%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS116+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n023.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 : Sun Jul 17 03:39:30 EDT 2022 % Result : Unsatisfiable 2.78s 2.99s % Output : Proof 2.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : KRS116+1 : TPTP v8.1.0. Released v3.1.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n023.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 Jun 7 18:01:38 EDT 2022 % 0.13/0.34 % CPUTime : % 2.78/2.99 (* PROOF-FOUND *) % 2.78/2.99 % SZS status Unsatisfiable % 2.78/2.99 (* BEGIN-PROOF *) % 2.78/2.99 % SZS output start Proof % 2.78/2.99 Theorem zenon_thm : False. % 2.78/2.99 Proof. % 2.78/2.99 assert (zenon_L1_ : forall (zenon_TY_w : zenon_U) (zenon_TY_x : zenon_U) (zenon_TY_y : zenon_U), (rp zenon_TY_y zenon_TY_x) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (~(rp zenon_TY_y zenon_TY_w)) -> (rp zenon_TY_x zenon_TY_w) -> False). % 2.78/2.99 do 3 intro. intros zenon_H12 zenon_H13 zenon_H14 zenon_H15. % 2.78/2.99 elim (classic ((~(zenon_TY_y = zenon_TY_x))/\(~(rp zenon_TY_y zenon_TY_x)))); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ]. % 2.78/2.99 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 2.78/2.99 exact (zenon_H1b zenon_H12). % 2.78/2.99 cut ((rp zenon_TY_x zenon_TY_w) = (rp zenon_TY_y zenon_TY_w)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H14. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H15. % 2.78/2.99 cut ((zenon_TY_w = zenon_TY_w)); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 2.78/2.99 cut ((zenon_TY_x = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 2.78/2.99 congruence. % 2.78/2.99 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 2.78/2.99 apply zenon_H20. zenon_intro zenon_H21. % 2.78/2.99 elim (classic (zenon_TY_y = zenon_TY_y)); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y) = (zenon_TY_x = zenon_TY_y)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H1e. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H22. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H23]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_x)); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 2.78/2.99 congruence. % 2.78/2.99 exact (zenon_H1c zenon_H21). % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H1f. zenon_intro zenon_H12. % 2.78/2.99 generalize (zenon_H13 zenon_TY_y). zenon_intro zenon_H24. % 2.78/2.99 generalize (zenon_H24 zenon_TY_x). zenon_intro zenon_H25. % 2.78/2.99 generalize (zenon_H25 zenon_TY_w). zenon_intro zenon_H26. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ]. % 2.78/2.99 exact (zenon_H1b zenon_H12). % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 2.78/2.99 exact (zenon_H29 zenon_H15). % 2.78/2.99 exact (zenon_H14 zenon_H28). % 2.78/2.99 apply zenon_H1d. apply refl_equal. % 2.78/2.99 (* end of lemma zenon_L1_ *) % 2.78/2.99 assert (zenon_L2_ : forall (zenon_TY_bs : zenon_U) (zenon_TY_w : zenon_U) (zenon_TY_x : zenon_U) (zenon_TY_y : zenon_U), (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_x zenon_TY_w) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (~(rp zenon_TY_y zenon_TY_bs)) -> (rp zenon_TY_w zenon_TY_bs) -> False). % 2.78/2.99 do 4 intro. intros zenon_H12 zenon_H15 zenon_H13 zenon_H2a zenon_H2b. % 2.78/2.99 elim (classic ((~(zenon_TY_y = zenon_TY_w))/\(~(rp zenon_TY_y zenon_TY_w)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 2.78/2.99 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H14. % 2.78/2.99 apply (zenon_L1_ zenon_TY_w zenon_TY_x zenon_TY_y); trivial. % 2.78/2.99 cut ((rp zenon_TY_w zenon_TY_bs) = (rp zenon_TY_y zenon_TY_bs)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H2a. