%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG162+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 14 18:30:49 EDT 2022 % Result : Unsatisfiable 7.87s 8.04s % Output : Proof 8.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG162+1 : TPTP v8.1.0. Released v2.7.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.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 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 8 14:01:37 EDT 2022 % 0.12/0.33 % CPUTime : % 7.87/8.04 (* PROOF-FOUND *) % 7.87/8.04 % SZS status Unsatisfiable % 7.87/8.04 (* BEGIN-PROOF *) % 7.87/8.04 % SZS output start Proof % 7.87/8.04 Theorem zenon_thm : False. % 7.87/8.04 Proof. % 7.87/8.04 assert (zenon_L1_ : (~((e0) = (e0))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H1d. % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L1_ *) % 7.87/8.04 assert (zenon_L2_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H1e zenon_H1f zenon_H20. % 7.87/8.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.04 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H20. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H21. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e0) (e0)) = (e0)) = ((e2) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H23. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H1e. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H24 zenon_H1f). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L2_ *) % 7.87/8.04 assert (zenon_L3_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H25 zenon_H26 zenon_H20. % 7.87/8.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.04 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H20. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H21. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H23. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H25. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H27 zenon_H26). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L3_ *) % 7.87/8.04 assert (zenon_L4_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H28 zenon_H1e zenon_H29. % 7.87/8.04 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H28. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H1e. % 7.87/8.04 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 7.87/8.04 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2b. apply refl_equal. % 7.87/8.04 apply zenon_H2a. apply sym_equal. exact zenon_H29. % 7.87/8.04 (* end of lemma zenon_L4_ *) % 7.87/8.04 assert (zenon_L5_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H2c zenon_H25 zenon_H2d. % 7.87/8.04 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H2c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H25. % 7.87/8.04 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 7.87/8.04 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2f. apply refl_equal. % 7.87/8.04 apply zenon_H2e. apply sym_equal. exact zenon_H2d. % 7.87/8.04 (* end of lemma zenon_L5_ *) % 7.87/8.04 assert (zenon_L6_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H30 zenon_H1e zenon_H31. % 7.87/8.04 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H30. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H1e. % 7.87/8.04 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 7.87/8.04 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2b. apply refl_equal. % 7.87/8.04 apply zenon_H32. apply sym_equal. exact zenon_H31. % 7.87/8.04 (* end of lemma zenon_L6_ *) % 7.87/8.04 assert (zenon_L7_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H33 zenon_H25 zenon_H34. % 7.87/8.04 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H33. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H25. % 7.87/8.04 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 7.87/8.04 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2f. apply refl_equal. % 7.87/8.04 apply zenon_H35. apply sym_equal. exact zenon_H34. % 7.87/8.04 (* end of lemma zenon_L7_ *) % 7.87/8.04 assert (zenon_L8_ : ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H36 zenon_H37 zenon_H38. % 7.87/8.04 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.04 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H38. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H39. % 7.87/8.04 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.04 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H3b. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H36. % 7.87/8.04 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 7.87/8.04 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H3a. apply refl_equal. % 7.87/8.04 apply zenon_H3c. apply sym_equal. exact zenon_H37. % 7.87/8.04 apply zenon_H3a. apply refl_equal. % 7.87/8.04 apply zenon_H3a. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L8_ *) % 7.87/8.04 assert (zenon_L9_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H3d zenon_H1e zenon_H3e. % 7.87/8.04 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H3d. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H1e. % 7.87/8.04 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 7.87/8.04 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2b. apply refl_equal. % 7.87/8.04 apply zenon_H3f. apply sym_equal. exact zenon_H3e. % 7.87/8.04 (* end of lemma zenon_L9_ *) % 7.87/8.04 assert (zenon_L10_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H40 zenon_H25 zenon_H41. % 7.87/8.04 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H40. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H25. % 7.87/8.04 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 7.87/8.04 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2f. apply refl_equal. % 7.87/8.04 apply zenon_H42. apply sym_equal. exact zenon_H41. % 7.87/8.04 (* end of lemma zenon_L10_ *) % 7.87/8.04 assert (zenon_L11_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H43 zenon_H37 zenon_H44. % 7.87/8.04 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H43. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H37. % 7.87/8.04 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 7.87/8.04 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H46. apply refl_equal. % 7.87/8.04 apply zenon_H45. apply sym_equal. exact zenon_H44. % 7.87/8.04 (* end of lemma zenon_L11_ *) % 7.87/8.04 assert (zenon_L12_ : ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H47 zenon_H48 zenon_H49. % 7.87/8.04 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H49. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H4a. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H4c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H47. % 7.87/8.04 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H4b. apply refl_equal. % 7.87/8.04 apply zenon_H4d. apply sym_equal. exact zenon_H48. % 7.87/8.04 apply zenon_H4b. apply refl_equal. % 7.87/8.04 apply zenon_H4b. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L12_ *) % 7.87/8.04 assert (zenon_L13_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H37 zenon_H43 zenon_H48 zenon_H49. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.04 apply (zenon_L9_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.04 apply (zenon_L10_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.04 apply (zenon_L11_); trivial. % 7.87/8.04 apply (zenon_L12_); trivial. % 7.87/8.04 (* end of lemma zenon_L13_ *) % 7.87/8.04 assert (zenon_L14_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H51 zenon_H30 zenon_H33 zenon_H38 zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H37 zenon_H43 zenon_H49. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L6_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L8_); trivial. % 7.87/8.04 apply (zenon_L13_); trivial. % 7.87/8.04 (* end of lemma zenon_L14_ *) % 7.87/8.04 assert (zenon_L15_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H31 zenon_H54 zenon_H55. % 7.87/8.04 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.87/8.04 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H55. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H56. % 7.87/8.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.04 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H58. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H31. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H59 zenon_H54). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L15_ *) % 7.87/8.04 assert (zenon_L16_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H5a zenon_H36 zenon_H44. % 7.87/8.04 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H5a. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H36. % 7.87/8.04 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 7.87/8.04 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H3a. apply refl_equal. % 7.87/8.04 apply zenon_H45. apply sym_equal. exact zenon_H44. % 7.87/8.04 (* end of lemma zenon_L16_ *) % 7.87/8.04 assert (zenon_L17_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H29 zenon_H5b zenon_H20. % 7.87/8.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.04 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H20. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H21. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H23. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H29. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H5c zenon_H5b). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L17_ *) % 7.87/8.04 assert (zenon_L18_ : ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H47 zenon_H5d zenon_H5e. % 7.87/8.04 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H5e. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H4a. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H5f. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H47. % 7.87/8.04 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 7.87/8.04 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H4b. apply refl_equal. % 7.87/8.04 apply zenon_H60. apply sym_equal. exact zenon_H5d. % 7.87/8.04 apply zenon_H4b. apply refl_equal. % 7.87/8.04 apply zenon_H4b. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L18_ *) % 7.87/8.04 assert (zenon_L19_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H61 zenon_H20 zenon_H5b zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H47 zenon_H5e. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.04 apply (zenon_L17_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.04 apply (zenon_L8_); trivial. % 7.87/8.04 apply (zenon_L18_); trivial. % 7.87/8.04 (* end of lemma zenon_L19_ *) % 7.87/8.04 assert (zenon_L20_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H40 zenon_H5a zenon_H61 zenon_H20 zenon_H5b zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.04 apply (zenon_L9_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.04 apply (zenon_L10_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.04 apply (zenon_L16_); trivial. % 7.87/8.04 apply (zenon_L19_); trivial. % 7.87/8.04 (* end of lemma zenon_L20_ *) % 7.87/8.04 assert (zenon_L21_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H64 zenon_H5d zenon_H48. % 7.87/8.04 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H64. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H5d. % 7.87/8.04 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 7.87/8.04 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H65. apply refl_equal. % 7.87/8.04 apply zenon_H4d. apply sym_equal. exact zenon_H48. % 7.87/8.04 (* end of lemma zenon_L21_ *) % 7.87/8.04 assert (zenon_L22_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H51 zenon_H55 zenon_H54 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H5b zenon_H20 zenon_H61 zenon_H5a zenon_H40 zenon_H3d zenon_H1e zenon_H4e zenon_H64 zenon_H5d. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L15_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L20_); trivial. % 7.87/8.04 apply (zenon_L21_); trivial. % 7.87/8.04 (* end of lemma zenon_L22_ *) % 7.87/8.04 assert (zenon_L23_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H28 zenon_H49 zenon_H43 zenon_H30 zenon_H51 zenon_H55 zenon_H54 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H5b zenon_H20 zenon_H61 zenon_H5a zenon_H40 zenon_H3d zenon_H1e zenon_H4e zenon_H64. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.04 apply (zenon_L4_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.04 apply (zenon_L14_); trivial. % 7.87/8.04 apply (zenon_L22_); trivial. % 7.87/8.04 (* end of lemma zenon_L23_ *) % 7.87/8.04 assert (zenon_L24_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H25 zenon_H66 zenon_H67. % 7.87/8.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.04 cut (((e3) = (e3)) = ((e0) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H67. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H68. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H6a. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H25. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H6b zenon_H66). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L24_ *) % 7.87/8.04 assert (zenon_L25_ : (~((e3) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H69. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L25_ *) % 7.87/8.04 assert (zenon_L26_ : (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H6c zenon_H6d zenon_H6e. % 7.87/8.04 cut (((op (e1) (e1)) = (e3)) = ((e2) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H6c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H6d. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H6f zenon_H6e). % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L26_ *) % 7.87/8.04 assert (zenon_L27_ : (~((e1) = (e1))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H57. % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L27_ *) % 7.87/8.04 assert (zenon_L28_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H70 zenon_H6e zenon_H71. % 7.87/8.04 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 7.87/8.04 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H71. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H72. % 7.87/8.04 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 7.87/8.04 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H74. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H70. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 7.87/8.04 congruence. % 7.87/8.04 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 7.87/8.04 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H75. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H72. % 7.87/8.04 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 7.87/8.04 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H6f zenon_H6e). % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 apply zenon_H73. apply refl_equal. % 7.87/8.04 apply zenon_H73. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 apply zenon_H73. apply refl_equal. % 7.87/8.04 apply zenon_H73. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L28_ *) % 7.87/8.04 assert (zenon_L29_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H36 zenon_H70 zenon_H6e. % 7.87/8.04 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 7.87/8.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 7.87/8.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H78. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H79. % 7.87/8.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 7.87/8.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e2)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H7b. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H36. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 7.87/8.04 congruence. % 7.87/8.04 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 7.87/8.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H7c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H79. % 7.87/8.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 7.87/8.04 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 7.87/8.04 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H6f zenon_H6e). % 7.87/8.04 exact (zenon_H6f zenon_H6e). % 7.87/8.04 apply zenon_H7a. apply refl_equal. % 7.87/8.04 apply zenon_H7a. apply refl_equal. % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H7a. apply refl_equal. % 7.87/8.04 apply zenon_H7a. apply refl_equal. % 7.87/8.04 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H7e | zenon_intro zenon_H71 ]. % 7.87/8.04 apply zenon_H7e. apply sym_equal. exact zenon_H6e. % 7.87/8.04 apply (zenon_L28_); trivial. % 7.87/8.04 (* end of lemma zenon_L29_ *) % 7.87/8.04 assert (zenon_L30_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H51 zenon_H55 zenon_H54 zenon_H25 zenon_H33 zenon_H6e zenon_H70 zenon_H64 zenon_H5d. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L15_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L29_); trivial. % 7.87/8.04 apply (zenon_L21_); trivial. % 7.87/8.04 (* end of lemma zenon_L30_ *) % 7.87/8.04 assert (zenon_L31_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H67 zenon_H7f zenon_H41. % 7.87/8.04 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H67. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H7f. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H80 zenon_H41). % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L31_ *) % 7.87/8.04 assert (zenon_L32_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H47 zenon_H5e. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.04 apply (zenon_L4_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.04 apply (zenon_L8_); trivial. % 7.87/8.04 apply (zenon_L18_); trivial. % 7.87/8.04 (* end of lemma zenon_L32_ *) % 7.87/8.04 assert (zenon_L33_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H4e zenon_H3d zenon_H7f zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.04 apply (zenon_L9_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.04 apply (zenon_L31_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.04 apply (zenon_L16_); trivial. % 7.87/8.04 apply (zenon_L32_); trivial. % 7.87/8.04 (* end of lemma zenon_L33_ *) % 7.87/8.04 assert (zenon_L34_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H7f zenon_H3d zenon_H4e zenon_H64 zenon_H5d. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L6_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L33_); trivial. % 7.87/8.04 apply (zenon_L21_); trivial. % 7.87/8.04 (* end of lemma zenon_L34_ *) % 7.87/8.04 assert (zenon_L35_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H81 zenon_H82 zenon_H83. % 7.87/8.04 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H81. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H82. % 7.87/8.04 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 7.87/8.04 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H85. apply refl_equal. % 7.87/8.04 apply zenon_H84. apply sym_equal. exact zenon_H83. % 7.87/8.04 (* end of lemma zenon_L35_ *) % 7.87/8.04 assert (zenon_L36_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H1e zenon_H86 zenon_H67. % 7.87/8.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.04 cut (((e3) = (e3)) = ((e0) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H67. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H68. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e0) (e0)) = (e0)) = ((e3) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H6a. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H1e. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H87 zenon_H86). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L36_ *) % 7.87/8.04 assert (zenon_L37_ : ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H6d zenon_H88 zenon_H89. % 7.87/8.04 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H89. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H8a. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H8c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H6d. % 7.87/8.04 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 apply zenon_H8d. apply sym_equal. exact zenon_H88. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L37_ *) % 7.87/8.04 assert (zenon_L38_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H54 zenon_H8e zenon_H8f. % 7.87/8.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.04 cut (((e3) = (e3)) = ((e1) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H8f. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H68. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H90. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H54. % 7.87/8.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.04 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H91 zenon_H8e). % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L38_ *) % 7.87/8.04 assert (zenon_L39_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H6c zenon_H92 zenon_H93. % 7.87/8.04 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H6c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H92. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H94 zenon_H93). % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L39_ *) % 7.87/8.04 assert (zenon_L40_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H95 zenon_H67 zenon_H1e zenon_H89 zenon_H6d zenon_H8f zenon_H54 zenon_H6c zenon_H93. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.04 apply (zenon_L36_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.04 apply (zenon_L37_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.04 apply (zenon_L38_); trivial. % 7.87/8.04 apply (zenon_L39_); trivial. % 7.87/8.04 (* end of lemma zenon_L40_ *) % 7.87/8.04 assert (zenon_L41_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H54 zenon_H98 zenon_H99. % 7.87/8.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.04 cut (((e2) = (e2)) = ((e1) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H99. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H21. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e0)) = (e1)) = ((e2) = (e1))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H9a. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H54. % 7.87/8.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.04 cut (((op (e2) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H9b zenon_H98). % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L41_ *) % 7.87/8.04 assert (zenon_L42_ : (~((e2) = (e2))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H22. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L42_ *) % 7.87/8.04 assert (zenon_L43_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H9c zenon_H70 zenon_H6c. % 7.87/8.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.04 cut (((e3) = (e3)) = ((e2) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H6c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H68. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H9d. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H9c. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_H9e zenon_H70). % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L43_ *) % 7.87/8.04 assert (zenon_L44_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H36 zenon_H9f zenon_H20. % 7.87/8.04 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.04 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H20. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H21. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e2)) = (e0)) = ((e2) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H23. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H36. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_Ha0 zenon_H9f). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L44_ *) % 7.87/8.04 assert (zenon_L45_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Ha1 zenon_Ha2 zenon_H64. % 7.87/8.04 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha4 ]. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H64. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_Ha3. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_Ha5. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_Ha1. % 7.87/8.04 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_Ha4. apply refl_equal. % 7.87/8.04 apply zenon_Ha6. apply sym_equal. exact zenon_Ha2. % 7.87/8.04 apply zenon_Ha4. apply refl_equal. % 7.87/8.04 apply zenon_Ha4. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L45_ *) % 7.87/8.04 assert (zenon_L46_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Ha7 zenon_H99 zenon_H54 zenon_H6c zenon_H70 zenon_H20 zenon_H36 zenon_Ha2 zenon_H64. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.04 apply (zenon_L41_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.04 apply (zenon_L43_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.04 apply (zenon_L44_); trivial. % 7.87/8.04 apply (zenon_L45_); trivial. % 7.87/8.04 (* end of lemma zenon_L46_ *) % 7.87/8.04 assert (zenon_L47_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_Haa zenon_H93 zenon_H8f zenon_H89 zenon_H95 zenon_Ha7 zenon_H99 zenon_H54 zenon_H6c zenon_H20 zenon_Ha2 zenon_H55 zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H3d zenon_H4e zenon_H64 zenon_H5d. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.04 apply (zenon_L24_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.04 apply (zenon_L40_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L15_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L46_); trivial. % 7.87/8.04 apply (zenon_L21_); trivial. % 7.87/8.04 apply (zenon_L34_); trivial. % 7.87/8.04 (* end of lemma zenon_L47_ *) % 7.87/8.04 assert (zenon_L48_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Had zenon_H86 zenon_H67. % 7.87/8.04 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.87/8.04 apply (zenon_L36_); trivial. % 7.87/8.04 (* end of lemma zenon_L48_ *) % 7.87/8.04 assert (zenon_L49_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> False). % 7.87/8.04 do 0 intro. intros zenon_Haf zenon_H86 zenon_Hb0. % 7.87/8.04 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_Haf. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H86. % 7.87/8.04 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 7.87/8.04 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H2b. apply refl_equal. % 7.87/8.04 apply zenon_Hb1. apply sym_equal. exact zenon_Hb0. % 7.87/8.04 (* end of lemma zenon_L49_ *) % 7.87/8.04 assert (zenon_L50_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H3e zenon_Hb2 zenon_H55. % 7.87/8.04 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.87/8.04 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H55. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H56. % 7.87/8.04 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.04 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H58. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H3e. % 7.87/8.04 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.04 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_Hb3 zenon_Hb2). % 7.87/8.04 apply zenon_H1d. apply refl_equal. % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 apply zenon_H57. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L50_ *) % 7.87/8.04 assert (zenon_L51_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H61 zenon_H1e zenon_H28 zenon_H2c zenon_H38 zenon_H4e zenon_H55 zenon_Hb2 zenon_H25 zenon_H40 zenon_H36 zenon_H5a zenon_H5e. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.04 apply (zenon_L4_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.04 apply (zenon_L8_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.04 apply (zenon_L50_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.04 apply (zenon_L10_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.04 apply (zenon_L16_); trivial. % 7.87/8.04 apply (zenon_L18_); trivial. % 7.87/8.04 (* end of lemma zenon_L51_ *) % 7.87/8.04 assert (zenon_L52_ : ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Hb4 zenon_Hb5 zenon_H99 zenon_H98 zenon_H61 zenon_H55 zenon_H40 zenon_H5a zenon_H5e zenon_H4e zenon_H36 zenon_H38 zenon_H25 zenon_H2c zenon_H1e zenon_H28 zenon_Hb6. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.04 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.04 exact (zenon_Hb7 zenon_Hbb). % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.04 apply (zenon_L41_); trivial. % 7.87/8.04 apply (zenon_L51_); trivial. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 (* end of lemma zenon_L52_ *) % 7.87/8.04 assert (zenon_L53_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Ha1 zenon_Hbc zenon_Hbd. % 7.87/8.04 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha4 ]. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_Hbd. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_Ha3. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_Hbe. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_Ha1. % 7.87/8.04 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 7.87/8.04 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_Ha4. apply refl_equal. % 7.87/8.04 apply zenon_Hbf. apply sym_equal. exact zenon_Hbc. % 7.87/8.04 apply zenon_Ha4. apply refl_equal. % 7.87/8.04 apply zenon_Ha4. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L53_ *) % 7.87/8.04 assert (zenon_L54_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Ha7 zenon_Hb6 zenon_H28 zenon_H1e zenon_H2c zenon_H25 zenon_H38 zenon_H4e zenon_H5e zenon_H5a zenon_H40 zenon_H55 zenon_H61 zenon_H99 zenon_Hb5 zenon_Hb4 zenon_H6c zenon_H70 zenon_H20 zenon_H36 zenon_Hbc zenon_Hbd. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.04 apply (zenon_L52_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.04 apply (zenon_L43_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.04 apply (zenon_L44_); trivial. % 7.87/8.04 apply (zenon_L53_); trivial. % 7.87/8.04 (* end of lemma zenon_L54_ *) % 7.87/8.04 assert (zenon_L55_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H51 zenon_H54 zenon_H33 zenon_Hbd zenon_Hbc zenon_H20 zenon_H70 zenon_H6c zenon_Hb4 zenon_Hb5 zenon_H99 zenon_H61 zenon_H55 zenon_H40 zenon_H5a zenon_H5e zenon_H4e zenon_H38 zenon_H25 zenon_H2c zenon_H1e zenon_H28 zenon_Hb6 zenon_Ha7 zenon_H64 zenon_H5d. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L15_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L54_); trivial. % 7.87/8.04 apply (zenon_L21_); trivial. % 7.87/8.04 (* end of lemma zenon_L55_ *) % 7.87/8.04 assert (zenon_L56_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H64 zenon_H4e zenon_H3d zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H5e zenon_H33 zenon_H30 zenon_H51 zenon_Hbd zenon_Hbc zenon_H20 zenon_H6c zenon_Hb4 zenon_Hb5 zenon_H99 zenon_H55 zenon_H40 zenon_Hb6 zenon_Ha7 zenon_H89 zenon_Haa zenon_H43 zenon_H49 zenon_H8f zenon_H54 zenon_Hc0. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.04 apply (zenon_L49_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.04 apply (zenon_L4_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.04 apply (zenon_L14_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.04 apply (zenon_L24_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.04 apply (zenon_L37_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.04 apply (zenon_L55_); trivial. % 7.87/8.04 apply (zenon_L34_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.04 apply (zenon_L38_); trivial. % 7.87/8.04 exact (zenon_Hc0 zenon_H92). % 7.87/8.04 (* end of lemma zenon_L56_ *) % 7.87/8.04 assert (zenon_L57_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Hbc zenon_Hc1 zenon_H6c. % 7.87/8.04 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.04 cut (((e3) = (e3)) = ((e2) = (e3))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H6c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H68. % 7.87/8.04 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.04 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H9d. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_Hbc. % 7.87/8.04 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.04 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 7.87/8.04 congruence. % 7.87/8.04 exact (zenon_Hc2 zenon_Hc1). % 7.87/8.04 apply zenon_H22. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 apply zenon_H69. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L57_ *) % 7.87/8.04 assert (zenon_L58_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Hc3 zenon_Had zenon_Hc0 zenon_H54 zenon_H8f zenon_H49 zenon_H43 zenon_Haa zenon_H89 zenon_Ha7 zenon_Hb6 zenon_H40 zenon_H55 zenon_H99 zenon_Hb5 zenon_Hb4 zenon_H20 zenon_Hbd zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H3d zenon_H4e zenon_H64 zenon_Haf zenon_H95 zenon_Hbc zenon_H6c. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.04 apply (zenon_L48_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.04 apply (zenon_L24_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.04 apply (zenon_L56_); trivial. % 7.87/8.04 apply (zenon_L57_); trivial. % 7.87/8.04 (* end of lemma zenon_L58_ *) % 7.87/8.04 assert (zenon_L59_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.04 do 0 intro. intros zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H5a zenon_H40 zenon_H25 zenon_Hb2 zenon_H55 zenon_H4e zenon_H38 zenon_H2c zenon_H28 zenon_H1e zenon_H61 zenon_H64 zenon_H5d. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.04 apply (zenon_L6_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.04 apply (zenon_L7_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.04 apply (zenon_L51_); trivial. % 7.87/8.04 apply (zenon_L21_); trivial. % 7.87/8.04 (* end of lemma zenon_L59_ *) % 7.87/8.04 assert (zenon_L60_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_H49 zenon_H43 zenon_H3d zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H5a zenon_H40 zenon_H25 zenon_Hb2 zenon_H55 zenon_H4e zenon_H38 zenon_H2c zenon_H28 zenon_H1e zenon_H61 zenon_H64. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.04 apply (zenon_L4_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.04 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.04 apply (zenon_L14_); trivial. % 7.87/8.04 apply (zenon_L59_); trivial. % 7.87/8.04 (* end of lemma zenon_L60_ *) % 7.87/8.04 assert (zenon_L61_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 7.87/8.04 do 0 intro. intros zenon_Hc6 zenon_Hc7 zenon_H2c. % 7.87/8.04 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_H2c. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H8a. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 7.87/8.04 congruence. % 7.87/8.04 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_Hc8. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_Hc6. % 7.87/8.04 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 apply zenon_Hc9. apply sym_equal. exact zenon_Hc7. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 (* end of lemma zenon_L61_ *) % 7.87/8.04 assert (zenon_L62_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 7.87/8.04 do 0 intro. intros zenon_Hca zenon_H6d zenon_H70. % 7.87/8.04 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 7.87/8.04 intro zenon_D_pnotp. % 7.87/8.04 apply zenon_Hca. % 7.87/8.04 rewrite <- zenon_D_pnotp. % 7.87/8.04 exact zenon_H6d. % 7.87/8.04 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 7.87/8.04 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.04 congruence. % 7.87/8.04 apply zenon_H8b. apply refl_equal. % 7.87/8.04 apply zenon_Hcb. apply sym_equal. exact zenon_H70. % 7.87/8.04 (* end of lemma zenon_L62_ *) % 7.87/8.04 assert (zenon_L63_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 7.87/8.04 do 0 intro. intros zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_H36 zenon_Hca zenon_H70. % 7.87/8.04 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.04 apply (zenon_L5_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.05 apply (zenon_L61_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.05 apply (zenon_L29_); trivial. % 7.87/8.05 apply (zenon_L62_); trivial. % 7.87/8.05 (* end of lemma zenon_L63_ *) % 7.87/8.05 assert (zenon_L64_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_H89 zenon_H88 zenon_Hca zenon_Hc7 zenon_Hcc zenon_H4e zenon_H3d zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L37_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L63_); trivial. % 7.87/8.05 apply (zenon_L33_); trivial. % 7.87/8.05 (* end of lemma zenon_L64_ *) % 7.87/8.05 assert (zenon_L65_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hcf zenon_H82 zenon_H99. % 7.87/8.05 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.05 cut (((e2) = (e2)) = ((e1) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H99. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H21. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e0) (e2)) = (e1)) = ((e2) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H9a. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hcf. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hd0 zenon_H82). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L65_ *) % 7.87/8.05 assert (zenon_L66_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hbb zenon_H88 zenon_H8f. % 7.87/8.05 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.05 cut (((e3) = (e3)) = ((e1) = (e3))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H8f. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H68. % 7.87/8.05 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.05 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H90. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hbb. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hd1 zenon_H88). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L66_ *) % 7.87/8.05 assert (zenon_L67_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hc6 zenon_H6e zenon_H99. % 7.87/8.05 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.05 cut (((e2) = (e2)) = ((e1) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H99. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H21. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e1)) = (e1)) = ((e2) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H9a. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hc6. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_H6f zenon_H6e). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L67_ *) % 7.87/8.05 assert (zenon_L68_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hd2 zenon_Hcf zenon_H81. % 7.87/8.05 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H46 ]. % 7.87/8.05 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H81. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hd3. % 7.87/8.05 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.87/8.05 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hd4. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hd2. % 7.87/8.05 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 7.87/8.05 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H46. apply refl_equal. % 7.87/8.05 apply zenon_Hd5. apply sym_equal. exact zenon_Hcf. % 7.87/8.05 apply zenon_H46. apply refl_equal. % 7.87/8.05 apply zenon_H46. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L68_ *) % 7.87/8.05 assert (zenon_L69_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H55 zenon_Hd6 zenon_H5d. % 7.87/8.05 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H55. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hd6. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hd7 zenon_H5d). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L69_ *) % 7.87/8.05 assert (zenon_L70_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hd8 zenon_H8f zenon_H88 zenon_H99 zenon_H6e zenon_H81 zenon_Hcf zenon_H55 zenon_H5d. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.05 apply (zenon_L66_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.05 apply (zenon_L67_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.05 apply (zenon_L68_); trivial. % 7.87/8.05 apply (zenon_L69_); trivial. % 7.87/8.05 (* end of lemma zenon_L70_ *) % 7.87/8.05 assert (zenon_L71_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hc6 zenon_H6d zenon_H8f. % 7.87/8.05 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.05 cut (((e3) = (e3)) = ((e1) = (e3))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H8f. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H68. % 7.87/8.05 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.05 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e1)) = (e1)) = ((e3) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H90. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hc6. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hdb zenon_H6d). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L71_ *) % 7.87/8.05 assert (zenon_L72_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_H8f zenon_Hc6 zenon_H6c zenon_H9c zenon_H4e zenon_H3d zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L71_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L43_); trivial. % 7.87/8.05 apply (zenon_L33_); trivial. % 7.87/8.05 (* end of lemma zenon_L72_ *) % 7.87/8.05 assert (zenon_L73_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H6c zenon_H7f zenon_Hdc. % 7.87/8.05 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H6c. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H7f. % 7.87/8.05 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.05 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hdd zenon_Hdc). % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L73_ *) % 7.87/8.05 assert (zenon_L74_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_H67 zenon_H89 zenon_H88 zenon_Hbd zenon_Hbc zenon_H36 zenon_H20 zenon_Hb4 zenon_Hb5 zenon_H99 zenon_H61 zenon_H55 zenon_H40 zenon_H5a zenon_H5e zenon_H4e zenon_H38 zenon_H25 zenon_H2c zenon_H1e zenon_H28 zenon_Hb6 zenon_Ha7 zenon_H6c zenon_Hdc. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L37_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L54_); trivial. % 7.87/8.05 apply (zenon_L73_); trivial. % 7.87/8.05 (* end of lemma zenon_L74_ *) % 7.87/8.05 assert (zenon_L75_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Had zenon_H1f zenon_H20. % 7.87/8.05 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.87/8.05 apply (zenon_L2_); trivial. % 7.87/8.05 (* end of lemma zenon_L75_ *) % 7.87/8.05 assert (zenon_L76_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_H89 zenon_H88 zenon_H64 zenon_Ha2 zenon_H20 zenon_H6c zenon_H54 zenon_H99 zenon_Ha7 zenon_H4e zenon_H3d zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L37_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L46_); trivial. % 7.87/8.05 apply (zenon_L33_); trivial. % 7.87/8.05 (* end of lemma zenon_L76_ *) % 7.87/8.05 assert (zenon_L77_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H3e zenon_H93 zenon_H20. % 7.87/8.05 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.05 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H20. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H21. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H23. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H3e. % 7.87/8.05 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.05 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_H94 zenon_H93). % 7.87/8.05 apply zenon_H1d. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L77_ *) % 7.87/8.05 assert (zenon_L78_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hb2 zenon_H93 zenon_H99. % 7.87/8.05 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.05 cut (((e2) = (e2)) = ((e1) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H99. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H21. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H9a. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hb2. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_H94 zenon_H93). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L78_ *) % 7.87/8.05 assert (zenon_L79_ : ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H41 zenon_Hde zenon_H55. % 7.87/8.05 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.87/8.05 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H55. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H56. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e3) (e1)) = (e0)) = ((e1) = (e0))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H58. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H41. % 7.87/8.05 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.05 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hdf zenon_Hde). % 7.87/8.05 apply zenon_H1d. apply refl_equal. % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L79_ *) % 7.87/8.05 assert (zenon_L80_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H43 zenon_Hd2 zenon_He0. % 7.87/8.05 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H43. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hd2. % 7.87/8.05 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 7.87/8.05 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H46. apply refl_equal. % 7.87/8.05 apply zenon_He1. apply sym_equal. exact zenon_He0. % 7.87/8.05 (* end of lemma zenon_L80_ *) % 7.87/8.05 assert (zenon_L81_ : ((op (e3) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_He2 zenon_He3 zenon_He4. % 7.87/8.05 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_He4. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H4a. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_He5. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_He2. % 7.87/8.05 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H4b. apply refl_equal. % 7.87/8.05 apply zenon_He6. apply sym_equal. exact zenon_He3. % 7.87/8.05 apply zenon_H4b. apply refl_equal. % 7.87/8.05 apply zenon_H4b. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L81_ *) % 7.87/8.05 assert (zenon_L82_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_He7 zenon_H99 zenon_H93 zenon_H55 zenon_H41 zenon_Hd2 zenon_H43 zenon_He3 zenon_He4. % 7.87/8.05 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.87/8.05 apply (zenon_L78_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.87/8.05 apply (zenon_L79_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.87/8.05 apply (zenon_L80_); trivial. % 7.87/8.05 apply (zenon_L81_); trivial. % 7.87/8.05 (* end of lemma zenon_L82_ *) % 7.87/8.05 assert (zenon_L83_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H4e zenon_He4 zenon_He3 zenon_H43 zenon_Hd2 zenon_H55 zenon_H93 zenon_H99 zenon_He7 zenon_H5a zenon_H61 zenon_H20 zenon_H5b zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.05 apply (zenon_L77_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.05 apply (zenon_L82_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.05 apply (zenon_L16_); trivial. % 7.87/8.05 apply (zenon_L19_); trivial. % 7.87/8.05 (* end of lemma zenon_L83_ *) % 7.87/8.05 assert (zenon_L84_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H6e zenon_H5b zenon_H89. % 7.87/8.05 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H89. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H8a. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H8c. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H6e. % 7.87/8.05 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 apply zenon_Hea. apply sym_equal. exact zenon_H5b. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L84_ *) % 7.87/8.05 assert (zenon_L85_ : (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H20 zenon_H6e zenon_H2d. % 7.87/8.05 cut (((op (e1) (e1)) = (e2)) = ((e0) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H20. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H6e. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Heb zenon_H2d). % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L85_ *) % 7.87/8.05 assert (zenon_L86_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H61 zenon_H1e zenon_H28 zenon_H6e zenon_H20 zenon_H38 zenon_H36 zenon_H47 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.05 apply (zenon_L4_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.05 apply (zenon_L85_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.05 apply (zenon_L8_); trivial. % 7.87/8.05 apply (zenon_L18_); trivial. % 7.87/8.05 (* end of lemma zenon_L86_ *) % 7.87/8.05 assert (zenon_L87_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H4e zenon_H3d zenon_He4 zenon_He3 zenon_H43 zenon_Hd2 zenon_H55 zenon_H93 zenon_H99 zenon_He7 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H6e zenon_H20 zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.05 apply (zenon_L9_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.05 apply (zenon_L82_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.05 apply (zenon_L16_); trivial. % 7.87/8.05 apply (zenon_L86_); trivial. % 7.87/8.05 (* end of lemma zenon_L87_ *) % 7.87/8.05 assert (zenon_L88_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hec zenon_H89 zenon_H54 zenon_H4e zenon_H3d zenon_He4 zenon_He3 zenon_H43 zenon_Hd2 zenon_H55 zenon_H99 zenon_He7 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H6e zenon_H20 zenon_H38 zenon_H36 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.05 apply (zenon_L2_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.05 apply (zenon_L84_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.05 apply (zenon_L41_); trivial. % 7.87/8.05 apply (zenon_L87_); trivial. % 7.87/8.05 (* end of lemma zenon_L88_ *) % 7.87/8.05 assert (zenon_L89_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 7.87/8.05 do 0 intro. intros zenon_He3 zenon_Hc1 zenon_H8f. % 7.87/8.05 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.05 cut (((e3) = (e3)) = ((e1) = (e3))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H8f. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H68. % 7.87/8.05 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.05 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H90. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_He3. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hc2 zenon_Hc1). % 7.87/8.05 apply zenon_H57. apply refl_equal. % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L89_ *) % 7.87/8.05 assert (zenon_L90_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hef zenon_Hc6 zenon_Hd2. % 7.87/8.05 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hef. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hc6. % 7.87/8.05 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 apply zenon_Hf0. apply sym_equal. exact zenon_Hd2. % 7.87/8.05 (* end of lemma zenon_L90_ *) % 7.87/8.05 assert (zenon_L91_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H8f zenon_H7f zenon_Hde. % 7.87/8.05 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H8f. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H7f. % 7.87/8.05 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.05 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hdf]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hdf zenon_Hde). % 7.87/8.05 apply zenon_H69. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L91_ *) % 7.87/8.05 assert (zenon_L92_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_He7 zenon_H99 zenon_H93 zenon_H7f zenon_H8f zenon_Hd2 zenon_H43 zenon_He3 zenon_He4. % 7.87/8.05 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.87/8.05 apply (zenon_L78_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.87/8.05 apply (zenon_L91_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.87/8.05 apply (zenon_L80_); trivial. % 7.87/8.05 apply (zenon_L81_); trivial. % 7.87/8.05 (* end of lemma zenon_L92_ *) % 7.87/8.05 assert (zenon_L93_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hd6 zenon_He3 zenon_Hf1. % 7.87/8.05 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H65 ]. % 7.87/8.05 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hf1. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hf2. % 7.87/8.05 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.87/8.05 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hf3. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hd6. % 7.87/8.05 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 7.87/8.05 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H65. apply refl_equal. % 7.87/8.05 apply zenon_He6. apply sym_equal. exact zenon_He3. % 7.87/8.05 apply zenon_H65. apply refl_equal. % 7.87/8.05 apply zenon_H65. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L93_ *) % 7.87/8.05 assert (zenon_L94_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hd8 zenon_He4 zenon_H43 zenon_H8f zenon_H93 zenon_H99 zenon_He7 zenon_H51 zenon_H55 zenon_H54 zenon_H25 zenon_H33 zenon_H6e zenon_H64 zenon_H5d zenon_H88 zenon_H89 zenon_H67 zenon_Haa zenon_He3 zenon_Hf1. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.05 apply (zenon_L66_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.05 apply (zenon_L67_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L37_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L30_); trivial. % 7.87/8.05 apply (zenon_L92_); trivial. % 7.87/8.05 apply (zenon_L93_); trivial. % 7.87/8.05 (* end of lemma zenon_L94_ *) % 7.87/8.05 assert (zenon_L95_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H61 zenon_H28 zenon_H20 zenon_H49 zenon_H40 zenon_H3d zenon_H1e zenon_H4e zenon_H38 zenon_H30 zenon_Hd8 zenon_He4 zenon_H43 zenon_H8f zenon_H93 zenon_H99 zenon_He7 zenon_H51 zenon_H55 zenon_H54 zenon_H25 zenon_H33 zenon_H6e zenon_H64 zenon_H88 zenon_H89 zenon_H67 zenon_Haa zenon_He3 zenon_Hf1. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.05 apply (zenon_L4_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.05 apply (zenon_L85_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.05 apply (zenon_L14_); trivial. % 7.87/8.05 apply (zenon_L94_); trivial. % 7.87/8.05 (* end of lemma zenon_L95_ *) % 7.87/8.05 assert (zenon_L96_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hec zenon_Hc3 zenon_H54 zenon_H8f zenon_H61 zenon_H28 zenon_H20 zenon_H49 zenon_H40 zenon_H3d zenon_H1e zenon_H4e zenon_H38 zenon_H30 zenon_Hd8 zenon_He4 zenon_H43 zenon_H99 zenon_He7 zenon_H51 zenon_H55 zenon_H25 zenon_H33 zenon_H6e zenon_H64 zenon_H89 zenon_H67 zenon_Haa zenon_He3 zenon_Hf1 zenon_Haf zenon_H95 zenon_Hbc zenon_H6c. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.05 apply (zenon_L2_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.05 apply (zenon_L84_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.05 apply (zenon_L41_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.05 apply (zenon_L36_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.05 apply (zenon_L49_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.05 apply (zenon_L95_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.05 apply (zenon_L38_); trivial. % 7.87/8.05 apply (zenon_L39_); trivial. % 7.87/8.05 apply (zenon_L57_); trivial. % 7.87/8.05 (* end of lemma zenon_L96_ *) % 7.87/8.05 assert (zenon_L97_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H99 zenon_H9c zenon_Hf4. % 7.87/8.05 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H99. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H9c. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 7.87/8.05 congruence. % 7.87/8.05 exact (zenon_Hf5 zenon_Hf4). % 7.87/8.05 apply zenon_H22. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L97_ *) % 7.87/8.05 assert (zenon_L98_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H6c zenon_H9c zenon_H8f zenon_Hde. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L37_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L43_); trivial. % 7.87/8.05 apply (zenon_L91_); trivial. % 7.87/8.05 (* end of lemma zenon_L98_ *) % 7.87/8.05 assert (zenon_L99_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6d zenon_H8f zenon_H54 zenon_H6c zenon_H93. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.05 apply (zenon_L49_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.05 apply (zenon_L37_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.05 apply (zenon_L38_); trivial. % 7.87/8.05 apply (zenon_L39_); trivial. % 7.87/8.05 (* end of lemma zenon_L99_ *) % 7.87/8.05 assert (zenon_L100_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hc3 zenon_H1e zenon_H67 zenon_H25 zenon_H93 zenon_H54 zenon_H8f zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_Hbc zenon_H6c. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.05 apply (zenon_L36_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.05 apply (zenon_L99_); trivial. % 7.87/8.05 apply (zenon_L57_); trivial. % 7.87/8.05 (* end of lemma zenon_L100_ *) % 7.87/8.05 assert (zenon_L101_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_H95 zenon_Haf zenon_H89 zenon_H8f zenon_H54 zenon_H93 zenon_H67 zenon_Hc3 zenon_Hbd zenon_Hbc zenon_H36 zenon_H20 zenon_Hb4 zenon_Hb5 zenon_H99 zenon_H61 zenon_H55 zenon_H40 zenon_H5a zenon_H5e zenon_H4e zenon_H38 zenon_H25 zenon_H2c zenon_H1e zenon_H28 zenon_Hb6 zenon_Ha7 zenon_H6c zenon_Hdc. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L100_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L54_); trivial. % 7.87/8.05 apply (zenon_L73_); trivial. % 7.87/8.05 (* end of lemma zenon_L101_ *) % 7.87/8.05 assert (zenon_L102_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H51 zenon_H1e zenon_H30 zenon_H33 zenon_H70 zenon_Hca zenon_Hc7 zenon_H2c zenon_H25 zenon_Hcc zenon_H64 zenon_H5d. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.05 apply (zenon_L6_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.05 apply (zenon_L7_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.05 apply (zenon_L63_); trivial. % 7.87/8.05 apply (zenon_L21_); trivial. % 7.87/8.05 (* end of lemma zenon_L102_ *) % 7.87/8.05 assert (zenon_L103_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H49 zenon_H43 zenon_H40 zenon_Haa zenon_H6c zenon_Hbc zenon_H95 zenon_Haf zenon_H89 zenon_H8f zenon_H54 zenon_H93 zenon_Hc3 zenon_Hcc zenon_Hc7 zenon_Hca zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H3d zenon_H4e zenon_H64. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.05 apply (zenon_L4_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.05 apply (zenon_L5_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.05 apply (zenon_L14_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L100_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L102_); trivial. % 7.87/8.05 apply (zenon_L34_); trivial. % 7.87/8.05 (* end of lemma zenon_L103_ *) % 7.87/8.05 assert (zenon_L104_ : ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H6d zenon_H66 zenon_H2c. % 7.87/8.05 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H2c. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H8a. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hc8. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H6d. % 7.87/8.05 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 7.87/8.05 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 apply zenon_Hf6. apply sym_equal. exact zenon_H66. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 apply zenon_H8b. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L104_ *) % 7.87/8.05 assert (zenon_L105_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hc3 zenon_H67 zenon_H1e zenon_H2c zenon_H93 zenon_H6c zenon_H54 zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_He3 zenon_H8f. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.05 apply (zenon_L36_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.05 apply (zenon_L104_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.05 apply (zenon_L99_); trivial. % 7.87/8.05 apply (zenon_L89_); trivial. % 7.87/8.05 (* end of lemma zenon_L105_ *) % 7.87/8.05 assert (zenon_L106_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Haa zenon_He3 zenon_H95 zenon_Haf zenon_H89 zenon_H6c zenon_H93 zenon_H2c zenon_H1e zenon_H67 zenon_Hc3 zenon_H5d zenon_H64 zenon_H6e zenon_H33 zenon_H25 zenon_H54 zenon_H55 zenon_H51 zenon_H8f zenon_Hde. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.05 apply (zenon_L24_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.05 apply (zenon_L105_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.05 apply (zenon_L30_); trivial. % 7.87/8.05 apply (zenon_L91_); trivial. % 7.87/8.05 (* end of lemma zenon_L106_ *) % 7.87/8.05 assert (zenon_L107_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H9f zenon_H83 zenon_H38. % 7.87/8.05 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H38. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H39. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H3b. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H9f. % 7.87/8.05 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H3a. apply refl_equal. % 7.87/8.05 apply zenon_H84. apply sym_equal. exact zenon_H83. % 7.87/8.05 apply zenon_H3a. apply refl_equal. % 7.87/8.05 apply zenon_H3a. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L107_ *) % 7.87/8.05 assert (zenon_L108_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hf7 zenon_Hb0 zenon_Hf8. % 7.87/8.05 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 7.87/8.05 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hf8. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hf9. % 7.87/8.05 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.87/8.05 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hfb. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hf7. % 7.87/8.05 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 7.87/8.05 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_Hfa. apply refl_equal. % 7.87/8.05 apply zenon_Hb1. apply sym_equal. exact zenon_Hb0. % 7.87/8.05 apply zenon_Hfa. apply refl_equal. % 7.87/8.05 apply zenon_Hfa. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L108_ *) % 7.87/8.05 assert (zenon_L109_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hfc zenon_Hfd zenon_H5e. % 7.87/8.05 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H5e. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H4a. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H5f. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hfc. % 7.87/8.05 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 7.87/8.05 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H4b. apply refl_equal. % 7.87/8.05 apply zenon_Hfe. apply sym_equal. exact zenon_Hfd. % 7.87/8.05 apply zenon_H4b. apply refl_equal. % 7.87/8.05 apply zenon_H4b. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L109_ *) % 7.87/8.05 assert (zenon_L110_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hff zenon_H47 zenon_Hf1 zenon_He3 zenon_H64 zenon_Ha1 zenon_Hfc zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.05 apply (zenon_L18_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.05 apply (zenon_L93_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.05 apply (zenon_L45_); trivial. % 7.87/8.05 apply (zenon_L109_); trivial. % 7.87/8.05 (* end of lemma zenon_L110_ *) % 7.87/8.05 assert (zenon_L111_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H102 zenon_H93 zenon_H6c zenon_Hde zenon_H8f zenon_Hf8 zenon_Hb0 zenon_Hff zenon_H47 zenon_Hf1 zenon_He3 zenon_H64 zenon_Ha1 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H92 | zenon_intro zenon_H103 ]. % 7.87/8.05 apply (zenon_L39_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H7f | zenon_intro zenon_H104 ]. % 7.87/8.05 apply (zenon_L91_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfc ]. % 7.87/8.05 apply (zenon_L108_); trivial. % 7.87/8.05 apply (zenon_L110_); trivial. % 7.87/8.05 (* end of lemma zenon_L111_ *) % 7.87/8.05 assert (zenon_L112_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H55 zenon_H36 zenon_H5a zenon_H102 zenon_H93 zenon_H6c zenon_Hde zenon_H8f zenon_Hf8 zenon_Hb0 zenon_Hff zenon_Hf1 zenon_He3 zenon_H64 zenon_Ha1 zenon_H5e. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.05 apply (zenon_L9_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.05 apply (zenon_L79_); trivial. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.05 apply (zenon_L16_); trivial. % 7.87/8.05 apply (zenon_L111_); trivial. % 7.87/8.05 (* end of lemma zenon_L112_ *) % 7.87/8.05 assert (zenon_L113_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hf1 zenon_Hbc zenon_Ha2. % 7.87/8.05 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_Hf1. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hbc. % 7.87/8.05 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 7.87/8.05 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H105. apply refl_equal. % 7.87/8.05 apply zenon_Ha6. apply sym_equal. exact zenon_Ha2. % 7.87/8.05 (* end of lemma zenon_L113_ *) % 7.87/8.05 assert (zenon_L114_ : (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> False). % 7.87/8.05 do 0 intro. intros zenon_H106 zenon_Hb5 zenon_H25. % 7.87/8.05 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 7.87/8.05 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 7.87/8.05 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H10a | zenon_intro zenon_Hb9 ]. % 7.87/8.05 exact (zenon_H10a zenon_H25). % 7.87/8.05 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.05 (* end of lemma zenon_L114_ *) % 7.87/8.05 assert (zenon_L115_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 7.87/8.05 do 0 intro. intros zenon_H9f zenon_H82 zenon_H10b. % 7.87/8.05 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H10b. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H39. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H10c. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H9f. % 7.87/8.05 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 7.87/8.05 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.05 congruence. % 7.87/8.05 apply zenon_H3a. apply refl_equal. % 7.87/8.05 apply zenon_H10d. apply sym_equal. exact zenon_H82. % 7.87/8.05 apply zenon_H3a. apply refl_equal. % 7.87/8.05 apply zenon_H3a. apply refl_equal. % 7.87/8.05 (* end of lemma zenon_L115_ *) % 7.87/8.05 assert (zenon_L116_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 7.87/8.05 do 0 intro. intros zenon_Hbb zenon_H5b zenon_H99. % 7.87/8.05 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.05 cut (((e2) = (e2)) = ((e1) = (e2))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H99. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_H21. % 7.87/8.05 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.05 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 7.87/8.05 congruence. % 7.87/8.05 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 7.87/8.05 intro zenon_D_pnotp. % 7.87/8.05 apply zenon_H9a. % 7.87/8.05 rewrite <- zenon_D_pnotp. % 7.87/8.05 exact zenon_Hbb. % 7.87/8.05 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.05 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H5c zenon_H5b). % 7.87/8.06 apply zenon_H57. apply refl_equal. % 7.87/8.06 apply zenon_H22. apply refl_equal. % 7.87/8.06 apply zenon_H22. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L116_ *) % 7.87/8.06 assert (zenon_L117_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H9f zenon_H98 zenon_H10e. % 7.87/8.06 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H10e. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H39. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H10f. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H9f. % 7.87/8.06 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 apply zenon_H110. apply sym_equal. exact zenon_H98. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L117_ *) % 7.87/8.06 assert (zenon_L118_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H111 zenon_Hb0 zenon_H67. % 7.87/8.06 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.06 cut (((e3) = (e3)) = ((e0) = (e3))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H67. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H68. % 7.87/8.06 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.06 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H6a. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H111. % 7.87/8.06 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.06 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H112 zenon_Hb0). % 7.87/8.06 apply zenon_H1d. apply refl_equal. % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L118_ *) % 7.87/8.06 assert (zenon_L119_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H113 zenon_H29 zenon_H37. % 7.87/8.06 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H113. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H29. % 7.87/8.06 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 7.87/8.06 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H114. apply refl_equal. % 7.87/8.06 apply zenon_H3c. apply sym_equal. exact zenon_H37. % 7.87/8.06 (* end of lemma zenon_L119_ *) % 7.87/8.06 assert (zenon_L120_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H81 zenon_Hb0 zenon_H115. % 7.87/8.06 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H81. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hb0. % 7.87/8.06 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 7.87/8.06 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H85. apply refl_equal. % 7.87/8.06 apply zenon_H116. apply sym_equal. exact zenon_H115. % 7.87/8.06 (* end of lemma zenon_L120_ *) % 7.87/8.06 assert (zenon_L121_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H117 zenon_H44 zenon_H43 zenon_H118 zenon_H38 zenon_H9f zenon_H81 zenon_Hb0. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.87/8.06 apply (zenon_L11_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.87/8.06 exact (zenon_H118 zenon_Hd2). % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.87/8.06 apply (zenon_L107_); trivial. % 7.87/8.06 apply (zenon_L120_); trivial. % 7.87/8.06 (* end of lemma zenon_L121_ *) % 7.87/8.06 assert (zenon_L122_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H11b zenon_H67 zenon_H29 zenon_H113 zenon_H20 zenon_H117 zenon_H43 zenon_H118 zenon_H38 zenon_H9f zenon_H81 zenon_Hb0. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.87/8.06 apply (zenon_L118_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.87/8.06 apply (zenon_L119_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.87/8.06 apply (zenon_L44_); trivial. % 7.87/8.06 apply (zenon_L121_); trivial. % 7.87/8.06 (* end of lemma zenon_L122_ *) % 7.87/8.06 assert (zenon_L123_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H31 zenon_H8e zenon_H67. % 7.87/8.06 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.06 cut (((e3) = (e3)) = ((e0) = (e3))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H67. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H68. % 7.87/8.06 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.06 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H6a. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H31. % 7.87/8.06 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.06 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H91 zenon_H8e). % 7.87/8.06 apply zenon_H1d. apply refl_equal. % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L123_ *) % 7.87/8.06 assert (zenon_L124_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H51 zenon_H67 zenon_H8e zenon_H25 zenon_H33 zenon_H6e zenon_H70 zenon_H64 zenon_H5d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L123_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L29_); trivial. % 7.87/8.06 apply (zenon_L21_); trivial. % 7.87/8.06 (* end of lemma zenon_L124_ *) % 7.87/8.06 assert (zenon_L125_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_Haa zenon_H6c zenon_H6e zenon_H8e zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H3d zenon_H4e zenon_H64 zenon_H5d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.06 apply (zenon_L124_); trivial. % 7.87/8.06 apply (zenon_L34_); trivial. % 7.87/8.06 (* end of lemma zenon_L125_ *) % 7.87/8.06 assert (zenon_L126_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H11e zenon_H99 zenon_Hbb zenon_H5d zenon_H64 zenon_H4e zenon_H3d zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H5e zenon_H33 zenon_H30 zenon_H51 zenon_H8e zenon_H6c zenon_Haa zenon_H38 zenon_H9f zenon_Hf1 zenon_Hbc. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L125_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_L107_); trivial. % 7.87/8.06 apply (zenon_L113_); trivial. % 7.87/8.06 (* end of lemma zenon_L126_ *) % 7.87/8.06 assert (zenon_L127_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H61 zenon_H28 zenon_H2c zenon_H49 zenon_H43 zenon_H40 zenon_H3d zenon_H1e zenon_H4e zenon_H38 zenon_H30 zenon_H51 zenon_H55 zenon_H54 zenon_H25 zenon_H33 zenon_H20 zenon_H9f zenon_H64. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L4_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L5_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_L14_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L15_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L44_); trivial. % 7.87/8.06 apply (zenon_L21_); trivial. % 7.87/8.06 (* end of lemma zenon_L127_ *) % 7.87/8.06 assert (zenon_L128_ : ((op (e1) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H6e zenon_H26 zenon_H2c. % 7.87/8.06 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H2c. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H8a. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_Hc8. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H6e. % 7.87/8.06 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H8b. apply refl_equal. % 7.87/8.06 apply zenon_H121. apply sym_equal. exact zenon_H26. % 7.87/8.06 apply zenon_H8b. apply refl_equal. % 7.87/8.06 apply zenon_H8b. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L128_ *) % 7.87/8.06 assert (zenon_L129_ : (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H122 zenon_H98 zenon_H10e. % 7.87/8.06 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 7.87/8.06 apply (zenon_L117_); trivial. % 7.87/8.06 (* end of lemma zenon_L129_ *) % 7.87/8.06 assert (zenon_L130_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H49 zenon_H43 zenon_H40 zenon_Haa zenon_H6c zenon_H6e zenon_H8e zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H3d zenon_H4e zenon_H64. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L4_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L5_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_L14_); trivial. % 7.87/8.06 apply (zenon_L125_); trivial. % 7.87/8.06 (* end of lemma zenon_L130_ *) % 7.87/8.06 assert (zenon_L131_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H8f zenon_Hbb zenon_H64 zenon_H4e zenon_H3d zenon_H67 zenon_H5a zenon_H61 zenon_H1e zenon_H28 zenon_H25 zenon_H2c zenon_H38 zenon_H5e zenon_H33 zenon_H30 zenon_H51 zenon_H6e zenon_Haa zenon_H40 zenon_H43 zenon_H49 zenon_H6c zenon_H93. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L66_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L130_); trivial. % 7.87/8.06 apply (zenon_L39_); trivial. % 7.87/8.06 (* end of lemma zenon_L131_ *) % 7.87/8.06 assert (zenon_L132_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H124 zenon_H10b zenon_H9f zenon_Hec zenon_H20 zenon_H99 zenon_H10e zenon_H122 zenon_Hc3 zenon_H49 zenon_H43 zenon_H40 zenon_Haa zenon_H6e zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H38 zenon_H2c zenon_H25 zenon_H28 zenon_H1e zenon_H61 zenon_H5a zenon_H67 zenon_H3d zenon_H4e zenon_H64 zenon_Hbb zenon_H8f zenon_Haf zenon_H95 zenon_H6c. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L128_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_L115_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L129_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_L131_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 (* end of lemma zenon_L132_ *) % 7.87/8.06 assert (zenon_L133_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H117 zenon_H44 zenon_H43 zenon_Hcf zenon_H38 zenon_H9f zenon_H81 zenon_Hb0. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.87/8.06 apply (zenon_L11_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.87/8.06 apply (zenon_L68_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.87/8.06 apply (zenon_L107_); trivial. % 7.87/8.06 apply (zenon_L120_); trivial. % 7.87/8.06 (* end of lemma zenon_L133_ *) % 7.87/8.06 assert (zenon_L134_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H11b zenon_H127 zenon_H29 zenon_H113 zenon_H20 zenon_H117 zenon_H43 zenon_Hcf zenon_H38 zenon_H9f zenon_H81 zenon_Hb0. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.87/8.06 exact (zenon_H127 zenon_H111). % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.87/8.06 apply (zenon_L119_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.87/8.06 apply (zenon_L44_); trivial. % 7.87/8.06 apply (zenon_L133_); trivial. % 7.87/8.06 (* end of lemma zenon_L134_ *) % 7.87/8.06 assert (zenon_L135_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hb6 zenon_Hb5 zenon_H122 zenon_H10e zenon_H6c zenon_H95 zenon_Haf zenon_Hf1 zenon_He3 zenon_Haa zenon_H67 zenon_H89 zenon_H6e zenon_He7 zenon_H99 zenon_He4 zenon_Hd8 zenon_H20 zenon_H8f zenon_Hc3 zenon_Hec zenon_H9f zenon_H10b zenon_H124 zenon_H49 zenon_H43 zenon_H3d zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_H5a zenon_H40 zenon_H25 zenon_H55 zenon_H4e zenon_H38 zenon_H2c zenon_H28 zenon_H1e zenon_H61 zenon_H64. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.06 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L84_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L129_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_L131_); trivial. % 7.87/8.06 apply (zenon_L89_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L128_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_L115_); trivial. % 7.87/8.06 apply (zenon_L96_); trivial. % 7.87/8.06 apply (zenon_L60_); trivial. % 7.87/8.06 (* end of lemma zenon_L135_ *) % 7.87/8.06 assert (zenon_L136_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H98 zenon_H8e zenon_H6c. % 7.87/8.06 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.06 cut (((e3) = (e3)) = ((e2) = (e3))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H6c. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H68. % 7.87/8.06 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.06 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H9d. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H98. % 7.87/8.06 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.06 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H91 zenon_H8e). % 7.87/8.06 apply zenon_H22. apply refl_equal. % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L136_ *) % 7.87/8.06 assert (zenon_L137_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hfc zenon_H92 zenon_H128. % 7.87/8.06 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H128. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H4a. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H129. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hfc. % 7.87/8.06 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 apply zenon_H12a. apply sym_equal. exact zenon_H92. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L137_ *) % 7.87/8.06 assert (zenon_L138_ : (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H12b zenon_H92 zenon_H128. % 7.87/8.06 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 7.87/8.06 apply (zenon_L137_); trivial. % 7.87/8.06 (* end of lemma zenon_L138_ *) % 7.87/8.06 assert (zenon_L139_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hfc zenon_H7f zenon_H12d. % 7.87/8.06 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H12d. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H4a. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H12e. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hfc. % 7.87/8.06 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 apply zenon_H12f. apply sym_equal. exact zenon_H7f. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L139_ *) % 7.87/8.06 assert (zenon_L140_ : (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H12b zenon_H7f zenon_H12d. % 7.87/8.06 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 7.87/8.06 apply (zenon_L139_); trivial. % 7.87/8.06 (* end of lemma zenon_L140_ *) % 7.87/8.06 assert (zenon_L141_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Haa zenon_H67 zenon_H6e zenon_H6c zenon_H5d zenon_H64 zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_Hca zenon_H33 zenon_H30 zenon_H1e zenon_H51 zenon_H12b zenon_H12d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.06 apply (zenon_L102_); trivial. % 7.87/8.06 apply (zenon_L140_); trivial. % 7.87/8.06 (* end of lemma zenon_L141_ *) % 7.87/8.06 assert (zenon_L142_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H130 zenon_H6e zenon_Ha2. % 7.87/8.06 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H130. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H6e. % 7.87/8.06 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H8b. apply refl_equal. % 7.87/8.06 apply zenon_Ha6. apply sym_equal. exact zenon_Ha2. % 7.87/8.06 (* end of lemma zenon_L142_ *) % 7.87/8.06 assert (zenon_L143_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H131 zenon_H41 zenon_H44. % 7.87/8.06 cut (((op (e3) (e1)) = (e0)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H131. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H41. % 7.87/8.06 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 7.87/8.06 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H132. apply refl_equal. % 7.87/8.06 apply zenon_H45. apply sym_equal. exact zenon_H44. % 7.87/8.06 (* end of lemma zenon_L143_ *) % 7.87/8.06 assert (zenon_L144_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H40 zenon_Hc7 zenon_Hde. % 7.87/8.06 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H40. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hc7. % 7.87/8.06 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 7.87/8.06 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H2f. apply refl_equal. % 7.87/8.06 apply zenon_H133. apply sym_equal. exact zenon_Hde. % 7.87/8.06 (* end of lemma zenon_L144_ *) % 7.87/8.06 assert (zenon_L145_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H134 zenon_H9c zenon_Hdc. % 7.87/8.06 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H134. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H9c. % 7.87/8.06 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 7.87/8.06 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H136. apply refl_equal. % 7.87/8.06 apply zenon_H135. apply sym_equal. exact zenon_Hdc. % 7.87/8.06 (* end of lemma zenon_L145_ *) % 7.87/8.06 assert (zenon_L146_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H137 zenon_H44 zenon_H131 zenon_Hc7 zenon_H40 zenon_H9c zenon_H134 zenon_Hfc zenon_H12d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 7.87/8.06 apply (zenon_L143_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 7.87/8.06 apply (zenon_L144_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 7.87/8.06 apply (zenon_L145_); trivial. % 7.87/8.06 apply (zenon_L139_); trivial. % 7.87/8.06 (* end of lemma zenon_L146_ *) % 7.87/8.06 assert (zenon_L147_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H4e zenon_H20 zenon_H93 zenon_H25 zenon_H12d zenon_Hfc zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H5d zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.06 apply (zenon_L77_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.06 apply (zenon_L10_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.06 apply (zenon_L146_); trivial. % 7.87/8.06 apply (zenon_L18_); trivial. % 7.87/8.06 (* end of lemma zenon_L147_ *) % 7.87/8.06 assert (zenon_L148_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Ha7 zenon_H6c zenon_H8e zenon_Hdc zenon_H134 zenon_H20 zenon_H36 zenon_H13a. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.06 apply (zenon_L136_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.06 apply (zenon_L145_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.06 apply (zenon_L44_); trivial. % 7.87/8.06 exact (zenon_H13a zenon_Ha1). % 7.87/8.06 (* end of lemma zenon_L148_ *) % 7.87/8.06 assert (zenon_L149_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H51 zenon_H67 zenon_H25 zenon_H33 zenon_H13a zenon_H20 zenon_H134 zenon_Hdc zenon_H8e zenon_H6c zenon_Ha7 zenon_H64 zenon_H5d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L123_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L148_); trivial. % 7.87/8.06 apply (zenon_L21_); trivial. % 7.87/8.06 (* end of lemma zenon_L149_ *) % 7.87/8.06 assert (zenon_L150_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H13b zenon_Ha2 zenon_H130 zenon_H5e zenon_H137 zenon_H131 zenon_Hc7 zenon_H40 zenon_Hfc zenon_H12d zenon_H93 zenon_H4e zenon_H51 zenon_H67 zenon_H25 zenon_H33 zenon_H13a zenon_H20 zenon_H134 zenon_H8e zenon_H6c zenon_Ha7 zenon_H64 zenon_H5d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L142_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_L147_); trivial. % 7.87/8.06 apply (zenon_L149_); trivial. % 7.87/8.06 (* end of lemma zenon_L150_ *) % 7.87/8.06 assert (zenon_L151_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H95 zenon_H67 zenon_H1e zenon_H89 zenon_H6d zenon_H6c zenon_H98 zenon_H12b zenon_H128. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L136_); trivial. % 7.87/8.06 apply (zenon_L138_); trivial. % 7.87/8.06 (* end of lemma zenon_L151_ *) % 7.87/8.06 assert (zenon_L152_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H12d zenon_Hfc zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H48 zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.06 apply (zenon_L9_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.06 apply (zenon_L10_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.06 apply (zenon_L146_); trivial. % 7.87/8.06 apply (zenon_L12_); trivial. % 7.87/8.06 (* end of lemma zenon_L152_ *) % 7.87/8.06 assert (zenon_L153_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Ha7 zenon_H6c zenon_H8e zenon_Hdc zenon_H134 zenon_H10b zenon_H82 zenon_H13a. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.06 apply (zenon_L136_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.06 apply (zenon_L145_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.06 apply (zenon_L115_); trivial. % 7.87/8.06 exact (zenon_H13a zenon_Ha1). % 7.87/8.06 (* end of lemma zenon_L153_ *) % 7.87/8.06 assert (zenon_L154_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6d zenon_H8f zenon_H54 zenon_Hfc zenon_H128. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L38_); trivial. % 7.87/8.06 apply (zenon_L137_); trivial. % 7.87/8.06 (* end of lemma zenon_L154_ *) % 7.87/8.06 assert (zenon_L155_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H36 zenon_H13e zenon_H55. % 7.87/8.06 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.87/8.06 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H55. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H56. % 7.87/8.06 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.06 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e2) (e2)) = (e0)) = ((e1) = (e0))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H58. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H36. % 7.87/8.06 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.06 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H13f zenon_H13e). % 7.87/8.06 apply zenon_H1d. apply refl_equal. % 7.87/8.06 apply zenon_H57. apply refl_equal. % 7.87/8.06 apply zenon_H57. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L155_ *) % 7.87/8.06 assert (zenon_L156_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H64 zenon_Hd6 zenon_H140. % 7.87/8.06 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H64. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hd6. % 7.87/8.06 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 7.87/8.06 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H65. apply refl_equal. % 7.87/8.06 apply zenon_H141. apply sym_equal. exact zenon_H140. % 7.87/8.06 (* end of lemma zenon_L156_ *) % 7.87/8.06 assert (zenon_L157_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hff zenon_H47 zenon_H140 zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.06 apply (zenon_L18_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.06 apply (zenon_L156_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.06 apply (zenon_L113_); trivial. % 7.87/8.06 apply (zenon_L109_); trivial. % 7.87/8.06 (* end of lemma zenon_L157_ *) % 7.87/8.06 assert (zenon_L158_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H36 zenon_H5a zenon_Hff zenon_H140 zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.06 apply (zenon_L9_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.06 apply (zenon_L10_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.06 apply (zenon_L16_); trivial. % 7.87/8.06 apply (zenon_L157_); trivial. % 7.87/8.06 (* end of lemma zenon_L158_ *) % 7.87/8.06 assert (zenon_L159_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H142 zenon_H128 zenon_H8f zenon_H6d zenon_H89 zenon_Haf zenon_Hb0 zenon_H95 zenon_H9c zenon_H99 zenon_H55 zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H36 zenon_H5a zenon_Hff zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.06 apply (zenon_L154_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.06 apply (zenon_L97_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.06 apply (zenon_L155_); trivial. % 7.87/8.06 apply (zenon_L158_); trivial. % 7.87/8.06 (* end of lemma zenon_L159_ *) % 7.87/8.06 assert (zenon_L160_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H51 zenon_H30 zenon_H33 zenon_H5e zenon_Hf1 zenon_Hbc zenon_H64 zenon_Hff zenon_H5a zenon_H55 zenon_H99 zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6d zenon_H8f zenon_H128 zenon_H142 zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H12d zenon_Hfc zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L6_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L159_); trivial. % 7.87/8.06 apply (zenon_L152_); trivial. % 7.87/8.06 (* end of lemma zenon_L160_ *) % 7.87/8.06 assert (zenon_L161_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6d zenon_H6c zenon_H98 zenon_Hfc zenon_H128. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L136_); trivial. % 7.87/8.06 apply (zenon_L137_); trivial. % 7.87/8.06 (* end of lemma zenon_L161_ *) % 7.87/8.06 assert (zenon_L162_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Ha7 zenon_H128 zenon_Hfc zenon_H6c zenon_H6d zenon_H89 zenon_Haf zenon_Hb0 zenon_H95 zenon_Hdc zenon_H134 zenon_H38 zenon_H83 zenon_H13a. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.06 apply (zenon_L161_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.06 apply (zenon_L145_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.06 apply (zenon_L107_); trivial. % 7.87/8.06 exact (zenon_H13a zenon_Ha1). % 7.87/8.06 (* end of lemma zenon_L162_ *) % 7.87/8.06 assert (zenon_L163_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H95 zenon_H67 zenon_H1e zenon_H89 zenon_H6d zenon_H8f zenon_H54 zenon_Hfc zenon_H128. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L38_); trivial. % 7.87/8.06 apply (zenon_L137_); trivial. % 7.87/8.06 (* end of lemma zenon_L163_ *) % 7.87/8.06 assert (zenon_L164_ : (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H67 zenon_H6d zenon_H2d. % 7.87/8.06 cut (((op (e1) (e1)) = (e3)) = ((e0) = (e3))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H67. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H6d. % 7.87/8.06 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.06 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_Heb zenon_H2d). % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L164_ *) % 7.87/8.06 assert (zenon_L165_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H55 zenon_Hd2 zenon_H37. % 7.87/8.06 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H55. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hd2. % 7.87/8.06 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.06 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H145 zenon_H37). % 7.87/8.06 apply zenon_H57. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L165_ *) % 7.87/8.06 assert (zenon_L166_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H61 zenon_H1e zenon_H28 zenon_H6d zenon_H67 zenon_H38 zenon_H36 zenon_H55 zenon_Hd6. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L4_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L164_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_L8_); trivial. % 7.87/8.06 apply (zenon_L69_); trivial. % 7.87/8.06 (* end of lemma zenon_L166_ *) % 7.87/8.06 assert (zenon_L167_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H8f zenon_H92 zenon_Hb2. % 7.87/8.06 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H8f. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H92. % 7.87/8.06 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.06 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb3]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_Hb3 zenon_Hb2). % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L167_ *) % 7.87/8.06 assert (zenon_L168_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H33 zenon_Hc7 zenon_Hf4. % 7.87/8.06 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H33. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hc7. % 7.87/8.06 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 7.87/8.06 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H2f. apply refl_equal. % 7.87/8.06 apply zenon_H146. apply sym_equal. exact zenon_Hf4. % 7.87/8.06 (* end of lemma zenon_L168_ *) % 7.87/8.06 assert (zenon_L169_ : (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H99 zenon_H9f zenon_H13e. % 7.87/8.06 cut (((op (e2) (e2)) = (e2)) = ((e1) = (e2))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H99. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H9f. % 7.87/8.06 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.06 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H13f zenon_H13e). % 7.87/8.06 apply zenon_H22. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L169_ *) % 7.87/8.06 assert (zenon_L170_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hff zenon_H48 zenon_H140 zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.06 apply (zenon_L21_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.06 apply (zenon_L156_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.06 apply (zenon_L113_); trivial. % 7.87/8.06 apply (zenon_L109_); trivial. % 7.87/8.06 (* end of lemma zenon_L170_ *) % 7.87/8.06 assert (zenon_L171_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H13b zenon_H5b zenon_H49 zenon_H137 zenon_H131 zenon_H40 zenon_H12d zenon_H3d zenon_H1e zenon_H4e zenon_H128 zenon_H6d zenon_H89 zenon_Haf zenon_Hb0 zenon_H95 zenon_H55 zenon_H5a zenon_H30 zenon_H51 zenon_H67 zenon_H25 zenon_H20 zenon_H142 zenon_H8f zenon_Hc7 zenon_H33 zenon_H13a zenon_H99 zenon_H134 zenon_H8e zenon_H6c zenon_Ha7 zenon_Hff zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L84_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_L160_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L123_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L148_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.06 apply (zenon_L38_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.06 apply (zenon_L168_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.06 apply (zenon_L136_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.06 apply (zenon_L145_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.06 apply (zenon_L169_); trivial. % 7.87/8.06 exact (zenon_H13a zenon_Ha1). % 7.87/8.06 apply (zenon_L170_); trivial. % 7.87/8.06 (* end of lemma zenon_L171_ *) % 7.87/8.06 assert (zenon_L172_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hc3 zenon_H67 zenon_H1e zenon_H2c zenon_H128 zenon_Hfc zenon_H98 zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_Hbc zenon_H6c. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L104_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_L161_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 (* end of lemma zenon_L172_ *) % 7.87/8.06 assert (zenon_L173_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hc3 zenon_H67 zenon_H1e zenon_H2c zenon_H128 zenon_Hfc zenon_H54 zenon_H8f zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_Hbc zenon_H6c. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L104_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_L154_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 (* end of lemma zenon_L173_ *) % 7.87/8.06 assert (zenon_L174_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H124 zenon_H20 zenon_H25 zenon_H99 zenon_Hcf zenon_Hc3 zenon_H67 zenon_H1e zenon_H2c zenon_H128 zenon_Hfc zenon_H54 zenon_H8f zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_H6c. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_L65_); trivial. % 7.87/8.06 apply (zenon_L173_); trivial. % 7.87/8.06 (* end of lemma zenon_L174_ *) % 7.87/8.06 assert (zenon_L175_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H10b zenon_Hcf zenon_H13e. % 7.87/8.06 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H10b. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hcf. % 7.87/8.06 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 7.87/8.06 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H85. apply refl_equal. % 7.87/8.06 apply zenon_H147. apply sym_equal. exact zenon_H13e. % 7.87/8.06 (* end of lemma zenon_L175_ *) % 7.87/8.06 assert (zenon_L176_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H13b zenon_H5e zenon_Hf1 zenon_Hbc zenon_H64 zenon_Hff zenon_H10b zenon_Hcf zenon_H99 zenon_H124 zenon_H20 zenon_H25 zenon_Hc3 zenon_H67 zenon_H1e zenon_H2c zenon_H8f zenon_H142 zenon_H55 zenon_H4e zenon_H3d zenon_H40 zenon_H5a zenon_H33 zenon_H8e zenon_H51 zenon_Ha7 zenon_H128 zenon_Hfc zenon_H6c zenon_H6d zenon_H89 zenon_Haf zenon_Hb0 zenon_H95 zenon_H134 zenon_H38 zenon_H83 zenon_H13a. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L123_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L159_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.06 apply (zenon_L174_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.06 apply (zenon_L97_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.06 apply (zenon_L175_); trivial. % 7.87/8.06 apply (zenon_L170_); trivial. % 7.87/8.06 apply (zenon_L162_); trivial. % 7.87/8.06 (* end of lemma zenon_L176_ *) % 7.87/8.06 assert (zenon_L177_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hf8 zenon_Hcf zenon_He0. % 7.87/8.06 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_Hf8. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hcf. % 7.87/8.06 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 7.87/8.06 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H85. apply refl_equal. % 7.87/8.06 apply zenon_He1. apply sym_equal. exact zenon_He0. % 7.87/8.06 (* end of lemma zenon_L177_ *) % 7.87/8.06 assert (zenon_L178_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H5a zenon_H9f zenon_H148. % 7.87/8.06 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H5a. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H9f. % 7.87/8.06 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 apply zenon_H149. apply sym_equal. exact zenon_H148. % 7.87/8.06 (* end of lemma zenon_L178_ *) % 7.87/8.06 assert (zenon_L179_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H14a zenon_H41 zenon_H131 zenon_Hcf zenon_H9f zenon_H5a zenon_Hb0 zenon_Hf8. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H44 | zenon_intro zenon_H14b ]. % 7.87/8.06 apply (zenon_L143_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_He0 | zenon_intro zenon_H14c ]. % 7.87/8.06 apply (zenon_L177_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H148 | zenon_intro zenon_Hf7 ]. % 7.87/8.06 apply (zenon_L178_); trivial. % 7.87/8.06 apply (zenon_L108_); trivial. % 7.87/8.06 (* end of lemma zenon_L179_ *) % 7.87/8.06 assert (zenon_L180_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H51 zenon_H1e zenon_H30 zenon_H25 zenon_H33 zenon_H20 zenon_H9f zenon_H47 zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L6_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L44_); trivial. % 7.87/8.06 apply (zenon_L12_); trivial. % 7.87/8.06 (* end of lemma zenon_L180_ *) % 7.87/8.06 assert (zenon_L181_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Ha7 zenon_H6c zenon_H8e zenon_Hdc zenon_H134 zenon_H49 zenon_H20 zenon_H33 zenon_H25 zenon_H30 zenon_H1e zenon_H51 zenon_H117 zenon_H43 zenon_Hcf zenon_H38 zenon_H81 zenon_Hb0 zenon_H14a zenon_H131 zenon_H5a zenon_Hf8 zenon_Hb2 zenon_H55 zenon_H4e zenon_H13a. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.06 apply (zenon_L136_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.06 apply (zenon_L145_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.06 apply (zenon_L50_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.06 apply (zenon_L179_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.06 apply (zenon_L133_); trivial. % 7.87/8.06 apply (zenon_L180_); trivial. % 7.87/8.06 exact (zenon_H13a zenon_Ha1). % 7.87/8.06 (* end of lemma zenon_L181_ *) % 7.87/8.06 assert (zenon_L182_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hd8 zenon_H99 zenon_H5b zenon_H8f zenon_H6d zenon_H81 zenon_Hcf zenon_H55 zenon_H5d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.06 apply (zenon_L71_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.06 apply (zenon_L68_); trivial. % 7.87/8.06 apply (zenon_L69_); trivial. % 7.87/8.06 (* end of lemma zenon_L182_ *) % 7.87/8.06 assert (zenon_L183_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hc3 zenon_H67 zenon_H1e zenon_H2c zenon_H128 zenon_Hfc zenon_H98 zenon_H6c zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_He3 zenon_H8f. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L104_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_L161_); trivial. % 7.87/8.06 apply (zenon_L89_); trivial. % 7.87/8.06 (* end of lemma zenon_L183_ *) % 7.87/8.06 assert (zenon_L184_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H13b zenon_H20 zenon_H25 zenon_Ha2 zenon_H130 zenon_Hf4 zenon_H99 zenon_Ha7 zenon_H6c zenon_H8e zenon_H134 zenon_H10b zenon_H82 zenon_H13a. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L142_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_L97_); trivial. % 7.87/8.06 apply (zenon_L153_); trivial. % 7.87/8.06 (* end of lemma zenon_L184_ *) % 7.87/8.06 assert (zenon_L185_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hca zenon_H6e zenon_H9c. % 7.87/8.06 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_Hca. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H6e. % 7.87/8.06 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H8b. apply refl_equal. % 7.87/8.06 apply zenon_H14d. apply sym_equal. exact zenon_H9c. % 7.87/8.06 (* end of lemma zenon_L185_ *) % 7.87/8.06 assert (zenon_L186_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hbd zenon_He3 zenon_H140. % 7.87/8.06 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_Hbd. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_He3. % 7.87/8.06 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 7.87/8.06 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H105. apply refl_equal. % 7.87/8.06 apply zenon_H141. apply sym_equal. exact zenon_H140. % 7.87/8.06 (* end of lemma zenon_L186_ *) % 7.87/8.06 assert (zenon_L187_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hfc zenon_H14e zenon_H49. % 7.87/8.06 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H49. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H4a. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H4c. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hfc. % 7.87/8.06 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 7.87/8.06 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 apply zenon_H14f. apply sym_equal. exact zenon_H14e. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 apply zenon_H4b. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L187_ *) % 7.87/8.06 assert (zenon_L188_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H150 zenon_H47 zenon_He3 zenon_Hbd zenon_H64 zenon_Ha2 zenon_Hfc zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H48 | zenon_intro zenon_H151 ]. % 7.87/8.06 apply (zenon_L12_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H140 | zenon_intro zenon_H152 ]. % 7.87/8.06 apply (zenon_L186_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H14e ]. % 7.87/8.06 apply (zenon_L45_); trivial. % 7.87/8.06 apply (zenon_L187_); trivial. % 7.87/8.06 (* end of lemma zenon_L188_ *) % 7.87/8.06 assert (zenon_L189_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H55 zenon_Hde zenon_H37 zenon_H43 zenon_H150 zenon_He3 zenon_Hbd zenon_H64 zenon_Ha2 zenon_Hfc zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.06 apply (zenon_L9_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.06 apply (zenon_L79_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.06 apply (zenon_L11_); trivial. % 7.87/8.06 apply (zenon_L188_); trivial. % 7.87/8.06 (* end of lemma zenon_L189_ *) % 7.87/8.06 assert (zenon_L190_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H5a zenon_H13e zenon_He0. % 7.87/8.06 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H5a. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H13e. % 7.87/8.06 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 apply zenon_He1. apply sym_equal. exact zenon_He0. % 7.87/8.06 (* end of lemma zenon_L190_ *) % 7.87/8.06 assert (zenon_L191_ : (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H8f zenon_Hfc zenon_He2. % 7.87/8.06 cut (((op (e3) (e3)) = (e3)) = ((e1) = (e3))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H8f. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hfc. % 7.87/8.06 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.06 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 7.87/8.06 congruence. % 7.87/8.06 exact (zenon_H153 zenon_He2). % 7.87/8.06 apply zenon_H69. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L191_ *) % 7.87/8.06 assert (zenon_L192_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_H11e zenon_Hbb zenon_H9c zenon_Hca zenon_H82 zenon_H81 zenon_He7 zenon_H99 zenon_H93 zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H150 zenon_H43 zenon_H37 zenon_H55 zenon_H3d zenon_H1e zenon_H4e zenon_H13e zenon_H5a zenon_H8f zenon_Hfc. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L185_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_L35_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.87/8.06 apply (zenon_L78_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.87/8.06 apply (zenon_L189_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.87/8.06 apply (zenon_L190_); trivial. % 7.87/8.06 apply (zenon_L191_); trivial. % 7.87/8.06 (* end of lemma zenon_L192_ *) % 7.87/8.06 assert (zenon_L193_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H150 zenon_H5d zenon_H64 zenon_He3 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H48 | zenon_intro zenon_H151 ]. % 7.87/8.06 apply (zenon_L21_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H140 | zenon_intro zenon_H152 ]. % 7.87/8.06 apply (zenon_L186_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H14e ]. % 7.87/8.06 exact (zenon_H13a zenon_Ha1). % 7.87/8.06 apply (zenon_L187_); trivial. % 7.87/8.06 (* end of lemma zenon_L193_ *) % 7.87/8.06 assert (zenon_L194_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hff zenon_H48 zenon_H64 zenon_He3 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.06 apply (zenon_L21_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.06 apply (zenon_L93_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.06 apply (zenon_L113_); trivial. % 7.87/8.06 apply (zenon_L109_); trivial. % 7.87/8.06 (* end of lemma zenon_L194_ *) % 7.87/8.06 assert (zenon_L195_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hd6 zenon_Hbb zenon_H154. % 7.87/8.06 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H65 ]. % 7.87/8.06 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H154. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hf2. % 7.87/8.06 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.87/8.06 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H155. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_Hd6. % 7.87/8.06 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 7.87/8.06 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H65. apply refl_equal. % 7.87/8.06 apply zenon_H156. apply sym_equal. exact zenon_Hbb. % 7.87/8.06 apply zenon_H65. apply refl_equal. % 7.87/8.06 apply zenon_H65. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L195_ *) % 7.87/8.06 assert (zenon_L196_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hff zenon_H154 zenon_Hbb zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H47 zenon_H150 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.06 apply (zenon_L18_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.06 apply (zenon_L195_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.06 apply (zenon_L188_); trivial. % 7.87/8.06 apply (zenon_L109_); trivial. % 7.87/8.06 (* end of lemma zenon_L196_ *) % 7.87/8.06 assert (zenon_L197_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H157 zenon_H158 zenon_H13a zenon_Hf1 zenon_Hbc zenon_Hff zenon_H154 zenon_Hbb zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H150 zenon_Hfc zenon_H5e. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 7.87/8.06 exact (zenon_H158 zenon_H15a). % 7.87/8.06 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 7.87/8.06 apply (zenon_L193_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 7.87/8.06 apply (zenon_L194_); trivial. % 7.87/8.06 apply (zenon_L196_); trivial. % 7.87/8.06 (* end of lemma zenon_L197_ *) % 7.87/8.06 assert (zenon_L198_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hd8 zenon_H99 zenon_H5b zenon_H8f zenon_H6d zenon_H37 zenon_H55 zenon_He3 zenon_Hf1. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.06 apply (zenon_L71_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.06 apply (zenon_L165_); trivial. % 7.87/8.06 apply (zenon_L93_); trivial. % 7.87/8.06 (* end of lemma zenon_L198_ *) % 7.87/8.06 assert (zenon_L199_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H61 zenon_H20 zenon_H25 zenon_H2c zenon_Hf1 zenon_H55 zenon_H6d zenon_H8f zenon_H5b zenon_H99 zenon_Hd8 zenon_H150 zenon_H64 zenon_He3 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L17_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L5_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_L198_); trivial. % 7.87/8.06 apply (zenon_L193_); trivial. % 7.87/8.06 (* end of lemma zenon_L199_ *) % 7.87/8.06 assert (zenon_L200_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H15c zenon_H8e zenon_H10e. % 7.87/8.06 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H10e. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H39. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 7.87/8.06 congruence. % 7.87/8.06 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_H10f. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H15c. % 7.87/8.06 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 7.87/8.06 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 apply zenon_H15d. apply sym_equal. exact zenon_H8e. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 apply zenon_H3a. apply refl_equal. % 7.87/8.06 (* end of lemma zenon_L200_ *) % 7.87/8.06 assert (zenon_L201_ : ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H15e zenon_H10e zenon_Hb5 zenon_Hb6 zenon_Hd8 zenon_H20 zenon_H1e zenon_H25 zenon_Hec zenon_H61 zenon_H64 zenon_H5e zenon_H81 zenon_H13b zenon_H10b zenon_Ha7 zenon_H33 zenon_H38 zenon_H4e zenon_H49 zenon_H131 zenon_H134 zenon_H12d zenon_Hfc zenon_H137 zenon_H40 zenon_H3d zenon_H51 zenon_H130 zenon_H11e zenon_H2c zenon_H28 zenon_H67 zenon_H89 zenon_H6d zenon_H6c zenon_H12b zenon_H128 zenon_H95 zenon_H99 zenon_Hc3 zenon_H30 zenon_H142 zenon_H5a zenon_Hff zenon_Hf1 zenon_H55 zenon_Haf zenon_H8f zenon_H124 zenon_H14a zenon_Hf8 zenon_H117 zenon_H43 zenon_Hca zenon_He7 zenon_H150 zenon_Hbd zenon_H157 zenon_H154 zenon_H158 zenon_H15f. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.87/8.06 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.06 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.06 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L151_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L4_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L5_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_L35_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L142_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L123_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L8_); trivial. % 7.87/8.06 apply (zenon_L152_); trivial. % 7.87/8.06 apply (zenon_L153_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_L35_); trivial. % 7.87/8.06 apply (zenon_L150_); trivial. % 7.87/8.06 apply (zenon_L137_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_L160_); trivial. % 7.87/8.06 apply (zenon_L162_); trivial. % 7.87/8.06 apply (zenon_L113_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.06 apply (zenon_L163_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L17_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L164_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.06 apply (zenon_L61_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.06 apply (zenon_L165_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L84_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.06 apply (zenon_L123_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.06 apply (zenon_L7_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.06 apply (zenon_L166_); trivial. % 7.87/8.06 apply (zenon_L152_); trivial. % 7.87/8.06 apply (zenon_L153_); trivial. % 7.87/8.06 apply (zenon_L59_); trivial. % 7.87/8.06 apply (zenon_L167_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L151_); trivial. % 7.87/8.06 apply (zenon_L78_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L104_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L171_); trivial. % 7.87/8.06 apply (zenon_L167_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L172_); trivial. % 7.87/8.06 apply (zenon_L78_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.06 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_L65_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L172_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_L176_); trivial. % 7.87/8.06 apply (zenon_L113_); trivial. % 7.87/8.06 apply (zenon_L39_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.06 apply (zenon_L174_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_L65_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L4_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L5_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.06 apply (zenon_L71_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.06 apply (zenon_L165_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.06 apply (zenon_L38_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.06 apply (zenon_L97_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.06 apply (zenon_L175_); trivial. % 7.87/8.06 apply (zenon_L156_); trivial. % 7.87/8.06 apply (zenon_L181_); trivial. % 7.87/8.06 apply (zenon_L182_); trivial. % 7.87/8.06 apply (zenon_L167_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L172_); trivial. % 7.87/8.06 apply (zenon_L78_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.06 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L183_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L49_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L66_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.06 apply (zenon_L4_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.06 apply (zenon_L164_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.06 apply (zenon_L116_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.06 apply (zenon_L26_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.06 apply (zenon_L35_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.06 apply (zenon_L3_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.06 apply (zenon_L142_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.06 apply (zenon_L38_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.06 apply (zenon_L184_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.06 apply (zenon_L192_); trivial. % 7.87/8.06 apply (zenon_L186_); trivial. % 7.87/8.06 apply (zenon_L153_); trivial. % 7.87/8.06 apply (zenon_L193_); trivial. % 7.87/8.06 apply (zenon_L39_); trivial. % 7.87/8.06 apply (zenon_L89_); trivial. % 7.87/8.06 apply (zenon_L197_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L199_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L183_); trivial. % 7.87/8.06 apply (zenon_L105_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.06 apply (zenon_L2_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.06 apply (zenon_L199_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.06 apply (zenon_L183_); trivial. % 7.87/8.06 apply (zenon_L78_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.06 apply (zenon_L200_); trivial. % 7.87/8.06 apply (zenon_L137_); trivial. % 7.87/8.06 (* end of lemma zenon_L201_ *) % 7.87/8.06 assert (zenon_L202_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.06 do 0 intro. intros zenon_H5e zenon_Hfc zenon_H81 zenon_H15e zenon_H10e zenon_Hb5 zenon_Hb6 zenon_Hd8 zenon_H20 zenon_H1e zenon_H25 zenon_Hec zenon_H61 zenon_H64 zenon_H13b zenon_H10b zenon_Ha7 zenon_H33 zenon_H38 zenon_H4e zenon_H49 zenon_H131 zenon_H134 zenon_H12d zenon_H137 zenon_H40 zenon_H3d zenon_H51 zenon_H130 zenon_H11e zenon_H2c zenon_H28 zenon_H67 zenon_H89 zenon_H12b zenon_H128 zenon_H95 zenon_H99 zenon_Hc3 zenon_H30 zenon_H142 zenon_H5a zenon_Hff zenon_Hf1 zenon_H55 zenon_Haf zenon_H8f zenon_H124 zenon_H14a zenon_Hf8 zenon_H117 zenon_H43 zenon_Hca zenon_He7 zenon_H150 zenon_Hbd zenon_H157 zenon_H154 zenon_H158 zenon_H15f zenon_Hbb zenon_H162 zenon_Hbc zenon_H6c. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.06 apply (zenon_L36_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.06 apply (zenon_L66_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.06 apply (zenon_L201_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.06 apply (zenon_L120_); trivial. % 7.87/8.06 apply (zenon_L109_); trivial. % 7.87/8.06 apply (zenon_L57_); trivial. % 7.87/8.06 (* end of lemma zenon_L202_ *) % 7.87/8.06 assert (zenon_L203_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hd8 zenon_H8f zenon_H88 zenon_H2c zenon_Hc7 zenon_H37 zenon_H55 zenon_H165. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.06 apply (zenon_L66_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.06 apply (zenon_L61_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.06 apply (zenon_L165_); trivial. % 7.87/8.06 exact (zenon_H165 zenon_Hd6). % 7.87/8.06 (* end of lemma zenon_L203_ *) % 7.87/8.06 assert (zenon_L204_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H6c zenon_H9c zenon_H12b zenon_H12d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.06 apply (zenon_L37_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.06 apply (zenon_L43_); trivial. % 7.87/8.06 apply (zenon_L140_); trivial. % 7.87/8.06 (* end of lemma zenon_L204_ *) % 7.87/8.06 assert (zenon_L205_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 7.87/8.06 do 0 intro. intros zenon_Hef zenon_H6d zenon_H115. % 7.87/8.06 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 7.87/8.06 intro zenon_D_pnotp. % 7.87/8.06 apply zenon_Hef. % 7.87/8.06 rewrite <- zenon_D_pnotp. % 7.87/8.06 exact zenon_H6d. % 7.87/8.06 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 7.87/8.06 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.06 congruence. % 7.87/8.06 apply zenon_H8b. apply refl_equal. % 7.87/8.06 apply zenon_H116. apply sym_equal. exact zenon_H115. % 7.87/8.06 (* end of lemma zenon_L205_ *) % 7.87/8.06 assert (zenon_L206_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.06 do 0 intro. intros zenon_Haa zenon_H67 zenon_H25 zenon_H115 zenon_Hef zenon_H6c zenon_H9c zenon_H12b zenon_H12d. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.06 apply (zenon_L24_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.06 apply (zenon_L205_); trivial. % 7.87/8.06 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.06 apply (zenon_L43_); trivial. % 7.87/8.06 apply (zenon_L140_); trivial. % 7.87/8.06 (* end of lemma zenon_L206_ *) % 7.87/8.06 assert (zenon_L207_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H162 zenon_H15f zenon_H158 zenon_H154 zenon_H157 zenon_Hbd zenon_H150 zenon_He7 zenon_Hca zenon_H43 zenon_H117 zenon_Hf8 zenon_H14a zenon_H124 zenon_H8f zenon_Haf zenon_H55 zenon_Hf1 zenon_Hff zenon_H5a zenon_H142 zenon_H30 zenon_Hc3 zenon_H99 zenon_H95 zenon_H128 zenon_H89 zenon_H28 zenon_H2c zenon_H11e zenon_H130 zenon_H51 zenon_H3d zenon_H40 zenon_H137 zenon_H134 zenon_H131 zenon_H49 zenon_H4e zenon_H38 zenon_H33 zenon_Ha7 zenon_H10b zenon_H13b zenon_H81 zenon_H64 zenon_H61 zenon_Hec zenon_H1e zenon_H20 zenon_Hd8 zenon_Hb6 zenon_Hb5 zenon_H10e zenon_H15e zenon_H12d zenon_H12b zenon_H9c zenon_H6c zenon_Hef zenon_H25 zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L204_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L201_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_L206_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L207_ *) % 7.87/8.07 assert (zenon_L208_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.07 do 0 intro. intros zenon_Haa zenon_H67 zenon_H89 zenon_H88 zenon_Hca zenon_H36 zenon_Hc7 zenon_H2c zenon_H25 zenon_Hcc zenon_H6c zenon_Hdc. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.07 apply (zenon_L24_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.07 apply (zenon_L37_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.07 apply (zenon_L63_); trivial. % 7.87/8.07 apply (zenon_L73_); trivial. % 7.87/8.07 (* end of lemma zenon_L208_ *) % 7.87/8.07 assert (zenon_L209_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H51 zenon_H55 zenon_H54 zenon_H33 zenon_Hdc zenon_H6c zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_Hca zenon_H88 zenon_H89 zenon_H67 zenon_Haa zenon_H64 zenon_H5d. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.07 apply (zenon_L15_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.07 apply (zenon_L7_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.07 apply (zenon_L208_); trivial. % 7.87/8.07 apply (zenon_L21_); trivial. % 7.87/8.07 (* end of lemma zenon_L209_ *) % 7.87/8.07 assert (zenon_L210_ : ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H5b zenon_H165 zenon_H5e zenon_Hfc zenon_Hef zenon_H12b zenon_H12d zenon_H15e zenon_H10e zenon_Hb5 zenon_Hb6 zenon_Hd8 zenon_H20 zenon_H1e zenon_Hec zenon_H61 zenon_H81 zenon_H13b zenon_H10b zenon_Ha7 zenon_H38 zenon_H4e zenon_H49 zenon_H131 zenon_H134 zenon_H137 zenon_H40 zenon_H3d zenon_H130 zenon_H11e zenon_H28 zenon_H128 zenon_H95 zenon_H99 zenon_Hc3 zenon_H30 zenon_H142 zenon_H5a zenon_Hff zenon_Hf1 zenon_Haf zenon_H8f zenon_H124 zenon_H14a zenon_Hf8 zenon_H117 zenon_H43 zenon_He7 zenon_H150 zenon_Hbd zenon_H157 zenon_H154 zenon_H158 zenon_H15f zenon_H162 zenon_H51 zenon_H55 zenon_H54 zenon_H33 zenon_H6c zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_Hca zenon_H88 zenon_H89 zenon_H67 zenon_Haa zenon_H64. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.07 apply (zenon_L17_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.07 apply (zenon_L5_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.07 apply (zenon_L203_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.07 apply (zenon_L3_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.07 apply (zenon_L141_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.07 apply (zenon_L207_); trivial. % 7.87/8.07 apply (zenon_L209_); trivial. % 7.87/8.07 (* end of lemma zenon_L210_ *) % 7.87/8.07 assert (zenon_L211_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H61 zenon_H28 zenon_H165 zenon_H8f zenon_Hd8 zenon_H13b zenon_H12b zenon_H1e zenon_H30 zenon_H5e zenon_H137 zenon_H131 zenon_H40 zenon_H134 zenon_Hfc zenon_H12d zenon_H93 zenon_H20 zenon_H4e zenon_H51 zenon_H55 zenon_H54 zenon_H33 zenon_H6c zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_Hca zenon_H88 zenon_H89 zenon_H67 zenon_Haa zenon_H64. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.07 apply (zenon_L4_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.07 apply (zenon_L5_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.07 apply (zenon_L203_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.07 apply (zenon_L3_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.07 apply (zenon_L141_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.07 apply (zenon_L147_); trivial. % 7.87/8.07 apply (zenon_L209_); trivial. % 7.87/8.07 (* end of lemma zenon_L211_ *) % 7.87/8.07 assert (zenon_L212_ : ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H98 zenon_H1f zenon_H30. % 7.87/8.07 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H166 | zenon_intro zenon_H167 ]. % 7.87/8.07 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e0) (e0)) = (op (e2) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H30. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H166. % 7.87/8.07 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 7.87/8.07 cut (((op (e2) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e0) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H168. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H98. % 7.87/8.07 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 7.87/8.07 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H167. apply refl_equal. % 7.87/8.07 apply zenon_H169. apply sym_equal. exact zenon_H1f. % 7.87/8.07 apply zenon_H167. apply refl_equal. % 7.87/8.07 apply zenon_H167. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L212_ *) % 7.87/8.07 assert (zenon_L213_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H28 zenon_H86 zenon_H88. % 7.87/8.07 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H28. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H86. % 7.87/8.07 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 7.87/8.07 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H2b. apply refl_equal. % 7.87/8.07 apply zenon_H8d. apply sym_equal. exact zenon_H88. % 7.87/8.07 (* end of lemma zenon_L213_ *) % 7.87/8.07 assert (zenon_L214_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H30 zenon_H86 zenon_H8e. % 7.87/8.07 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H30. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H86. % 7.87/8.07 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 7.87/8.07 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H2b. apply refl_equal. % 7.87/8.07 apply zenon_H15d. apply sym_equal. exact zenon_H8e. % 7.87/8.07 (* end of lemma zenon_L214_ *) % 7.87/8.07 assert (zenon_L215_ : (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H67 zenon_H15c zenon_H36. % 7.87/8.07 cut (((op (e2) (e2)) = (e3)) = ((e0) = (e3))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H67. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H15c. % 7.87/8.07 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.07 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 7.87/8.07 congruence. % 7.87/8.07 exact (zenon_H16a zenon_H36). % 7.87/8.07 apply zenon_H69. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L215_ *) % 7.87/8.07 assert (zenon_L216_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H16b zenon_H86 zenon_H30 zenon_H6d zenon_Hca zenon_H36 zenon_H67 zenon_Hfc zenon_H49. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 7.87/8.07 apply (zenon_L214_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 7.87/8.07 apply (zenon_L62_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 7.87/8.07 apply (zenon_L215_); trivial. % 7.87/8.07 apply (zenon_L187_); trivial. % 7.87/8.07 (* end of lemma zenon_L216_ *) % 7.87/8.07 assert (zenon_L217_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H16e zenon_H86 zenon_H66. % 7.87/8.07 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H16e. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H86. % 7.87/8.07 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 7.87/8.07 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H2b. apply refl_equal. % 7.87/8.07 apply zenon_Hf6. apply sym_equal. exact zenon_H66. % 7.87/8.07 (* end of lemma zenon_L217_ *) % 7.87/8.07 assert (zenon_L218_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Haa zenon_H86 zenon_H16e zenon_H115 zenon_Hef zenon_Hca zenon_H36 zenon_Hc7 zenon_H2c zenon_H25 zenon_Hcc zenon_Hfc zenon_H12d. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.07 apply (zenon_L217_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.07 apply (zenon_L205_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.07 apply (zenon_L63_); trivial. % 7.87/8.07 apply (zenon_L139_); trivial. % 7.87/8.07 (* end of lemma zenon_L218_ *) % 7.87/8.07 assert (zenon_L219_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H162 zenon_H28 zenon_H49 zenon_H67 zenon_H30 zenon_H16b zenon_H12d zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_H36 zenon_Hca zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L213_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L216_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_L218_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L219_ *) % 7.87/8.07 assert (zenon_L220_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H162 zenon_H8f zenon_Hbb zenon_H49 zenon_H67 zenon_H30 zenon_H16b zenon_H12d zenon_Hcc zenon_H25 zenon_H2c zenon_Hc7 zenon_H36 zenon_Hca zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L66_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L216_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_L218_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L220_ *) % 7.87/8.07 assert (zenon_L221_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hc6 zenon_Hbb zenon_H89. % 7.87/8.07 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 7.87/8.07 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H89. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H8a. % 7.87/8.07 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.07 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H8c. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_Hc6. % 7.87/8.07 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 7.87/8.07 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H8b. apply refl_equal. % 7.87/8.07 apply zenon_H156. apply sym_equal. exact zenon_Hbb. % 7.87/8.07 apply zenon_H8b. apply refl_equal. % 7.87/8.07 apply zenon_H8b. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L221_ *) % 7.87/8.07 assert (zenon_L222_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H162 zenon_H8f zenon_Hbb zenon_H49 zenon_H67 zenon_Hca zenon_H30 zenon_H16b zenon_H12d zenon_H36 zenon_H6e zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L66_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L216_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.07 apply (zenon_L217_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.07 apply (zenon_L205_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.07 apply (zenon_L29_); trivial. % 7.87/8.07 apply (zenon_L139_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L222_ *) % 7.87/8.07 assert (zenon_L223_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H15a zenon_Hbc zenon_H20. % 7.87/8.07 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.07 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H20. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H21. % 7.87/8.07 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.07 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H23. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H15a. % 7.87/8.07 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.07 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H16f]. % 7.87/8.07 congruence. % 7.87/8.07 exact (zenon_H16f zenon_Hbc). % 7.87/8.07 apply zenon_H1d. apply refl_equal. % 7.87/8.07 apply zenon_H22. apply refl_equal. % 7.87/8.07 apply zenon_H22. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L223_ *) % 7.87/8.07 assert (zenon_L224_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H154 zenon_H29 zenon_H5d. % 7.87/8.07 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H154. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H29. % 7.87/8.07 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 7.87/8.07 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H114. apply refl_equal. % 7.87/8.07 apply zenon_H60. apply sym_equal. exact zenon_H5d. % 7.87/8.07 (* end of lemma zenon_L224_ *) % 7.87/8.07 assert (zenon_L225_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H40 zenon_H26 zenon_Hdc. % 7.87/8.07 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H40. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H26. % 7.87/8.07 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 7.87/8.07 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H2f. apply refl_equal. % 7.87/8.07 apply zenon_H135. apply sym_equal. exact zenon_Hdc. % 7.87/8.07 (* end of lemma zenon_L225_ *) % 7.87/8.07 assert (zenon_L226_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H33 zenon_H66 zenon_H70. % 7.87/8.07 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H33. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H66. % 7.87/8.07 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 7.87/8.07 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H2f. apply refl_equal. % 7.87/8.07 apply zenon_Hcb. apply sym_equal. exact zenon_H70. % 7.87/8.07 (* end of lemma zenon_L226_ *) % 7.87/8.07 assert (zenon_L227_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H170 zenon_H2d zenon_H2c zenon_Hf4 zenon_Hdc zenon_H40 zenon_H33 zenon_H70. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H25 | zenon_intro zenon_H171 ]. % 7.87/8.07 apply (zenon_L5_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H172 ]. % 7.87/8.07 apply (zenon_L168_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H26 | zenon_intro zenon_H66 ]. % 7.87/8.07 apply (zenon_L225_); trivial. % 7.87/8.07 apply (zenon_L226_); trivial. % 7.87/8.07 (* end of lemma zenon_L227_ *) % 7.87/8.07 assert (zenon_L228_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hca zenon_Hc6 zenon_Hf4. % 7.87/8.07 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_Hca. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_Hc6. % 7.87/8.07 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 7.87/8.07 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H8b. apply refl_equal. % 7.87/8.07 apply zenon_H146. apply sym_equal. exact zenon_Hf4. % 7.87/8.07 (* end of lemma zenon_L228_ *) % 7.87/8.07 assert (zenon_L229_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hff zenon_H48 zenon_H64 zenon_H165 zenon_H6e zenon_H130 zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.07 apply (zenon_L21_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.07 exact (zenon_H165 zenon_Hd6). % 7.87/8.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_L142_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L229_ *) % 7.87/8.07 assert (zenon_L230_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hcc zenon_H33 zenon_H40 zenon_Hdc zenon_H2c zenon_H170 zenon_Hf4 zenon_H5e zenon_Hfc zenon_H130 zenon_H165 zenon_H64 zenon_H48 zenon_Hff zenon_Hca zenon_H70. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.07 apply (zenon_L227_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.07 apply (zenon_L228_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.07 apply (zenon_L229_); trivial. % 7.87/8.07 apply (zenon_L62_); trivial. % 7.87/8.07 (* end of lemma zenon_L230_ *) % 7.87/8.07 assert (zenon_L231_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H173 zenon_H6e zenon_Hdc. % 7.87/8.07 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H173. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H6e. % 7.87/8.07 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 7.87/8.07 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H8b. apply refl_equal. % 7.87/8.07 apply zenon_H135. apply sym_equal. exact zenon_Hdc. % 7.87/8.07 (* end of lemma zenon_L231_ *) % 7.87/8.07 assert (zenon_L232_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H174 zenon_H6d. % 7.87/8.07 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 7.87/8.07 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 7.87/8.07 congruence. % 7.87/8.07 exact (zenon_Hdb zenon_H6d). % 7.87/8.07 exact (zenon_Hdb zenon_H6d). % 7.87/8.07 (* end of lemma zenon_L232_ *) % 7.87/8.07 assert (zenon_L233_ : (~((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H175 zenon_H6d. % 7.87/8.07 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.07 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 7.87/8.07 congruence. % 7.87/8.07 exact (zenon_Hdb zenon_H6d). % 7.87/8.07 apply zenon_H57. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L233_ *) % 7.87/8.07 assert (zenon_L234_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (e1)) (e1)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hdc zenon_H6d zenon_H176. % 7.87/8.07 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 7.87/8.07 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e2) = (op (op (e1) (e1)) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H176. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H72. % 7.87/8.07 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 7.87/8.07 cut (((op (op (e1) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (e1)) (e1)) = (e2))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H177. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_Hdc. % 7.87/8.07 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.07 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 7.87/8.07 congruence. % 7.87/8.07 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 7.87/8.07 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H178. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H72. % 7.87/8.07 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 7.87/8.07 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 7.87/8.07 congruence. % 7.87/8.07 apply (zenon_L233_); trivial. % 7.87/8.07 apply zenon_H73. apply refl_equal. % 7.87/8.07 apply zenon_H73. apply refl_equal. % 7.87/8.07 apply zenon_H22. apply refl_equal. % 7.87/8.07 apply zenon_H73. apply refl_equal. % 7.87/8.07 apply zenon_H73. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L234_ *) % 7.87/8.07 assert (zenon_L235_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H47 zenon_Hdc zenon_H6d. % 7.87/8.07 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H78 | zenon_intro zenon_H179 ]. % 7.87/8.07 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 7.87/8.07 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e0) = (op (op (e1) (e1)) (op (e1) (e1))))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H78. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H79. % 7.87/8.07 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 7.87/8.07 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e3) (e3)) = (e0)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e0))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H7b. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H47. % 7.87/8.07 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.07 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 7.87/8.07 congruence. % 7.87/8.07 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 7.87/8.07 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H17a. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H79. % 7.87/8.07 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 7.87/8.07 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 7.87/8.07 congruence. % 7.87/8.07 apply (zenon_L232_); trivial. % 7.87/8.07 apply zenon_H7a. apply refl_equal. % 7.87/8.07 apply zenon_H7a. apply refl_equal. % 7.87/8.07 apply zenon_H1d. apply refl_equal. % 7.87/8.07 apply zenon_H7a. apply refl_equal. % 7.87/8.07 apply zenon_H7a. apply refl_equal. % 7.87/8.07 apply (zenon_notand_s _ _ zenon_H179); [ zenon_intro zenon_H17b | zenon_intro zenon_H176 ]. % 7.87/8.07 apply zenon_H17b. apply sym_equal. exact zenon_H6d. % 7.87/8.07 apply (zenon_L234_); trivial. % 7.87/8.07 (* end of lemma zenon_L235_ *) % 7.87/8.07 assert (zenon_L236_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hcc zenon_H25 zenon_H2c zenon_H89 zenon_Hbb zenon_H173 zenon_H47 zenon_Hdc. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.07 apply (zenon_L5_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.07 apply (zenon_L221_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.07 apply (zenon_L231_); trivial. % 7.87/8.07 apply (zenon_L235_); trivial. % 7.87/8.07 (* end of lemma zenon_L236_ *) % 7.87/8.07 assert (zenon_L237_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H13b zenon_H16e zenon_H99 zenon_H162 zenon_H8f zenon_H49 zenon_H36 zenon_H30 zenon_H86 zenon_H16b zenon_H12d zenon_H157 zenon_H20 zenon_Hbc zenon_H29 zenon_H154 zenon_Hca zenon_Hff zenon_H64 zenon_H165 zenon_H130 zenon_Hf4 zenon_H170 zenon_H40 zenon_H33 zenon_Hcc zenon_H25 zenon_H2c zenon_H89 zenon_Hbb zenon_H173 zenon_Hef zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.07 apply (zenon_L3_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.07 apply (zenon_L222_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.07 apply (zenon_L97_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L66_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L216_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.07 apply (zenon_L24_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.07 apply (zenon_L205_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 7.87/8.07 apply (zenon_L223_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 7.87/8.07 apply (zenon_L224_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 7.87/8.07 apply (zenon_L230_); trivial. % 7.87/8.07 apply (zenon_L236_); trivial. % 7.87/8.07 apply (zenon_L139_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L237_ *) % 7.87/8.07 assert (zenon_L238_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H9c zenon_H98 zenon_H17c. % 7.87/8.07 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H136 ]. % 7.87/8.07 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H17c. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H17d. % 7.87/8.07 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 7.87/8.07 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H17e. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H9c. % 7.87/8.07 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 7.87/8.07 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H136. apply refl_equal. % 7.87/8.07 apply zenon_H110. apply sym_equal. exact zenon_H98. % 7.87/8.07 apply zenon_H136. apply refl_equal. % 7.87/8.07 apply zenon_H136. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L238_ *) % 7.87/8.07 assert (zenon_L239_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H170 zenon_H2d zenon_H2c zenon_Hde zenon_Hdc zenon_H40 zenon_H33 zenon_H70. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H25 | zenon_intro zenon_H171 ]. % 7.87/8.07 apply (zenon_L5_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H172 ]. % 7.87/8.07 apply (zenon_L144_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H26 | zenon_intro zenon_H66 ]. % 7.87/8.07 apply (zenon_L225_); trivial. % 7.87/8.07 apply (zenon_L226_); trivial. % 7.87/8.07 (* end of lemma zenon_L239_ *) % 7.87/8.07 assert (zenon_L240_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hcc zenon_H70 zenon_H33 zenon_H40 zenon_Hde zenon_H2c zenon_H170 zenon_H89 zenon_Hbb zenon_Hdc zenon_H173 zenon_Hef zenon_H115. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.07 apply (zenon_L239_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.07 apply (zenon_L221_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.07 apply (zenon_L231_); trivial. % 7.87/8.07 apply (zenon_L205_); trivial. % 7.87/8.07 (* end of lemma zenon_L240_ *) % 7.87/8.07 assert (zenon_L241_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H162 zenon_H28 zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_H86 zenon_H16b zenon_Hde zenon_H8f zenon_Hcc zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H89 zenon_Hbb zenon_Hdc zenon_H173 zenon_Hef zenon_H25 zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L213_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L216_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.07 apply (zenon_L24_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.07 apply (zenon_L205_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.07 apply (zenon_L240_); trivial. % 7.87/8.07 apply (zenon_L91_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L241_ *) % 7.87/8.07 assert (zenon_L242_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H13b zenon_H20 zenon_H16e zenon_H17c zenon_H98 zenon_H162 zenon_H28 zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_H86 zenon_H16b zenon_Hde zenon_H8f zenon_Hcc zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H89 zenon_Hbb zenon_H173 zenon_Hef zenon_H25 zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.07 apply (zenon_L3_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.07 apply (zenon_L66_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.07 apply (zenon_L216_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.07 apply (zenon_L217_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.07 apply (zenon_L205_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.07 apply (zenon_L29_); trivial. % 7.87/8.07 apply (zenon_L91_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.07 apply (zenon_L238_); trivial. % 7.87/8.07 apply (zenon_L241_); trivial. % 7.87/8.07 (* end of lemma zenon_L242_ *) % 7.87/8.07 assert (zenon_L243_ : (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 7.87/8.07 do 0 intro. intros zenon_H6c zenon_H86 zenon_H1f. % 7.87/8.07 cut (((op (e0) (e0)) = (e3)) = ((e2) = (e3))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H6c. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H86. % 7.87/8.07 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.07 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 7.87/8.07 congruence. % 7.87/8.07 exact (zenon_H24 zenon_H1f). % 7.87/8.07 apply zenon_H69. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L243_ *) % 7.87/8.07 assert (zenon_L244_ : ((op (e3) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hb2 zenon_H54 zenon_H17f. % 7.87/8.07 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H180 | zenon_intro zenon_H181 ]. % 7.87/8.07 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H17f. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H180. % 7.87/8.07 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 7.87/8.07 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H182. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_Hb2. % 7.87/8.07 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 7.87/8.07 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_H181. apply refl_equal. % 7.87/8.07 apply zenon_H183. apply sym_equal. exact zenon_H54. % 7.87/8.07 apply zenon_H181. apply refl_equal. % 7.87/8.07 apply zenon_H181. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L244_ *) % 7.87/8.07 assert (zenon_L245_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H142 zenon_H17f zenon_Hb2 zenon_Hc6 zenon_Hca zenon_Hcf zenon_H10b zenon_H157 zenon_H20 zenon_H29 zenon_H154 zenon_Hff zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.07 apply (zenon_L244_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.07 apply (zenon_L228_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.07 apply (zenon_L175_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 7.87/8.07 apply (zenon_L223_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 7.87/8.07 apply (zenon_L224_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 7.87/8.07 apply (zenon_L170_); trivial. % 7.87/8.07 apply (zenon_L157_); trivial. % 7.87/8.07 (* end of lemma zenon_L245_ *) % 7.87/8.07 assert (zenon_L246_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hff zenon_H29 zenon_H154 zenon_H165 zenon_H6e zenon_H130 zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.07 apply (zenon_L224_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.07 exact (zenon_H165 zenon_Hd6). % 7.87/8.07 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.07 apply (zenon_L142_); trivial. % 7.87/8.07 apply (zenon_L109_); trivial. % 7.87/8.07 (* end of lemma zenon_L246_ *) % 7.87/8.07 assert (zenon_L247_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H13b zenon_H20 zenon_H130 zenon_H165 zenon_H154 zenon_H29 zenon_Hff zenon_H17c zenon_H98 zenon_H162 zenon_H28 zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_H86 zenon_H16b zenon_Hde zenon_H8f zenon_Hcc zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H89 zenon_Hbb zenon_H173 zenon_Hef zenon_H25 zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.07 apply (zenon_L3_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.07 apply (zenon_L246_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.07 apply (zenon_L238_); trivial. % 7.87/8.07 apply (zenon_L241_); trivial. % 7.87/8.07 (* end of lemma zenon_L247_ *) % 7.87/8.07 assert (zenon_L248_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (e1))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hd8 zenon_Haa zenon_H67 zenon_H25 zenon_Hef zenon_H173 zenon_H89 zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_Hcc zenon_H8f zenon_H16b zenon_H86 zenon_H30 zenon_H36 zenon_H49 zenon_H28 zenon_H162 zenon_H98 zenon_H17c zenon_H130 zenon_H13b zenon_H16e zenon_H99 zenon_H12d zenon_H184 zenon_H5e zenon_Hfc zenon_Hf1 zenon_Hbc zenon_H64 zenon_Hff zenon_H154 zenon_H29 zenon_H20 zenon_H157 zenon_H10b zenon_Hca zenon_Hb2 zenon_H17f zenon_H142 zenon_H81 zenon_Hcf zenon_H165. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.87/8.07 apply (zenon_L220_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.87/8.07 apply (zenon_L245_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.87/8.07 apply (zenon_L237_); trivial. % 7.87/8.07 apply (zenon_L247_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.07 apply (zenon_L245_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.07 apply (zenon_L68_); trivial. % 7.87/8.07 exact (zenon_H165 zenon_Hd6). % 7.87/8.07 (* end of lemma zenon_L248_ *) % 7.87/8.07 assert (zenon_L249_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H15a zenon_He3 zenon_H55. % 7.87/8.07 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.87/8.07 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H55. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H56. % 7.87/8.07 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.07 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H58. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_H15a. % 7.87/8.07 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.07 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H187]. % 7.87/8.07 congruence. % 7.87/8.07 exact (zenon_H187 zenon_He3). % 7.87/8.07 apply zenon_H1d. apply refl_equal. % 7.87/8.07 apply zenon_H57. apply refl_equal. % 7.87/8.07 apply zenon_H57. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L249_ *) % 7.87/8.07 assert (zenon_L250_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_Ha1 zenon_H98 zenon_H188. % 7.87/8.07 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha4 ]. % 7.87/8.07 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H188. