.20/0.50 assert (zenon_L1_ : forall (zenon_TB_f : zenon_U) (zenon_TA_g : zenon_U), (forall Y : zenon_U, ((q Y)->(p Y))) -> (~(exists X : zenon_U, (((p X)->(p zenon_TA_g))/\((q X)->(p zenon_TB_f))))) -> (~(p zenon_TB_f)) -> False). % 0.20/0.50 do 2 intro. intros zenon_H2 zenon_H3 zenon_H4. % 0.20/0.50 generalize (zenon_H2 zenon_TB_f). zenon_intro zenon_H7. % 0.20/0.50 apply (zenon_imply_s _ _ zenon_H7); [ zenon_intro zenon_H9 | zenon_intro zenon_H8 ]. % 0.20/0.50 apply zenon_H3. exists zenon_TB_f. apply NNPP. zenon_intro zenon_Ha. % 0.20/0.50 apply (zenon_notand_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_H8. zenon_intro zenon_Hd. % 0.20/0.50 exact (zenon_H4 zenon_H8). % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_Hb). zenon_intro zenon_He. zenon_intro zenon_H4. % 0.20/0.50 exact (zenon_H9 zenon_He). % 0.20/0.50 exact (zenon_H4 zenon_H8). % 0.20/0.50 (* end of lemma zenon_L1_ *) % 0.20/0.50 apply NNPP. intro zenon_G. % 0.20/0.50 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((forall Y : zenon_U, ((q Y)->(p Y)))->(exists X : zenon_U, (((p X)->(p A))/\((q X)->(p B))))))) zenon_G); [ zenon_intro zenon_Hf; idtac ]. % 0.20/0.50 elim zenon_Hf. zenon_intro zenon_TA_g. zenon_intro zenon_H10. % 0.20/0.50 apply (zenon_notallex_s (fun B : zenon_U => ((forall Y : zenon_U, ((q Y)->(p Y)))->(exists X : zenon_U, (((p X)->(p zenon_TA_g))/\((q X)->(p B)))))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 0.20/0.50 elim zenon_H11. zenon_intro zenon_TB_f. zenon_intro zenon_H12. % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H12). zenon_intro zenon_H2. zenon_intro zenon_H3. % 0.20/0.50 apply zenon_H3. exists zenon_E. apply NNPP. zenon_intro zenon_H13. % 0.20/0.50 apply (zenon_notand_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H16. zenon_intro zenon_Hd. % 0.20/0.50 apply zenon_H3. exists zenon_TA_g. apply NNPP. zenon_intro zenon_H17. % 0.20/0.50 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1a. zenon_intro zenon_Hd. % 0.20/0.50 exact (zenon_Hd zenon_H1a). % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H18). zenon_intro zenon_H1b. zenon_intro zenon_H4. % 0.20/0.50 apply (zenon_L1_ zenon_TB_f zenon_TA_g); trivial. % 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_H1c. zenon_intro zenon_H4. % 0.20/0.50 apply (zenon_L1_ zenon_TB_f zenon_TA_g); trivial. % 0.20/0.50 Qed. % 0.20/0.50 % SZS output end Proof % 0.20/0.50 (* END-PROOF *) % 0.20/0.50 nodes searched: 29 % 0.20/0.50 max branch formulas: 21 % 0.20/0.50 proof nodes created: 21 % 0.20/0.50 formulas created: 175 % 0.20/0.50 %------------------------------------------------------------------------------