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H2b. % 2.78/2.99 cut ((zenon_TY_bs = zenon_TY_bs)); [idtac | apply NNPP; zenon_intro zenon_H30]. % 2.78/2.99 cut ((zenon_TY_w = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H31]. % 2.78/2.99 congruence. % 2.78/2.99 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 2.78/2.99 apply zenon_H33. zenon_intro zenon_H34. % 2.78/2.99 elim (classic (zenon_TY_y = zenon_TY_y)); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y) = (zenon_TY_w = zenon_TY_y)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H31. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H22. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H23]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_w)); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 2.78/2.99 congruence. % 2.78/2.99 exact (zenon_H2f zenon_H34). % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H32. zenon_intro zenon_H28. % 2.78/2.99 generalize (zenon_H13 zenon_TY_y). zenon_intro zenon_H24. % 2.78/2.99 generalize (zenon_H24 zenon_TY_w). zenon_intro zenon_H35. % 2.78/2.99 generalize (zenon_H35 zenon_TY_bs). zenon_intro zenon_H36. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H14 | zenon_intro zenon_H37 ]. % 2.78/2.99 exact (zenon_H14 zenon_H28). % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 2.78/2.99 exact (zenon_H39 zenon_H2b). % 2.78/2.99 exact (zenon_H2a zenon_H38). % 2.78/2.99 apply zenon_H30. apply refl_equal. % 2.78/2.99 (* end of lemma zenon_L2_ *) % 2.78/2.99 assert (zenon_L3_ : forall (zenon_TY_ci : zenon_U) (zenon_TY_bs : zenon_U) (zenon_TY_y : zenon_U) (zenon_TY_w : zenon_U) (zenon_TY_x : zenon_U), (rp zenon_TY_x zenon_TY_w) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_w zenon_TY_bs) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (~(rp zenon_TY_y zenon_TY_ci)) -> (rp zenon_TY_bs zenon_TY_ci) -> False). % 2.78/2.99 do 5 intro. intros zenon_H15 zenon_H12 zenon_H2b zenon_H13 zenon_H3a zenon_H3b. % 2.78/2.99 elim (classic ((~(zenon_TY_y = zenon_TY_bs))/\(~(rp zenon_TY_y zenon_TY_bs)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 2.78/2.99 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H2a. % 2.78/2.99 apply (zenon_L2_ zenon_TY_bs zenon_TY_w zenon_TY_x zenon_TY_y); trivial. % 2.78/2.99 cut ((rp zenon_TY_bs zenon_TY_ci) = (rp zenon_TY_y zenon_TY_ci)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H3a. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H3b. % 2.78/2.99 cut ((zenon_TY_ci = zenon_TY_ci)); [idtac | apply NNPP; zenon_intro zenon_H40]. % 2.78/2.99 cut ((zenon_TY_bs = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 2.78/2.99 congruence. % 2.78/2.99 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 2.78/2.99 apply zenon_H43. zenon_intro zenon_H44. % 2.78/2.99 elim (classic (zenon_TY_y = zenon_TY_y)); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y) = (zenon_TY_bs = zenon_TY_y)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H41. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H22. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H23]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_bs)); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 2.78/2.99 congruence. % 2.78/2.99 exact (zenon_H3f zenon_H44). % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H42. zenon_intro zenon_H38. % 2.78/2.99 generalize (zenon_H13 zenon_TY_y). zenon_intro zenon_H24. % 2.78/2.99 generalize (zenon_H24 zenon_TY_bs). zenon_intro zenon_H45. % 2.78/2.99 generalize (zenon_H45 zenon_TY_ci). zenon_intro zenon_H46. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H2a | zenon_intro zenon_H47 ]. % 2.78/2.99 exact (zenon_H2a zenon_H38). % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 2.78/2.99 exact (zenon_H49 zenon_H3b). % 2.78/2.99 exact (zenon_H3a zenon_H48). % 2.78/2.99 apply zenon_H40. apply refl_equal. % 2.78/2.99 (* end of lemma zenon_L3_ *) % 2.78/2.99 assert (zenon_L4_ : forall (zenon_TY_cy : zenon_U) (zenon_TY_ci : zenon_U) (zenon_TY_x : zenon_U) (zenon_TY_y : zenon_U) (zenon_TY_bs : zenon_U) (zenon_TY_w : zenon_U), (rp zenon_TY_w zenon_TY_bs) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_x zenon_TY_w) -> (rp zenon_TY_bs zenon_TY_ci) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (~(rp zenon_TY_y zenon_TY_cy)) -> (rp zenon_TY_ci zenon_TY_cy) -> False). % 2.78/2.99 do 6 intro. intros zenon_H2b zenon_H12 zenon_H15 zenon_H3b zenon_H13 zenon_H4a zenon_H4b. % 2.78/2.99 elim (classic ((~(zenon_TY_y = zenon_TY_ci))/\(~(rp zenon_TY_y zenon_TY_ci)))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 2.78/2.99 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H4f. zenon_intro zenon_H3a. % 2.78/2.99 apply (zenon_L3_ zenon_TY_ci zenon_TY_bs zenon_TY_y zenon_TY_w zenon_TY_x); trivial. % 2.78/2.99 cut ((rp zenon_TY_ci zenon_TY_cy) = (rp zenon_TY_y zenon_TY_cy)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H4a. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H4b. % 2.78/2.99 cut ((zenon_TY_cy = zenon_TY_cy)); [idtac | apply NNPP; zenon_intro zenon_H50]. % 2.78/2.99 cut ((zenon_TY_ci = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H51]. % 2.78/2.99 congruence. % 2.78/2.99 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 2.78/2.99 apply zenon_H53. zenon_intro zenon_H54. % 2.78/2.99 elim (classic (zenon_TY_y = zenon_TY_y)); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y) = (zenon_TY_ci = zenon_TY_y)). % 2.78/2.99 intro zenon_D_pnotp. % 2.78/2.99 apply zenon_H51. % 2.78/2.99 rewrite <- zenon_D_pnotp. % 2.78/2.99 exact zenon_H22. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_y)); [idtac | apply NNPP; zenon_intro zenon_H23]. % 2.78/2.99 cut ((zenon_TY_y = zenon_TY_ci)); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 2.78/2.99 congruence. % 2.78/2.99 exact (zenon_H4f zenon_H54). % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H23. apply refl_equal. % 2.78/2.99 apply zenon_H52. zenon_intro zenon_H48. % 2.78/2.99 generalize (zenon_H13 zenon_TY_y). zenon_intro zenon_H24. % 2.78/2.99 generalize (zenon_H24 zenon_TY_ci). zenon_intro zenon_H55. % 2.78/2.99 generalize (zenon_H55 zenon_TY_cy). zenon_intro zenon_H56. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H3a | zenon_intro zenon_H57 ]. % 2.78/2.99 exact (zenon_H3a zenon_H48). % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 2.78/2.99 exact (zenon_H59 zenon_H4b). % 2.78/2.99 exact (zenon_H4a zenon_H58). % 2.78/2.99 apply zenon_H50. apply refl_equal. % 2.78/2.99 (* end of lemma zenon_L4_ *) % 2.78/2.99 assert (zenon_L5_ : (caxcomp (i2003_11_14_17_21_33997)) -> False). % 2.78/2.99 do 0 intro. intros zenon_H5a. % 2.78/2.99 generalize (axiom_5 (i2003_11_14_17_21_33997)). zenon_intro zenon_H5b. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H5e; zenon_intro zenon_H5d | zenon_intro zenon_H5a; zenon_intro zenon_H5c ]. % 2.78/2.99 exact (zenon_H5e zenon_H5a). % 2.78/2.99 generalize (axiom_2 (i2003_11_14_17_21_33997)). zenon_intro zenon_H5f. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 2.78/2.99 exact (zenon_H61 axiom_17). % 2.78/2.99 generalize (axiom_4 (i2003_11_14_17_21_33997)). zenon_intro zenon_H62. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H62); [ zenon_intro zenon_H64; zenon_intro zenon_H63 | zenon_intro zenon_H60; zenon_intro zenon_H5d ]. % 2.78/2.99 exact (zenon_H64 zenon_H60). % 2.78/2.99 exact (zenon_H5d zenon_H5c). % 2.78/2.99 (* end of lemma zenon_L5_ *) % 2.78/2.99 assert (zenon_L6_ : forall (zenon_TY_y : zenon_U), (ca_Vx6 zenon_TY_y) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> False). % 2.78/2.99 do 1 intro. intros zenon_H65 zenon_H66. % 2.78/2.99 generalize (axiom_11 zenon_TY_y). zenon_intro zenon_H67. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H6a; zenon_intro zenon_H69 | zenon_intro zenon_H65; zenon_intro zenon_H68 ]. % 2.78/2.99 exact (zenon_H6a zenon_H65). % 2.78/2.99 generalize (zenon_H68 (i2003_11_14_17_21_33997)). zenon_intro zenon_H6b. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6c | zenon_intro zenon_H5a ]. % 2.78/2.99 generalize (axiom_15 zenon_TY_y). zenon_intro zenon_H6d. % 2.78/2.99 generalize (zenon_H6d (i2003_11_14_17_21_33997)). zenon_intro zenon_H6e. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H6e); [ zenon_intro zenon_H6c; zenon_intro zenon_H70 | zenon_intro zenon_H6f; zenon_intro zenon_H66 ]. % 2.78/2.99 exact (zenon_H70 zenon_H66). % 2.78/2.99 exact (zenon_H6c zenon_H6f). % 2.78/2.99 apply (zenon_L5_); trivial. % 2.78/2.99 (* end of lemma zenon_L6_ *) % 2.78/2.99 assert (zenon_L7_ : forall (zenon_TY_y : zenon_U) (zenon_TY_w : zenon_U) (zenon_TY_x : zenon_U) (zenon_TY_ci : zenon_U) (zenon_TY_bs : zenon_U) (zenon_TY_cy : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (ca_Vx7 zenon_TY_cy) -> (rp zenon_TY_bs zenon_TY_ci) -> (rp zenon_TY_x zenon_TY_w) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_w zenon_TY_bs) -> (rp zenon_TY_ci zenon_TY_cy) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> False). % 2.78/2.99 do 6 intro. intros zenon_H13 zenon_H71 zenon_H3b zenon_H15 zenon_H12 zenon_H2b zenon_H4b zenon_H66. % 2.78/2.99 generalize (axiom_12 zenon_TY_cy). zenon_intro zenon_H72. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H75; zenon_intro zenon_H74 | zenon_intro zenon_H71; zenon_intro zenon_H73 ]. % 2.78/2.99 exact (zenon_H75 zenon_H71). % 2.78/2.99 generalize (zenon_H73 zenon_TY_y). zenon_intro zenon_H76. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H76); [ zenon_intro zenon_H77 | zenon_intro zenon_H65 ]. % 2.78/2.99 generalize (axiom_13 zenon_TY_cy). zenon_intro zenon_H78. % 2.78/2.99 generalize (zenon_H78 zenon_TY_y). zenon_intro zenon_H79. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H79); [ zenon_intro zenon_H77; zenon_intro zenon_H4a | zenon_intro zenon_H7a; zenon_intro zenon_H58 ]. % 2.78/2.99 apply (zenon_L4_ zenon_TY_cy zenon_TY_ci zenon_TY_x zenon_TY_y zenon_TY_bs zenon_TY_w); trivial. % 2.78/2.99 exact (zenon_H77 zenon_H7a). % 2.78/2.99 apply (zenon_L6_ zenon_TY_y); trivial. % 2.78/2.99 (* end of lemma zenon_L7_ *) % 2.78/2.99 assert (zenon_L8_ : forall (zenon_TY_x : zenon_U) (zenon_TY_bs : zenon_U) (zenon_TY_w : zenon_U) (zenon_TY_ci : zenon_U) (zenon_TY_y : zenon_U) (zenon_TY_cy : zenon_U) (zenon_TY_ev : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (cc zenon_TY_ev) -> (rr zenon_TY_cy zenon_TY_ev) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> (rp zenon_TY_ci zenon_TY_cy) -> (rp zenon_TY_w zenon_TY_bs) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_x zenon_TY_w) -> (rp zenon_TY_bs zenon_TY_ci) -> False). % 2.78/2.99 do 7 intro. intros zenon_H13 zenon_H7b zenon_H7c zenon_H66 zenon_H4b zenon_H2b zenon_H12 zenon_H15 zenon_H3b. % 2.78/2.99 generalize (axiom_6 zenon_TY_ev). zenon_intro zenon_H7e. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H7e); [ zenon_intro zenon_H81; zenon_intro zenon_H80 | zenon_intro zenon_H7b; zenon_intro zenon_H7f ]. % 2.78/2.99 exact (zenon_H81 zenon_H7b). % 2.78/2.99 generalize (zenon_H7f zenon_TY_cy). zenon_intro zenon_H82. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H83 | zenon_intro zenon_H71 ]. % 2.78/2.99 generalize (axiom_14 zenon_TY_ev). zenon_intro zenon_H84. % 2.78/2.99 generalize (zenon_H84 zenon_TY_cy). zenon_intro zenon_H85. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H85); [ zenon_intro zenon_H83; zenon_intro zenon_H87 | zenon_intro zenon_H86; zenon_intro zenon_H7c ]. % 2.78/2.99 exact (zenon_H87 zenon_H7c). % 2.78/2.99 exact (zenon_H83 zenon_H86). % 2.78/2.99 apply (zenon_L7_ zenon_TY_y zenon_TY_w zenon_TY_x zenon_TY_ci zenon_TY_bs zenon_TY_cy); trivial. % 2.78/2.99 (* end of lemma zenon_L8_ *) % 2.78/2.99 assert (zenon_L9_ : forall (zenon_TY_x : zenon_U) (zenon_TY_bs : zenon_U) (zenon_TY_w : zenon_U) (zenon_TY_y : zenon_U) (zenon_TY_ci : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (ca_Vx4 zenon_TY_ci) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx3 Y))) -> (rp zenon_TY_w zenon_TY_bs) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_x zenon_TY_w) -> (rp zenon_TY_bs zenon_TY_ci) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx5 Y))) -> False). % 2.78/2.99 do 5 intro. intros zenon_H13 zenon_H88 zenon_H89 zenon_H2b zenon_H12 zenon_H15 zenon_H3b zenon_H66 zenon_H8a. % 2.78/2.99 generalize (axiom_9 zenon_TY_ci). zenon_intro zenon_H8b. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H8b); [ zenon_intro zenon_H8e; zenon_intro zenon_H8d | zenon_intro zenon_H88; zenon_intro zenon_H8c ]. % 2.78/2.99 exact (zenon_H8e zenon_H88). % 2.78/2.99 elim zenon_H8c. zenon_intro zenon_TY_cy. zenon_intro zenon_H8f. % 2.78/2.99 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H4b. zenon_intro zenon_H90. % 2.78/2.99 generalize (zenon_H89 zenon_TY_cy). zenon_intro zenon_H91. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H4a | zenon_intro zenon_H92 ]. % 2.78/2.99 apply (zenon_L4_ zenon_TY_cy zenon_TY_ci zenon_TY_x zenon_TY_y zenon_TY_bs zenon_TY_w); trivial. % 2.78/2.99 generalize (axiom_8 zenon_TY_cy). zenon_intro zenon_H93. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H96; zenon_intro zenon_H95 | zenon_intro zenon_H92; zenon_intro zenon_H94 ]. % 2.78/2.99 exact (zenon_H96 zenon_H92). % 2.78/2.99 elim zenon_H94. zenon_intro zenon_TY_ev. zenon_intro zenon_H97. % 2.78/2.99 apply (zenon_and_s _ _ zenon_H97). zenon_intro zenon_H7c. zenon_intro zenon_H98. % 2.78/2.99 generalize (zenon_H8a zenon_TY_cy). zenon_intro zenon_H99. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H4a | zenon_intro zenon_H9a ]. % 2.78/2.99 apply (zenon_L4_ zenon_TY_cy zenon_TY_ci zenon_TY_x zenon_TY_y zenon_TY_bs zenon_TY_w); trivial. % 2.78/2.99 generalize (axiom_10 zenon_TY_cy). zenon_intro zenon_H9b. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_H9b); [ zenon_intro zenon_H9e; zenon_intro zenon_H9d | zenon_intro zenon_H9a; zenon_intro zenon_H9c ]. % 2.78/2.99 exact (zenon_H9e zenon_H9a). % 2.78/2.99 generalize (zenon_H9c zenon_TY_ev). zenon_intro zenon_H9f. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_H9f); [ zenon_intro zenon_H87 | zenon_intro zenon_H7b ]. % 2.78/2.99 exact (zenon_H87 zenon_H7c). % 2.78/2.99 apply (zenon_L8_ zenon_TY_x zenon_TY_bs zenon_TY_w zenon_TY_ci zenon_TY_y zenon_TY_cy zenon_TY_ev); trivial. % 2.78/2.99 (* end of lemma zenon_L9_ *) % 2.78/2.99 assert (zenon_L10_ : forall (zenon_TY_w : zenon_U) (zenon_TY_x : zenon_U) (zenon_TY_y : zenon_U) (zenon_TY_bs : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (ca_Vx4 zenon_TY_bs) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx4 Y))) -> (rp zenon_TY_x zenon_TY_w) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_w zenon_TY_bs) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx5 Y))) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx3 Y))) -> False). % 2.78/2.99 do 4 intro. intros zenon_H13 zenon_Ha0 zenon_Ha1 zenon_H15 zenon_H12 zenon_H2b zenon_H8a zenon_H66 zenon_H89. % 2.78/2.99 generalize (axiom_9 zenon_TY_bs). zenon_intro zenon_Ha2. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha5; zenon_intro zenon_Ha4 | zenon_intro zenon_Ha0; zenon_intro zenon_Ha3 ]. % 2.78/2.99 exact (zenon_Ha5 zenon_Ha0). % 2.78/2.99 elim zenon_Ha3. zenon_intro zenon_TY_ci. zenon_intro zenon_Ha6. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_H3b. zenon_intro zenon_Ha7. % 2.78/2.99 generalize (zenon_Ha1 zenon_TY_ci). zenon_intro zenon_Ha8. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_H3a | zenon_intro zenon_H88 ]. % 2.78/2.99 apply (zenon_L3_ zenon_TY_ci zenon_TY_bs zenon_TY_y zenon_TY_w zenon_TY_x); trivial. % 2.78/2.99 apply (zenon_L9_ zenon_TY_x zenon_TY_bs zenon_TY_w zenon_TY_y zenon_TY_ci); trivial. % 2.78/2.99 (* end of lemma zenon_L10_ *) % 2.78/2.99 assert (zenon_L11_ : forall (zenon_TY_x : zenon_U) (zenon_TY_y : zenon_U) (zenon_TY_w : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (ca_Vx4 zenon_TY_w) -> (rp zenon_TY_y zenon_TY_x) -> (rp zenon_TY_x zenon_TY_w) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx3 Y))) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx5 Y))) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx4 Y))) -> False). % 2.78/2.99 do 3 intro. intros zenon_H13 zenon_Ha9 zenon_H12 zenon_H15 zenon_H89 zenon_H66 zenon_H8a zenon_Ha1. % 2.78/2.99 generalize (axiom_9 zenon_TY_w). zenon_intro zenon_Haa. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_Haa); [ zenon_intro zenon_Had; zenon_intro zenon_Hac | zenon_intro zenon_Ha9; zenon_intro zenon_Hab ]. % 2.78/2.99 exact (zenon_Had zenon_Ha9). % 2.78/2.99 elim zenon_Hab. zenon_intro zenon_TY_bs. zenon_intro zenon_Hae. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H2b. zenon_intro zenon_Haf. % 2.78/2.99 generalize (zenon_Ha1 zenon_TY_bs). zenon_intro zenon_Hb0. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_Hb0); [ zenon_intro zenon_H2a | zenon_intro zenon_Ha0 ]. % 2.78/2.99 apply (zenon_L2_ zenon_TY_bs zenon_TY_w zenon_TY_x zenon_TY_y); trivial. % 2.78/2.99 apply (zenon_L10_ zenon_TY_w zenon_TY_x zenon_TY_y zenon_TY_bs); trivial. % 2.78/2.99 (* end of lemma zenon_L11_ *) % 2.78/2.99 assert (zenon_L12_ : forall (zenon_TY_y : zenon_U) (zenon_TY_x : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (ca_Vx4 zenon_TY_x) -> (rp zenon_TY_y zenon_TY_x) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx4 Y))) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx5 Y))) -> (rs (i2003_11_14_17_21_33997) zenon_TY_y) -> (forall Y : zenon_U, ((rp zenon_TY_y Y)->(ca_Vx3 Y))) -> False). % 2.78/2.99 do 2 intro. intros zenon_H13 zenon_Hb1 zenon_H12 zenon_Ha1 zenon_H8a zenon_H66 zenon_H89. % 2.78/2.99 generalize (axiom_9 zenon_TY_x). zenon_intro zenon_Hb2. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb5; zenon_intro zenon_Hb4 | zenon_intro zenon_Hb1; zenon_intro zenon_Hb3 ]. % 2.78/2.99 exact (zenon_Hb5 zenon_Hb1). % 2.78/2.99 elim zenon_Hb3. zenon_intro zenon_TY_w. zenon_intro zenon_Hb6. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hb6). zenon_intro zenon_H15. zenon_intro zenon_Hb7. % 2.78/2.99 generalize (zenon_Ha1 zenon_TY_w). zenon_intro zenon_Hb8. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_H14 | zenon_intro zenon_Ha9 ]. % 2.78/2.99 apply (zenon_L1_ zenon_TY_w zenon_TY_x zenon_TY_y); trivial. % 2.78/2.99 apply (zenon_L11_ zenon_TY_x zenon_TY_y zenon_TY_w); trivial. % 2.78/2.99 (* end of lemma zenon_L12_ *) % 2.78/2.99 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z))))))); [ zenon_intro zenon_H13 | zenon_intro zenon_Hb9 ]. % 2.78/2.99 generalize (axiom_3 (i2003_11_14_17_21_33997)). zenon_intro zenon_Hba. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_Hba); [ zenon_intro zenon_H61 | zenon_intro zenon_Hbb ]. % 2.78/2.99 exact (zenon_H61 axiom_17). % 2.78/2.99 elim zenon_Hbb. zenon_intro zenon_TY_y. zenon_intro zenon_Hbc. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_H66. zenon_intro zenon_Hbd. % 2.78/2.99 generalize (axiom_7 zenon_TY_y). zenon_intro zenon_Hbe. % 2.78/2.99 apply (zenon_equiv_s _ _ zenon_Hbe); [ zenon_intro zenon_Hc1; zenon_intro zenon_Hc0 | zenon_intro zenon_Hbd; zenon_intro zenon_Hbf ]. % 2.78/2.99 exact (zenon_Hc1 zenon_Hbd). % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hbf). zenon_intro zenon_H89. zenon_intro zenon_Hc2. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H8a. zenon_intro zenon_Hc3. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hc7. zenon_intro zenon_Hc6. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc8. zenon_intro zenon_Ha1. % 2.78/2.99 elim zenon_Hc8. zenon_intro zenon_TY_x. zenon_intro zenon_Hc9. % 2.78/2.99 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H12. zenon_intro zenon_Hca. % 2.78/2.99 generalize (zenon_Ha1 zenon_TY_x). zenon_intro zenon_Hcb. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_Hcb); [ zenon_intro zenon_H1b | zenon_intro zenon_Hb1 ]. % 2.78/2.99 exact (zenon_H1b zenon_H12). % 2.78/2.99 apply (zenon_L12_ zenon_TY_y zenon_TY_x); trivial. % 2.78/2.99 apply zenon_Hb9. zenon_intro zenon_Tx_hw. apply NNPP. zenon_intro zenon_Hcd. % 2.78/2.99 apply zenon_Hcd. zenon_intro zenon_Ty_hy. apply NNPP. zenon_intro zenon_Hcf. % 2.78/2.99 apply zenon_Hcf. zenon_intro zenon_Tz_ia. apply NNPP. zenon_intro zenon_Hd1. % 2.78/2.99 apply (zenon_notimply_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 2.78/2.99 apply (zenon_notimply_s _ _ zenon_Hd2). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4. % 2.78/2.99 generalize (axiom_16 zenon_Tx_hw). zenon_intro zenon_Hd6. % 2.78/2.99 generalize (zenon_Hd6 zenon_Ty_hy). zenon_intro zenon_Hd7. % 2.78/2.99 generalize (zenon_Hd7 zenon_Tz_ia). zenon_intro zenon_Hd8. % 2.78/2.99 apply (zenon_imply_s _ _ zenon_Hd8); [ zenon_intro zenon_Hda | zenon_intro zenon_Hd9 ]. % 2.78/2.99 apply (zenon_notand_s _ _ zenon_Hda); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdb ]. % 2.78/2.99 exact (zenon_Hdc zenon_Hd3). % 2.78/2.99 exact (zenon_Hdb zenon_Hd5). % 2.78/2.99 exact (zenon_Hd4 zenon_Hd9). % 2.78/2.99 Qed. % 2.78/2.99 % SZS output end Proof % 2.78/2.99 (* END-PROOF *) % 2.78/2.99 nodes searched: 119904 % 2.78/2.99 max branch formulas: 4035 % 2.78/2.99 proof nodes created: 2120 % 2.78/2.99 formulas created: 259893 % 2.78/2.99 %------------------------------------------------------------------------------