%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET776+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 06:38:29 EDT 2022 % Result : Theorem 1.40s 1.63s % Output : Proof 1.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET776+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n025.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 08:47:02 EDT 2022 % 0.13/0.33 % CPUTime : % 1.40/1.63 (* PROOF-FOUND *) % 1.40/1.63 % SZS status Theorem % 1.40/1.63 (* BEGIN-PROOF *) % 1.40/1.63 % SZS output start Proof % 1.40/1.63 Theorem thIII12 : (forall E : zenon_U, (forall P : zenon_U, (forall R : zenon_U, (((pre_order P E)/\(forall A : zenon_U, (forall B : zenon_U, (((member A E)/\(member B E))->((apply R A B)<->((apply P A B)/\(apply P B A)))))))->(forall X1 : zenon_U, (forall X2 : zenon_U, (forall Y1 : zenon_U, (forall Y2 : zenon_U, (((member X1 E)/\((member X2 E)/\((member Y1 E)/\(member Y2 E))))->(((apply R X1 Y1)/\((apply R X2 Y2)/\(apply P X1 X2)))->(apply P Y1 Y2))))))))))). % 1.40/1.63 Proof. % 1.40/1.63 apply NNPP. intro zenon_G. % 1.40/1.63 apply (zenon_notallex_s (fun E : zenon_U => (forall P : zenon_U, (forall R : zenon_U, (((pre_order P E)/\(forall A : zenon_U, (forall B : zenon_U, (((member A E)/\(member B E))->((apply R A B)<->((apply P A B)/\(apply P B A)))))))->(forall X1 : zenon_U, (forall X2 : zenon_U, (forall Y1 : zenon_U, (forall Y2 : zenon_U, (((member X1 E)/\((member X2 E)/\((member Y1 E)/\(member Y2 E))))->(((apply R X1 Y1)/\((apply R X2 Y2)/\(apply P X1 X2)))->(apply P Y1 Y2))))))))))) zenon_G); [ zenon_intro zenon_H11; idtac ]. % 1.40/1.63 elim zenon_H11. zenon_intro zenon_TE_s. zenon_intro zenon_H13. % 1.40/1.63 apply (zenon_notallex_s (fun P : zenon_U => (forall R : zenon_U, (((pre_order P zenon_TE_s)/\(forall A : zenon_U, (forall B : zenon_U, (((member A zenon_TE_s)/\(member B zenon_TE_s))->((apply R A B)<->((apply P A B)/\(apply P B A)))))))->(forall X1 : zenon_U, (forall X2 : zenon_U, (forall Y1 : zenon_U, (forall Y2 : zenon_U, (((member X1 zenon_TE_s)/\((member X2 zenon_TE_s)/\((member Y1 zenon_TE_s)/\(member Y2 zenon_TE_s))))->(((apply R X1 Y1)/\((apply R X2 Y2)/\(apply P X1 X2)))->(apply P Y1 Y2)))))))))) zenon_H13); [ zenon_intro zenon_H14; idtac ]. % 1.40/1.63 elim zenon_H14. zenon_intro zenon_TP_v. zenon_intro zenon_H16. % 1.40/1.63 apply (zenon_notallex_s (fun R : zenon_U => (((pre_order zenon_TP_v zenon_TE_s)/\(forall A : zenon_U, (forall B : zenon_U, (((member A zenon_TE_s)/\(member B zenon_TE_s))->((apply R A B)<->((apply zenon_TP_v A B)/\(apply zenon_TP_v B A)))))))->(forall X1 : zenon_U, (forall X2 : zenon_U, (forall Y1 : zenon_U, (forall Y2 : zenon_U, (((member X1 zenon_TE_s)/\((member X2 zenon_TE_s)/\((member Y1 zenon_TE_s)/\(member Y2 zenon_TE_s))))->(((apply R X1 Y1)/\((apply R X2 Y2)/\(apply zenon_TP_v X1 X2)))->(apply zenon_TP_v Y1 Y2))))))))) zenon_H16); [ zenon_intro zenon_H17; idtac ]. % 1.48/1.63 elim zenon_H17. zenon_intro zenon_TR_y. zenon_intro zenon_H19. % 1.48/1.63 apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 1.48/1.63 apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 1.48/1.63 generalize (pre_order zenon_TP_v). zenon_intro zenon_H1e. % 1.48/1.63 generalize (zenon_H1e zenon_TE_s). zenon_intro zenon_H1f. % 1.48/1.63 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1d; zenon_intro zenon_H20 ]. % 1.48/1.63 exact (zenon_H22 zenon_H1d). % 1.48/1.63 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23. % 1.48/1.63 apply (zenon_notallex_s (fun X1 : zenon_U => (forall X2 : zenon_U, (forall Y1 : zenon_U, (forall Y2 : zenon_U, (((member X1 zenon_TE_s)/\((member X2 zenon_TE_s)/\((member Y1 zenon_TE_s)/\(member Y2 zenon_TE_s))))->(((apply zenon_TR_y X1 Y1)/\((apply zenon_TR_y X2 Y2)/\(apply zenon_TP_v X1 X2)))->(apply zenon_TP_v Y1 Y2))))))) zenon_H1a); [ zenon_intro zenon_H25; idtac ]. % 1.48/1.63 elim zenon_H25. zenon_intro zenon_TX1_bm. zenon_intro zenon_H27. % 1.48/1.63 apply (zenon_notallex_s (fun X2 : zenon_U => (forall Y1 : zenon_U, (forall Y2 : zenon_U, (((member zenon_TX1_bm zenon_TE_s)/\((member X2 zenon_TE_s)/\((member Y1 zenon_TE_s)/\(member Y2 zenon_TE_s))))->(((apply zenon_TR_y zenon_TX1_bm Y1)/\((apply zenon_TR_y X2 Y2)/\(apply zenon_TP_v zenon_TX1_bm X2)))->(apply zenon_TP_v Y1 Y2)))))) zenon_H27); [ zenon_intro zenon_H28; idtac ]. % 1.48/1.63 elim