%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n014.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 13:49:28 EDT 2022 % Result : Theorem 0.21s 0.51s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN078+1 : TPTP v8.1.0. Released v2.0.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n014.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Mon Jul 11 12:14:49 EDT 2022 % 0.14/0.34 % CPUTime : % 0.21/0.51 (* PROOF-FOUND *) % 0.21/0.51 % SZS status Theorem % 0.21/0.51 (* BEGIN-PROOF *) % 0.21/0.51 % SZS output start Proof % 0.21/0.51 Theorem pel56 : ((forall X : zenon_U, ((exists Y : zenon_U, ((big_p Y)/\(X = (f Y))))->(big_p X)))<->(forall U : zenon_U, ((big_p U)->(big_p (f U))))). % 0.21/0.51 Proof. % 0.21/0.51 apply NNPP. intro zenon_G. % 0.21/0.51 apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H2; zenon_intro zenon_H1 ]. % 0.21/0.51 apply (zenon_notallex_s (fun X : zenon_U => ((exists Y : zenon_U, ((big_p Y)/\(X = (f Y))))->(big_p X))) zenon_H4); [ zenon_intro zenon_H5; idtac ]. % 0.21/0.51 elim zenon_H5. zenon_intro zenon_TX_g. zenon_intro zenon_H7. % 0.21/0.51 apply (zenon_notimply_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.21/0.51 elim zenon_H9. zenon_intro zenon_TY_k. zenon_intro zenon_Hb. % 0.21/0.51 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.21/0.51 generalize (zenon_H3 zenon_TY_k). zenon_intro zenon_He. % 0.21/0.51 apply (zenon_imply_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.21/0.51 exact (zenon_H10 zenon_Hd). % 0.21/0.51 cut ((big_p (f zenon_TY_k)) = (big_p zenon_TX_g)). % 0.21/0.51 intro zenon_D_pnotp. % 0.21/0.51 apply zenon_H8. % 0.21/0.51 rewrite <- zenon_D_pnotp. % 0.21/0.51 exact zenon_Hf. % 0.21/0.51 cut (((f zenon_TY_k) = zenon_TX_g)); [idtac | apply NNPP; zenon_intro zenon_H11]. % 0.21/0.51 congruence. % 0.21/0.51 apply zenon_H11. apply sym_equal. exact zenon_Hc. % 0.21/0.51 apply (zenon_notallex_s (fun U : zenon_U => ((big_p U)->(big_p (f U)))) zenon_H1); [ zenon_intro zenon_H12; idtac ]. % 0.21/0.51 elim zenon_H12. zenon_intro zenon_TU_t. zenon_intro zenon_H14. % 0.21/0.51 apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.21/0.51 generalize (zenon_H2 (f zenon_TU_t)). zenon_intro zenon_H17. % 0.21/0.51 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.21/0.51 apply zenon_H19. exists zenon_TU_t. apply NNPP. zenon_intro zenon_H1a. % 0.21/0.51 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.21/0.51 exact (zenon_H1c zenon_H16). % 0.21/0.51 apply zenon_H1b. apply refl_equal. % 0.21/0.51 exact (zenon_H15 zenon_H18). % 0.21/0.51 Qed. % 0.21/0.51 % SZS output end Proof % 0.21/0.51 (* END-PROOF *) % 0.21/0.51 nodes searched: 39 % 0.21/0.51 max branch formulas: 20 % 0.21/0.51 proof nodes created: 19 % 0.21/0.51 formulas created: 205 % 0.21/0.51 %------------------------------------------------------------------------------