%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET751+4 : TPTP v8.1.0. Bugfixed v2.2.1. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n007.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 : Tue Jul 19 06:38:20 EDT 2022 % Result : Theorem 1.14s 1.36s % Output : Proof 1.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET751+4 : TPTP v8.1.0. Bugfixed v2.2.1. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n007.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 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jul 9 19:32:01 EDT 2022 % 0.12/0.34 % CPUTime : % 1.14/1.36 (* PROOF-FOUND *) % 1.14/1.36 % SZS status Theorem % 1.14/1.36 (* BEGIN-PROOF *) % 1.14/1.36 % SZS output start Proof % 1.14/1.36 Theorem thIIa01 : (forall F : zenon_U, (forall A : zenon_U, (forall B : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (((maps F A B)/\((subset X A)/\((subset Y A)/\(subset X Y))))->(subset (image2 F X) (image2 F Y)))))))). % 1.14/1.36 Proof. % 1.14/1.36 assert (zenon_L1_ : forall (zenon_TY_bg : zenon_U) (zenon_TX_bh : zenon_U) (zenon_TF_bi : zenon_U) (zenon_TX_bj : zenon_U), (exists E : zenon_U, ((member E zenon_TX_bj)/\(apply zenon_TF_bi E zenon_TX_bh))) -> (~(exists E : zenon_U, ((member E zenon_TY_bg)/\(apply zenon_TF_bi E zenon_TX_bh)))) -> (forall X : zenon_U, ((member X zenon_TX_bj)->(member X zenon_TY_bg))) -> False). % 1.14/1.36 do 4 intro. intros zenon_H1d zenon_H1e zenon_H1f. % 1.14/1.36 elim zenon_H1d. zenon_intro zenon_TE_bk. zenon_intro zenon_H25. % 1.14/1.36 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 1.14/1.36 apply zenon_H1e. exists zenon_TE_bk. apply NNPP. zenon_intro zenon_H28. % 1.14/1.36 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 1.14/1.36 generalize (zenon_H1f zenon_TE_bk). zenon_intro zenon_H2b. % 1.14/1.36 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 1.14/1.36 exact (zenon_H2d zenon_H27). % 1.14/1.36 exact (zenon_H2a zenon_H2c). % 1.14/1.36 exact (zenon_H29 zenon_H26). % 1.14/1.36 (* end of lemma zenon_L1_ *) % 1.14/1.36 apply NNPP. intro zenon_G. % 1.14/1.36 apply (zenon_notallex_s (fun F : zenon_U => (forall A : zenon_U, (forall B : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (((maps F A B)/\((subset X A)/\((subset Y A)/\(subset X Y))))->(subset (image2 F X) (image2 F Y)))))))) zenon_G); [ zenon_intro zenon_H2e; idtac ]. % 1.14/1.36 elim zenon_H2e. zenon_intro zenon_TF_bi. zenon_intro zenon_H2f. % 1.14/1.36 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (((maps zenon_TF_bi A B)/\((subset X A)/\((subset Y A)/\(subset X Y))))->(subset (image2 zenon_TF_bi X) (image2 zenon_TF_bi Y))))))) zenon_H2f); [ zenon_intro zenon_H30; idtac ]. % 1.14/1.36 elim zenon_H30. zenon_intro zenon_TA_bx. zenon_intro zenon_H32. % 1.14/1.36 apply (zenon_notallex_s (fun B : zenon_U => (forall X : zenon_U, (forall Y : zenon_U, (((maps zenon_TF_bi zenon_TA_bx B)/\((subset X zenon_TA_bx)/\((subset Y zenon_TA_bx)/\(subset X Y))))->(subset (image2 zenon_TF_bi X) (image2 zenon_TF_bi Y)))))) zenon_H32); [ zenon_intro zenon_H33; idtac ]. % 1.14/1.36 elim zenon_H33. zenon_intro zenon_TB_ca. zenon_intro zenon_H35. % 1.14/1.36 