zenon_H28. zenon_intro zenon_TX2_bp. zenon_intro zenon_H2a. % 1.48/1.63 apply (zenon_notallex_s (fun Y1 : zenon_U => (forall Y2 : zenon_U, (((member zenon_TX1_bm zenon_TE_s)/\((member zenon_TX2_bp zenon_TE_s)/\((member Y1 zenon_TE_s)/\(member Y2 zenon_TE_s))))->(((apply zenon_TR_y zenon_TX1_bm Y1)/\((apply zenon_TR_y zenon_TX2_bp Y2)/\(apply zenon_TP_v zenon_TX1_bm zenon_TX2_bp)))->(apply zenon_TP_v Y1 Y2))))) zenon_H2a); [ zenon_intro zenon_H2b; idtac ]. % 1.48/1.63 elim zenon_H2b. zenon_intro zenon_TY1_bs. zenon_intro zenon_H2d. % 1.48/1.63 apply (zenon_notallex_s (fun Y2 : zenon_U => (((member zenon_TX1_bm zenon_TE_s)/\((member zenon_TX2_bp zenon_TE_s)/\((member zenon_TY1_bs zenon_TE_s)/\(member Y2 zenon_TE_s))))->(((apply zenon_TR_y zenon_TX1_bm zenon_TY1_bs)/\((apply zenon_TR_y zenon_TX2_bp Y2)/\(apply zenon_TP_v zenon_TX1_bm zenon_TX2_bp)))->(apply zenon_TP_v zenon_TY1_bs Y2)))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 1.48/1.63 elim zenon_H2e. zenon_intro zenon_TY2_bv. zenon_intro zenon_H30. % 1.48/1.63 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 1.48/1.63 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 1.48/1.63 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 1.48/1.63 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H38. zenon_intro zenon_H37. % 1.48/1.63 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H3a. zenon_intro zenon_H39. % 1.48/1.63 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3c. zenon_intro zenon_H3b. % 1.48/1.63 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 1.48/1.63 generalize (zenon_H23 zenon_TY1_bs). zenon_intro zenon_H3f. % 1.48/1.63 generalize (zenon_H3f zenon_TX2_bp). zenon_intro zenon_H40. % 1.48/1.63 generalize (zenon_H3f zenon_TX1_bm). zenon_intro zenon_H41. % 1.48/1.63 generalize (zenon_H40 zenon_TY2_bv). zenon_intro zenon_H42. % 1.48/1.63 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 1.48/1.63 exact (zenon_H46 zenon_H3e). % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 1.48/1.63 exact (zenon_H48 zenon_H3c). % 1.48/1.63 exact (zenon_H47 zenon_H3d). % 1.48/1.63 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 1.48/1.63 generalize (zenon_H41 zenon_TX2_bp). zenon_intro zenon_H4d. % 1.48/1.63 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H46 | zenon_intro zenon_H50 ]. % 1.48/1.63 exact (zenon_H46 zenon_H3e). % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H48 ]. % 1.48/1.63 exact (zenon_H51 zenon_H3a). % 1.48/1.63 exact (zenon_H48 zenon_H3c). % 1.48/1.63 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 1.48/1.63 generalize (zenon_H1c zenon_TX1_bm). zenon_intro zenon_H56. % 1.48/1.63 generalize (zenon_H56 zenon_TY1_bs). zenon_intro zenon_H57. % 1.48/1.63 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H51 | zenon_intro zenon_H46 ]. % 1.48/1.63 exact (zenon_H51 zenon_H3a). % 1.48/1.63 exact (zenon_H46 zenon_H3e). % 1.48/1.63 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H5c; zenon_intro zenon_H5b | zenon_intro zenon_H36; zenon_intro zenon_H5a ]. % 1.48/1.63 exact (zenon_H5c zenon_H36). % 1.48/1.63 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 1.48/1.63 exact (zenon_H55 zenon_H5d). % 1.48/1.63 exact (zenon_H54 zenon_H37). % 1.48/1.63 exact (zenon_H4c zenon_H52). % 1.48/1.63 generalize (zenon_H1c zenon_TX2_bp). zenon_intro zenon_H5f. % 1.48/1.63 generalize (zenon_H5f zenon_TY2_bv). zenon_intro zenon_H60. % 1.48/1.63 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H45 | zenon_intro zenon_H61 ]. % 1.48/1.63 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 1.48/1.63 exact (zenon_H48 zenon_H3c). % 1.48/1.63 exact (zenon_H47 zenon_H3d). % 1.48/1.63 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H64; zenon_intro zenon_H63 | zenon_intro zenon_H38; zenon_intro zenon_H62 ]. % 1.48/1.63 exact (zenon_H64 zenon_H38). % 1.48/1.63 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H66. zenon_intro zenon_H65. % 1.48/1.63 exact (zenon_H4b zenon_H66). % 1.48/1.63 exact (zenon_H33 zenon_H49). % 1.48/1.63 Qed. % 1.48/1.63 % SZS output end Proof % 1.48/1.63 (* END-PROOF *) % 1.48/1.63 nodes searched: 10284 % 1.48/1.63 max branch formulas: 2377 % 1.48/1.63 proof nodes created: 595 % 1.48/1.63 formulas created: 49410 % 1.48/1.63 %------------------------------------------------------------------------------