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_Ha3. % 7.87/8.07 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 7.87/8.07 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 7.87/8.07 congruence. % 7.87/8.07 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 7.87/8.07 intro zenon_D_pnotp. % 7.87/8.07 apply zenon_H189. % 7.87/8.07 rewrite <- zenon_D_pnotp. % 7.87/8.07 exact zenon_Ha1. % 7.87/8.07 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 7.87/8.07 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 7.87/8.07 congruence. % 7.87/8.07 apply zenon_Ha4. apply refl_equal. % 7.87/8.07 apply zenon_H110. apply sym_equal. exact zenon_H98. % 7.87/8.07 apply zenon_Ha4. apply refl_equal. % 7.87/8.07 apply zenon_Ha4. apply refl_equal. % 7.87/8.07 (* end of lemma zenon_L250_ *) % 7.87/8.07 assert (zenon_L251_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.07 do 0 intro. intros zenon_H150 zenon_H5d zenon_H64 zenon_He3 zenon_Hbd zenon_H188 zenon_H98 zenon_Hfc zenon_H49. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H48 | zenon_intro zenon_H151 ]. % 7.87/8.07 apply (zenon_L21_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H140 | zenon_intro zenon_H152 ]. % 7.87/8.07 apply (zenon_L186_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H14e ]. % 7.87/8.07 apply (zenon_L250_); trivial. % 7.87/8.07 apply (zenon_L187_); trivial. % 7.87/8.07 (* end of lemma zenon_L251_ *) % 7.87/8.07 assert (zenon_L252_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.07 do 0 intro. intros zenon_Hcc zenon_H70 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_Hf4 zenon_Hca zenon_Ha2 zenon_H130 zenon_H47 zenon_Hdc. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.07 apply (zenon_L227_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.07 apply (zenon_L228_); trivial. % 7.87/8.07 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.08 apply (zenon_L142_); trivial. % 7.87/8.08 apply (zenon_L235_); trivial. % 7.87/8.08 (* end of lemma zenon_L252_ *) % 7.87/8.08 assert (zenon_L253_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.08 do 0 intro. intros zenon_H157 zenon_H55 zenon_H49 zenon_H98 zenon_H188 zenon_Hbd zenon_He3 zenon_H150 zenon_Hff zenon_H64 zenon_H165 zenon_Hfc zenon_H5e zenon_Hcc zenon_H70 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_Hf4 zenon_Hca zenon_Ha2 zenon_H130 zenon_Hdc. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 7.87/8.08 apply (zenon_L249_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 7.87/8.08 apply (zenon_L251_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 7.87/8.08 apply (zenon_L230_); trivial. % 7.87/8.08 apply (zenon_L252_); trivial. % 7.87/8.08 (* end of lemma zenon_L253_ *) % 7.87/8.08 assert (zenon_L254_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 7.87/8.08 do 0 intro. intros zenon_H142 zenon_H99 zenon_Hdc zenon_H130 zenon_Ha2 zenon_Hca zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H70 zenon_Hcc zenon_H5e zenon_Hfc zenon_H165 zenon_H64 zenon_Hff zenon_H150 zenon_H188 zenon_H98 zenon_H49 zenon_H157 zenon_H55 zenon_H36 zenon_Hbd zenon_He3. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.08 apply (zenon_L41_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.08 apply (zenon_L253_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.08 apply (zenon_L155_); trivial. % 7.87/8.08 apply (zenon_L186_); trivial. % 7.87/8.08 (* end of lemma zenon_L254_ *) % 7.87/8.08 assert (zenon_L255_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H13b zenon_H20 zenon_H17c zenon_H162 zenon_H28 zenon_H30 zenon_H86 zenon_H16b zenon_H6c zenon_H142 zenon_H99 zenon_H130 zenon_Ha2 zenon_Hca zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_Hcc zenon_H165 zenon_H64 zenon_Hff zenon_H150 zenon_H188 zenon_H98 zenon_H49 zenon_H157 zenon_H55 zenon_H36 zenon_Hbd zenon_He3 zenon_Hef zenon_H25 zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.08 apply (zenon_L142_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.08 apply (zenon_L238_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.08 apply (zenon_L213_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.08 apply (zenon_L216_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.08 apply (zenon_L205_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.08 apply (zenon_L254_); trivial. % 7.87/8.08 apply (zenon_L73_); trivial. % 7.87/8.08 apply (zenon_L109_); trivial. % 7.87/8.08 (* end of lemma zenon_L255_ *) % 7.87/8.08 assert (zenon_L256_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_Hff zenon_H165 zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H47 zenon_H150 zenon_Hfc zenon_H5e. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.87/8.08 apply (zenon_L18_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.87/8.08 exact (zenon_H165 zenon_Hd6). % 7.87/8.08 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.87/8.08 apply (zenon_L188_); trivial. % 7.87/8.08 apply (zenon_L109_); trivial. % 7.87/8.08 (* end of lemma zenon_L256_ *) % 7.87/8.08 assert (zenon_L257_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H157 zenon_H55 zenon_H29 zenon_H154 zenon_Hf1 zenon_Hbc zenon_Hff zenon_H165 zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H150 zenon_Hfc zenon_H5e. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 7.87/8.08 apply (zenon_L249_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 7.87/8.08 apply (zenon_L224_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 7.87/8.08 apply (zenon_L194_); trivial. % 7.87/8.08 apply (zenon_L256_); trivial. % 7.87/8.08 (* end of lemma zenon_L257_ *) % 7.87/8.08 assert (zenon_L258_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H61 zenon_H5e zenon_H165 zenon_Hff zenon_Hbc zenon_Hf1 zenon_H154 zenon_H55 zenon_H157 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H150 zenon_H64 zenon_He3 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.08 apply (zenon_L257_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.08 apply (zenon_L5_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.08 apply (zenon_L8_); trivial. % 7.87/8.08 apply (zenon_L193_); trivial. % 7.87/8.08 (* end of lemma zenon_L258_ *) % 7.87/8.08 assert (zenon_L259_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H15f zenon_H17f zenon_H10b zenon_H184 zenon_H12d zenon_H16e zenon_H8f zenon_H89 zenon_H173 zenon_Hd8 zenon_Hb5 zenon_Hb6 zenon_H124 zenon_Haa zenon_H67 zenon_Hef zenon_H98 zenon_H188 zenon_Hcc zenon_H33 zenon_H40 zenon_H170 zenon_Hca zenon_H130 zenon_H99 zenon_H142 zenon_H6c zenon_H16b zenon_H86 zenon_H30 zenon_H28 zenon_H162 zenon_H17c zenon_H20 zenon_H13b zenon_H81 zenon_H29 zenon_H11e zenon_H61 zenon_H5e zenon_H165 zenon_Hff zenon_Hf1 zenon_H154 zenon_H55 zenon_H157 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H150 zenon_H64 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.87/8.08 apply (zenon_L219_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.08 apply (zenon_L212_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.08 apply (zenon_L65_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.87/8.08 apply (zenon_L220_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.87/8.08 apply (zenon_L221_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.87/8.08 apply (zenon_L237_); trivial. % 7.87/8.08 apply (zenon_L242_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.08 apply (zenon_L41_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.08 apply (zenon_L243_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.08 apply (zenon_L65_); trivial. % 7.87/8.08 apply (zenon_L248_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.08 apply (zenon_L212_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.08 apply (zenon_L17_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.08 apply (zenon_L246_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.08 apply (zenon_L35_); trivial. % 7.87/8.08 apply (zenon_L255_); trivial. % 7.87/8.08 apply (zenon_L258_); trivial. % 7.87/8.08 (* end of lemma zenon_L259_ *) % 7.87/8.08 assert (zenon_L260_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 7.87/8.08 do 0 intro. intros zenon_H20 zenon_H98 zenon_H31. % 7.87/8.08 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 7.87/8.08 intro zenon_D_pnotp. % 7.87/8.08 apply zenon_H20. % 7.87/8.08 rewrite <- zenon_D_pnotp. % 7.87/8.08 exact zenon_H98. % 7.87/8.08 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.08 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 7.87/8.08 congruence. % 7.87/8.08 exact (zenon_H18a zenon_H31). % 7.87/8.08 apply zenon_H22. apply refl_equal. % 7.87/8.08 (* end of lemma zenon_L260_ *) % 7.87/8.08 assert (zenon_L261_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.87/8.08 do 0 intro. intros zenon_He7 zenon_H55 zenon_H3e zenon_H115 zenon_Hef zenon_H173 zenon_Hdc zenon_Hbb zenon_H89 zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H70 zenon_Hcc zenon_Hcf zenon_Hf8 zenon_H8f zenon_Hfc. % 7.87/8.08 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.87/8.08 apply (zenon_L50_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.87/8.08 apply (zenon_L240_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.87/8.08 apply (zenon_L177_); trivial. % 7.87/8.08 apply (zenon_L191_); trivial. % 7.87/8.08 (* end of lemma zenon_L261_ *) % 7.87/8.08 assert (zenon_L262_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H162 zenon_H28 zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_H86 zenon_H16b zenon_Hdc zenon_H6c zenon_He7 zenon_H55 zenon_H3e zenon_Hef zenon_H173 zenon_Hbb zenon_H89 zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_Hcc zenon_Hcf zenon_Hf8 zenon_H8f zenon_H25 zenon_H67 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.08 apply (zenon_L213_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.08 apply (zenon_L216_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.08 apply (zenon_L205_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.08 apply (zenon_L261_); trivial. % 7.87/8.08 apply (zenon_L73_); trivial. % 7.87/8.08 apply (zenon_L109_); trivial. % 7.87/8.08 (* end of lemma zenon_L262_ *) % 7.87/8.08 assert (zenon_L263_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H61 zenon_H5e zenon_Haa zenon_H67 zenon_Hef zenon_H55 zenon_H157 zenon_H98 zenon_H188 zenon_Hff zenon_H165 zenon_Hcc zenon_H33 zenon_H40 zenon_H170 zenon_Hca zenon_H130 zenon_H99 zenon_H142 zenon_H6c zenon_H16b zenon_H86 zenon_H30 zenon_H28 zenon_H162 zenon_H17c zenon_H20 zenon_H13b zenon_H81 zenon_H82 zenon_H154 zenon_Hbb zenon_H11e zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H150 zenon_H64 zenon_He3 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.08 apply (zenon_L116_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.08 apply (zenon_L246_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.08 apply (zenon_L35_); trivial. % 7.87/8.08 apply (zenon_L255_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.08 apply (zenon_L5_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.08 apply (zenon_L8_); trivial. % 7.87/8.08 apply (zenon_L193_); trivial. % 7.87/8.08 (* end of lemma zenon_L263_ *) % 7.87/8.08 assert (zenon_L264_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H15f zenon_H16e zenon_H12d zenon_He7 zenon_H173 zenon_H89 zenon_Hf8 zenon_H8f zenon_Hb6 zenon_Hb5 zenon_H49 zenon_Hfc zenon_H13a zenon_Hbd zenon_H64 zenon_H150 zenon_H36 zenon_H38 zenon_H2c zenon_H25 zenon_H157 zenon_H154 zenon_Hf1 zenon_Hff zenon_H165 zenon_H5e zenon_H61 zenon_Haa zenon_H67 zenon_Hef zenon_H188 zenon_Hcc zenon_H33 zenon_H40 zenon_H170 zenon_Hca zenon_H130 zenon_H142 zenon_H6c zenon_H16b zenon_H86 zenon_H30 zenon_H28 zenon_H162 zenon_H17c zenon_H20 zenon_H13b zenon_H81 zenon_H11e zenon_H124 zenon_H99 zenon_H98 zenon_H3e zenon_H55. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.08 apply (zenon_L220_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.08 apply (zenon_L41_); trivial. % 7.87/8.08 apply (zenon_L50_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.08 apply (zenon_L222_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.08 apply (zenon_L238_); trivial. % 7.87/8.08 apply (zenon_L262_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.08 apply (zenon_L41_); trivial. % 7.87/8.08 apply (zenon_L50_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.08 apply (zenon_L243_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.08 apply (zenon_L263_); trivial. % 7.87/8.08 apply (zenon_L258_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.08 apply (zenon_L41_); trivial. % 7.87/8.08 apply (zenon_L50_); trivial. % 7.87/8.08 (* end of lemma zenon_L264_ *) % 7.87/8.08 assert (zenon_L265_ : ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H15e zenon_H67 zenon_H86 zenon_H15f zenon_H11e zenon_H55 zenon_H150 zenon_H188 zenon_Hbd zenon_H61 zenon_H38 zenon_H124 zenon_H8f zenon_H89 zenon_H13b zenon_H154 zenon_H64 zenon_H165 zenon_H130 zenon_Hff zenon_H33 zenon_H40 zenon_H170 zenon_H173 zenon_H157 zenon_H17c zenon_H184 zenon_H99 zenon_H20 zenon_H98 zenon_H17f zenon_H10b zenon_Hf1 zenon_H142 zenon_H81 zenon_Hd8 zenon_H6c zenon_Hb6 zenon_H28 zenon_H16b zenon_Hfc zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_Haa zenon_H12d zenon_H2c zenon_H25 zenon_Hcc zenon_Hef zenon_H16e zenon_H5e zenon_H162 zenon_Hb5 zenon_Hf8 zenon_He7 zenon_H18b. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.87/8.08 apply (zenon_L36_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.87/8.08 apply (zenon_L259_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.87/8.08 apply (zenon_L260_); trivial. % 7.87/8.08 apply (zenon_L264_); trivial. % 7.87/8.08 apply (zenon_L215_); trivial. % 7.87/8.08 (* end of lemma zenon_L265_ *) % 7.87/8.08 assert (zenon_L266_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H8f zenon_Hbb zenon_H6c zenon_H98 zenon_Hfc zenon_H128. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.08 apply (zenon_L49_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.08 apply (zenon_L66_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.08 apply (zenon_L136_); trivial. % 7.87/8.08 apply (zenon_L137_); trivial. % 7.87/8.08 (* end of lemma zenon_L266_ *) % 7.87/8.08 assert (zenon_L267_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H142 zenon_H17f zenon_Hb2 zenon_Hc6 zenon_Hca zenon_H55 zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H36 zenon_H5a zenon_Hff zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.08 apply (zenon_L244_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.08 apply (zenon_L228_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.08 apply (zenon_L155_); trivial. % 7.87/8.08 apply (zenon_L158_); trivial. % 7.87/8.08 (* end of lemma zenon_L267_ *) % 7.87/8.08 assert (zenon_L268_ : ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H15e zenon_H15f zenon_H11e zenon_H150 zenon_H188 zenon_Hbd zenon_H61 zenon_H38 zenon_H89 zenon_H13b zenon_H154 zenon_H130 zenon_H33 zenon_H170 zenon_H173 zenon_H157 zenon_H17c zenon_H184 zenon_H10b zenon_Hb6 zenon_H28 zenon_H16b zenon_H49 zenon_H30 zenon_Haa zenon_H12d zenon_H2c zenon_Hcc zenon_Hef zenon_H16e zenon_H162 zenon_Hb5 zenon_Hf8 zenon_He7 zenon_H18b zenon_H124 zenon_H20 zenon_H99 zenon_Hc3 zenon_H67 zenon_H128 zenon_Hfc zenon_H98 zenon_Hd8 zenon_H8f zenon_H5e zenon_Hf1 zenon_H64 zenon_Hff zenon_H5a zenon_H36 zenon_H40 zenon_H25 zenon_H3d zenon_H1e zenon_H4e zenon_H55 zenon_Hca zenon_H17f zenon_H142 zenon_H81 zenon_Hcf zenon_H165 zenon_Haf zenon_H95 zenon_H6c. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.08 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.08 apply (zenon_L212_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.08 apply (zenon_L65_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.08 apply (zenon_L265_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.08 apply (zenon_L266_); trivial. % 7.87/8.08 apply (zenon_L57_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.08 apply (zenon_L41_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.08 apply (zenon_L2_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.08 apply (zenon_L65_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.08 apply (zenon_L36_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.08 apply (zenon_L49_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.08 apply (zenon_L66_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.08 apply (zenon_L267_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.08 apply (zenon_L68_); trivial. % 7.87/8.08 exact (zenon_H165 zenon_Hd6). % 7.87/8.08 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.08 apply (zenon_L136_); trivial. % 7.87/8.08 apply (zenon_L137_); trivial. % 7.87/8.08 apply (zenon_L57_); trivial. % 7.87/8.08 (* end of lemma zenon_L268_ *) % 7.87/8.08 assert (zenon_L269_ : ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H5b zenon_H158 zenon_H43 zenon_H117 zenon_H14a zenon_H12b zenon_H137 zenon_H134 zenon_H131 zenon_Hec zenon_H10e zenon_H5d zenon_H64 zenon_Ha7 zenon_H95 zenon_Haf zenon_H165 zenon_Hcf zenon_H81 zenon_H142 zenon_H17f zenon_Hca zenon_H55 zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H5a zenon_Hff zenon_Hf1 zenon_H5e zenon_H8f zenon_Hd8 zenon_Hfc zenon_H128 zenon_H67 zenon_Hc3 zenon_H99 zenon_H124 zenon_H18b zenon_He7 zenon_Hf8 zenon_Hb5 zenon_H162 zenon_H16e zenon_Hef zenon_Hcc zenon_H2c zenon_H12d zenon_Haa zenon_H30 zenon_H49 zenon_H16b zenon_H28 zenon_Hb6 zenon_H10b zenon_H184 zenon_H17c zenon_H157 zenon_H173 zenon_H170 zenon_H33 zenon_H130 zenon_H154 zenon_H13b zenon_H89 zenon_H38 zenon_H61 zenon_Hbd zenon_H188 zenon_H150 zenon_H11e zenon_H15f zenon_H15e zenon_H20 zenon_H13a zenon_H51 zenon_H6c. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.08 apply (zenon_L84_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.08 apply (zenon_L207_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.08 apply (zenon_L201_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.08 apply (zenon_L6_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.08 apply (zenon_L7_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.08 apply (zenon_L268_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.08 apply (zenon_L43_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.08 apply (zenon_L44_); trivial. % 7.87/8.08 exact (zenon_H13a zenon_Ha1). % 7.87/8.08 apply (zenon_L21_); trivial. % 7.87/8.08 apply (zenon_L73_); trivial. % 7.87/8.08 (* end of lemma zenon_L269_ *) % 7.87/8.08 assert (zenon_L270_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.08 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6d zenon_H67 zenon_H31 zenon_H6c zenon_H93. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.08 apply (zenon_L49_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.08 apply (zenon_L37_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.08 apply (zenon_L123_); trivial. % 7.87/8.08 apply (zenon_L39_); trivial. % 7.87/8.08 (* end of lemma zenon_L270_ *) % 7.87/8.08 assert (zenon_L271_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H13b zenon_H20 zenon_H5d zenon_H64 zenon_H142 zenon_H8f zenon_H99 zenon_H55 zenon_H4e zenon_H1e zenon_H3d zenon_H25 zenon_H40 zenon_H5a zenon_Hff zenon_Hbc zenon_Hf1 zenon_H5e zenon_H33 zenon_H67 zenon_H93 zenon_H51 zenon_Ha7 zenon_H128 zenon_Hfc zenon_H6c zenon_H6d zenon_H89 zenon_Haf zenon_Hb0 zenon_H95 zenon_H134 zenon_H38 zenon_H83 zenon_H13a. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.08 apply (zenon_L3_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.08 apply (zenon_L26_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.08 apply (zenon_L270_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.08 apply (zenon_L7_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.08 apply (zenon_L159_); trivial. % 7.87/8.08 apply (zenon_L21_); trivial. % 7.87/8.08 apply (zenon_L162_); trivial. % 7.87/8.08 (* end of lemma zenon_L271_ *) % 7.87/8.08 assert (zenon_L272_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 7.87/8.08 do 0 intro. intros zenon_H11e zenon_Hcf zenon_H81 zenon_Hd8 zenon_H13a zenon_H38 zenon_H134 zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6d zenon_H6c zenon_Hfc zenon_H128 zenon_Ha7 zenon_H51 zenon_H93 zenon_H67 zenon_H33 zenon_H5e zenon_Hff zenon_H5a zenon_H40 zenon_H25 zenon_H3d zenon_H1e zenon_H4e zenon_H55 zenon_H99 zenon_H8f zenon_H142 zenon_H64 zenon_H5d zenon_H20 zenon_H13b zenon_Hf1 zenon_Hbc. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.08 apply (zenon_L182_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.08 apply (zenon_L26_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.08 apply (zenon_L271_); trivial. % 7.87/8.08 apply (zenon_L113_); trivial. % 7.87/8.08 (* end of lemma zenon_L272_ *) % 7.87/8.08 assert (zenon_L273_ : ((op (e2) (e2)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H15c zenon_H70 zenon_H18e. % 7.87/8.08 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 7.87/8.08 intro zenon_D_pnotp. % 7.87/8.08 apply zenon_H18e. % 7.87/8.08 rewrite <- zenon_D_pnotp. % 7.87/8.08 exact zenon_H39. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 7.87/8.08 congruence. % 7.87/8.08 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 7.87/8.08 intro zenon_D_pnotp. % 7.87/8.08 apply zenon_H18f. % 7.87/8.08 rewrite <- zenon_D_pnotp. % 7.87/8.08 exact zenon_H15c. % 7.87/8.08 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.08 congruence. % 7.87/8.08 apply zenon_H3a. apply refl_equal. % 7.87/8.08 apply zenon_Hcb. apply sym_equal. exact zenon_H70. % 7.87/8.08 apply zenon_H3a. apply refl_equal. % 7.87/8.08 apply zenon_H3a. apply refl_equal. % 7.87/8.08 (* end of lemma zenon_L273_ *) % 7.87/8.08 assert (zenon_L274_ : ((op (e2) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_H15c zenon_Hb0 zenon_H10b. % 7.87/8.08 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 7.87/8.08 intro zenon_D_pnotp. % 7.87/8.08 apply zenon_H10b. % 7.87/8.08 rewrite <- zenon_D_pnotp. % 7.87/8.08 exact zenon_H39. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 7.87/8.08 congruence. % 7.87/8.08 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 7.87/8.08 intro zenon_D_pnotp. % 7.87/8.08 apply zenon_H10c. % 7.87/8.08 rewrite <- zenon_D_pnotp. % 7.87/8.08 exact zenon_H15c. % 7.87/8.08 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 7.87/8.08 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.08 congruence. % 7.87/8.08 apply zenon_H3a. apply refl_equal. % 7.87/8.08 apply zenon_Hb1. apply sym_equal. exact zenon_Hb0. % 7.87/8.08 apply zenon_H3a. apply refl_equal. % 7.87/8.08 apply zenon_H3a. apply refl_equal. % 7.87/8.08 (* end of lemma zenon_L274_ *) % 7.87/8.08 assert (zenon_L275_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.08 do 0 intro. intros zenon_Hc3 zenon_H1e zenon_H67 zenon_H25 zenon_H10b zenon_H15c zenon_Hbc zenon_H6c. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.08 apply (zenon_L36_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.08 apply (zenon_L274_); trivial. % 7.87/8.08 apply (zenon_L57_); trivial. % 7.87/8.08 (* end of lemma zenon_L275_ *) % 7.87/8.08 assert (zenon_L276_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.08 do 0 intro. intros zenon_Haa zenon_H67 zenon_H25 zenon_H6c zenon_H6e zenon_H36 zenon_Hfc zenon_H12d. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.08 apply (zenon_L24_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.08 apply (zenon_L26_); trivial. % 7.87/8.08 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.08 apply (zenon_L29_); trivial. % 7.87/8.08 apply (zenon_L139_); trivial. % 7.87/8.08 (* end of lemma zenon_L276_ *) % 7.87/8.08 assert (zenon_L277_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H124 zenon_H8f zenon_H95 zenon_Haf zenon_H6c zenon_H98 zenon_H128 zenon_H25 zenon_H67 zenon_H61 zenon_Haa zenon_Hef zenon_H55 zenon_H188 zenon_H165 zenon_Hcc zenon_H33 zenon_H40 zenon_H170 zenon_Hca zenon_H130 zenon_H99 zenon_H142 zenon_H16b zenon_H30 zenon_H28 zenon_H162 zenon_H17c zenon_H20 zenon_H13b zenon_H81 zenon_H11e zenon_H2c zenon_H38 zenon_H36 zenon_Hc3 zenon_H157 zenon_H158 zenon_H13a zenon_Hf1 zenon_Hff zenon_H154 zenon_Hbb zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H150 zenon_Hfc zenon_H5e. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.09 apply (zenon_L212_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.09 apply (zenon_L3_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.09 apply (zenon_L263_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.09 apply (zenon_L266_); trivial. % 7.87/8.09 apply (zenon_L89_); trivial. % 7.87/8.09 apply (zenon_L197_); trivial. % 7.87/8.09 (* end of lemma zenon_L277_ *) % 7.87/8.09 assert (zenon_L278_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H142 zenon_H99 zenon_H130 zenon_Hca zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_Hcc zenon_H5e zenon_Hfc zenon_H165 zenon_H64 zenon_Hff zenon_H150 zenon_H188 zenon_H49 zenon_H157 zenon_H55 zenon_H36 zenon_Hbd zenon_He3 zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H128 zenon_H25 zenon_H67 zenon_Haa zenon_H12b zenon_H12d zenon_H20 zenon_H13b zenon_H81 zenon_H82 zenon_H29 zenon_H154 zenon_H11e zenon_H6c zenon_H98 zenon_H8f zenon_Hb2. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.09 apply (zenon_L49_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.09 apply (zenon_L17_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.09 apply (zenon_L246_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.09 apply (zenon_L35_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.09 apply (zenon_L3_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.09 apply (zenon_L142_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.09 apply (zenon_L204_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.09 apply (zenon_L161_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.09 apply (zenon_L254_); trivial. % 7.87/8.09 apply (zenon_L73_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.09 apply (zenon_L136_); trivial. % 7.87/8.09 apply (zenon_L167_); trivial. % 7.87/8.09 (* end of lemma zenon_L278_ *) % 7.87/8.09 assert (zenon_L279_ : (~((op (e0) (e3)) = (e0))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H158 zenon_H8f zenon_H98 zenon_H6c zenon_H11e zenon_H81 zenon_H13b zenon_H20 zenon_H12d zenon_H12b zenon_Haa zenon_H67 zenon_H128 zenon_H89 zenon_Haf zenon_H95 zenon_H188 zenon_Hcc zenon_H33 zenon_H40 zenon_H170 zenon_Hca zenon_H130 zenon_H99 zenon_H142 zenon_H15e zenon_H15f zenon_H124 zenon_H173 zenon_H17c zenon_H184 zenon_H17f zenon_H10b zenon_Hd8 zenon_Hb6 zenon_H28 zenon_H16b zenon_H30 zenon_Hef zenon_H16e zenon_H162 zenon_Hb5 zenon_Hf8 zenon_He7 zenon_H18b zenon_Hc3 zenon_H61 zenon_H5e zenon_H165 zenon_Hff zenon_Hf1 zenon_H154 zenon_H55 zenon_H157 zenon_H25 zenon_H2c zenon_H38 zenon_H36 zenon_H150 zenon_H64 zenon_He3 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.09 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.09 apply (zenon_L277_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.09 apply (zenon_L41_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.09 apply (zenon_L212_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.09 apply (zenon_L3_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.09 apply (zenon_L265_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.87/8.09 apply (zenon_L278_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.87/8.09 apply (zenon_L5_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.87/8.09 apply (zenon_L8_); trivial. % 7.87/8.09 apply (zenon_L193_); trivial. % 7.87/8.09 apply (zenon_L89_); trivial. % 7.87/8.09 apply (zenon_L258_); trivial. % 7.87/8.09 (* end of lemma zenon_L279_ *) % 7.87/8.09 assert (zenon_L280_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H13b zenon_H20 zenon_Ha2 zenon_H130 zenon_H12d zenon_H12b zenon_Haa zenon_H67 zenon_H89 zenon_H88 zenon_Hca zenon_H36 zenon_Hc7 zenon_H2c zenon_H25 zenon_Hcc zenon_H6c. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.09 apply (zenon_L3_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.09 apply (zenon_L142_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.09 apply (zenon_L204_); trivial. % 7.87/8.09 apply (zenon_L208_); trivial. % 7.87/8.09 (* end of lemma zenon_L280_ *) % 7.87/8.09 assert (zenon_L281_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H11e zenon_H5e zenon_Hfc zenon_H165 zenon_H154 zenon_H29 zenon_Hff zenon_H82 zenon_H81 zenon_H13b zenon_H20 zenon_H130 zenon_H12d zenon_H12b zenon_Haa zenon_H67 zenon_H89 zenon_H88 zenon_Hca zenon_H36 zenon_Hc7 zenon_H2c zenon_H25 zenon_Hcc zenon_H6c. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.09 apply (zenon_L17_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.09 apply (zenon_L246_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.09 apply (zenon_L35_); trivial. % 7.87/8.09 apply (zenon_L280_); trivial. % 7.87/8.09 (* end of lemma zenon_L281_ *) % 7.87/8.09 assert (zenon_L282_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H157 zenon_H158 zenon_H29 zenon_H154 zenon_Hff zenon_H140 zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 7.87/8.09 exact (zenon_H158 zenon_H15a). % 7.87/8.09 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 7.87/8.09 apply (zenon_L224_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 7.87/8.09 apply (zenon_L170_); trivial. % 7.87/8.09 apply (zenon_L157_); trivial. % 7.87/8.09 (* end of lemma zenon_L282_ *) % 7.87/8.09 assert (zenon_L283_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H190 zenon_H150 zenon_Hbd zenon_H49 zenon_H13a zenon_Hbb zenon_H5e zenon_Hf1 zenon_Hbc zenon_H64 zenon_Hff zenon_H154 zenon_H29 zenon_H158 zenon_H157 zenon_H8f zenon_Hfc. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_He3 | zenon_intro zenon_H191 ]. % 7.87/8.09 apply (zenon_L197_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H192 ]. % 7.87/8.09 apply (zenon_L195_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H140 | zenon_intro zenon_He2 ]. % 7.87/8.09 apply (zenon_L282_); trivial. % 7.87/8.09 apply (zenon_L191_); trivial. % 7.87/8.09 (* end of lemma zenon_L283_ *) % 7.87/8.09 assert (zenon_L284_ : ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H193 zenon_H18b zenon_He7 zenon_Hf8 zenon_Hb5 zenon_H162 zenon_H5e zenon_H16e zenon_Hef zenon_Hcc zenon_H25 zenon_H2c zenon_H12d zenon_Haa zenon_H30 zenon_Hca zenon_H36 zenon_H49 zenon_Hfc zenon_H16b zenon_H28 zenon_Hb6 zenon_H6c zenon_Hd8 zenon_H81 zenon_H142 zenon_Hf1 zenon_H10b zenon_H17f zenon_H98 zenon_H20 zenon_H99 zenon_H184 zenon_H17c zenon_H157 zenon_H173 zenon_H170 zenon_H40 zenon_H33 zenon_Hff zenon_H130 zenon_H64 zenon_H154 zenon_H13b zenon_H89 zenon_H8f zenon_H124 zenon_H38 zenon_H61 zenon_Hbd zenon_H188 zenon_H150 zenon_H55 zenon_H11e zenon_H15f zenon_H86 zenon_H67 zenon_H15e. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 7.87/8.09 apply (zenon_L265_); trivial. % 7.87/8.09 apply (zenon_L216_); trivial. % 7.87/8.09 (* end of lemma zenon_L284_ *) % 7.87/8.09 assert (zenon_L285_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_Hc3 zenon_H15e zenon_H15f zenon_H11e zenon_H55 zenon_H150 zenon_H188 zenon_Hbd zenon_H61 zenon_H38 zenon_H124 zenon_H8f zenon_H13b zenon_H154 zenon_H64 zenon_H130 zenon_Hff zenon_H33 zenon_H40 zenon_H170 zenon_H173 zenon_H157 zenon_H17c zenon_H184 zenon_H99 zenon_H20 zenon_H17f zenon_H10b zenon_Hf1 zenon_H142 zenon_H81 zenon_Hd8 zenon_Hb6 zenon_H28 zenon_H16b zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_Haa zenon_H12d zenon_H2c zenon_Hcc zenon_Hef zenon_H16e zenon_H5e zenon_H162 zenon_Hb5 zenon_Hf8 zenon_He7 zenon_H18b zenon_H193 zenon_H67 zenon_H25 zenon_H128 zenon_Hfc zenon_H98 zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_Hbc zenon_H6c. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.09 apply (zenon_L284_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.09 apply (zenon_L161_); trivial. % 7.87/8.09 apply (zenon_L57_); trivial. % 7.87/8.09 (* end of lemma zenon_L285_ *) % 7.87/8.09 assert (zenon_L286_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_Hc3 zenon_H49 zenon_H36 zenon_Hca zenon_H30 zenon_H16b zenon_H67 zenon_H25 zenon_H128 zenon_Hfc zenon_H98 zenon_H6c zenon_H6d zenon_H89 zenon_Haf zenon_H95 zenon_He3 zenon_H8f. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.09 apply (zenon_L216_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.09 apply (zenon_L161_); trivial. % 7.87/8.09 apply (zenon_L89_); trivial. % 7.87/8.09 (* end of lemma zenon_L286_ *) % 7.87/8.09 assert (zenon_L287_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 7.87/8.09 do 0 intro. intros zenon_Hec zenon_Had zenon_H5e zenon_H47 zenon_H36 zenon_H38 zenon_H2c zenon_H25 zenon_H20 zenon_H61 zenon_H99 zenon_H54 zenon_H6c zenon_H92. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.09 apply (zenon_L75_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.09 apply (zenon_L19_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.09 apply (zenon_L41_); trivial. % 7.87/8.09 apply (zenon_L39_); trivial. % 7.87/8.09 (* end of lemma zenon_L287_ *) % 7.87/8.09 assert (zenon_L288_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H28 zenon_H1f zenon_H5b. % 7.87/8.09 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H28. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H1f. % 7.87/8.09 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 7.87/8.09 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H2b. apply refl_equal. % 7.87/8.09 apply zenon_Hea. apply sym_equal. exact zenon_H5b. % 7.87/8.09 (* end of lemma zenon_L288_ *) % 7.87/8.09 assert (zenon_L289_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H3d zenon_H1f zenon_H93. % 7.87/8.09 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H3d. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H1f. % 7.87/8.09 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 7.87/8.09 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H2b. apply refl_equal. % 7.87/8.09 apply zenon_H194. apply sym_equal. exact zenon_H93. % 7.87/8.09 (* end of lemma zenon_L289_ *) % 7.87/8.09 assert (zenon_L290_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H47 zenon_H195 zenon_H20. % 7.87/8.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.09 cut (((e2) = (e2)) = ((e0) = (e2))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H20. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H21. % 7.87/8.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.09 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e3) (e3)) = (e0)) = ((e2) = (e0))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H23. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H47. % 7.87/8.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.09 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 7.87/8.09 congruence. % 7.87/8.09 exact (zenon_H196 zenon_H195). % 7.87/8.09 apply zenon_H1d. apply refl_equal. % 7.87/8.09 apply zenon_H22. apply refl_equal. % 7.87/8.09 apply zenon_H22. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L290_ *) % 7.87/8.09 assert (zenon_L291_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H197 zenon_H1f zenon_H3d zenon_H6e zenon_H173 zenon_H9f zenon_H5a zenon_H47 zenon_H20. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.87/8.09 apply (zenon_L289_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.87/8.09 apply (zenon_L231_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.87/8.09 apply (zenon_L178_); trivial. % 7.87/8.09 apply (zenon_L290_); trivial. % 7.87/8.09 (* end of lemma zenon_L291_ *) % 7.87/8.09 assert (zenon_L292_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H47 zenon_H41 zenon_H12d. % 7.87/8.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H12d. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H4a. % 7.87/8.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.09 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H12e. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H47. % 7.87/8.09 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 7.87/8.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H4b. apply refl_equal. % 7.87/8.09 apply zenon_H42. apply sym_equal. exact zenon_H41. % 7.87/8.09 apply zenon_H4b. apply refl_equal. % 7.87/8.09 apply zenon_H4b. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L292_ *) % 7.87/8.09 assert (zenon_L293_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_Hca zenon_H2d zenon_H34. % 7.87/8.09 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_Hca. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H2d. % 7.87/8.09 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 7.87/8.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H8b. apply refl_equal. % 7.87/8.09 apply zenon_H35. apply sym_equal. exact zenon_H34. % 7.87/8.09 (* end of lemma zenon_L293_ *) % 7.87/8.09 assert (zenon_L294_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H173 zenon_H6d zenon_H7f. % 7.87/8.09 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H173. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H6d. % 7.87/8.09 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 7.87/8.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H8b. apply refl_equal. % 7.87/8.09 apply zenon_H12f. apply sym_equal. exact zenon_H7f. % 7.87/8.09 (* end of lemma zenon_L294_ *) % 7.87/8.09 assert (zenon_L295_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 7.87/8.09 do 0 intro. intros zenon_Hcc zenon_H34 zenon_Hca zenon_Hc7 zenon_H2c zenon_H26 zenon_H173 zenon_H7f. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.09 apply (zenon_L293_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.09 apply (zenon_L61_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.09 apply (zenon_L128_); trivial. % 7.87/8.09 apply (zenon_L294_); trivial. % 7.87/8.09 (* end of lemma zenon_L295_ *) % 7.87/8.09 assert (zenon_L296_ : ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H9c zenon_H26 zenon_H33. % 7.87/8.09 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H136 ]. % 7.87/8.09 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H33. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H17d. % 7.87/8.09 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 7.87/8.09 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H19a. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H9c. % 7.87/8.09 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 7.87/8.09 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H136. apply refl_equal. % 7.87/8.09 apply zenon_H121. apply sym_equal. exact zenon_H26. % 7.87/8.09 apply zenon_H136. apply refl_equal. % 7.87/8.09 apply zenon_H136. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L296_ *) % 7.87/8.09 assert (zenon_L297_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H19b zenon_H173 zenon_H2c zenon_Hca zenon_Hcc zenon_Hc7 zenon_H33 zenon_H26 zenon_H7f zenon_H134. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H34 | zenon_intro zenon_H19c ]. % 7.87/8.09 apply (zenon_L295_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H19d ]. % 7.87/8.09 apply (zenon_L168_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H9c | zenon_intro zenon_H70 ]. % 7.87/8.09 apply (zenon_L296_); trivial. % 7.87/8.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H19e | zenon_intro zenon_H132 ]. % 7.87/8.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H134. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H19e. % 7.87/8.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.87/8.09 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H19f. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H7f. % 7.87/8.09 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 7.87/8.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H132. apply refl_equal. % 7.87/8.09 apply zenon_Hcb. apply sym_equal. exact zenon_H70. % 7.87/8.09 apply zenon_H132. apply refl_equal. % 7.87/8.09 apply zenon_H132. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L297_ *) % 7.87/8.09 assert (zenon_L298_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H137 zenon_H12d zenon_H47 zenon_H40 zenon_H19b zenon_H173 zenon_H2c zenon_Hca zenon_Hcc zenon_Hc7 zenon_H33 zenon_H26 zenon_H134. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 7.87/8.09 apply (zenon_L292_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 7.87/8.09 apply (zenon_L144_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 7.87/8.09 apply (zenon_L225_); trivial. % 7.87/8.09 apply (zenon_L297_); trivial. % 7.87/8.09 (* end of lemma zenon_L298_ *) % 7.87/8.09 assert (zenon_L299_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H9f zenon_H9c zenon_H18e. % 7.87/8.09 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.87/8.09 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H18e. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H39. % 7.87/8.09 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.09 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H18f. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H9f. % 7.87/8.09 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 7.87/8.09 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H3a. apply refl_equal. % 7.87/8.09 apply zenon_H14d. apply sym_equal. exact zenon_H9c. % 7.87/8.09 apply zenon_H3a. apply refl_equal. % 7.87/8.09 apply zenon_H3a. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L299_ *) % 7.87/8.09 assert (zenon_L300_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H11e zenon_H28 zenon_H20 zenon_H5a zenon_H3d zenon_H1f zenon_H197 zenon_H38 zenon_H13b zenon_H134 zenon_H33 zenon_Hc7 zenon_Hca zenon_H19b zenon_H40 zenon_H12d zenon_H137 zenon_H130 zenon_H18e zenon_H9f zenon_Hcc zenon_H25 zenon_H2c zenon_H89 zenon_Hbb zenon_H173 zenon_H47. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.09 apply (zenon_L288_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.09 apply (zenon_L291_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.09 apply (zenon_L107_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.09 apply (zenon_L298_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.09 apply (zenon_L142_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.09 apply (zenon_L299_); trivial. % 7.87/8.09 apply (zenon_L236_); trivial. % 7.87/8.09 (* end of lemma zenon_L300_ *) % 7.87/8.09 assert (zenon_L301_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 7.87/8.09 do 0 intro. intros zenon_Hd6 zenon_Ha2 zenon_H99. % 7.87/8.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H21 | zenon_intro zenon_H22 ]. % 7.87/8.09 cut (((e2) = (e2)) = ((e1) = (e2))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H99. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H21. % 7.87/8.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.09 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H9a. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_Hd6. % 7.87/8.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.09 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 7.87/8.09 congruence. % 7.87/8.09 exact (zenon_H1a0 zenon_Ha2). % 7.87/8.09 apply zenon_H57. apply refl_equal. % 7.87/8.09 apply zenon_H22. apply refl_equal. % 7.87/8.09 apply zenon_H22. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L301_ *) % 7.87/8.09 assert (zenon_L302_ : (~((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H1a1 zenon_H2d. % 7.87/8.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.09 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 7.87/8.09 congruence. % 7.87/8.09 exact (zenon_Heb zenon_H2d). % 7.87/8.09 apply zenon_H57. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L302_ *) % 7.87/8.09 assert (zenon_L303_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e3) = (op (op (e1) (e1)) (e1)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H66 zenon_H2d zenon_H71. % 7.87/8.09 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 7.87/8.09 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e3) = (op (op (e1) (e1)) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H71. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H72. % 7.87/8.09 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 7.87/8.09 cut (((op (op (e1) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (e1)) (e1)) = (e3))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H74. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H66. % 7.87/8.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.09 cut (((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 7.87/8.09 congruence. % 7.87/8.09 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 7.87/8.09 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (e1) (e1)) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H1a2. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H72. % 7.87/8.09 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 7.87/8.09 cut (((op (op (e1) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 7.87/8.09 congruence. % 7.87/8.09 apply (zenon_L302_); trivial. % 7.87/8.09 apply zenon_H73. apply refl_equal. % 7.87/8.09 apply zenon_H73. apply refl_equal. % 7.87/8.09 apply zenon_H69. apply refl_equal. % 7.87/8.09 apply zenon_H73. apply refl_equal. % 7.87/8.09 apply zenon_H73. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L303_ *) % 7.87/8.09 assert (zenon_L304_ : ((op (e0) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H1f zenon_H66 zenon_H2d. % 7.87/8.09 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a3 ]. % 7.87/8.09 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 7.87/8.09 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H1a4. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H79. % 7.87/8.09 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 7.87/8.09 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e0) (e0)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H1a5. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H1f. % 7.87/8.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.09 cut (((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 7.87/8.09 congruence. % 7.87/8.09 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 7.87/8.09 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e0) (e0)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H1a6. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_H79. % 7.87/8.09 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 7.87/8.09 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 7.87/8.09 congruence. % 7.87/8.09 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 7.87/8.09 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 7.87/8.09 congruence. % 7.87/8.09 exact (zenon_Heb zenon_H2d). % 7.87/8.09 exact (zenon_Heb zenon_H2d). % 7.87/8.09 apply zenon_H7a. apply refl_equal. % 7.87/8.09 apply zenon_H7a. apply refl_equal. % 7.87/8.09 apply zenon_H22. apply refl_equal. % 7.87/8.09 apply zenon_H7a. apply refl_equal. % 7.87/8.09 apply zenon_H7a. apply refl_equal. % 7.87/8.09 apply (zenon_notand_s _ _ zenon_H1a3); [ zenon_intro zenon_H2e | zenon_intro zenon_H71 ]. % 7.87/8.09 apply zenon_H2e. apply sym_equal. exact zenon_H2d. % 7.87/8.09 apply (zenon_L303_); trivial. % 7.87/8.09 (* end of lemma zenon_L304_ *) % 7.87/8.09 assert (zenon_L305_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 7.87/8.09 do 0 intro. intros zenon_Haa zenon_H1f zenon_H67 zenon_H33 zenon_H40 zenon_Hdc zenon_H2c zenon_H2d zenon_H170 zenon_H8f zenon_Hde. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.09 apply (zenon_L304_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.09 apply (zenon_L164_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.09 apply (zenon_L239_); trivial. % 7.87/8.09 apply (zenon_L91_); trivial. % 7.87/8.09 (* end of lemma zenon_L305_ *) % 7.87/8.09 assert (zenon_L306_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H173 zenon_Hc6 zenon_Hde. % 7.87/8.09 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H173. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_Hc6. % 7.87/8.09 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 7.87/8.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.09 congruence. % 7.87/8.09 apply zenon_H8b. apply refl_equal. % 7.87/8.09 apply zenon_H133. apply sym_equal. exact zenon_Hde. % 7.87/8.09 (* end of lemma zenon_L306_ *) % 7.87/8.09 assert (zenon_L307_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H13b zenon_H25 zenon_H18e zenon_Hcc zenon_H8f zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H67 zenon_Haa zenon_Hde zenon_H20 zenon_H5a zenon_H9f zenon_H173 zenon_H3d zenon_H1f zenon_H197 zenon_H47. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.09 apply (zenon_L3_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.09 apply (zenon_L291_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.09 apply (zenon_L299_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.87/8.09 apply (zenon_L305_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.87/8.09 apply (zenon_L306_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.87/8.09 apply (zenon_L291_); trivial. % 7.87/8.09 apply (zenon_L235_); trivial. % 7.87/8.09 (* end of lemma zenon_L307_ *) % 7.87/8.09 assert (zenon_L308_ : (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_H55 zenon_He2 zenon_H47. % 7.87/8.09 cut (((op (e3) (e3)) = (e1)) = ((e0) = (e1))). % 7.87/8.09 intro zenon_D_pnotp. % 7.87/8.09 apply zenon_H55. % 7.87/8.09 rewrite <- zenon_D_pnotp. % 7.87/8.09 exact zenon_He2. % 7.87/8.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.09 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 7.87/8.09 congruence. % 7.87/8.09 exact (zenon_H1a8 zenon_H47). % 7.87/8.09 apply zenon_H57. apply refl_equal. % 7.87/8.09 (* end of lemma zenon_L308_ *) % 7.87/8.09 assert (zenon_L309_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 7.87/8.09 do 0 intro. intros zenon_He7 zenon_H92 zenon_H197 zenon_H1f zenon_H3d zenon_H173 zenon_H9f zenon_H5a zenon_H20 zenon_Haa zenon_H67 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H8f zenon_Hcc zenon_H18e zenon_H25 zenon_H13b zenon_Hcf zenon_Hf8 zenon_H55 zenon_H47. % 7.87/8.09 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.87/8.09 apply (zenon_L167_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.87/8.09 apply (zenon_L307_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.87/8.09 apply (zenon_L177_); trivial. % 7.87/8.09 apply (zenon_L308_); trivial. % 7.87/8.09 (* end of lemma zenon_L309_ *) % 7.87/8.09 assert (zenon_L310_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H15f zenon_Hb5 zenon_H99 zenon_H28 zenon_H11e zenon_H134 zenon_Hca zenon_H19b zenon_H12d zenon_H137 zenon_H130 zenon_H89 zenon_Hd8 zenon_H47 zenon_H55 zenon_Hf8 zenon_H13b zenon_H18e zenon_Hcc zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_Haa zenon_H5a zenon_H173 zenon_H3d zenon_H197 zenon_H92 zenon_He7 zenon_Hc3 zenon_H1f zenon_H6c zenon_H25 zenon_H81 zenon_H9f zenon_H38 zenon_H118 zenon_H43 zenon_H117 zenon_H20 zenon_H113 zenon_H29 zenon_H67 zenon_H11b zenon_H8f. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.87/8.09 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.09 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 7.87/8.09 apply (zenon_L300_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 7.87/8.09 apply (zenon_L61_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 7.87/8.09 exact (zenon_H118 zenon_Hd2). % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.09 apply (zenon_L288_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.09 apply (zenon_L291_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.09 apply (zenon_L107_); trivial. % 7.87/8.09 apply (zenon_L301_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.87/8.09 apply (zenon_L309_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.87/8.09 apply (zenon_L243_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.87/8.09 apply (zenon_L122_); trivial. % 7.87/8.09 apply (zenon_L89_); trivial. % 7.87/8.09 (* end of lemma zenon_L310_ *) % 7.87/8.09 assert (zenon_L311_ : (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H122 zenon_H9c zenon_H18e. % 7.87/8.09 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 7.87/8.09 apply (zenon_L299_); trivial. % 7.87/8.09 (* end of lemma zenon_L311_ *) % 7.87/8.09 assert (zenon_L312_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 7.87/8.09 do 0 intro. intros zenon_H11e zenon_Hbb zenon_H38 zenon_H13b zenon_H20 zenon_H5a zenon_H173 zenon_H3d zenon_H1f zenon_H197 zenon_H18e zenon_H122 zenon_Haa zenon_H67 zenon_H25 zenon_He3 zenon_Hbd zenon_H99 zenon_H9f zenon_Hcc zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_Hca zenon_H130 zenon_H47 zenon_H31 zenon_H55 zenon_H142 zenon_H6c. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.09 apply (zenon_L116_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.09 apply (zenon_L291_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.09 apply (zenon_L107_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.09 apply (zenon_L3_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.09 apply (zenon_L291_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.09 apply (zenon_L311_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.09 apply (zenon_L24_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.09 apply (zenon_L235_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.09 apply (zenon_L15_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.09 apply (zenon_L252_); trivial. % 7.87/8.09 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.09 apply (zenon_L169_); trivial. % 7.87/8.09 apply (zenon_L186_); trivial. % 7.87/8.09 apply (zenon_L73_); trivial. % 7.87/8.09 (* end of lemma zenon_L312_ *) % 7.87/8.09 assert (zenon_L313_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H67 zenon_H92 zenon_H3e. % 7.87/8.10 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H67. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H92. % 7.87/8.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.10 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H1a9 zenon_H3e). % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L313_ *) % 7.87/8.10 assert (zenon_L314_ : ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1aa zenon_H20 zenon_H1f zenon_H15f zenon_H6c zenon_H11b zenon_H43 zenon_H81 zenon_H117 zenon_H113 zenon_Hc3 zenon_H8f zenon_H92 zenon_Haa zenon_H170 zenon_H67 zenon_Hf8 zenon_H55 zenon_He7 zenon_H11e zenon_H137 zenon_Hcc zenon_H2c zenon_Hca zenon_H33 zenon_H134 zenon_H19b zenon_H40 zenon_H12d zenon_H130 zenon_H18e zenon_H89 zenon_H25 zenon_H13b zenon_H38 zenon_H3d zenon_H173 zenon_H5a zenon_H9f zenon_H47 zenon_H197 zenon_H28 zenon_H99 zenon_Hd8 zenon_Hb5 zenon_H122 zenon_Hbd zenon_H142 zenon_Hb6 zenon_H18b. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.87/8.10 apply (zenon_L2_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.87/8.10 apply (zenon_L310_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.10 apply (zenon_L300_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.10 apply (zenon_L15_); trivial. % 7.87/8.10 apply (zenon_L167_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.87/8.10 apply (zenon_L309_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.10 apply (zenon_L312_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.10 apply (zenon_L15_); trivial. % 7.87/8.10 apply (zenon_L167_); trivial. % 7.87/8.10 apply (zenon_L313_); trivial. % 7.87/8.10 apply (zenon_L291_); trivial. % 7.87/8.10 (* end of lemma zenon_L314_ *) % 7.87/8.10 assert (zenon_L315_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 7.87/8.10 do 0 intro. intros zenon_Hec zenon_H18b zenon_Hb6 zenon_H142 zenon_Hbd zenon_Hb5 zenon_Hd8 zenon_H28 zenon_H197 zenon_H47 zenon_H9f zenon_H5a zenon_H173 zenon_H3d zenon_H38 zenon_H13b zenon_H25 zenon_H89 zenon_H18e zenon_H130 zenon_H12d zenon_H40 zenon_H19b zenon_H134 zenon_H33 zenon_Hca zenon_H2c zenon_Hcc zenon_H137 zenon_H11e zenon_He7 zenon_H55 zenon_Hf8 zenon_H67 zenon_H170 zenon_Haa zenon_H8f zenon_Hc3 zenon_H113 zenon_H117 zenon_H81 zenon_H43 zenon_H11b zenon_H15f zenon_H20 zenon_H1aa zenon_H99 zenon_Hbb zenon_H10e zenon_H122 zenon_H6c zenon_H92. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.10 apply (zenon_L314_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.10 apply (zenon_L116_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.10 apply (zenon_L129_); trivial. % 7.87/8.10 apply (zenon_L39_); trivial. % 7.87/8.10 (* end of lemma zenon_L315_ *) % 7.87/8.10 assert (zenon_L316_ : (~((e2) = (e3))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H6c zenon_H122 zenon_H10e zenon_H99 zenon_H1aa zenon_H20 zenon_H15f zenon_H11b zenon_H43 zenon_H81 zenon_H117 zenon_H113 zenon_Hc3 zenon_Haa zenon_H170 zenon_H67 zenon_Hf8 zenon_He7 zenon_H11e zenon_H137 zenon_Hcc zenon_H2c zenon_Hca zenon_H33 zenon_H134 zenon_H19b zenon_H40 zenon_H12d zenon_H130 zenon_H18e zenon_H89 zenon_H25 zenon_H13b zenon_H38 zenon_H3d zenon_H173 zenon_H5a zenon_H9f zenon_H47 zenon_H197 zenon_H28 zenon_Hd8 zenon_Hb5 zenon_Hbd zenon_H142 zenon_Hb6 zenon_H18b zenon_Hec zenon_H55 zenon_H31 zenon_H8f zenon_H92. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.10 apply (zenon_L315_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.10 apply (zenon_L15_); trivial. % 7.87/8.10 apply (zenon_L167_); trivial. % 7.87/8.10 (* end of lemma zenon_L316_ *) % 7.87/8.10 assert (zenon_L317_ : ((((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0)))))))\/((((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1)))))))\/((((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2)))))))\/(((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3)))))))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1ab zenon_H5e zenon_H61 zenon_Hb5 zenon_Hec zenon_H10e zenon_H18b zenon_Hb6 zenon_H142 zenon_Hbd zenon_Hd8 zenon_H99 zenon_H28 zenon_H197 zenon_H5a zenon_H173 zenon_H3d zenon_H38 zenon_H13b zenon_H89 zenon_H18e zenon_H130 zenon_H12d zenon_H40 zenon_H19b zenon_H134 zenon_Hca zenon_H2c zenon_Hcc zenon_H137 zenon_H11e zenon_He7 zenon_H55 zenon_Hf8 zenon_H67 zenon_H170 zenon_Haa zenon_H8f zenon_Hc3 zenon_H113 zenon_H117 zenon_H81 zenon_H43 zenon_H11b zenon_H6c zenon_H15f zenon_H30 zenon_H33 zenon_H25 zenon_H20 zenon_H49 zenon_H47 zenon_H51 zenon_H92 zenon_H128. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 7.87/8.10 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.87/8.10 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.10 exact (zenon_Hb7 zenon_Hbb). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.10 apply (zenon_L15_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.10 apply (zenon_L7_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.10 apply (zenon_L287_); trivial. % 7.87/8.10 apply (zenon_L12_); trivial. % 7.87/8.10 apply (zenon_L167_); trivial. % 7.87/8.10 apply (zenon_L5_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 7.87/8.10 apply (zenon_L114_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.87/8.10 apply (zenon_L180_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.10 apply (zenon_L315_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.10 apply (zenon_L310_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.10 apply (zenon_L17_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.10 apply (zenon_L41_); trivial. % 7.87/8.10 apply (zenon_L39_); trivial. % 7.87/8.10 apply (zenon_L167_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.87/8.10 apply (zenon_L316_); trivial. % 7.87/8.10 apply (zenon_L313_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.87/8.10 apply (zenon_L315_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.10 apply (zenon_L291_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.10 apply (zenon_L84_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.10 apply (zenon_L41_); trivial. % 7.87/8.10 apply (zenon_L39_); trivial. % 7.87/8.10 apply (zenon_L167_); trivial. % 7.87/8.10 apply (zenon_L138_); trivial. % 7.87/8.10 (* end of lemma zenon_L317_ *) % 7.87/8.10 assert (zenon_L318_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H111 zenon_H1e zenon_Haf. % 7.87/8.10 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H85 ]. % 7.87/8.10 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_Haf. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H1b4. % 7.87/8.10 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.10 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1b5. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H111. % 7.87/8.10 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 7.87/8.10 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H85. apply refl_equal. % 7.87/8.10 apply zenon_H1b6. apply sym_equal. exact zenon_H1e. % 7.87/8.10 apply zenon_H85. apply refl_equal. % 7.87/8.10 apply zenon_H85. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L318_ *) % 7.87/8.10 assert (zenon_L319_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_Had zenon_H111 zenon_Haf. % 7.87/8.10 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.87/8.10 apply (zenon_L318_); trivial. % 7.87/8.10 (* end of lemma zenon_L319_ *) % 7.87/8.10 assert (zenon_L320_ : (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H106 zenon_Hbb zenon_H89. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 7.87/8.10 apply (zenon_L221_); trivial. % 7.87/8.10 (* end of lemma zenon_L320_ *) % 7.87/8.10 assert (zenon_L321_ : (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H122 zenon_H24 zenon_H111. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H127 | zenon_intro zenon_H1f ]. % 7.87/8.10 exact (zenon_H127 zenon_H111). % 7.87/8.10 exact (zenon_H24 zenon_H1f). % 7.87/8.10 (* end of lemma zenon_L321_ *) % 7.87/8.10 assert (zenon_L322_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H111 zenon_Hcf zenon_H55. % 7.87/8.10 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.87/8.10 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H55. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H56. % 7.87/8.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.87/8.10 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H58. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H111. % 7.87/8.10 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.10 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H1b7 zenon_Hcf). % 7.87/8.10 apply zenon_H1d. apply refl_equal. % 7.87/8.10 apply zenon_H57. apply refl_equal. % 7.87/8.10 apply zenon_H57. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L322_ *) % 7.87/8.10 assert (zenon_L323_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_Hd2 zenon_Hbb zenon_H113. % 7.87/8.10 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H46 ]. % 7.87/8.10 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H113. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_Hd3. % 7.87/8.10 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.87/8.10 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1b8. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_Hd2. % 7.87/8.10 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 7.87/8.10 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H46. apply refl_equal. % 7.87/8.10 apply zenon_H156. apply sym_equal. exact zenon_Hbb. % 7.87/8.10 apply zenon_H46. apply refl_equal. % 7.87/8.10 apply zenon_H46. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L323_ *) % 7.87/8.10 assert (zenon_L324_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H115 zenon_H13e zenon_H1b9. % 7.87/8.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.87/8.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1b9. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H1ba. % 7.87/8.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.87/8.10 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1bc. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H115. % 7.87/8.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.10 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 7.87/8.10 congruence. % 7.87/8.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.87/8.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1bd. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H1ba. % 7.87/8.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.87/8.10 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.10 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H13f zenon_H13e). % 7.87/8.10 apply zenon_H22. apply refl_equal. % 7.87/8.10 apply zenon_H1bb. apply refl_equal. % 7.87/8.10 apply zenon_H1bb. apply refl_equal. % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 apply zenon_H1bb. apply refl_equal. % 7.87/8.10 apply zenon_H1bb. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L324_ *) % 7.87/8.10 assert (zenon_L325_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H2d zenon_H115 zenon_H13e. % 7.87/8.10 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H1bf ]. % 7.87/8.10 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.87/8.10 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1c0. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H1c1. % 7.87/8.10 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.87/8.10 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e1) (e1)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1c3. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H2d. % 7.87/8.10 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.87/8.10 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 7.87/8.10 congruence. % 7.87/8.10 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.87/8.10 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1c4. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H1c1. % 7.87/8.10 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.87/8.10 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 7.87/8.10 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H13f zenon_H13e). % 7.87/8.10 exact (zenon_H13f zenon_H13e). % 7.87/8.10 apply zenon_H1c2. apply refl_equal. % 7.87/8.10 apply zenon_H1c2. apply refl_equal. % 7.87/8.10 apply zenon_H1d. apply refl_equal. % 7.87/8.10 apply zenon_H1c2. apply refl_equal. % 7.87/8.10 apply zenon_H1c2. apply refl_equal. % 7.87/8.10 apply (zenon_notand_s _ _ zenon_H1bf); [ zenon_intro zenon_H147 | zenon_intro zenon_H1b9 ]. % 7.87/8.10 apply zenon_H147. apply sym_equal. exact zenon_H13e. % 7.87/8.10 apply (zenon_L324_); trivial. % 7.87/8.10 (* end of lemma zenon_L325_ *) % 7.87/8.10 assert (zenon_L326_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H10b zenon_H111 zenon_H36. % 7.87/8.10 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H10b. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H111. % 7.87/8.10 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 7.87/8.10 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H85. apply refl_equal. % 7.87/8.10 apply zenon_H1c6. apply sym_equal. exact zenon_H36. % 7.87/8.10 (* end of lemma zenon_L326_ *) % 7.87/8.10 assert (zenon_L327_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1c7 zenon_H111 zenon_H10b zenon_He0 zenon_H5a zenon_H10e zenon_H98 zenon_H70 zenon_H18e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.87/8.10 apply (zenon_L326_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.87/8.10 apply (zenon_L190_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.87/8.10 apply (zenon_L117_); trivial. % 7.87/8.10 apply (zenon_L273_); trivial. % 7.87/8.10 (* end of lemma zenon_L327_ *) % 7.87/8.10 assert (zenon_L328_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H8f zenon_H67 zenon_H12d zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H98 zenon_H18e zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.87/8.10 apply (zenon_L322_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.87/8.10 apply (zenon_L323_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_L327_); trivial. % 7.87/8.10 apply (zenon_L139_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L328_ *) % 7.87/8.10 assert (zenon_L329_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H95 zenon_H5e zenon_Hfc zenon_Haa zenon_H16e zenon_Hef zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H2d zenon_H113 zenon_H55 zenon_H1ca zenon_H12d zenon_H67 zenon_H162 zenon_H8f zenon_Hbb zenon_H6c zenon_H98 zenon_H12b zenon_H128. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.10 apply (zenon_L328_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.10 apply (zenon_L136_); trivial. % 7.87/8.10 apply (zenon_L138_); trivial. % 7.87/8.10 (* end of lemma zenon_L329_ *) % 7.87/8.10 assert (zenon_L330_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H173 zenon_H2d zenon_H41. % 7.87/8.10 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H173. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H2d. % 7.87/8.10 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 7.87/8.10 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H8b. apply refl_equal. % 7.87/8.10 apply zenon_H42. apply sym_equal. exact zenon_H41. % 7.87/8.10 (* end of lemma zenon_L330_ *) % 7.87/8.10 assert (zenon_L331_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.87/8.10 do 0 intro. intros zenon_Hf8 zenon_H111 zenon_H44. % 7.87/8.10 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_Hf8. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H111. % 7.87/8.10 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 7.87/8.10 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H85. apply refl_equal. % 7.87/8.10 apply zenon_H45. apply sym_equal. exact zenon_H44. % 7.87/8.10 (* end of lemma zenon_L331_ *) % 7.87/8.10 assert (zenon_L332_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H4e zenon_H20 zenon_H93 zenon_H2d zenon_H111 zenon_Hf8 zenon_H137 zenon_H12d zenon_H40 zenon_H19b zenon_H173 zenon_H2c zenon_Hca zenon_Hcc zenon_Hc7 zenon_H33 zenon_H26 zenon_H134. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.10 apply (zenon_L77_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.10 apply (zenon_L330_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.10 apply (zenon_L331_); trivial. % 7.87/8.10 apply (zenon_L298_); trivial. % 7.87/8.10 (* end of lemma zenon_L332_ *) % 7.87/8.10 assert (zenon_L333_ : (~((e1) = (e3))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H8f zenon_H86 zenon_Hb9. % 7.87/8.10 cut (((op (e0) (e0)) = (e3)) = ((e1) = (e3))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H8f. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H86. % 7.87/8.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.10 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_Hb5 zenon_Hb9). % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L333_ *) % 7.87/8.10 assert (zenon_L334_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H95 zenon_Hb9 zenon_H8f zenon_H89 zenon_H6d zenon_H10e zenon_H15c zenon_Hfc zenon_H128. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.10 apply (zenon_L333_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.10 apply (zenon_L37_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.10 apply (zenon_L200_); trivial. % 7.87/8.10 apply (zenon_L137_); trivial. % 7.87/8.10 (* end of lemma zenon_L334_ *) % 7.87/8.10 assert (zenon_L335_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_Hfc zenon_Hf7 zenon_H1cd. % 7.87/8.10 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1cd. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H4a. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H1ce. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_Hfc. % 7.87/8.10 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H4b. apply refl_equal. % 7.87/8.10 apply zenon_H1cf. apply sym_equal. exact zenon_Hf7. % 7.87/8.10 apply zenon_H4b. apply refl_equal. % 7.87/8.10 apply zenon_H4b. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L335_ *) % 7.87/8.10 assert (zenon_L336_ : (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H12b zenon_Hf7 zenon_H1cd. % 7.87/8.10 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 7.87/8.10 apply (zenon_L335_); trivial. % 7.87/8.10 (* end of lemma zenon_L336_ *) % 7.87/8.10 assert (zenon_L337_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H128 zenon_Hfc zenon_H10e zenon_H6d zenon_H89 zenon_H8f zenon_Hb9 zenon_H95 zenon_H12b zenon_H1cd. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.87/8.10 apply (zenon_L118_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.87/8.10 apply (zenon_L334_); trivial. % 7.87/8.10 apply (zenon_L336_); trivial. % 7.87/8.10 (* end of lemma zenon_L337_ *) % 7.87/8.10 assert (zenon_L338_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H26 zenon_H66 zenon_H6c. % 7.87/8.10 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.87/8.10 cut (((e3) = (e3)) = ((e2) = (e3))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H6c. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H68. % 7.87/8.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.10 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H9d. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H26. % 7.87/8.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.87/8.10 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H6b zenon_H66). % 7.87/8.10 apply zenon_H22. apply refl_equal. % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L338_ *) % 7.87/8.10 assert (zenon_L339_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.10 do 0 intro. intros zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_He0 zenon_H10b zenon_H111 zenon_H1c7 zenon_H6c zenon_H70 zenon_H38 zenon_H83 zenon_H13a. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.10 apply (zenon_L327_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.10 apply (zenon_L43_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.10 apply (zenon_L107_); trivial. % 7.87/8.10 exact (zenon_H13a zenon_Ha1). % 7.87/8.10 (* end of lemma zenon_L339_ *) % 7.87/8.10 assert (zenon_L340_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H115 zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H6c zenon_H70 zenon_H38 zenon_H83 zenon_H13a. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.87/8.10 apply (zenon_L322_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.87/8.10 apply (zenon_L323_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_L339_); trivial. % 7.87/8.10 (* end of lemma zenon_L340_ *) % 7.87/8.10 assert (zenon_L341_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H1cd zenon_H95 zenon_Hb9 zenon_H8f zenon_H89 zenon_H128 zenon_H67 zenon_H1d0 zenon_H12d zenon_H12b zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H6c zenon_H38 zenon_H83 zenon_H13a zenon_Hef zenon_H26 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L337_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L338_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L340_); trivial. % 7.87/8.10 apply (zenon_L140_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L341_ *) % 7.87/8.10 assert (zenon_L342_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H115 zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_H6c zenon_H70 zenon_H10b zenon_H82 zenon_H13a. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.87/8.10 apply (zenon_L322_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.87/8.10 apply (zenon_L323_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.10 apply (zenon_L327_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.10 apply (zenon_L43_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.10 apply (zenon_L115_); trivial. % 7.87/8.10 exact (zenon_H13a zenon_Ha1). % 7.87/8.10 (* end of lemma zenon_L342_ *) % 7.87/8.10 assert (zenon_L343_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H8f zenon_H67 zenon_H134 zenon_H26 zenon_H33 zenon_Hc7 zenon_Hcc zenon_Hca zenon_H2c zenon_H173 zenon_H19b zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_H6c zenon_H10b zenon_H82 zenon_H13a zenon_Hef zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L338_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L342_); trivial. % 7.87/8.10 apply (zenon_L297_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L343_ *) % 7.87/8.10 assert (zenon_L344_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_Haa zenon_H86 zenon_H16e zenon_H115 zenon_Hef zenon_H6c zenon_H9c zenon_Hfc zenon_H12d. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L43_); trivial. % 7.87/8.10 apply (zenon_L139_); trivial. % 7.87/8.10 (* end of lemma zenon_L344_ *) % 7.87/8.10 assert (zenon_L345_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H28 zenon_H2d zenon_H67 zenon_H12d zenon_H9c zenon_H6c zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L213_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_L344_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L345_ *) % 7.87/8.10 assert (zenon_L346_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H28 zenon_H67 zenon_Hdc zenon_H6c zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_H10b zenon_H82 zenon_H13a zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L213_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L342_); trivial. % 7.87/8.10 apply (zenon_L73_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L346_ *) % 7.87/8.10 assert (zenon_L347_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H11e zenon_H99 zenon_H20 zenon_H81 zenon_H13b zenon_H19b zenon_H173 zenon_H2c zenon_Hca zenon_Hcc zenon_Hc7 zenon_H33 zenon_H134 zenon_H8f zenon_H130 zenon_H12d zenon_H162 zenon_H28 zenon_H67 zenon_H6c zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_H10b zenon_H82 zenon_H13a zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.10 apply (zenon_L116_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.10 apply (zenon_L85_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.10 apply (zenon_L35_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.10 apply (zenon_L343_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.10 apply (zenon_L142_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.10 apply (zenon_L345_); trivial. % 7.87/8.10 apply (zenon_L346_); trivial. % 7.87/8.10 (* end of lemma zenon_L347_ *) % 7.87/8.10 assert (zenon_L348_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.87/8.10 do 0 intro. intros zenon_Haa zenon_H86 zenon_H16e zenon_Hef zenon_H5e zenon_Hfc zenon_Hf1 zenon_Hbc zenon_H64 zenon_Hff zenon_H2d zenon_H115 zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H98 zenon_H99 zenon_H142 zenon_H10b zenon_H111 zenon_Hca zenon_H20 zenon_H51 zenon_H6c zenon_Hdc. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.87/8.10 apply (zenon_L260_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.87/8.10 apply (zenon_L293_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.87/8.10 apply (zenon_L326_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.10 apply (zenon_L41_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.10 apply (zenon_L227_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_L170_); trivial. % 7.87/8.10 apply (zenon_L73_); trivial. % 7.87/8.10 (* end of lemma zenon_L348_ *) % 7.87/8.10 assert (zenon_L349_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H28 zenon_H67 zenon_Hdc zenon_H6c zenon_Ha7 zenon_H51 zenon_H20 zenon_Hca zenon_H111 zenon_H10b zenon_H142 zenon_H99 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H2d zenon_Hff zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_H38 zenon_H83 zenon_H13a zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L213_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.10 apply (zenon_L348_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.10 apply (zenon_L43_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.10 apply (zenon_L107_); trivial. % 7.87/8.10 exact (zenon_H13a zenon_Ha1). % 7.87/8.10 apply (zenon_L73_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L349_ *) % 7.87/8.10 assert (zenon_L350_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H11e zenon_H5e zenon_Hfc zenon_H13a zenon_H38 zenon_Haa zenon_H86 zenon_H16e zenon_Hef zenon_H64 zenon_Hff zenon_H2d zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H99 zenon_H142 zenon_H10b zenon_H111 zenon_Hca zenon_H20 zenon_H51 zenon_Ha7 zenon_H6c zenon_H67 zenon_H28 zenon_H162 zenon_H12d zenon_H8f zenon_H134 zenon_Hc7 zenon_Hcc zenon_H173 zenon_H19b zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H18e zenon_H10e zenon_H5a zenon_H1c7 zenon_H13b zenon_Hf1 zenon_Hbc. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.10 apply (zenon_L116_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.10 apply (zenon_L85_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L338_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L340_); trivial. % 7.87/8.10 apply (zenon_L297_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.10 apply (zenon_L85_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.10 apply (zenon_L345_); trivial. % 7.87/8.10 apply (zenon_L349_); trivial. % 7.87/8.10 apply (zenon_L113_); trivial. % 7.87/8.10 (* end of lemma zenon_L350_ *) % 7.87/8.10 assert (zenon_L351_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H124 zenon_H137 zenon_Hf8 zenon_H4e zenon_H31 zenon_H24 zenon_Hec zenon_H130 zenon_H81 zenon_H11e zenon_H5e zenon_Hfc zenon_H13a zenon_H38 zenon_Haa zenon_H86 zenon_H16e zenon_Hef zenon_H64 zenon_Hff zenon_H2d zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H99 zenon_H142 zenon_H10b zenon_H111 zenon_Hca zenon_H20 zenon_H51 zenon_Ha7 zenon_H6c zenon_H67 zenon_H28 zenon_H162 zenon_H12d zenon_H8f zenon_H134 zenon_Hc7 zenon_Hcc zenon_H173 zenon_H19b zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H18e zenon_H10e zenon_H5a zenon_H1c7 zenon_H13b zenon_Hf1. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.10 exact (zenon_H24 zenon_H1f). % 7.87/8.10 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.87/8.10 exact (zenon_H24 zenon_H1f). % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.87/8.10 apply (zenon_L116_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.87/8.10 apply (zenon_L260_); trivial. % 7.87/8.10 apply (zenon_L332_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.10 apply (zenon_L347_); trivial. % 7.87/8.10 apply (zenon_L350_); trivial. % 7.87/8.10 (* end of lemma zenon_L351_ *) % 7.87/8.10 assert (zenon_L352_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H142 zenon_H31 zenon_H13a zenon_H83 zenon_H38 zenon_H99 zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H70 zenon_H18e zenon_Ha7 zenon_Hbb zenon_H113 zenon_H55 zenon_H1ca zenon_H115 zenon_H2d zenon_Hbd zenon_He3. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.10 apply (zenon_L15_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.87/8.10 apply (zenon_L322_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.87/8.10 apply (zenon_L323_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.10 apply (zenon_L327_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.10 apply (zenon_L97_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.10 apply (zenon_L107_); trivial. % 7.87/8.10 exact (zenon_H13a zenon_Ha1). % 7.87/8.10 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_L186_); trivial. % 7.87/8.10 (* end of lemma zenon_L352_ *) % 7.87/8.10 assert (zenon_L353_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H28 zenon_H67 zenon_H12d zenon_H142 zenon_H31 zenon_H13a zenon_H83 zenon_H38 zenon_H99 zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H18e zenon_Ha7 zenon_Hbb zenon_H113 zenon_H55 zenon_H1ca zenon_H2d zenon_Hbd zenon_He3 zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L213_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L352_); trivial. % 7.87/8.10 apply (zenon_L139_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L353_ *) % 7.87/8.10 assert (zenon_L354_ : (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H8f zenon_H15c zenon_H13e. % 7.87/8.10 cut (((op (e2) (e2)) = (e3)) = ((e1) = (e3))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H8f. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H15c. % 7.87/8.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.10 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H13f zenon_H13e). % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L354_ *) % 7.87/8.10 assert (zenon_L355_ : (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e2)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H6c zenon_Hf7 zenon_H148. % 7.87/8.10 cut (((op (e3) (e2)) = (e3)) = ((e2) = (e3))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H6c. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_Hf7. % 7.87/8.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.87/8.10 cut (((op (e3) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 7.87/8.10 congruence. % 7.87/8.10 exact (zenon_H1d3 zenon_H148). % 7.87/8.10 apply zenon_H69. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L355_ *) % 7.87/8.10 assert (zenon_L356_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1d0 zenon_H67 zenon_H111 zenon_H2d zenon_H13e zenon_H8f zenon_H6c zenon_H148. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.87/8.10 apply (zenon_L118_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.87/8.10 apply (zenon_L325_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.87/8.10 apply (zenon_L354_); trivial. % 7.87/8.10 apply (zenon_L355_); trivial. % 7.87/8.10 (* end of lemma zenon_L356_ *) % 7.87/8.10 assert (zenon_L357_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H1c7 zenon_H10b zenon_H6c zenon_H8f zenon_H2d zenon_H111 zenon_H67 zenon_H1d0 zenon_H148 zenon_H5a zenon_H70 zenon_H18e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.87/8.10 apply (zenon_L326_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.87/8.10 apply (zenon_L356_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.87/8.10 apply (zenon_L178_); trivial. % 7.87/8.10 apply (zenon_L273_); trivial. % 7.87/8.10 (* end of lemma zenon_L357_ *) % 7.87/8.10 assert (zenon_L358_ : ((op (e3) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H195 zenon_Ha2 zenon_H5e. % 7.87/8.10 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H5e. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H4a. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 7.87/8.10 congruence. % 7.87/8.10 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 7.87/8.10 intro zenon_D_pnotp. % 7.87/8.10 apply zenon_H5f. % 7.87/8.10 rewrite <- zenon_D_pnotp. % 7.87/8.10 exact zenon_H195. % 7.87/8.10 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 7.87/8.10 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.87/8.10 congruence. % 7.87/8.10 apply zenon_H4b. apply refl_equal. % 7.87/8.10 apply zenon_Ha6. apply sym_equal. exact zenon_Ha2. % 7.87/8.10 apply zenon_H4b. apply refl_equal. % 7.87/8.10 apply zenon_H4b. apply refl_equal. % 7.87/8.10 (* end of lemma zenon_L358_ *) % 7.87/8.10 assert (zenon_L359_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H197 zenon_H20 zenon_H3e zenon_H33 zenon_H40 zenon_Hf4 zenon_H2c zenon_H170 zenon_H18e zenon_H70 zenon_H5a zenon_H1d0 zenon_H67 zenon_H111 zenon_H2d zenon_H8f zenon_H6c zenon_H10b zenon_H1c7 zenon_Ha2 zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.87/8.10 apply (zenon_L77_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.87/8.10 apply (zenon_L227_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.87/8.10 apply (zenon_L357_); trivial. % 7.87/8.10 apply (zenon_L358_); trivial. % 7.87/8.10 (* end of lemma zenon_L359_ *) % 7.87/8.10 assert (zenon_L360_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H4e zenon_H5e zenon_H1c7 zenon_H10b zenon_H6c zenon_H8f zenon_H67 zenon_H1d0 zenon_H5a zenon_H70 zenon_H18e zenon_H170 zenon_H2c zenon_Hf4 zenon_H40 zenon_H33 zenon_H20 zenon_H197 zenon_H2d zenon_H173 zenon_H111 zenon_Hf8 zenon_H150 zenon_He3 zenon_Hbd zenon_H64 zenon_Ha2 zenon_Hfc zenon_H49. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.10 apply (zenon_L359_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.10 apply (zenon_L330_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.10 apply (zenon_L331_); trivial. % 7.87/8.10 apply (zenon_L188_); trivial. % 7.87/8.10 (* end of lemma zenon_L360_ *) % 7.87/8.10 assert (zenon_L361_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_H86 zenon_H28 zenon_H12d zenon_H4e zenon_H1c7 zenon_H10b zenon_H6c zenon_H8f zenon_H67 zenon_H1d0 zenon_H5a zenon_H18e zenon_H170 zenon_H2c zenon_Hf4 zenon_H40 zenon_H33 zenon_H20 zenon_H197 zenon_H2d zenon_H173 zenon_H111 zenon_Hf8 zenon_H150 zenon_He3 zenon_Hbd zenon_H64 zenon_Ha2 zenon_H49 zenon_Hef zenon_H26 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L213_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L338_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L360_); trivial. % 7.87/8.10 apply (zenon_L139_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L361_ *) % 7.87/8.10 assert (zenon_L362_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H162 zenon_Hbb zenon_H67 zenon_Hde zenon_H8f zenon_H170 zenon_H2d zenon_H2c zenon_Hdc zenon_H40 zenon_H33 zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L217_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.10 apply (zenon_L239_); trivial. % 7.87/8.10 apply (zenon_L91_); trivial. % 7.87/8.10 apply (zenon_L109_); trivial. % 7.87/8.10 (* end of lemma zenon_L362_ *) % 7.87/8.10 assert (zenon_L363_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.10 do 0 intro. intros zenon_H13b zenon_He3 zenon_Hbd zenon_H1ca zenon_H55 zenon_H113 zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H99 zenon_H38 zenon_H83 zenon_H13a zenon_H31 zenon_H142 zenon_H20 zenon_H6c zenon_H12d zenon_H28 zenon_H162 zenon_Hbb zenon_H67 zenon_Hde zenon_H8f zenon_H170 zenon_H2d zenon_H2c zenon_H40 zenon_H33 zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.10 apply (zenon_L66_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.10 apply (zenon_L164_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.10 apply (zenon_L338_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.10 apply (zenon_L205_); trivial. % 7.87/8.10 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.11 apply (zenon_L352_); trivial. % 7.87/8.11 apply (zenon_L91_); trivial. % 7.87/8.11 apply (zenon_L109_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.87/8.11 apply (zenon_L85_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.87/8.11 apply (zenon_L345_); trivial. % 7.87/8.11 apply (zenon_L362_); trivial. % 7.87/8.11 (* end of lemma zenon_L363_ *) % 7.87/8.11 assert (zenon_L364_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.87/8.11 do 0 intro. intros zenon_Haa zenon_H26 zenon_H115 zenon_Hef zenon_H5e zenon_Ha2 zenon_H1c7 zenon_H10b zenon_H6c zenon_H8f zenon_H2d zenon_H111 zenon_H67 zenon_H1d0 zenon_H5a zenon_H18e zenon_H170 zenon_H2c zenon_Hf4 zenon_H40 zenon_H33 zenon_H3e zenon_H20 zenon_H197 zenon_H12b zenon_H12d. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.11 apply (zenon_L338_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.11 apply (zenon_L205_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.11 apply (zenon_L359_); trivial. % 7.87/8.11 apply (zenon_L140_); trivial. % 7.87/8.11 (* end of lemma zenon_L364_ *) % 7.87/8.11 assert (zenon_L365_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.87/8.11 do 0 intro. intros zenon_H162 zenon_Hbb zenon_He3 zenon_Hbd zenon_H2d zenon_H4e zenon_H12d zenon_H12b zenon_H197 zenon_H20 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H18e zenon_H5a zenon_H1d0 zenon_H67 zenon_H8f zenon_H6c zenon_H10b zenon_H1c7 zenon_Hef zenon_H26 zenon_Haa zenon_H55 zenon_Hde zenon_H111 zenon_Hf8 zenon_H150 zenon_H64 zenon_Ha2 zenon_H49 zenon_H31 zenon_H142 zenon_Hfc zenon_H5e. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.11 apply (zenon_L66_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.11 apply (zenon_L164_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.11 apply (zenon_L15_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.87/8.11 apply (zenon_L364_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.87/8.11 apply (zenon_L79_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.87/8.11 apply (zenon_L331_); trivial. % 7.87/8.11 apply (zenon_L188_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.11 apply (zenon_L325_); trivial. % 7.87/8.11 apply (zenon_L186_); trivial. % 7.87/8.11 apply (zenon_L109_); trivial. % 7.87/8.11 (* end of lemma zenon_L365_ *) % 7.87/8.11 assert (zenon_L366_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.87/8.11 do 0 intro. intros zenon_H1ca zenon_H113 zenon_Hbb zenon_H115 zenon_H2d zenon_Ha7 zenon_H18e zenon_H70 zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_Hf4 zenon_H99 zenon_H10b zenon_H82 zenon_H13a. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.87/8.11 apply (zenon_L65_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.87/8.11 apply (zenon_L323_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.87/8.11 apply (zenon_L325_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.87/8.11 apply (zenon_L327_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.87/8.11 apply (zenon_L97_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.87/8.11 apply (zenon_L115_); trivial. % 7.87/8.11 exact (zenon_H13a zenon_Ha1). % 7.87/8.11 (* end of lemma zenon_L366_ *) % 7.87/8.11 assert (zenon_L367_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 7.87/8.11 do 0 intro. intros zenon_H142 zenon_H55 zenon_H31 zenon_H13a zenon_H82 zenon_H10b zenon_H99 zenon_H1c7 zenon_H111 zenon_H5a zenon_H10e zenon_H70 zenon_H18e zenon_Ha7 zenon_Hbb zenon_H113 zenon_H1ca zenon_H115 zenon_H2d zenon_Hbd zenon_He3. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.11 apply (zenon_L15_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.11 apply (zenon_L366_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.11 apply (zenon_L325_); trivial. % 7.87/8.11 apply (zenon_L186_); trivial. % 7.87/8.11 (* end of lemma zenon_L367_ *) % 7.87/8.11 assert (zenon_L368_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.11 do 0 intro. intros zenon_H124 zenon_H24 zenon_H49 zenon_H64 zenon_H150 zenon_Hf8 zenon_H6c zenon_H8f zenon_H1d0 zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H197 zenon_H12b zenon_H4e zenon_H13b zenon_H173 zenon_H89 zenon_H134 zenon_Hcc zenon_Hca zenon_H19b zenon_H184 zenon_H11e zenon_H20 zenon_H5e zenon_Hfc zenon_Haa zenon_H86 zenon_H16e zenon_Hef zenon_He3 zenon_Hbd zenon_H2d zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H99 zenon_H38 zenon_H13a zenon_H31 zenon_H142 zenon_H12d zenon_H67 zenon_H28 zenon_H162 zenon_Hf1. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.87/8.11 exact (zenon_H24 zenon_H1f). % 7.87/8.11 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.11 apply (zenon_L116_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.11 apply (zenon_L85_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.11 apply (zenon_L353_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.11 apply (zenon_L66_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.11 apply (zenon_L164_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.11 apply (zenon_L217_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.11 apply (zenon_L205_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.87/8.11 apply (zenon_L15_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.87/8.11 apply (zenon_L360_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.87/8.11 apply (zenon_L325_); trivial. % 7.87/8.11 apply (zenon_L186_); trivial. % 7.87/8.11 apply (zenon_L297_); trivial. % 7.87/8.11 apply (zenon_L109_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.87/8.11 apply (zenon_L221_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.11 apply (zenon_L116_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.11 apply (zenon_L128_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.11 apply (zenon_L353_); trivial. % 7.87/8.11 apply (zenon_L361_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.11 apply (zenon_L116_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.11 apply (zenon_L85_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.11 apply (zenon_L363_); trivial. % 7.87/8.11 apply (zenon_L365_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.87/8.11 apply (zenon_L213_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.87/8.11 apply (zenon_L164_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.87/8.11 apply (zenon_L217_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.87/8.11 apply (zenon_L205_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.87/8.11 apply (zenon_L367_); trivial. % 7.87/8.11 apply (zenon_L139_); trivial. % 7.87/8.11 apply (zenon_L109_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.87/8.11 apply (zenon_L116_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.87/8.11 apply (zenon_L85_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.87/8.11 apply (zenon_L353_); trivial. % 7.87/8.11 apply (zenon_L113_); trivial. % 7.87/8.11 (* end of lemma zenon_L368_ *) % 7.87/8.11 assert (zenon_L369_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 7.87/8.11 do 0 intro. intros zenon_H15f zenon_H51 zenon_Hff zenon_H81 zenon_H130 zenon_Hec zenon_H137 zenon_H124 zenon_H24 zenon_H49 zenon_H64 zenon_H150 zenon_Hf8 zenon_H6c zenon_H8f zenon_H1d0 zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H197 zenon_H12b zenon_H4e zenon_H13b zenon_H173 zenon_H89 zenon_H134 zenon_Hcc zenon_Hca zenon_H19b zenon_H184 zenon_H11e zenon_H20 zenon_H5e zenon_Hfc zenon_Haa zenon_H86 zenon_H16e zenon_Hef zenon_Hbd zenon_H2d zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H99 zenon_H38 zenon_H13a zenon_H31 zenon_H142 zenon_H12d zenon_H67 zenon_H28 zenon_H162 zenon_Hf1. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.87/8.11 apply (zenon_L333_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.87/8.11 apply (zenon_L351_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.87/8.11 apply (zenon_L322_); trivial. % 7.87/8.11 apply (zenon_L368_); trivial. % 7.87/8.11 (* end of lemma zenon_L369_ *) % 7.87/8.11 assert (zenon_L370_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.87/8.11 do 0 intro. intros zenon_H95 zenon_Hf1 zenon_H162 zenon_H28 zenon_H12d zenon_H142 zenon_H13a zenon_H38 zenon_H99 zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H18e zenon_Ha7 zenon_H113 zenon_H55 zenon_H1ca zenon_H2d zenon_Hbd zenon_Hef zenon_H16e zenon_Haa zenon_Hfc zenon_H5e zenon_H20 zenon_H11e zenon_H184 zenon_H19b zenon_Hca zenon_Hcc zenon_H134 zenon_H89 zenon_H173 zenon_H13b zenon_H4e zenon_H12b zenon_H197 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H1d0 zenon_Hf8 zenon_H150 zenon_H64 zenon_H49 zenon_H24 zenon_H124 zenon_H137 zenon_Hec zenon_H130 zenon_H81 zenon_Hff zenon_H51 zenon_H15f zenon_H8f zenon_Hbb zenon_H67 zenon_H31 zenon_H6c zenon_H93. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.87/8.11 apply (zenon_L369_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.87/8.11 apply (zenon_L66_); trivial. % 7.87/8.11 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.87/8.11 apply (zenon_L123_); trivial. % 7.87/8.11 apply (zenon_L39_); trivial. % 7.87/8.11 (* end of lemma zenon_L370_ *) % 7.87/8.11 assert (zenon_L371_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H128 zenon_H95 zenon_Hf1 zenon_H162 zenon_H28 zenon_H12d zenon_H142 zenon_H13a zenon_H38 zenon_H99 zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H18e zenon_Ha7 zenon_H113 zenon_H55 zenon_H1ca zenon_H2d zenon_Hbd zenon_Hef zenon_H16e zenon_Haa zenon_Hfc zenon_H5e zenon_H20 zenon_H11e zenon_H184 zenon_H19b zenon_Hca zenon_Hcc zenon_H134 zenon_H89 zenon_H173 zenon_H13b zenon_H4e zenon_H12b zenon_H197 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H1d0 zenon_Hf8 zenon_H150 zenon_H64 zenon_H49 zenon_H24 zenon_H124 zenon_H137 zenon_Hec zenon_H130 zenon_H81 zenon_Hff zenon_H51 zenon_H15f zenon_H8f zenon_Hbb zenon_H67 zenon_H31 zenon_H6c. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.11 exact (zenon_H24 zenon_H1f). % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.11 apply (zenon_L116_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.11 apply (zenon_L329_); trivial. % 7.95/8.11 apply (zenon_L370_); trivial. % 7.95/8.11 (* end of lemma zenon_L371_ *) % 7.95/8.11 assert (zenon_L372_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H197 zenon_H20 zenon_H3e zenon_H70 zenon_H33 zenon_H40 zenon_Hde zenon_H2c zenon_H2d zenon_H170 zenon_H9f zenon_H5a zenon_Ha2 zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.95/8.11 apply (zenon_L77_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.95/8.11 apply (zenon_L239_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.95/8.11 apply (zenon_L178_); trivial. % 7.95/8.11 apply (zenon_L358_); trivial. % 7.95/8.11 (* end of lemma zenon_L372_ *) % 7.95/8.11 assert (zenon_L373_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1d4 zenon_H3e zenon_H41. % 7.95/8.11 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1d4. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H3e. % 7.95/8.11 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 7.95/8.11 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 7.95/8.11 congruence. % 7.95/8.11 apply zenon_H181. apply refl_equal. % 7.95/8.11 apply zenon_H42. apply sym_equal. exact zenon_H41. % 7.95/8.11 (* end of lemma zenon_L373_ *) % 7.95/8.11 assert (zenon_L374_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H95 zenon_H1f zenon_H6c zenon_H89 zenon_H6d zenon_H10e zenon_H15c zenon_Hfc zenon_H128. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.11 apply (zenon_L243_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.11 apply (zenon_L37_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.11 apply (zenon_L200_); trivial. % 7.95/8.11 apply (zenon_L137_); trivial. % 7.95/8.11 (* end of lemma zenon_L374_ *) % 7.95/8.11 assert (zenon_L375_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H128 zenon_Hfc zenon_H10e zenon_H6d zenon_H89 zenon_H6c zenon_H1f zenon_H95 zenon_H12b zenon_H1cd. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.11 apply (zenon_L118_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.11 apply (zenon_L374_); trivial. % 7.95/8.11 apply (zenon_L336_); trivial. % 7.95/8.11 (* end of lemma zenon_L375_ *) % 7.95/8.11 assert (zenon_L376_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_Hcc zenon_H66 zenon_Hde zenon_H173 zenon_H9c zenon_Hca zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H128 zenon_Hfc zenon_H10e zenon_H89 zenon_H6c zenon_H1f zenon_H95 zenon_H12b zenon_H1cd. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.11 apply (zenon_L304_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.11 apply (zenon_L306_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.11 apply (zenon_L185_); trivial. % 7.95/8.11 apply (zenon_L375_); trivial. % 7.95/8.11 (* end of lemma zenon_L376_ *) % 7.95/8.11 assert (zenon_L377_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H137 zenon_H3e zenon_H1d4 zenon_H1cd zenon_H12b zenon_H95 zenon_H1f zenon_H6c zenon_H89 zenon_H10e zenon_H128 zenon_Hef zenon_H111 zenon_H67 zenon_H1d0 zenon_Hca zenon_H173 zenon_H66 zenon_Hcc zenon_H9c zenon_H134 zenon_Hfc zenon_H12d. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 7.95/8.11 apply (zenon_L373_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 7.95/8.11 apply (zenon_L376_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 7.95/8.11 apply (zenon_L145_); trivial. % 7.95/8.11 apply (zenon_L139_); trivial. % 7.95/8.11 (* end of lemma zenon_L377_ *) % 7.95/8.11 assert (zenon_L378_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_Haa zenon_H134 zenon_Hcc zenon_H173 zenon_Hca zenon_H1d4 zenon_H3e zenon_H137 zenon_H1cd zenon_H12b zenon_H95 zenon_H1f zenon_H89 zenon_H10e zenon_H128 zenon_Hef zenon_H111 zenon_H67 zenon_H1d0 zenon_H6c zenon_H9c zenon_Hfc zenon_H12d. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.11 apply (zenon_L377_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.11 apply (zenon_L375_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.11 apply (zenon_L43_); trivial. % 7.95/8.11 apply (zenon_L139_); trivial. % 7.95/8.11 (* end of lemma zenon_L378_ *) % 7.95/8.11 assert (zenon_L379_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 7.95/8.11 do 0 intro. intros zenon_Hec zenon_H12d zenon_Hfc zenon_H6c zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H128 zenon_H10e zenon_H89 zenon_H95 zenon_H12b zenon_H1cd zenon_H137 zenon_H1d4 zenon_Hca zenon_H173 zenon_Hcc zenon_H134 zenon_Haa zenon_H99 zenon_Hbb zenon_H17c zenon_H9c zenon_H3e zenon_H20. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.11 apply (zenon_L378_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.11 apply (zenon_L116_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.11 apply (zenon_L238_); trivial. % 7.95/8.11 apply (zenon_L77_); trivial. % 7.95/8.11 (* end of lemma zenon_L379_ *) % 7.95/8.11 assert (zenon_L380_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1d5 zenon_H15c. % 7.95/8.11 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 7.95/8.11 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 7.95/8.11 congruence. % 7.95/8.11 exact (zenon_H1d6 zenon_H15c). % 7.95/8.11 exact (zenon_H1d6 zenon_H15c). % 7.95/8.11 (* end of lemma zenon_L380_ *) % 7.95/8.11 assert (zenon_L381_ : (~((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1d7 zenon_H15c. % 7.95/8.11 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.11 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 7.95/8.11 congruence. % 7.95/8.11 exact (zenon_H1d6 zenon_H15c). % 7.95/8.11 apply zenon_H22. apply refl_equal. % 7.95/8.11 (* end of lemma zenon_L381_ *) % 7.95/8.11 assert (zenon_L382_ : ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_He0 zenon_H15c zenon_H1d8. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1d8. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1ba. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 7.95/8.11 congruence. % 7.95/8.11 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1d9. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_He0. % 7.95/8.11 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.11 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 7.95/8.11 congruence. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1da. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1ba. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 7.95/8.11 congruence. % 7.95/8.11 apply (zenon_L381_); trivial. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 apply zenon_H57. apply refl_equal. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 (* end of lemma zenon_L382_ *) % 7.95/8.11 assert (zenon_L383_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H47 zenon_He0 zenon_H15c. % 7.95/8.11 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H1db ]. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1c0. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1c1. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 7.95/8.11 congruence. % 7.95/8.11 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1c3. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H47. % 7.95/8.11 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.11 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 7.95/8.11 congruence. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1dc. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1c1. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 7.95/8.11 congruence. % 7.95/8.11 apply (zenon_L380_); trivial. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply zenon_H1d. apply refl_equal. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply (zenon_notand_s _ _ zenon_H1db); [ zenon_intro zenon_H1dd | zenon_intro zenon_H1d8 ]. % 7.95/8.11 apply zenon_H1dd. apply sym_equal. exact zenon_H15c. % 7.95/8.11 apply (zenon_L382_); trivial. % 7.95/8.11 (* end of lemma zenon_L383_ *) % 7.95/8.11 assert (zenon_L384_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1c7 zenon_H111 zenon_H5a zenon_H10b zenon_H82 zenon_H47 zenon_He0. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.95/8.11 apply (zenon_L326_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.95/8.11 apply (zenon_L190_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.95/8.11 apply (zenon_L115_); trivial. % 7.95/8.11 apply (zenon_L383_); trivial. % 7.95/8.11 (* end of lemma zenon_L384_ *) % 7.95/8.11 assert (zenon_L385_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H11e zenon_H165 zenon_H154 zenon_H29 zenon_Hff zenon_H81 zenon_H13b zenon_H18e zenon_H55 zenon_H19b zenon_H2c zenon_H33 zenon_H130 zenon_H5e zenon_Hfc zenon_H1ca zenon_H113 zenon_H4e zenon_H20 zenon_H17c zenon_Hbb zenon_H99 zenon_Haa zenon_Hcc zenon_Hca zenon_H1d4 zenon_H1cd zenon_H12b zenon_H95 zenon_H89 zenon_H10e zenon_H128 zenon_Hef zenon_H67 zenon_H1d0 zenon_Hec zenon_H2d zenon_H173 zenon_H12d zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H1c7 zenon_H111 zenon_H5a zenon_H8f zenon_H162 zenon_Ha7 zenon_H6c zenon_H8e zenon_H134 zenon_H10b zenon_H82 zenon_H13a. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.11 apply (zenon_L116_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.11 apply (zenon_L246_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.11 apply (zenon_L35_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.11 apply (zenon_L343_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.11 apply (zenon_L142_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.11 apply (zenon_L66_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.11 apply (zenon_L164_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.11 apply (zenon_L65_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.11 apply (zenon_L323_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.11 apply (zenon_L325_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.11 apply (zenon_L379_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.11 apply (zenon_L330_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.11 apply (zenon_L146_); trivial. % 7.95/8.11 apply (zenon_L384_); trivial. % 7.95/8.11 apply (zenon_L109_); trivial. % 7.95/8.11 apply (zenon_L153_); trivial. % 7.95/8.11 (* end of lemma zenon_L385_ *) % 7.95/8.11 assert (zenon_L386_ : (~((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e0)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1de zenon_H36. % 7.95/8.11 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.11 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 7.95/8.11 congruence. % 7.95/8.11 exact (zenon_H16a zenon_H36). % 7.95/8.11 apply zenon_H22. apply refl_equal. % 7.95/8.11 (* end of lemma zenon_L386_ *) % 7.95/8.11 assert (zenon_L387_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((e3) = (op (op (e2) (e2)) (e2)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_Hb0 zenon_H36 zenon_H1b9. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e3) = (op (op (e2) (e2)) (e2)))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1b9. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1ba. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 7.95/8.11 congruence. % 7.95/8.11 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (e2)) (e2)) = (e3))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1bc. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_Hb0. % 7.95/8.11 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.11 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 7.95/8.11 congruence. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1df. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1ba. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.95/8.11 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 7.95/8.11 congruence. % 7.95/8.11 apply (zenon_L386_); trivial. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 apply zenon_H69. apply refl_equal. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 apply zenon_H1bb. apply refl_equal. % 7.95/8.11 (* end of lemma zenon_L387_ *) % 7.95/8.11 assert (zenon_L388_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 7.95/8.11 do 0 intro. intros zenon_Hb9 zenon_Hb0 zenon_H36. % 7.95/8.11 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e0 ]. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1e1. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1c1. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 7.95/8.11 congruence. % 7.95/8.11 cut (((op (e0) (e0)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1e2. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_Hb9. % 7.95/8.11 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.11 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 7.95/8.11 congruence. % 7.95/8.11 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H1e3. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_H1c1. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.95/8.11 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 7.95/8.11 congruence. % 7.95/8.11 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 7.95/8.11 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 7.95/8.11 congruence. % 7.95/8.11 exact (zenon_H16a zenon_H36). % 7.95/8.11 exact (zenon_H16a zenon_H36). % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply zenon_H57. apply refl_equal. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply zenon_H1c2. apply refl_equal. % 7.95/8.11 apply (zenon_notand_s _ _ zenon_H1e0); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H1b9 ]. % 7.95/8.11 apply zenon_H1c6. apply sym_equal. exact zenon_H36. % 7.95/8.11 apply (zenon_L387_); trivial. % 7.95/8.11 (* end of lemma zenon_L388_ *) % 7.95/8.11 assert (zenon_L389_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1d0 zenon_Hb9 zenon_H6d zenon_Hef zenon_H36 zenon_H67 zenon_Hfc zenon_H1cd. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.11 apply (zenon_L388_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.11 apply (zenon_L215_); trivial. % 7.95/8.11 apply (zenon_L335_); trivial. % 7.95/8.11 (* end of lemma zenon_L389_ *) % 7.95/8.11 assert (zenon_L390_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H38 zenon_Hd2 zenon_H13e. % 7.95/8.11 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H38. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_Hd2. % 7.95/8.11 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 7.95/8.11 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 7.95/8.11 congruence. % 7.95/8.11 apply zenon_H46. apply refl_equal. % 7.95/8.11 apply zenon_H147. apply sym_equal. exact zenon_H13e. % 7.95/8.11 (* end of lemma zenon_L390_ *) % 7.95/8.11 assert (zenon_L391_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1c7 zenon_H44 zenon_H5a zenon_Hd2 zenon_H38 zenon_H18e zenon_H9c zenon_Hb0 zenon_H10b. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.95/8.11 apply (zenon_L16_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.95/8.11 apply (zenon_L390_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.95/8.11 apply (zenon_L299_); trivial. % 7.95/8.11 apply (zenon_L274_); trivial. % 7.95/8.11 (* end of lemma zenon_L391_ *) % 7.95/8.11 assert (zenon_L392_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H67 zenon_Hf7 zenon_H44. % 7.95/8.11 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 7.95/8.11 intro zenon_D_pnotp. % 7.95/8.11 apply zenon_H67. % 7.95/8.11 rewrite <- zenon_D_pnotp. % 7.95/8.11 exact zenon_Hf7. % 7.95/8.11 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.11 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 7.95/8.11 congruence. % 7.95/8.11 exact (zenon_H1e5 zenon_H44). % 7.95/8.11 apply zenon_H69. apply refl_equal. % 7.95/8.11 (* end of lemma zenon_L392_ *) % 7.95/8.11 assert (zenon_L393_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1d0 zenon_H10b zenon_H9c zenon_H18e zenon_H38 zenon_Hd2 zenon_H5a zenon_H1c7 zenon_H6d zenon_Hef zenon_H10e zenon_H8e zenon_H67 zenon_H44. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.11 apply (zenon_L391_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.11 apply (zenon_L200_); trivial. % 7.95/8.11 apply (zenon_L392_); trivial. % 7.95/8.11 (* end of lemma zenon_L393_ *) % 7.95/8.11 assert (zenon_L394_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H11b zenon_H12b zenon_H95 zenon_H8f zenon_H89 zenon_H128 zenon_H55 zenon_H1cd zenon_Hfc zenon_Hb9 zenon_Ha7 zenon_H6c zenon_H67 zenon_H8e zenon_H10e zenon_Hef zenon_H6d zenon_H1c7 zenon_H5a zenon_Hd2 zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H82 zenon_H13a. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.11 apply (zenon_L337_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.11 apply (zenon_L165_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.11 apply (zenon_L389_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.95/8.11 apply (zenon_L136_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.95/8.11 apply (zenon_L393_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.95/8.11 apply (zenon_L115_); trivial. % 7.95/8.11 exact (zenon_H13a zenon_Ha1). % 7.95/8.11 (* end of lemma zenon_L394_ *) % 7.95/8.11 assert (zenon_L395_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H117 zenon_H44 zenon_H43 zenon_H13a zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_H8e zenon_H67 zenon_H6c zenon_Ha7 zenon_Hb9 zenon_Hfc zenon_H1cd zenon_H55 zenon_H128 zenon_H89 zenon_H8f zenon_H95 zenon_H12b zenon_H11b zenon_H82 zenon_H81 zenon_Hef zenon_H6d. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.95/8.11 apply (zenon_L11_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.95/8.11 apply (zenon_L394_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.95/8.11 apply (zenon_L35_); trivial. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 (* end of lemma zenon_L395_ *) % 7.95/8.11 assert (zenon_L396_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H1e6 zenon_H29 zenon_H28 zenon_H6d zenon_Hef zenon_H81 zenon_H82 zenon_H11b zenon_H12b zenon_H95 zenon_H8f zenon_H89 zenon_H128 zenon_H55 zenon_H1cd zenon_Hfc zenon_Ha7 zenon_H6c zenon_H67 zenon_H10e zenon_H1c7 zenon_H5a zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H13a zenon_H43 zenon_H44 zenon_H117 zenon_H93 zenon_H3d zenon_H30 zenon_H8e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e | zenon_intro zenon_H1e7 ]. % 7.95/8.11 apply (zenon_L4_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H1e8 ]. % 7.95/8.11 apply (zenon_L395_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f | zenon_intro zenon_H86 ]. % 7.95/8.11 apply (zenon_L289_); trivial. % 7.95/8.11 apply (zenon_L214_); trivial. % 7.95/8.11 (* end of lemma zenon_L396_ *) % 7.95/8.11 assert (zenon_L397_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> False). % 7.95/8.11 do 0 intro. intros zenon_H113 zenon_Hb9 zenon_H1e6 zenon_H29 zenon_H28 zenon_H6d zenon_Hef zenon_H81 zenon_H82 zenon_H11b zenon_H12b zenon_H95 zenon_H8f zenon_H89 zenon_H128 zenon_H55 zenon_H1cd zenon_Hfc zenon_Ha7 zenon_H6c zenon_H67 zenon_H10e zenon_H1c7 zenon_H5a zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H13a zenon_H43 zenon_H117 zenon_H93 zenon_H3d zenon_H30 zenon_H8e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.11 apply (zenon_L337_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.11 apply (zenon_L119_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.11 apply (zenon_L389_); trivial. % 7.95/8.11 apply (zenon_L396_); trivial. % 7.95/8.11 (* end of lemma zenon_L397_ *) % 7.95/8.11 assert (zenon_L398_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H13b zenon_H66 zenon_Ha2 zenon_H130 zenon_Hf4 zenon_H99 zenon_Ha7 zenon_H6c zenon_H8e zenon_H134 zenon_H10b zenon_H82 zenon_H13a. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.11 apply (zenon_L338_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.11 apply (zenon_L142_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.11 apply (zenon_L97_); trivial. % 7.95/8.11 apply (zenon_L153_); trivial. % 7.95/8.11 (* end of lemma zenon_L398_ *) % 7.95/8.11 assert (zenon_L399_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H162 zenon_H67 zenon_Hde zenon_H8f zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_H6c zenon_H10b zenon_H82 zenon_H13a zenon_Hef zenon_H26 zenon_Haa zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.11 apply (zenon_L66_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.11 apply (zenon_L164_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.11 apply (zenon_L338_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.11 apply (zenon_L342_); trivial. % 7.95/8.11 apply (zenon_L91_); trivial. % 7.95/8.11 apply (zenon_L109_); trivial. % 7.95/8.11 (* end of lemma zenon_L399_ *) % 7.95/8.11 assert (zenon_L400_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H162 zenon_H28 zenon_H67 zenon_H12d zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H111 zenon_H1c7 zenon_H6c zenon_H38 zenon_H83 zenon_H13a zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.11 apply (zenon_L213_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.11 apply (zenon_L164_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.11 apply (zenon_L217_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.11 apply (zenon_L340_); trivial. % 7.95/8.11 apply (zenon_L139_); trivial. % 7.95/8.11 apply (zenon_L109_); trivial. % 7.95/8.11 (* end of lemma zenon_L400_ *) % 7.95/8.11 assert (zenon_L401_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.95/8.11 do 0 intro. intros zenon_Haa zenon_H86 zenon_H16e zenon_H115 zenon_Hef zenon_H33 zenon_H40 zenon_Hf4 zenon_H2c zenon_H2d zenon_H170 zenon_H6c zenon_Hdc. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.11 apply (zenon_L217_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.11 apply (zenon_L227_); trivial. % 7.95/8.11 apply (zenon_L73_); trivial. % 7.95/8.11 (* end of lemma zenon_L401_ *) % 7.95/8.11 assert (zenon_L402_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H162 zenon_H8f zenon_Hbb zenon_H67 zenon_Hdc zenon_H6c zenon_H170 zenon_H2d zenon_H2c zenon_Hf4 zenon_H40 zenon_H33 zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.11 apply (zenon_L66_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.11 apply (zenon_L164_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.11 apply (zenon_L401_); trivial. % 7.95/8.11 apply (zenon_L109_); trivial. % 7.95/8.11 (* end of lemma zenon_L402_ *) % 7.95/8.11 assert (zenon_L403_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H13b zenon_H49 zenon_H64 zenon_Hbd zenon_He3 zenon_H150 zenon_Hf8 zenon_H111 zenon_H173 zenon_H197 zenon_H20 zenon_H18e zenon_H5a zenon_H1d0 zenon_H10b zenon_H1c7 zenon_H4e zenon_H12d zenon_H28 zenon_Ha2 zenon_H130 zenon_H99 zenon_H162 zenon_H8f zenon_Hbb zenon_H67 zenon_H6c zenon_H170 zenon_H2d zenon_H2c zenon_Hf4 zenon_H40 zenon_H33 zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.11 apply (zenon_L361_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.11 apply (zenon_L142_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.11 apply (zenon_L97_); trivial. % 7.95/8.11 apply (zenon_L402_); trivial. % 7.95/8.11 (* end of lemma zenon_L403_ *) % 7.95/8.11 assert (zenon_L404_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_Hff zenon_H48 zenon_H64 zenon_Hf1 zenon_He3 zenon_H195 zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H5d | zenon_intro zenon_H100 ]. % 7.95/8.11 apply (zenon_L21_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H101 ]. % 7.95/8.11 apply (zenon_L93_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Hfd ]. % 7.95/8.11 apply (zenon_L358_); trivial. % 7.95/8.11 apply (zenon_L109_); trivial. % 7.95/8.11 (* end of lemma zenon_L404_ *) % 7.95/8.11 assert (zenon_L405_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H197 zenon_H20 zenon_H3e zenon_H33 zenon_H40 zenon_Hde zenon_H2c zenon_H170 zenon_H18e zenon_H70 zenon_H5a zenon_H1d0 zenon_H67 zenon_H111 zenon_H2d zenon_H8f zenon_H6c zenon_H10b zenon_H1c7 zenon_Hff zenon_H48 zenon_H64 zenon_Hf1 zenon_He3 zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.95/8.11 apply (zenon_L77_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.95/8.11 apply (zenon_L239_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.95/8.11 apply (zenon_L357_); trivial. % 7.95/8.11 apply (zenon_L404_); trivial. % 7.95/8.11 (* end of lemma zenon_L405_ *) % 7.95/8.11 assert (zenon_L406_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.11 do 0 intro. intros zenon_H184 zenon_H134 zenon_Hcc zenon_H19b zenon_H137 zenon_H93 zenon_H89 zenon_H99 zenon_H130 zenon_H173 zenon_H13b zenon_H11e zenon_H29 zenon_H13a zenon_H38 zenon_H10e zenon_Ha7 zenon_H113 zenon_H1ca zenon_H28 zenon_H8f zenon_H51 zenon_H142 zenon_H150 zenon_Haa zenon_H26 zenon_Hef zenon_H12b zenon_H12d zenon_Hbd zenon_Hbb zenon_H162 zenon_Hca zenon_H4e zenon_He3 zenon_Hf1 zenon_H64 zenon_Hff zenon_H1c7 zenon_H10b zenon_H6c zenon_H2d zenon_H67 zenon_H1d0 zenon_H5a zenon_H18e zenon_H170 zenon_H2c zenon_H40 zenon_H33 zenon_H20 zenon_H197 zenon_H55 zenon_H111 zenon_Hf8 zenon_H49 zenon_H16e zenon_H86 zenon_Hfc zenon_H5e. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.11 apply (zenon_L332_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.11 apply (zenon_L221_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.11 apply (zenon_L116_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.11 apply (zenon_L128_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.11 apply (zenon_L400_); trivial. % 7.95/8.11 apply (zenon_L403_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.11 apply (zenon_L17_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.11 apply (zenon_L85_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.11 apply (zenon_L400_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.11 apply (zenon_L213_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.11 apply (zenon_L164_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.11 apply (zenon_L217_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.11 apply (zenon_L205_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.95/8.11 apply (zenon_L365_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.95/8.11 apply (zenon_L293_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.95/8.11 apply (zenon_L326_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.11 apply (zenon_L405_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.11 apply (zenon_L79_); trivial. % 7.95/8.11 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.11 apply (zenon_L331_); trivial. % 7.95/8.11 apply (zenon_L12_); trivial. % 7.95/8.11 apply (zenon_L91_); trivial. % 7.95/8.11 apply (zenon_L109_); trivial. % 7.95/8.11 (* end of lemma zenon_L406_ *) % 7.95/8.11 assert (zenon_L407_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H184 zenon_H134 zenon_Hcc zenon_Hca zenon_H19b zenon_H89 zenon_H33 zenon_H40 zenon_H2c zenon_H170 zenon_H99 zenon_H4e zenon_H1d0 zenon_H197 zenon_H173 zenon_Hf8 zenon_H150 zenon_He3 zenon_Hbd zenon_H64 zenon_H49 zenon_H81 zenon_Hff zenon_H154 zenon_H165 zenon_H11e zenon_H29 zenon_H20 zenon_H38 zenon_H13b zenon_H8f zenon_H130 zenon_H12d zenon_H162 zenon_H28 zenon_H67 zenon_H6c zenon_H1ca zenon_H55 zenon_H113 zenon_Hbb zenon_H2d zenon_Ha7 zenon_H18e zenon_H10e zenon_H5a zenon_H111 zenon_H1c7 zenon_H10b zenon_H82 zenon_H13a zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.12 apply (zenon_L347_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.12 apply (zenon_L221_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.12 apply (zenon_L116_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.12 apply (zenon_L246_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.12 apply (zenon_L35_); trivial. % 7.95/8.12 apply (zenon_L403_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.12 apply (zenon_L17_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.12 apply (zenon_L85_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.12 apply (zenon_L400_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.12 apply (zenon_L399_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.12 apply (zenon_L142_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.12 apply (zenon_L345_); trivial. % 7.95/8.12 apply (zenon_L346_); trivial. % 7.95/8.12 (* end of lemma zenon_L407_ *) % 7.95/8.12 assert (zenon_L408_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H11e zenon_H99 zenon_H20 zenon_H5e zenon_Hfc zenon_Haa zenon_H86 zenon_H16e zenon_Hef zenon_H13a zenon_H38 zenon_H6c zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H18e zenon_Ha7 zenon_H2d zenon_Hbb zenon_H113 zenon_H55 zenon_H1ca zenon_H12d zenon_H67 zenon_H28 zenon_H162 zenon_Hf1 zenon_Hbc. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.12 apply (zenon_L116_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.12 apply (zenon_L85_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.12 apply (zenon_L400_); trivial. % 7.95/8.12 apply (zenon_L113_); trivial. % 7.95/8.12 (* end of lemma zenon_L408_ *) % 7.95/8.12 assert (zenon_L409_ : ((op (e2) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H15c zenon_H115 zenon_H38. % 7.95/8.12 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H39 | zenon_intro zenon_H3a ]. % 7.95/8.12 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H38. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H39. % 7.95/8.12 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.95/8.12 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H3b. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H15c. % 7.95/8.12 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 7.95/8.12 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H3a. apply refl_equal. % 7.95/8.12 apply zenon_H116. apply sym_equal. exact zenon_H115. % 7.95/8.12 apply zenon_H3a. apply refl_equal. % 7.95/8.12 apply zenon_H3a. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L409_ *) % 7.95/8.12 assert (zenon_L410_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H162 zenon_H86 zenon_H28 zenon_H2d zenon_H67 zenon_H38 zenon_H15c zenon_Hfc zenon_H5e. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.12 apply (zenon_L213_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.12 apply (zenon_L164_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.12 apply (zenon_L409_); trivial. % 7.95/8.12 apply (zenon_L109_); trivial. % 7.95/8.12 (* end of lemma zenon_L410_ *) % 7.95/8.12 assert (zenon_L411_ : ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H15e zenon_H67 zenon_H86 zenon_H15f zenon_H89 zenon_H49 zenon_Hbd zenon_H150 zenon_H1d0 zenon_H197 zenon_H12b zenon_H184 zenon_H165 zenon_H154 zenon_H24 zenon_Hec zenon_H173 zenon_Hf8 zenon_H137 zenon_Hcc zenon_H2c zenon_Hca zenon_H33 zenon_H134 zenon_H19b zenon_H40 zenon_H4e zenon_Hbb zenon_H2d zenon_Haa zenon_Hfc zenon_H12d zenon_H55 zenon_H111 zenon_H113 zenon_H1c7 zenon_H18e zenon_H10e zenon_H5a zenon_H10b zenon_H1ca zenon_Hef zenon_H16e zenon_H5e zenon_H162 zenon_H20 zenon_H11e zenon_H6c zenon_Ha7 zenon_H130 zenon_H28 zenon_H13b zenon_H81 zenon_H99 zenon_H38 zenon_H51 zenon_H170 zenon_Hff zenon_Hf1 zenon_H64 zenon_H142 zenon_H124 zenon_H8f zenon_H18b. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.95/8.12 apply (zenon_L36_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.95/8.12 apply (zenon_L333_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.12 apply (zenon_L17_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.12 apply (zenon_L328_); trivial. % 7.95/8.12 apply (zenon_L332_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.12 apply (zenon_L347_); trivial. % 7.95/8.12 apply (zenon_L350_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.95/8.12 apply (zenon_L322_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.12 apply (zenon_L116_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.12 apply (zenon_L328_); trivial. % 7.95/8.12 apply (zenon_L406_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.12 apply (zenon_L407_); trivial. % 7.95/8.12 apply (zenon_L408_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.95/8.12 apply (zenon_L369_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.12 apply (zenon_L116_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.12 apply (zenon_L328_); trivial. % 7.95/8.12 apply (zenon_L77_); trivial. % 7.95/8.12 apply (zenon_L410_); trivial. % 7.95/8.12 (* end of lemma zenon_L411_ *) % 7.95/8.12 assert (zenon_L412_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H162 zenon_Hbb zenon_H2c zenon_H66 zenon_He3 zenon_Hbd zenon_H2d zenon_H99 zenon_H9c zenon_H8e zenon_H8f zenon_H142 zenon_Hfc zenon_H5e. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.12 apply (zenon_L66_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.12 apply (zenon_L104_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.12 apply (zenon_L38_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.12 apply (zenon_L97_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.12 apply (zenon_L325_); trivial. % 7.95/8.12 apply (zenon_L186_); trivial. % 7.95/8.12 apply (zenon_L109_); trivial. % 7.95/8.12 (* end of lemma zenon_L412_ *) % 7.95/8.12 assert (zenon_L413_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hec zenon_H24 zenon_H99 zenon_H128 zenon_H12b zenon_H6c zenon_Hbb zenon_H8f zenon_H162 zenon_H67 zenon_H12d zenon_H1ca zenon_H55 zenon_H113 zenon_H2d zenon_H1c7 zenon_H111 zenon_H10b zenon_H5a zenon_H10e zenon_H18e zenon_Hef zenon_H16e zenon_Haa zenon_Hfc zenon_H5e zenon_H95 zenon_H3e zenon_H20. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.12 apply (zenon_L116_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.12 apply (zenon_L329_); trivial. % 7.95/8.12 apply (zenon_L77_); trivial. % 7.95/8.12 (* end of lemma zenon_L413_ *) % 7.95/8.12 assert (zenon_L414_ : ((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H193 zenon_H18b zenon_H8f zenon_H124 zenon_H142 zenon_H64 zenon_Hf1 zenon_Hff zenon_H170 zenon_H51 zenon_H38 zenon_H99 zenon_H81 zenon_H13b zenon_H28 zenon_H130 zenon_Ha7 zenon_H6c zenon_H11e zenon_H20 zenon_H162 zenon_H5e zenon_H16e zenon_Hef zenon_H1ca zenon_H10b zenon_H5a zenon_H10e zenon_H18e zenon_H1c7 zenon_H113 zenon_H111 zenon_H55 zenon_H12d zenon_Hfc zenon_Haa zenon_H2d zenon_Hbb zenon_H4e zenon_H40 zenon_H19b zenon_H134 zenon_H33 zenon_Hca zenon_H2c zenon_Hcc zenon_H137 zenon_Hf8 zenon_H173 zenon_Hec zenon_H24 zenon_H154 zenon_H184 zenon_H12b zenon_H197 zenon_H1d0 zenon_H150 zenon_Hbd zenon_H49 zenon_H89 zenon_H15f zenon_H86 zenon_H67 zenon_H15e. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 7.95/8.12 apply (zenon_L411_); trivial. % 7.95/8.12 apply (zenon_L164_); trivial. % 7.95/8.12 (* end of lemma zenon_L414_ *) % 7.95/8.12 assert (zenon_L415_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H137 zenon_H12d zenon_H47 zenon_Hc6 zenon_H173 zenon_H26 zenon_H40 zenon_H1e9. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 7.95/8.12 apply (zenon_L292_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 7.95/8.12 apply (zenon_L306_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 7.95/8.12 apply (zenon_L225_); trivial. % 7.95/8.12 exact (zenon_H1e9 zenon_H7f). % 7.95/8.12 (* end of lemma zenon_L415_ *) % 7.95/8.12 assert (zenon_L416_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H3d zenon_Hb9 zenon_Hb2. % 7.95/8.12 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H3d. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_Hb9. % 7.95/8.12 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 7.95/8.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H2b. apply refl_equal. % 7.95/8.12 apply zenon_H1ea. apply sym_equal. exact zenon_Hb2. % 7.95/8.12 (* end of lemma zenon_L416_ *) % 7.95/8.12 assert (zenon_L417_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_He7 zenon_Hb9 zenon_H3d zenon_Hc6 zenon_H173 zenon_H13e zenon_H5a zenon_H55 zenon_H47. % 7.95/8.12 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.12 apply (zenon_L416_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.12 apply (zenon_L306_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.12 apply (zenon_L190_); trivial. % 7.95/8.12 apply (zenon_L308_); trivial. % 7.95/8.12 (* end of lemma zenon_L417_ *) % 7.95/8.12 assert (zenon_L418_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H81 zenon_H111 zenon_H37. % 7.95/8.12 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H81. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H111. % 7.95/8.12 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 7.95/8.12 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H85. apply refl_equal. % 7.95/8.12 apply zenon_H3c. apply sym_equal. exact zenon_H37. % 7.95/8.12 (* end of lemma zenon_L418_ *) % 7.95/8.12 assert (zenon_L419_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H61 zenon_H20 zenon_H5b zenon_H66 zenon_H33 zenon_H1eb zenon_Hca zenon_Hc6 zenon_H19b zenon_H111 zenon_H81 zenon_H47 zenon_H5e. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.12 apply (zenon_L17_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H34 | zenon_intro zenon_H19c ]. % 7.95/8.12 apply (zenon_L293_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H19d ]. % 7.95/8.12 apply (zenon_L228_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H9c | zenon_intro zenon_H70 ]. % 7.95/8.12 exact (zenon_H1eb zenon_H9c). % 7.95/8.12 apply (zenon_L226_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.12 apply (zenon_L418_); trivial. % 7.95/8.12 apply (zenon_L18_); trivial. % 7.95/8.12 (* end of lemma zenon_L419_ *) % 7.95/8.12 assert (zenon_L420_ : (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H106 zenon_Hef zenon_Hd2. % 7.95/8.12 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 7.95/8.12 apply (zenon_L90_); trivial. % 7.95/8.12 (* end of lemma zenon_L420_ *) % 7.95/8.12 assert (zenon_L421_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H124 zenon_H24 zenon_H1e9 zenon_H40 zenon_H12d zenon_H137 zenon_Hc3 zenon_H8f zenon_Hf1 zenon_H1ca zenon_Hef zenon_H106 zenon_H55 zenon_H173 zenon_Hc6 zenon_H3d zenon_Hb9 zenon_He7 zenon_H1c7 zenon_H10b zenon_H5a zenon_H38 zenon_H47 zenon_H99 zenon_H61 zenon_H20 zenon_H33 zenon_H1eb zenon_Hca zenon_H19b zenon_H81 zenon_H5e zenon_H11e zenon_H67 zenon_H111 zenon_H6c. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.12 apply (zenon_L415_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.12 apply (zenon_L65_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.12 apply (zenon_L90_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.12 apply (zenon_L417_); trivial. % 7.95/8.12 apply (zenon_L384_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.12 apply (zenon_L333_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.12 apply (zenon_L419_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.12 apply (zenon_L67_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.12 apply (zenon_L322_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.12 apply (zenon_L420_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.12 apply (zenon_L417_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.95/8.12 apply (zenon_L326_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.95/8.12 apply (zenon_L190_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.95/8.12 apply (zenon_L107_); trivial. % 7.95/8.12 apply (zenon_L383_); trivial. % 7.95/8.12 apply (zenon_L113_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.12 apply (zenon_L118_); trivial. % 7.95/8.12 apply (zenon_L57_); trivial. % 7.95/8.12 (* end of lemma zenon_L421_ *) % 7.95/8.12 assert (zenon_L422_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H30 zenon_Hb9 zenon_H54. % 7.95/8.12 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H30. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_Hb9. % 7.95/8.12 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 7.95/8.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H2b. apply refl_equal. % 7.95/8.12 apply zenon_H183. apply sym_equal. exact zenon_H54. % 7.95/8.12 (* end of lemma zenon_L422_ *) % 7.95/8.12 assert (zenon_L423_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hf7 zenon_H92 zenon_H1ec. % 7.95/8.12 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 7.95/8.12 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1ec. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_Hf9. % 7.95/8.12 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.95/8.12 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1ed. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_Hf7. % 7.95/8.12 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 7.95/8.12 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_Hfa. apply refl_equal. % 7.95/8.12 apply zenon_H12a. apply sym_equal. exact zenon_H92. % 7.95/8.12 apply zenon_Hfa. apply refl_equal. % 7.95/8.12 apply zenon_Hfa. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L423_ *) % 7.95/8.12 assert (zenon_L424_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H1d0 zenon_H67 zenon_H111 zenon_H2d zenon_H13e zenon_H8f zenon_H92 zenon_H1ec. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.12 apply (zenon_L118_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.12 apply (zenon_L325_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.12 apply (zenon_L354_); trivial. % 7.95/8.12 apply (zenon_L423_); trivial. % 7.95/8.12 (* end of lemma zenon_L424_ *) % 7.95/8.12 assert (zenon_L425_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H99 zenon_Ha1 zenon_H140. % 7.95/8.12 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H99. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_Ha1. % 7.95/8.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.12 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 7.95/8.12 congruence. % 7.95/8.12 exact (zenon_H1ee zenon_H140). % 7.95/8.12 apply zenon_H22. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L425_ *) % 7.95/8.12 assert (zenon_L426_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H3d zenon_H86 zenon_H92. % 7.95/8.12 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H3d. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H86. % 7.95/8.12 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 7.95/8.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H2b. apply refl_equal. % 7.95/8.12 apply zenon_H12a. apply sym_equal. exact zenon_H92. % 7.95/8.12 (* end of lemma zenon_L426_ *) % 7.95/8.12 assert (zenon_L427_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hc3 zenon_H92 zenon_H3d zenon_H5e zenon_H47 zenon_H81 zenon_H19b zenon_Hc6 zenon_Hca zenon_H1eb zenon_H33 zenon_H5b zenon_H20 zenon_H61 zenon_H67 zenon_H111 zenon_Hbc zenon_H6c. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.12 apply (zenon_L426_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.12 apply (zenon_L419_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.12 apply (zenon_L118_); trivial. % 7.95/8.12 apply (zenon_L57_); trivial. % 7.95/8.12 (* end of lemma zenon_L427_ *) % 7.95/8.12 assert (zenon_L428_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H124 zenon_H1e9 zenon_H40 zenon_H173 zenon_H12d zenon_H137 zenon_H99 zenon_H10b zenon_Ha7 zenon_H1d0 zenon_H8f zenon_H1ec zenon_H30 zenon_Hb9 zenon_H142 zenon_Hec zenon_H24 zenon_H111 zenon_H67 zenon_H61 zenon_H33 zenon_H1eb zenon_Hca zenon_Hc6 zenon_H19b zenon_H81 zenon_H47 zenon_H5e zenon_H3d zenon_Hc3 zenon_H31 zenon_H20 zenon_H6c zenon_H92. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.12 apply (zenon_L415_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.12 apply (zenon_L17_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.12 apply (zenon_L422_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.12 apply (zenon_L228_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.12 apply (zenon_L424_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.95/8.12 apply (zenon_L260_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.95/8.12 exact (zenon_H1eb zenon_H9c). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.95/8.12 apply (zenon_L115_); trivial. % 7.95/8.12 apply (zenon_L425_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.12 apply (zenon_L418_); trivial. % 7.95/8.12 apply (zenon_L18_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.12 apply (zenon_L260_); trivial. % 7.95/8.12 apply (zenon_L39_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.12 exact (zenon_H24 zenon_H1f). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.12 apply (zenon_L427_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.12 apply (zenon_L260_); trivial. % 7.95/8.12 apply (zenon_L39_); trivial. % 7.95/8.12 (* end of lemma zenon_L428_ *) % 7.95/8.12 assert (zenon_L429_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H61 zenon_H20 zenon_H5b zenon_H1ec zenon_H92 zenon_H8f zenon_H13e zenon_H67 zenon_H1d0 zenon_H111 zenon_H81 zenon_H47 zenon_H5e. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.12 apply (zenon_L17_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.12 apply (zenon_L424_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.12 apply (zenon_L418_); trivial. % 7.95/8.12 apply (zenon_L18_); trivial. % 7.95/8.12 (* end of lemma zenon_L429_ *) % 7.95/8.12 assert (zenon_L430_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_He4 zenon_H15a zenon_H47. % 7.95/8.12 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_He4. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H15a. % 7.95/8.12 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 7.95/8.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H105. apply refl_equal. % 7.95/8.12 apply zenon_H1ef. apply sym_equal. exact zenon_H47. % 7.95/8.12 (* end of lemma zenon_L430_ *) % 7.95/8.12 assert (zenon_L431_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H2d zenon_H173 zenon_H36 zenon_H5a zenon_He4 zenon_H15a. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.12 apply (zenon_L9_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.12 apply (zenon_L330_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.12 apply (zenon_L16_); trivial. % 7.95/8.12 apply (zenon_L430_); trivial. % 7.95/8.12 (* end of lemma zenon_L431_ *) % 7.95/8.12 assert (zenon_L432_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hf1 zenon_H15a zenon_H5d. % 7.95/8.12 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_Hf1. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H15a. % 7.95/8.12 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 7.95/8.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H105. apply refl_equal. % 7.95/8.12 apply zenon_H60. apply sym_equal. exact zenon_H5d. % 7.95/8.12 (* end of lemma zenon_L432_ *) % 7.95/8.12 assert (zenon_L433_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H61 zenon_H28 zenon_He4 zenon_H5a zenon_H173 zenon_H3d zenon_H1e zenon_H4e zenon_H38 zenon_H36 zenon_Hf1 zenon_H15a. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.12 apply (zenon_L4_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.12 apply (zenon_L431_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.12 apply (zenon_L8_); trivial. % 7.95/8.12 apply (zenon_L432_); trivial. % 7.95/8.12 (* end of lemma zenon_L433_ *) % 7.95/8.12 assert (zenon_L434_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_Had zenon_H61 zenon_H28 zenon_He4 zenon_H5a zenon_H173 zenon_H3d zenon_H4e zenon_H38 zenon_H36 zenon_Hf1 zenon_H15a. % 7.95/8.12 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.95/8.12 apply (zenon_L433_); trivial. % 7.95/8.12 (* end of lemma zenon_L434_ *) % 7.95/8.12 assert (zenon_L435_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hbd zenon_H15a zenon_H48. % 7.95/8.12 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_Hbd. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H15a. % 7.95/8.12 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 7.95/8.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.95/8.12 congruence. % 7.95/8.12 apply zenon_H105. apply refl_equal. % 7.95/8.12 apply zenon_H4d. apply sym_equal. exact zenon_H48. % 7.95/8.12 (* end of lemma zenon_L435_ *) % 7.95/8.12 assert (zenon_L436_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H51 zenon_H67 zenon_H8e zenon_H2d zenon_Hca zenon_H20 zenon_H9f zenon_Hbd zenon_H15a. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.95/8.12 apply (zenon_L123_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.95/8.12 apply (zenon_L293_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 7.95/8.12 apply (zenon_L44_); trivial. % 7.95/8.12 apply (zenon_L435_); trivial. % 7.95/8.12 (* end of lemma zenon_L436_ *) % 7.95/8.12 assert (zenon_L437_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H95 zenon_H87 zenon_H8f zenon_Hbb zenon_Hbd zenon_Hca zenon_H51 zenon_H11b zenon_H15a zenon_He4 zenon_H173 zenon_H2d zenon_H67 zenon_H4e zenon_H20 zenon_H117 zenon_H43 zenon_H118 zenon_H38 zenon_H9f zenon_H81 zenon_Hb0. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.12 apply (zenon_L66_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.12 apply (zenon_L436_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.12 apply (zenon_L118_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.12 apply (zenon_L313_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.12 apply (zenon_L330_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.12 apply (zenon_L11_); trivial. % 7.95/8.12 apply (zenon_L430_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.12 apply (zenon_L44_); trivial. % 7.95/8.12 apply (zenon_L121_); trivial. % 7.95/8.12 (* end of lemma zenon_L437_ *) % 7.95/8.12 assert (zenon_L438_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H15a zenon_Hc1 zenon_H67. % 7.95/8.12 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.95/8.12 cut (((e3) = (e3)) = ((e0) = (e3))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H67. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H68. % 7.95/8.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.12 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H6a. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H15a. % 7.95/8.12 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.12 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 7.95/8.12 congruence. % 7.95/8.12 exact (zenon_Hc2 zenon_Hc1). % 7.95/8.12 apply zenon_H1d. apply refl_equal. % 7.95/8.12 apply zenon_H69. apply refl_equal. % 7.95/8.12 apply zenon_H69. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L438_ *) % 7.95/8.12 assert (zenon_L439_ : ((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H1aa zenon_H87 zenon_H2d zenon_H1f zenon_H95 zenon_H4e zenon_He4 zenon_H43 zenon_H173 zenon_H117 zenon_H81 zenon_H38 zenon_H11b zenon_H67 zenon_Hca zenon_H20 zenon_H9f zenon_Hbd zenon_H15a zenon_H51 zenon_Hbb zenon_H8f zenon_Hc3. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.12 apply (zenon_L304_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.12 apply (zenon_L437_); trivial. % 7.95/8.12 apply (zenon_L438_); trivial. % 7.95/8.12 apply (zenon_L85_); trivial. % 7.95/8.12 (* end of lemma zenon_L439_ *) % 7.95/8.12 assert (zenon_L440_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hc3 zenon_H6c zenon_H26 zenon_H81 zenon_H9f zenon_H38 zenon_H118 zenon_H43 zenon_H117 zenon_H20 zenon_H4e zenon_H2d zenon_H173 zenon_He4 zenon_H11b zenon_H51 zenon_Hca zenon_Hbd zenon_Hbb zenon_H8f zenon_H87 zenon_H95 zenon_H15a zenon_H67. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.12 apply (zenon_L338_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.12 apply (zenon_L437_); trivial. % 7.95/8.12 apply (zenon_L438_); trivial. % 7.95/8.12 (* end of lemma zenon_L440_ *) % 7.95/8.12 assert (zenon_L441_ : (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H12b zenon_H87 zenon_H15a. % 7.95/8.12 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 7.95/8.12 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 7.95/8.12 exact (zenon_H158 zenon_H15a). % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 (* end of lemma zenon_L441_ *) % 7.95/8.12 assert (zenon_L442_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H1e zenon_Hb9 zenon_H55. % 7.95/8.12 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H56 | zenon_intro zenon_H57 ]. % 7.95/8.12 cut (((e1) = (e1)) = ((e0) = (e1))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H55. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H56. % 7.95/8.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.12 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e0) (e0)) = (e0)) = ((e1) = (e0))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H58. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H1e. % 7.95/8.12 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.12 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 7.95/8.12 congruence. % 7.95/8.12 exact (zenon_Hb5 zenon_Hb9). % 7.95/8.12 apply zenon_H1d. apply refl_equal. % 7.95/8.12 apply zenon_H57. apply refl_equal. % 7.95/8.12 apply zenon_H57. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L442_ *) % 7.95/8.12 assert (zenon_L443_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H1e6 zenon_H29 zenon_H28 zenon_H36 zenon_Hb0 zenon_H30 zenon_H98 zenon_H87. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e | zenon_intro zenon_H1e7 ]. % 7.95/8.12 apply (zenon_L4_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H1e8 ]. % 7.95/8.12 apply (zenon_L388_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f | zenon_intro zenon_H86 ]. % 7.95/8.12 apply (zenon_L212_); trivial. % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 (* end of lemma zenon_L443_ *) % 7.95/8.12 assert (zenon_L444_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H61 zenon_H87 zenon_H98 zenon_H30 zenon_Hb0 zenon_H28 zenon_H1e6 zenon_He4 zenon_H5a zenon_H173 zenon_H3d zenon_H1e zenon_H4e zenon_H38 zenon_H36 zenon_Hf1 zenon_H15a. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.12 apply (zenon_L443_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.12 apply (zenon_L431_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.12 apply (zenon_L8_); trivial. % 7.95/8.12 apply (zenon_L432_); trivial. % 7.95/8.12 (* end of lemma zenon_L444_ *) % 7.95/8.12 assert (zenon_L445_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H124 zenon_H67 zenon_H61 zenon_H87 zenon_H98 zenon_H30 zenon_H28 zenon_H1e6 zenon_He4 zenon_H5a zenon_H173 zenon_H3d zenon_H1e zenon_H4e zenon_H38 zenon_H36 zenon_Hf1 zenon_H6c zenon_Hc3 zenon_H99 zenon_Hcf zenon_H15a zenon_H20. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.12 apply (zenon_L2_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.12 apply (zenon_L338_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.12 apply (zenon_L444_); trivial. % 7.95/8.12 apply (zenon_L438_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.12 apply (zenon_L65_); trivial. % 7.95/8.12 apply (zenon_L223_); trivial. % 7.95/8.12 (* end of lemma zenon_L445_ *) % 7.95/8.12 assert (zenon_L446_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 7.95/8.12 do 0 intro. intros zenon_Hc3 zenon_H87 zenon_H6c zenon_H26 zenon_H36 zenon_Hb9 zenon_H15a zenon_H67. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.12 exact (zenon_H87 zenon_H86). % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.12 apply (zenon_L338_); trivial. % 7.95/8.12 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.12 apply (zenon_L388_); trivial. % 7.95/8.12 apply (zenon_L438_); trivial. % 7.95/8.12 (* end of lemma zenon_L446_ *) % 7.95/8.12 assert (zenon_L447_ : (~((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H1f2 zenon_Hb9. % 7.95/8.12 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.12 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 7.95/8.12 congruence. % 7.95/8.12 exact (zenon_Hb5 zenon_Hb9). % 7.95/8.12 apply zenon_H1d. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L447_ *) % 7.95/8.12 assert (zenon_L448_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 7.95/8.12 do 0 intro. intros zenon_H88 zenon_Hb9 zenon_H1f3. % 7.95/8.12 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 7.95/8.12 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1f3. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H1f4. % 7.95/8.12 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 7.95/8.12 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1f6. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H88. % 7.95/8.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.12 cut (((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 7.95/8.12 congruence. % 7.95/8.12 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 7.95/8.12 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e1) (e0)) = (op (op (e0) (e0)) (e0)))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1f7. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H1f4. % 7.95/8.12 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 7.95/8.12 cut (((op (op (e0) (e0)) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 7.95/8.12 congruence. % 7.95/8.12 apply (zenon_L447_); trivial. % 7.95/8.12 apply zenon_H1f5. apply refl_equal. % 7.95/8.12 apply zenon_H1f5. apply refl_equal. % 7.95/8.12 apply zenon_H69. apply refl_equal. % 7.95/8.12 apply zenon_H1f5. apply refl_equal. % 7.95/8.12 apply zenon_H1f5. apply refl_equal. % 7.95/8.12 (* end of lemma zenon_L448_ *) % 7.95/8.12 assert (zenon_L449_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 7.95/8.12 do 0 intro. intros zenon_H6e zenon_H88 zenon_Hb9. % 7.95/8.12 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H1f8 ]. % 7.95/8.12 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 7.95/8.12 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1f9. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H1fa. % 7.95/8.12 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 7.95/8.12 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e1) (e1)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1fc. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H6e. % 7.95/8.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.12 cut (((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 7.95/8.12 congruence. % 7.95/8.12 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 7.95/8.12 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e1) (e1)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 7.95/8.12 intro zenon_D_pnotp. % 7.95/8.12 apply zenon_H1fd. % 7.95/8.12 rewrite <- zenon_D_pnotp. % 7.95/8.12 exact zenon_H1fa. % 7.95/8.12 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 7.95/8.12 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 7.95/8.12 congruence. % 7.95/8.12 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 7.95/8.12 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 7.95/8.12 congruence. % 7.95/8.12 exact (zenon_Hb5 zenon_Hb9). % 7.95/8.12 exact (zenon_Hb5 zenon_Hb9). % 7.95/8.12 apply zenon_H1fb. apply refl_equal. % 7.95/8.12 apply zenon_H1fb. apply refl_equal. % 7.95/8.12 apply zenon_H22. apply refl_equal. % 7.95/8.12 apply zenon_H1fb. apply refl_equal. % 7.95/8.12 apply zenon_H1fb. apply refl_equal. % 7.95/8.12 apply (zenon_notand_s _ _ zenon_H1f8); [ zenon_intro zenon_H1ff | zenon_intro zenon_H1f3 ]. % 7.95/8.13 apply zenon_H1ff. apply sym_equal. exact zenon_Hb9. % 7.95/8.13 apply (zenon_L448_); trivial. % 7.95/8.13 (* end of lemma zenon_L449_ *) % 7.95/8.13 assert (zenon_L450_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H15a zenon_H111 zenon_H200. % 7.95/8.13 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H201 | zenon_intro zenon_H105 ]. % 7.95/8.13 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H200. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_H201. % 7.95/8.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.95/8.13 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H202]. % 7.95/8.13 congruence. % 7.95/8.13 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H202. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_H15a. % 7.95/8.13 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 7.95/8.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 7.95/8.13 congruence. % 7.95/8.13 apply zenon_H105. apply refl_equal. % 7.95/8.13 apply zenon_H203. apply sym_equal. exact zenon_H111. % 7.95/8.13 apply zenon_H105. apply refl_equal. % 7.95/8.13 apply zenon_H105. apply refl_equal. % 7.95/8.13 (* end of lemma zenon_L450_ *) % 7.95/8.13 assert (zenon_L451_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H117 zenon_H44 zenon_H43 zenon_Hc6 zenon_Hef zenon_H82 zenon_H81 zenon_H15c zenon_H38. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.95/8.13 apply (zenon_L11_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.95/8.13 apply (zenon_L90_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.95/8.13 apply (zenon_L35_); trivial. % 7.95/8.13 apply (zenon_L409_); trivial. % 7.95/8.13 (* end of lemma zenon_L451_ *) % 7.95/8.13 assert (zenon_L452_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H11b zenon_H200 zenon_H15a zenon_H29 zenon_H113 zenon_H67 zenon_H117 zenon_H43 zenon_Hc6 zenon_Hef zenon_H82 zenon_H81 zenon_H15c zenon_H38. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.13 apply (zenon_L450_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.13 apply (zenon_L119_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.13 apply (zenon_L215_); trivial. % 7.95/8.13 apply (zenon_L451_); trivial. % 7.95/8.13 (* end of lemma zenon_L452_ *) % 7.95/8.13 assert (zenon_L453_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_Hf7 zenon_H115 zenon_H43. % 7.95/8.13 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 7.95/8.13 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H43. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_Hf9. % 7.95/8.13 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.95/8.13 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H204]. % 7.95/8.13 congruence. % 7.95/8.13 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H204. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_Hf7. % 7.95/8.13 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 7.95/8.13 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.95/8.13 congruence. % 7.95/8.13 apply zenon_Hfa. apply refl_equal. % 7.95/8.13 apply zenon_H116. apply sym_equal. exact zenon_H115. % 7.95/8.13 apply zenon_Hfa. apply refl_equal. % 7.95/8.13 apply zenon_Hfa. apply refl_equal. % 7.95/8.13 (* end of lemma zenon_L453_ *) % 7.95/8.13 assert (zenon_L454_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H102 zenon_H3e zenon_H67 zenon_H1e9 zenon_H43 zenon_H115 zenon_H14e zenon_H49. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H92 | zenon_intro zenon_H103 ]. % 7.95/8.13 apply (zenon_L313_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H7f | zenon_intro zenon_H104 ]. % 7.95/8.13 exact (zenon_H1e9 zenon_H7f). % 7.95/8.13 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfc ]. % 7.95/8.13 apply (zenon_L453_); trivial. % 7.95/8.13 apply (zenon_L187_); trivial. % 7.95/8.13 (* end of lemma zenon_L454_ *) % 7.95/8.13 assert (zenon_L455_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_Ha7 zenon_H99 zenon_H54 zenon_H1eb zenon_H20 zenon_H36 zenon_Ha2 zenon_H64. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 7.95/8.13 apply (zenon_L41_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 7.95/8.13 exact (zenon_H1eb zenon_H9c). % 7.95/8.13 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 7.95/8.13 apply (zenon_L44_); trivial. % 7.95/8.13 apply (zenon_L45_); trivial. % 7.95/8.13 (* end of lemma zenon_L455_ *) % 7.95/8.13 assert (zenon_L456_ : ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_He2 zenon_H140 zenon_H49. % 7.95/8.13 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H49. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_H4a. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 7.95/8.13 congruence. % 7.95/8.13 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H4c. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_He2. % 7.95/8.13 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.13 congruence. % 7.95/8.13 apply zenon_H4b. apply refl_equal. % 7.95/8.13 apply zenon_H141. apply sym_equal. exact zenon_H140. % 7.95/8.13 apply zenon_H4b. apply refl_equal. % 7.95/8.13 apply zenon_H4b. apply refl_equal. % 7.95/8.13 (* end of lemma zenon_L456_ *) % 7.95/8.13 assert (zenon_L457_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H142 zenon_H64 zenon_Ha2 zenon_H20 zenon_H1eb zenon_H99 zenon_Ha7 zenon_Hc6 zenon_Hca zenon_H55 zenon_H36 zenon_He2 zenon_H49. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.13 apply (zenon_L455_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.13 apply (zenon_L228_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.13 apply (zenon_L155_); trivial. % 7.95/8.13 apply (zenon_L456_); trivial. % 7.95/8.13 (* end of lemma zenon_L457_ *) % 7.95/8.13 assert (zenon_L458_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H195 zenon_Hdc zenon_H12d. % 7.95/8.13 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H12d. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_H4a. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 7.95/8.13 congruence. % 7.95/8.13 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H12e. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_H195. % 7.95/8.13 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 7.95/8.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.13 congruence. % 7.95/8.13 apply zenon_H4b. apply refl_equal. % 7.95/8.13 apply zenon_H135. apply sym_equal. exact zenon_Hdc. % 7.95/8.13 apply zenon_H4b. apply refl_equal. % 7.95/8.13 apply zenon_H4b. apply refl_equal. % 7.95/8.13 (* end of lemma zenon_L458_ *) % 7.95/8.13 assert (zenon_L459_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H205 zenon_H41 zenon_H36 zenon_H55 zenon_Hca zenon_Hc6 zenon_Ha7 zenon_H99 zenon_H1eb zenon_H20 zenon_Ha2 zenon_H64 zenon_H142 zenon_H12d zenon_Hdc zenon_H14e zenon_H49. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 7.95/8.13 apply (zenon_L292_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 7.95/8.13 apply (zenon_L457_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 7.95/8.13 apply (zenon_L458_); trivial. % 7.95/8.13 apply (zenon_L187_); trivial. % 7.95/8.13 (* end of lemma zenon_L459_ *) % 7.95/8.13 assert (zenon_L460_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.13 do 0 intro. intros zenon_H4e zenon_H115 zenon_H43 zenon_H1e9 zenon_H67 zenon_H102 zenon_H49 zenon_H14e zenon_Hdc zenon_H12d zenon_H142 zenon_H64 zenon_Ha2 zenon_H20 zenon_H1eb zenon_H99 zenon_Ha7 zenon_Hc6 zenon_Hca zenon_H55 zenon_H205 zenon_H36 zenon_H5a zenon_He4 zenon_H15a. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.13 apply (zenon_L454_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.13 apply (zenon_L459_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.13 apply (zenon_L16_); trivial. % 7.95/8.13 apply (zenon_L430_); trivial. % 7.95/8.13 (* end of lemma zenon_L460_ *) % 7.95/8.13 assert (zenon_L461_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H117 zenon_H38 zenon_H36 zenon_He0 zenon_H82 zenon_H81 zenon_Hf7 zenon_H43. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.95/8.13 apply (zenon_L8_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.95/8.13 apply (zenon_L80_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.95/8.13 apply (zenon_L35_); trivial. % 7.95/8.13 apply (zenon_L453_); trivial. % 7.95/8.13 (* end of lemma zenon_L461_ *) % 7.95/8.13 assert (zenon_L462_ : (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 7.95/8.13 do 0 intro. intros zenon_H99 zenon_H1f zenon_Hb9. % 7.95/8.13 cut (((op (e0) (e0)) = (e2)) = ((e1) = (e2))). % 7.95/8.13 intro zenon_D_pnotp. % 7.95/8.13 apply zenon_H99. % 7.95/8.13 rewrite <- zenon_D_pnotp. % 7.95/8.13 exact zenon_H1f. % 7.95/8.13 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.13 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 7.95/8.13 congruence. % 7.95/8.13 exact (zenon_Hb5 zenon_Hb9). % 7.95/8.13 apply zenon_H22. apply refl_equal. % 7.95/8.13 (* end of lemma zenon_L462_ *) % 7.95/8.13 assert (zenon_L463_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H142 zenon_Hb9 zenon_H30 zenon_Hc6 zenon_Hca zenon_H55 zenon_H36 zenon_He2 zenon_H49. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.13 apply (zenon_L422_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.13 apply (zenon_L228_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.13 apply (zenon_L155_); trivial. % 7.95/8.13 apply (zenon_L456_); trivial. % 7.95/8.13 (* end of lemma zenon_L463_ *) % 7.95/8.13 assert (zenon_L464_ : ((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H208 zenon_H55 zenon_Hb9 zenon_H124 zenon_H95 zenon_H1ec zenon_H20 zenon_H81 zenon_H13b zenon_H99 zenon_Hef zenon_Hc6 zenon_H16b zenon_H4e zenon_He4 zenon_H5a zenon_H12d zenon_H142 zenon_Hca zenon_H64 zenon_Ha7 zenon_H205 zenon_H49 zenon_H102 zenon_H1d0 zenon_H200 zenon_H113 zenon_H117 zenon_H38 zenon_H43 zenon_H11b zenon_H33 zenon_H1ca zenon_H1eb zenon_H130 zenon_H11e zenon_H87 zenon_H6c zenon_H36 zenon_H67 zenon_H15a zenon_Hc3 zenon_H98 zenon_H30 zenon_H106 zenon_H18b. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1e9 | zenon_intro zenon_He2 ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.95/8.13 apply (zenon_L442_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.13 apply (zenon_L212_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.13 apply (zenon_L446_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.13 exact (zenon_H87 zenon_H86). % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.13 exact (zenon_H87 zenon_H86). % 7.95/8.13 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.13 apply (zenon_L17_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.13 apply (zenon_L449_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.13 apply (zenon_L35_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.13 apply (zenon_L338_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.13 apply (zenon_L142_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.13 exact (zenon_H1eb zenon_H9c). % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.13 apply (zenon_L65_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.13 apply (zenon_L90_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.13 apply (zenon_L155_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 7.95/8.13 apply (zenon_L136_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 7.95/8.13 apply (zenon_L226_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 7.95/8.13 apply (zenon_L452_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.13 apply (zenon_L388_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.13 apply (zenon_L460_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.13 apply (zenon_L452_); trivial. % 7.95/8.13 apply (zenon_L461_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.13 apply (zenon_L136_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.13 apply (zenon_L17_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.13 apply (zenon_L67_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.13 apply (zenon_L35_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.13 apply (zenon_L446_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.13 apply (zenon_L142_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.13 exact (zenon_H1eb zenon_H9c). % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 7.95/8.13 apply (zenon_L136_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 7.95/8.13 apply (zenon_L226_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 7.95/8.13 apply (zenon_L215_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.13 apply (zenon_L388_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.13 apply (zenon_L460_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.13 apply (zenon_L452_); trivial. % 7.95/8.13 apply (zenon_L423_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.13 apply (zenon_L388_); trivial. % 7.95/8.13 apply (zenon_L438_); trivial. % 7.95/8.13 apply (zenon_L223_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.95/8.13 apply (zenon_L260_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.13 apply (zenon_L446_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.13 exact (zenon_H87 zenon_H86). % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.13 apply (zenon_L65_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.13 apply (zenon_L420_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.13 apply (zenon_L155_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 7.95/8.13 apply (zenon_L136_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 7.95/8.13 apply (zenon_L226_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 7.95/8.13 apply (zenon_L215_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.13 apply (zenon_L388_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.13 apply (zenon_L454_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.13 apply (zenon_L215_); trivial. % 7.95/8.13 apply (zenon_L461_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.13 apply (zenon_L388_); trivial. % 7.95/8.13 apply (zenon_L438_); trivial. % 7.95/8.13 apply (zenon_L223_); trivial. % 7.95/8.13 apply (zenon_L463_); trivial. % 7.95/8.13 (* end of lemma zenon_L464_ *) % 7.95/8.13 assert (zenon_L465_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> False). % 7.95/8.13 do 0 intro. intros zenon_Had zenon_Heb zenon_Hbb. % 7.95/8.13 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.95/8.13 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 7.95/8.13 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 7.95/8.13 exact (zenon_Hb7 zenon_Hbb). % 7.95/8.13 exact (zenon_Heb zenon_H2d). % 7.95/8.13 (* end of lemma zenon_L465_ *) % 7.95/8.13 assert (zenon_L466_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 7.95/8.13 do 0 intro. intros zenon_H209 zenon_H127 zenon_He0 zenon_Hf8 zenon_H10b zenon_H9f zenon_H81 zenon_H115. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H111 | zenon_intro zenon_H20a ]. % 7.95/8.13 exact (zenon_H127 zenon_H111). % 7.95/8.13 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_Hcf | zenon_intro zenon_H20b ]. % 7.95/8.13 apply (zenon_L177_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H82 | zenon_intro zenon_Hb0 ]. % 7.95/8.13 apply (zenon_L115_); trivial. % 7.95/8.13 apply (zenon_L120_); trivial. % 7.95/8.13 (* end of lemma zenon_L466_ *) % 7.95/8.13 assert (zenon_L467_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H117 zenon_H44 zenon_H43 zenon_H38 zenon_H209 zenon_H127 zenon_He0 zenon_Hf8 zenon_H10b zenon_H9f zenon_H81. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.95/8.13 apply (zenon_L11_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.95/8.13 apply (zenon_L80_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.95/8.13 apply (zenon_L107_); trivial. % 7.95/8.13 apply (zenon_L466_); trivial. % 7.95/8.13 (* end of lemma zenon_L467_ *) % 7.95/8.13 assert (zenon_L468_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H1ca zenon_Hb0 zenon_H113 zenon_Hbb zenon_H99 zenon_H117 zenon_H44 zenon_H43 zenon_H38 zenon_H209 zenon_H127 zenon_Hf8 zenon_H10b zenon_H9f zenon_H81. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.13 apply (zenon_L133_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.13 apply (zenon_L323_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.13 apply (zenon_L169_); trivial. % 7.95/8.13 apply (zenon_L467_); trivial. % 7.95/8.13 (* end of lemma zenon_L468_ *) % 7.95/8.13 assert (zenon_L469_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H11b zenon_H29 zenon_Hb9 zenon_H1ca zenon_Hb0 zenon_H113 zenon_Hbb zenon_H99 zenon_H117 zenon_H43 zenon_H38 zenon_H209 zenon_H127 zenon_Hf8 zenon_H10b zenon_H9f zenon_H81. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.13 exact (zenon_H127 zenon_H111). % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.13 apply (zenon_L119_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.13 apply (zenon_L388_); trivial. % 7.95/8.13 apply (zenon_L468_); trivial. % 7.95/8.13 (* end of lemma zenon_L469_ *) % 7.95/8.13 assert (zenon_L470_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.95/8.13 do 0 intro. intros zenon_H95 zenon_H8f zenon_Hb9 zenon_H6e zenon_H67 zenon_H31 zenon_H6c zenon_H93. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.13 apply (zenon_L333_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.13 apply (zenon_L449_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.13 apply (zenon_L123_); trivial. % 7.95/8.13 apply (zenon_L39_); trivial. % 7.95/8.13 (* end of lemma zenon_L470_ *) % 7.95/8.13 assert (zenon_L471_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> False). % 7.95/8.13 do 0 intro. intros zenon_Hec zenon_H99 zenon_H89 zenon_H10e zenon_H9f zenon_H95 zenon_H8f zenon_Hb9 zenon_H6e zenon_H67 zenon_H31 zenon_H6c. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.13 apply (zenon_L84_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.13 apply (zenon_L117_); trivial. % 7.95/8.13 apply (zenon_L470_); trivial. % 7.95/8.13 (* end of lemma zenon_L471_ *) % 7.95/8.13 assert (zenon_L472_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H18b zenon_H55 zenon_H11b zenon_H1ca zenon_H113 zenon_Hbb zenon_H117 zenon_H43 zenon_H38 zenon_H209 zenon_H127 zenon_Hf8 zenon_H10b zenon_H81 zenon_H25 zenon_Hc3 zenon_H2c zenon_H124 zenon_H6c zenon_H67 zenon_H8f zenon_H95 zenon_Hec zenon_Hb9 zenon_H99 zenon_H89 zenon_H6e zenon_H10e zenon_H9f zenon_H20. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.95/8.13 apply (zenon_L442_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.13 apply (zenon_L128_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.13 apply (zenon_L115_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.13 apply (zenon_L333_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.13 apply (zenon_L24_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.13 apply (zenon_L469_); trivial. % 7.95/8.13 apply (zenon_L57_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.95/8.13 apply (zenon_L471_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.13 apply (zenon_L84_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.13 apply (zenon_L117_); trivial. % 7.95/8.13 apply (zenon_L77_); trivial. % 7.95/8.13 (* end of lemma zenon_L472_ *) % 7.95/8.13 assert (zenon_L473_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H95 zenon_Hb9 zenon_H8f zenon_H89 zenon_H6d zenon_H6c zenon_H98 zenon_Hfc zenon_H128. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.13 apply (zenon_L333_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.13 apply (zenon_L37_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.13 apply (zenon_L136_); trivial. % 7.95/8.13 apply (zenon_L137_); trivial. % 7.95/8.13 (* end of lemma zenon_L473_ *) % 7.95/8.13 assert (zenon_L474_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.95/8.13 do 0 intro. intros zenon_H30 zenon_H3d zenon_H117 zenon_H43 zenon_H13a zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_H67 zenon_Ha7 zenon_Hfc zenon_H1cd zenon_H55 zenon_H128 zenon_H89 zenon_H8f zenon_H95 zenon_H12b zenon_H11b zenon_H82 zenon_H81 zenon_Hef zenon_H6d zenon_H28 zenon_H29 zenon_H1e6 zenon_Hb9 zenon_H113 zenon_H6c zenon_H93. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.13 apply (zenon_L333_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.13 apply (zenon_L37_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.13 apply (zenon_L397_); trivial. % 7.95/8.13 apply (zenon_L39_); trivial. % 7.95/8.13 (* end of lemma zenon_L474_ *) % 7.95/8.13 assert (zenon_L475_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H95 zenon_Hb9 zenon_H8f zenon_H89 zenon_H6d zenon_H67 zenon_H31 zenon_H12b zenon_H128. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.13 apply (zenon_L333_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.13 apply (zenon_L37_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.13 apply (zenon_L123_); trivial. % 7.95/8.13 apply (zenon_L138_); trivial. % 7.95/8.13 (* end of lemma zenon_L475_ *) % 7.95/8.13 assert (zenon_L476_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> False). % 7.95/8.13 do 0 intro. intros zenon_H18b zenon_H157 zenon_H158 zenon_H154 zenon_Hff zenon_H64 zenon_Hf1 zenon_H5e zenon_H13a zenon_H49 zenon_Hbd zenon_H150 zenon_H190 zenon_H30 zenon_H3d zenon_H117 zenon_H43 zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_Ha7 zenon_H1cd zenon_H55 zenon_H11b zenon_H81 zenon_Hef zenon_H28 zenon_H1e6 zenon_H113 zenon_H25 zenon_H124 zenon_H12b zenon_H67 zenon_Hec zenon_H99 zenon_Hbb zenon_H128 zenon_Hfc zenon_H6c zenon_H6d zenon_H89 zenon_H8f zenon_Hb9 zenon_H95 zenon_H20. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.95/8.13 apply (zenon_L442_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.13 apply (zenon_L3_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.13 apply (zenon_L116_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.13 apply (zenon_L473_); trivial. % 7.95/8.13 apply (zenon_L474_); trivial. % 7.95/8.13 apply (zenon_L283_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.95/8.13 apply (zenon_L475_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.13 apply (zenon_L462_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.13 apply (zenon_L116_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.13 apply (zenon_L473_); trivial. % 7.95/8.13 apply (zenon_L77_); trivial. % 7.95/8.13 (* end of lemma zenon_L476_ *) % 7.95/8.13 assert (zenon_L477_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 7.95/8.13 do 0 intro. intros zenon_Hcc zenon_Heb zenon_H89 zenon_Hbb zenon_Hdc zenon_H173 zenon_Hca zenon_H70. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.13 exact (zenon_Heb zenon_H2d). % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.13 apply (zenon_L221_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.13 apply (zenon_L231_); trivial. % 7.95/8.13 apply (zenon_L62_); trivial. % 7.95/8.13 (* end of lemma zenon_L477_ *) % 7.95/8.13 assert (zenon_L478_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.95/8.13 do 0 intro. intros zenon_Haa zenon_H20 zenon_H95 zenon_Hb9 zenon_H8f zenon_Hfc zenon_H128 zenon_H99 zenon_Hec zenon_H67 zenon_H12b zenon_H124 zenon_H25 zenon_H113 zenon_H1e6 zenon_H28 zenon_Hef zenon_H81 zenon_H11b zenon_H55 zenon_H1cd zenon_Ha7 zenon_H10e zenon_H1c7 zenon_H5a zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H43 zenon_H117 zenon_H3d zenon_H30 zenon_H190 zenon_H150 zenon_Hbd zenon_H49 zenon_H13a zenon_H5e zenon_Hf1 zenon_H64 zenon_Hff zenon_H154 zenon_H158 zenon_H157 zenon_H18b zenon_Hca zenon_H173 zenon_Hbb zenon_H89 zenon_Heb zenon_Hcc zenon_H6c zenon_Hdc. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.13 apply (zenon_L24_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.13 apply (zenon_L476_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.13 apply (zenon_L477_); trivial. % 7.95/8.13 apply (zenon_L73_); trivial. % 7.95/8.13 (* end of lemma zenon_L478_ *) % 7.95/8.13 assert (zenon_L479_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_Hcc zenon_Heb zenon_H89 zenon_Hbb zenon_H173 zenon_Hca zenon_H18b zenon_H157 zenon_H158 zenon_H154 zenon_Hff zenon_H64 zenon_Hf1 zenon_H5e zenon_H13a zenon_H49 zenon_Hbd zenon_H150 zenon_H190 zenon_H30 zenon_H3d zenon_H117 zenon_H43 zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_Ha7 zenon_H1cd zenon_H55 zenon_H11b zenon_H81 zenon_Hef zenon_H28 zenon_H1e6 zenon_H113 zenon_H25 zenon_H124 zenon_H12b zenon_H67 zenon_Hec zenon_H99 zenon_H8f zenon_Hb9 zenon_H95 zenon_H20 zenon_Haa zenon_H17c zenon_H130 zenon_H13b zenon_H82 zenon_H11e zenon_H6c zenon_H98 zenon_Hfc zenon_H128. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.13 apply (zenon_L333_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.13 apply (zenon_L116_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.13 apply (zenon_L449_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.13 apply (zenon_L35_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.13 apply (zenon_L3_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.13 apply (zenon_L142_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.13 apply (zenon_L238_); trivial. % 7.95/8.13 apply (zenon_L478_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.13 apply (zenon_L136_); trivial. % 7.95/8.13 apply (zenon_L137_); trivial. % 7.95/8.13 (* end of lemma zenon_L479_ *) % 7.95/8.13 assert (zenon_L480_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.13 do 0 intro. intros zenon_Haa zenon_H25 zenon_H128 zenon_H12b zenon_H31 zenon_H67 zenon_H89 zenon_H8f zenon_Hb9 zenon_H95 zenon_H6c zenon_H9c zenon_Hfc zenon_H12d. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.13 apply (zenon_L24_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.13 apply (zenon_L475_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.13 apply (zenon_L43_); trivial. % 7.95/8.13 apply (zenon_L139_); trivial. % 7.95/8.13 (* end of lemma zenon_L480_ *) % 7.95/8.13 assert (zenon_L481_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 7.95/8.13 do 0 intro. intros zenon_H11e zenon_H99 zenon_H6c zenon_Hcc zenon_Heb zenon_H89 zenon_Hbb zenon_H173 zenon_Hca zenon_Ha7 zenon_H128 zenon_Hfc zenon_Haf zenon_Hb0 zenon_H95 zenon_H134 zenon_H38 zenon_H13a zenon_H25 zenon_H67 zenon_Haa zenon_H88 zenon_H12b zenon_H12d zenon_Hb9 zenon_H20 zenon_H13b zenon_Hf1 zenon_Hbc. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 7.95/8.13 apply (zenon_L116_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 7.95/8.13 apply (zenon_L449_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.13 apply (zenon_L3_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.13 apply (zenon_L449_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.13 apply (zenon_L204_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.13 apply (zenon_L24_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.13 apply (zenon_L162_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.13 apply (zenon_L477_); trivial. % 7.95/8.13 apply (zenon_L73_); trivial. % 7.95/8.13 apply (zenon_L113_); trivial. % 7.95/8.13 (* end of lemma zenon_L481_ *) % 7.95/8.13 assert (zenon_L482_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.95/8.13 do 0 intro. intros zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H18e zenon_H15c zenon_H6c zenon_Hdc. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.13 apply (zenon_L24_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.13 apply (zenon_L37_); trivial. % 7.95/8.13 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.13 apply (zenon_L273_); trivial. % 7.95/8.14 apply (zenon_L73_); trivial. % 7.95/8.14 (* end of lemma zenon_L482_ *) % 7.95/8.14 assert (zenon_L483_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H13b zenon_H20 zenon_Ha2 zenon_H130 zenon_H12d zenon_H12b zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H18e zenon_H15c zenon_H6c. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.14 apply (zenon_L3_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.14 apply (zenon_L142_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_L482_); trivial. % 7.95/8.14 (* end of lemma zenon_L483_ *) % 7.95/8.14 assert (zenon_L484_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Hc3 zenon_Hb9 zenon_H8f zenon_H67 zenon_H25 zenon_H10b zenon_H15c zenon_Hbc zenon_H6c. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.14 apply (zenon_L333_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.14 apply (zenon_L24_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.14 apply (zenon_L274_); trivial. % 7.95/8.14 apply (zenon_L57_); trivial. % 7.95/8.14 (* end of lemma zenon_L484_ *) % 7.95/8.14 assert (zenon_L485_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.95/8.14 do 0 intro. intros zenon_He7 zenon_H99 zenon_H93 zenon_H55 zenon_H41 zenon_H13e zenon_H5a zenon_H8f zenon_Hfc. % 7.95/8.14 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.14 apply (zenon_L78_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.14 apply (zenon_L79_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.14 apply (zenon_L190_); trivial. % 7.95/8.14 apply (zenon_L191_); trivial. % 7.95/8.14 (* end of lemma zenon_L485_ *) % 7.95/8.14 assert (zenon_L486_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e0)) -> False). % 7.95/8.14 do 0 intro. intros zenon_He7 zenon_H99 zenon_H93 zenon_Hc7 zenon_H40 zenon_H13e zenon_H5a zenon_H55 zenon_H47. % 7.95/8.14 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.14 apply (zenon_L78_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.14 apply (zenon_L144_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.14 apply (zenon_L190_); trivial. % 7.95/8.14 apply (zenon_L308_); trivial. % 7.95/8.14 (* end of lemma zenon_L486_ *) % 7.95/8.14 assert (zenon_L487_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_Hfc zenon_H8f zenon_H37 zenon_H43 zenon_He7 zenon_H99 zenon_H93 zenon_Hc7 zenon_H40 zenon_H13e zenon_H5a zenon_H55. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.14 apply (zenon_L9_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.14 apply (zenon_L485_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.14 apply (zenon_L11_); trivial. % 7.95/8.14 apply (zenon_L486_); trivial. % 7.95/8.14 (* end of lemma zenon_L487_ *) % 7.95/8.14 assert (zenon_L488_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H4e zenon_H20 zenon_H8f zenon_H5a zenon_H13e zenon_H55 zenon_H93 zenon_H99 zenon_He7 zenon_H12d zenon_Hfc zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H5d zenon_H5e. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.14 apply (zenon_L77_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.14 apply (zenon_L485_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.14 apply (zenon_L146_); trivial. % 7.95/8.14 apply (zenon_L18_); trivial. % 7.95/8.14 (* end of lemma zenon_L488_ *) % 7.95/8.14 assert (zenon_L489_ : (~((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> False). % 7.95/8.14 do 0 intro. intros zenon_H20c zenon_H1f. % 7.95/8.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.14 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 7.95/8.14 congruence. % 7.95/8.14 exact (zenon_H24 zenon_H1f). % 7.95/8.14 apply zenon_H1d. apply refl_equal. % 7.95/8.14 (* end of lemma zenon_L489_ *) % 7.95/8.14 assert (zenon_L490_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (op (e0) (e0)) (e0)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H8e zenon_H1f zenon_H1f3. % 7.95/8.14 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 7.95/8.14 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e3) = (op (op (e0) (e0)) (e0)))). % 7.95/8.14 intro zenon_D_pnotp. % 7.95/8.14 apply zenon_H1f3. % 7.95/8.14 rewrite <- zenon_D_pnotp. % 7.95/8.14 exact zenon_H1f4. % 7.95/8.14 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 7.95/8.14 cut (((op (op (e0) (e0)) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 7.95/8.14 congruence. % 7.95/8.14 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (e0)) (e0)) = (e3))). % 7.95/8.14 intro zenon_D_pnotp. % 7.95/8.14 apply zenon_H1f6. % 7.95/8.14 rewrite <- zenon_D_pnotp. % 7.95/8.14 exact zenon_H8e. % 7.95/8.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.14 cut (((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 7.95/8.14 congruence. % 7.95/8.14 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 7.95/8.14 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e2) (e0)) = (op (op (e0) (e0)) (e0)))). % 7.95/8.14 intro zenon_D_pnotp. % 7.95/8.14 apply zenon_H20d. % 7.95/8.14 rewrite <- zenon_D_pnotp. % 7.95/8.14 exact zenon_H1f4. % 7.95/8.14 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 7.95/8.14 cut (((op (op (e0) (e0)) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 7.95/8.14 congruence. % 7.95/8.14 apply (zenon_L489_); trivial. % 7.95/8.14 apply zenon_H1f5. apply refl_equal. % 7.95/8.14 apply zenon_H1f5. apply refl_equal. % 7.95/8.14 apply zenon_H69. apply refl_equal. % 7.95/8.14 apply zenon_H1f5. apply refl_equal. % 7.95/8.14 apply zenon_H1f5. apply refl_equal. % 7.95/8.14 (* end of lemma zenon_L490_ *) % 7.95/8.14 assert (zenon_L491_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 7.95/8.14 do 0 intro. intros zenon_H13e zenon_H8e zenon_H1f. % 7.95/8.14 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 7.95/8.14 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 7.95/8.14 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 7.95/8.14 intro zenon_D_pnotp. % 7.95/8.14 apply zenon_H20f. % 7.95/8.14 rewrite <- zenon_D_pnotp. % 7.95/8.14 exact zenon_H1fa. % 7.95/8.14 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 7.95/8.14 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 7.95/8.14 congruence. % 7.95/8.14 cut (((op (e2) (e2)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 7.95/8.14 intro zenon_D_pnotp. % 7.95/8.14 apply zenon_H210. % 7.95/8.14 rewrite <- zenon_D_pnotp. % 7.95/8.14 exact zenon_H13e. % 7.95/8.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.14 cut (((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 7.95/8.14 congruence. % 7.95/8.14 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 7.95/8.14 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e2) (e2)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 7.95/8.14 intro zenon_D_pnotp. % 7.95/8.14 apply zenon_H211. % 7.95/8.14 rewrite <- zenon_D_pnotp. % 7.95/8.14 exact zenon_H1fa. % 7.95/8.14 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 7.95/8.14 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 7.95/8.14 congruence. % 7.95/8.14 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 7.95/8.14 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 7.95/8.14 congruence. % 7.95/8.14 exact (zenon_H24 zenon_H1f). % 7.95/8.14 exact (zenon_H24 zenon_H1f). % 7.95/8.14 apply zenon_H1fb. apply refl_equal. % 7.95/8.14 apply zenon_H1fb. apply refl_equal. % 7.95/8.14 apply zenon_H57. apply refl_equal. % 7.95/8.14 apply zenon_H1fb. apply refl_equal. % 7.95/8.14 apply zenon_H1fb. apply refl_equal. % 7.95/8.14 apply (zenon_notand_s _ _ zenon_H20e); [ zenon_intro zenon_H169 | zenon_intro zenon_H1f3 ]. % 7.95/8.14 apply zenon_H169. apply sym_equal. exact zenon_H1f. % 7.95/8.14 apply (zenon_L490_); trivial. % 7.95/8.14 (* end of lemma zenon_L491_ *) % 7.95/8.14 assert (zenon_L492_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H95 zenon_H12d zenon_H12b zenon_H9c zenon_H6c zenon_H89 zenon_H25 zenon_H67 zenon_Haa zenon_H1f zenon_H13e zenon_Hfc zenon_H128. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L243_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_L491_); trivial. % 7.95/8.14 apply (zenon_L137_); trivial. % 7.95/8.14 (* end of lemma zenon_L492_ *) % 7.95/8.14 assert (zenon_L493_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H16b zenon_H86 zenon_H30 zenon_H6d zenon_Hca zenon_H13e zenon_H8f zenon_Hfc zenon_H49. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 7.95/8.14 apply (zenon_L214_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 7.95/8.14 apply (zenon_L62_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 7.95/8.14 apply (zenon_L354_); trivial. % 7.95/8.14 apply (zenon_L187_); trivial. % 7.95/8.14 (* end of lemma zenon_L493_ *) % 7.95/8.14 assert (zenon_L494_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H162 zenon_H28 zenon_H49 zenon_H8f zenon_H13e zenon_Hca zenon_H30 zenon_H16b zenon_H12d zenon_H9c zenon_H6c zenon_Hef zenon_H16e zenon_H86 zenon_Haa zenon_Hfc zenon_H5e. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.14 apply (zenon_L213_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.14 apply (zenon_L493_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.14 apply (zenon_L344_); trivial. % 7.95/8.14 apply (zenon_L109_); trivial. % 7.95/8.14 (* end of lemma zenon_L494_ *) % 7.95/8.14 assert (zenon_L495_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Hcc zenon_H66 zenon_H2c zenon_Hc7 zenon_H9c zenon_Hca zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H128 zenon_Hfc zenon_H10e zenon_H89 zenon_H6c zenon_H1f zenon_H95 zenon_H12b zenon_H1cd. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.14 apply (zenon_L304_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.14 apply (zenon_L61_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.14 apply (zenon_L185_); trivial. % 7.95/8.14 apply (zenon_L375_); trivial. % 7.95/8.14 (* end of lemma zenon_L495_ *) % 7.95/8.14 assert (zenon_L496_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Haa zenon_Hca zenon_Hc7 zenon_H2c zenon_Hcc zenon_H1cd zenon_H95 zenon_H1f zenon_H89 zenon_H10e zenon_Hfc zenon_H128 zenon_Hef zenon_H111 zenon_H67 zenon_H1d0 zenon_H6c zenon_H9c zenon_H12b zenon_H12d. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.14 apply (zenon_L495_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.14 apply (zenon_L375_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.14 apply (zenon_L43_); trivial. % 7.95/8.14 apply (zenon_L140_); trivial. % 7.95/8.14 (* end of lemma zenon_L496_ *) % 7.95/8.14 assert (zenon_L497_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H117 zenon_H111 zenon_H13e zenon_H38 zenon_H82 zenon_H81 zenon_Hf7 zenon_H43. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.95/8.14 apply (zenon_L418_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.95/8.14 apply (zenon_L390_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.95/8.14 apply (zenon_L35_); trivial. % 7.95/8.14 apply (zenon_L453_); trivial. % 7.95/8.14 (* end of lemma zenon_L497_ *) % 7.95/8.14 assert (zenon_L498_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e3)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H1d0 zenon_H67 zenon_H6d zenon_Hef zenon_H10e zenon_H8e zenon_H117 zenon_H111 zenon_H13e zenon_H38 zenon_H82 zenon_H81 zenon_H43. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.14 apply (zenon_L118_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.14 apply (zenon_L205_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.14 apply (zenon_L200_); trivial. % 7.95/8.14 apply (zenon_L497_); trivial. % 7.95/8.14 (* end of lemma zenon_L498_ *) % 7.95/8.14 assert (zenon_L499_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.95/8.14 do 0 intro. intros zenon_H95 zenon_H5e zenon_Hfc zenon_Haa zenon_H16e zenon_H9c zenon_H12d zenon_H16b zenon_H30 zenon_Hca zenon_H8f zenon_H49 zenon_H28 zenon_H162 zenon_H89 zenon_H43 zenon_H81 zenon_H82 zenon_H38 zenon_H13e zenon_H111 zenon_H117 zenon_H10e zenon_Hef zenon_H6d zenon_H67 zenon_H1d0 zenon_H6c zenon_H93. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L494_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L37_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_L498_); trivial. % 7.95/8.14 apply (zenon_L39_); trivial. % 7.95/8.14 (* end of lemma zenon_L499_ *) % 7.95/8.14 assert (zenon_L500_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Hc3 zenon_H49 zenon_Hfc zenon_H8f zenon_H13e zenon_Hca zenon_H30 zenon_H16b zenon_H2c zenon_H6d zenon_H67 zenon_H111 zenon_Hbc zenon_H6c. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.14 apply (zenon_L493_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.14 apply (zenon_L104_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.14 apply (zenon_L118_); trivial. % 7.95/8.14 apply (zenon_L57_); trivial. % 7.95/8.14 (* end of lemma zenon_L500_ *) % 7.95/8.14 assert (zenon_L501_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Hc3 zenon_H5e zenon_Hfc zenon_Haa zenon_H16e zenon_Hef zenon_H6c zenon_H9c zenon_H12d zenon_H16b zenon_H30 zenon_Hca zenon_H13e zenon_H49 zenon_H28 zenon_H162 zenon_H2c zenon_H6d zenon_H67 zenon_H111 zenon_He3 zenon_H8f. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.14 apply (zenon_L494_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.14 apply (zenon_L104_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.14 apply (zenon_L118_); trivial. % 7.95/8.14 apply (zenon_L89_); trivial. % 7.95/8.14 (* end of lemma zenon_L501_ *) % 7.95/8.14 assert (zenon_L502_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H15f zenon_Hec zenon_H12b zenon_H128 zenon_H1cd zenon_Hcc zenon_H20 zenon_H29 zenon_H17c zenon_H95 zenon_H89 zenon_H43 zenon_H81 zenon_H38 zenon_H117 zenon_H10e zenon_H1d0 zenon_H33 zenon_H124 zenon_H55 zenon_Hc3 zenon_H5e zenon_Hfc zenon_Haa zenon_H16e zenon_Hef zenon_H6c zenon_H9c zenon_H12d zenon_H16b zenon_H30 zenon_Hca zenon_H13e zenon_H49 zenon_H28 zenon_H162 zenon_H2c zenon_H6d zenon_H67 zenon_H111 zenon_H8f. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.95/8.14 apply (zenon_L337_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.14 apply (zenon_L496_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.14 apply (zenon_L296_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.14 apply (zenon_L496_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.14 apply (zenon_L17_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.14 apply (zenon_L238_); trivial. % 7.95/8.14 apply (zenon_L499_); trivial. % 7.95/8.14 apply (zenon_L500_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.95/8.14 apply (zenon_L322_); trivial. % 7.95/8.14 apply (zenon_L501_); trivial. % 7.95/8.14 (* end of lemma zenon_L502_ *) % 7.95/8.14 assert (zenon_L503_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e3)) -> False). % 7.95/8.14 do 0 intro. intros zenon_H2c zenon_H162 zenon_H49 zenon_Hca zenon_H16b zenon_H12d zenon_H9c zenon_H16e zenon_Haa zenon_H5e zenon_Hc3 zenon_H124 zenon_H33 zenon_H17c zenon_H20 zenon_Hcc zenon_Hec zenon_H15f zenon_H113 zenon_H13e zenon_H1e6 zenon_H29 zenon_H28 zenon_H6d zenon_Hef zenon_H81 zenon_H82 zenon_H11b zenon_H12b zenon_H95 zenon_H8f zenon_H89 zenon_H128 zenon_H55 zenon_H1cd zenon_Hfc zenon_Ha7 zenon_H6c zenon_H67 zenon_H10e zenon_H1c7 zenon_H5a zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H13a zenon_H43 zenon_H117 zenon_H93 zenon_H3d zenon_H30 zenon_H8e. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.14 apply (zenon_L502_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.14 apply (zenon_L119_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.14 apply (zenon_L155_); trivial. % 7.95/8.14 apply (zenon_L396_); trivial. % 7.95/8.14 (* end of lemma zenon_L503_ *) % 7.95/8.14 assert (zenon_L504_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H5e zenon_Hfc zenon_Haa zenon_H67 zenon_H25 zenon_Hef zenon_H6c zenon_H9c zenon_H12d zenon_H2c zenon_H162 zenon_H49 zenon_Hca zenon_H16b zenon_H16e zenon_Hc3 zenon_H124 zenon_H33 zenon_H17c zenon_H20 zenon_Hcc zenon_Hec zenon_H15f zenon_H113 zenon_H13e zenon_H1e6 zenon_H29 zenon_H28 zenon_H81 zenon_H82 zenon_H11b zenon_H95 zenon_H8f zenon_H89 zenon_H55 zenon_H1cd zenon_Ha7 zenon_H10e zenon_H1c7 zenon_H5a zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H13a zenon_H43 zenon_H117 zenon_H93 zenon_H3d zenon_H30 zenon_H12b zenon_H128. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L494_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.14 apply (zenon_L503_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.14 apply (zenon_L206_); trivial. % 7.95/8.14 apply (zenon_L109_); trivial. % 7.95/8.14 apply (zenon_L138_); trivial. % 7.95/8.14 (* end of lemma zenon_L504_ *) % 7.95/8.14 assert (zenon_L505_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Hec zenon_H67 zenon_H13e zenon_Haa zenon_H25 zenon_H89 zenon_H6c zenon_H12b zenon_H12d zenon_H95 zenon_H99 zenon_Hbb zenon_H17c zenon_H9c zenon_H3e zenon_H20. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L243_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_L491_); trivial. % 7.95/8.14 apply (zenon_L313_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.14 apply (zenon_L116_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.14 apply (zenon_L238_); trivial. % 7.95/8.14 apply (zenon_L77_); trivial. % 7.95/8.14 (* end of lemma zenon_L505_ *) % 7.95/8.14 assert (zenon_L506_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H4e zenon_H20 zenon_H9c zenon_H17c zenon_Hbb zenon_H95 zenon_H12d zenon_H12b zenon_H6c zenon_H89 zenon_H25 zenon_Haa zenon_H67 zenon_Hec zenon_Hfc zenon_H8f zenon_H37 zenon_H43 zenon_He7 zenon_H99 zenon_H93 zenon_Hc7 zenon_H40 zenon_H13e zenon_H5a zenon_H55. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.14 apply (zenon_L505_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.14 apply (zenon_L485_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.14 apply (zenon_L11_); trivial. % 7.95/8.14 apply (zenon_L486_); trivial. % 7.95/8.14 (* end of lemma zenon_L506_ *) % 7.95/8.14 assert (zenon_L507_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H95 zenon_H6c zenon_H89 zenon_H6d zenon_H1f zenon_H13e zenon_H12b zenon_H128. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L243_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L37_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_L491_); trivial. % 7.95/8.14 apply (zenon_L138_); trivial. % 7.95/8.14 (* end of lemma zenon_L507_ *) % 7.95/8.14 assert (zenon_L508_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.95/8.14 do 0 intro. intros zenon_H30 zenon_H3d zenon_H117 zenon_H43 zenon_H13a zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_H67 zenon_Ha7 zenon_Hfc zenon_H1cd zenon_H55 zenon_H128 zenon_H89 zenon_H8f zenon_H95 zenon_H12b zenon_H11b zenon_H82 zenon_H81 zenon_Hef zenon_H6d zenon_H28 zenon_H29 zenon_H1e6 zenon_H13e zenon_H113 zenon_H15f zenon_Hec zenon_Hcc zenon_H20 zenon_H17c zenon_H33 zenon_H124 zenon_Hc3 zenon_H5e zenon_Haa zenon_H16e zenon_H9c zenon_H12d zenon_H16b zenon_Hca zenon_H49 zenon_H162 zenon_H2c zenon_H6c zenon_H93. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L493_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L37_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_L503_); trivial. % 7.95/8.14 apply (zenon_L39_); trivial. % 7.95/8.14 (* end of lemma zenon_L508_ *) % 7.95/8.14 assert (zenon_L509_ : (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H99 zenon_Hbb zenon_H30 zenon_H3d zenon_H117 zenon_H43 zenon_H13a zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_H67 zenon_Ha7 zenon_Hfc zenon_H1cd zenon_H55 zenon_H128 zenon_H89 zenon_H8f zenon_H95 zenon_H12b zenon_H11b zenon_H82 zenon_H81 zenon_Hef zenon_H6d zenon_H28 zenon_H29 zenon_H1e6 zenon_H13e zenon_H113 zenon_H15f zenon_Hec zenon_Hcc zenon_H20 zenon_H17c zenon_H33 zenon_H124 zenon_Hc3 zenon_H5e zenon_Haa zenon_H16e zenon_H9c zenon_H12d zenon_H16b zenon_Hca zenon_H49 zenon_H162 zenon_H2c zenon_H6c. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.14 apply (zenon_L507_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.14 apply (zenon_L116_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.14 apply (zenon_L238_); trivial. % 7.95/8.14 apply (zenon_L508_); trivial. % 7.95/8.14 (* end of lemma zenon_L509_ *) % 7.95/8.14 assert (zenon_L510_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H11b zenon_H6c zenon_Hbc zenon_H67 zenon_H6d zenon_H2c zenon_H16b zenon_H30 zenon_Hca zenon_H8f zenon_H49 zenon_Hc3 zenon_H29 zenon_H113 zenon_H55 zenon_H13e zenon_H137 zenon_H131 zenon_Hc7 zenon_H40 zenon_H9c zenon_H134 zenon_Hfc zenon_H12d. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.14 apply (zenon_L500_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.14 apply (zenon_L119_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.14 apply (zenon_L155_); trivial. % 7.95/8.14 apply (zenon_L146_); trivial. % 7.95/8.14 (* end of lemma zenon_L510_ *) % 7.95/8.14 assert (zenon_L511_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H162 zenon_H16e zenon_Haa zenon_H5e zenon_H124 zenon_H33 zenon_H17c zenon_H20 zenon_Hcc zenon_Hec zenon_H15f zenon_H1e6 zenon_H28 zenon_Hef zenon_H81 zenon_H12b zenon_H95 zenon_H89 zenon_H128 zenon_H1cd zenon_Ha7 zenon_H10e zenon_H1c7 zenon_H5a zenon_H38 zenon_H18e zenon_H1d0 zenon_H10b zenon_H13a zenon_H43 zenon_H117 zenon_H3d zenon_Hbb zenon_H99 zenon_H11b zenon_H6c zenon_H67 zenon_H6d zenon_H2c zenon_H16b zenon_H30 zenon_Hca zenon_H8f zenon_H49 zenon_Hc3 zenon_H29 zenon_H113 zenon_H55 zenon_H13e zenon_H137 zenon_H131 zenon_Hc7 zenon_H40 zenon_H9c zenon_H134 zenon_Hfc zenon_H12d. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.14 apply (zenon_L507_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.14 apply (zenon_L296_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.14 apply (zenon_L509_); trivial. % 7.95/8.14 apply (zenon_L510_); trivial. % 7.95/8.14 (* end of lemma zenon_L511_ *) % 7.95/8.14 assert (zenon_L512_ : ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H25 zenon_H12d zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H13e zenon_H55 zenon_H113 zenon_H29 zenon_Hc3 zenon_H49 zenon_H8f zenon_Hca zenon_H30 zenon_H16b zenon_H2c zenon_H67 zenon_H6c zenon_H11b zenon_H99 zenon_Hbb zenon_H3d zenon_H117 zenon_H43 zenon_H13a zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_Ha7 zenon_H1cd zenon_H128 zenon_H89 zenon_H95 zenon_H12b zenon_Hef zenon_H28 zenon_H1e6 zenon_H15f zenon_Hec zenon_Hcc zenon_H20 zenon_H17c zenon_H33 zenon_H124 zenon_Haa zenon_H16e zenon_H162 zenon_Hb0 zenon_H81 zenon_Hfc zenon_H5e. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.14 apply (zenon_L511_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.14 apply (zenon_L120_); trivial. % 7.95/8.14 apply (zenon_L109_); trivial. % 7.95/8.14 (* end of lemma zenon_L512_ *) % 7.95/8.14 assert (zenon_L513_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.14 do 0 intro. intros zenon_H95 zenon_Hb0 zenon_Haf zenon_H12d zenon_H9c zenon_H6c zenon_H89 zenon_H25 zenon_H67 zenon_Haa zenon_H1f zenon_H13e zenon_H12b zenon_H128. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.14 apply (zenon_L49_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.14 apply (zenon_L204_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.14 apply (zenon_L491_); trivial. % 7.95/8.14 apply (zenon_L138_); trivial. % 7.95/8.14 (* end of lemma zenon_L513_ *) % 7.95/8.14 assert (zenon_L514_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.95/8.14 do 0 intro. intros zenon_Hc3 zenon_H128 zenon_H12b zenon_H13e zenon_H1f zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H6c zenon_H9c zenon_H12d zenon_Haf zenon_H95 zenon_He3 zenon_H8f. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.14 apply (zenon_L243_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.14 apply (zenon_L24_); trivial. % 7.95/8.14 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.14 apply (zenon_L513_); trivial. % 7.95/8.14 apply (zenon_L89_); trivial. % 7.95/8.14 (* end of lemma zenon_L514_ *) % 7.95/8.14 assert (zenon_L515_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H184 zenon_H137 zenon_H131 zenon_H40 zenon_H134 zenon_Hbb zenon_H99 zenon_H25 zenon_H8e zenon_H30 zenon_H3d zenon_H93 zenon_H117 zenon_H43 zenon_H13a zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H5a zenon_H1c7 zenon_H10e zenon_H67 zenon_H6c zenon_Ha7 zenon_H1cd zenon_H55 zenon_H128 zenon_H89 zenon_H8f zenon_H95 zenon_H12b zenon_H11b zenon_H82 zenon_Hef zenon_H28 zenon_H29 zenon_H1e6 zenon_H13e zenon_H113 zenon_H15f zenon_Hec zenon_Hcc zenon_H20 zenon_H17c zenon_H33 zenon_H124 zenon_Hc3 zenon_Haa zenon_H16e zenon_H9c zenon_H12d zenon_H16b zenon_Hca zenon_H49 zenon_H162 zenon_H2c zenon_Hb0 zenon_H81 zenon_Hfc zenon_H5e. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.15 apply (zenon_L512_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.15 apply (zenon_L221_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.15 apply (zenon_L97_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.15 apply (zenon_L98_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.15 apply (zenon_L503_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.15 apply (zenon_L120_); trivial. % 7.95/8.15 apply (zenon_L109_); trivial. % 7.95/8.15 (* end of lemma zenon_L515_ *) % 7.95/8.15 assert (zenon_L516_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H17c zenon_H31 zenon_H34. % 7.95/8.15 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H17c. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H31. % 7.95/8.15 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 7.95/8.15 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 7.95/8.15 congruence. % 7.95/8.15 apply zenon_H167. apply refl_equal. % 7.95/8.15 apply zenon_H35. apply sym_equal. exact zenon_H34. % 7.95/8.15 (* end of lemma zenon_L516_ *) % 7.95/8.15 assert (zenon_L517_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hcc zenon_H41 zenon_H173 zenon_H2c zenon_Hc7 zenon_H9c zenon_Hca zenon_H88 zenon_H89. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.15 apply (zenon_L330_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.15 apply (zenon_L61_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.15 apply (zenon_L185_); trivial. % 7.95/8.15 apply (zenon_L37_); trivial. % 7.95/8.15 (* end of lemma zenon_L517_ *) % 7.95/8.15 assert (zenon_L518_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e1))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H184 zenon_H88 zenon_Hca zenon_H2c zenon_H173 zenon_Hcc zenon_H89 zenon_Hbb zenon_H9c zenon_H99 zenon_H41 zenon_H55. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.15 apply (zenon_L517_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.15 apply (zenon_L221_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.15 apply (zenon_L97_); trivial. % 7.95/8.15 apply (zenon_L79_); trivial. % 7.95/8.15 (* end of lemma zenon_L518_ *) % 7.95/8.15 assert (zenon_L519_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H213 zenon_H12d zenon_H12b zenon_H6c zenon_H67 zenon_Haa zenon_Heb zenon_H31 zenon_H17c zenon_H184 zenon_H88 zenon_Hca zenon_H2c zenon_H173 zenon_Hcc zenon_H89 zenon_Hbb zenon_H9c zenon_H99 zenon_H55. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 7.95/8.15 apply (zenon_L204_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 7.95/8.15 exact (zenon_Heb zenon_H2d). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 7.95/8.15 apply (zenon_L516_); trivial. % 7.95/8.15 apply (zenon_L518_); trivial. % 7.95/8.15 (* end of lemma zenon_L519_ *) % 7.95/8.15 assert (zenon_L520_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H95 zenon_H5e zenon_Hfc zenon_H16e zenon_Hef zenon_H16b zenon_H30 zenon_H13e zenon_H8f zenon_H49 zenon_H28 zenon_H162 zenon_H55 zenon_H99 zenon_H9c zenon_Hbb zenon_H89 zenon_Hcc zenon_H173 zenon_H2c zenon_Hca zenon_H184 zenon_H17c zenon_Heb zenon_Haa zenon_H12b zenon_H12d zenon_H213 zenon_H67 zenon_H31 zenon_H6c zenon_H93. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.15 apply (zenon_L494_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.15 apply (zenon_L519_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.15 apply (zenon_L123_); trivial. % 7.95/8.15 apply (zenon_L39_); trivial. % 7.95/8.15 (* end of lemma zenon_L520_ *) % 7.95/8.15 assert (zenon_L521_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H4e zenon_H20 zenon_H17c zenon_Hbb zenon_Haa zenon_Hcc zenon_H173 zenon_Hca zenon_H1d4 zenon_H1cd zenon_H12b zenon_H95 zenon_H89 zenon_H10e zenon_H128 zenon_Hef zenon_H111 zenon_H67 zenon_H1d0 zenon_H6c zenon_Hec zenon_H8f zenon_H12d zenon_Hfc zenon_H134 zenon_H9c zenon_H131 zenon_H137 zenon_He7 zenon_H99 zenon_H93 zenon_Hc7 zenon_H40 zenon_H13e zenon_H5a zenon_H55. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.15 apply (zenon_L379_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.15 apply (zenon_L485_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.15 apply (zenon_L146_); trivial. % 7.95/8.15 apply (zenon_L486_); trivial. % 7.95/8.15 (* end of lemma zenon_L521_ *) % 7.95/8.15 assert (zenon_L522_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hcc zenon_H34 zenon_Hde zenon_H173 zenon_H9c zenon_Hca zenon_H88 zenon_H89. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.15 apply (zenon_L293_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.15 apply (zenon_L306_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.15 apply (zenon_L185_); trivial. % 7.95/8.15 apply (zenon_L37_); trivial. % 7.95/8.15 (* end of lemma zenon_L522_ *) % 7.95/8.15 assert (zenon_L523_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H184 zenon_H55 zenon_H5a zenon_H13e zenon_H40 zenon_H93 zenon_He7 zenon_H137 zenon_H131 zenon_H134 zenon_Hfc zenon_H12d zenon_H8f zenon_Hec zenon_H6c zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H128 zenon_H10e zenon_H95 zenon_H12b zenon_H1cd zenon_H1d4 zenon_Haa zenon_H17c zenon_H20 zenon_H4e zenon_Hbb zenon_H99 zenon_Hcc zenon_H34 zenon_H173 zenon_H9c zenon_Hca zenon_H88 zenon_H89. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.15 apply (zenon_L521_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.15 apply (zenon_L221_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.15 apply (zenon_L97_); trivial. % 7.95/8.15 apply (zenon_L522_); trivial. % 7.95/8.15 (* end of lemma zenon_L523_ *) % 7.95/8.15 assert (zenon_L524_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hc3 zenon_H5e zenon_H16b zenon_H30 zenon_H49 zenon_H28 zenon_H162 zenon_H128 zenon_H12b zenon_H13e zenon_H1f zenon_H213 zenon_H12d zenon_Haa zenon_Heb zenon_H1d0 zenon_Hef zenon_Hfc zenon_H10e zenon_H6c zenon_H95 zenon_H1cd zenon_H184 zenon_Hca zenon_H2c zenon_H173 zenon_Hcc zenon_H89 zenon_Hbb zenon_H9c zenon_H99 zenon_H55 zenon_H16e zenon_H67 zenon_H111 zenon_He3 zenon_H8f. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.15 apply (zenon_L494_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.15 apply (zenon_L217_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 7.95/8.15 apply (zenon_L204_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 7.95/8.15 exact (zenon_Heb zenon_H2d). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.15 apply (zenon_L495_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.15 apply (zenon_L221_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.15 apply (zenon_L97_); trivial. % 7.95/8.15 apply (zenon_L522_); trivial. % 7.95/8.15 apply (zenon_L518_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.15 apply (zenon_L491_); trivial. % 7.95/8.15 apply (zenon_L138_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.15 apply (zenon_L118_); trivial. % 7.95/8.15 apply (zenon_L89_); trivial. % 7.95/8.15 (* end of lemma zenon_L524_ *) % 7.95/8.15 assert (zenon_L525_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e1)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H95 zenon_H16e zenon_H55 zenon_H99 zenon_H9c zenon_Hbb zenon_H89 zenon_Hcc zenon_H173 zenon_H2c zenon_Hca zenon_H184 zenon_H17c zenon_Heb zenon_H66 zenon_H213 zenon_H67 zenon_H31 zenon_Hfc zenon_H128. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.15 apply (zenon_L217_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 7.95/8.15 apply (zenon_L24_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 7.95/8.15 exact (zenon_Heb zenon_H2d). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 7.95/8.15 apply (zenon_L516_); trivial. % 7.95/8.15 apply (zenon_L518_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.15 apply (zenon_L123_); trivial. % 7.95/8.15 apply (zenon_L137_); trivial. % 7.95/8.15 (* end of lemma zenon_L525_ *) % 7.95/8.15 assert (zenon_L526_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H61 zenon_H8e zenon_H30 zenon_H117 zenon_H10b zenon_H1d0 zenon_H18e zenon_H38 zenon_H1c7 zenon_H10e zenon_H67 zenon_H6c zenon_Ha7 zenon_H1cd zenon_H128 zenon_H89 zenon_H95 zenon_H12b zenon_H11b zenon_Hef zenon_H6d zenon_H28 zenon_H1e6 zenon_H113 zenon_H15f zenon_Hec zenon_Hcc zenon_H20 zenon_H17c zenon_H33 zenon_H124 zenon_Hc3 zenon_H5e zenon_Haa zenon_H16e zenon_H12d zenon_H16b zenon_H162 zenon_H2c zenon_Heb zenon_H8f zenon_H5a zenon_H13e zenon_H4e zenon_H1e zenon_H3d zenon_H55 zenon_H43 zenon_H93 zenon_H99 zenon_He7 zenon_H81 zenon_H82 zenon_Hca zenon_H9c zenon_Hbb zenon_H11e zenon_H150 zenon_H64 zenon_He3 zenon_Hbd zenon_H13a zenon_Hfc zenon_H49. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.15 apply (zenon_L503_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.15 exact (zenon_Heb zenon_H2d). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.15 apply (zenon_L192_); trivial. % 7.95/8.15 apply (zenon_L193_); trivial. % 7.95/8.15 (* end of lemma zenon_L526_ *) % 7.95/8.15 assert (zenon_L527_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H11b zenon_Haf zenon_H1e zenon_H5e zenon_H5d zenon_H43 zenon_He7 zenon_H99 zenon_H93 zenon_H5a zenon_H8f zenon_Hec zenon_H67 zenon_Haa zenon_H25 zenon_H89 zenon_H6c zenon_H12b zenon_H95 zenon_Hbb zenon_H17c zenon_H20 zenon_H4e zenon_H55 zenon_H13e zenon_H137 zenon_H131 zenon_Hc7 zenon_H40 zenon_H9c zenon_H134 zenon_Hfc zenon_H12d. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.15 apply (zenon_L318_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.15 apply (zenon_L505_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.15 apply (zenon_L485_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.15 apply (zenon_L11_); trivial. % 7.95/8.15 apply (zenon_L18_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.15 apply (zenon_L155_); trivial. % 7.95/8.15 apply (zenon_L146_); trivial. % 7.95/8.15 (* end of lemma zenon_L527_ *) % 7.95/8.15 assert (zenon_L528_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H95 zenon_H49 zenon_H8f zenon_H13e zenon_Hca zenon_H30 zenon_H16b zenon_H89 zenon_H6d zenon_H67 zenon_H31 zenon_Hfc zenon_H128. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.15 apply (zenon_L493_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.15 apply (zenon_L37_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.15 apply (zenon_L123_); trivial. % 7.95/8.15 apply (zenon_L137_); trivial. % 7.95/8.15 (* end of lemma zenon_L528_ *) % 7.95/8.15 assert (zenon_L529_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H7f zenon_H66 zenon_H40. % 7.95/8.15 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H19e | zenon_intro zenon_H132 ]. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H40. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H19e. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H216]. % 7.95/8.15 congruence. % 7.95/8.15 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H216. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H7f. % 7.95/8.15 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.95/8.15 congruence. % 7.95/8.15 apply zenon_H132. apply refl_equal. % 7.95/8.15 apply zenon_Hf6. apply sym_equal. exact zenon_H66. % 7.95/8.15 apply zenon_H132. apply refl_equal. % 7.95/8.15 apply zenon_H132. apply refl_equal. % 7.95/8.15 (* end of lemma zenon_L529_ *) % 7.95/8.15 assert (zenon_L530_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H37 zenon_H43 zenon_H55 zenon_He2. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.15 apply (zenon_L9_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.15 apply (zenon_L31_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.15 apply (zenon_L11_); trivial. % 7.95/8.15 apply (zenon_L308_); trivial. % 7.95/8.15 (* end of lemma zenon_L530_ *) % 7.95/8.15 assert (zenon_L531_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H11b zenon_He2 zenon_H55 zenon_H67 zenon_H7f zenon_H3d zenon_H1e zenon_H4e zenon_H20 zenon_H1ca zenon_Hb0 zenon_H113 zenon_Hbb zenon_H99 zenon_H117 zenon_H43 zenon_H38 zenon_H209 zenon_H127 zenon_Hf8 zenon_H10b zenon_H9f zenon_H81. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.15 exact (zenon_H127 zenon_H111). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.15 apply (zenon_L530_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.15 apply (zenon_L44_); trivial. % 7.95/8.15 apply (zenon_L468_); trivial. % 7.95/8.15 (* end of lemma zenon_L531_ *) % 7.95/8.15 assert (zenon_L532_ : (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H99 zenon_H195 zenon_He2. % 7.95/8.15 cut (((op (e3) (e3)) = (e2)) = ((e1) = (e2))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H99. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H195. % 7.95/8.15 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.15 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 7.95/8.15 congruence. % 7.95/8.15 exact (zenon_H153 zenon_He2). % 7.95/8.15 apply zenon_H22. apply refl_equal. % 7.95/8.15 (* end of lemma zenon_L532_ *) % 7.95/8.15 assert (zenon_L533_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H197 zenon_H1f zenon_H3d zenon_H7f zenon_H6c zenon_H9f zenon_H5a zenon_H99 zenon_He2. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.95/8.15 apply (zenon_L289_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.95/8.15 apply (zenon_L73_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.95/8.15 apply (zenon_L178_); trivial. % 7.95/8.15 apply (zenon_L532_); trivial. % 7.95/8.15 (* end of lemma zenon_L533_ *) % 7.95/8.15 assert (zenon_L534_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H11b zenon_H127 zenon_He2 zenon_H55 zenon_H67 zenon_H7f zenon_H3d zenon_H1e zenon_H4e zenon_H20 zenon_H117 zenon_H43 zenon_Hcf zenon_H38 zenon_H9f zenon_H81 zenon_Hb0. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.15 exact (zenon_H127 zenon_H111). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.15 apply (zenon_L530_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.15 apply (zenon_L44_); trivial. % 7.95/8.15 apply (zenon_L133_); trivial. % 7.95/8.15 (* end of lemma zenon_L534_ *) % 7.95/8.15 assert (zenon_L535_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hc3 zenon_H40 zenon_H81 zenon_H9f zenon_H38 zenon_Hcf zenon_H43 zenon_H117 zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H127 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.15 apply (zenon_L36_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.15 apply (zenon_L529_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.15 apply (zenon_L534_); trivial. % 7.95/8.15 apply (zenon_L57_); trivial. % 7.95/8.15 (* end of lemma zenon_L535_ *) % 7.95/8.15 assert (zenon_L536_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H124 zenon_H5a zenon_H197 zenon_H25 zenon_H99 zenon_Hc3 zenon_H40 zenon_H81 zenon_H9f zenon_H38 zenon_Hcf zenon_H43 zenon_H117 zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H127 zenon_H11b zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.15 apply (zenon_L533_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.15 apply (zenon_L3_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.15 apply (zenon_L65_); trivial. % 7.95/8.15 apply (zenon_L535_); trivial. % 7.95/8.15 (* end of lemma zenon_L536_ *) % 7.95/8.15 assert (zenon_L537_ : (~((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H217 zenon_H86. % 7.95/8.15 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 7.95/8.15 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 7.95/8.15 congruence. % 7.95/8.15 exact (zenon_H87 zenon_H86). % 7.95/8.15 exact (zenon_H87 zenon_H86). % 7.95/8.15 (* end of lemma zenon_L537_ *) % 7.95/8.15 assert (zenon_L538_ : (~((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H218 zenon_H86. % 7.95/8.15 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.15 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 7.95/8.15 congruence. % 7.95/8.15 exact (zenon_H87 zenon_H86). % 7.95/8.15 apply zenon_H1d. apply refl_equal. % 7.95/8.15 (* end of lemma zenon_L538_ *) % 7.95/8.15 assert (zenon_L539_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (e0)) (e0)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H93 zenon_H86 zenon_H219. % 7.95/8.15 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 7.95/8.15 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e2) = (op (op (e0) (e0)) (e0)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H219. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H1f4. % 7.95/8.15 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 7.95/8.15 cut (((op (op (e0) (e0)) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 7.95/8.15 congruence. % 7.95/8.15 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (e0)) (e0)) = (e2))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H21a. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H93. % 7.95/8.15 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.15 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 7.95/8.15 congruence. % 7.95/8.15 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 7.95/8.15 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H21b. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H1f4. % 7.95/8.15 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 7.95/8.15 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 7.95/8.15 congruence. % 7.95/8.15 apply (zenon_L538_); trivial. % 7.95/8.15 apply zenon_H1f5. apply refl_equal. % 7.95/8.15 apply zenon_H1f5. apply refl_equal. % 7.95/8.15 apply zenon_H22. apply refl_equal. % 7.95/8.15 apply zenon_H1f5. apply refl_equal. % 7.95/8.15 apply zenon_H1f5. apply refl_equal. % 7.95/8.15 (* end of lemma zenon_L539_ *) % 7.95/8.15 assert (zenon_L540_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 7.95/8.15 do 0 intro. intros zenon_He2 zenon_H93 zenon_H86. % 7.95/8.15 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H20f | zenon_intro zenon_H21c ]. % 7.95/8.15 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 7.95/8.15 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e1) = (op (op (e0) (e0)) (op (e0) (e0))))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H20f. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H1fa. % 7.95/8.15 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 7.95/8.15 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 7.95/8.15 congruence. % 7.95/8.15 cut (((op (e3) (e3)) = (e1)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e1))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H210. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_He2. % 7.95/8.15 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.15 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 7.95/8.15 congruence. % 7.95/8.15 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 7.95/8.15 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H21d. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H1fa. % 7.95/8.15 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 7.95/8.15 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 7.95/8.15 congruence. % 7.95/8.15 apply (zenon_L537_); trivial. % 7.95/8.15 apply zenon_H1fb. apply refl_equal. % 7.95/8.15 apply zenon_H1fb. apply refl_equal. % 7.95/8.15 apply zenon_H57. apply refl_equal. % 7.95/8.15 apply zenon_H1fb. apply refl_equal. % 7.95/8.15 apply zenon_H1fb. apply refl_equal. % 7.95/8.15 apply (zenon_notand_s _ _ zenon_H21c); [ zenon_intro zenon_H21e | zenon_intro zenon_H219 ]. % 7.95/8.15 apply zenon_H21e. apply sym_equal. exact zenon_H86. % 7.95/8.15 apply (zenon_L539_); trivial. % 7.95/8.15 (* end of lemma zenon_L540_ *) % 7.95/8.15 assert (zenon_L541_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hc3 zenon_H93 zenon_H40 zenon_H81 zenon_H9f zenon_H10b zenon_Hf8 zenon_H127 zenon_H209 zenon_H38 zenon_H43 zenon_H117 zenon_H99 zenon_Hbb zenon_H113 zenon_H1ca zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.15 apply (zenon_L540_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.15 apply (zenon_L529_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.15 apply (zenon_L531_); trivial. % 7.95/8.15 apply (zenon_L57_); trivial. % 7.95/8.15 (* end of lemma zenon_L541_ *) % 7.95/8.15 assert (zenon_L542_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hec zenon_H89 zenon_H6e zenon_H10e zenon_H122 zenon_Hc3 zenon_H40 zenon_H81 zenon_H9f zenon_H10b zenon_Hf8 zenon_H127 zenon_H209 zenon_H38 zenon_H43 zenon_H117 zenon_H99 zenon_Hbb zenon_H113 zenon_H1ca zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.15 apply (zenon_L2_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.15 apply (zenon_L84_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.15 apply (zenon_L129_); trivial. % 7.95/8.15 apply (zenon_L541_); trivial. % 7.95/8.15 (* end of lemma zenon_L542_ *) % 7.95/8.15 assert (zenon_L543_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H124 zenon_H5a zenon_H197 zenon_H2c zenon_Hcf zenon_Hec zenon_H89 zenon_H6e zenon_H10e zenon_H122 zenon_Hc3 zenon_H40 zenon_H81 zenon_H9f zenon_H10b zenon_Hf8 zenon_H127 zenon_H209 zenon_H38 zenon_H43 zenon_H117 zenon_H99 zenon_Hbb zenon_H113 zenon_H1ca zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H11b zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.15 apply (zenon_L533_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.15 apply (zenon_L128_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.15 apply (zenon_L65_); trivial. % 7.95/8.15 apply (zenon_L542_); trivial. % 7.95/8.15 (* end of lemma zenon_L543_ *) % 7.95/8.15 assert (zenon_L544_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hec zenon_H20 zenon_H10e zenon_H122 zenon_Hc3 zenon_He2 zenon_H40 zenon_H7f zenon_H81 zenon_H9f zenon_H10b zenon_Hf8 zenon_H127 zenon_H209 zenon_H38 zenon_H43 zenon_H117 zenon_H99 zenon_Hbb zenon_H113 zenon_H1ca zenon_Hb9 zenon_H29 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.15 apply (zenon_L462_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.15 apply (zenon_L17_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.15 apply (zenon_L129_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.15 apply (zenon_L540_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.15 apply (zenon_L529_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.15 apply (zenon_L469_); trivial. % 7.95/8.15 apply (zenon_L57_); trivial. % 7.95/8.15 (* end of lemma zenon_L544_ *) % 7.95/8.15 assert (zenon_L545_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H209 zenon_H127 zenon_He0 zenon_Hf8 zenon_H10b zenon_H9f zenon_Haf zenon_H86. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H111 | zenon_intro zenon_H20a ]. % 7.95/8.15 exact (zenon_H127 zenon_H111). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_Hcf | zenon_intro zenon_H20b ]. % 7.95/8.15 apply (zenon_L177_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H82 | zenon_intro zenon_Hb0 ]. % 7.95/8.15 apply (zenon_L115_); trivial. % 7.95/8.15 apply (zenon_L49_); trivial. % 7.95/8.15 (* end of lemma zenon_L545_ *) % 7.95/8.15 assert (zenon_L546_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H11b zenon_H20 zenon_H1ca zenon_Hb0 zenon_H81 zenon_H38 zenon_H43 zenon_H117 zenon_H113 zenon_Hbb zenon_H99 zenon_H1e6 zenon_H29 zenon_H28 zenon_H88 zenon_H6e zenon_H93 zenon_H3d zenon_H209 zenon_H127 zenon_Hf8 zenon_H10b zenon_H9f zenon_Haf. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.15 exact (zenon_H127 zenon_H111). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.15 apply (zenon_L119_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.15 apply (zenon_L44_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.15 apply (zenon_L133_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.15 apply (zenon_L323_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.15 apply (zenon_L169_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e | zenon_intro zenon_H1e7 ]. % 7.95/8.15 apply (zenon_L4_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H1e8 ]. % 7.95/8.15 apply (zenon_L449_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f | zenon_intro zenon_H86 ]. % 7.95/8.15 apply (zenon_L289_); trivial. % 7.95/8.15 apply (zenon_L545_); trivial. % 7.95/8.15 (* end of lemma zenon_L546_ *) % 7.95/8.15 assert (zenon_L547_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H142 zenon_H8f zenon_H8e zenon_Hc7 zenon_H33 zenon_H9f zenon_H99 zenon_He2 zenon_H49. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.15 apply (zenon_L38_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.15 apply (zenon_L168_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.15 apply (zenon_L169_); trivial. % 7.95/8.15 apply (zenon_L456_); trivial. % 7.95/8.15 (* end of lemma zenon_L547_ *) % 7.95/8.15 assert (zenon_L548_ : ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H7f zenon_H92 zenon_H1d4. % 7.95/8.15 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H19e | zenon_intro zenon_H132 ]. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H1d4. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H19e. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 7.95/8.15 congruence. % 7.95/8.15 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 7.95/8.15 intro zenon_D_pnotp. % 7.95/8.15 apply zenon_H21f. % 7.95/8.15 rewrite <- zenon_D_pnotp. % 7.95/8.15 exact zenon_H7f. % 7.95/8.15 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 7.95/8.15 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 7.95/8.15 congruence. % 7.95/8.15 apply zenon_H132. apply refl_equal. % 7.95/8.15 apply zenon_H12a. apply sym_equal. exact zenon_H92. % 7.95/8.15 apply zenon_H132. apply refl_equal. % 7.95/8.15 apply zenon_H132. apply refl_equal. % 7.95/8.15 (* end of lemma zenon_L548_ *) % 7.95/8.15 assert (zenon_L549_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_Hec zenon_H99 zenon_H5a zenon_H3d zenon_H197 zenon_H10e zenon_H122 zenon_Hc3 zenon_He2 zenon_H40 zenon_H7f zenon_H81 zenon_H9f zenon_H38 zenon_Hcf zenon_H43 zenon_H117 zenon_H20 zenon_H113 zenon_H29 zenon_H127 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.15 apply (zenon_L533_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.15 apply (zenon_L17_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.15 apply (zenon_L129_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.15 apply (zenon_L540_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.15 apply (zenon_L529_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.15 apply (zenon_L134_); trivial. % 7.95/8.15 apply (zenon_L57_); trivial. % 7.95/8.15 (* end of lemma zenon_L549_ *) % 7.95/8.15 assert (zenon_L550_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 7.95/8.15 do 0 intro. intros zenon_H213 zenon_H20 zenon_H26 zenon_Heb zenon_H31 zenon_H17c zenon_H67 zenon_H7f. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 7.95/8.15 apply (zenon_L3_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 7.95/8.15 exact (zenon_Heb zenon_H2d). % 7.95/8.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 7.95/8.15 apply (zenon_L516_); trivial. % 7.95/8.15 apply (zenon_L31_); trivial. % 7.95/8.15 (* end of lemma zenon_L550_ *) % 7.95/8.15 assert (zenon_L551_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> False). % 7.95/8.15 do 0 intro. intros zenon_H124 zenon_H134 zenon_H33 zenon_Hc7 zenon_Hcc zenon_Hca zenon_H2c zenon_H173 zenon_H19b zenon_Hec zenon_H89 zenon_H6e zenon_H10e zenon_H122 zenon_Hc3 zenon_H40 zenon_H81 zenon_H9f zenon_H10b zenon_Hf8 zenon_H127 zenon_H209 zenon_H38 zenon_H43 zenon_H117 zenon_H99 zenon_Hbb zenon_H113 zenon_H1ca zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H11b zenon_H6c. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.15 apply (zenon_L2_); trivial. % 7.95/8.15 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L115_); trivial. % 7.95/8.16 apply (zenon_L542_); trivial. % 7.95/8.16 (* end of lemma zenon_L551_ *) % 7.95/8.16 assert (zenon_L552_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hc3 zenon_H93 zenon_H25 zenon_H81 zenon_H9f zenon_H38 zenon_Hcf zenon_H43 zenon_H117 zenon_H20 zenon_H4e zenon_H1e zenon_H3d zenon_H7f zenon_H67 zenon_H55 zenon_He2 zenon_H127 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.16 apply (zenon_L540_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.16 apply (zenon_L24_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.16 apply (zenon_L534_); trivial. % 7.95/8.16 apply (zenon_L57_); trivial. % 7.95/8.16 (* end of lemma zenon_L552_ *) % 7.95/8.16 assert (zenon_L553_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1e6 zenon_H31 zenon_H30 zenon_H88 zenon_H6e zenon_H3d zenon_He2 zenon_H93. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e | zenon_intro zenon_H1e7 ]. % 7.95/8.16 apply (zenon_L6_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H1e8 ]. % 7.95/8.16 apply (zenon_L449_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f | zenon_intro zenon_H86 ]. % 7.95/8.16 apply (zenon_L289_); trivial. % 7.95/8.16 apply (zenon_L540_); trivial. % 7.95/8.16 (* end of lemma zenon_L553_ *) % 7.95/8.16 assert (zenon_L554_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H197 zenon_H20 zenon_H3e zenon_H6e zenon_H173 zenon_H9f zenon_H5a zenon_H99 zenon_He2. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.95/8.16 apply (zenon_L77_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.95/8.16 apply (zenon_L231_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.95/8.16 apply (zenon_L178_); trivial. % 7.95/8.16 apply (zenon_L532_); trivial. % 7.95/8.16 (* end of lemma zenon_L554_ *) % 7.95/8.16 assert (zenon_L555_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H18b zenon_H4e zenon_H55 zenon_He4 zenon_H124 zenon_H2c zenon_H122 zenon_Hc3 zenon_H40 zenon_H81 zenon_H38 zenon_H43 zenon_H117 zenon_H113 zenon_H127 zenon_H11b zenon_H134 zenon_Hcc zenon_Hca zenon_H19b zenon_H25 zenon_H142 zenon_H8f zenon_H33 zenon_H49 zenon_H1ca zenon_Hbb zenon_H28 zenon_H209 zenon_Hf8 zenon_H10b zenon_Haf zenon_H15f zenon_H6c zenon_H67 zenon_H1e6 zenon_H30 zenon_H3d zenon_H95 zenon_H10e zenon_H89 zenon_H7f zenon_Hec zenon_H197 zenon_H20 zenon_H6e zenon_H173 zenon_H9f zenon_H5a zenon_H99 zenon_He2. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.95/8.16 apply (zenon_L442_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.95/8.16 apply (zenon_L551_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L65_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.16 apply (zenon_L84_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.16 apply (zenon_L117_); trivial. % 7.95/8.16 apply (zenon_L552_); trivial. % 7.95/8.16 apply (zenon_L81_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.16 apply (zenon_L462_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L128_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L115_); trivial. % 7.95/8.16 apply (zenon_L544_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L115_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.16 apply (zenon_L84_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.16 apply (zenon_L117_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.16 apply (zenon_L540_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.16 apply (zenon_L24_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L49_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_L546_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L547_); trivial. % 7.95/8.16 apply (zenon_L39_); trivial. % 7.95/8.16 apply (zenon_L57_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L128_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L65_); trivial. % 7.95/8.16 apply (zenon_L549_); trivial. % 7.95/8.16 apply (zenon_L81_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.16 apply (zenon_L84_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.16 apply (zenon_L117_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L540_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_L553_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L123_); trivial. % 7.95/8.16 apply (zenon_L39_); trivial. % 7.95/8.16 apply (zenon_L554_); trivial. % 7.95/8.16 (* end of lemma zenon_L555_ *) % 7.95/8.16 assert (zenon_L556_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H197 zenon_H20 zenon_H3e zenon_H26 zenon_H40 zenon_H9f zenon_H5a zenon_H99 zenon_He2. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 7.95/8.16 apply (zenon_L77_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 7.95/8.16 apply (zenon_L225_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 7.95/8.16 apply (zenon_L178_); trivial. % 7.95/8.16 apply (zenon_L532_); trivial. % 7.95/8.16 (* end of lemma zenon_L556_ *) % 7.95/8.16 assert (zenon_L557_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H124 zenon_He2 zenon_H99 zenon_H5a zenon_H6c zenon_H3d zenon_H197 zenon_H134 zenon_H7f zenon_H33 zenon_Hc7 zenon_Hcc zenon_Hca zenon_H2c zenon_H173 zenon_H19b zenon_H10b zenon_H9f zenon_H15a zenon_H20. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L115_); trivial. % 7.95/8.16 apply (zenon_L223_); trivial. % 7.95/8.16 (* end of lemma zenon_L557_ *) % 7.95/8.16 assert (zenon_L558_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1ec zenon_H3e zenon_H44. % 7.95/8.16 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H1ec. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H3e. % 7.95/8.16 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 7.95/8.16 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 7.95/8.16 congruence. % 7.95/8.16 apply zenon_H181. apply refl_equal. % 7.95/8.16 apply zenon_H45. apply sym_equal. exact zenon_H44. % 7.95/8.16 (* end of lemma zenon_L558_ *) % 7.95/8.16 assert (zenon_L559_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hf7 zenon_H7f zenon_H131. % 7.95/8.16 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 7.95/8.16 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H131. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_Hf9. % 7.95/8.16 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.95/8.16 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 7.95/8.16 congruence. % 7.95/8.16 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H220. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_Hf7. % 7.95/8.16 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 7.95/8.16 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 7.95/8.16 congruence. % 7.95/8.16 apply zenon_Hfa. apply refl_equal. % 7.95/8.16 apply zenon_H12f. apply sym_equal. exact zenon_H7f. % 7.95/8.16 apply zenon_Hfa. apply refl_equal. % 7.95/8.16 apply zenon_Hfa. apply refl_equal. % 7.95/8.16 (* end of lemma zenon_L559_ *) % 7.95/8.16 assert (zenon_L560_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H14a zenon_H3e zenon_H1ec zenon_Hcf zenon_Hf8 zenon_H9f zenon_H5a zenon_H7f zenon_H131. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H44 | zenon_intro zenon_H14b ]. % 7.95/8.16 apply (zenon_L558_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_He0 | zenon_intro zenon_H14c ]. % 7.95/8.16 apply (zenon_L177_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H148 | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L178_); trivial. % 7.95/8.16 apply (zenon_L559_); trivial. % 7.95/8.16 (* end of lemma zenon_L560_ *) % 7.95/8.16 assert (zenon_L561_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H4e zenon_H131 zenon_H5a zenon_H9f zenon_Hf8 zenon_Hcf zenon_H1ec zenon_H14a zenon_H7f zenon_H67 zenon_H37 zenon_H43 zenon_He4 zenon_H15a. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.16 apply (zenon_L560_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.16 apply (zenon_L31_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.16 apply (zenon_L11_); trivial. % 7.95/8.16 apply (zenon_L430_); trivial. % 7.95/8.16 (* end of lemma zenon_L561_ *) % 7.95/8.16 assert (zenon_L562_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H61 zenon_H20 zenon_H5b zenon_Heb zenon_He4 zenon_H43 zenon_H67 zenon_H7f zenon_H14a zenon_H1ec zenon_Hcf zenon_Hf8 zenon_H9f zenon_H5a zenon_H131 zenon_H4e zenon_Hf1 zenon_H15a. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.16 apply (zenon_L17_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.16 exact (zenon_Heb zenon_H2d). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.16 apply (zenon_L561_); trivial. % 7.95/8.16 apply (zenon_L432_); trivial. % 7.95/8.16 (* end of lemma zenon_L562_ *) % 7.95/8.16 assert (zenon_L563_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H61 zenon_Hb0 zenon_H81 zenon_H38 zenon_H117 zenon_H20 zenon_H113 zenon_H127 zenon_H11b zenon_Heb zenon_He4 zenon_H43 zenon_H67 zenon_H7f zenon_H14a zenon_H1ec zenon_Hcf zenon_Hf8 zenon_H9f zenon_H5a zenon_H131 zenon_H4e zenon_Hf1 zenon_H15a. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 7.95/8.16 apply (zenon_L134_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 7.95/8.16 exact (zenon_Heb zenon_H2d). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 7.95/8.16 apply (zenon_L561_); trivial. % 7.95/8.16 apply (zenon_L432_); trivial. % 7.95/8.16 (* end of lemma zenon_L563_ *) % 7.95/8.16 assert (zenon_L564_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hc3 zenon_H93 zenon_He2 zenon_H40 zenon_Hf1 zenon_H4e zenon_H131 zenon_H5a zenon_H9f zenon_Hf8 zenon_Hcf zenon_H1ec zenon_H14a zenon_H7f zenon_H43 zenon_He4 zenon_Heb zenon_H11b zenon_H127 zenon_H113 zenon_H20 zenon_H117 zenon_H38 zenon_H81 zenon_H61 zenon_H15a zenon_H67. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.16 apply (zenon_L540_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.16 apply (zenon_L529_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.16 apply (zenon_L563_); trivial. % 7.95/8.16 apply (zenon_L438_); trivial. % 7.95/8.16 (* end of lemma zenon_L564_ *) % 7.95/8.16 assert (zenon_L565_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hec zenon_H99 zenon_H6c zenon_H3d zenon_H197 zenon_H10e zenon_Hc3 zenon_He2 zenon_H40 zenon_Hf1 zenon_H4e zenon_H131 zenon_H5a zenon_H9f zenon_Hf8 zenon_Hcf zenon_H1ec zenon_H14a zenon_H7f zenon_H43 zenon_He4 zenon_Heb zenon_H11b zenon_H127 zenon_H113 zenon_H20 zenon_H117 zenon_H38 zenon_H81 zenon_H61 zenon_H15a zenon_H67. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.16 apply (zenon_L533_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.16 apply (zenon_L562_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.16 apply (zenon_L117_); trivial. % 7.95/8.16 apply (zenon_L564_); trivial. % 7.95/8.16 (* end of lemma zenon_L565_ *) % 7.95/8.16 assert (zenon_L566_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Had zenon_Hb9 zenon_H55. % 7.95/8.16 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 7.95/8.16 apply (zenon_L442_); trivial. % 7.95/8.16 (* end of lemma zenon_L566_ *) % 7.95/8.16 assert (zenon_L567_ : (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H122 zenon_H6f zenon_Hd2. % 7.95/8.16 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 7.95/8.16 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 7.95/8.16 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 7.95/8.16 exact (zenon_H118 zenon_Hd2). % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 (* end of lemma zenon_L567_ *) % 7.95/8.16 assert (zenon_L568_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hcc zenon_H25 zenon_H2c zenon_Hde zenon_H173 zenon_H6f zenon_Hca zenon_H70. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.16 apply (zenon_L5_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.16 apply (zenon_L306_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_L62_); trivial. % 7.95/8.16 (* end of lemma zenon_L568_ *) % 7.95/8.16 assert (zenon_L569_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_He7 zenon_Hb9 zenon_H3d zenon_H70 zenon_Hca zenon_H6f zenon_H173 zenon_H2c zenon_H25 zenon_Hcc zenon_Hd2 zenon_H43 zenon_H8f zenon_Hfc. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.16 apply (zenon_L416_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.16 apply (zenon_L568_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.16 apply (zenon_L80_); trivial. % 7.95/8.16 apply (zenon_L191_); trivial. % 7.95/8.16 (* end of lemma zenon_L569_ *) % 7.95/8.16 assert (zenon_L570_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 7.95/8.16 do 0 intro. intros zenon_Haa zenon_H67 zenon_H89 zenon_H88 zenon_Hfc zenon_H8f zenon_H43 zenon_Hd2 zenon_Hcc zenon_H25 zenon_H2c zenon_H173 zenon_H6f zenon_Hca zenon_H3d zenon_Hb9 zenon_He7 zenon_H6c zenon_Hdc. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 7.95/8.16 apply (zenon_L24_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 7.95/8.16 apply (zenon_L37_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 7.95/8.16 apply (zenon_L569_); trivial. % 7.95/8.16 apply (zenon_L73_); trivial. % 7.95/8.16 (* end of lemma zenon_L570_ *) % 7.95/8.16 assert (zenon_L571_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H20 zenon_H12d zenon_H12b zenon_Haa zenon_H67 zenon_H89 zenon_H88 zenon_Hfc zenon_H8f zenon_H43 zenon_Hd2 zenon_Hcc zenon_H25 zenon_H2c zenon_H173 zenon_H6f zenon_Hca zenon_H3d zenon_Hb9 zenon_He7 zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L204_); trivial. % 7.95/8.16 apply (zenon_L570_); trivial. % 7.95/8.16 (* end of lemma zenon_L571_ *) % 7.95/8.16 assert (zenon_L572_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hcc zenon_H25 zenon_H2c zenon_Hde zenon_H173 zenon_H6f zenon_Hef zenon_H115. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.16 apply (zenon_L5_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.16 apply (zenon_L306_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_L205_); trivial. % 7.95/8.16 (* end of lemma zenon_L572_ *) % 7.95/8.16 assert (zenon_L573_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_He7 zenon_Hb9 zenon_H3d zenon_H115 zenon_Hef zenon_H6f zenon_H173 zenon_H2c zenon_H25 zenon_Hcc zenon_Hd2 zenon_H43 zenon_H8f zenon_Hfc. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.16 apply (zenon_L416_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.16 apply (zenon_L572_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.16 apply (zenon_L80_); trivial. % 7.95/8.16 apply (zenon_L191_); trivial. % 7.95/8.16 (* end of lemma zenon_L573_ *) % 7.95/8.16 assert (zenon_L574_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H142 zenon_Hb9 zenon_H30 zenon_H9c zenon_H99 zenon_Hd2 zenon_H38 zenon_H157 zenon_H158 zenon_H29 zenon_H154 zenon_Hff zenon_H64 zenon_Hbc zenon_Hf1 zenon_Hfc zenon_H5e. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.16 apply (zenon_L422_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.16 apply (zenon_L97_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.16 apply (zenon_L390_); trivial. % 7.95/8.16 apply (zenon_L282_); trivial. % 7.95/8.16 (* end of lemma zenon_L574_ *) % 7.95/8.16 assert (zenon_L575_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H162 zenon_Hca zenon_H67 zenon_Haa zenon_H13a zenon_H83 zenon_H38 zenon_H134 zenon_Hdc zenon_H95 zenon_Hb0 zenon_Haf zenon_H89 zenon_H6c zenon_H128 zenon_Ha7 zenon_H8f zenon_H43 zenon_Hd2 zenon_Hcc zenon_H25 zenon_H2c zenon_H173 zenon_H6f zenon_Hef zenon_H3d zenon_Hb9 zenon_He7 zenon_Hfc zenon_H5e. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.16 apply (zenon_L570_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.16 apply (zenon_L162_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.16 apply (zenon_L573_); trivial. % 7.95/8.16 apply (zenon_L109_); trivial. % 7.95/8.16 (* end of lemma zenon_L575_ *) % 7.95/8.16 assert (zenon_L576_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_He7 zenon_H55 zenon_H3e zenon_Hc7 zenon_H40 zenon_Hd2 zenon_H43 zenon_H8f zenon_Hfc. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.16 apply (zenon_L50_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.16 apply (zenon_L144_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.16 apply (zenon_L80_); trivial. % 7.95/8.16 apply (zenon_L191_); trivial. % 7.95/8.16 (* end of lemma zenon_L576_ *) % 7.95/8.16 assert (zenon_L577_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H20 zenon_H6f zenon_Hf4 zenon_H99 zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H18e zenon_H15c zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L97_); trivial. % 7.95/8.16 apply (zenon_L482_); trivial. % 7.95/8.16 (* end of lemma zenon_L577_ *) % 7.95/8.16 assert (zenon_L578_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1d0 zenon_H111 zenon_Hfc zenon_H8f zenon_H43 zenon_Hd2 zenon_Hcc zenon_H2c zenon_H173 zenon_Hef zenon_H3d zenon_Hb9 zenon_He7 zenon_H6c zenon_H18e zenon_H88 zenon_H89 zenon_H25 zenon_H67 zenon_Haa zenon_H99 zenon_Hf4 zenon_H6f zenon_H20 zenon_H13b zenon_H12b zenon_H1cd. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.16 apply (zenon_L118_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.16 apply (zenon_L573_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L577_); trivial. % 7.95/8.16 apply (zenon_L336_); trivial. % 7.95/8.16 (* end of lemma zenon_L578_ *) % 7.95/8.16 assert (zenon_L579_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1d0 zenon_Hb9 zenon_Hef zenon_H6f zenon_H173 zenon_Hde zenon_H2c zenon_H25 zenon_Hcc zenon_H36 zenon_H67 zenon_Hfc zenon_H1cd. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.16 apply (zenon_L388_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.16 apply (zenon_L572_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L215_); trivial. % 7.95/8.16 apply (zenon_L335_); trivial. % 7.95/8.16 (* end of lemma zenon_L579_ *) % 7.95/8.16 assert (zenon_L580_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_He7 zenon_H55 zenon_H3e zenon_H1cd zenon_H67 zenon_H36 zenon_Hcc zenon_H25 zenon_H2c zenon_H173 zenon_H6f zenon_Hef zenon_Hb9 zenon_H1d0 zenon_Hd2 zenon_H43 zenon_H8f zenon_Hfc. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 7.95/8.16 apply (zenon_L50_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 7.95/8.16 apply (zenon_L579_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 7.95/8.16 apply (zenon_L80_); trivial. % 7.95/8.16 apply (zenon_L191_); trivial. % 7.95/8.16 (* end of lemma zenon_L580_ *) % 7.95/8.16 assert (zenon_L581_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H20 zenon_H6f zenon_H12d zenon_H12b zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H18e zenon_H15c zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L204_); trivial. % 7.95/8.16 apply (zenon_L482_); trivial. % 7.95/8.16 (* end of lemma zenon_L581_ *) % 7.95/8.16 assert (zenon_L582_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H20 zenon_H6f zenon_H12d zenon_Hfc zenon_H95 zenon_Hb9 zenon_H8f zenon_H31 zenon_H12b zenon_H128 zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H18e zenon_H15c zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L480_); trivial. % 7.95/8.16 apply (zenon_L482_); trivial. % 7.95/8.16 (* end of lemma zenon_L582_ *) % 7.95/8.16 assert (zenon_L583_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H20 zenon_H6f zenon_Hde zenon_H8f zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H88 zenon_H18e zenon_H15c zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L98_); trivial. % 7.95/8.16 apply (zenon_L482_); trivial. % 7.95/8.16 (* end of lemma zenon_L583_ *) % 7.95/8.16 assert (zenon_L584_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H18b zenon_Hec zenon_H12d zenon_H12b zenon_H95 zenon_Hb9 zenon_H6c zenon_H18e zenon_H89 zenon_H25 zenon_H67 zenon_Haa zenon_H8f zenon_H6f zenon_H20 zenon_H13b zenon_H99 zenon_Hef zenon_Hd2 zenon_He7 zenon_H55 zenon_H40 zenon_H43 zenon_H184 zenon_H10e zenon_H15c zenon_Hfc zenon_H128. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 7.95/8.16 apply (zenon_L442_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 7.95/8.16 apply (zenon_L462_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 7.95/8.16 apply (zenon_L17_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L333_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_L581_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L136_); trivial. % 7.95/8.16 apply (zenon_L137_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L333_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_L581_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L200_); trivial. % 7.95/8.16 apply (zenon_L39_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L333_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_L582_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L200_); trivial. % 7.95/8.16 apply (zenon_L137_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L333_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.16 apply (zenon_L576_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.16 apply (zenon_L90_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.16 apply (zenon_L577_); trivial. % 7.95/8.16 apply (zenon_L583_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L200_); trivial. % 7.95/8.16 apply (zenon_L137_); trivial. % 7.95/8.16 (* end of lemma zenon_L584_ *) % 7.95/8.16 assert (zenon_L585_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1d0 zenon_H111 zenon_H173 zenon_Hde zenon_H2c zenon_Hcc zenon_H128 zenon_Hfc zenon_H10e zenon_H184 zenon_H43 zenon_H40 zenon_H55 zenon_He7 zenon_Hd2 zenon_Hef zenon_H99 zenon_H13b zenon_H20 zenon_H6f zenon_H8f zenon_Haa zenon_H67 zenon_H25 zenon_H89 zenon_H18e zenon_H6c zenon_Hb9 zenon_H95 zenon_H12d zenon_Hec zenon_H18b zenon_H12b zenon_H1cd. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.16 apply (zenon_L118_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.16 apply (zenon_L572_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L584_); trivial. % 7.95/8.16 apply (zenon_L336_); trivial. % 7.95/8.16 (* end of lemma zenon_L585_ *) % 7.95/8.16 assert (zenon_L586_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H11b zenon_H12b zenon_H18b zenon_Hec zenon_H12d zenon_H95 zenon_H6c zenon_H18e zenon_H89 zenon_Haa zenon_H8f zenon_H20 zenon_H13b zenon_H99 zenon_He7 zenon_H40 zenon_H43 zenon_H184 zenon_H10e zenon_H128 zenon_Hd2 zenon_H55 zenon_H1cd zenon_Hfc zenon_H67 zenon_Hcc zenon_H25 zenon_H2c zenon_Hde zenon_H173 zenon_H6f zenon_Hef zenon_Hb9 zenon_H1d0 zenon_H1ec zenon_H3e. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.16 apply (zenon_L585_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.16 apply (zenon_L165_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.16 apply (zenon_L579_); trivial. % 7.95/8.16 apply (zenon_L558_); trivial. % 7.95/8.16 (* end of lemma zenon_L586_ *) % 7.95/8.16 assert (zenon_L587_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H3d zenon_H88 zenon_H11b zenon_H12b zenon_H18b zenon_Hec zenon_H12d zenon_H95 zenon_H6c zenon_H18e zenon_H89 zenon_Haa zenon_H8f zenon_H20 zenon_H13b zenon_H99 zenon_He7 zenon_H40 zenon_H43 zenon_H184 zenon_H10e zenon_H128 zenon_Hd2 zenon_H55 zenon_H1cd zenon_Hfc zenon_H67 zenon_Hcc zenon_H25 zenon_H2c zenon_H173 zenon_H6f zenon_Hef zenon_Hb9 zenon_H1d0 zenon_H1ec zenon_H3e. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 7.95/8.16 apply (zenon_L576_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 7.95/8.16 apply (zenon_L90_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.16 apply (zenon_L578_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.16 apply (zenon_L165_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.16 apply (zenon_L580_); trivial. % 7.95/8.16 apply (zenon_L558_); trivial. % 7.95/8.16 apply (zenon_L586_); trivial. % 7.95/8.16 (* end of lemma zenon_L587_ *) % 7.95/8.16 assert (zenon_L588_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H20 zenon_H25 zenon_H6f zenon_Hf4 zenon_H99 zenon_Ha7 zenon_H6c zenon_H8e zenon_H134 zenon_H10b zenon_H82 zenon_H13a. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L3_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L97_); trivial. % 7.95/8.16 apply (zenon_L153_); trivial. % 7.95/8.16 (* end of lemma zenon_L588_ *) % 7.95/8.16 assert (zenon_L589_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H11b zenon_H67 zenon_Hd2 zenon_H55 zenon_Hb0 zenon_Hb9 zenon_H1ec zenon_H3e. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.16 apply (zenon_L118_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.16 apply (zenon_L165_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.16 apply (zenon_L388_); trivial. % 7.95/8.16 apply (zenon_L558_); trivial. % 7.95/8.16 (* end of lemma zenon_L589_ *) % 7.95/8.16 assert (zenon_L590_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hc3 zenon_H8f zenon_H25 zenon_H3e zenon_H1ec zenon_Hb9 zenon_H55 zenon_Hd2 zenon_H67 zenon_H11b zenon_Hbc zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.16 apply (zenon_L333_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.16 apply (zenon_L24_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.16 apply (zenon_L589_); trivial. % 7.95/8.16 apply (zenon_L57_); trivial. % 7.95/8.16 (* end of lemma zenon_L590_ *) % 7.95/8.16 assert (zenon_L591_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H4e zenon_H1e zenon_H3d zenon_H89 zenon_H88 zenon_Hca zenon_H9c zenon_Hc7 zenon_H2c zenon_H173 zenon_Hcc zenon_H36 zenon_H5a zenon_H55 zenon_He2. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 7.95/8.16 apply (zenon_L9_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 7.95/8.16 apply (zenon_L517_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 7.95/8.16 apply (zenon_L16_); trivial. % 7.95/8.16 apply (zenon_L308_); trivial. % 7.95/8.16 (* end of lemma zenon_L591_ *) % 7.95/8.16 assert (zenon_L592_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H134 zenon_H33 zenon_H19b zenon_H6f zenon_He2 zenon_H55 zenon_H5a zenon_H36 zenon_Hcc zenon_H173 zenon_H2c zenon_Hc7 zenon_Hca zenon_H88 zenon_H89 zenon_H3d zenon_H1e zenon_H4e zenon_H6c zenon_H7f. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L591_); trivial. % 7.95/8.16 apply (zenon_L73_); trivial. % 7.95/8.16 (* end of lemma zenon_L592_ *) % 7.95/8.16 assert (zenon_L593_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H95 zenon_H67 zenon_Had zenon_H7f zenon_H6c zenon_H4e zenon_H1e zenon_H3d zenon_H89 zenon_Hca zenon_Hc7 zenon_H2c zenon_H173 zenon_Hcc zenon_H36 zenon_H5a zenon_H55 zenon_He2 zenon_H6f zenon_H19b zenon_H33 zenon_H134 zenon_H13b zenon_H8f zenon_H54 zenon_Hc0. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 7.95/8.16 apply (zenon_L48_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 7.95/8.16 apply (zenon_L592_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 7.95/8.16 apply (zenon_L38_); trivial. % 7.95/8.16 exact (zenon_Hc0 zenon_H92). % 7.95/8.16 (* end of lemma zenon_L593_ *) % 7.95/8.16 assert (zenon_L594_ : ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H221 zenon_Had zenon_H55 zenon_Hb6 zenon_H142 zenon_H49 zenon_H99 zenon_H17f zenon_H67 zenon_H13b zenon_H6c zenon_H3d zenon_H1e zenon_H89 zenon_H5a zenon_H36 zenon_He2 zenon_H4e zenon_H6f zenon_Hcc zenon_H7f zenon_H173 zenon_H2c zenon_Hca zenon_H33 zenon_H134 zenon_H19b zenon_H8f zenon_H95 zenon_Hd2 zenon_H113 zenon_H81 zenon_He4 zenon_H15f. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 7.95/8.16 apply (zenon_L566_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 7.95/8.16 apply (zenon_L566_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 7.95/8.16 apply (zenon_L323_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 7.95/8.16 apply (zenon_L593_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.16 apply (zenon_L244_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.16 apply (zenon_L97_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.16 apply (zenon_L155_); trivial. % 7.95/8.16 apply (zenon_L456_); trivial. % 7.95/8.16 apply (zenon_L73_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 7.95/8.16 apply (zenon_L68_); trivial. % 7.95/8.16 apply (zenon_L81_); trivial. % 7.95/8.16 apply (zenon_L308_); trivial. % 7.95/8.16 (* end of lemma zenon_L594_ *) % 7.95/8.16 assert (zenon_L595_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1c7 zenon_H15f zenon_He4 zenon_H81 zenon_H113 zenon_H95 zenon_H8f zenon_H19b zenon_H134 zenon_H33 zenon_Hca zenon_H2c zenon_H173 zenon_H7f zenon_Hcc zenon_H6f zenon_H4e zenon_He2 zenon_H5a zenon_H89 zenon_H1e zenon_H3d zenon_H6c zenon_H13b zenon_H67 zenon_H17f zenon_H99 zenon_H49 zenon_H142 zenon_Hb6 zenon_H55 zenon_Had zenon_H221 zenon_Hd2 zenon_H38 zenon_H18e zenon_H9c zenon_Hb0 zenon_H10b. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.95/8.16 apply (zenon_L594_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.95/8.16 apply (zenon_L390_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.95/8.16 apply (zenon_L299_); trivial. % 7.95/8.16 apply (zenon_L274_); trivial. % 7.95/8.16 (* end of lemma zenon_L595_ *) % 7.95/8.16 assert (zenon_L596_ : ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hc7 zenon_H10b zenon_Hb0 zenon_H18e zenon_H38 zenon_Hd2 zenon_H221 zenon_Had zenon_H55 zenon_Hb6 zenon_H142 zenon_H49 zenon_H99 zenon_H17f zenon_H67 zenon_H13b zenon_H3d zenon_H1e zenon_H89 zenon_H5a zenon_He2 zenon_H4e zenon_H6f zenon_Hcc zenon_H173 zenon_H2c zenon_Hca zenon_H33 zenon_H134 zenon_H19b zenon_H8f zenon_H95 zenon_H113 zenon_H81 zenon_He4 zenon_H15f zenon_H1c7 zenon_H6c zenon_H7f. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L595_); trivial. % 7.95/8.16 apply (zenon_L73_); trivial. % 7.95/8.16 (* end of lemma zenon_L596_ *) % 7.95/8.16 assert (zenon_L597_ : ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H44 zenon_H15c zenon_H222. % 7.95/8.16 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.95/8.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H222. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H1ba. % 7.95/8.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.95/8.16 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 7.95/8.16 congruence. % 7.95/8.16 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H223. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H44. % 7.95/8.16 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 7.95/8.16 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 7.95/8.16 congruence. % 7.95/8.16 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 7.95/8.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H1da. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H1ba. % 7.95/8.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 7.95/8.16 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 7.95/8.16 congruence. % 7.95/8.16 apply (zenon_L381_); trivial. % 7.95/8.16 apply zenon_H1bb. apply refl_equal. % 7.95/8.16 apply zenon_H1bb. apply refl_equal. % 7.95/8.16 apply zenon_H1d. apply refl_equal. % 7.95/8.16 apply zenon_H1bb. apply refl_equal. % 7.95/8.16 apply zenon_H1bb. apply refl_equal. % 7.95/8.16 (* end of lemma zenon_L597_ *) % 7.95/8.16 assert (zenon_L598_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_He2 zenon_H44 zenon_H15c. % 7.95/8.16 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H224 ]. % 7.95/8.16 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.95/8.16 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H1e1. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H1c1. % 7.95/8.16 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.95/8.16 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 7.95/8.16 congruence. % 7.95/8.16 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H1e2. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_He2. % 7.95/8.16 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.16 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 7.95/8.16 congruence. % 7.95/8.16 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1c2 ]. % 7.95/8.16 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H1dc. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H1c1. % 7.95/8.16 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 7.95/8.16 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 7.95/8.16 congruence. % 7.95/8.16 apply (zenon_L380_); trivial. % 7.95/8.16 apply zenon_H1c2. apply refl_equal. % 7.95/8.16 apply zenon_H1c2. apply refl_equal. % 7.95/8.16 apply zenon_H57. apply refl_equal. % 7.95/8.16 apply zenon_H1c2. apply refl_equal. % 7.95/8.16 apply zenon_H1c2. apply refl_equal. % 7.95/8.16 apply (zenon_notand_s _ _ zenon_H224); [ zenon_intro zenon_H1dd | zenon_intro zenon_H222 ]. % 7.95/8.16 apply zenon_H1dd. apply sym_equal. exact zenon_H15c. % 7.95/8.16 apply (zenon_L597_); trivial. % 7.95/8.16 (* end of lemma zenon_L598_ *) % 7.95/8.16 assert (zenon_L599_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1c7 zenon_H5a zenon_H115 zenon_H2d zenon_H18e zenon_H9c zenon_He2 zenon_H44. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 7.95/8.16 apply (zenon_L16_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 7.95/8.16 apply (zenon_L325_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 7.95/8.16 apply (zenon_L299_); trivial. % 7.95/8.16 apply (zenon_L598_); trivial. % 7.95/8.16 (* end of lemma zenon_L599_ *) % 7.95/8.16 assert (zenon_L600_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H11b zenon_Haf zenon_H88 zenon_H1d0 zenon_H6c zenon_H15f zenon_He4 zenon_H81 zenon_H113 zenon_H95 zenon_H8f zenon_H19b zenon_H134 zenon_H33 zenon_Hca zenon_H173 zenon_H4e zenon_H89 zenon_H1e zenon_H3d zenon_H13b zenon_H67 zenon_H17f zenon_H99 zenon_H49 zenon_H142 zenon_Hb6 zenon_H55 zenon_Had zenon_H221 zenon_Hd2 zenon_H38 zenon_H10b zenon_Hef zenon_H6f zenon_Hc7 zenon_H2c zenon_H1c7 zenon_H5a zenon_H18e zenon_H9c zenon_Hcc zenon_He2 zenon_H7f zenon_H131. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.16 apply (zenon_L318_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.16 apply (zenon_L165_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.16 apply (zenon_L591_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.16 apply (zenon_L596_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.16 apply (zenon_L599_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.16 apply (zenon_L61_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_L205_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L598_); trivial. % 7.95/8.16 apply (zenon_L559_); trivial. % 7.95/8.16 (* end of lemma zenon_L600_ *) % 7.95/8.16 assert (zenon_L601_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H131 zenon_He2 zenon_Hcc zenon_H18e zenon_H5a zenon_H1c7 zenon_H2c zenon_Hc7 zenon_H6f zenon_Hef zenon_H10b zenon_H38 zenon_Hd2 zenon_H221 zenon_Had zenon_H55 zenon_Hb6 zenon_H142 zenon_H49 zenon_H99 zenon_H17f zenon_H67 zenon_H13b zenon_H3d zenon_H1e zenon_H89 zenon_H4e zenon_H173 zenon_Hca zenon_H33 zenon_H134 zenon_H19b zenon_H8f zenon_H95 zenon_H113 zenon_H81 zenon_He4 zenon_H15f zenon_H1d0 zenon_H88 zenon_Haf zenon_H11b zenon_H6c zenon_H7f. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_L600_); trivial. % 7.95/8.16 apply (zenon_L73_); trivial. % 7.95/8.16 (* end of lemma zenon_L601_ *) % 7.95/8.16 assert (zenon_L602_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H13b zenon_H134 zenon_H33 zenon_Hc7 zenon_Hcc zenon_Hca zenon_H2c zenon_H173 zenon_H19b zenon_H6f zenon_H49 zenon_He2 zenon_H38 zenon_Hd2 zenon_H99 zenon_H8e zenon_H8f zenon_H142 zenon_H6c zenon_H7f. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 7.95/8.16 apply (zenon_L297_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 7.95/8.16 exact (zenon_H6f zenon_H6e). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.16 apply (zenon_L38_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.16 apply (zenon_L97_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.16 apply (zenon_L390_); trivial. % 7.95/8.16 apply (zenon_L456_); trivial. % 7.95/8.16 apply (zenon_L73_); trivial. % 7.95/8.16 (* end of lemma zenon_L602_ *) % 7.95/8.16 assert (zenon_L603_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hd6 zenon_Hc6 zenon_H130. % 7.95/8.16 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H65 ]. % 7.95/8.16 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H130. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_Hf2. % 7.95/8.16 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.95/8.16 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H225]. % 7.95/8.16 congruence. % 7.95/8.16 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H225. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_Hd6. % 7.95/8.16 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 7.95/8.16 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 7.95/8.16 congruence. % 7.95/8.16 apply zenon_H65. apply refl_equal. % 7.95/8.16 apply zenon_H226. apply sym_equal. exact zenon_Hc6. % 7.95/8.16 apply zenon_H65. apply refl_equal. % 7.95/8.16 apply zenon_H65. apply refl_equal. % 7.95/8.16 (* end of lemma zenon_L603_ *) % 7.95/8.16 assert (zenon_L604_ : (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H106 zenon_Hd6 zenon_H130. % 7.95/8.16 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 7.95/8.16 apply (zenon_L603_); trivial. % 7.95/8.16 (* end of lemma zenon_L604_ *) % 7.95/8.16 assert (zenon_L605_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hd6 zenon_Hfd zenon_H8f. % 7.95/8.16 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.95/8.16 cut (((e3) = (e3)) = ((e1) = (e3))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H8f. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H68. % 7.95/8.16 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.16 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 7.95/8.16 congruence. % 7.95/8.16 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H90. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_Hd6. % 7.95/8.16 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 7.95/8.16 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 7.95/8.16 congruence. % 7.95/8.16 exact (zenon_H227 zenon_Hfd). % 7.95/8.16 apply zenon_H57. apply refl_equal. % 7.95/8.16 apply zenon_H69. apply refl_equal. % 7.95/8.16 apply zenon_H69. apply refl_equal. % 7.95/8.16 (* end of lemma zenon_L605_ *) % 7.95/8.16 assert (zenon_L606_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H162 zenon_Hb9 zenon_H6e zenon_Hdb zenon_Hb0 zenon_H81 zenon_Hd6 zenon_H8f. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 7.95/8.16 apply (zenon_L449_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 7.95/8.16 exact (zenon_Hdb zenon_H6d). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 7.95/8.16 apply (zenon_L120_); trivial. % 7.95/8.16 apply (zenon_L605_); trivial. % 7.95/8.16 (* end of lemma zenon_L606_ *) % 7.95/8.16 assert (zenon_L607_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H124 zenon_H99 zenon_H2c zenon_H10b zenon_H9f zenon_Hc3 zenon_H67 zenon_H25 zenon_H8f zenon_Hd6 zenon_H81 zenon_Hdb zenon_H6e zenon_Hb9 zenon_H162 zenon_H6c. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 7.95/8.16 apply (zenon_L462_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 7.95/8.16 apply (zenon_L128_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 7.95/8.16 apply (zenon_L115_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.16 apply (zenon_L333_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.16 apply (zenon_L24_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.16 apply (zenon_L606_); trivial. % 7.95/8.16 apply (zenon_L57_); trivial. % 7.95/8.16 (* end of lemma zenon_L607_ *) % 7.95/8.16 assert (zenon_L608_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H142 zenon_H55 zenon_Hdb zenon_Hec zenon_H89 zenon_H10e zenon_H95 zenon_H8f zenon_Hb9 zenon_H67 zenon_H31 zenon_H6c zenon_Hca zenon_H2c zenon_H25 zenon_Hcc zenon_H9f zenon_H99 zenon_H64 zenon_Hd6. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 7.95/8.16 apply (zenon_L15_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.16 apply (zenon_L5_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.16 apply (zenon_L228_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.16 apply (zenon_L471_); trivial. % 7.95/8.16 exact (zenon_Hdb zenon_H6d). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 7.95/8.16 apply (zenon_L169_); trivial. % 7.95/8.16 apply (zenon_L156_); trivial. % 7.95/8.16 (* end of lemma zenon_L608_ *) % 7.95/8.16 assert (zenon_L609_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 7.95/8.16 do 0 intro. intros zenon_H11b zenon_H127 zenon_H29 zenon_H113 zenon_H20 zenon_H9f zenon_H1ec zenon_H3e. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 7.95/8.16 exact (zenon_H127 zenon_H111). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 7.95/8.16 apply (zenon_L119_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 7.95/8.16 apply (zenon_L44_); trivial. % 7.95/8.16 apply (zenon_L558_); trivial. % 7.95/8.16 (* end of lemma zenon_L609_ *) % 7.95/8.16 assert (zenon_L610_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_Hcc zenon_H25 zenon_H2c zenon_H130 zenon_H8f zenon_Hd6 zenon_H81 zenon_Hb0 zenon_Hb9 zenon_H162 zenon_Hdb. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.16 apply (zenon_L5_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.16 apply (zenon_L603_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.16 apply (zenon_L606_); trivial. % 7.95/8.16 exact (zenon_Hdb zenon_H6d). % 7.95/8.16 (* end of lemma zenon_L610_ *) % 7.95/8.16 assert (zenon_L611_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H102 zenon_H67 zenon_H131 zenon_Hcf zenon_H1ec zenon_H3e zenon_H14a zenon_H37 zenon_H43 zenon_H115 zenon_H81 zenon_H10b zenon_Hf8 zenon_H127 zenon_H209 zenon_H9f zenon_H5a zenon_H1cd. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H92 | zenon_intro zenon_H103 ]. % 7.95/8.16 apply (zenon_L313_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H7f | zenon_intro zenon_H104 ]. % 7.95/8.16 apply (zenon_L560_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfc ]. % 7.95/8.16 apply (zenon_L453_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H14a); [ zenon_intro zenon_H44 | zenon_intro zenon_H14b ]. % 7.95/8.16 apply (zenon_L11_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_He0 | zenon_intro zenon_H14c ]. % 7.95/8.16 apply (zenon_L466_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H148 | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L178_); trivial. % 7.95/8.16 apply (zenon_L335_); trivial. % 7.95/8.16 (* end of lemma zenon_L611_ *) % 7.95/8.16 assert (zenon_L612_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H9f zenon_H15c zenon_H6c. % 7.95/8.16 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 7.95/8.16 cut (((e3) = (e3)) = ((e2) = (e3))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H6c. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H68. % 7.95/8.16 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.95/8.16 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 7.95/8.16 congruence. % 7.95/8.16 cut (((op (e2) (e2)) = (e2)) = ((e3) = (e2))). % 7.95/8.16 intro zenon_D_pnotp. % 7.95/8.16 apply zenon_H9d. % 7.95/8.16 rewrite <- zenon_D_pnotp. % 7.95/8.16 exact zenon_H9f. % 7.95/8.16 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 7.95/8.16 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 7.95/8.16 congruence. % 7.95/8.16 exact (zenon_H1d6 zenon_H15c). % 7.95/8.16 apply zenon_H22. apply refl_equal. % 7.95/8.16 apply zenon_H69. apply refl_equal. % 7.95/8.16 apply zenon_H69. apply refl_equal. % 7.95/8.16 (* end of lemma zenon_L612_ *) % 7.95/8.16 assert (zenon_L613_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.16 do 0 intro. intros zenon_H1d0 zenon_Hdb zenon_H162 zenon_Hb9 zenon_Hd6 zenon_H8f zenon_H130 zenon_H2c zenon_H25 zenon_Hcc zenon_H81 zenon_H6c zenon_H209 zenon_H127 zenon_He0 zenon_H10b zenon_H9f zenon_Hf8. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.16 apply (zenon_L610_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.16 apply (zenon_L466_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.16 apply (zenon_L612_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H111 | zenon_intro zenon_H20a ]. % 7.95/8.16 exact (zenon_H127 zenon_H111). % 7.95/8.16 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_Hcf | zenon_intro zenon_H20b ]. % 7.95/8.16 apply (zenon_L177_); trivial. % 7.95/8.16 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H82 | zenon_intro zenon_Hb0 ]. % 7.95/8.16 apply (zenon_L115_); trivial. % 7.95/8.16 apply (zenon_L108_); trivial. % 7.95/8.16 (* end of lemma zenon_L613_ *) % 7.95/8.16 assert (zenon_L614_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H1ca zenon_H228 zenon_H70 zenon_H18e zenon_H102 zenon_H67 zenon_H131 zenon_H1ec zenon_H3e zenon_H14a zenon_H37 zenon_H43 zenon_H5a zenon_H1cd zenon_H118 zenon_H99 zenon_H1d0 zenon_Hdb zenon_H162 zenon_Hb9 zenon_Hd6 zenon_H8f zenon_H130 zenon_H2c zenon_H25 zenon_Hcc zenon_H81 zenon_H6c zenon_H209 zenon_H127 zenon_H10b zenon_H9f zenon_Hf8. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.17 apply (zenon_L610_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.17 apply (zenon_L611_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.17 apply (zenon_L273_); trivial. % 7.95/8.17 exact (zenon_H228 zenon_Hf7). % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.17 exact (zenon_H118 zenon_Hd2). % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.17 apply (zenon_L169_); trivial. % 7.95/8.17 apply (zenon_L613_); trivial. % 7.95/8.17 (* end of lemma zenon_L614_ *) % 7.95/8.17 assert (zenon_L615_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H1ca zenon_H131 zenon_H7f zenon_H5a zenon_H1ec zenon_H3e zenon_H14a zenon_H118 zenon_H99 zenon_H1d0 zenon_Hdb zenon_H162 zenon_Hb9 zenon_Hd6 zenon_H8f zenon_H130 zenon_H2c zenon_H25 zenon_Hcc zenon_H81 zenon_H6c zenon_H209 zenon_H127 zenon_H10b zenon_H9f zenon_Hf8. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.17 apply (zenon_L560_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.17 exact (zenon_H118 zenon_Hd2). % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.17 apply (zenon_L169_); trivial. % 7.95/8.17 apply (zenon_L613_); trivial. % 7.95/8.17 (* end of lemma zenon_L615_ *) % 7.95/8.17 assert (zenon_L616_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 7.95/8.17 do 0 intro. intros zenon_Hc3 zenon_H67 zenon_Hdb zenon_H162 zenon_Hb9 zenon_H81 zenon_Hd6 zenon_H8f zenon_H130 zenon_H2c zenon_H25 zenon_Hcc zenon_Hbc zenon_H6c. % 7.95/8.17 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 7.95/8.17 apply (zenon_L333_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 7.95/8.17 apply (zenon_L24_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 7.95/8.17 apply (zenon_L610_); trivial. % 7.95/8.17 apply (zenon_L57_); trivial. % 7.95/8.17 (* end of lemma zenon_L616_ *) % 7.95/8.17 assert (zenon_L617_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H195 zenon_H93 zenon_H128. % 7.95/8.17 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 7.95/8.17 intro zenon_D_pnotp. % 7.95/8.17 apply zenon_H128. % 7.95/8.17 rewrite <- zenon_D_pnotp. % 7.95/8.17 exact zenon_H4a. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 7.95/8.17 congruence. % 7.95/8.17 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 7.95/8.17 intro zenon_D_pnotp. % 7.95/8.17 apply zenon_H129. % 7.95/8.17 rewrite <- zenon_D_pnotp. % 7.95/8.17 exact zenon_H195. % 7.95/8.17 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.17 congruence. % 7.95/8.17 apply zenon_H4b. apply refl_equal. % 7.95/8.17 apply zenon_H194. apply sym_equal. exact zenon_H93. % 7.95/8.17 apply zenon_H4b. apply refl_equal. % 7.95/8.17 apply zenon_H4b. apply refl_equal. % 7.95/8.17 (* end of lemma zenon_L617_ *) % 7.95/8.17 assert (zenon_L618_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H137 zenon_H3e zenon_H1d4 zenon_Hc6 zenon_H173 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 7.95/8.17 apply (zenon_L373_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 7.95/8.17 apply (zenon_L306_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 7.95/8.17 apply (zenon_L458_); trivial. % 7.95/8.17 apply (zenon_L559_); trivial. % 7.95/8.17 (* end of lemma zenon_L618_ *) % 7.95/8.17 assert (zenon_L619_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 7.95/8.17 do 0 intro. intros zenon_H229 zenon_H37 zenon_H113 zenon_H154 zenon_Hd6 zenon_H89 zenon_H6e zenon_Hb9. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H29 | zenon_intro zenon_H22a ]. % 7.95/8.17 apply (zenon_L119_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_Hbb | zenon_intro zenon_H22b ]. % 7.95/8.17 apply (zenon_L195_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H5b | zenon_intro zenon_H88 ]. % 7.95/8.17 apply (zenon_L84_); trivial. % 7.95/8.17 apply (zenon_L449_); trivial. % 7.95/8.17 (* end of lemma zenon_L619_ *) % 7.95/8.17 assert (zenon_L620_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 7.95/8.17 do 0 intro. intros zenon_Hcc zenon_H25 zenon_H2c zenon_H131 zenon_Hf7 zenon_H195 zenon_H12d zenon_H173 zenon_H1d4 zenon_H3e zenon_H137 zenon_Hb9 zenon_H89 zenon_Hd6 zenon_H154 zenon_H113 zenon_H37 zenon_H229 zenon_Hdb. % 7.95/8.17 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 7.95/8.17 apply (zenon_L5_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 7.95/8.17 apply (zenon_L618_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 7.95/8.17 apply (zenon_L619_); trivial. % 7.95/8.17 exact (zenon_Hdb zenon_H6d). % 7.95/8.17 (* end of lemma zenon_L620_ *) % 7.95/8.17 assert (zenon_L621_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H1ca zenon_H229 zenon_H37 zenon_H113 zenon_H154 zenon_H89 zenon_H137 zenon_H3e zenon_H1d4 zenon_H173 zenon_H12d zenon_H195 zenon_H131 zenon_H70 zenon_H18e zenon_H102 zenon_H67 zenon_H1ec zenon_H14a zenon_H43 zenon_H5a zenon_H1cd zenon_H118 zenon_H99 zenon_H1d0 zenon_Hdb zenon_H162 zenon_Hb9 zenon_Hd6 zenon_H8f zenon_H130 zenon_H2c zenon_H25 zenon_Hcc zenon_H81 zenon_H6c zenon_H209 zenon_H127 zenon_H10b zenon_H9f zenon_Hf8. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1d0); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1d1 ]. % 7.95/8.17 apply (zenon_L610_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H115 | zenon_intro zenon_H1d2 ]. % 7.95/8.17 apply (zenon_L611_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H15c | zenon_intro zenon_Hf7 ]. % 7.95/8.17 apply (zenon_L273_); trivial. % 7.95/8.17 apply (zenon_L620_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 7.95/8.17 exact (zenon_H118 zenon_Hd2). % 7.95/8.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 7.95/8.17 apply (zenon_L169_); trivial. % 7.95/8.17 apply (zenon_L613_); trivial. % 7.95/8.17 (* end of lemma zenon_L621_ *) % 7.95/8.17 assert (zenon_L622_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H195 zenon_Hbc zenon_He4. % 7.95/8.17 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H4a | zenon_intro zenon_H4b ]. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 7.95/8.17 intro zenon_D_pnotp. % 7.95/8.17 apply zenon_He4. % 7.95/8.17 rewrite <- zenon_D_pnotp. % 7.95/8.17 exact zenon_H4a. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 7.95/8.17 congruence. % 7.95/8.17 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 7.95/8.17 intro zenon_D_pnotp. % 7.95/8.17 apply zenon_He5. % 7.95/8.17 rewrite <- zenon_D_pnotp. % 7.95/8.17 exact zenon_H195. % 7.95/8.17 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 7.95/8.17 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 7.95/8.17 congruence. % 7.95/8.17 apply zenon_H4b. apply refl_equal. % 7.95/8.17 apply zenon_Hbf. apply sym_equal. exact zenon_Hbc. % 7.95/8.17 apply zenon_H4b. apply refl_equal. % 7.95/8.17 apply zenon_H4b. apply refl_equal. % 7.95/8.17 (* end of lemma zenon_L622_ *) % 7.95/8.17 assert (zenon_L623_ : (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> False). % 7.95/8.17 do 0 intro. intros zenon_H12b zenon_Hdb zenon_Hd6. % 7.95/8.17 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 7.95/8.17 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 7.95/8.17 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 7.95/8.17 exact (zenon_H165 zenon_Hd6). % 7.95/8.17 exact (zenon_Hdb zenon_H6d). % 7.95/8.17 (* end of lemma zenon_L623_ *) % 7.95/8.17 assert (zenon_L624_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 7.95/8.17 do 0 intro. intros zenon_H117 zenon_H44 zenon_H43 zenon_H38 zenon_H82 zenon_H81 zenon_H2d zenon_H13e. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 7.95/8.17 apply (zenon_L11_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 7.95/8.17 apply (zenon_L390_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 7.95/8.17 apply (zenon_L35_); trivial. % 7.95/8.17 apply (zenon_L325_); trivial. % 7.95/8.17 (* end of lemma zenon_L624_ *) % 7.95/8.17 assert (zenon_L625_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 7.95/8.17 do 0 intro. intros zenon_H51 zenon_H30 zenon_Hca zenon_H55 zenon_H4e zenon_H1e zenon_H3d zenon_H173 zenon_H13e zenon_H2d zenon_H81 zenon_H82 zenon_H38 zenon_H43 zenon_H117 zenon_H49. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 7.95/8.17 apply (zenon_L6_); trivial. % 7.95/8.17 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 7.95/8.17 apply (zenon_L293_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.17 apply (zenon_L155_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.17 apply (zenon_L9_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.17 apply (zenon_L330_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.17 apply (zenon_L624_); trivial. % 8.02/8.17 apply (zenon_L12_); trivial. % 8.02/8.17 (* end of lemma zenon_L625_ *) % 8.02/8.17 assert (zenon_L626_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H51 zenon_H67 zenon_H8e zenon_H2d zenon_Hca zenon_H55 zenon_H13e zenon_H47 zenon_H49. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.17 apply (zenon_L123_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.17 apply (zenon_L293_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.17 apply (zenon_L155_); trivial. % 8.02/8.17 apply (zenon_L12_); trivial. % 8.02/8.17 (* end of lemma zenon_L626_ *) % 8.02/8.17 assert (zenon_L627_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H5e zenon_Hd6 zenon_He2. % 8.02/8.17 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H5e. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_Hd6. % 8.02/8.17 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H22d]. % 8.02/8.17 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 8.02/8.17 congruence. % 8.02/8.17 apply zenon_H65. apply refl_equal. % 8.02/8.17 apply zenon_H22d. apply sym_equal. exact zenon_He2. % 8.02/8.17 (* end of lemma zenon_L627_ *) % 8.02/8.17 assert (zenon_L628_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H205 zenon_H49 zenon_H13e zenon_H55 zenon_Hca zenon_H2d zenon_H8e zenon_H67 zenon_H51 zenon_Hd6 zenon_H5e zenon_He4 zenon_Hbc zenon_H7f zenon_H12d. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 8.02/8.17 apply (zenon_L626_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 8.02/8.17 apply (zenon_L627_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 8.02/8.17 apply (zenon_L622_); trivial. % 8.02/8.17 apply (zenon_L139_); trivial. % 8.02/8.17 (* end of lemma zenon_L628_ *) % 8.02/8.17 assert (zenon_L629_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H102 zenon_Hc0 zenon_Hbc zenon_He4 zenon_H5e zenon_Hd6 zenon_H51 zenon_H8e zenon_H2d zenon_Hca zenon_H55 zenon_H13e zenon_H49 zenon_H205 zenon_H67 zenon_H137 zenon_H44 zenon_H131 zenon_Hc7 zenon_H40 zenon_H9c zenon_H134 zenon_H12d. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H92 | zenon_intro zenon_H103 ]. % 8.02/8.17 exact (zenon_Hc0 zenon_H92). % 8.02/8.17 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H7f | zenon_intro zenon_H104 ]. % 8.02/8.17 apply (zenon_L628_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hfc ]. % 8.02/8.17 apply (zenon_L392_); trivial. % 8.02/8.17 apply (zenon_L146_); trivial. % 8.02/8.17 (* end of lemma zenon_L629_ *) % 8.02/8.17 assert (zenon_L630_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H4e zenon_Hb2 zenon_H173 zenon_H12d zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H67 zenon_H205 zenon_H13e zenon_H55 zenon_Hca zenon_H2d zenon_H8e zenon_H51 zenon_Hd6 zenon_H5e zenon_He4 zenon_Hbc zenon_Hc0 zenon_H102 zenon_H48 zenon_H49. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.17 apply (zenon_L50_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.17 apply (zenon_L330_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.17 apply (zenon_L629_); trivial. % 8.02/8.17 apply (zenon_L12_); trivial. % 8.02/8.17 (* end of lemma zenon_L630_ *) % 8.02/8.17 assert (zenon_L631_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H22e zenon_H1e zenon_H30 zenon_H17f zenon_H9b zenon_H4e zenon_Hb2 zenon_H173 zenon_H12d zenon_H134 zenon_H9c zenon_H40 zenon_Hc7 zenon_H131 zenon_H137 zenon_H67 zenon_H205 zenon_H13e zenon_H55 zenon_Hca zenon_H2d zenon_H51 zenon_Hd6 zenon_H5e zenon_He4 zenon_Hbc zenon_Hc0 zenon_H102 zenon_H48 zenon_H49. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H31 | zenon_intro zenon_H22f ]. % 8.02/8.17 apply (zenon_L6_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H54 | zenon_intro zenon_H230 ]. % 8.02/8.17 apply (zenon_L244_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H98 | zenon_intro zenon_H8e ]. % 8.02/8.17 exact (zenon_H9b zenon_H98). % 8.02/8.17 apply (zenon_L630_); trivial. % 8.02/8.17 (* end of lemma zenon_L631_ *) % 8.02/8.17 assert (zenon_L632_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H51 zenon_H1e zenon_H30 zenon_H2d zenon_Hca zenon_H55 zenon_H13e zenon_H47 zenon_H49. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.17 apply (zenon_L6_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.17 apply (zenon_L293_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.17 apply (zenon_L155_); trivial. % 8.02/8.17 apply (zenon_L12_); trivial. % 8.02/8.17 (* end of lemma zenon_L632_ *) % 8.02/8.17 assert (zenon_L633_ : ((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H231 zenon_H15f zenon_Hf1 zenon_H10b zenon_H154 zenon_Hd6 zenon_H124 zenon_He7 zenon_H5a zenon_H17f zenon_H205 zenon_H12d zenon_He4 zenon_H5e zenon_H67 zenon_H137 zenon_H134 zenon_H40 zenon_H131 zenon_H102 zenon_H22e zenon_H30 zenon_Hca zenon_H2d zenon_H13e zenon_H4e zenon_H49 zenon_H43 zenon_H38 zenon_H81 zenon_H117 zenon_H173 zenon_H3d zenon_H51 zenon_H9c zenon_H33 zenon_H20 zenon_Had zenon_Hb6 zenon_H1e zenon_H55 zenon_H221. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H9b | zenon_intro zenon_H36 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.17 apply (zenon_L442_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.17 apply (zenon_L442_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.17 apply (zenon_L195_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.17 apply (zenon_L75_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.17 apply (zenon_L296_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.17 apply (zenon_L625_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.17 apply (zenon_L15_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.17 apply (zenon_L293_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.17 apply (zenon_L155_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 8.02/8.17 apply (zenon_L631_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 8.02/8.17 apply (zenon_L144_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 8.02/8.17 apply (zenon_L190_); trivial. % 8.02/8.17 apply (zenon_L627_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.17 apply (zenon_L2_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.17 apply (zenon_L296_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.17 apply (zenon_L625_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.17 apply (zenon_L6_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.17 apply (zenon_L293_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.17 apply (zenon_L155_); trivial. % 8.02/8.17 apply (zenon_L631_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.17 apply (zenon_L175_); trivial. % 8.02/8.17 apply (zenon_L93_); trivial. % 8.02/8.17 apply (zenon_L632_); trivial. % 8.02/8.17 apply (zenon_L155_); trivial. % 8.02/8.17 (* end of lemma zenon_L633_ *) % 8.02/8.17 assert (zenon_L634_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e2)) -> False). % 8.02/8.17 do 0 intro. intros zenon_Had zenon_H16a zenon_H98. % 8.02/8.17 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.17 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.17 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.17 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H9b | zenon_intro zenon_H36 ]. % 8.02/8.17 exact (zenon_H9b zenon_H98). % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 (* end of lemma zenon_L634_ *) % 8.02/8.17 assert (zenon_L635_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H1d4 zenon_Hb2 zenon_Hde. % 8.02/8.17 cut (((op (e3) (e0)) = (e1)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H1d4. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_Hb2. % 8.02/8.17 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 8.02/8.17 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 8.02/8.17 congruence. % 8.02/8.17 apply zenon_H181. apply refl_equal. % 8.02/8.17 apply zenon_H133. apply sym_equal. exact zenon_Hde. % 8.02/8.17 (* end of lemma zenon_L635_ *) % 8.02/8.17 assert (zenon_L636_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H137 zenon_H44 zenon_H131 zenon_Hb2 zenon_H1d4 zenon_H6e zenon_H173 zenon_Hfc zenon_H12d. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 8.02/8.17 apply (zenon_L143_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 8.02/8.17 apply (zenon_L635_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 8.02/8.17 apply (zenon_L231_); trivial. % 8.02/8.17 apply (zenon_L139_); trivial. % 8.02/8.17 (* end of lemma zenon_L636_ *) % 8.02/8.17 assert (zenon_L637_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H162 zenon_H86 zenon_H28 zenon_H6e zenon_H6c zenon_H38 zenon_H15c zenon_Hfc zenon_H5e. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.17 apply (zenon_L213_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.17 apply (zenon_L26_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.17 apply (zenon_L409_); trivial. % 8.02/8.17 apply (zenon_L109_); trivial. % 8.02/8.17 (* end of lemma zenon_L637_ *) % 8.02/8.17 assert (zenon_L638_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H1c7 zenon_H16a zenon_Hd2 zenon_H10e zenon_H98 zenon_H162 zenon_H86 zenon_H28 zenon_H6e zenon_H6c zenon_H38 zenon_Hfc zenon_H5e. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 8.02/8.17 apply (zenon_L390_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 8.02/8.17 apply (zenon_L117_); trivial. % 8.02/8.17 apply (zenon_L637_); trivial. % 8.02/8.17 (* end of lemma zenon_L638_ *) % 8.02/8.17 assert (zenon_L639_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H95 zenon_H5e zenon_Hfc zenon_H38 zenon_H28 zenon_H162 zenon_H10e zenon_Hd2 zenon_H16a zenon_H1c7 zenon_Hb9 zenon_H6e zenon_H6c zenon_H98 zenon_H67 zenon_H3e. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.17 apply (zenon_L638_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.17 apply (zenon_L449_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.17 apply (zenon_L136_); trivial. % 8.02/8.17 apply (zenon_L313_); trivial. % 8.02/8.17 (* end of lemma zenon_L639_ *) % 8.02/8.17 assert (zenon_L640_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 8.02/8.17 do 0 intro. intros zenon_Hc3 zenon_H67 zenon_H1e zenon_H12d zenon_H195 zenon_H98 zenon_H17c zenon_Hc6 zenon_H99 zenon_H6c zenon_H13b zenon_Hf8 zenon_Hf7 zenon_He3 zenon_H8f. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.17 apply (zenon_L36_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.17 apply (zenon_L338_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.17 apply (zenon_L67_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.17 apply (zenon_L238_); trivial. % 8.02/8.17 apply (zenon_L458_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.17 apply (zenon_L108_); trivial. % 8.02/8.17 apply (zenon_L89_); trivial. % 8.02/8.17 (* end of lemma zenon_L640_ *) % 8.02/8.17 assert (zenon_L641_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e2)) -> False). % 8.02/8.17 do 0 intro. intros zenon_He7 zenon_Hb9 zenon_H3d zenon_Hc6 zenon_H173 zenon_H13e zenon_H5a zenon_H99 zenon_H195. % 8.02/8.17 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 8.02/8.17 apply (zenon_L416_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 8.02/8.17 apply (zenon_L306_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 8.02/8.17 apply (zenon_L190_); trivial. % 8.02/8.17 apply (zenon_L532_); trivial. % 8.02/8.17 (* end of lemma zenon_L641_ *) % 8.02/8.17 assert (zenon_L642_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H137 zenon_H3e zenon_H1d4 zenon_Hc6 zenon_H173 zenon_H26 zenon_H40 zenon_Hf7 zenon_H131. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 8.02/8.17 apply (zenon_L373_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 8.02/8.17 apply (zenon_L306_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 8.02/8.17 apply (zenon_L225_); trivial. % 8.02/8.17 apply (zenon_L559_); trivial. % 8.02/8.17 (* end of lemma zenon_L642_ *) % 8.02/8.17 assert (zenon_L643_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 8.02/8.17 do 0 intro. intros zenon_Haa zenon_H6c zenon_H26 zenon_H8f zenon_Hc6 zenon_H18e zenon_H15c zenon_H67 zenon_H41. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.17 apply (zenon_L338_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.17 apply (zenon_L71_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.17 apply (zenon_L273_); trivial. % 8.02/8.17 apply (zenon_L31_); trivial. % 8.02/8.17 (* end of lemma zenon_L643_ *) % 8.02/8.17 assert (zenon_L644_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H1c7 zenon_H16a zenon_He0 zenon_H5a zenon_H38 zenon_H83 zenon_Haa zenon_H6c zenon_H26 zenon_H8f zenon_Hc6 zenon_H18e zenon_H67 zenon_H41. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 8.02/8.17 apply (zenon_L190_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 8.02/8.17 apply (zenon_L107_); trivial. % 8.02/8.17 apply (zenon_L643_); trivial. % 8.02/8.17 (* end of lemma zenon_L644_ *) % 8.02/8.17 assert (zenon_L645_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H1ca zenon_H55 zenon_H111 zenon_Hef zenon_H195 zenon_H99 zenon_H3d zenon_Hb9 zenon_He7 zenon_H4e zenon_H131 zenon_H1d4 zenon_H18e zenon_H8f zenon_H6c zenon_Haa zenon_H83 zenon_H38 zenon_H5a zenon_H16a zenon_H1c7 zenon_Hf7 zenon_H67 zenon_H137 zenon_H12d zenon_Hc6 zenon_H173 zenon_H26 zenon_H40 zenon_H1e9. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.17 apply (zenon_L322_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.17 apply (zenon_L90_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.17 apply (zenon_L641_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.17 apply (zenon_L642_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.17 apply (zenon_L644_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.17 apply (zenon_L392_); trivial. % 8.02/8.17 apply (zenon_L415_); trivial. % 8.02/8.17 (* end of lemma zenon_L645_ *) % 8.02/8.17 assert (zenon_L646_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H117 zenon_H29 zenon_H113 zenon_He0 zenon_H82 zenon_H81 zenon_Hf7 zenon_H43. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H37 | zenon_intro zenon_H119 ]. % 8.02/8.17 apply (zenon_L119_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H11a ]. % 8.02/8.17 apply (zenon_L80_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H83 | zenon_intro zenon_H115 ]. % 8.02/8.17 apply (zenon_L35_); trivial. % 8.02/8.17 apply (zenon_L453_); trivial. % 8.02/8.17 (* end of lemma zenon_L646_ *) % 8.02/8.17 assert (zenon_L647_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H1ca zenon_H99 zenon_Hc6 zenon_Hef zenon_H38 zenon_H111 zenon_H117 zenon_H29 zenon_H113 zenon_H82 zenon_H81 zenon_Hf7 zenon_H43. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.17 apply (zenon_L65_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.17 apply (zenon_L90_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.17 apply (zenon_L497_); trivial. % 8.02/8.17 apply (zenon_L646_); trivial. % 8.02/8.17 (* end of lemma zenon_L647_ *) % 8.02/8.17 assert (zenon_L648_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H11b zenon_H43 zenon_H81 zenon_H82 zenon_H117 zenon_H38 zenon_Hef zenon_Hc6 zenon_H99 zenon_H1ca zenon_H29 zenon_H113 zenon_H16a zenon_H67 zenon_Hf7. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 8.02/8.17 apply (zenon_L647_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 8.02/8.17 apply (zenon_L119_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 apply (zenon_L392_); trivial. % 8.02/8.17 (* end of lemma zenon_L648_ *) % 8.02/8.17 assert (zenon_L649_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H124 zenon_H5e zenon_H1e9 zenon_H40 zenon_H173 zenon_H12d zenon_H137 zenon_H1c7 zenon_H5a zenon_Haa zenon_H6c zenon_H8f zenon_H18e zenon_H1d4 zenon_H131 zenon_H4e zenon_He7 zenon_Hb9 zenon_H3d zenon_H55 zenon_H2c zenon_H20 zenon_H11e zenon_Hf7 zenon_H67 zenon_H16a zenon_H113 zenon_H29 zenon_H1ca zenon_H99 zenon_Hc6 zenon_Hef zenon_H38 zenon_H117 zenon_H81 zenon_H43 zenon_H11b zenon_H195 zenon_He4. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.17 apply (zenon_L462_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.17 apply (zenon_L17_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.17 apply (zenon_L128_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 8.02/8.17 apply (zenon_L645_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 8.02/8.17 apply (zenon_L119_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 apply (zenon_L392_); trivial. % 8.02/8.17 apply (zenon_L358_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.17 apply (zenon_L648_); trivial. % 8.02/8.17 apply (zenon_L622_); trivial. % 8.02/8.17 (* end of lemma zenon_L649_ *) % 8.02/8.17 assert (zenon_L650_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H18b zenon_He4 zenon_H11b zenon_H43 zenon_H81 zenon_H117 zenon_H38 zenon_Hef zenon_H99 zenon_H1ca zenon_H113 zenon_H16a zenon_H67 zenon_H11e zenon_H2c zenon_H55 zenon_H3d zenon_Hb9 zenon_He7 zenon_H4e zenon_H18e zenon_H8f zenon_H6c zenon_Haa zenon_H5a zenon_H1c7 zenon_H40 zenon_H1e9 zenon_H5e zenon_H124 zenon_H98 zenon_H20 zenon_H137 zenon_H1d4 zenon_Hc6 zenon_H173 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.17 apply (zenon_L442_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.17 apply (zenon_L649_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.17 apply (zenon_L260_); trivial. % 8.02/8.17 apply (zenon_L618_); trivial. % 8.02/8.17 (* end of lemma zenon_L650_ *) % 8.02/8.17 assert (zenon_L651_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (op (op (e0) (e0)) (e0)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_Hb2 zenon_H86 zenon_H232. % 8.02/8.17 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 8.02/8.17 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((e1) = (op (op (e0) (e0)) (e0)))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H232. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_H1f4. % 8.02/8.17 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 8.02/8.17 cut (((op (op (e0) (e0)) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 8.02/8.17 congruence. % 8.02/8.17 cut (((op (e3) (e0)) = (e1)) = ((op (op (e0) (e0)) (e0)) = (e1))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H233. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_Hb2. % 8.02/8.17 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H57]. % 8.02/8.17 cut (((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 8.02/8.17 congruence. % 8.02/8.17 elim (classic ((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f5 ]. % 8.02/8.17 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0))) = ((op (e3) (e0)) = (op (op (e0) (e0)) (e0)))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H21b. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_H1f4. % 8.02/8.17 cut (((op (op (e0) (e0)) (e0)) = (op (op (e0) (e0)) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 8.02/8.17 cut (((op (op (e0) (e0)) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 8.02/8.17 congruence. % 8.02/8.17 apply (zenon_L538_); trivial. % 8.02/8.17 apply zenon_H1f5. apply refl_equal. % 8.02/8.17 apply zenon_H1f5. apply refl_equal. % 8.02/8.17 apply zenon_H57. apply refl_equal. % 8.02/8.17 apply zenon_H1f5. apply refl_equal. % 8.02/8.17 apply zenon_H1f5. apply refl_equal. % 8.02/8.17 (* end of lemma zenon_L651_ *) % 8.02/8.17 assert (zenon_L652_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H195 zenon_Hb2 zenon_H86. % 8.02/8.17 apply (zenon_notand_s _ _ ax19); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H234 ]. % 8.02/8.17 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 8.02/8.17 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((e2) = (op (op (e0) (e0)) (op (e0) (e0))))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H1f9. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_H1fa. % 8.02/8.17 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 8.02/8.17 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 8.02/8.17 congruence. % 8.02/8.17 cut (((op (e3) (e3)) = (e2)) = ((op (op (e0) (e0)) (op (e0) (e0))) = (e2))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H1fc. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_H195. % 8.02/8.17 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 8.02/8.17 cut (((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 8.02/8.17 congruence. % 8.02/8.17 elim (classic ((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1fb ]. % 8.02/8.17 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0)))) = ((op (e3) (e3)) = (op (op (e0) (e0)) (op (e0) (e0))))). % 8.02/8.17 intro zenon_D_pnotp. % 8.02/8.17 apply zenon_H21d. % 8.02/8.17 rewrite <- zenon_D_pnotp. % 8.02/8.17 exact zenon_H1fa. % 8.02/8.17 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (op (e0) (e0)) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 8.02/8.17 cut (((op (op (e0) (e0)) (op (e0) (e0))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 8.02/8.17 congruence. % 8.02/8.17 apply (zenon_L537_); trivial. % 8.02/8.17 apply zenon_H1fb. apply refl_equal. % 8.02/8.17 apply zenon_H1fb. apply refl_equal. % 8.02/8.17 apply zenon_H22. apply refl_equal. % 8.02/8.17 apply zenon_H1fb. apply refl_equal. % 8.02/8.17 apply zenon_H1fb. apply refl_equal. % 8.02/8.17 apply (zenon_notand_s _ _ zenon_H234); [ zenon_intro zenon_H21e | zenon_intro zenon_H232 ]. % 8.02/8.17 apply zenon_H21e. apply sym_equal. exact zenon_H86. % 8.02/8.17 apply (zenon_L651_); trivial. % 8.02/8.17 (* end of lemma zenon_L652_ *) % 8.02/8.17 assert (zenon_L653_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 8.02/8.17 do 0 intro. intros zenon_Hc3 zenon_Hb2 zenon_H195 zenon_H6c zenon_H26 zenon_H67 zenon_H111 zenon_He3 zenon_H8f. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.17 apply (zenon_L652_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.17 apply (zenon_L338_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.17 apply (zenon_L118_); trivial. % 8.02/8.17 apply (zenon_L89_); trivial. % 8.02/8.17 (* end of lemma zenon_L653_ *) % 8.02/8.17 assert (zenon_L654_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H124 zenon_H30 zenon_H98 zenon_H8f zenon_He3 zenon_H67 zenon_H6c zenon_Hb2 zenon_Hc3 zenon_H43 zenon_Hf7 zenon_H81 zenon_H38 zenon_H13e zenon_H111 zenon_H117 zenon_H195 zenon_He4. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.17 apply (zenon_L212_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.17 apply (zenon_L653_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.17 apply (zenon_L497_); trivial. % 8.02/8.17 apply (zenon_L622_); trivial. % 8.02/8.17 (* end of lemma zenon_L654_ *) % 8.02/8.17 assert (zenon_L655_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H11b zenon_H200 zenon_H15a zenon_H29 zenon_H113 zenon_H16a zenon_H67 zenon_Hf7. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 8.02/8.17 apply (zenon_L450_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 8.02/8.17 apply (zenon_L119_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 apply (zenon_L392_); trivial. % 8.02/8.17 (* end of lemma zenon_L655_ *) % 8.02/8.17 assert (zenon_L656_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H18b zenon_H55 zenon_Hb9 zenon_H67 zenon_H16a zenon_H113 zenon_H15a zenon_H200 zenon_H11b zenon_H98 zenon_H20 zenon_H137 zenon_H1d4 zenon_Hc6 zenon_H173 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.17 apply (zenon_L442_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.17 apply (zenon_L655_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.17 apply (zenon_L260_); trivial. % 8.02/8.17 apply (zenon_L618_); trivial. % 8.02/8.17 (* end of lemma zenon_L656_ *) % 8.02/8.17 assert (zenon_L657_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H235 zenon_Hf8 zenon_H13b zenon_H17c zenon_H10a zenon_He4 zenon_H117 zenon_H38 zenon_H81 zenon_H43 zenon_Hc3 zenon_H6c zenon_H8f zenon_H30 zenon_H124 zenon_H99 zenon_H89 zenon_Hef zenon_H1ca zenon_H11e zenon_H3d zenon_He7 zenon_H4e zenon_H18e zenon_Haa zenon_H5a zenon_H1c7 zenon_H40 zenon_H1e9 zenon_H5e zenon_Hb6 zenon_H15f zenon_H131 zenon_Hf7 zenon_H195 zenon_H12d zenon_H173 zenon_H1d4 zenon_H137 zenon_H20 zenon_H98 zenon_H11b zenon_H200 zenon_H113 zenon_H16a zenon_H67 zenon_H18b zenon_H2c zenon_Hc6 zenon_H13e zenon_H10b zenon_H55. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1e | zenon_intro zenon_H236 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.17 apply (zenon_L442_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.17 apply (zenon_L61_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.17 apply (zenon_L175_); trivial. % 8.02/8.17 apply (zenon_L640_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H25 | zenon_intro zenon_H237 ]. % 8.02/8.17 exact (zenon_H10a zenon_H25). % 8.02/8.17 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H111 | zenon_intro zenon_H15a ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.17 apply (zenon_L650_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.17 apply (zenon_L61_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.17 apply (zenon_L322_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.17 apply (zenon_L650_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.17 apply (zenon_L221_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.17 apply (zenon_L41_); trivial. % 8.02/8.17 apply (zenon_L654_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.17 apply (zenon_L656_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.17 apply (zenon_L61_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.17 apply (zenon_L175_); trivial. % 8.02/8.17 apply (zenon_L249_); trivial. % 8.02/8.17 (* end of lemma zenon_L657_ *) % 8.02/8.17 assert (zenon_L658_ : (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 8.02/8.17 do 0 intro. intros zenon_H55 zenon_H10b zenon_H2c zenon_H18b zenon_H16a zenon_H113 zenon_H200 zenon_H11b zenon_H98 zenon_H20 zenon_H137 zenon_H1d4 zenon_H173 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131 zenon_H15f zenon_Hb6 zenon_H5e zenon_H1e9 zenon_H40 zenon_H1c7 zenon_H5a zenon_H4e zenon_He7 zenon_H3d zenon_H11e zenon_H1ca zenon_Hef zenon_H89 zenon_H99 zenon_H124 zenon_H30 zenon_Hc3 zenon_H43 zenon_H81 zenon_H117 zenon_He4 zenon_H10a zenon_H17c zenon_H13b zenon_Hf8 zenon_H235 zenon_H38 zenon_H83 zenon_Haa zenon_H6c zenon_H26 zenon_H8f zenon_Hc6 zenon_H18e zenon_H67 zenon_H41. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 8.02/8.17 exact (zenon_H16a zenon_H36). % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 8.02/8.17 apply (zenon_L657_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 8.02/8.17 apply (zenon_L107_); trivial. % 8.02/8.17 apply (zenon_L643_); trivial. % 8.02/8.17 (* end of lemma zenon_L658_ *) % 8.02/8.17 assert (zenon_L659_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H18e zenon_H8f zenon_H6c zenon_Haa zenon_H83 zenon_H38 zenon_H235 zenon_Hf8 zenon_H13b zenon_H17c zenon_H10a zenon_He4 zenon_H117 zenon_H81 zenon_H43 zenon_Hc3 zenon_H30 zenon_H124 zenon_H99 zenon_H89 zenon_Hef zenon_H1ca zenon_H11e zenon_H3d zenon_He7 zenon_H4e zenon_H5a zenon_H1c7 zenon_H5e zenon_Hb6 zenon_H15f zenon_H131 zenon_H195 zenon_H1d4 zenon_H20 zenon_H98 zenon_H11b zenon_H200 zenon_H113 zenon_H16a zenon_H18b zenon_H2c zenon_H10b zenon_H55 zenon_Hf7 zenon_H67 zenon_H137 zenon_H12d zenon_Hc6 zenon_H173 zenon_H26 zenon_H40 zenon_H1e9. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.17 apply (zenon_L618_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.17 apply (zenon_L658_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.17 apply (zenon_L392_); trivial. % 8.02/8.17 apply (zenon_L415_); trivial. % 8.02/8.17 (* end of lemma zenon_L659_ *) % 8.02/8.17 assert (zenon_L660_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_H18b zenon_He4 zenon_H1ca zenon_H99 zenon_Hef zenon_H38 zenon_H111 zenon_H117 zenon_H113 zenon_H81 zenon_H43 zenon_H11e zenon_H2c zenon_H1e9 zenon_H40 zenon_H67 zenon_H1c7 zenon_H16a zenon_H5a zenon_Haa zenon_H6c zenon_H8f zenon_H18e zenon_H4e zenon_He7 zenon_Hb9 zenon_H3d zenon_H55 zenon_H5e zenon_H124 zenon_H98 zenon_H20 zenon_H137 zenon_H1d4 zenon_Hc6 zenon_H173 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.17 apply (zenon_L442_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.17 apply (zenon_L462_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.17 apply (zenon_L17_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.17 apply (zenon_L128_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.17 apply (zenon_L645_); trivial. % 8.02/8.17 apply (zenon_L358_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.17 apply (zenon_L647_); trivial. % 8.02/8.17 apply (zenon_L622_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.17 apply (zenon_L260_); trivial. % 8.02/8.17 apply (zenon_L618_); trivial. % 8.02/8.17 (* end of lemma zenon_L660_ *) % 8.02/8.17 assert (zenon_L661_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.17 do 0 intro. intros zenon_Hf8 zenon_H13b zenon_H17c zenon_H18b zenon_He4 zenon_H11b zenon_H43 zenon_H81 zenon_H117 zenon_H38 zenon_Hef zenon_H99 zenon_H1ca zenon_H113 zenon_H16a zenon_H67 zenon_Hc3 zenon_H6c zenon_H111 zenon_H8f zenon_H30 zenon_H124 zenon_H89 zenon_H5e zenon_H1e9 zenon_H40 zenon_H1c7 zenon_H5a zenon_Haa zenon_H18e zenon_H4e zenon_He7 zenon_H3d zenon_H55 zenon_H2c zenon_H11e zenon_Hb6 zenon_H15f zenon_H98 zenon_H20 zenon_H137 zenon_H1d4 zenon_Hc6 zenon_H173 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.17 apply (zenon_L660_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.17 apply (zenon_L61_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.17 apply (zenon_L322_); trivial. % 8.02/8.17 apply (zenon_L640_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.17 apply (zenon_L649_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.17 apply (zenon_L61_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.17 apply (zenon_L322_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.17 apply (zenon_L649_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.17 apply (zenon_L221_); trivial. % 8.02/8.17 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.18 apply (zenon_L41_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.18 apply (zenon_L212_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.18 apply (zenon_L653_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.18 apply (zenon_L648_); trivial. % 8.02/8.18 apply (zenon_L622_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.18 apply (zenon_L260_); trivial. % 8.02/8.18 apply (zenon_L618_); trivial. % 8.02/8.18 (* end of lemma zenon_L661_ *) % 8.02/8.18 assert (zenon_L662_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H238 zenon_H1e zenon_H3d zenon_H17f zenon_H54 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H3e | zenon_intro zenon_H239 ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H23a ]. % 8.02/8.18 apply (zenon_L244_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 8.02/8.18 apply (zenon_L617_); trivial. % 8.02/8.18 apply (zenon_L423_); trivial. % 8.02/8.18 (* end of lemma zenon_L662_ *) % 8.02/8.18 assert (zenon_L663_ : (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H106 zenon_H13f zenon_H9c. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23d. zenon_intro zenon_H208. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1eb | zenon_intro zenon_H13e ]. % 8.02/8.18 exact (zenon_H1eb zenon_H9c). % 8.02/8.18 exact (zenon_H13f zenon_H13e). % 8.02/8.18 (* end of lemma zenon_L663_ *) % 8.02/8.18 assert (zenon_L664_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H142 zenon_H17f zenon_Hb2 zenon_Hc6 zenon_Hca zenon_H13f zenon_Hbd zenon_He3. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 8.02/8.18 apply (zenon_L244_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 8.02/8.18 apply (zenon_L228_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 8.02/8.18 exact (zenon_H13f zenon_H13e). % 8.02/8.18 apply (zenon_L186_); trivial. % 8.02/8.18 (* end of lemma zenon_L664_ *) % 8.02/8.18 assert (zenon_L665_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H238 zenon_H12d zenon_H134 zenon_H9c zenon_Hcc zenon_H66 zenon_H173 zenon_H1d0 zenon_H67 zenon_H111 zenon_Hef zenon_H10e zenon_H89 zenon_H6c zenon_H95 zenon_H12b zenon_H1cd zenon_H1d4 zenon_H137 zenon_He3 zenon_Hbd zenon_H13f zenon_Hca zenon_Hc6 zenon_H17f zenon_H142 zenon_H1f zenon_H3d zenon_Hfc zenon_H128. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H3e | zenon_intro zenon_H239 ]. % 8.02/8.18 apply (zenon_L377_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H23a ]. % 8.02/8.18 apply (zenon_L664_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 8.02/8.18 apply (zenon_L289_); trivial. % 8.02/8.18 apply (zenon_L137_); trivial. % 8.02/8.18 (* end of lemma zenon_L665_ *) % 8.02/8.18 assert (zenon_L666_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Haa zenon_H26 zenon_H8f zenon_Hc6 zenon_H6c zenon_H9c zenon_Hf7 zenon_H131. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.18 apply (zenon_L338_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.18 apply (zenon_L71_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L43_); trivial. % 8.02/8.18 apply (zenon_L559_); trivial. % 8.02/8.18 (* end of lemma zenon_L666_ *) % 8.02/8.18 assert (zenon_L667_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H137 zenon_H47 zenon_Hb2 zenon_H1d4 zenon_H12d zenon_H195 zenon_H66 zenon_H40. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 8.02/8.18 apply (zenon_L292_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 8.02/8.18 apply (zenon_L635_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L458_); trivial. % 8.02/8.18 apply (zenon_L529_); trivial. % 8.02/8.18 (* end of lemma zenon_L667_ *) % 8.02/8.18 assert (zenon_L668_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H238 zenon_H1e zenon_H3d zenon_H40 zenon_H66 zenon_H12d zenon_H1d4 zenon_H47 zenon_H137 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H3e | zenon_intro zenon_H239 ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H23a ]. % 8.02/8.18 apply (zenon_L667_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 8.02/8.18 apply (zenon_L617_); trivial. % 8.02/8.18 apply (zenon_L423_); trivial. % 8.02/8.18 (* end of lemma zenon_L668_ *) % 8.02/8.18 assert (zenon_L669_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H4e zenon_H2d zenon_H173 zenon_H67 zenon_H238 zenon_H1e zenon_H3d zenon_H40 zenon_H66 zenon_H12d zenon_H1d4 zenon_H137 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.18 apply (zenon_L330_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.18 apply (zenon_L392_); trivial. % 8.02/8.18 apply (zenon_L668_); trivial. % 8.02/8.18 (* end of lemma zenon_L669_ *) % 8.02/8.18 assert (zenon_L670_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Hcc zenon_H1ec zenon_Hf7 zenon_H195 zenon_H128 zenon_H137 zenon_H1d4 zenon_H12d zenon_H40 zenon_H3d zenon_H1e zenon_H238 zenon_H67 zenon_H173 zenon_H4e zenon_Hc7 zenon_H89 zenon_H5b zenon_H66 zenon_H2c. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 8.02/8.18 apply (zenon_L669_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 8.02/8.18 apply (zenon_L61_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 8.02/8.18 apply (zenon_L84_); trivial. % 8.02/8.18 apply (zenon_L104_); trivial. % 8.02/8.18 (* end of lemma zenon_L670_ *) % 8.02/8.18 assert (zenon_L671_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H184 zenon_H2c zenon_H66 zenon_H5b zenon_H89 zenon_H4e zenon_H173 zenon_H67 zenon_H238 zenon_H1e zenon_H3d zenon_H40 zenon_H12d zenon_H137 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec zenon_Hcc zenon_Hd2 zenon_Hef zenon_H9c zenon_H99 zenon_H1d4 zenon_Hb2. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.18 apply (zenon_L670_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.18 apply (zenon_L90_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.18 apply (zenon_L97_); trivial. % 8.02/8.18 apply (zenon_L635_); trivial. % 8.02/8.18 (* end of lemma zenon_L671_ *) % 8.02/8.18 assert (zenon_L672_ : ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H41 zenon_H6d zenon_H23e. % 8.02/8.18 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 8.02/8.18 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H23e. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H72. % 8.02/8.18 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 8.02/8.18 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H23f]. % 8.02/8.18 congruence. % 8.02/8.18 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H23f. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H41. % 8.02/8.18 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 8.02/8.18 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 8.02/8.18 congruence. % 8.02/8.18 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H72 | zenon_intro zenon_H73 ]. % 8.02/8.18 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H178. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H72. % 8.02/8.18 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 8.02/8.18 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 8.02/8.18 congruence. % 8.02/8.18 apply (zenon_L233_); trivial. % 8.02/8.18 apply zenon_H73. apply refl_equal. % 8.02/8.18 apply zenon_H73. apply refl_equal. % 8.02/8.18 apply zenon_H1d. apply refl_equal. % 8.02/8.18 apply zenon_H73. apply refl_equal. % 8.02/8.18 apply zenon_H73. apply refl_equal. % 8.02/8.18 (* end of lemma zenon_L672_ *) % 8.02/8.18 assert (zenon_L673_ : ((op (e3) (e3)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H195 zenon_H41 zenon_H6d. % 8.02/8.18 apply (zenon_notand_s _ _ ax21); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H240 ]. % 8.02/8.18 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 8.02/8.18 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H1a4. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H79. % 8.02/8.18 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.02/8.18 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 8.02/8.18 congruence. % 8.02/8.18 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H1a5. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H195. % 8.02/8.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 8.02/8.18 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 8.02/8.18 congruence. % 8.02/8.18 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H79 | zenon_intro zenon_H7a ]. % 8.02/8.18 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H17a. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H79. % 8.02/8.18 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 8.02/8.18 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 8.02/8.18 congruence. % 8.02/8.18 apply (zenon_L232_); trivial. % 8.02/8.18 apply zenon_H7a. apply refl_equal. % 8.02/8.18 apply zenon_H7a. apply refl_equal. % 8.02/8.18 apply zenon_H22. apply refl_equal. % 8.02/8.18 apply zenon_H7a. apply refl_equal. % 8.02/8.18 apply zenon_H7a. apply refl_equal. % 8.02/8.18 apply (zenon_notand_s _ _ zenon_H240); [ zenon_intro zenon_H17b | zenon_intro zenon_H23e ]. % 8.02/8.18 apply zenon_H17b. apply sym_equal. exact zenon_H6d. % 8.02/8.18 apply (zenon_L672_); trivial. % 8.02/8.18 (* end of lemma zenon_L673_ *) % 8.02/8.18 assert (zenon_L674_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H137 zenon_H47 zenon_Hb2 zenon_H1d4 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H41 | zenon_intro zenon_H138 ]. % 8.02/8.18 apply (zenon_L292_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_Hde | zenon_intro zenon_H139 ]. % 8.02/8.18 apply (zenon_L635_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hdc | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L458_); trivial. % 8.02/8.18 apply (zenon_L559_); trivial. % 8.02/8.18 (* end of lemma zenon_L674_ *) % 8.02/8.18 assert (zenon_L675_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e3)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H238 zenon_H1e zenon_H3d zenon_H131 zenon_H12d zenon_H1d4 zenon_H47 zenon_H137 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H3e | zenon_intro zenon_H239 ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H23a ]. % 8.02/8.18 apply (zenon_L674_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 8.02/8.18 apply (zenon_L617_); trivial. % 8.02/8.18 apply (zenon_L423_); trivial. % 8.02/8.18 (* end of lemma zenon_L675_ *) % 8.02/8.18 assert (zenon_L676_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H4e zenon_H6d zenon_H67 zenon_H238 zenon_H1e zenon_H3d zenon_H131 zenon_H12d zenon_H1d4 zenon_H137 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.18 apply (zenon_L673_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.18 apply (zenon_L392_); trivial. % 8.02/8.18 apply (zenon_L675_); trivial. % 8.02/8.18 (* end of lemma zenon_L676_ *) % 8.02/8.18 assert (zenon_L677_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Haa zenon_Hb2 zenon_H99 zenon_Hef zenon_Hd2 zenon_Hcc zenon_H40 zenon_H173 zenon_H89 zenon_H5b zenon_H2c zenon_H184 zenon_H1ec zenon_H195 zenon_H128 zenon_H137 zenon_H1d4 zenon_H12d zenon_H3d zenon_H1e zenon_H238 zenon_H67 zenon_H4e zenon_H6c zenon_H9c zenon_Hf7 zenon_H131. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.18 apply (zenon_L671_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.18 apply (zenon_L676_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L43_); trivial. % 8.02/8.18 apply (zenon_L559_); trivial. % 8.02/8.18 (* end of lemma zenon_L677_ *) % 8.02/8.18 assert (zenon_L678_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H238 zenon_H1e zenon_H3d zenon_Hde zenon_H1d4 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H3e | zenon_intro zenon_H239 ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H23a ]. % 8.02/8.18 apply (zenon_L635_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H93 | zenon_intro zenon_H92 ]. % 8.02/8.18 apply (zenon_L617_); trivial. % 8.02/8.18 apply (zenon_L423_); trivial. % 8.02/8.18 (* end of lemma zenon_L678_ *) % 8.02/8.18 assert (zenon_L679_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H142 zenon_H8f zenon_H8e zenon_Hc7 zenon_H33 zenon_H13f zenon_H64 zenon_Hd6. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 8.02/8.18 apply (zenon_L38_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 8.02/8.18 apply (zenon_L168_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 8.02/8.18 exact (zenon_H13f zenon_H13e). % 8.02/8.18 apply (zenon_L156_); trivial. % 8.02/8.18 (* end of lemma zenon_L679_ *) % 8.02/8.18 assert (zenon_L680_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e1)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H184 zenon_H64 zenon_H13f zenon_H33 zenon_H8e zenon_H8f zenon_H142 zenon_H130 zenon_Hd6 zenon_H9c zenon_H99 zenon_H1d4 zenon_Hb2. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.18 apply (zenon_L679_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.18 apply (zenon_L603_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.18 apply (zenon_L97_); trivial. % 8.02/8.18 apply (zenon_L635_); trivial. % 8.02/8.18 (* end of lemma zenon_L680_ *) % 8.02/8.18 assert (zenon_L681_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Hec zenon_H20 zenon_Had zenon_Hc0 zenon_Hd8 zenon_Hb7 zenon_H26 zenon_H131 zenon_Hf7 zenon_H6c zenon_H4e zenon_H67 zenon_H238 zenon_H1e zenon_H3d zenon_H12d zenon_H137 zenon_H128 zenon_H195 zenon_H1ec zenon_H2c zenon_H89 zenon_H173 zenon_H40 zenon_Hcc zenon_Hef zenon_Haa zenon_H184 zenon_H64 zenon_H13f zenon_H33 zenon_H8f zenon_H142 zenon_H130 zenon_H9c zenon_H1d4 zenon_H95 zenon_H9b zenon_Hb2 zenon_H99. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.18 apply (zenon_L75_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.18 apply (zenon_L652_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.18 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.18 apply (zenon_L666_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.18 apply (zenon_L677_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.18 apply (zenon_L670_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.18 apply (zenon_L37_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L43_); trivial. % 8.02/8.18 apply (zenon_L559_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.18 apply (zenon_L603_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.18 apply (zenon_L97_); trivial. % 8.02/8.18 apply (zenon_L678_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.18 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.18 apply (zenon_L666_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.18 apply (zenon_L677_); trivial. % 8.02/8.18 apply (zenon_L680_); trivial. % 8.02/8.18 exact (zenon_Hc0 zenon_H92). % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.18 exact (zenon_H9b zenon_H98). % 8.02/8.18 apply (zenon_L78_); trivial. % 8.02/8.18 (* end of lemma zenon_L681_ *) % 8.02/8.18 assert (zenon_L682_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H1c7 zenon_H43 zenon_Hf7 zenon_H81 zenon_He0 zenon_H38 zenon_H117 zenon_H13f zenon_H10b zenon_H82 zenon_H8e zenon_H10e. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 8.02/8.18 apply (zenon_L461_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 8.02/8.18 exact (zenon_H13f zenon_H13e). % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 8.02/8.18 apply (zenon_L115_); trivial. % 8.02/8.18 apply (zenon_L200_); trivial. % 8.02/8.18 (* end of lemma zenon_L682_ *) % 8.02/8.18 assert (zenon_L683_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Hec zenon_H20 zenon_H10e zenon_H82 zenon_H10b zenon_H13f zenon_H117 zenon_H38 zenon_H81 zenon_Hf7 zenon_H43 zenon_H1c7 zenon_Hb2 zenon_H17f zenon_H30 zenon_H1e zenon_H22e zenon_Haa zenon_H99 zenon_Hef zenon_Hcc zenon_H40 zenon_H173 zenon_H89 zenon_H2c zenon_H184 zenon_H1ec zenon_H137 zenon_H1d4 zenon_H12d zenon_H3d zenon_H238 zenon_H67 zenon_H4e zenon_H6c zenon_H9c zenon_H131 zenon_H1ca zenon_H9b zenon_H195 zenon_H128. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.18 apply (zenon_L2_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.18 apply (zenon_L65_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.18 apply (zenon_L677_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.18 exact (zenon_H13f zenon_H13e). % 8.02/8.18 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H31 | zenon_intro zenon_H22f ]. % 8.02/8.18 apply (zenon_L6_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H54 | zenon_intro zenon_H230 ]. % 8.02/8.18 apply (zenon_L244_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H98 | zenon_intro zenon_H8e ]. % 8.02/8.18 exact (zenon_H9b zenon_H98). % 8.02/8.18 apply (zenon_L682_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.18 exact (zenon_H9b zenon_H98). % 8.02/8.18 apply (zenon_L617_); trivial. % 8.02/8.18 (* end of lemma zenon_L683_ *) % 8.02/8.18 assert (zenon_L684_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H4e zenon_H2d zenon_H173 zenon_H67 zenon_H238 zenon_H1e zenon_H3d zenon_H131 zenon_H12d zenon_H1d4 zenon_H137 zenon_H128 zenon_H195 zenon_Hf7 zenon_H1ec. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.18 apply (zenon_L9_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.18 apply (zenon_L330_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.18 apply (zenon_L392_); trivial. % 8.02/8.18 apply (zenon_L675_); trivial. % 8.02/8.18 (* end of lemma zenon_L684_ *) % 8.02/8.18 assert (zenon_L685_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 8.02/8.18 do 0 intro. intros zenon_Hd8 zenon_Hb7 zenon_H8f zenon_H26 zenon_H131 zenon_Hf7 zenon_H9c zenon_H6c zenon_H4e zenon_H67 zenon_H238 zenon_H1e zenon_H3d zenon_H12d zenon_H1d4 zenon_H137 zenon_H128 zenon_H195 zenon_H1ec zenon_H184 zenon_H2c zenon_H5b zenon_H89 zenon_H173 zenon_H40 zenon_Hcc zenon_Hef zenon_H99 zenon_Hb2 zenon_Haa zenon_H55 zenon_H5d. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.18 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.18 apply (zenon_L666_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.18 apply (zenon_L677_); trivial. % 8.02/8.18 apply (zenon_L69_); trivial. % 8.02/8.18 (* end of lemma zenon_L685_ *) % 8.02/8.18 assert (zenon_L686_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H4e zenon_H55 zenon_H2d zenon_H173 zenon_H36 zenon_H5a zenon_H137 zenon_Hb2 zenon_H1d4 zenon_H12d zenon_H195 zenon_Hf7 zenon_H131. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.18 apply (zenon_L50_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.18 apply (zenon_L330_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.18 apply (zenon_L16_); trivial. % 8.02/8.18 apply (zenon_L674_); trivial. % 8.02/8.18 (* end of lemma zenon_L686_ *) % 8.02/8.18 assert (zenon_L687_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H1ca zenon_H99 zenon_Hc6 zenon_Hef zenon_H13f zenon_H117 zenon_H38 zenon_H36 zenon_H82 zenon_H81 zenon_Hf7 zenon_H43. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.18 apply (zenon_L65_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.18 apply (zenon_L90_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.18 exact (zenon_H13f zenon_H13e). % 8.02/8.18 apply (zenon_L461_); trivial. % 8.02/8.18 (* end of lemma zenon_L687_ *) % 8.02/8.18 assert (zenon_L688_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 8.02/8.18 do 0 intro. intros zenon_Hd8 zenon_Hb7 zenon_H43 zenon_H81 zenon_H82 zenon_H36 zenon_H38 zenon_H117 zenon_H13f zenon_H1ca zenon_Hb2 zenon_H1d4 zenon_H99 zenon_H9c zenon_Hef zenon_Hcc zenon_H1ec zenon_Hf7 zenon_H195 zenon_H128 zenon_H137 zenon_H12d zenon_H40 zenon_H3d zenon_H1e zenon_H238 zenon_H67 zenon_H173 zenon_H4e zenon_H89 zenon_H5b zenon_H66 zenon_H2c zenon_H184 zenon_H55 zenon_H5d. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.18 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.18 apply (zenon_L687_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.18 apply (zenon_L671_); trivial. % 8.02/8.18 apply (zenon_L69_); trivial. % 8.02/8.18 (* end of lemma zenon_L688_ *) % 8.02/8.18 assert (zenon_L689_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Haa zenon_H5d zenon_H55 zenon_H184 zenon_H2c zenon_H5b zenon_H89 zenon_H173 zenon_H40 zenon_Hcc zenon_Hef zenon_H99 zenon_Hb2 zenon_H1ca zenon_H13f zenon_H117 zenon_H38 zenon_H36 zenon_H82 zenon_H81 zenon_H43 zenon_Hb7 zenon_Hd8 zenon_H1ec zenon_H195 zenon_H128 zenon_H137 zenon_H1d4 zenon_H12d zenon_H3d zenon_H1e zenon_H238 zenon_H67 zenon_H4e zenon_H6c zenon_H9c zenon_Hf7 zenon_H131. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.18 apply (zenon_L688_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.18 apply (zenon_L676_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L43_); trivial. % 8.02/8.18 apply (zenon_L559_); trivial. % 8.02/8.18 (* end of lemma zenon_L689_ *) % 8.02/8.18 assert (zenon_L690_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Ha1 zenon_H14e zenon_H6c. % 8.02/8.18 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H68 | zenon_intro zenon_H69 ]. % 8.02/8.18 cut (((e3) = (e3)) = ((e2) = (e3))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H6c. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_H68. % 8.02/8.18 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 8.02/8.18 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 8.02/8.18 congruence. % 8.02/8.18 cut (((op (e2) (e3)) = (e2)) = ((e3) = (e2))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H9d. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_Ha1. % 8.02/8.18 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 8.02/8.18 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 8.02/8.18 congruence. % 8.02/8.18 exact (zenon_H241 zenon_H14e). % 8.02/8.18 apply zenon_H22. apply refl_equal. % 8.02/8.18 apply zenon_H69. apply refl_equal. % 8.02/8.18 apply zenon_H69. apply refl_equal. % 8.02/8.18 (* end of lemma zenon_L690_ *) % 8.02/8.18 assert (zenon_L691_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H16b zenon_H8f zenon_H54 zenon_H66 zenon_H33 zenon_H1d6 zenon_Ha1 zenon_H6c. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 8.02/8.18 apply (zenon_L38_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 8.02/8.18 apply (zenon_L226_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 8.02/8.18 exact (zenon_H1d6 zenon_H15c). % 8.02/8.18 apply (zenon_L690_); trivial. % 8.02/8.18 (* end of lemma zenon_L691_ *) % 8.02/8.18 assert (zenon_L692_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H16b zenon_H1f zenon_H13e zenon_H66 zenon_H33 zenon_H1d6 zenon_Ha1 zenon_H6c. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 8.02/8.18 apply (zenon_L491_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 8.02/8.18 apply (zenon_L226_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 8.02/8.18 exact (zenon_H1d6 zenon_H15c). % 8.02/8.18 apply (zenon_L690_); trivial. % 8.02/8.18 (* end of lemma zenon_L692_ *) % 8.02/8.18 assert (zenon_L693_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Ha1 zenon_H9f zenon_H242. % 8.02/8.18 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha4 ]. % 8.02/8.18 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H242. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_Ha3. % 8.02/8.18 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 8.02/8.18 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 8.02/8.18 congruence. % 8.02/8.18 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H243. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_Ha1. % 8.02/8.18 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 8.02/8.18 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 8.02/8.18 congruence. % 8.02/8.18 apply zenon_Ha4. apply refl_equal. % 8.02/8.18 apply zenon_H244. apply sym_equal. exact zenon_H9f. % 8.02/8.18 apply zenon_Ha4. apply refl_equal. % 8.02/8.18 apply zenon_Ha4. apply refl_equal. % 8.02/8.18 (* end of lemma zenon_L693_ *) % 8.02/8.18 assert (zenon_L694_ : (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H122 zenon_Ha1 zenon_H242. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.18 apply (zenon_L693_); trivial. % 8.02/8.18 (* end of lemma zenon_L694_ *) % 8.02/8.18 assert (zenon_L695_ : (((op (e3) (e3)) = (e3))/\(((~((op (e0) (e3)) = (e0)))\/((op (e0) (e0)) = (e3)))/\(((~((op (e1) (e3)) = (e1)))\/((op (e1) (e1)) = (e3)))/\(((~((op (e2) (e3)) = (e2)))\/((op (e2) (e2)) = (e3)))/\((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H12b zenon_H1d6 zenon_Ha1. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.18 exact (zenon_H13a zenon_Ha1). % 8.02/8.18 exact (zenon_H1d6 zenon_H15c). % 8.02/8.18 (* end of lemma zenon_L695_ *) % 8.02/8.18 assert (zenon_L696_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H1c7 zenon_H6e zenon_H70 zenon_Hd2 zenon_H38 zenon_H10b zenon_H82 zenon_H1d6. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H36 | zenon_intro zenon_H1c8 ]. % 8.02/8.18 apply (zenon_L29_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H13e | zenon_intro zenon_H1c9 ]. % 8.02/8.18 apply (zenon_L390_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_H9f | zenon_intro zenon_H15c ]. % 8.02/8.18 apply (zenon_L115_); trivial. % 8.02/8.18 exact (zenon_H1d6 zenon_H15c). % 8.02/8.18 (* end of lemma zenon_L696_ *) % 8.02/8.18 assert (zenon_L697_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Hec zenon_H20 zenon_H1e zenon_H89 zenon_H6e zenon_H188 zenon_Ha1 zenon_Hb2 zenon_H99. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.18 apply (zenon_L2_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.18 apply (zenon_L84_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.18 apply (zenon_L250_); trivial. % 8.02/8.18 apply (zenon_L78_); trivial. % 8.02/8.18 (* end of lemma zenon_L697_ *) % 8.02/8.18 assert (zenon_L698_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H49 zenon_Ha1 zenon_H195. % 8.02/8.18 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 8.02/8.18 intro zenon_D_pnotp. % 8.02/8.18 apply zenon_H49. % 8.02/8.18 rewrite <- zenon_D_pnotp. % 8.02/8.18 exact zenon_Ha1. % 8.02/8.18 cut (((e2) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 8.02/8.18 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 8.02/8.18 congruence. % 8.02/8.18 apply zenon_Ha4. apply refl_equal. % 8.02/8.18 apply zenon_H246. apply sym_equal. exact zenon_H195. % 8.02/8.18 (* end of lemma zenon_L698_ *) % 8.02/8.18 assert (zenon_L699_ : (((op (e0) (e0)) = (e0))/\(((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0)))/\(((~((op (e1) (e0)) = (e1)))\/((op (e1) (e1)) = (e0)))/\(((~((op (e2) (e0)) = (e2)))\/((op (e2) (e2)) = (e0)))/\((~((op (e3) (e0)) = (e3)))\/((op (e3) (e3)) = (e0))))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e0)) = (e3)) -> False). % 8.02/8.18 do 0 intro. intros zenon_Had zenon_H1a8 zenon_H92. % 8.02/8.18 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.18 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.18 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.18 exact (zenon_Hc0 zenon_H92). % 8.02/8.18 exact (zenon_H1a8 zenon_H47). % 8.02/8.18 (* end of lemma zenon_L699_ *) % 8.02/8.18 assert (zenon_L700_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H11e zenon_H1f zenon_H28 zenon_H6d zenon_H6c zenon_H38 zenon_H9f zenon_Hd6 zenon_H99. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.18 apply (zenon_L288_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.18 apply (zenon_L26_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.18 apply (zenon_L107_); trivial. % 8.02/8.18 apply (zenon_L301_); trivial. % 8.02/8.18 (* end of lemma zenon_L700_ *) % 8.02/8.18 assert (zenon_L701_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.02/8.18 do 0 intro. intros zenon_H142 zenon_Hb9 zenon_H30 zenon_Hc6 zenon_Hca zenon_H15c zenon_H8f zenon_H99 zenon_Ha1. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 8.02/8.18 apply (zenon_L422_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 8.02/8.18 apply (zenon_L228_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 8.02/8.18 apply (zenon_L354_); trivial. % 8.02/8.18 apply (zenon_L425_); trivial. % 8.02/8.18 (* end of lemma zenon_L701_ *) % 8.02/8.18 assert (zenon_L702_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_Haa zenon_H6c zenon_H26 zenon_H8f zenon_Hc6 zenon_H18e zenon_H15c zenon_H92 zenon_H1d4. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.18 apply (zenon_L338_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.18 apply (zenon_L71_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.18 apply (zenon_L273_); trivial. % 8.02/8.18 apply (zenon_L548_); trivial. % 8.02/8.18 (* end of lemma zenon_L702_ *) % 8.02/8.18 assert (zenon_L703_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H124 zenon_H20 zenon_H1e zenon_H1d4 zenon_H92 zenon_H15c zenon_H18e zenon_Hc6 zenon_H8f zenon_H6c zenon_Haa zenon_H99 zenon_Hcf zenon_Ha1 zenon_Hbd. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.18 apply (zenon_L2_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.18 apply (zenon_L702_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.18 apply (zenon_L65_); trivial. % 8.02/8.18 apply (zenon_L53_); trivial. % 8.02/8.18 (* end of lemma zenon_L703_ *) % 8.02/8.18 assert (zenon_L704_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H205 zenon_H1a8 zenon_He4 zenon_He3 zenon_Ha1 zenon_H49 zenon_Hfd zenon_H5e. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 8.02/8.18 exact (zenon_H1a8 zenon_H47). % 8.02/8.18 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 8.02/8.18 apply (zenon_L81_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 8.02/8.18 apply (zenon_L698_); trivial. % 8.02/8.18 apply (zenon_L109_); trivial. % 8.02/8.18 (* end of lemma zenon_L704_ *) % 8.02/8.18 assert (zenon_L705_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 8.02/8.18 do 0 intro. intros zenon_H247 zenon_H8f zenon_H5e zenon_H49 zenon_He3 zenon_He4 zenon_H1a8 zenon_H205 zenon_H6c zenon_Ha1 zenon_H92 zenon_H128. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H248 ]. % 8.02/8.18 apply (zenon_L89_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_Hfd | zenon_intro zenon_H249 ]. % 8.02/8.18 apply (zenon_L704_); trivial. % 8.02/8.18 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H14e | zenon_intro zenon_Hfc ]. % 8.02/8.18 apply (zenon_L690_); trivial. % 8.02/8.18 apply (zenon_L137_); trivial. % 8.02/8.18 (* end of lemma zenon_L705_ *) % 8.02/8.18 assert (zenon_L706_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H15f zenon_H2c zenon_Hc6 zenon_Hbd zenon_Ha1 zenon_H99 zenon_Hc3 zenon_H1e zenon_H6c zenon_H10b zenon_H15c zenon_H67 zenon_H20 zenon_H124 zenon_H15a zenon_H55. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_L61_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L338_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L274_); trivial. % 8.02/8.19 apply (zenon_L438_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L53_); trivial. % 8.02/8.19 apply (zenon_L249_); trivial. % 8.02/8.19 (* end of lemma zenon_L706_ *) % 8.02/8.19 assert (zenon_L707_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H142 zenon_H17f zenon_Hb2 zenon_Hc6 zenon_Hca zenon_H15c zenon_H8f zenon_H99 zenon_Ha1. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 8.02/8.19 apply (zenon_L244_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 8.02/8.19 apply (zenon_L228_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 8.02/8.19 apply (zenon_L354_); trivial. % 8.02/8.19 apply (zenon_L425_); trivial. % 8.02/8.19 (* end of lemma zenon_L707_ *) % 8.02/8.19 assert (zenon_L708_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H209 zenon_H200 zenon_H15a zenon_He0 zenon_Hf8 zenon_H38 zenon_H81 zenon_Hef zenon_Hc6 zenon_H43 zenon_H44 zenon_H117 zenon_H15c zenon_H10b. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H111 | zenon_intro zenon_H20a ]. % 8.02/8.19 apply (zenon_L450_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_Hcf | zenon_intro zenon_H20b ]. % 8.02/8.19 apply (zenon_L177_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H82 | zenon_intro zenon_Hb0 ]. % 8.02/8.19 apply (zenon_L451_); trivial. % 8.02/8.19 apply (zenon_L274_); trivial. % 8.02/8.19 (* end of lemma zenon_L708_ *) % 8.02/8.19 assert (zenon_L709_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H142 zenon_H55 zenon_H31 zenon_Hc6 zenon_Hca zenon_H15c zenon_H8f zenon_H99 zenon_Ha1. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 8.02/8.19 apply (zenon_L15_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 8.02/8.19 apply (zenon_L228_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 8.02/8.19 apply (zenon_L354_); trivial. % 8.02/8.19 apply (zenon_L425_); trivial. % 8.02/8.19 (* end of lemma zenon_L709_ *) % 8.02/8.19 assert (zenon_L710_ : (((op (e1) (e1)) = (e1))/\(((~((op (e0) (e1)) = (e0)))\/((op (e0) (e0)) = (e1)))/\(((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1)))/\(((~((op (e2) (e1)) = (e2)))\/((op (e2) (e2)) = (e1)))/\((~((op (e3) (e1)) = (e3)))\/((op (e3) (e3)) = (e1))))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e1)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H106 zenon_H153 zenon_H7f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23d. zenon_intro zenon_H208. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1e9 | zenon_intro zenon_He2 ]. % 8.02/8.19 exact (zenon_H1e9 zenon_H7f). % 8.02/8.19 exact (zenon_H153 zenon_He2). % 8.02/8.19 (* end of lemma zenon_L710_ *) % 8.02/8.19 assert (zenon_L711_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 8.02/8.19 do 0 intro. intros zenon_He7 zenon_H99 zenon_H93 zenon_H7f zenon_H8f zenon_Hcf zenon_Hf8 zenon_H153. % 8.02/8.19 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 8.02/8.19 apply (zenon_L78_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 8.02/8.19 apply (zenon_L91_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 8.02/8.19 apply (zenon_L177_); trivial. % 8.02/8.19 exact (zenon_H153 zenon_He2). % 8.02/8.19 (* end of lemma zenon_L711_ *) % 8.02/8.19 assert (zenon_L712_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H197 zenon_H153 zenon_Hf8 zenon_Hcf zenon_H8f zenon_H7f zenon_H99 zenon_He7 zenon_H26 zenon_H40 zenon_H9f zenon_H5a zenon_Hb2 zenon_H86. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 8.02/8.19 apply (zenon_L711_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 8.02/8.19 apply (zenon_L225_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 8.02/8.19 apply (zenon_L178_); trivial. % 8.02/8.19 apply (zenon_L652_); trivial. % 8.02/8.19 (* end of lemma zenon_L712_ *) % 8.02/8.19 assert (zenon_L713_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H124 zenon_H6c zenon_H153 zenon_Hf8 zenon_Hcf zenon_H8f zenon_H7f zenon_H197 zenon_H99 zenon_He7 zenon_H40 zenon_H5a zenon_H86 zenon_H10b zenon_H9f zenon_H15a zenon_H20. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L243_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 8.02/8.19 apply (zenon_L712_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 8.02/8.19 apply (zenon_L91_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 8.02/8.19 apply (zenon_L177_); trivial. % 8.02/8.19 exact (zenon_H153 zenon_He2). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L223_); trivial. % 8.02/8.19 (* end of lemma zenon_L713_ *) % 8.02/8.19 assert (zenon_L714_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H209 zenon_H127 zenon_H13e zenon_H10b zenon_H9f zenon_Haf zenon_H86. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H111 | zenon_intro zenon_H20a ]. % 8.02/8.19 exact (zenon_H127 zenon_H111). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_Hcf | zenon_intro zenon_H20b ]. % 8.02/8.19 apply (zenon_L175_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H82 | zenon_intro zenon_Hb0 ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 (* end of lemma zenon_L714_ *) % 8.02/8.19 assert (zenon_L715_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H124 zenon_H86 zenon_H6c zenon_H2c zenon_H6e zenon_H10b zenon_H9f zenon_H15a zenon_H20. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L243_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L128_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L223_); trivial. % 8.02/8.19 (* end of lemma zenon_L715_ *) % 8.02/8.19 assert (zenon_L716_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H205 zenon_H15c zenon_He0 zenon_H153 zenon_Ha1 zenon_H49 zenon_H7f zenon_H12d. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 8.02/8.19 apply (zenon_L383_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 8.02/8.19 exact (zenon_H153 zenon_He2). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 8.02/8.19 apply (zenon_L698_); trivial. % 8.02/8.19 apply (zenon_L139_); trivial. % 8.02/8.19 (* end of lemma zenon_L716_ *) % 8.02/8.19 assert (zenon_L717_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H22e zenon_H1e zenon_H30 zenon_H17f zenon_Hb2 zenon_H9b zenon_H15c zenon_H10e. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H31 | zenon_intro zenon_H22f ]. % 8.02/8.19 apply (zenon_L6_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H54 | zenon_intro zenon_H230 ]. % 8.02/8.19 apply (zenon_L244_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H98 | zenon_intro zenon_H8e ]. % 8.02/8.19 exact (zenon_H9b zenon_H98). % 8.02/8.19 apply (zenon_L200_); trivial. % 8.02/8.19 (* end of lemma zenon_L717_ *) % 8.02/8.19 assert (zenon_L718_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H20 zenon_Ha1 zenon_H48. % 8.02/8.19 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 8.02/8.19 intro zenon_D_pnotp. % 8.02/8.19 apply zenon_H20. % 8.02/8.19 rewrite <- zenon_D_pnotp. % 8.02/8.19 exact zenon_Ha1. % 8.02/8.19 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 8.02/8.19 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 8.02/8.19 congruence. % 8.02/8.19 exact (zenon_H24a zenon_H48). % 8.02/8.19 apply zenon_H22. apply refl_equal. % 8.02/8.19 (* end of lemma zenon_L718_ *) % 8.02/8.19 assert (zenon_L719_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H51 zenon_H1e zenon_H30 zenon_H2d zenon_Hca zenon_H15c zenon_H67 zenon_H20 zenon_Ha1. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.19 apply (zenon_L6_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.19 apply (zenon_L293_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.19 apply (zenon_L215_); trivial. % 8.02/8.19 apply (zenon_L718_); trivial. % 8.02/8.19 (* end of lemma zenon_L719_ *) % 8.02/8.19 assert (zenon_L720_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H170 zenon_H10a zenon_H2c zenon_H131 zenon_Hf7 zenon_H40 zenon_H173 zenon_Hc6 zenon_H1d4 zenon_H3e zenon_H137 zenon_H16e zenon_H86. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H25 | zenon_intro zenon_H171 ]. % 8.02/8.19 exact (zenon_H10a zenon_H25). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H172 ]. % 8.02/8.19 apply (zenon_L61_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H26 | zenon_intro zenon_H66 ]. % 8.02/8.19 apply (zenon_L642_); trivial. % 8.02/8.19 apply (zenon_L217_); trivial. % 8.02/8.19 (* end of lemma zenon_L720_ *) % 8.02/8.19 assert (zenon_L721_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H197 zenon_H86 zenon_He2 zenon_H26 zenon_H40 zenon_Hf7 zenon_H6c zenon_H196. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 8.02/8.19 apply (zenon_L540_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 8.02/8.19 apply (zenon_L225_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 8.02/8.19 apply (zenon_L355_); trivial. % 8.02/8.19 exact (zenon_H196 zenon_H195). % 8.02/8.19 (* end of lemma zenon_L721_ *) % 8.02/8.19 assert (zenon_L722_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H205 zenon_H12d zenon_H41 zenon_H6c zenon_H40 zenon_H26 zenon_H86 zenon_H197 zenon_H196 zenon_Hf7 zenon_H1cd. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 8.02/8.19 apply (zenon_L292_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 8.02/8.19 apply (zenon_L721_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 8.02/8.19 exact (zenon_H196 zenon_H195). % 8.02/8.19 apply (zenon_L335_); trivial. % 8.02/8.19 (* end of lemma zenon_L722_ *) % 8.02/8.19 assert (zenon_L723_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H170 zenon_H10a zenon_H2c zenon_Hc6 zenon_H1cd zenon_Hf7 zenon_H196 zenon_H197 zenon_H40 zenon_H6c zenon_H41 zenon_H12d zenon_H205 zenon_H16e zenon_H86. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H25 | zenon_intro zenon_H171 ]. % 8.02/8.19 exact (zenon_H10a zenon_H25). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H172 ]. % 8.02/8.19 apply (zenon_L61_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H26 | zenon_intro zenon_H66 ]. % 8.02/8.19 apply (zenon_L722_); trivial. % 8.02/8.19 apply (zenon_L217_); trivial. % 8.02/8.19 (* end of lemma zenon_L723_ *) % 8.02/8.19 assert (zenon_L724_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H170 zenon_H10a zenon_H2c zenon_Hc6 zenon_Hdc zenon_H40 zenon_H16e zenon_H86. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H25 | zenon_intro zenon_H171 ]. % 8.02/8.19 exact (zenon_H10a zenon_H25). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H172 ]. % 8.02/8.19 apply (zenon_L61_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H26 | zenon_intro zenon_H66 ]. % 8.02/8.19 apply (zenon_L225_); trivial. % 8.02/8.19 apply (zenon_L217_); trivial. % 8.02/8.19 (* end of lemma zenon_L724_ *) % 8.02/8.19 assert (zenon_L725_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H197 zenon_He2 zenon_H86 zenon_H16e zenon_H40 zenon_Hc6 zenon_H2c zenon_H10a zenon_H170 zenon_Hf7 zenon_H6c zenon_H196. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 8.02/8.19 apply (zenon_L540_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 8.02/8.19 apply (zenon_L724_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 8.02/8.19 apply (zenon_L355_); trivial. % 8.02/8.19 exact (zenon_H196 zenon_H195). % 8.02/8.19 (* end of lemma zenon_L725_ *) % 8.02/8.19 assert (zenon_L726_ : (((op (e2) (e2)) = (e2))/\(((~((op (e0) (e2)) = (e0)))\/((op (e0) (e0)) = (e2)))/\(((~((op (e1) (e2)) = (e1)))\/((op (e1) (e1)) = (e2)))/\(((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2)))/\((~((op (e3) (e2)) = (e3)))\/((op (e3) (e3)) = (e2))))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e3) (e2)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H122 zenon_H196 zenon_Hf7. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H24c. zenon_intro zenon_H24b. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H228 | zenon_intro zenon_H195 ]. % 8.02/8.19 exact (zenon_H228 zenon_Hf7). % 8.02/8.19 exact (zenon_H196 zenon_H195). % 8.02/8.19 (* end of lemma zenon_L726_ *) % 8.02/8.19 assert (zenon_L727_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 8.02/8.19 do 0 intro. intros zenon_H95 zenon_H67 zenon_H1e zenon_H89 zenon_H6d zenon_H8f zenon_H54 zenon_Hf7 zenon_H1ec. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L37_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 apply (zenon_L423_); trivial. % 8.02/8.19 (* end of lemma zenon_L727_ *) % 8.02/8.19 assert (zenon_L728_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 8.02/8.19 do 0 intro. intros zenon_Hb6 zenon_H55 zenon_Hb7 zenon_H1ec zenon_H8f zenon_H89 zenon_H1e zenon_H67 zenon_H95 zenon_H197 zenon_H99 zenon_H6d zenon_H47 zenon_Hf7 zenon_H6c zenon_H196. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L727_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H197); [ zenon_intro zenon_H93 | zenon_intro zenon_H198 ]. % 8.02/8.19 apply (zenon_L78_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H198); [ zenon_intro zenon_Hdc | zenon_intro zenon_H199 ]. % 8.02/8.19 apply (zenon_L235_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H199); [ zenon_intro zenon_H148 | zenon_intro zenon_H195 ]. % 8.02/8.19 apply (zenon_L355_); trivial. % 8.02/8.19 exact (zenon_H196 zenon_H195). % 8.02/8.19 (* end of lemma zenon_L728_ *) % 8.02/8.19 assert (zenon_L729_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 8.02/8.19 do 0 intro. intros zenon_H5a zenon_H15c zenon_Hf7. % 8.02/8.19 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 8.02/8.19 intro zenon_D_pnotp. % 8.02/8.19 apply zenon_H5a. % 8.02/8.19 rewrite <- zenon_D_pnotp. % 8.02/8.19 exact zenon_H15c. % 8.02/8.19 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 8.02/8.19 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 8.02/8.19 congruence. % 8.02/8.19 apply zenon_H3a. apply refl_equal. % 8.02/8.19 apply zenon_H1cf. apply sym_equal. exact zenon_Hf7. % 8.02/8.19 (* end of lemma zenon_L729_ *) % 8.02/8.19 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H1e6. zenon_intro zenon_H24d. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H24d). zenon_intro zenon_H170. zenon_intro zenon_H24e. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H24e). zenon_intro zenon_H209. zenon_intro zenon_H24f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H24f). zenon_intro zenon_H251. zenon_intro zenon_H250. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H250). zenon_intro zenon_H229. zenon_intro zenon_H252. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H252). zenon_intro zenon_Hcc. zenon_intro zenon_H253. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H253). zenon_intro zenon_H117. zenon_intro zenon_H254. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H254). zenon_intro zenon_Hff. zenon_intro zenon_H255. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H255). zenon_intro zenon_H22e. zenon_intro zenon_H256. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H256). zenon_intro zenon_H19b. zenon_intro zenon_H257. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H257). zenon_intro zenon_H1c7. zenon_intro zenon_H258. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H258). zenon_intro zenon_H150. zenon_intro zenon_H259. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_H238. zenon_intro zenon_H25a. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H25a). zenon_intro zenon_H137. zenon_intro zenon_H25b. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H25b). zenon_intro zenon_H14a. zenon_intro zenon_H205. % 8.02/8.19 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H235. zenon_intro zenon_H25c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H25c). zenon_intro zenon_H18b. zenon_intro zenon_H25d. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H15f. zenon_intro zenon_H25e. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H25e). zenon_intro zenon_Hb6. zenon_intro zenon_H25f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H25f). zenon_intro zenon_H124. zenon_intro zenon_H260. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H260). zenon_intro zenon_Hec. zenon_intro zenon_H261. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_Hc3. zenon_intro zenon_H262. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H95. zenon_intro zenon_H263. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H263). zenon_intro zenon_H61. zenon_intro zenon_H264. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H213. zenon_intro zenon_H265. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H265). zenon_intro zenon_Hd8. zenon_intro zenon_H266. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H266). zenon_intro zenon_H184. zenon_intro zenon_H267. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H267). zenon_intro zenon_H11e. zenon_intro zenon_H268. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H268). zenon_intro zenon_H13b. zenon_intro zenon_H269. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H269). zenon_intro zenon_H162. zenon_intro zenon_H26a. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H26a). zenon_intro zenon_Haa. zenon_intro zenon_H26b. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H51. zenon_intro zenon_H26c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H26c). zenon_intro zenon_H11b. zenon_intro zenon_H26d. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H26d). zenon_intro zenon_H142. zenon_intro zenon_H26e. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H26e). zenon_intro zenon_H1ca. zenon_intro zenon_H26f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H26f). zenon_intro zenon_Ha7. zenon_intro zenon_H270. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H272. zenon_intro zenon_H271. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_H16b. zenon_intro zenon_H273. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H1d0. zenon_intro zenon_H274. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_H4e. zenon_intro zenon_H275. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H157. zenon_intro zenon_H276. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H276). zenon_intro zenon_He7. zenon_intro zenon_H277. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H277). zenon_intro zenon_H190. zenon_intro zenon_H278. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H278). zenon_intro zenon_H197. zenon_intro zenon_H279. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H279). zenon_intro zenon_H27b. zenon_intro zenon_H27a. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H27a). zenon_intro zenon_H102. zenon_intro zenon_H247. % 8.02/8.19 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H28. zenon_intro zenon_H27c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_H30. zenon_intro zenon_H27d. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H27d). zenon_intro zenon_H3d. zenon_intro zenon_H27e. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H27e). zenon_intro zenon_H280. zenon_intro zenon_H27f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H282. zenon_intro zenon_H281. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_H17f. zenon_intro zenon_H283. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H283). zenon_intro zenon_H2c. zenon_intro zenon_H284. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H284). zenon_intro zenon_H33. zenon_intro zenon_H285. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H285). zenon_intro zenon_H40. zenon_intro zenon_H286. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H286). zenon_intro zenon_Hca. zenon_intro zenon_H287. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H287). zenon_intro zenon_H173. zenon_intro zenon_H288. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H134. zenon_intro zenon_H289. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H289). zenon_intro zenon_H81. zenon_intro zenon_H28a. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H28a). zenon_intro zenon_H10b. zenon_intro zenon_H28b. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H28b). zenon_intro zenon_Hf8. zenon_intro zenon_H28c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H28c). zenon_intro zenon_H38. zenon_intro zenon_H28d. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H43. zenon_intro zenon_H28e. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H28e). zenon_intro zenon_H5a. zenon_intro zenon_H28f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H28f). zenon_intro zenon_Hf1. zenon_intro zenon_H290. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H290). zenon_intro zenon_Hbd. zenon_intro zenon_H291. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_He4. zenon_intro zenon_H292. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H64. zenon_intro zenon_H293. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_H5e. zenon_intro zenon_H294. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H49. zenon_intro zenon_H295. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_H16e. zenon_intro zenon_H296. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_Haf. zenon_intro zenon_H297. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H297). zenon_intro zenon_H299. zenon_intro zenon_H298. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H29b. zenon_intro zenon_H29a. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H200. zenon_intro zenon_H29e. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H89. zenon_intro zenon_H29f. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H29f). zenon_intro zenon_H113. zenon_intro zenon_H2a0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H154. zenon_intro zenon_H2a1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a1). zenon_intro zenon_Hef. zenon_intro zenon_H2a2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H130. zenon_intro zenon_H2a3. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H2a5. zenon_intro zenon_H2a4. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H17c. zenon_intro zenon_H2a6. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H10e. zenon_intro zenon_H2a7. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H188. zenon_intro zenon_H2a8. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H18e. zenon_intro zenon_H2a9. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ab. zenon_intro zenon_H2aa. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H242. zenon_intro zenon_H2ac. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H1d4. zenon_intro zenon_H2ad. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_H1ec. zenon_intro zenon_H2ae. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H128. zenon_intro zenon_H2af. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H131. zenon_intro zenon_H2b0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H12d. zenon_intro zenon_H1cd. % 8.02/8.19 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H55. zenon_intro zenon_H2b1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H20. zenon_intro zenon_H2b2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H67. zenon_intro zenon_H2b3. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H99. zenon_intro zenon_H2b4. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H8f. zenon_intro zenon_H6c. % 8.02/8.19 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H2b5. zenon_intro zenon_H1ab. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H2b7 | zenon_intro zenon_H2b6 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H1e. zenon_intro zenon_H2b8. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H2ba. zenon_intro zenon_H2b9. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.02/8.19 exact (zenon_H2ba zenon_H1e). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2b6); [ zenon_intro zenon_H2bc | zenon_intro zenon_H2bb ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H1e. zenon_intro zenon_H2bd. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H2ba. zenon_intro zenon_H2be. % 8.02/8.19 exact (zenon_H2ba zenon_H1e). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H2c0 | zenon_intro zenon_H2bf ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H1e. zenon_intro zenon_H2c1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c1). zenon_intro zenon_H2ba. zenon_intro zenon_H2c2. % 8.02/8.19 exact (zenon_H2ba zenon_H1e). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2c4 | zenon_intro zenon_H2c3 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H1e. zenon_intro zenon_H2c5. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H2ba. zenon_intro zenon_H2c6. % 8.02/8.19 exact (zenon_H2ba zenon_H1e). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2c3); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2c7 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c8). zenon_intro zenon_H25. zenon_intro zenon_H2c9. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_Hb5. zenon_intro zenon_H2b9. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.19 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H9b | zenon_intro zenon_H36 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L23_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 exact (zenon_H9b zenon_H98). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L23_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L26_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_L30_); trivial. % 8.02/8.19 apply (zenon_L34_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_L47_); trivial. % 8.02/8.19 apply (zenon_L58_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_L18_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L48_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L64_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 exact (zenon_Hc0 zenon_H92). % 8.02/8.19 apply (zenon_L51_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L8_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L70_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L72_); trivial. % 8.02/8.19 apply (zenon_L74_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.19 apply (zenon_L68_); trivial. % 8.02/8.19 apply (zenon_L69_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 exact (zenon_Hc0 zenon_H92). % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L75_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L75_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L20_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L52_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L48_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L20_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L67_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_L76_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L83_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L88_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_L76_); trivial. % 8.02/8.19 apply (zenon_L69_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 exact (zenon_Hc0 zenon_H92). % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L84_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L72_); trivial. % 8.02/8.19 apply (zenon_L74_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L64_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L90_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L96_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L97_); trivial. % 8.02/8.19 apply (zenon_L74_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L88_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L98_); trivial. % 8.02/8.19 apply (zenon_L74_); trivial. % 8.02/8.19 apply (zenon_L93_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 exact (zenon_Hc0 zenon_H92). % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L48_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L8_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.19 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L95_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L72_); trivial. % 8.02/8.19 apply (zenon_L101_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L103_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L90_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L88_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L97_); trivial. % 8.02/8.19 apply (zenon_L101_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L84_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L98_); trivial. % 8.02/8.19 apply (zenon_L101_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L106_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L37_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 8.02/8.19 apply (zenon_L43_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 8.02/8.19 apply (zenon_L107_); trivial. % 8.02/8.19 apply (zenon_L112_); trivial. % 8.02/8.19 apply (zenon_L92_); trivial. % 8.02/8.19 apply (zenon_L113_); trivial. % 8.02/8.19 apply (zenon_L69_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 exact (zenon_Hc0 zenon_H92). % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L51_); trivial. % 8.02/8.19 apply (zenon_L32_); trivial. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L114_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H127 | zenon_intro zenon_H1f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L117_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L122_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_L126_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L127_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L132_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L84_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_L103_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L132_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L84_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L134_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_L70_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_L135_); trivial. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L141_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_L150_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L202_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L210_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L211_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L202_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_L269_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L269_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L67_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L272_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.19 apply (zenon_L15_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.19 apply (zenon_L7_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 8.02/8.19 apply (zenon_L268_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 8.02/8.19 apply (zenon_L43_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 8.02/8.19 apply (zenon_L107_); trivial. % 8.02/8.19 exact (zenon_H13a zenon_Ha1). % 8.02/8.19 apply (zenon_L21_); trivial. % 8.02/8.19 apply (zenon_L139_); trivial. % 8.02/8.19 apply (zenon_L113_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.19 apply (zenon_L68_); trivial. % 8.02/8.19 exact (zenon_H165 zenon_Hd6). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L38_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_L60_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L14_); trivial. % 8.02/8.19 apply (zenon_L193_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L200_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L163_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_L273_); trivial. % 8.02/8.19 apply (zenon_L139_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L203_); trivial. % 8.02/8.19 apply (zenon_L59_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L200_); trivial. % 8.02/8.19 apply (zenon_L167_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L275_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L274_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L201_); trivial. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2ca ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2cb). zenon_intro zenon_H25. zenon_intro zenon_H2cc. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_Hb5. zenon_intro zenon_H2be. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H2d. zenon_intro zenon_Hbb. % 8.02/8.19 apply (zenon_L5_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H2ce | zenon_intro zenon_H2cd ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H25. zenon_intro zenon_H2cf. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_Hb5. zenon_intro zenon_H2c2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H36. zenon_intro zenon_H98. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.19 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.19 apply (zenon_L52_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L114_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_L129_); trivial. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L276_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_L208_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L268_); trivial. % 8.02/8.19 apply (zenon_L279_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L259_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L281_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L219_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L281_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L167_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L259_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L246_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L246_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L204_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L162_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_L63_); trivial. % 8.02/8.19 apply (zenon_L73_); trivial. % 8.02/8.19 apply (zenon_L113_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L248_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hd9 ]. % 8.02/8.19 apply (zenon_L266_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hda ]. % 8.02/8.19 apply (zenon_L245_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd6 ]. % 8.02/8.19 apply (zenon_L68_); trivial. % 8.02/8.19 exact (zenon_H165 zenon_Hd6). % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L277_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L259_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L278_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L258_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_L260_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L264_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_L50_); trivial. % 8.02/8.19 apply (zenon_L215_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 exact (zenon_Hb5 zenon_Hb9). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L219_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L37_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L285_); trivial. % 8.02/8.19 apply (zenon_L286_); trivial. % 8.02/8.19 apply (zenon_L284_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2d1 | zenon_intro zenon_H2d0 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H25. zenon_intro zenon_H2d2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2d2). zenon_intro zenon_Hb5. zenon_intro zenon_H2c6. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H47. zenon_intro zenon_H92. % 8.02/8.19 apply (zenon_L317_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H2d4 | zenon_intro zenon_H2d3 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2d4). zenon_intro zenon_H111. zenon_intro zenon_H2d5. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2d5). zenon_intro zenon_H24. zenon_intro zenon_H2b9. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d6 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H111. zenon_intro zenon_H2d8. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2d8). zenon_intro zenon_H24. zenon_intro zenon_H2be. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H2d. zenon_intro zenon_Hbb. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_L319_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L320_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_L321_); trivial. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L329_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L332_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L341_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.19 apply (zenon_L164_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L338_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L205_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.19 apply (zenon_L371_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.19 apply (zenon_L293_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.19 apply (zenon_L326_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.19 apply (zenon_L359_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.19 apply (zenon_L330_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_L331_); trivial. % 8.02/8.19 apply (zenon_L12_); trivial. % 8.02/8.19 apply (zenon_L139_); trivial. % 8.02/8.19 apply (zenon_L109_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L128_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L341_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.19 apply (zenon_L164_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L338_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L205_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.19 apply (zenon_L370_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.19 apply (zenon_L293_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.19 apply (zenon_L326_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.19 apply (zenon_L322_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.19 apply (zenon_L323_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.19 apply (zenon_L325_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha8 ]. % 8.02/8.19 apply (zenon_L327_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_H9c | zenon_intro zenon_Ha9 ]. % 8.02/8.19 apply (zenon_L43_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_H9f | zenon_intro zenon_Ha1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.19 apply (zenon_L372_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.19 apply (zenon_L79_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_L331_); trivial. % 8.02/8.19 apply (zenon_L12_); trivial. % 8.02/8.19 exact (zenon_H13a zenon_Ha1). % 8.02/8.19 apply (zenon_L91_); trivial. % 8.02/8.19 apply (zenon_L109_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L329_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L333_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L385_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.19 apply (zenon_L397_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.19 apply (zenon_L398_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.19 apply (zenon_L205_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.19 apply (zenon_L366_); trivial. % 8.02/8.19 apply (zenon_L140_); trivial. % 8.02/8.19 apply (zenon_L109_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L399_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L142_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.19 apply (zenon_L164_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.19 apply (zenon_L323_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.19 apply (zenon_L325_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.19 apply (zenon_L379_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.19 apply (zenon_L79_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_L331_); trivial. % 8.02/8.19 apply (zenon_L384_); trivial. % 8.02/8.19 apply (zenon_L109_); trivial. % 8.02/8.19 apply (zenon_L153_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L329_); trivial. % 8.02/8.19 apply (zenon_L332_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L411_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L385_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L322_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L329_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L406_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L338_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L118_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L329_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L407_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L217_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L343_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L142_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L412_); trivial. % 8.02/8.19 apply (zenon_L153_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L246_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_L398_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L399_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L142_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L412_); trivial. % 8.02/8.19 apply (zenon_L153_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L118_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L197_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_L371_); trivial. % 8.02/8.19 apply (zenon_L413_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L329_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L414_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L200_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L260_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L410_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L123_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L413_); trivial. % 8.02/8.19 apply (zenon_L164_); trivial. % 8.02/8.19 apply (zenon_L414_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H2da | zenon_intro zenon_H2d9 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2da). zenon_intro zenon_H111. zenon_intro zenon_H2db. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H24. zenon_intro zenon_H2c2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H36. zenon_intro zenon_H98. % 8.02/8.19 apply (zenon_L326_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2d9); [ zenon_intro zenon_H2dd | zenon_intro zenon_H2dc ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H111. zenon_intro zenon_H2de. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H24. zenon_intro zenon_H2c6. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H47. zenon_intro zenon_H92. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_L319_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23d. zenon_intro zenon_H208. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1eb | zenon_intro zenon_H13e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1e9 | zenon_intro zenon_He2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 apply (zenon_L421_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L167_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 apply (zenon_L428_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L320_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L15_); trivial. % 8.02/8.19 apply (zenon_L167_); trivial. % 8.02/8.19 apply (zenon_L313_); trivial. % 8.02/8.19 apply (zenon_L308_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 apply (zenon_L417_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 exact (zenon_H24 zenon_H1f). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L429_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L167_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_L321_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H2e0 | zenon_intro zenon_H2df ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H15a. zenon_intro zenon_H2e1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2e1). zenon_intro zenon_H87. zenon_intro zenon_H2b9. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H1e. zenon_intro zenon_H1e. % 8.02/8.19 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 8.02/8.19 intro zenon_D_pnotp. % 8.02/8.19 apply zenon_H299. % 8.02/8.19 rewrite <- zenon_D_pnotp. % 8.02/8.19 exact zenon_H1e. % 8.02/8.19 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2e2]. % 8.02/8.19 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 8.02/8.19 congruence. % 8.02/8.19 apply zenon_H2b. apply refl_equal. % 8.02/8.19 apply zenon_H2e2. apply sym_equal. exact zenon_H15a. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_H2e4 | zenon_intro zenon_H2e3 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2e4). zenon_intro zenon_H15a. zenon_intro zenon_H2e5. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H87. zenon_intro zenon_H2be. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H2d. zenon_intro zenon_Hbb. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.19 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 exact (zenon_H87 zenon_H86). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L66_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H31 | zenon_intro zenon_H52 ]. % 8.02/8.19 apply (zenon_L123_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H34 | zenon_intro zenon_H53 ]. % 8.02/8.19 apply (zenon_L293_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H36 | zenon_intro zenon_H48 ]. % 8.02/8.19 apply (zenon_L434_); trivial. % 8.02/8.19 apply (zenon_L435_); trivial. % 8.02/8.19 exact (zenon_Hc0 zenon_H92). % 8.02/8.19 apply (zenon_L430_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L320_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L439_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L440_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L223_); trivial. % 8.02/8.19 apply (zenon_L85_); trivial. % 8.02/8.19 apply (zenon_L441_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H2e7 | zenon_intro zenon_H2e6 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H15a. zenon_intro zenon_H2e8. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2e8). zenon_intro zenon_H87. zenon_intro zenon_H2c2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H36. zenon_intro zenon_H98. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_L434_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23d. zenon_intro zenon_H208. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1eb | zenon_intro zenon_H13e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_L61_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L445_); trivial. % 8.02/8.19 apply (zenon_L249_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L464_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_L61_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L212_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 exact (zenon_H87 zenon_H86). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L338_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L443_); trivial. % 8.02/8.19 apply (zenon_L438_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L223_); trivial. % 8.02/8.19 apply (zenon_L249_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_L260_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.19 apply (zenon_L464_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.19 apply (zenon_L41_); trivial. % 8.02/8.19 apply (zenon_L50_); trivial. % 8.02/8.19 apply (zenon_L155_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_L129_); trivial. % 8.02/8.19 apply (zenon_L441_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H2ea | zenon_intro zenon_H2e9 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_H15a. zenon_intro zenon_H2eb. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2eb). zenon_intro zenon_H87. zenon_intro zenon_H2c6. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H47. zenon_intro zenon_H92. % 8.02/8.19 apply (zenon_L430_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2e9); [ zenon_intro zenon_H2ed | zenon_intro zenon_H2ec ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ed). zenon_intro zenon_Hbb. zenon_intro zenon_H2ee. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_Heb. zenon_intro zenon_H2ef. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_Hb9. zenon_intro zenon_H25. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_L465_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L320_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H127 | zenon_intro zenon_H1f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L472_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L107_); trivial. % 8.02/8.19 apply (zenon_L113_); trivial. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L246_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L142_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.19 apply (zenon_L204_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.19 apply (zenon_L476_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.19 apply (zenon_L206_); trivial. % 8.02/8.19 apply (zenon_L109_); trivial. % 8.02/8.19 apply (zenon_L478_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L479_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L470_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L142_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L480_); trivial. % 8.02/8.19 apply (zenon_L478_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L260_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L333_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L481_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L123_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L479_); trivial. % 8.02/8.19 apply (zenon_L77_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L333_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L481_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L136_); trivial. % 8.02/8.19 apply (zenon_L313_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_L77_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L333_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L449_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L35_); trivial. % 8.02/8.19 apply (zenon_L483_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L200_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_L484_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_L476_); trivial. % 8.02/8.19 apply (zenon_L334_); trivial. % 8.02/8.19 apply (zenon_L333_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2ec); [ zenon_intro zenon_H2f1 | zenon_intro zenon_H2f0 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_Hbb. zenon_intro zenon_H2f2. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_Heb. zenon_intro zenon_H2f3. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc6. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2f0); [ zenon_intro zenon_H2f5 | zenon_intro zenon_H2f4 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f5). zenon_intro zenon_Hbb. zenon_intro zenon_H2f6. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_Heb. zenon_intro zenon_H2f7. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f7). zenon_intro zenon_H13e. zenon_intro zenon_H9c. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_L465_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L320_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_L311_); trivial. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1e | zenon_intro zenon_H236 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L487_); trivial. % 8.02/8.19 apply (zenon_L488_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L175_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L4_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L192_); trivial. % 8.02/8.19 apply (zenon_L193_); trivial. % 8.02/8.19 apply (zenon_L197_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H25 | zenon_intro zenon_H237 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L492_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L492_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L504_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L506_); trivial. % 8.02/8.19 apply (zenon_L488_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L512_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L506_); trivial. % 8.02/8.19 apply (zenon_L488_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L175_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L514_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L514_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L494_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L204_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L515_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L192_); trivial. % 8.02/8.19 apply (zenon_L193_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L197_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L492_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L492_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_L504_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L243_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L519_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L123_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L260_); trivial. % 8.02/8.19 apply (zenon_L520_); trivial. % 8.02/8.19 apply (zenon_L505_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H111 | zenon_intro zenon_H15a ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L333_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 8.02/8.19 apply (zenon_L204_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 8.02/8.19 apply (zenon_L523_); trivial. % 8.02/8.19 apply (zenon_L518_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L521_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_L97_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 8.02/8.19 apply (zenon_L306_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_L185_); trivial. % 8.02/8.19 apply (zenon_L498_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L496_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_L521_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L175_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L524_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L524_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L494_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L494_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 8.02/8.19 apply (zenon_L523_); trivial. % 8.02/8.19 apply (zenon_L485_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L521_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_L97_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.19 apply (zenon_L522_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.19 apply (zenon_L498_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.19 apply (zenon_L77_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.19 apply (zenon_L79_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H15a | zenon_intro zenon_H159 ]. % 8.02/8.19 exact (zenon_H158 zenon_H15a). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H5d | zenon_intro zenon_H15b ]. % 8.02/8.19 apply (zenon_L193_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_H1e | zenon_intro zenon_H1e7 ]. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H1e8 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 8.02/8.19 apply (zenon_L306_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_L229_); trivial. % 8.02/8.19 apply (zenon_L395_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_H1f | zenon_intro zenon_H86 ]. % 8.02/8.19 apply (zenon_L376_); trivial. % 8.02/8.19 apply (zenon_L344_); trivial. % 8.02/8.19 apply (zenon_L256_); trivial. % 8.02/8.19 apply (zenon_L196_); trivial. % 8.02/8.19 apply (zenon_L109_); trivial. % 8.02/8.19 apply (zenon_L485_); trivial. % 8.02/8.19 apply (zenon_L137_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L118_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L197_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L462_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L260_); trivial. % 8.02/8.19 apply (zenon_L520_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L496_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_L520_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L322_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L494_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L525_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L118_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L379_); trivial. % 8.02/8.19 exact (zenon_H158 zenon_H15a). % 8.02/8.19 apply (zenon_L354_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1e | zenon_intro zenon_H236 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L507_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L511_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L487_); trivial. % 8.02/8.19 apply (zenon_L488_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L175_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L104_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L37_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L526_); trivial. % 8.02/8.19 apply (zenon_L39_); trivial. % 8.02/8.19 apply (zenon_L89_); trivial. % 8.02/8.19 apply (zenon_L197_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H25 | zenon_intro zenon_H237 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L507_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L507_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L493_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L37_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L503_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L506_); trivial. % 8.02/8.19 apply (zenon_L527_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.19 apply (zenon_L510_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.19 apply (zenon_L506_); trivial. % 8.02/8.19 apply (zenon_L527_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L175_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L514_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L514_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L116_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L238_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L204_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L526_); trivial. % 8.02/8.19 apply (zenon_L138_); trivial. % 8.02/8.19 apply (zenon_L197_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L507_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L509_); trivial. % 8.02/8.19 apply (zenon_L283_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_L528_); trivial. % 8.02/8.19 apply (zenon_L505_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H111 | zenon_intro zenon_H15a ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_L318_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_L502_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_L528_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L337_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L496_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L296_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L493_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_L37_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L498_); trivial. % 8.02/8.19 apply (zenon_L313_); trivial. % 8.02/8.19 apply (zenon_L500_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L322_); trivial. % 8.02/8.19 apply (zenon_L501_); trivial. % 8.02/8.19 exact (zenon_H158 zenon_H15a). % 8.02/8.19 apply (zenon_L354_); trivial. % 8.02/8.19 apply (zenon_L494_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2f9 | zenon_intro zenon_H2f8 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f9). zenon_intro zenon_Hbb. zenon_intro zenon_H2fa. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2fa). zenon_intro zenon_Heb. zenon_intro zenon_H2fb. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_He2. zenon_intro zenon_H7f. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.19 apply (zenon_L465_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.19 apply (zenon_L320_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H127 | zenon_intro zenon_H1f ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1e | zenon_intro zenon_H236 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L297_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L529_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L531_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H25 | zenon_intro zenon_H214 ]. % 8.02/8.19 apply (zenon_L536_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H2d | zenon_intro zenon_H215 ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H34 | zenon_intro zenon_H41 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.19 apply (zenon_L295_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.19 apply (zenon_L221_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 8.02/8.19 exact (zenon_Heb zenon_H2d). % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 8.02/8.19 apply (zenon_L228_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 8.02/8.19 apply (zenon_L543_); trivial. % 8.02/8.19 apply (zenon_L294_); trivial. % 8.02/8.19 apply (zenon_L91_); trivial. % 8.02/8.19 apply (zenon_L31_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L535_); trivial. % 8.02/8.19 apply (zenon_L81_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H25 | zenon_intro zenon_H237 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L2_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L36_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L531_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L544_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L129_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L540_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L24_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.19 apply (zenon_L49_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.19 apply (zenon_L546_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.19 apply (zenon_L107_); trivial. % 8.02/8.19 apply (zenon_L113_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.19 apply (zenon_L547_); trivial. % 8.02/8.19 apply (zenon_L548_); trivial. % 8.02/8.19 apply (zenon_L57_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L3_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L65_); trivial. % 8.02/8.19 apply (zenon_L549_); trivial. % 8.02/8.19 apply (zenon_L81_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L550_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L555_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L299_); trivial. % 8.02/8.19 apply (zenon_L73_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.19 apply (zenon_L556_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.19 apply (zenon_L555_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.19 apply (zenon_L299_); trivial. % 8.02/8.19 apply (zenon_L73_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H111 | zenon_intro zenon_H15a ]. % 8.02/8.19 exact (zenon_H127 zenon_H111). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_L442_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_L557_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L565_); trivial. % 8.02/8.19 apply (zenon_L81_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.19 apply (zenon_L17_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.19 apply (zenon_L129_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.19 apply (zenon_L540_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.19 apply (zenon_L529_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.19 apply (zenon_L469_); trivial. % 8.02/8.19 apply (zenon_L438_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.19 apply (zenon_L557_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.19 apply (zenon_L565_); trivial. % 8.02/8.19 apply (zenon_L249_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L550_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L223_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.19 apply (zenon_L556_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.19 apply (zenon_L115_); trivial. % 8.02/8.19 apply (zenon_L223_); trivial. % 8.02/8.19 apply (zenon_L533_); trivial. % 8.02/8.19 apply (zenon_L140_); trivial. % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_H2fd | zenon_intro zenon_H2fc ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2fd). zenon_intro zenon_Hc6. zenon_intro zenon_H2fe. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H2ff. zenon_intro zenon_H2ef. % 8.02/8.19 exact (zenon_H2ff zenon_Hc6). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H2fc); [ zenon_intro zenon_H301 | zenon_intro zenon_H300 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_Hc6. zenon_intro zenon_H302. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H2ff. zenon_intro zenon_H2f3. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc6. % 8.02/8.19 exact (zenon_H2ff zenon_Hc6). % 8.02/8.19 apply (zenon_or_s _ _ zenon_H300); [ zenon_intro zenon_H304 | zenon_intro zenon_H303 ]. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H304). zenon_intro zenon_Hc6. zenon_intro zenon_H305. % 8.02/8.19 apply (zenon_and_s _ _ zenon_H305). zenon_intro zenon_H2ff. zenon_intro zenon_H2f7. % 8.02/8.20 exact (zenon_H2ff zenon_Hc6). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H307 | zenon_intro zenon_H306 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_Hc6. zenon_intro zenon_H308. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H2ff. zenon_intro zenon_H2fb. % 8.02/8.20 exact (zenon_H2ff zenon_Hc6). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H306); [ zenon_intro zenon_H30a | zenon_intro zenon_H309 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_Hd2. zenon_intro zenon_H30b. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H30b). zenon_intro zenon_H6f. zenon_intro zenon_H2ef. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_Hb9. zenon_intro zenon_H25. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L566_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L420_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L567_); trivial. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H15e. zenon_intro zenon_H245. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1f1); [ zenon_intro zenon_H158 | zenon_intro zenon_H86 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H13a | zenon_intro zenon_H15c ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_L3_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.20 apply (zenon_L333_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.20 apply (zenon_L571_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H88 | zenon_intro zenon_H163 ]. % 8.02/8.20 apply (zenon_L571_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H6d | zenon_intro zenon_H164 ]. % 8.02/8.20 apply (zenon_L394_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H115 | zenon_intro zenon_Hfd ]. % 8.02/8.20 apply (zenon_L573_); trivial. % 8.02/8.20 apply (zenon_L109_); trivial. % 8.02/8.20 apply (zenon_L137_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.20 apply (zenon_L333_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.20 apply (zenon_L24_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.20 apply (zenon_L17_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.20 exact (zenon_H6f zenon_H6e). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H26 | zenon_intro zenon_H13c ]. % 8.02/8.20 apply (zenon_L3_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_H6e | zenon_intro zenon_H13d ]. % 8.02/8.20 exact (zenon_H6f zenon_H6e). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H9c | zenon_intro zenon_Hdc ]. % 8.02/8.20 apply (zenon_L574_); trivial. % 8.02/8.20 apply (zenon_L575_); trivial. % 8.02/8.20 apply (zenon_L113_); trivial. % 8.02/8.20 apply (zenon_L57_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.20 apply (zenon_L333_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.20 apply (zenon_L571_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.20 apply (zenon_L123_); trivial. % 8.02/8.20 apply (zenon_L137_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_L3_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.20 apply (zenon_L333_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.20 apply (zenon_L587_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.20 apply (zenon_L576_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.20 apply (zenon_L90_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.20 apply (zenon_L588_); trivial. % 8.02/8.20 apply (zenon_L586_); trivial. % 8.02/8.20 apply (zenon_L137_); trivial. % 8.02/8.20 apply (zenon_L590_); trivial. % 8.02/8.20 apply (zenon_L584_); trivial. % 8.02/8.20 apply (zenon_L333_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H30d | zenon_intro zenon_H30c ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H30d). zenon_intro zenon_Hd2. zenon_intro zenon_H30e. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H30e). zenon_intro zenon_H6f. zenon_intro zenon_H2f3. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc6. % 8.02/8.20 apply (zenon_L90_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H30c); [ zenon_intro zenon_H310 | zenon_intro zenon_H30f ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_Hd2. zenon_intro zenon_H311. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H311). zenon_intro zenon_H6f. zenon_intro zenon_H2f7. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2f7). zenon_intro zenon_H13e. zenon_intro zenon_H9c. % 8.02/8.20 apply (zenon_L390_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H313 | zenon_intro zenon_H312 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H313). zenon_intro zenon_Hd2. zenon_intro zenon_H314. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H314). zenon_intro zenon_H6f. zenon_intro zenon_H2fb. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_He2. zenon_intro zenon_H7f. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L566_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H86 | zenon_intro zenon_H96 ]. % 8.02/8.20 apply (zenon_L48_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H88 | zenon_intro zenon_H97 ]. % 8.02/8.20 apply (zenon_L601_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H8e | zenon_intro zenon_H92 ]. % 8.02/8.20 apply (zenon_L602_); trivial. % 8.02/8.20 exact (zenon_Hc0 zenon_H92). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_L68_); trivial. % 8.02/8.20 apply (zenon_L81_); trivial. % 8.02/8.20 apply (zenon_L308_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L420_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L567_); trivial. % 8.02/8.20 apply (zenon_L140_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H316 | zenon_intro zenon_H315 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H316). zenon_intro zenon_Hd6. zenon_intro zenon_H317. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H317). zenon_intro zenon_Hdb. zenon_intro zenon_H2ef. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2ef). zenon_intro zenon_Hb9. zenon_intro zenon_H25. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L566_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L604_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1b3). zenon_intro zenon_H24c. zenon_intro zenon_H24b. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H127 | zenon_intro zenon_H1f ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H228 | zenon_intro zenon_H195 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H5b | zenon_intro zenon_H11f ]. % 8.02/8.20 apply (zenon_L17_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11f); [ zenon_intro zenon_H6e | zenon_intro zenon_H120 ]. % 8.02/8.20 apply (zenon_L607_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H83 | zenon_intro zenon_Ha2 ]. % 8.02/8.20 apply (zenon_L107_); trivial. % 8.02/8.20 apply (zenon_L301_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.20 apply (zenon_L608_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.20 apply (zenon_L609_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.20 apply (zenon_L5_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.20 apply (zenon_L338_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.20 exact (zenon_Hdb zenon_H6d). % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.20 apply (zenon_L614_); trivial. % 8.02/8.20 apply (zenon_L615_); trivial. % 8.02/8.20 apply (zenon_L69_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_L115_); trivial. % 8.02/8.20 apply (zenon_L616_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.20 apply (zenon_L17_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.20 apply (zenon_L129_); trivial. % 8.02/8.20 apply (zenon_L617_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.20 apply (zenon_L608_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.20 apply (zenon_L609_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.20 apply (zenon_L5_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H66 | zenon_intro zenon_Hab ]. % 8.02/8.20 apply (zenon_L338_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H6d | zenon_intro zenon_Hac ]. % 8.02/8.20 exact (zenon_Hdb zenon_H6d). % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H70 | zenon_intro zenon_H7f ]. % 8.02/8.20 apply (zenon_L621_); trivial. % 8.02/8.20 apply (zenon_L615_); trivial. % 8.02/8.20 apply (zenon_L69_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_L115_); trivial. % 8.02/8.20 apply (zenon_L622_); trivial. % 8.02/8.20 apply (zenon_L607_); trivial. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_L623_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H319 | zenon_intro zenon_H318 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H319). zenon_intro zenon_Hd6. zenon_intro zenon_H31a. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_Hdb. zenon_intro zenon_H2f3. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2f3). zenon_intro zenon_Hc6. zenon_intro zenon_Hc6. % 8.02/8.20 apply (zenon_L603_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H31c | zenon_intro zenon_H31b ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_Hd6. zenon_intro zenon_H31d. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H31d). zenon_intro zenon_Hdb. zenon_intro zenon_H2f7. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2f7). zenon_intro zenon_H13e. zenon_intro zenon_H9c. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hcd ]. % 8.02/8.20 apply (zenon_L633_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hce ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 8.02/8.20 apply (zenon_L185_); trivial. % 8.02/8.20 exact (zenon_Hdb zenon_H6d). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_L175_); trivial. % 8.02/8.20 apply (zenon_L93_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L604_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L311_); trivial. % 8.02/8.20 apply (zenon_L623_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_H31f | zenon_intro zenon_H31e ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H31f). zenon_intro zenon_Hd6. zenon_intro zenon_H320. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_Hdb. zenon_intro zenon_H2fb. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_He2. zenon_intro zenon_H7f. % 8.02/8.20 apply (zenon_L627_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H322 | zenon_intro zenon_H321 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H322). zenon_intro zenon_H98. zenon_intro zenon_H323. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H16a. zenon_intro zenon_H324. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H1f. zenon_intro zenon_H111. % 8.02/8.20 apply (zenon_L212_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H321); [ zenon_intro zenon_H326 | zenon_intro zenon_H325 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_H98. zenon_intro zenon_H327. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H16a. zenon_intro zenon_H328. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H6e. zenon_intro zenon_Hd2. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L634_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L420_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L129_); trivial. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H12c). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H193. zenon_intro zenon_H22c. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H165 | zenon_intro zenon_H6d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 apply (zenon_L323_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_L41_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 8.02/8.20 apply (zenon_L318_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 8.02/8.20 apply (zenon_L165_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 8.02/8.20 exact (zenon_H16a zenon_H36). % 8.02/8.20 apply (zenon_L636_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.20 apply (zenon_L246_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.20 apply (zenon_L260_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L639_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 apply (zenon_L323_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_L41_); trivial. % 8.02/8.20 apply (zenon_L50_); trivial. % 8.02/8.20 apply (zenon_L26_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H32a | zenon_intro zenon_H329 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_H98. zenon_intro zenon_H32b. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H16a. zenon_intro zenon_H32c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H9f. zenon_intro zenon_H9f. % 8.02/8.20 apply (zenon_L117_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_H32e | zenon_intro zenon_H32d ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H98. zenon_intro zenon_H32f. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H16a. zenon_intro zenon_H330. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H195. zenon_intro zenon_Hf7. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L634_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23d. zenon_intro zenon_H208. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H10a | zenon_intro zenon_Hb9 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1e9 | zenon_intro zenon_He2 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1e | zenon_intro zenon_H236 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L212_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H82 | zenon_intro zenon_H331 ]. % 8.02/8.20 apply (zenon_L65_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H331); [ zenon_intro zenon_H83 | zenon_intro zenon_H332 ]. % 8.02/8.20 apply (zenon_L659_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H332); [ zenon_intro zenon_H9f | zenon_intro zenon_H148 ]. % 8.02/8.20 apply (zenon_L117_); trivial. % 8.02/8.20 apply (zenon_L355_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_L65_); trivial. % 8.02/8.20 apply (zenon_L622_); trivial. % 8.02/8.20 apply (zenon_L640_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H25 | zenon_intro zenon_H237 ]. % 8.02/8.20 exact (zenon_H10a zenon_H25). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H111 | zenon_intro zenon_H15a ]. % 8.02/8.20 apply (zenon_L661_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 apply (zenon_L221_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_L662_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L212_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.20 apply (zenon_L652_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.20 apply (zenon_L338_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.20 apply (zenon_L108_); trivial. % 8.02/8.20 apply (zenon_L438_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_L65_); trivial. % 8.02/8.20 apply (zenon_L223_); trivial. % 8.02/8.20 apply (zenon_L249_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.20 apply (zenon_L655_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.20 apply (zenon_L260_); trivial. % 8.02/8.20 apply (zenon_L618_); trivial. % 8.02/8.20 apply (zenon_L532_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1e9 | zenon_intro zenon_He2 ]. % 8.02/8.20 apply (zenon_L650_); trivial. % 8.02/8.20 apply (zenon_L532_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L129_); trivial. % 8.02/8.20 apply (zenon_L336_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H32d); [ zenon_intro zenon_H334 | zenon_intro zenon_H333 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H9c. zenon_intro zenon_H335. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H13f. zenon_intro zenon_H324. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H1f. zenon_intro zenon_H111. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L75_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L663_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L311_); trivial. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H12b). zenon_intro zenon_Hfc. zenon_intro zenon_H12c. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_L496_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_L322_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.20 apply (zenon_L243_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H185 ]. % 8.02/8.20 apply (zenon_L496_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H186 ]. % 8.02/8.20 apply (zenon_L665_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hde ]. % 8.02/8.20 apply (zenon_L97_); trivial. % 8.02/8.20 apply (zenon_L376_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.20 apply (zenon_L118_); trivial. % 8.02/8.20 apply (zenon_L89_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H333); [ zenon_intro zenon_H337 | zenon_intro zenon_H336 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H9c. zenon_intro zenon_H338. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H13f. zenon_intro zenon_H328. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H6e. zenon_intro zenon_Hd2. % 8.02/8.20 apply (zenon_L185_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H336); [ zenon_intro zenon_H33a | zenon_intro zenon_H339 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H9c. zenon_intro zenon_H33b. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H13f. zenon_intro zenon_H32c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H9f. zenon_intro zenon_H9f. % 8.02/8.20 apply (zenon_L299_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H339); [ zenon_intro zenon_H33d | zenon_intro zenon_H33c ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H9c. zenon_intro zenon_H33e. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_H13f. zenon_intro zenon_H330. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H195. zenon_intro zenon_Hf7. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H9b | zenon_intro zenon_H36 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_Hc0 | zenon_intro zenon_H47 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_L662_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L2_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_L681_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_L683_); trivial. % 8.02/8.20 apply (zenon_L622_); trivial. % 8.02/8.20 apply (zenon_L675_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_L662_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L75_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.20 apply (zenon_L75_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.20 apply (zenon_L17_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.20 apply (zenon_L684_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.20 apply (zenon_L8_); trivial. % 8.02/8.20 apply (zenon_L685_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.20 apply (zenon_L238_); trivial. % 8.02/8.20 apply (zenon_L78_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.20 apply (zenon_L2_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.20 apply (zenon_L17_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.20 apply (zenon_L686_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.20 apply (zenon_L8_); trivial. % 8.02/8.20 apply (zenon_L689_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.20 apply (zenon_L238_); trivial. % 8.02/8.20 apply (zenon_L617_); trivial. % 8.02/8.20 apply (zenon_L622_); trivial. % 8.02/8.20 apply (zenon_L684_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L663_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L311_); trivial. % 8.02/8.20 apply (zenon_L336_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H33c); [ zenon_intro zenon_H340 | zenon_intro zenon_H33f ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H9f. zenon_intro zenon_H341. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H341). zenon_intro zenon_Ha0. zenon_intro zenon_H324. % 8.02/8.20 exact (zenon_Ha0 zenon_H9f). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H343 | zenon_intro zenon_H342 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H343). zenon_intro zenon_H9f. zenon_intro zenon_H344. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_Ha0. zenon_intro zenon_H328. % 8.02/8.20 exact (zenon_Ha0 zenon_H9f). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H346 | zenon_intro zenon_H345 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H9f. zenon_intro zenon_H347. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H347). zenon_intro zenon_Ha0. zenon_intro zenon_H32c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H9f. zenon_intro zenon_H9f. % 8.02/8.20 exact (zenon_Ha0 zenon_H9f). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H349 | zenon_intro zenon_H348 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H349). zenon_intro zenon_H9f. zenon_intro zenon_H34a. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_Ha0. zenon_intro zenon_H330. % 8.02/8.20 exact (zenon_Ha0 zenon_H9f). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H348); [ zenon_intro zenon_H34c | zenon_intro zenon_H34b ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_Ha1. zenon_intro zenon_H34d. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H34d). zenon_intro zenon_H1d6. zenon_intro zenon_H324. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H1f. zenon_intro zenon_H111. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L75_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L462_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_L322_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H86 | zenon_intro zenon_Hc4 ]. % 8.02/8.20 apply (zenon_L243_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H54 | zenon_intro zenon_H143 ]. % 8.02/8.20 apply (zenon_L691_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H144 ]. % 8.02/8.20 apply (zenon_L228_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H13e | zenon_intro zenon_H140 ]. % 8.02/8.20 apply (zenon_L692_); trivial. % 8.02/8.20 apply (zenon_L425_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Hc1 ]. % 8.02/8.20 apply (zenon_L118_); trivial. % 8.02/8.20 apply (zenon_L89_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L694_); trivial. % 8.02/8.20 apply (zenon_L695_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H34b); [ zenon_intro zenon_H34f | zenon_intro zenon_H34e ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_Ha1. zenon_intro zenon_H350. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H1d6. zenon_intro zenon_H328. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H6e. zenon_intro zenon_Hd2. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H1f | zenon_intro zenon_H125 ]. % 8.02/8.20 apply (zenon_L2_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H26 | zenon_intro zenon_H126 ]. % 8.02/8.20 apply (zenon_L128_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H82 | zenon_intro zenon_Hbc ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H8e | zenon_intro zenon_H16c ]. % 8.02/8.20 apply (zenon_L38_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H70 | zenon_intro zenon_H16d ]. % 8.02/8.20 apply (zenon_L696_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_H15c | zenon_intro zenon_H14e ]. % 8.02/8.20 exact (zenon_H1d6 zenon_H15c). % 8.02/8.20 apply (zenon_L690_); trivial. % 8.02/8.20 apply (zenon_L53_); trivial. % 8.02/8.20 apply (zenon_L697_); trivial. % 8.02/8.20 apply (zenon_L85_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L420_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L694_); trivial. % 8.02/8.20 apply (zenon_L695_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H34e); [ zenon_intro zenon_H352 | zenon_intro zenon_H351 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_Ha1. zenon_intro zenon_H353. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H353). zenon_intro zenon_H1d6. zenon_intro zenon_H32c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H9f. zenon_intro zenon_H9f. % 8.02/8.20 apply (zenon_L693_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H351); [ zenon_intro zenon_H355 | zenon_intro zenon_H354 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_Ha1. zenon_intro zenon_H356. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H1d6. zenon_intro zenon_H330. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H195. zenon_intro zenon_Hf7. % 8.02/8.20 apply (zenon_L698_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H354); [ zenon_intro zenon_H358 | zenon_intro zenon_H357 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H358). zenon_intro zenon_H92. zenon_intro zenon_H359. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H1a8. zenon_intro zenon_H35a. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35a). zenon_intro zenon_H86. zenon_intro zenon_H15a. % 8.02/8.20 apply (zenon_L426_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H357); [ zenon_intro zenon_H35c | zenon_intro zenon_H35b ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35c). zenon_intro zenon_H92. zenon_intro zenon_H35d. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H1a8. zenon_intro zenon_H35e. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H6d. zenon_intro zenon_Hd6. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L699_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L604_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_H1f | zenon_intro zenon_Hed ]. % 8.02/8.20 apply (zenon_L700_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_H5b | zenon_intro zenon_Hee ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 8.02/8.20 apply (zenon_L17_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H2d | zenon_intro zenon_H63 ]. % 8.02/8.20 apply (zenon_L164_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H37 | zenon_intro zenon_H5d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.20 apply (zenon_L313_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 8.02/8.20 exact (zenon_H1a8 zenon_H47). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 8.02/8.20 apply (zenon_L627_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 8.02/8.20 apply (zenon_L673_); trivial. % 8.02/8.20 apply (zenon_L137_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.20 apply (zenon_L11_); trivial. % 8.02/8.20 exact (zenon_H1a8 zenon_H47). % 8.02/8.20 apply (zenon_L69_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H98 | zenon_intro zenon_H93 ]. % 8.02/8.20 apply (zenon_L117_); trivial. % 8.02/8.20 apply (zenon_L39_); trivial. % 8.02/8.20 apply (zenon_L138_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H35b); [ zenon_intro zenon_H360 | zenon_intro zenon_H35f ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H92. zenon_intro zenon_H361. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H361). zenon_intro zenon_H1a8. zenon_intro zenon_H362. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H15c. zenon_intro zenon_Ha1. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L699_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H10a | zenon_intro zenon_Hb9 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1e | zenon_intro zenon_H236 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L701_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_L703_); trivial. % 8.02/8.20 apply (zenon_L705_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H25 | zenon_intro zenon_H237 ]. % 8.02/8.20 exact (zenon_H10a zenon_H25). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H111 | zenon_intro zenon_H15a ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H160 ]. % 8.02/8.20 apply (zenon_L701_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H161 ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_Hcf | zenon_intro zenon_He3 ]. % 8.02/8.20 apply (zenon_L322_); trivial. % 8.02/8.20 apply (zenon_L705_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H1e | zenon_intro zenon_H18c ]. % 8.02/8.20 apply (zenon_L706_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H29 | zenon_intro zenon_H18d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11b); [ zenon_intro zenon_H111 | zenon_intro zenon_H11c ]. % 8.02/8.20 apply (zenon_L450_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H37 | zenon_intro zenon_H11d ]. % 8.02/8.20 apply (zenon_L119_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_H36 | zenon_intro zenon_H44 ]. % 8.02/8.20 apply (zenon_L215_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 8.02/8.20 apply (zenon_L707_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 8.02/8.20 apply (zenon_L306_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 8.02/8.20 apply (zenon_L708_); trivial. % 8.02/8.20 apply (zenon_L598_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H31 | zenon_intro zenon_H3e ]. % 8.02/8.20 apply (zenon_L709_); trivial. % 8.02/8.20 apply (zenon_L313_); trivial. % 8.02/8.20 apply (zenon_L701_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L694_); trivial. % 8.02/8.20 apply (zenon_L138_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H364 | zenon_intro zenon_H363 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H364). zenon_intro zenon_H92. zenon_intro zenon_H365. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H365). zenon_intro zenon_H1a8. zenon_intro zenon_H366. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_Hfc. zenon_intro zenon_Hfc. % 8.02/8.20 apply (zenon_L137_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H363); [ zenon_intro zenon_H368 | zenon_intro zenon_H367 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H368). zenon_intro zenon_H7f. zenon_intro zenon_H369. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H369). zenon_intro zenon_H153. zenon_intro zenon_H35a. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35a). zenon_intro zenon_H86. zenon_intro zenon_H15a. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L48_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L710_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H122). zenon_intro zenon_H9f. zenon_intro zenon_H123. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H123). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H1aa. zenon_intro zenon_H1b3. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H127 | zenon_intro zenon_H1f ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1aa); [ zenon_intro zenon_H118 | zenon_intro zenon_H6e ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1cb ]. % 8.02/8.20 apply (zenon_L713_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H1cc ]. % 8.02/8.20 exact (zenon_H118 zenon_Hd2). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H13e | zenon_intro zenon_He0 ]. % 8.02/8.20 apply (zenon_L714_); trivial. % 8.02/8.20 apply (zenon_L545_); trivial. % 8.02/8.20 apply (zenon_L715_); trivial. % 8.02/8.20 apply (zenon_L243_); trivial. % 8.02/8.20 apply (zenon_L140_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H367); [ zenon_intro zenon_H36b | zenon_intro zenon_H36a ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H36b). zenon_intro zenon_H7f. zenon_intro zenon_H36c. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_H153. zenon_intro zenon_H35e. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H6d. zenon_intro zenon_Hd6. % 8.02/8.20 apply (zenon_L294_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H36a); [ zenon_intro zenon_H36e | zenon_intro zenon_H36d ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H36e). zenon_intro zenon_H7f. zenon_intro zenon_H36f. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_H153. zenon_intro zenon_H362. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H15c. zenon_intro zenon_Ha1. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H231. zenon_intro zenon_H221. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H9b | zenon_intro zenon_H36 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 8.02/8.20 apply (zenon_L442_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 8.02/8.20 exact (zenon_Hb7 zenon_Hbb). % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hba); [ zenon_intro zenon_H54 | zenon_intro zenon_Hb2 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hb2 | zenon_intro zenon_He8 ]. % 8.02/8.20 apply (zenon_L244_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hde | zenon_intro zenon_He9 ]. % 8.02/8.20 apply (zenon_L91_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_He0 | zenon_intro zenon_He2 ]. % 8.02/8.20 apply (zenon_L716_); trivial. % 8.02/8.20 exact (zenon_H153 zenon_He2). % 8.02/8.20 apply (zenon_L717_); trivial. % 8.02/8.20 apply (zenon_L215_); trivial. % 8.02/8.20 apply (zenon_L719_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L710_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L694_); trivial. % 8.02/8.20 apply (zenon_L140_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H36d); [ zenon_intro zenon_H371 | zenon_intro zenon_H370 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_H7f. zenon_intro zenon_H372. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H372). zenon_intro zenon_H153. zenon_intro zenon_H366. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_Hfc. zenon_intro zenon_Hfc. % 8.02/8.20 apply (zenon_L139_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H370); [ zenon_intro zenon_H374 | zenon_intro zenon_H373 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_Hf7. zenon_intro zenon_H375. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_H196. zenon_intro zenon_H35a. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35a). zenon_intro zenon_H86. zenon_intro zenon_H15a. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_L48_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_Hc6. zenon_intro zenon_H107. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H23c. zenon_intro zenon_H23b. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H23d. zenon_intro zenon_H208. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H10a | zenon_intro zenon_Hb9 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H1e9 | zenon_intro zenon_He2 ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3e | zenon_intro zenon_H4f ]. % 8.02/8.20 apply (zenon_L720_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H41 | zenon_intro zenon_H50 ]. % 8.02/8.20 apply (zenon_L723_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H44 | zenon_intro zenon_H47 ]. % 8.02/8.20 apply (zenon_L392_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H25 | zenon_intro zenon_H171 ]. % 8.02/8.20 exact (zenon_H10a zenon_H25). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H172 ]. % 8.02/8.20 apply (zenon_L61_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H26 | zenon_intro zenon_H66 ]. % 8.02/8.20 apply (zenon_L415_); trivial. % 8.02/8.20 apply (zenon_L217_); trivial. % 8.02/8.20 apply (zenon_L725_); trivial. % 8.02/8.20 apply (zenon_L333_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L726_); trivial. % 8.02/8.20 apply (zenon_L336_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H373); [ zenon_intro zenon_H377 | zenon_intro zenon_H376 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_Hf7. zenon_intro zenon_H378. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H196. zenon_intro zenon_H35e. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H6d. zenon_intro zenon_Hd6. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ab); [ zenon_intro zenon_Had | zenon_intro zenon_H1ac ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H1e. zenon_intro zenon_Hae. % 8.02/8.20 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_Hb4. zenon_intro zenon_H1af. % 8.02/8.20 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H2d ]. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H47 | zenon_intro zenon_H206 ]. % 8.02/8.20 apply (zenon_L728_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_He2 | zenon_intro zenon_H207 ]. % 8.02/8.20 apply (zenon_L627_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H195 | zenon_intro zenon_Hfc ]. % 8.02/8.20 exact (zenon_H196 zenon_H195). % 8.02/8.20 apply (zenon_L335_); trivial. % 8.02/8.20 apply (zenon_L164_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1ac); [ zenon_intro zenon_H106 | zenon_intro zenon_H1b0 ]. % 8.02/8.20 apply (zenon_L604_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H1b0); [ zenon_intro zenon_H122 | zenon_intro zenon_H12b ]. % 8.02/8.20 apply (zenon_L726_); trivial. % 8.02/8.20 apply (zenon_L336_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H376); [ zenon_intro zenon_H37a | zenon_intro zenon_H379 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H37a). zenon_intro zenon_Hf7. zenon_intro zenon_H37b. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H37b). zenon_intro zenon_H196. zenon_intro zenon_H362. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H15c. zenon_intro zenon_Ha1. % 8.02/8.20 apply (zenon_L729_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H37d | zenon_intro zenon_H37c ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H37d). zenon_intro zenon_Hf7. zenon_intro zenon_H37e. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H196. zenon_intro zenon_H366. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_Hfc. zenon_intro zenon_Hfc. % 8.02/8.20 apply (zenon_L335_); trivial. % 8.02/8.20 apply (zenon_or_s _ _ zenon_H37c); [ zenon_intro zenon_H380 | zenon_intro zenon_H37f ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_Hfc. zenon_intro zenon_H381. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H381). zenon_intro zenon_H382. zenon_intro zenon_H35a. % 8.02/8.20 exact (zenon_H382 zenon_Hfc). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H37f); [ zenon_intro zenon_H384 | zenon_intro zenon_H383 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_Hfc. zenon_intro zenon_H385. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H385). zenon_intro zenon_H382. zenon_intro zenon_H35e. % 8.02/8.20 exact (zenon_H382 zenon_Hfc). % 8.02/8.20 apply (zenon_or_s _ _ zenon_H383); [ zenon_intro zenon_H387 | zenon_intro zenon_H386 ]. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H387). zenon_intro zenon_Hfc. zenon_intro zenon_H388. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H388). zenon_intro zenon_H382. zenon_intro zenon_H362. % 8.02/8.20 exact (zenon_H382 zenon_Hfc). % 8.02/8.20 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_Hfc. zenon_intro zenon_H389. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H389). zenon_intro zenon_H382. zenon_intro zenon_H366. % 8.02/8.20 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_Hfc. zenon_intro zenon_Hfc. % 8.02/8.20 exact (zenon_H382 zenon_Hfc). % 8.02/8.20 Qed. % 8.02/8.20 % SZS output end Proof % 8.02/8.20 (* END-PROOF *) % 8.02/8.20 nodes searched: 149433 % 8.02/8.20 max branch formulas: 303 % 8.02/8.20 proof nodes created: 8387 % 8.02/8.20 formulas created: 52902 % 8.02/8.20 %------------------------------------------------------------------------------