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((maps zenon_TF_bi zenon_TA_bx zenon_TB_ca)/\((subset X zenon_TA_bx)/\((subset Y zenon_TA_bx)/\(subset X Y))))->(subset (image2 zenon_TF_bi X) (image2 zenon_TF_bi Y))))) zenon_H35); [ zenon_intro zenon_H36; idtac ]. % 1.14/1.36 elim zenon_H36. zenon_intro zenon_TX_bj. zenon_intro zenon_H37. % 1.14/1.36 apply (zenon_notallex_s (fun Y : zenon_U => (((maps zenon_TF_bi zenon_TA_bx zenon_TB_ca)/\((subset zenon_TX_bj zenon_TA_bx)/\((subset Y zenon_TA_bx)/\(subset zenon_TX_bj Y))))->(subset (image2 zenon_TF_bi zenon_TX_bj) (image2 zenon_TF_bi Y)))) zenon_H37); [ zenon_intro zenon_H38; idtac ]. % 1.14/1.36 elim zenon_H38. zenon_intro zenon_TY_bg. zenon_intro zenon_H39. % 1.14/1.36 apply (zenon_notimply_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 1.14/1.36 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 1.14/1.36 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 1.14/1.36 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40. % 1.14/1.36 generalize (subset zenon_TX_bj). zenon_intro zenon_H42. % 1.14/1.36 generalize (zenon_H42 zenon_TY_bg). zenon_intro zenon_H43. % 1.14/1.36 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H45; zenon_intro zenon_H44 | zenon_intro zenon_H40; zenon_intro zenon_H1f ]. % 1.14/1.36 exact (zenon_H45 zenon_H40). % 1.14/1.36 generalize (subset (image2 zenon_TF_bi zenon_TX_bj)). zenon_intro zenon_H46. % 1.14/1.36 generalize (zenon_H46 (image2 zenon_TF_bi zenon_TY_bg)). zenon_intro zenon_H47. % 1.14/1.36 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H3a; zenon_intro zenon_H4a | zenon_intro zenon_H49; zenon_intro zenon_H48 ]. % 1.14/1.36 apply (zenon_notallex_s (fun X : zenon_U => ((member X (image2 zenon_TF_bi zenon_TX_bj))->(member X (image2 zenon_TF_bi zenon_TY_bg)))) zenon_H4a); [ zenon_intro zenon_H4b; idtac ]. % 1.14/1.37 elim zenon_H4b. zenon_intro zenon_TX_bh. zenon_intro zenon_H4c. % 1.14/1.37 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 1.14/1.37 generalize (image2 zenon_TF_bi). zenon_intro zenon_H4f. % 1.14/1.37 generalize (zenon_H4f zenon_TY_bg). zenon_intro zenon_H50. % 1.14/1.37 generalize (zenon_H50 zenon_TX_bh). zenon_intro zenon_H51. % 1.14/1.37 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H4d; zenon_intro zenon_H1e | zenon_intro zenon_H53; zenon_intro zenon_H52 ]. % 1.14/1.37 generalize (zenon_H4f zenon_TX_bj). zenon_intro zenon_H54. % 1.14/1.37 generalize (zenon_H54 zenon_TX_bh). zenon_intro zenon_H55. % 1.14/1.37 apply (zenon_equiv_s _ _ zenon_H55); [ zenon_intro zenon_H57; zenon_intro zenon_H56 | zenon_intro zenon_H4e; zenon_intro zenon_H1d ]. % 1.14/1.37 exact (zenon_H57 zenon_H4e). % 1.14/1.37 apply (zenon_L1_ zenon_TY_bg zenon_TX_bh zenon_TF_bi zenon_TX_bj); trivial. % 1.14/1.37 exact (zenon_H4d zenon_H53). % 1.14/1.37 exact (zenon_H3a zenon_H49). % 1.14/1.37 Qed. % 1.14/1.37 % SZS output end Proof % 1.14/1.37 (* END-PROOF *) % 1.14/1.37 nodes searched: 26965 % 1.14/1.37 max branch formulas: 7566 % 1.14/1.37 proof nodes created: 1394 % 1.14/1.37 formulas created: 172578 % 1.14/1.37 %------------------------------------------------------------------------------